Alexane, Claire Alexandre

Clémence

Noémie Anatole Thomas

Félix Jules Mo

Hub, Benjamin, Maeva Manon Mathieu

J'ai réussi à écrire ces 5 chapitres de thèse, et me voilà devant cette page blanche des remerciements, exercice somme toute assez classique mais finalement difficile à écrire. En effet, plus de 3 années de travail (mais pas que !), c'est évidemment beaucoup d'interactions avec de très nombreux interlocuteurs. Cet aboutissement, que constitue ma thèse, je le dois à tant de personnes que la crainte d'en oublier est bien présente au moment où je rédige ces lignes.

Je tiens tout d'abord à remercier chaleureusement mes encadrants de thèse sans qui ce travail n'aurait pas été possible. Un grand merci à mon directeur de thèse Anatoli, merci pour ton optimisme et de m'avoir toujours encouragé même dans les moments de doute. Laurent, Guillaume et Phillipe, je vous remercie pour votre encadrement, votre disponibilité sans faille. Je tiens également à remercier mes encadrants industriels, Patrick, Bernard et Nathan. Je vous suis très reconnaissante d'avoir pu bénéficier de votre expertise pendant 3 ans, de vos conseils toujours avisés et merci pour la confiance que vous m'avez accordée pour mener à bien ce projet. Grâce à votre professionnalisme, j'ai vraiment appris et progressé dans la démarche académique mais également (et ça va de pair !) dans la coopération constante. Merci à tous, pour ces réunions que nous avons toujours faites dans la bonne humeur, et je considère que j'ai été bien chanceuse d'avoir bénéficié de votre encadrement ! J'adresse également mes plus sincères remerciements à M. Vanel, M. Feller, Mme. Royaud ainsi que Mme. Genix pour avoir accepté de faire partie de ce jury et pour avoir relu avec attention ce manuscrit. Merci pour l'intérêt que vous portez à ce travail et pour le temps que vous y avez consacré. Je souhaiterais remercier vivement Stéphane Delaunay pour son aide et sa disponibilité. C'était un réel plaisir de travailler avec toi. Je tiens également à dire merci à Sylvie Ducrot pour ton aide administrative mais pas seulement, merci également pour ton écoute. Les échanges avec toi m'ont beaucoup apporté.

Merci à Isabelle Morfin qui a contribué à l'obtention des résultats de ce manuscrit sur les expériences de SAXS/WAXS et qui a toujours répondu présente lorsque j'avais besoin d'aide.

Milles merci à l'ensemble des doctorants et post-doctorants de l'IMP, sans qui la vie du laboratoire n'aurait pas la même saveur. Il y a un vrai esprit d'entraide dans les bons et les moins bons moments de la thèse. J'ai d'abord une pensée particulière pour le bureau 428, qui a vu passer du monde : Renaud, Hub', Thib', Léa, Mathurin, Baptiste et le petit dernier Théo. Je remercie la première génération pour l'accueil dans le bureau qui a été parfait ! Je pense aussi à la nouvelle génération qui a dû me supporter pendant la phase de rédaction et qui m'a permis de surmonter cette période très dure. J'ai passé trois formidables années en grande partie grâce à vous.

Je pense évidemment à Laura et Renaud avec qui j'aurai bien fait la fête pendant ces 3 années, on s'est bien marré !

Aelec:

Area between loading/unloading conductivity vs. strain curve Amec: Area between loading/unloading stress vs. strain curve RM: Mullins ratio "Smart rubbers" are defined as elastomeric materials that respond to external stimuli through a macroscopic output. They are envisioned for specific and new applications taking advantage of their "smart" features. Their growing demand drives a research which has increased drastically over the last few decades.

In most industrial applications, the electrical properties of elastomer matrices can be tailored by the incorporation of conductive fillers (anti-electrostatic effects of a conductive filler).

In addition, this type of conductive nanocomposite materials could have a specific potential in the field of strain or damage sensing. The real-time conductivity monitoring could be very easily implemented for industrial purposes due to the simplicity of the testing process. Therefore, measurement of electrical properties seems to be a non-destructive method that can be industrialized for real-time monitoring of the damage of rubbers composites. This approach could transform the paradigm for maintenance used in industry which is nowadays standardized (change the specimen at constant frequency) as preventive maintenance. In this view, the use of the intrinsic properties of the material would reveal information on its state of damage, which would allow the optimization of the material's lifetime and therefore a reduction in the industrial waste.

A deeper understanding of the evolution of the electrical properties of elastomeric composite materials undergoing mechanical deformations of different types and amplitude is an essential prerequisite for the development of non-destructive approaches to detect the impact of fatigue that leads to material damage and loss of functionality. This can have numerous applications in the fields of in situ monitoring, preventive maintenance, smart rubber materials, strain sensor or/and damage sensor. The objective of my thesis is to understand the mechanisms related to electrical, structural properties of elastomer filled with carbon black undergoing mechanical deformation and to identify if electrical properties are a suitable descriptor to detect damage. First, Chapter I of this manuscript reviews some important bibliographical aspects related to conductive elastomer composites and their physical properties. The main observation is that there is a lack of information in the literature to correlate structural and electrical properties as synthesized in this following scheme.

Scheme highlighting the main question that remains unanswered in the literature. How to relate the evolution of electrical and structural properties under mechanical deformation?

Then Chapter II presents the materials and methods used and developed for this project. The manuscript is based on three scientific publications (Chapter III, IV, and V): one published in Composite Science and Technology (Chapter III), another submitted to Macromolecules (Chapter IV) and the third in the process of submission (Chapter V). In Chapter III a better understanding of the electrical property evolution under cyclic mechanical deformation, in situ coupled electrical/mechanical investigations on EPDM-based composite materials filled with carbon black of different structures (low and high structures) and at different concentrations have been systematically carried out. The evolution of electrical properties and mechanical properties have been compared and correlated for the description of an electrical Mullins effect. This characteristic electrical/mechanical coupling signature potentially originates from a balance between two percolation/depercolation mechanisms. Microstructural investigations in particular the reorganization of the filler network could be studied to confirm these interpretations and could help identify other possible microscopic scenarios. The simultaneous study of the electrical conductivity and of the microstructure by X-ray scattering under mechanical deformation is proposed in Chapter IV. The real-time correlation between the electrical conductivity and the microstructural evolution of the composite morphology reveals distinct subsequent mechanisms governing the relationship between structure and properties with deformation. The structural study has thus allowed to understand the damage mechanisms clearly evidenced by electrical monitoring and that the depercolation mechanism is driven by (nano-cavitation). Chapter V focuses on the choice of an electrical descriptor as end-of-life criterion by in situ electrical/mechanical coupling during mechanical fatigue tests. The dependence of electrical and mechanical properties as a function of fatigue cycles was investigated and the detailed mechanism was discussed. The non-destructive electrical measurement presents a high potential for real-time detecting damage of filled elastomers and predicting the fatigue life in practical applications. A conclusion highlighting the main results of this work is then presented and future perspectives are discussed.

CHAPTER I. Bibliography 1. Ethylene Propylene Diene Monomer (EPDM): generalities

Elastomers often called "rubbers" represent a large family of natural or synthetic polymeric materials and are used for many applications. Elastomers are made up of long chains entangled with each other and once the cross-linking reaction is completed, these materials are characterized by great reversible deformability. The cross-linking is carried out by a process of creation of chemical bonds between the macromolecular chains, called vulcanization when the crosslinking agent is sulfur, giving rise to a stable three-dimensional network. Elastomeric materials can be used for many industrial applications, however, in most cases, the incorporation of reinforcing fillers is required. The fillers are generally intended to increase the mechanical properties (fracture toughness, ageing, etc.) and to increase their capacity to dissipate a part of the energy (thermal or electrical) [1]. The interpretation of the elastomer chains and the addition of filler is still subject to much research.

Ethylene Propylene Diene Monomer (EPDM) belongs to the family of synthetic elastomers. It is an elastomer with a hydrocarbon backbone and a small number of side groups resulting from the copolymerization of three monomers: ethylene, propylene, and a diene (non-conjugated unsaturated monomer). Many commercial grades are available, and they differ in their structural characteristics related to:

Nature of the diene monomer: The most commonly used dienes for the preparation of EPDM are 5-ethylidene-2-norbornene (ENB), Hexa-1,4-diene (HD) and dicyclopentadiene (DCPD) (Figure I-1). For the same crosslinking agent, vulcanization [2][3][4], ageing [5], and oxidation [6,7] of EPDM composites are dependent on the nature of the diene introduced.

Figure I-1. Topological formulas of the most common commercial diene monomers [8]: ENB, HD and DCPD.

ENB HD DCPD

The proportions of the various constituent monomers: If the polyethene content is greater than 65 w%, then the elastomer will be semi-crystalline otherwise it will be considered amorphous [9,10]. In the case of EPDM, the rate of crystallinity which is fixed by the PE monomer remains low and the morphology of the crystallites is generally in the form of fringed micelles. The crystallinity has an impact on the mechanical properties and in particular the breaking strength which is higher for semicrystalline EPDM based materials than for amorphous EPDM based ones [9].

Distribution of the average molar mass and the molar mass of the matrix (before cross-linking): These parameters will influence the viscosity of the elastomer during its processing and also the final mechanical properties of the composite.

Processing conditions: many processing factors can influence the properties of the final composite, such as temperature, processing speed or curing time.

The processing step for preparing EPDM composites is reported in the next section.

Processing of EPDM composites 1.Elastomeric materials

To obtain the desired properties at the industrial level, the processing step is essential.

Indeed, the elastomer itself, even when vulcanized, does not have the necessary properties, which is why different materials must be added and each of them has a well-defined role:

Crosslinking agents: Their role are to promote the formation of inter-and intra-chain chemical bonds. The choice of the cross-linking agent is made firstly by considering the compatibility with the elastomer. Indeed, crosslinking with sulfur is limited to unsaturated elastomers [11], while it is not the case for crosslinking with peroxide. On the other hand, crosslinking with peroxide is not effective for butyl elastomers because it causes chain breaks during the crosslinking process [12]. However, if the two main curing agents (sulfur and peroxide) are compatible with the elastomer then peroxide allows the creation of C-C bonds which are less sensitive to thermal degradation (Ebond = 352 kJ/mol) [13] than S-S bonds (Ebond 200 kJ/mol) or C-S bonds (Ebond 270 kJ/mol) [13,14]. Sulfurcured elastomers have superior mechanical properties (i.e. fatigue strength [16]) and higher strain at break [12]. In addition, sulfur-cured composites are less expensive than those cured with peroxide. Other factors may influence the choice of the cross-linking agent. For instance, sulfur requires the addition of gas pedals and cross-linking activators to reduce the reaction time, while peroxide has shorter crosslinking times due to its higher reactivity, limiting thereby the premature ageing due to high temperature during vulcanization. In addition, cross-linking with peroxide is more homogeneous than with sulfur [10].

Fillers: They improve the mechanical properties, thus broadening the fields of application of elastomers. Their morphologies are varied as well as their size, ranging from filler close to sphere of about ten nanometres to a very irregular surface of about one hundred microns. Moreover, in some cases the fillers are less expensive than the matrix, their addition reduces the total price, so for economic and performance reasons, industrial elastomers are rarely used without fillers. The addition of fillers help increasing the properties (mechanical, thermal, electrical etc.) of the materials and the main fillers used in the industry are carbon black, silica, graphite etc. [17] Plasticizers: They are used to improve processability, indeed, they allow better incorporation of various compounds and their dispersion. Thus, they contribute to the final mechanical properties of the elastomer after cross-linking [18].

Antioxidant/stabilizer: These are additives introduced into the materials to ensure certain specific properties, in the case of the antioxidant the aim is to prevent oxidative ageing.

Crosslinking: Sulfur vulcanization

The fundamental principle of vulcanization is the forming of chemical cross-links between rubber macromolecules which lead to the formation of a 3D network of rubber matrix by the reactions between functional groups of elastomer chains and suitable curing agent. In the cross-linked vulcanized network, physical couplings are also present as hydrogen bounds between elastomer chains and various intramolecular and intermolecular entanglements. The vulcanization of an elastomer is ensured by three essential factors: a contribution of energy which is usually of thermal origin, an agent of vulcanization as well as the existence or the creation of reactive sites on the macromolecular chains.

The most common inter-chain bridges are groups of sulfur atoms of mono-or polysulfide structure. In order to carry out the vulcanization step, the vulcanizing agent is incorporated into the elastomeric material and the vulcanization is achieved during hot press molding. The temperature and time of vulcanization are fundamental parameters of the cross-linking, which can considerably influence the architecture of the elastomer network and thus the final properties. To obtain optimal curing conditions, rheological tests on raw samples are performed. The principle of these tests is to impose a sinusoidal deformation and to measure the transmitted torque, which corresponds to the resistance of the material to the imposed deformation [19]. Then, for a given temperature, the variation of the torque is measured as a function of time as shown in Figure I-2.

Figure I-2. A typical rheometer cure curve obtained from MDR for sulfur vulcanization at

T=140°C [20,21] Thus, four parameters can be determined from the test described above:

Smin is the minimum torque. This parameter reflects the viscosity of the material before vulcanization.

ts2 is the time necessary to reach Smin + 2 dN.m. This time is conventionally chosen as the starting time of the vulcanization reaction [20,21].

Smax is the maximum torque obtained for the investigated material at this temperature. It corresponds to the elasticity of the blend assuming complete cross-linking.

t98% corresponds to the time needed to reach 98% of the variation between the minimum Smin and the maximum Smax torque. It is then possible to determine the torque S98% by Eq 1. This is generally considered to be the time for optimal vulcanization. % = 0.98 × ( ) + 1 Sulfur crosslinking is used for natural rubber (NR) or synthetic elastomers containing double bonds such as Styrene Butadiene Rubber (SBR), polybutadiene, EPDM etc. In order to achieve sulfur cross-linking, activators such as zinc oxide (ZnO) and stearic acid and gas pedals (MBT, TMTD etc.) have a combined action with sulfur which is summarized in the Figure I-3. In Table I-1 the typical composition of the sulfur cross-linking compounds for EPDM are reported. [24] A key factor in determining the number of sulfur atoms in the cross-linking network is the amount of sulfur introduced (S) and the ratio of gas pedals to sulfur (A/S). Based on this data, the sulfur curing systems reported in Table I-2 [24] can be classified as conventional, semiefficient or efficient. The cross-linking network obtained for the conventional system consists mainly of polysulfide bridges (between 70-95%). These polysulfide bonds with lower dissociation energies are temperature sensitive, therefore these materials cannot be used for applications at temperatures above 70 °C. For the semi-efficient materials, where the sulfur and gas pedal content are close, the cross-linking network is made up of about half polysulfide bridges and half monosulfide bridges. This leads to an increase in the temperature resistance of the materials. For the last type of sulfur vulcanization, called efficient, where the quantity of sulfur is low compared to that of the gas pedal, the cross-linking network is then made up of a majority of monosulfide bridges. These types of sulfur vulcanization are the ones that are the most resistant to high temperatures and oxidative ageing. However, the initial mechanical properties of these systems (deformation at break) are not as good as those obtained for conventional systems, but they are more resistant over time.

Figure I-3. Simplified reaction sequences in sulfur vulcanization

Table I-1. Industrial elastomers composites vulcanized by sulfur [22,23] Ratio: A/S 0.1-0.6 0.7-2.5 2.5-12.0

Component

Crosslinking: Peroxide

The use of an organic peroxide as a crosslinking agent for an elastomer was first reported by Ostromislensky in 1915. The introduction of organic peroxides in cross-linking elastomers leads to the formation of covalent carbon-carbon cross-links between the elastomer chain segments.

Based on the heat stability that can be obtained by peroxide crosslinking of diene rubbers, especially of EPDM, this type of crosslinking has achieved great importance [24]. Peroxide crosslinkers are widely used because their crosslinking confers a high heat aging resistance due to the high stability of the C-C bonds. It can also be noticed that the performance of peroxidecuring without co-agent is sometimes low due to the occurrence of side-reactions which can deplete free radicals. Moreover, peroxides are sensitive to oxygen and can also be considered very dangerous. Indeed, peroxides and their by-products from decomposition are volatile organic compounds (VOCs) and present significant risks of fire and explosion.

Physical properties of filled elastomers composites

The glass transition temperatures of elastomers being low (-50°C for EPDM), it is imperative to achieve the state of vulcanization to have elastic properties. Moreover, in order to resist repeated stresses, in addition to the high elasticity, an industrial piece must have good fatigue resistance properties. For this reason, fillers are essential because they improve the physical properties of elastomers. In this section, the mechanical properties are discussed first, because the correlation between electrical and mechanical properties requires a deep understanding of mechanical mechanisms of damage in elastomeric materials. Then, the electrical properties of filled elastomers are discussed, to understand the evolution of electrical properties under mechanical deformation.

Mechanical properties

Rubber materials are characterized by high deformability (they can resist large deformations) and can recover a geometry close to their initial state when the mechanical stress is released. This behavior is called quasi-elastic. However, elastomeric composites are complex materials, and their mechanical response is also complex and depends on many factors such as the type of mechanical stress, time, temperature, etc. In the following section, various types of mechanical tests are presented, to analyze the mechanical "signature" of filled rubber materials under mechanical deformation.

Properties for continuous tensile test

The incorporation of fillers in an elastomer modifies the mechanical behavior of the elastomer composite. Indeed, they cause a non-linearity of the mechanical behavior which is more marked as the rate of deformation is important. At room temperature, for a static uniaxial tensile loading at large deformation, the typical behavior of an elastomer can be summarized as illustrated in Domain I: For small strains, the increase in stress is related to the stiffness of the material.

The stiffness corresponds to the displacement of the chains in relation to each other.

There is a linear part where the Yong modulus can be calculated using Hooke's law. Due to the difficulty to determine in bounds in the linear part, mechanical behavior laws such as Neo-Hookean or Mooney-Rivlin are more accurate [27].

Domain II:

In this zone, the increase in deformation is accompanied by a small increase in stress. This is due to the fact that low stress is sufficient to orient the elastically active chains.

Domain III:

For high deformations, the stress strongly increases until the material breaks.

The macromolecular chains reach their extensibility limits and contribute to a significant hardening of the elastomer.

For filled elastomers, the results reported in the scientific literature on the influence of the load on the elongation at break are rather divergent. The introduction of fillers increases the stiffness of the material, which induce defects within the composite and then generate stress concentrations which leads to premature breakdown of the composite. That is the reason why for composite with high content of fillers, deformation at break is decreasing with the addition of fillers.

Mullins Effect

Rubber-like materials exhibit a change in their mechanical properties resulting from the first extension. This property, reported mostly in filled elastomeric materials has been investigated

intensively by Mullins and his co-workers and consequently referred as the Mullins effect [29,30].

Although observations of the Mullins effect date back some years (1957) [29], no consensus has been found on the mechanical modelling or the physical origin of this effect. Figure I-5 illustrates the two main characteristics of the Mullins effect: (i) Most of the stress softening, which is characterized by a lower stress for the same applied deformation, appears after the first loading.

After a few mechanical loading/unloading cycles, the mechanical response is stabilized. (ii) When the maximum strain previously applied is exceeded, the stress then follows the same behavior as the virgin sample, as if the previous cycles had never taken place. In addition to this loss of stiffness observed after the first cycle, we can also notice that a remanent deformation appears when unloading to zero stress. The phenomenon of remanent deformation depends on time and temperature, this is due to the viscoelasticity of the matrix and the Mullins effect. The Mullins effect is a phenomenon may be recovered at least partially at room temperature. At elevated temperature (close to the vulcanization temperature), the completeness and rate of recovery are higher.

Figure I-5. Stress-strain responses of a carbon-black filled SBR submitted to a simple uniaxial

tension and a cyclic uniaxial tension with increasing maximum strain every 5 cycles. [31] Several origins are evoked to explain this phenomenon. It can be associated with the reorganization of the reinforcement network during mechanical deformation, in addition to a rupture of the secondary network (agglomerates). This phenomenon can also be interpreted by the rupture of macromolecular chains during elongation, as a result of reaching their extensibility limit. These chains no longer participate in the following deformations, thus causing a softening of the stress. The main physical interpretations and their representation are summarized in Table I-3. They involve microstructural ruptures as well as microstructural changes. The various explanations suggested for explaining the Mullins effect show that there is still no general agreement on the origin of this phenomenon at the microscopic or mesoscopic scale.

Table I-3. Physical explanations of Mullins effect [31]

Physical source Sketch

Filler rupture

Bond rupture

Molecules slipping

Mechanical fatigue

There are two main approaches to analyze mechanical fatigue: the propagation approach and the initiation approach. Fatigue lifetime of elastomers can be summarized by different phases:

first the initiation and then the propagation phase of a defect/crack. The propagation approach aims at predicting the kinetics of a crack in the case of a previously notched specimen. In this case, the growth rate of the crack as a function of the tearing energy is studied. On the contrary, the initiation approach aims to determine the number of cycles necessary for the appearance of a macroscopic or critical crack, assuming that the specimen is initially free of defect. This approach gives information about the initiation of the crack and the propagation phase until mechanical failure, while in the case of the propagation approach, only the propagation of the crack is studied.

When rubber components are used in applications that involve repeated loading cycles, they can undergo fatigue failure even if the level of deformation is well below the maximum extensibility of the material. In recent years, studies on the mechanical fatigue of elastomers have become more and more numerous. We can distinguish macroscopic and microscopic approaches:

From a macroscopic point of view, many works concern the establishment of criteria for predicting the service life. For instance, Saintier et al. [32] developed a lifetime prediction model capable of locating the initiation of cracks as well as their orientation.

From a microscopic point of view, the mechanisms of damage are more and more studied, highlighting the phenomena of cavitation [33][34][35].

The fatigue characterization corresponding to the initiation approach is usually carried-out by the construction of an endurance curve (also called Wöhler curve), where the maximal stress or represented [36] b) typical endurance curve for rubber materials [37] where the local maximum strain is represented at 20%, 40%, and 60% of the average fatigue lifetime.

Zone I: at higher strain values, failure occurs at lower number of cycles and is preceded by noticeable plastic deformation. This is often known as oligocyclic fatigue.

Zone II: fatigue or limited endurance, where the breakdown is reached after a limited number of cycles. This number increases as the strain decreases.

Zone III: unlimited endurance, under low strain, where breakdown does not occur before a given number of cycles that is usually fixed at 10 6 or 10 7 cycles.

The endurance curve gives access to the estimated average fatigue lifetime and is used as a tool for industrial applications to quantify the replacement frequency in standardized maintenance (specimens replaced at regular intervals). For standardized maintenance, the pieces are usually replaced after reaching 50% of the average fatigue lifetime to avoid failure in service.

Nonetheless, from an economical and environmental point of view, this method is not optimal because the specimens are not used until the end of their real lifetime. This requires the definition of an end-of-life criterion and choosing a relevant predictive variable.

Specimen break: it is the most natural and the first used criterion [START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF]. It is very easy to implement but it is not always relevant for industrial applications.

Optical detection of a crack: this criterion requires the appearance of cracks on the material surface and relies on the definition of a critical crack size. This approach is based on the hypothesis that the initiation phase stops when the crack reaches the critical size.

Nonetheless, the critical size of the crack depends on the geometry of the specimen, it is therefore difficult to justify the chosen value of the critical crack objectively. In the literature the values reported vary from 1 to 3 mm [39].

Evolution of critical macroscopic properties: this criterion is generally based on the monitoring of the maximal force as shown in Figure I-7. Indeed, during cyclic loading,

(1) a drop of stress is firstly detected, due to the accommodation phase to the mechanical strain. Then, (2) a plateau is observed. Finally, in some cases, a sudden drop is observed before failure (3).

Figure I-7. Evolution of the effort during a fatigue test [39].

Designing elastomeric composites to minimize the impact of fatigue remains a difficult task because of their complex microstructure that combines a highly nonlinear smooth matrix with a complex network of hard fillers. This involves furthermore a strong coupling to manufacturing effects, from compounding to mixing, injection and curing. The influent parameters are therefore very numerous, and their optimization requires speeding up the fatigue characterization. In recent studies, thermal properties have been studied to characterize fatigue effects. A parallel between thermal and electrical conductivity can be made, thermal conductivity is characterized by the ability of the materials to conduct thermal energy. Electrical conductivity of elastomeric composite is the ability of the material to transfer electrons. As thermal conductivity seems to be a relevant descriptor to detect damages for filled elastomers, electrical conductivity could also be used as an end-of-life descriptor for filled elastomers.

Electrical properties of filled elastomers

When conductive fillers are used, electrical measurements can potentially represent a nondestructive method to detect defects in filled rubber composites. Nonetheless, electrical properties as a function of the filler structure, content, mechanical deformation, etc. must be systematically studied in this case.

Percolation threshold

Elastomeric materials are insulating with a conductivity around 10 -16 S.cm -1 . As explained before, fillers are added to improve mechanical properties such as stress at break. In most industrial applications the selected fillers are conductive, and recent studies [27,28] aimed at tailoring the electrical properties by the incorporation of conductive fillers, carbon black (CB) in particular.

Above a certain content of conductive fillers, the conductivity increases strongly, the volume concentration of fillers is important enough to create a continuous network. (composite filled with 20 phr of CB) [42]. The preparation of electrically conductive polymer composites through the addition of carbonbased or metallic fillers has been widely studied. In a review [43], Y. Li et al. have listed a large number of characteristics obtained for this type of composite. The electrical percolation is an essential phenomenon for filled polymer composites and illustrates the transition from not connected filler network to the formation of conductive pathways inside the polymer matrix. This phenomenon is known as electrical percolation and the content of fillers allowing the formation of continuous network corresponds to a critical threshold called the percolation threshold.

Theoretical models have been developed [44] where the composite electrical conductivity elec follows a power law in which the dimension of the medium (2D or 3D) intervenes as following:

= ( ) 2
In Eq 2, corresponds to the intrinsic conductivity of the particles, p is the volume fraction of particles, pc corresponds to the volume fraction of filler at the percolation threshold, and t is a critical exponent dependent on the dimension of the percolated system (for a 2D system 1.1 < t < 1.3 while for a 3D system 1.6 < t < 2). A theory of excluded volume is also reported [45],

describing the phenomenon of percolation in three-dimensional systems. The excluded volume surface [46] Formula for describing the excluded volume (Vexc) for randomly oriented spherical [34,35] or cylindrical [49] particles are given in Eq. 3 and Eq. 4 respectively.

= 4 3 (2 ) 3 = 32 3 + 8 + 4
Where the superscripts s and c represent spherical and cylindrical, respectively, and where rs is the radius of the sphere, rc and Lc are the radius of the cylinder and its length, respectively. In the case of carbon nanotubes (CNT), as L >> d, the first equation represents a close approximation of the excluded volume. Using this approximation, it is possible to determine the ratio between the excluded volume for cylindrical particles (typically carbon nanotubes) and spherical particles (typically carbon black) as noted in Eq. 5 However, in the case of cylindrical particles, there is no more space available and thus a larger excluded volume is observed (Figure I-9b). Moreover, it can be noticed that there is no contact possible in spherical particles, while for cylindrical particles vertical percolation can be observed. This is why the geometry of the filler is a very important factor in the electrical properties since it influences the percolation threshold [37,[START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF]. Nevertheless, there are notable differences between the theoretical and experimentally observed percolation. The deviation observed illustrates well the difference between a statistical model with an assumed perfect system and experimental reality. In practice, CNT are not straight but rather flexible. In addition, CB are dispersed rather in aggregates rather than homogeneously distributed within the matrix.

As it can be seen for the percolation threshold, the choice of the conductive fillers is important for electrical but also for mechanical properties. In the following section, the most commonly used conductive fillers are discussed.

Conductive fillers

The form factor is a geometrical parameter that is crucial for the process of conductive composites and for the determination of the minimum quantity of fillers to be introduced in order to reach the percolation threshold. It is possible to classify conductive fillers into two categories: those with a low aspect ratio and those with a high aspect ratio.

Fillers with low aspect ratio

For this type of conductive fillers, all their three dimensions have equivalent values. These fillers have geometries close to a spherical form.

Carbon black (CB):

CB is obtained in special furnaces by partial thermal decomposition of natural gases or heavy hydrocarbons. It exists in the form of more than thirty grades. The nomenclature of CB includes a letter and 3 numbers, Nxyz (ASTM-D 157665) where x is related to the average size of aggregates, y indicates the level of structure and z is most often specific to a given producer [START_REF] Thomine | Relations viscoélasticité / tribologie des élastomères chargés : application aux joints d'étanchéité dans les roulements à billes[END_REF]. CB is made up of "elementary" particles of predominantly spherical shape (nodules). These Carbon black is currently the most widely used conductive particle in the development of conductive composites and nanocomposites, due to its relatively low cost, and its low density close to that of polymers. However, it is reported in the literature that the intrinsic conductivity of carbon black depends strongly on its specific surface, its structure and its chemical composition. The intrinsic conductivity of CB fillers, however, is a physical parameter that is difficult to measure, because it depends on the applied pressure. For pressures of the order of a few tens of MPa, conductivity values of carbon black between 10 -4 and 10 S/cm are reported [START_REF] Sánchez-González | Electrical conductivity of carbon blacks under compression[END_REF].

Since CB has a low aspect ratio, its concentration in a polymer composite must be close to 10 vol%-12 vol% to achieve electrical percolation [START_REF] Lux | Models proposed to explain the electrical conductivity of mixtures made of conductive and insulating materials[END_REF][START_REF] Ghosh | Conducting carbon black filled EPDM vulcanizates: assessment of dependence of physical and mechanical properties and conducting character on variation of filler loading[END_REF].

Metallic fillers:

Metallic fillers with low form factors (silver, nickel, copper or aluminium) but also with higher form factor (nanowires, for instance) are reported in the scientific literature [START_REF] Muhammad Abdul | Synthesis of nickel-rubber nanocomposites and evaluation of their dielectric properties[END_REF][START_REF] Joy | CHAPTER 11:Micro and Nano Metal Particle Filled Natural Rubber Composites[END_REF][START_REF] Vinod | Degradation behavior of natural rubber-aluminium powder composites: effect of heat, ozone and high energy radiation[END_REF][START_REF] Hassar | Influence des nano-charges de noir de carbone sur le comportement mécanique de matériaux composites : application au blindage électromagnétique[END_REF].

Consequently, for low factor fillers a higher concentration is required to reach the percolation threshold. The use of metallic fillers in composites aims at obtaining a maximum level of conductivity. Indeed, metals have the highest intrinsic conductivity properties at room temperature (typically, about 10 7 S/m). However, metallic fillers have a high expansion coefficient and, because of their high surface energy, they oxidize easily. The incorporation of a high content of metallic particles can make the processability difficult, increase the density of the composite, or deteriorate the ageing properties of the composite [START_REF] Anuar | Properties of Aluminium and Zinc-Filled Natural Rubber Composites[END_REF][START_REF] Kilik | Mechanical properties of adhesive filled with metal powders[END_REF]. In addition, the use of this type of filler has a very high economic cost which restricts industrial applications.

High aspect ratio fillers

High form factor particles have one spatial dimension much larger than the other two.

Carbon nanotubes:

Carbon nanotubes were identified in the 1990s by Sumio Iijima [START_REF] Iijima | Helical microtubules of graphitic carbon[END_REF][START_REF] Iijima | Single-shell carbon nanotubes of 1-nm diameter[END_REF] Their physical properties combined with high intrinsic conductivity make CNTs a natural candidate for low-filled conductive nanocomposites. Nonetheless, for industrial applications CNT fillers are less optimal, because CNTs are more expensive than CB (80$/g to 2720$/g vs 0.01 $/g) [START_REF] Thines | Application potential of carbon nanomaterials in water and wastewater treatment: A review[END_REF].

Carbon fibers and nanofibers

Carbon fibers can be produced from three main precursors: rayon, polyacrylonitrile (PAN) or petroleum pitch [START_REF] Chaabani | Carbon fibers composites : recovery of fibers by hydrothermal solvolysis. Impact on fibers quality and valorization of liquid phase, Theses[END_REF]. Carbon fibers have an ordered nanostructure which improve the tensile strength [START_REF] Jiang | Preparation and electrical property evaluation of vapor-grown carbon nanofibers reinforced natural rubber composites[END_REF]. The high form factor of this type of fillers allows the creation of a conductive network using relatively low concentrations. For example, a percolation threshold of 5 w% was reported for NR composite filled with carbon nanofibers obtained by vapor-grown phase [START_REF] Jiang | Preparation and electrical property evaluation of vapor-grown carbon nanofibers reinforced natural rubber composites[END_REF].

Carbon fibers are a good intermediate choice between CB and CNT.

Coupling of mechanical and electrical conductivity

In the previous sections, the incorporation of fillers exhibited an increase in physical properties of rubber composites (stress, strain at break, electrical properties etc.). The electrical response can be tailored by the addition of various fillers. In recent years, there has been a strong demand to couple several functionalities and to allow the development of different types of electro-mechanical sensors [71]. The possible applications are various and can range from intelligent textiles [START_REF] Castano | Smart fabric sensors and e-textile technologies: a review[END_REF] to flexible sensors [START_REF] Jo | Graphene-based electrodes for flexible electronics[END_REF] but also to intelligent materials for in situ monitoring of composite damages. Coupling of mechanical deformation and electrical conductivity allowed to deepen the knowledge on the filler network modification with strain. The electrical response under mechanical deformation have been reported for various type of polymer composites filled with CB [START_REF] Focatiis | Roles of prestrain and hysteresis on piezoresistance in conductive elastomers for strain sensor applications[END_REF][START_REF] Kumar | Structure-property relationship in silicone rubber nanocomposites reinforced with carbon nanomaterials for sensors and actuators[END_REF][START_REF] Aneli | Effects of mechanical deformations on the structurization and electric conductivity of electric conducting polymer composites[END_REF], graphite [START_REF] Lu | The piezoresistive behaviors of polyethylene/foliated graphite nanocomposites[END_REF][START_REF] Qu | Piezoresistive behavior of polymer reinforced by expanded graphite[END_REF], CNT [START_REF] Yang | Strain-sensitive electrical conductivity of carbon nanotube-graphene-filled rubber composites under cyclic loading[END_REF][START_REF] Zhang | Strain sensing behavior of elastomeric composite films containing carbon nanotubes under cyclic loading[END_REF][START_REF] Lozano-Pérez | Influence of rigid segment and carbon nanotube concentration on the cyclic piezoresistive and hysteretic behavior of multiwall carbon nanotube/segmented polyurethane composites[END_REF][START_REF] Costa | Electro-mechanical properties of triblock copolymer styrene-butadiene-styrene/carbon nanotube composites for large deformation sensor applications[END_REF][START_REF] Duan | The resistivity-strain behavior of conductive polymer composites: stability and sensitivity[END_REF] or carbon fibers [START_REF] Wang | Short-carbon-fiber-reinforced epoxy as a piezoresistive strain sensor[END_REF][START_REF] Chung | Fibrous Composite Interfaces Studied by Electrical Resistance Measurement[END_REF]. The properties of filled elastomers make them candidate materials for the development of piezoresistive sensors, based on the measurement of the electrical resistance as a function of elongation [46]. Piezoresistivity is the evolution of an electrical quantity (resistance, resistivity, or conductivity) of a material under mechanical loading. The piezoresistive behavior in quasistatic tension of elastomers reinforced with carbon black depends on the quantity of reinforcement introduced into the matrix. The influence of mechanical loading is crucial on the response of the electrical properties. Firstly, the question asked was how the electrical conductivity is changing during continuous stretching? Are there similarities between electrical and mechanical properties under cyclic deformation? Finally, is it possible to detect damage by measuring electrical conductivity during a mechanical fatigue test?

Continuous stretching

For potential applications of composites in the field of stretchable electronics, it is necessary to investigate the stretching effects on electrical conductivity of composites in order to accurately predict and control the device performance. In situ monitoring of the evolution of the electrical conductivity under strain could represent an effective approach to identify permanent changes in the conductive rubber composite's microstructure. Existing experiments have demonstrated that stretching may significantly influence the electrical behavior of conductive polymer composites [START_REF] Flandin | Interrelationships between electrical and mechanical properties of a carbon black-filled ethylene-octene elastomer[END_REF][START_REF] Flandin | Effect of strain on the properties of an ethylene-octene elastomer with conductive carbon fillers[END_REF][START_REF] Das | Effect of axial stretching on electrical resistivity of short carbon fibre and carbon black filled conductive rubber composites[END_REF]. The electrical response gives information about the structural evolution of the conductive network, which indicates if the conductive pathways are destroyed (electrical conductivity is decreasing), stays intact (electrical conductivity stays the same) or is reformed (electrical conductivity is increasing) with strain. Different approaches have been followed to tune the conductivity-strain behavior such as using different types of fillers [START_REF] Ning | A new insight on the variation of the electric conductivity and conductive network of silver-coated glass particles/silicone elastomer composites under tensile strain[END_REF],

varying their aspect ratio [21] or employing polymers blends [START_REF] Su | Selective location and conductive network formation of multiwalled carbon nanotubes in polycarbonate/poly(vinylidene fluoride) blends[END_REF]. Several authors investigated the evolution of the electrical behavior of CB/polymer composites under tensile tests [START_REF] Flandin | Interrelationships between electrical and mechanical properties of a carbon black-filled ethylene-octene elastomer[END_REF][START_REF] Das | Effect of axial stretching on electrical resistivity of short carbon fibre and carbon black filled conductive rubber composites[END_REF][START_REF] Kost | Effects of axial stretching on the resistivity of carbon black filled silicone rubber[END_REF][START_REF] Aneli | Effects of mechanical deformations on the structurization and electric conductivity of electric conducting polymer composites[END_REF][START_REF] Yamaguchi | Electrical and mechanical behavior of filled elastomers. I. The effect of strain[END_REF][START_REF] Kraj | Relationship between conductivity and stress-strain curve of electroconductive composite with SBR or polycaprolactone matrices[END_REF]. Some studies showed an increase in electrical conductivity (decrease of the resistivity) of CB/elastomers composites during stretching due to reduction in the distance between the aggregates, particularly, in the perpendicular direction in respect to the stretching direction [START_REF] Flandin | Interrelationships between electrical and mechanical properties of a carbon black-filled ethylene-octene elastomer[END_REF][START_REF] Aneli | Effects of mechanical deformations on the structurization and electric conductivity of electric conducting polymer composites[END_REF][START_REF] Yamaguchi | Electrical and mechanical behavior of filled elastomers. I. The effect of strain[END_REF][START_REF] Kraj | Relationship between conductivity and stress-strain curve of electroconductive composite with SBR or polycaprolactone matrices[END_REF]. This results in the creation of additional conduction paths, leading to an increase in conductivity. However, some other works showed the opposite trend, i.e. stretching decreases the electrical conductivity of CB/elastomers composites due to the breakdown of existing conductive networks [START_REF] Das | Effect of axial stretching on electrical resistivity of short carbon fibre and carbon black filled conductive rubber composites[END_REF][START_REF] Kost | Effects of axial stretching on the resistivity of carbon black filled silicone rubber[END_REF]. Nonetheless, in all studies, we can notice that there is a change in conductivity (or resistivity) as a function of strain and in some cases a non-monotonic electrical response to strain was reported. Flandin et al. [START_REF] Flandin | Interrelationships between electrical and mechanical properties of a carbon black-filled ethylene-octene elastomer[END_REF], for instance, reported four regimes of resistivity variation four regimes in the resistivity-strain relationship. [START_REF] Flandin | Interrelationships between electrical and mechanical properties of a carbon black-filled ethylene-octene elastomer[END_REF] The resistivity during uniaxial stretching did not exhibit a monotonic variation. This behavior is explained by two simultaneous processes, namely, the rotation and translation of asymmetric particles, which results in the formation of new conductive pathways and in the destruction of existing conductive pathways due to uniaxial stretching. In the literature, coupled electrical/mechanical measurement is well described. Nevertheless, there is a lack of coupled electrical/structural/mechanical investigation to understand the variation of electrical and mechanical properties. The development of new conductive composites requires an understanding of the mechanism underlying the structure/properties relationship that might occur in service.

Cyclic tensile test

It is well known that an increased filler fraction in rubbers leads to higher mechanical properties [START_REF] Buckley | Experimental Methods for Rubberlike Solids[END_REF]. The deformation history plays an important role in the mechanical response of elastomers. This is best known through the manifestation of the softening phenomenon studied by Mullins and co-workers in the 1950s and known as the Mullins effect [29,30] (see section 2.1.2). In the Mullins effect, deformation causes permanent changes in the elastomer microstructure, which influences the mechanical response of the material during subsequent deformations. Therefore, smaller stress is required to generate a given deformation in subsequent loadings, as long as the original deformation amplitude is not exceeded. If the deformation amplitude exceeds the maximum amplitude previously reached, the stress needed to deform the material becomes independent of its history and returns to a value close to that needed to deform a virgin specimen to the same strain [31,[START_REF] Buckley | Experimental Methods for Rubberlike Solids[END_REF]. Different micro-mechanical interpretations have been provided to explain this softening phenomenon, nonetheless, more than seven decades after the pioneering works of Mullins, the interpretation of this behavior remains still a challenging task. Measurements of resistivity under strain brings further insight into physical processes involved in deformation of filled elastomers. This could lead to various applications and deepen the knowledge of the origin of the Mullins effect. In the previous section 2.3.1, the electrical response has been reported. However, the repeatable electrical conductivity-strain behavior under cyclic service conditions is very important in particular for strain sensors application. Bokobaza et al. [START_REF] Bokobza | Mechanical and Electrical Properties of Elastomer Nanocomposites Based on Different Carbon Nanomaterials[END_REF] showed a strain dependance of the electrical resistivity for natural rubber filled with MWCNT as reported in Figure I-12 shows that the resistivity is gradually increasing during unloading and after total removal of the stress, the resistivity is much higher than that of the virgin sample showing that the initial contacts are not reformed. Upon unloading the width and the thickness of the samples are increasing, causing a loss of contacts between conductive particles and an increase in resistivity (decrease in electrical conductivity).

Several authors investigated the evolution of the electrical behavior of CB/polymer composites under cyclic loading [START_REF] Focatiis | Roles of prestrain and hysteresis on piezoresistance in conductive elastomers for strain sensor applications[END_REF][START_REF] Zhu | Strain-Sensing Elastomer/Carbon Nanofiber "Metacomposites[END_REF][START_REF] Zhao | A comparison between strain sensing behaviors of carbon black/polypropylene and carbon nanotubes/polypropylene electrically conductive composites[END_REF][START_REF] Zheng | A highly-deformable piezoresistive film composed of a network of carbon blacks and highly oriented lamellae of high-density polyethylene[END_REF] and viscoelastic relaxation phenomena [START_REF] Melnykowycz | Comparison of Piezoresistive Monofilament Polymer Sensors[END_REF] but just a few of them have pointed out hysteresis effects [START_REF] Focatiis | Roles of prestrain and hysteresis on piezoresistance in conductive elastomers for strain sensor applications[END_REF][START_REF] Zheng | A highly-deformable piezoresistive film composed of a network of carbon blacks and highly oriented lamellae of high-density polyethylene[END_REF]. Among the few studies dealing with the phenomenon of electrical hysteresis, De Focatiis et al. [START_REF] Focatiis | Roles of prestrain and hysteresis on piezoresistance in conductive elastomers for strain sensor applications[END_REF] reported that the resistivity-strain relationship for rubber materials exhibits a dependence on the history of the mechanical deformation. The observed resistivity-related hysteresis behavior was associated with irreversible phenomena occurring in the conductive network as it can be seen in of an EPDM rubber filled with carbon black (100 V) [START_REF] Focatiis | Roles of prestrain and hysteresis on piezoresistance in conductive elastomers for strain sensor applications[END_REF] Zheng et al. [START_REF] Zheng | A highly-deformable piezoresistive film composed of a network of carbon blacks and highly oriented lamellae of high-density polyethylene[END_REF] concluded that the correlation between the electrical resistivity and mechanical strain for high-density polyethene/CB composites depends on the structure of the matrix and that the electrical resistivity is very sensitive to irreversible phenomena which occur within the polymer matrix. Some studies reported a non-monotonic resistance response, where a maximum resistivity is observed during cyclic loading [START_REF] Focatiis | Roles of prestrain and hysteresis on piezoresistance in conductive elastomers for strain sensor applications[END_REF][START_REF] Zheng | A highly-deformable piezoresistive film composed of a network of carbon blacks and highly oriented lamellae of high-density polyethylene[END_REF][START_REF] Liu | Electrically conductive thermoplastic elastomer nanocomposites at ultralow graphene loading levels for strain sensor applications[END_REF]. This behavior is often explained by the competition between the destruction and reconstruction of the conductive network during cyclic loading and the time-dependent mechanical properties of the polymer matrix, but the origin of percolation/"depercolation" mechanisms are still not fully understood.

Damage detection via mechanical fatigue testing

One of the critical issues in the successful application of smart rubber is an on-board or in situ assessment of the damage state and accurate prediction of the remaining service lifetime of the composite. The damage identification and prediction of remaining lifetime of filled elastomers components exposed to complex loading states play a key role in the service function and systems safety. Under service conditions, filled elastomers composites are generally submitted to severe loadings such as mechanical fatigue. However, damage mechanisms in polymer composites are still an open debate that animates the scientific community. These mechanisms are heterogeneous and initiate mostly in-depth and then propagate at different length scales (micro-, meso-or macroscales). Moreover, the scenario of damage evolution depends on the composite constituents (fillers, matrix, and interfacial bonding). Making the appropriate choice of suitable non-destructive testing (NDT) techniques is required to unambiguously detect mechanical damage occurring in the material. According to Hild et al. [START_REF] Hild | Damage measurements via DIC[END_REF], NDT techniques can be classified into major categories: micrography, density measurements, ultrasonic waves/acoustic emission, electrical resistance, and microhardness. In the case of filled elastomers composites, numerous classification criteria such as contact and non-contact methods or direct and indirect methods are also available [START_REF] Duchene | A review of non-destructive techniques used for mechanical damage assessment in polymer composites[END_REF]. The indirect NDT techniques consist in monitoring the effect of the global material deterioration on mechanical or physical properties such as stiffness loss, energy dissipation, high strain localization or electrical resistivity loss.

Techniques based on measuring changes in electrical resistivity are restricted to conductive materials, which is often the case of elastomer composites filled with conductive fillers (CB, CNT etc.). Electrical measurements can therefore enable real-time monitoring of the damage state through simple measurement of the electrical resistance. To our knowledge, there are no studies reported in the scientific literature dealing with the characterization of the mechanical fatigue lifetime of filled elastomers using in situ electrical measurements. E. Harea.

et al [START_REF] Harea | Electrical conductivity degradation of fatigued carbon black reinforced natural rubber composites: Effects of carbon nanotubes and strain amplitudes[END_REF] have investigated the impact of fatigue loading on volume electrical conductivity of NR reinforced with 30 phr of fillers (mix of CB and CNT) by ex-situ measurement (post-mortem analysis). Nonetheless, there are articles for carbon fiber-reinforced plastics (CFRP) [START_REF] Todoroki | Delamination monitoring of graphite/epoxy laminated composite plate of electric resistance change method[END_REF][START_REF] Nag-Chowdhury | Interfacial nanocomposite sensors (sQRS) for the core monitoring of polymer composites' fatigue and damage analysis[END_REF][START_REF] Suzuki | Impact-damage visualization in CFRP by resistive heating: Development of a new detection method for indentations caused by impact loads[END_REF][START_REF] Todoroki | Multi-prove electric potential change method for delamination monitoring of graphite/epoxy composite plates using normalized response surfaces[END_REF][START_REF] Todoroki | The effect of number of electrodes and diagnostic tool for monitoring the delamination of CFRP laminates by changes in electrical resistance[END_REF][START_REF] Todoroki | Matrix crack detection of CFRP using electrical resistance change with integrated surface probes[END_REF][START_REF] Todoroki | Electrical Resistance Change of Unidirectional CFRP Due to Applied Load[END_REF],

where in situ electrical investigations were widely employed to identify CFRP damage mechanisms, such as delamination [START_REF] Todoroki | Delamination monitoring of graphite/epoxy laminated composite plate of electric resistance change method[END_REF][START_REF] Nag-Chowdhury | Interfacial nanocomposite sensors (sQRS) for the core monitoring of polymer composites' fatigue and damage analysis[END_REF][START_REF] Suzuki | Impact-damage visualization in CFRP by resistive heating: Development of a new detection method for indentations caused by impact loads[END_REF], matrix cracking [START_REF] Todoroki | Matrix crack detection of CFRP using electrical resistance change with integrated surface probes[END_REF] and fiber breakage [START_REF] Todoroki | Electrical Resistance Change of Unidirectional CFRP Due to Applied Load[END_REF].

Wang et al. [START_REF] Wang | Sensing delamination in a carbon fiber polymer-matrix composite during fatigue by electrical resistance measurement[END_REF] studied the delamination sensing in carbon fiber polymer-matrix during fatigue by electrical resistance measurement.

Figure I-14. Variation of R/R0 with cycle number during tension-tension fatigue testing for epoxy filled with carbon fibers composites

In Figure I-14, an increase in the amplitude of variation of R/R0 is noticeable at 69,987 cycles.

The jump in the peak of the electrical response is due to the appearance of a crack into the polymer matrix and fiber fracture. The increase in the maximum of R/R0 is due to the presence of such matrix cracks, proving that electrical investigations can be able to probe mechanical damages.

Electrical measurement is an easy-to-implement technique that can be used to move from standardized maintenance to preventive maintenance.

Structural properties

Accurate description of the morphology of CB/rubber composite materials often presents a challenge due to the overlap of features on many length scales and because carbon-based fillers absorb most visible light [START_REF] Bond | Light Absorption by Carbonaceous Particles: An Investigative Review[END_REF][START_REF] Wright | Failure of Plastics and Rubber Products: Causes, Effects and Case Studies Involving Degradation[END_REF]. Especially when the CB content is above the percolation threshold, techniques such as optical microscopy and light scattering are precluded. For electron microscopy, the superimposition of three-dimensional and multiscaled CB network can lead to dif culty in the interpretation of the micrographs. X-ray scattering techniques, such as Smallangle X-ray scattering (SAXS) and Wide-angle X-ray scattering (WAXS), are well known for the study of nanofiller/polymer materials, but they can be only used to probe microstructure in the reciprocal space, necessitating a microstructural model for the interpretation [START_REF] Beaucage | Morphology of polyethylene-carbon black composites[END_REF].

Small Angle X-ray Scattering (SAXS)

Small-angle scattering techniques (SAXS, Ultra-SAXS, Small-angle Neutron Scattering, Ultra-SANS) have been used to investigate the structure of mass fractal aggregates [START_REF] Takenaka | Analysis of structures of rubber-filler systems with combined scattering methods[END_REF]. These techniques probe microstructure over several orders of magnitude in length-scale which include primary particle, their small scale aggregates and larger scale agglomerates. They may be adapted to probe the morphology of CB in suspensions, powders, or pellets, as well as in CB/polymer composites. CB mass fractal aggregates exhibit several scattering regimes in the Intensity vs q (scattering vector) scattering plots, in the form of different power laws High q region: Porod's law I(q)=C/q a accounts for (rough) surface scattering from the primary particles Lower q region: attributed to scattering from the CB aggregates and agglomerates with different fractal exponents.

In the literature, it was reported that the morphology of the CB aggregates can be studied by SAXS in the low-q region (q < 0.085 Å -1 ) [START_REF] Rieker | Small-Angle X-ray Scattering Study of the Morphology of Carbon Black Mass Fractal Aggregates in Polymeric Composites[END_REF][START_REF] Ehrburger-Dolle | Role of fractal features in the structure-property relationships of carbon black filled polymers[END_REF]. In this domain, the power law is characteristic of mass fractal aggregates. Rieker et al. [START_REF] Rieker | Small-Angle X-ray Scattering Study of the Morphology of Carbon Black Mass Fractal Aggregates in Polymeric Composites[END_REF] studied the influence of the processing on the interpenetration of aggregates in CB/polymer composites by SAXS. SAXS curves for fluffy, pelletized, and depelletized N330 carbon black according to [START_REF] Wang | Sensing delamination in a carbon fiber polymer-matrix composite during fatigue by electrical resistance measurement[END_REF] are shown in Figure I-15. This study concluded that the exponent a of the power law in the low-q region (I(q) q a ) can be related to the CB structure. Ehrburger et al. [START_REF] Ehrburger-Dolle | Role of fractal features in the structure-property relationships of carbon black filled polymers[END_REF] evidenced, for a given CB (N330), that the scattering pattern for "fluffy" CB and pelletized CB exhibit different power law exponents corresponding to different fractal dimensions and, thus, to different degrees of interpenetration of aggregates. A higher compaction of CB aggregates was related to lower exponent values [START_REF] Ehrburger-Dolle | Role of fractal features in the structure-property relationships of carbon black filled polymers[END_REF][START_REF] Ehrburger-Dolle | Filler networks in elastomers[END_REF]. the SAXS data corresponding to depelletized samples. [START_REF] Rieker | Small-Angle X-ray Scattering Study of the Morphology of Carbon Black Mass Fractal Aggregates in Polymeric Composites[END_REF] Furthermore, since the development of high flux (synchrotron) X-ray facilities, SAXS and USAXS have been used for real-time detection of microstructure changes during mechanical deformation with time-resolved accuracy. There are only a few studies that focus on filled elastomers under uniaxial extension [START_REF] Ehrburger-Dolle | Filler networks in elastomers[END_REF][START_REF] Baeza | Multiscale Filler Structure in Simplified Industrial Nanocomposite Silica/SBR Systems Studied by SAXS and TEM[END_REF][START_REF] Ramier | In situ SALS and volume variation measurements during deformation of treated silica filled SBR[END_REF][START_REF] Ehrburger-Dolle | Anisotropic Ultra-Small-Angle X-ray Scattering in Carbon Black Filled Polymers[END_REF][START_REF] Hagita | Two-dimensional pattern reverse Monte Carlo method for modelling the structures of nano-particles in uniaxial elongated rubbers[END_REF][START_REF] Schneider | Strain induced anisotropies in silica polydimethylsiloxane composites[END_REF][START_REF] Shinohara | Characterization of two-dimensional ultra-small-angle X-ray scattering apparatus for application to rubber filled with spherical silica under elongation[END_REF][START_REF] Zhang | Nanocavitation in Carbon Black Filled Styrene-Butadiene Rubber under Tension Detected by Real Time Small Angle X-ray Scattering[END_REF][START_REF] Zhang | Strain induced nanocavitation and crystallization in natural rubber probed by real time small and wide angle X-ray scattering[END_REF]. Most of them focused on the change in the anisotropy of the system [START_REF] Ehrburger-Dolle | Filler networks in elastomers[END_REF][START_REF] Ehrburger-Dolle | Anisotropic Ultra-Small-Angle X-ray Scattering in Carbon Black Filled Polymers[END_REF] and on the rearrangement of fillers in real space under external loading [START_REF] Baeza | Multiscale Filler Structure in Simplified Industrial Nanocomposite Silica/SBR Systems Studied by SAXS and TEM[END_REF][START_REF] Hagita | Two-dimensional pattern reverse Monte Carlo method for modelling the structures of nano-particles in uniaxial elongated rubbers[END_REF][START_REF] Schneider | Strain induced anisotropies in silica polydimethylsiloxane composites[END_REF][START_REF] Shinohara | Characterization of two-dimensional ultra-small-angle X-ray scattering apparatus for application to rubber filled with spherical silica under elongation[END_REF] and only a few studied mechanical damages such as cavitation phenomena [START_REF] Zhang | Nanocavitation in Carbon Black Filled Styrene-Butadiene Rubber under Tension Detected by Real Time Small Angle X-ray Scattering[END_REF][START_REF] Zhang | Strain induced nanocavitation and crystallization in natural rubber probed by real time small and wide angle X-ray scattering[END_REF].

Wild Angle X-ray Scattering (WAXS)

Concerning the characterization of the polymer matrix, molecular orientation is often viewed as an important parameter in relation to material properties, especially those related to mechanical behavior [START_REF] Koerner | Deformation-morphology correlations in electrically conductive carbon nanotube-thermoplastic polyurethane nanocomposites[END_REF][START_REF] Bitinis | Deformation mechanisms in polylactic acid/natural rubber/organoclay bionanocomposites as revealed by synchrotron X-ray scattering[END_REF]. WAXS is one of the experimental techniques which offer the most complete tools to assess molecular orientation and especially crystalline orientation. The Hermans' orientation factor is a scalar descriptor which quantifies the orientation of polymer crystals or polymer chains in amorphous systems [START_REF] Hermans | Quantitative evaluation of orientation in cellulose fibres from the X-ray fibre diagram[END_REF][START_REF] Guenoun | Crystalline orientation assessment in transversely isotropic semicrystalline polymer: Application to oedometric compaction of PTFE[END_REF]. This factor is null when the distribution is isotropic and ranges from 0.5 (when all chains are perpendicular to the reference direction) to 1 (when all chains are parallel to the reference direction).

Munch et al. [START_REF] Munch | Molecular mobility of crosslinked elastomers stretched above Tg[END_REF] studied the orientation of the amorphous chains after mechanical deformation for styrene-butadiene elastomers and nitrile butadiene elastomers. The values of Hermans' orientation factor determined for SBR and NBR are given in Table I-5. The uniaxial deformation induces an increase of the Hermans' factor for SBR and NBR [START_REF] Munch | Molecular mobility of crosslinked elastomers stretched above Tg[END_REF]. This indicates a significant trend in the alignment of the main chain axis. In a stretched elastomer network, it has been observed that the amorphous scattering halo, which comes from liquid-like monomer-monomer or chain-chain short range interactions becomes anisotropic under elongation, with more intensity in the direction perpendicular to stretching [START_REF] Sotta | Crosslinked Elastomers: Structure-Property Relationships and Stress-Optical Law[END_REF]. Sotta et al. [START_REF] Sotta | Crosslinked Elastomers: Structure-Property Relationships and Stress-Optical Law[END_REF] studied the orientation parameters as a function of an elongation parameter . It is reported that the orientation of the amorphous chains increases linearly with . The slope of the orientation vs. was increasing with the sulfur content, the orientation being related to the mobility of the vulcanized network. In conclusion, structural properties measured by SAXS and WAXS give essential information about the morphology of elastomer composites.

Project positioning and orientation in respect to the state-of-the-art.

The bibliographical study highlights the complexity of physical and structural properties of rubber composites filled with reinforcement fillers and vulcanized by using activators and accelerators compounds. Due to their good resistance to repeated stresses, high elasticity and good fatigue resistance, elastomeric materials are used in many industrial applications (tires, seals, foam etc.).

Nowadays, research in the field of elastomeric materials focus on the understanding of the different characteristics of these materials and, in particular, of the origin of their intrinsic properties. As it was explained in the bibliography, the addition of filler has a strong impact on the final mechanical properties of rubber composites. In many industrial application, conductive fillers are added. For conductive elastomeric materials, the electrical conductivity can be monitored to give access to new information (percolation/depercolation mechanisms) under mechanical deformation. The bibliographical study highlights the complexity of the evolution of electrical properties of elastomeric composite undergoing mechanical deformation (continuous stretching, cyclic loading, and fatigue test).

To sum up, the evolution of electrical conductivity (or resistivity) for filled elastomer exhibits a hysteretic behavior during mechanical cycles. The electrical behavior under uniaxial tensile for CB/polymer is often non-monotonic. Both observations are still not fully understood. In this context, our study aims first to improve the understanding of electrical hysteresis by comparing the electrical and mechanical properties under cyclic deformation. Then a microstructural approach was chosen to explain the non-monotonic relationship between electrical conductivity and continuous deformation. Finally, the electrical conductivity was measured simultaneously with fatigue tests to find out if it is possible to detect damage by nondestructive electrical measurement for CB/elastomers.

Additional agents

Vulcanization agent

The crosslinking was achieved thanks to the addition of sulfur which allows the creation of sulfur bridges. Sulfur was provided by the LRCCP.

Paraffinic oil Torilis 6200

The plasticizer Torilis 6200 provided by Total (Ferrybridge, UK) with a density of 0.89 g/cm 3 at 15°C and a viscosity of 114 mm²/s at 40°C has been used.

(a) (b)

Activator of vulcanization Activators are inorganic metal derivatives (e.g., metal oxides or hydroxides) used together with co-activators (generally fatty acids or derivatives, such as stearic acid), able to form adducts with accelerators and to further increase their efficiency [2]. As previously observed, Zinc oxide (ZnO) is considered to be the most efficient activator for sulfur vulcanization, where it plays a main role both in the first steps improving the kinetics of the curing reaction and at the end promoting the formation of short sulfide cross-links with the achievement of higher cross-linking densities. ZnO and stearic acid were provided by the LRCCP.

Accelerator of vulcanization

Accelerators such as zinc dibutyl dithiocarbamate (ZDBC-80), Zinc diethyldithiocarbamate (ZDEC-75), N, N'-dibutyl thiourea (DPTT) and 2-Mercaptobenzothiazole (MBT) have been used.

It should be noted that the vulcanization of sulfur elastomers in the absence of an accelerator can take several hours, compared to ten minutes or so with accelerators. All the vulcanization accelerators are provided by the LRCCP. The efficient system is selected as presented in Chapter I, section 1.1.2, the ratio between the accelerator and the cross-linking agent is / = 2.7.

Antioxidant

Trimethyldihydroquinoline (TMQ) has been used to avoid thermal ageing. TMQ was provided by the LRCCP.

Details of the composition of the rubber composites are presented in section 3.

Process

The sample preparation has been done in three steps, schematized in Figure II-2.

Step 1: Mixing the blends of the elastomer, processing oil and CB in an internal batch mixer (Banbury 3.2 L) at 60 °C and 60 round per minute (rpm) for 4 min.

Step 2: Mixing using a two-roll mixing mill (Agila, roll dimensions: 300 x 700 mm) the vulcanization systems (sulfur, accelerator, activator, and antioxidant) with the blend obtained at step 1, at 60 °C and 20 rpm for 5 min.

Step 3: Then, slabs of rubber were vulcanized during press molding at 200 bar at 170 °C for a duration equal to t98% as defined in Chapter I, section 1.1.2.

Summary of rubber composites prepared

A deeper understanding of the evolution of the electrical properties of elastomeric composite materials undergoing mechanical deformations is needed. In order to address this challenge, in situ coupled electrical/mechanical investigations on EPDM based composite materials (Keltan 5470 or Keltan 9650) filled with CB of various content (0% vol,15% vol,25% vol and 35%vol), and CB structure (N326 or N347) have been systematically carried-out. The composition of each composite is reported in Table II-2. Other composites have been used by changing the CB content from 9%vol to 13%vol, these composites have been useful for electrical measurement in order to obtain the percolation curve and the detail of the composites are reported in Appendix 1.

Characterizations

Various characterizations have been performed to study the impact of CB content, structure, and EPDM matrix on:

Thermal properties

Electrical properties

Mechanical properties

Structural properties

The initial properties of the elastomeric materials have been summarized in Appendix 2. Then the impact of mechanical deformation on structural and electrical properties has been studied.

Thermal properties -Differential Scanning Calorimetry (DSC)

Differential Scanning Calorimetry, commonly referred to as DSC, is a thermal analysis technique that allows the identification and quantification of the various thermal phenomena accompanying a change in the physical state of a material or a chemical modification. The principle of this technique is based on the measurement of the differential heat flow between a sample and a reference maintained at the same temperature. DSC able to identify for polymers: the glass transition temperature "Tg" visible by a variation of heat capacity, the melting phenomena (endothermic peak) and the crystallization phenomena (exothermic peak). The DSC analyses were performed on a TA Q200 (TA Instruments, New Castle, DE, USA) equipped with a liquid nitrogen cooling system. DSC experiments were performed on 10-15 mg samples under a helium atmosphere with a heating/cooling/heating cycle comprised between -100 °C and 100 °C or between 25 °C and 100 °C at a temperature scan rate of 10 °C•min 1 .

Electrical properties 4.2.1. DC and AC measurement

The AC-electrical conductivity was measured with a Novocontrol Alpha Broadband The AC-electrical conductivity was measured in the frequency range from 10 5 Hz to 10 0 Hz. The electrical resistance was measured using a Keysight multimeter at 5 V and the electrical conductivity, was calculated using the following formula:

= × Eq 1
The electrical conductivity can be measured in the perpendicular direction in respect to the surface

Mechanical properties

The mechanical parameters: true stain ( ), nominal strain ( ) or elongation have been studied respectively for cyclic loading/unloading study, fatigue study and structural/ electrical/ mechanical investigation. We used , ,and to be in better agreement with the literature that we found for each part.

Continuous stretching

Continuous tensile testing was performed using a Shimadzu AG-X+ testing machine at room temperature and constant crosshead displacement for different velocities. Specimens were cut with a dumbbell cutting die, specimen of H2 (to follow the ISO 37 standard) with characteristic dimension of: L0=20 mm, width = 4 mm, and thickness = 2 mm or H3 where only the gauge length change with L0=10 mm (after checking that the electrical response was the same for H2 and H3).

Considering iso-volume deformation conditions (theorical Poisson ratio equal to 0.5 for incompressibility hypothesis and was validated by various studies [4][5][6]), true strain and true stress were calculated (respectively Eq 2 and Eq 3).

= ln(1 + ) 2

where is the gauge length and is the crosshead displacement corresponding to the undeformed state and = . The nominal stress, is defined as

=
where F is the measured force and is the initial cross-sectional area of the specimen.

= (1 + ) 3
A

Cyclic tensile test

As for continuous tensile testing, cyclic loadings were performed using a Shimadzu AG-X+ testing machine at room temperature and constant crosshead displacement for various velocities.

Mechanical fatigue testing

Fatigue lifetime can be summarized by different phases, first the initiation and then the propagation phase of a defect/crack. Endurance fatigue at various strain amplitude can be used for uncracked specimens, and the objective is to determine a limit criterion, this criterion is either determined by specimen breakdown or by a loss of specimen stiffness. The fatigue test campaign has been conducted at the LRCCP, using an electrodynamic test machine Acumen from MTS.

Specimens were cut with a dumbbell cutting die type H2 according to NF ISO37 with a gauge length of 20 mm, a width of 4 mm and a thickness of 2 mm. It is necessary to know the correlation between the displacement of the crosshead, and therefore between the fixing grips and the local uniaxial tensile deformation effectively imposed on the useful part of the H2 specimens. The correlation between the displacement of the crosshead (corresponding to the distance between the fixing grips) and the local uniaxial tensile deformation effectively imposed on the gauge length of the specimens is determined using a cathetometer. Indeed, the endurance curve must be established for the local uniaxial tensile deformation imposed on the gauge length of these specimens and the number of cycles until breakdown. The cathetometer is an optical instrument which allows precise sighting and positional readings. A spirit level and a vertical vernier ruler are fixed on a tripod. On the latter, a telescope with a reticule that can go up or down is attached.

The horizontality of this reticule is ensured by another spirit level. The setup allowing to make this correlation is shown in Figure II-8. -The initial length at zero fixture displacement between the external marks ;

-The imposed displacement between external marks P4 P1;

-The imposed deformation between outer marks ;

-The initial length with zero fixture displacement between the inside marks ;

-The imposed displacement between inner marks P3 P2;

-The imposed deformation between outer marks ;

For the external part of the marks

= P4 P1 = (P4 P1)/
For the inner part of the marks

= P3 P2 = (P3 P2)/

Type of deformation

The case of uniaxial loading has been chosen for the mechanical fatigue tests: samples are loaded along a single axis in traction. Fatigue tests were performed with imposed displacement amplitude, the imposed strain is determined using the correlation presented before. For all tests, the imposed displacement follows a sinusoidal signal (the displacement increases progressively for the 5 first cycles) over time with a constant frequency throughout the test. Fatigue loading under fixed displacement can be characterized by the parameters defined in Figure II-11. The maximal displacement ( max) and the minimal displacement ( min), allow the definition of the load ratio R using the correlation between displacement and nominal deformation (Eq 4).

= 4

where and are respectively the minimal nominal deformation and the maximal nominal deformation.

Structural properties

SAXS

The incident photon energy was set to 15.7 keV and the cross-section of the beam size was 0.42 × 0.45 m². The SAXS intensity I was collected using the 2D D5 detector. The scattering vector q was calculated (Eq 5) from the wavelength and the scattering angle 2 .

= 4 sin( ) 5

The SAXS q-calibration was achieved using silver behenate powder standard. The sample-todetector distance was set to 1.760 m, corresponding to a q-range from 6.6 10 -3 Å -1 to 2.2 10 -1 Å -1 .

The exposure time was 10 s. The 2D pattern was obtained after correction of the exposure and subtraction of the empty cell image.

WAXS

WAXS intensity I was collected using the X-ray detector (IMXPAD WOS-S700). The WAXS q-calibration was achieved using lanthanum hexaboride powder standard. The sample-todetector distance was set to 12 cm, corresponding to a q-range from 0.7 Å -1 to 6.0 Å -1 . The exposure time was 10 s. The 2D pattern was obtained after correction of the exposure and subtraction of the empty cell image.

Characterization of the crosslinked network

Equilibrium swelling measurement

The density of vulcanized chains can be calculated by a swelling experiment at equilibrium.

Swelling rates of cross-linked polymers are related to their degree of cross-linking, but their ability to swell also depends on the polymer-solvent affinity (0.43 for EPDM/p-xylene at 80 °C). The study of EPDM swelling is used to characterize both the degree of crosslinking as well as to estimate the degradation of the crosslinking network after mechanical fatigue.

The procedure used for the swelling measurements is schematized in Figure II-14 and detailed as follows: a sample with an initial mass Mi is introduced into p-xylene for 24 h at 80 °C to reach its equilibrium swelling, then it is weighed in its swollen state (corresponding to the mass Ms). It is then dried under vacuum at 80 °C for 1 day and weighed again, where its mass is Md . The swelling G of the polymer and the soluble fraction is deduced from the relationships ( 6):

= 1 + . ( )
6
where EPDM = 0.86 g/cm 3 is the density of the matrix and solvent = 0.86 g/cm 3 is the density of pxylene in our experiments. In the case of filled materials, the filler mass fraction is described by w and it must be subtracted because the fillers are considered to not participate in swelling.

Based on the assumption of additivity of the free energy of mixing and the free energy of elasticity, the Flory-Rehner theory [10] for the swelling of a rubber network gives the expression of the crosslink density as:(

Electrical/ mechanical fatigue parameters

The sinusoidal signal is the same that we have used in section 4. The fatigue behavior of rubbers is influenced by several parameters, which are the load ratio, frequency, and strain amplitude.

Frequency

To study the impact of frequency on the fatigue behavior, loading cycles have been performed at different frequencies ranging from 0.1 to 3 Hz. We have chosen to limit the self-heating which is mainly caused by the viscoelasticity property of the material at 10°C. The temperature of the specimen was measured via an IR-camera during fatigue test and 3 Hz is the maximal frequency because EPDM-35LS for a maximal strain of 60%, the measurement temperature was 35°C

(fatigue test are all done at room temperature: 25°C)

Loading ratio

The R-ratio, = is a useful descriptor of mechanical loading, and its value considerably affects the fatigue behavior. For R=0, i.e., the minimum loading quantity is zero, the mechanical loading conditions are said to be relaxing. Nonetheless, due to of the viscoelasticity of the matrix and also to residual deformation, the maximum strain imposed to the specimen is decreasing during cyclic loading because the fatigue was performed under imposed displacement.

Therefore, a buckling phenomenon is observed after a few deformation cycles. The impact of the R-ratio has been studied in both case with and without bucking phenomenon for R ranging from 0 to 0.6. The specimens are fixed between polycarbonate pieces and brass electrodes by two screws. The micromachine itself was mounted on a vertical displacement stage, and a position correction of -/2 is applied when the mobile crosshead is moved by . In this way, the centre of the sample is maintained under the incident beam all through the elongation test. At the same time, the electrical conductivity was determined by taking into account the variation of geometry of the specimens during a tensile test assuming isovolume deformation, using (Eq 10):

Electrical/structural/mechanical coupling setup

= × = × 10
where L is the sample length, S the sample cross-section (L0 and S0 are initial values in the For image data treatments, the intensity is further normalized by the thickness of the sample, still considering isovolume deformation conditions. The intensity ( , ) of each pixel of the detector is localized by 2 polar coordinates, namely the scattering vector and the azimuthal angle ( = 0° in the stretching direction). Chain orientation and crystallinity index were evaluated by WAXS.

The intensity profiles were treated using Fityk software. The amorphous halo and the other scattering peaks were modelled using Gaussian profiles. The orientation of the EPDM chains was then quantified by calculation of the apparent Herman factor ( ) (Eq 11) [14,15]:

( ) = 3 2 < > 1 2 11 with < >= ( , ) ( ). ( ) ( , ) . ( )
( ) = 0.5 when the polymer chains are ideally oriented parallel to the stretching direction, it tends to 1 when the polymer chains are perpendicular to the stretching direction, and it is 0 for a purely isotropic distribution of chain axis or reticular plane orientation.

Real time small angle X-ray scattering (SAXS) was used to probe the cavitation damage in filled elastomers, using the scattering invariant Q during uniaxial loading [34,35]. The scattering invariant Q is directly related to the mean square fluctuation of electron density and irradiated volume V and is independent of the shape of the scatterers and their spatial distribution [39] as reported in Eq 12.

= ( ) = 2 . < ( ) > 12
Where < > stands for a spatial average and =< >.In our case, it can be calculated by separating the integral in three terms; the first one corresponds to an extrapolation of the low-q power law, the second one to the experimental data, and the last one to an extrapolation of the high-q power law (Porod regime) as shown in Eq 13:

= + ( ) + 13
the extrapolation of experimental data from 0 to qmin and from qmax to + . In the Porod region, the value of exponent b is always -3.2 and -3.8 and the last term can be integrated. Thus, the Q is practically (Eq 14):

2 + 1 + ( ) 2 + 1 14
Typical scattering invariant Q as a function of the elongation is shown in Figure II-19g. CB mass fractal aggregates exhibit several scattering regimes in the Intensity(q) vs q (scattering vector) scattering plots, in the form of different power laws. In the range of larger q values, a first generalized Porod's law I(q)=C/q a accounts for (rough) surface scattering from the primary particles but other power law regions at lower q values may be due to scattering from the CB aggregates and agglomerates with different fractal exponents (S(q)) as represented in Figure

II-19f.

Introduction

Electrically conductive rubber composite materials are appropriate candidates for the development of a new generation of smart materials [1]. Due to their large deformation at the break, impact resistance and flexibility, elastomers are a promising choice for the development of composite materials for sensor or actuator applications. In order to extend their range of applicability, in particular in the field of sensor applications, the electrical properties of the elastomer matrix can be tailored by the incorporation of conductive particles. This type of conductive nanocomposite materials could have a great potential in the field of strain and damage sensing, with multiple applications in domains as different as health, automotive industry or electromagnetic interference shielding. The introduction of fillers into an elastomeric material impacts significantly its physical behavior. Typically, this leads to an increase of the static and dynamic moduli [2] as well as to changes in other properties such as strength [3], fatigue resistance [4] and electrical conductivity [5]. The type and shape of fillers influence the viscoelastic behavior of rubber materials [6]. For example, it is well known that an increased filler fraction in rubbers leads to both higher mechanical properties and mechanical hysteresis [7]. The deformation history plays an important role in the mechanical response of elastomers. This is best known through the manifestation of the softening phenomenon studied by Mullins and co-workers in the 1950s and known as the Mullins effect [8,9]. In the Mullins effect, deformation causes permanent changes in the elastomer microstructure, which influences the mechanical response of the material during subsequent deformations. As a consequence, a smaller stress is required to generate a given deformation in subsequent loadings, as long as the original deformation amplitude is not exceeded. If the deformation amplitude exceeds the maximum amplitude previously reached, the stress needed to deform the material becomes independent of its history, and returns to a value close to that needed to deform a virgin specimen to the same strain [7,10].

Different micro-mechanical interpretations have been provided to explain this softening phenomenon, nonetheless, more than seven decades after the pioneering works of Mullins, the interpretation of the behavior of such materials remains still a challenging task.

In situ monitoring the evolution of the electrical conductivity under mechanical strain could represent an effective approach to identify permanent changes in the conductive rubber composite materials accompanying the Mullins effect. Different approaches have been followed to tune the conductivity-strain behavior such as using different types of fillers [11], varying their aspect ratio [12] or employing polymers blends [13]. In most industrial applications, fillers are added to increase the mechanical properties of the rubber composites but some of the fillers, such as for instance carbon black (CB) or carbon nanotubes (CNTs), bring also enhanced conductive properties. Several authors investigated the evolution of the electrical behavior of CB/polymer composites under cyclic loading [14][15][16][17] and viscoelastic relaxation phenomena but just a few of them have pointed out hysteresis effects [15,17]. Among the few studies dealing with the phenomenon of electrical hysteresis in this kind of nanocomposite materials, De Focatiis et al. [15] reported that the resistivity-strain relationship for rubber materials exhibits a dependence on the history of the mechanical deformation. The observed resistivity-related hysteresis behavior was associated with irreversible phenomena occurring in the conductive network. Zheng et al. [17] concluded that the correlation between the electrical resistance and mechanical strain for high-density polyethylene/CB composites depends on the structure of the matrix and that the electrical resistance is very sensitive to irreversible phenomena which occur within the polymer matrix. Some studies reported a non-monotonic resistance response, where a maximum of resistivity is observed during cyclic loading [15,17,18]. This behavior is often explained by the competition between destruction and reconstruction of the conductive network during cyclic loading and the time-dependent mechanical properties of the polymer matrix, but it is still not fully understood.

In the present work, an in situ coupled mechanical/electrical approach is employed to

Sample preparation

The sample preparation was done in three steps. The 1 st step was to blend the elastomer, the processing oil, and the CB fillers in an internal batch mixer (Banbury 3.2 L) at the temperature of 60 °C at 60 rpm for around 4 min. The 2 nd step was to add and mix the vulcanization systems (sulfur, accelerator, activator, and antioxidant) with the blend obtained at step 1, using a two-roll mixing mill (Agila, roll dimensions: 300 x 700 mm) at 60 °C with a velocity of 20 rpm for 5 min.

The last step was to measure the kinetics of vulcanization for each composite at 170 °C using a moving die rheometer (MDR one, TA instruments). The time to reach 98 % of vulcanized network t98% was measured. Then, slabs of rubber were vulcanized during press moulding at 200 bar and 170 °C for a time equal to t98%, as reported in Table III-1.

Mechanical measurements

Uniaxial tensile testing and cyclic loading were performed using a Shimadzu AG-X+ testing machine at room temperature and constant crosshead displacement velocity of 10 mm/min.

Specimens were cut with a dumbbell cutting die at the following dimensions: 30 × 4 × 2 mm .

The true strain is calculated as = ln(1 + ), where is the gauge length and is the crosshead displacement corresponding to the undeformed state and = . The nominal stress, is defined as = , where F is the measured force and is the initial crosssectional area of the specimen. Considering iso-volume deformation conditions (Poisson coefficient equal to 0.5), the true stress can be expressed as

= (1 + ).
The experiments to investigate the mechanical properties of our materials were performed using two different approaches. The 1 st approach was to apply a continuous deformation until failure.

The 2 nd one was to perform 50 cycles at true deformation amplitudes reaching max of 0.09, 0.18, 0.35, 0.47, 0.57, 0.69 and returning to min values corresponding to complete unloading (F = 0).

Electrical measurements

The electrical conductivity was measured with a Novocontrol Alpha Broadband Dielectric/Impedance Spectrometer and a Keysight B2980A multimeter for double-checking the measured values. The AC-electrical conductivity was measured using a Novocontrol Alpha Broadband Dielectric/Impedance Spectrometer (BDS) in the frequency range from 10 5 Hz to 10 0

Hz. The electrical resistance was measured using Keysight multimeter at 5 V and calculated using the following formula:

= ×
L represents the sample length (conductivity parallel to the surface of the sample) or thickness of the sample (conductivity perpendicular to the surface of the sample), S the sample cross-section and R the electrical resistance.

In situ coupled mechanical/electrical investigations

The measurement setup for in situ coupled mechanical/electrical investigations is illustrated in

Small-angle X-rays scattering (SAXS)

SAXS experiments were carried out at the European Synchrotron Radiation Facility (ESRF) in Grenoble (France) on the D2AM beamline. The incident photon energy was set to 15.7 keV and the cross-section of the beam size was 0.42 × 0.45 m². The SAXS intensity I was collected using the 2D D5 detector. The scattering vector q was calculated from the wavelength and the scattering angle 2 as = sin ( ). The q-calibration was carried-out using silver behenate powder standard. The sample-to-detector distance was set to 1.760 m, leading to a q-range between 6.6 10 -3 Å -1 and 2.2 10 -1 Å -1 . The exposure time was 10 s. In situ SAXS measurement during tensile tests was performed using a homemade remotely controlled tensile test device. The tensile device was composed of two crossheads, one of them being mobile and guided by two stainless-steel guide bars and displaced using a threaded shaft, a DC electric motor and a LVDT sensor to control the crosshead position. The samples were stretched in the vertical direction and the true strain was varied between 0 and 0.69. For the data treatment, the intensity was normalized is respect to the sample thickness taking into account iso-volume deformation conditions. To highlight the hysteresis behavior and the irreversible changes of the microstructure, the image during unloading was subtracted from the image during loading at the same strain of 0.55.

Verification tests

This part is devoted to all experimental verifications carried-out before launching systematic investigations on the influence of mechanical deformation on electrical properties. First, the electrical conductivity under AC and DC field was measured and the obtained values were compared. Then, the electrical conductivity was measured at room temperature before and after thermal treatment, in order to validate that the samples were brought into an equilibrium state.

The We were interested in the influence of the electrical/mechanical setup on the measurements of mechanical properties. To this purpose, we verified that the home-made fixation system used for integrating in situ electrical measurements did not influence the mechanical measurements. and after 10 loading/unloading cycles from 0% to -75% of strain (redline).

Results and Discussion

Mechanical Mullins effect

The To quantify the mechanical hysteresis,

Figure III-13. Mechanical hysteresis of a) EPDM-25LS b) EPDM-25HS c) EPDM-35LS during the 1st, 5th and 50th cycle as a function of and d) , corresponding to the dissipated energy for the 1st and the 50th cycle as a function of .

For the same content of HS CB, EPDM-25HS (Figure III-13b) shows an evolution with the number of cycles similar to that of EPDM-25LS. Yet, the initial value of is lower and, starting from = 0.34 where = 41.6 %, increases with increasing . The difference between at = 0.34 and at = 0.69 is 17.1 %. The hysteresis behavior can be explained by considering the interactions at the polymer/filler interface and the reorganization of the filler aggregates. For CB of higher structure, the filler/polymer interface and filler/filler friction increase, contributing to the hysteresis behavior at high deformations [21]. For elastomeric matrices filled with LS CB, the mechanical hysteresis increases with increasing the filler content, as shown in Figure III-13c, and this effect is more pronounced at high values of [22]. For all investigated composites, the mechanical hysteresis area is increasing with increasing , as reported in Figure III-13d. also increases with the CB content and structure.

Electrical Mullins effect

In the current section, the impact of the Mullins effect on the percolation of the CB network is investigated, through a coupled mechanical/electrical approach. Two important factors are taken ). Thus, a reversible behavior can be observed at small strains. This does not seem to be the case for higher

, where the electrical behavior appears to become irreversible, as shown by a hysteresis behavior that increases with . A notable difference between the electrical and mechanical hysteresis can be distinguished: the loading/unloading conductivity curves cross each other while this is not the case for the mechanical results. For instance, during the unloading after reaching = 0.67, the conductivity decreases and become smaller than the conductivity during loading. The equilibrium electrical behavior (5 last cycles out of a total of 50 cycles) of all investigated EPDM/CB composites for = 0.69 is reported in Figure-III-16.

Figure-III-16. Normalized conductivity according to the initial conductivity 0 as a function of strain for the 5 last cycles (out of a total of 50 cycles).

The phenomenon of electric hysteresis appears thus to be more complex than the mechanical one.

A non-monotonic electrical response under cyclic loading has been previously reported in the literature [15,19,[23][24][25]. Several theories based on electron tunnelling effects and the creation/destruction of conductive networks indicate that the conductivity decreases under stretching due to filler-to-filler separation [26]. Conventionally, during the unloading cycle, the conductivity increases by the reduction in the filler/filler distance which increases the number of conductive paths [14,27]. Disorder effects of the polymer chains and the CB network could also contribute to this behavior, as proposed by Aneli et al. [28]. Another aspect to be considered is related to the fact that throughout the loading the strain increases and the width and thickness of the sample decrease, reducing thereby the distance between the CB aggregates in the transverse direction.

As in the mechanical Mullins effect, the electrical behavior during the 1 st loading is markedly During cyclic deformations at low strains ( < 0.15), all composite materials investigated in our study display a maximum in the -plots and low hysteresis. Loading will first induce new filler-filler contacts due to the negative deformation in the perpendicular direction and thus an increase of conductivity. Above the maximal conductivity threshold (that depends on the maximal applied strain), loose contacts or separation of CB particles and aggregates resulting from the axial positive deformation will dominate the electrical behavior, leading to a decrease of conductivity. This behavior appears to be reversible with decreasing the axial during unloading.

For larger applied axial ( > 0.15), unloading still displays a conductivity maximum that systematically appears at a higher than upon loading.

Reconnecting the CB fillers along the axial direction by reduction of inter-particle distance appears to be a faster process than the competing mechanism taking place in the perpendicular direction and leading to disconnection of the particles/aggregates by the evolution of the perpendicular . This indicates that the configuration of the CB network evolves with both axial and perpendicular , according to the CB structure and applied maximal strain . Such difference in the axial and perpendicular restructuration dynamics results from the interactions between the rubber matrix and the filler as well as from the non-elastic deformation within the confined polymer matrix [28]. The conductivity peaks, related to the points in the plots where the creation of new conductive pathways in one direction (axial or transverse) compensates the destruction of the percolation network in the other direction, clearly depend on the applied as well as on the CB structure and concentration. To fully explain the observed phenomena, a simulation of tri-dimensional (axial and transverse) motions of the CB aggregate network could be very helpful, but it is still a challenge to provide accurate insights [29].

To confirm the percolation/de-percolation/re-percolation mechanisms taking place parallel and perpendicular to the stretching direction, in situ coupled Small Angle X-Ray Scattering above > 0.2 (for EPDM-25HS and EPDM-35LS), displaying thus a minimum in conductivity.

On contrary, during the subsequent cycles, a conductivity maximum is observed during unloading. As in the mechanical response (Figure III-17b), the first loading exhibits a specific electrical response as compared to the following cycles. Similarly, to the mechanical results, the vs curves show a hysteresis behavior: the conductivity evolution during loading is different from the one during unloading. Thus, similarly to the classical mechanical Mullins effect, the coupled electrical response of all investigated materials measured during mechanical deformation exhibits also an electrical Mullins effect, with a specific electrical signature. Notable differences between the mechanical and the electrical Mullins effects can be however observed.

For instance, the evolution of electrical conductivity takes significantly more than 5 cycles before settling to an equilibrated loop. In this sense, the conductivity seems to be considerably more time-dependent than the .

In order to further compare the number of cycles necessary to reach the equilibrium state for the .

The mechanical Mullins effect is not significantly affected by the variation of the unloading rate , except for a small non-recovered at the end of the unloading step at =0, increasing, as expected, with the unloading rate. The kinetics of the strain recovery appears to be faster as compared to the applied unloading rates, in agreement with a highly cross-linked matrix that exhibits a strong elastic recovery. On contrary, the electrical Mullins effect is highly dependent on the unloading displacement rate (Figure III-20b). When < , the -vs electrical response for 0.25< <0.35 is the same during loading and unloading, almost no electrical Mullins hysteresis is detected in this range. For 0.35< <0.69 a hysteresis becomes noticeable, with conductivity upon unloading systematically higher than the conductivity upon loading. When > (i.e. set to 50 mm/min or conditions, the conductivity maximum is obtained at a higher and the unloading curve generally remains well below the loading curve. Thus, at high values of , the repercolation of the CB network is less developed, due to the limited time imposed by the fast unloading rate. This results in a lower conductivity value and higher conductivity variation during one cycle (up to 2 decades). The evolution with is thus proven to be considerably sensitive to the deformation rates. This is partly due to the anelasticity of the polymer matrix implied in the restructuration of the CB network during the loading and unloading. Since limited variations of the Mullins effect were noticed under the same conditions, it may be concluded that the electrical Mullins hysteresis is due to slower/larger scale microstructural reorganization events. Thus, the matrix anelasticity strongly affects the destruction/reconstruction of the 3D CB network electrical percolation during cyclic loading, the apparent crosslinking density of the composites being less affected.

Conclusion

In This is demonstrated by performing unloading experiments at different displacement rates between 0.5 mm/min and 500 mm/min. It is shown that, unlike for mechanical Mullins effect, the electrical Mullins effect strongly depends on the unloading displacement rate. This is due to the kinetics of re-percolation that is becoming too slow compared to the unloading rate. Our study brings new light into the understanding of the Mullins effect, by revealing, though an in situ coupled mechanical/electrical approach, a different facet of this phenomenon related to a kinetic reorganization of the fillers upon mechanical deformation. This could be of potential interest in numerous applications for monitoring the evolution of mechanical properties of elastomeric materials by in situ coupled electrical measurements.

Acknowledgements:

The financial support given by ANRT through the CIFRE project no. 0479-

Introduction

Elastomers are envisioned for new applications such as flexible sensors [1,2] or electromechanical sensors [3,4]. Such complex materials are also known as "smart rubbers", defined as elastomeric materials that respond through a macroscopic output to an external stimulus [5].

Elastomers materials are widely used due to their high range of mechanical properties required in many applications. Real-time monitoring of elastomers damages is a new lead for the development of smart rubbers. Due to the incorporation of fillers, which are very often electrically conductive (carbon black, carbon nanotubes, graphene etc.), in situ conductivity monitoring could be used as a non-destructive testing technique to probe mechanical damages. Electrical measurement exhibits the advantage of being easily implementable for materials working under real functioning conditions. A deeper understanding of the evolution of the electrical conductivity under strain is necessary to identify permanent or reversible specific changes in the microstructure of the conductive network.

In situ coupled electrical/mechanical measurement of CB/elastomers composites under mechanical strain has already been reported in the literature and different approaches have been followed to tune the conductivity-deformation behavior [6][7][8][9][10][11][12][13][14] such as using different types of polymers [8], types of conductive fillers [6,9], and filler contents [7,10]. The stress and strain sensitivities of conductivity are still difficult to control or interpret, in fact electrical behavior varies from one system to another, and it exhibits a non-monotonic response with strain [11][12][13][14].

For these reasons, the development of new smart conductive composites requires a fine understanding of the changes in their microstructure leading to a change of conductivity.

However, to our knowledge, there is no study where the electrical behavior has been compared simultaneously to structural investigations, to correlate the evolution of the electrical behavior with a structural state.

Accurate description of the morphology of CB/polymer composite materials often presents a challenge since it extends on many length scales and because carbon-based particles absorb most visible light [15,16]. Thus, techniques such as optical microscopy and light scattering are precluded. Electron microscopy is also difficult to exploit since the superimposition of threedimensional and multiscale CB networks can lead to dif culty in the interpretation of micrographs. In situ investigations of the material morphology and structure, and mechanical properties has been the focus of rubber research for decades. X-Ray Scattering techniques, such as Small-angle X-ray scattering (SAXS) and Wide-angle X-ray scattering (WAXS) are well known for the study of nanofiller dispersion and distribution in polymer-based composite materials, but they can be used to probe microstructure in reciprocal space, necessitating a microstructural model for the interpretation [17]. SAXS and WAXS asses structural evolution and especially chains and crystallites orientation by WAXS. Concerning the characterization of the polymer matrix, molecular orientation is often viewed as an important parameter in relation with its mechanical properties [18]. In situ WAXS/mechanical investigations quantify the orientation of polymer crystals or chain orientation in amorphous systems using a scalar descriptor known as the Hermans orientation factor [19]. For the characterization of CB (amorphous and rigid) fillers, small-angle scattering techniques (SAXS, Ultra-SAXS, Small-angle Neutron Scattering, Ultra-SANS) are used to investigate the structure of mass fractal aggregates [20],

probing microstructure over several orders of magnitude in length which include both the primary particle, their small scale aggregates and larger scale agglomerates. These techniques may be adapted to probe the morphology of CB as suspensions, powders, or pellets, as well as in CB/polymer composites [21,22]. Furthermore, since the development of high flux (synchrotron) X-ray facilities, SAXS and USAXS have been used for real-time detection of microstructure changes with time-resolved accuracy, for example during deformation [23]. Only a few structural studies are focusing on filled elastomers in situ SAXS/WAXS under uniaxial extension [24][25][26][27][28][29][30][31].

These works are devoted to the characterization of anisotropy of the polymer component [22,26],

the rearrangement of fillers under deformation [24,[27][28][29] and other studies focused on damage in particular with nano-cavitation [30,31]. Zhang et al. [30] have detected nanocavitation for the first time in carbon black filled styrene-butadiene rubber (CB/SBR) under uniaxial loading by real-time small-angle X-ray scattering (SAXS) using a synchrotron source. A three-phase model was developed to calculate the void volume fraction from the scattering invariant Q determined from the observed SAXS patterns. In all these studies, the correlation between damages and/or rearrangement of CB network and the electrical properties is not mentioned. To highlight the origin of the evolution of electrical conductivity under mechanical deformation, an in situ mechanical/electrical/SAXS/WAXS investigation could be studied.

In the present work, an in situ coupled mechanical/electrical/SAXS/WAXS approach is employed to identify the mechanisms underlying the structure/properties relationship under uniaxial tensile stretching for EPDM/CB filled elastomers. This correlation opens the possibility to distinguish the different mechanisms and their successions from small strain to large strains up to mechanical failure. First, the orientation of EPDM chains is quantified by Herman's factor with strain. Then, we demonstrate the deep relationship linking electrical conductivity evolution with aggregates interpenetration of EPDM/CB composites. Finally, at larger strains, the decrease of the conductivity has been related to the nanovoid formation by SAXS experiments. The evolution of the electrical properties of elastomeric composite materials under mechanical strain can be thus correlated, which can have potential applications in developing new smart rubber materials where microstructural changes can be in situ monitored by coupled electrical measurements.

Experimental

Sample preparation

The sample preparation was performed in three steps, as follow:

Step 1: mixing the blends of the elastomer, processing oil and CB in an internal batch mixer (Banbury 3.2 L) at 60 °C and 60 rpm for 4 min.

Step 2: mixing the vulcanization compounds (Sulphur, accelerator, activator, and antioxidant) with the blend obtained at step 1, using a two-roll mixing mill (Agila, roll dimensions: 300 x 700 mm) at 60 °C and 20 rpm for 5 min.

Step 3: Then, slabs of rubber were vulcanized during press molding under 200 bars at 170 °C for a time equal to t98%. This time corresponds to the time needed to reach 98% of the maximum torque obtained using a moving die rheometer at 170 °C to follow the evolution of the crosslinking reaction.

Specimens were cut with a dumbbell cutting die type H3 according to NF ISO 37. These specimens used for mechanical, structural, and electrical investigation have a gauge length =10 mm, a width of 4 mm and a thickness of 1 mm. The term "gauge length" refers to the part of a test specimen being measured during a tensile test.

Structural investigations: SAXS/WAXS

SAXS and WAXS experiments were carried out simultaneously at the European Synchrotron Radiation Facility (ESRF) in Grenoble (France) on the D2AM beamline. The incident photon energy was set to 15.7 keV and the cross-section of the beam size was 0.42 × 0.45 m². The SAXS intensity I was collected using a 2D D5 detector and the WAXS intensity was collected using a X-ray detector IMXPAD WOS-S700. Scattered intensities are usually plotted against the scattering vector q, defined as = sin ( ), where is the incident wavelength (0.78968 Å) and 2 is the scattering angle. The SAXS q-calibration was achieved using silver behenate powder standard. The sample-to-D5 detector distance was 1.760 m, leading to a q-range between 6.6 10 -3 Å -1 and 2.2 10 -1 Å -1 . The WAXS q-calibration was achieved using lanthanum hexaboride powder standard. The sample-to-WOS detector distance was 12.0 cm, leading to a q-range between 0.7 Å -1 and 6.0 Å -1 . The exposure time was 10 s. The 2D pattern was

Mechanical investigations

The mechanical behavior of elastomers can be described using the Neo Hookean hyperelastic model [33,34]. Using this constitutive law, the calculation of the true stress at large uniaxial extension ratios is given by the equation:

= 2C ( )

Where C is a material constant, and is the elongation. For unfilled and filled composites [35,36], C = = where N is the number of crosslinked chains per unity of volume, k is the Boltzmann constant, T the temperature in Kelvin, and G is the shear modulus. The reinforcement effect can be quantified by the ratio of C of the reinforced system compared to the one without CB.

In situ coupled structural/mechanical and electrical investigations

Combined For image data treatments, the intensity was further normalized in respect to the sample thickness. The intensity ( , ) of each pixel of the detector is localized by 2 polar coordinates, namely, the scattering vector and the azimuthal angle ( = 0° in the stretching direction).

Chain orientation and crystallinity index were evaluated by WAXS. The intensity profiles were treated using the Fityk software. The amorphous halo and the other scattering peaks were modelled using Gaussian profiles. The orientation of the EPDM chains was then quantified by calculating the apparent Herman factor ( ) defined as:

( ) = 3 2 < > 1 2 with < >= ( , ) ( ). ( ) ( , ) . ( )
( ) = 0.5 when the polymer chains are ideally oriented parallel to the stretching direction, it tends to 1 when the polymer chains are perpendicular to the stretching direction, and it is 0 for an isotropic distribution of chain axis or reticular plane orientation.

Real time small angle X-ray scattering (SAXS) was used to probe the cavitation damage in filled elastomers, using the scattering invariant Q during uniaxial loading [30,31]. The scattering invariant Q is directly related to the mean square fluctuation of electron density and irradiated volume V and is independent of the shape of the scatterers and their spatial distribution [37]:

= ( ) = 2 . < ( ) >
Where < > stands for a spatial average and =< >. In our case, it can be calculated by separating the integral in three terms: the first term corresponds to an extrapolation of the low-q power law, the second one to the experimental data, and the last one to an extrapolation of the high-q power law (Porod regime):

= + ( ) ² +
The extrapolation of experimental data from 0 to qmin and from qmax to + are represented in linear and logarithm scale in the Supplementary information in and the second one at 3 is broader. For E1, the peak at q = 1.36

Verification tests

Å -1 can be deconvoluted into two peaks (see Appendix 3). As it can be seen in the literature, this WAXS pattern could be the signature of a pseudo-hexagonal or an orthorhombic form of polyethene [51]. The presence of crystallites for E1, can also be seen by the SAXS pattern in WAXS profiles of c) both matrix E1 and E2 where the inlets are a zoom of the intensity near the maximum from q = 1.0 to 1.7d) both CB HS and LS.

In the literature, it was reported that the morphology of CB aggregates can be studied by SAXS in the low-q region (q < 0.085 Å -1 ) [21,[START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF]. The SAXS low-q power law exponent for initial CB, CB grinded with a mortar and CB grinded with a coffee grinder are shown in Figure IV-4, for CB powders and CB dispersed in dibutylphthalate (DBP).

Figure IV-4. Low-q power law exponent for CB powders and CB dispersed in dibutylphthalate (DBP). a) CB HS at its initial state that we assume to be pelletized, after grinding CB using a mortar, and after grinding CB using a coffee grinder. b) CB LS at its initial state that we assume to be pelletized, after grinding CB using a mortar, and after grinding CB using a coffee grinder.

The low-q power law exponent for initial CB and CB grinded with coffee grinder are nearly is noticeable for CB grinded with a mortal, i.e., a the fractal dimension and thus the degree of aggregate interpenetration has changed. This agrees with the results of Rieker et al. [21] and Ehrburger et al. [START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF] which concluded that the exponent a of the power law in the low-q region (I(q) q a ) can be related to the CB structure.

Results and discussion

Orientation of EPDM chains during stretching

Thermal properties of the unfilled crosslinked composites for both E1 (Keltan 5470) and E2

(Keltan 9650) matrices were studied to obtain crystallinity information about the matrices (thermal transition, crystallinity) (see Table IV-1). The thermograms corresponding to the first and second heating run of E2-0 and E1-0 are presented in Figure IV-5.

The thermograms of E1-0 and E2-0 exhibit a heat flow increase at -46 °C and -53 °C, respectively, corresponding to the glass transition of the EPDM segments. Then, an endothermic peak for E2-0 at about -24 °C was observed, attributed to the melting of the crystalline phase. E1-0 thermogram exhibits two endothermic peaks at 20 °C and 35 °C during the 1 st heating run and only one at 25 °C for the 2 nd run. These peaks were attributed to the melting of the crystalline phase. Both EPDM matrices are semi-crystalline, with the melting temperature of the crystalline phase of E2-0 being below ambient temperature whereas the melting temperature of E1-0 is close to the ambient temperature. The resulting crystallinities of both matrices were further studied at room temperature (Figure IV-5c). E2-25LS is amorphous at room temperature since there is no melting in the thermogram, but there is a modest melting peak for E1-25LS which suggests that there is a residual crystallinity (Xc ~ 0.2%) at room temperature [39]. WAXS analysis was further performed on the same matrices and also on filled EPDM composites. of rubber [40,41]. The two CB halo peaks, centered around q values of 1.7 Å -1 and 3.0 Å -1 and indexed as the (002) and (10) planes of carbon material [42][43][44], correspond to the graphitic nature of CB. Furthermore, ZnO, introduced as a vulcanization activator, is present in all composites.

The diffraction peaks of ZnO are well-known to be around 2.2 Å -1 , 2.4 Å -1 , 2.5 Å -1 , 3.2 Å -1 , and 3.8 Å -1 . These peaks are indexed as ( 110), (002), ( 101), ( 102) and ( 110), respectively, and can be used as an internal standard for q range calibration and intensity normalization.

To go a step further, we investigated EPDM-CB dumbbell specimens by WAXS, in situ under stretching.

Reorganisation of CB network during tensile test: Correlation between structural and electrical properties

The The shear modulus is increasing with the CB content and structure. At large , the elastomer behavior is no longer linear and exhibits strain stiffening with the onset of chain orientation. It can be observed that the strain hardening effect is lower for E2 than for E1 (Figure IV-10a,b).

Such lower reinforcement effect agrees with the apparent. Herman's factor evolution with strain presented in Figure IV-9, showing that the orientation of EPDM chains is lower for E2 than for E1 As expected, the structural evolution of the EPDM composites strongly impacts their electrical I(q)=B/q a in the low q range (I) and a second power law I(q)=B/q b in the q-range II. In the literature, it was reported that the morphology of the CB aggregates can be studied by SAXS in the low-q region (q < 0.085 Å -1 ) [21,[START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF]. In this range, the power law is characteristic of mass fractal aggregates. Rieker et al. [21] concluded that the exponent a of the power law in the low-q region (I(q) q a ) can be related to the CB structure (i.e. fractal dimension of the aggregates). Ehrburger et al. [START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF] evidenced, for a given CB (N330), that the scattering pattern for "fluffy" CB and pelletized CB exhibit different power law exponents, i.e. different fractal dimensions and thus different degrees of interpenetration of aggregates, higher compaction being related with lower exponent values. Similarly, in our data, the exponent value a during stretching is decreasing in the meridional direction which implies that the degree of interpenetration decreases along the stretching direction. Figure IV-13c, d displays the changes observed in the low-q range (S(q) region) and in the exponents a// (in I// ) and a (in I ) during stretching of the E1-35LS sample. The value of a// is decreasing during stretching, associated with a disentanglement of aggregates along the meridional direction. On the contrary, the value of a is increasing during stretching until = 1.8, showing CB aggregates interpenetrating each other in the equatorial direction during stretching. This microstructural scenario is in good agreement with results reported in the scientific literature on the evolution of conductivity during stretching performed on the same materials [13]. However, at higher elongation ( > 1.8), the value of a is decreasing, revealing thus a different deformation mechanism.

In the high-q region (0.02 < q < 0.1 Å -1 ), the scattered intensity is the signature of the surface fractal of the primary CB particles [21,[START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF]. This scattering regime was analyzed in our study using a power law (I(q) q b ). The value of the exponent b is also reported in Figure IV-13c, d, in the meridional (b//) directions. According to the literature, the typical value for b is between -3.3 and -3.8 [21,[START_REF] Cadwell | Dynamic Fatigue Life of Rubber[END_REF]. In both directions, b// stays almost constant for < 1.8, and it is slightly decreasing for > 1.8. This observation is not expected to originate from a modification of the surface of primary particles (CB) since it is not likely to be affected by stretching the nanocomposite material. Therefore, this variation of b// should be explained by the contribution of new scatterers such as nano-voids (nv) with "net" interface, exhibiting thus a more conventional Porod's behavior with bnv=-4. The apparition of nanovoids by cavitation has been subsequently confirmed by analyzing the evolution of the scattering invariant Q (see below). SAXS in the equatorial region is also strongly impacted by the evolution of the microstructure of the CB network occurring upon stretching. The exponents of the two power laws at low-q (a ) and high-q (b ) have been determined in the equatorial direction for various composites and they are plotted in In the equatorial direction, all investigated composites exhibited an increase of the exponent (a ) in the low-q region (S(q) region) upon stretching associated with CB aggregates compaction corresponding to minimum inter-aggregate distance, due to the negative strain in the transverse direction. This compaction and contacting mechanism explain well the increase of the

Introduction

Rubber is widely used in many applications due to its excellent mechanical proper-ties. Some of the common applications are tires, seals, hoses and vibration isolators. During their service, most rubber components undergo cyclic loading which lead to fatigue fracture. In general, investigations on fatigue effects in rubber mate-rials are carried out using two distinct approaches [1]: endurance and crack propagation. In the endurance approach, the end-of-life is experimentally defined as a loss of the mechanical stiffness or as the occurrence of small cracks or complete fracture for specimens that are initially defect free. The crack propagation approach is used when the initial crack shape and position are known. The crack growth is estimated through the calculation of the tearing energy. Due to the importance of pre-venting the fracture of rubber components in service, studies focusing on durability have significantly increased in the past few decades [2].

Many works concern the establishment of criteria for predicting the service lifetime of elastomeric materials where two approaches can be distinguished: macroscopic and microscopic approaches [3][4][5][6][7][8]. Damage mechanisms are more and more studied using microscopic information which highlights the phenomena of cavitation and decohesion [9][10][11][12]. Intrinsic material properties, such as thermal properties, have been studied for the characterization of fatigue properties [13][14][15][16].

Marco et al. [13] relate the fatigue lifetime to the energy dissipation and the crack population for a natural rubber compound filled with carbon black (CB). The dissipated energy is measured by thermal measurements and its evolution with the local strain is de-scribed. The design of elastomeric composites with enhanced fatigue resistance re-mains a difficult task because of their complex microstructure that mixes a highly nonlinear smooth matrix with a complex network of hard fillers. That is the reason why there is still is no criterion for predicting the service lifetime of elastomeric materials. Therefore, there is a strong demand for the development of a nondestructive methods that can be industrialized for real-time monitoring of the damage of rubber composites. This development would change the type of maintenance used in the industry, from standardized maintenance (change the specimen at a constant frequency) to preventive maintenance.

Non-destructive testing (NDT) techniques are required to do in situ monitoring to detect mechanical damage occurring in the material. According to Hild et al. [17], NDT techniques can be classified into several major categories: micrography, density measurements, ultrasonic waves/acoustic emission, electrical measurements, and microhardness. The indirect NDT techniques consist in monitoring the effect of the global material deterioration on mechanical or physical properties such as stiffness loss, energy dissipation, high strain localization or change in electrical properties [18]. The real-time conductivity monitoring for conductive elastomers could be very easily achieved due to the simplicity of the testing process (conductive electrodes and multimeter), which makes the in situ electrical measurement one of the best candidates to develop preventive maintenance.

Techniques based on the variation of electrical conductivity are restricted to conductive materials, among which elastomer composites filled with conductive fillers (e.g. CB, CNT, etc.) can be found. Electrical measurement enables real-time monitoring of the damage state through the measurement of the electrical resistance. To our knowledge, only few investigations are dealing with lifetime monitoring using electrical measurements for filled elastomers. For instance, studies on carbon fiber-reinforced plastics (CFRP) [19][20][21][22][23][24][25][26][27], in which the variation of electrical resistance has been widely used to identify CFRP damage mechanisms, such as delamination [19][20][21]26],

matrix cracking [24] and fiber breakage [25] have been reported. The evolution of the electrical resistance increases due to the presence of such matrix cracks, indicating that electrical properties are a probe for mechanical damage.

The objective of the current work is to develop a methodology to correlate mechanical damage and electrical properties. Since in situ electrical monitoring is easily implementable during the mechanical testing process, the non-destructive electrical measurements present high potential in real-time damage detection for filled elastomers. In this study, we demonstrate the strong relationship linking the evolution of the electrical conductivity during mechanical fatigue to the damage. Firstly, an in-crease of the amplitude of the conductivity was correlated to damages in the cross-linked network allowing greater freedom of movement of the CB network. Then, a decrease in the conductivity was linked to the apparition and propagation of nano-voids before fracture.

Sample preparation

The sample preparation was performed in three steps:

Step 1: Mixing the elastomer, processing oil and CB using an internal batch mixer (Banbury 3.2 L) at 60 °C and 60 rpm for 4 min.

Step 2: Mixing the vulcanization compounds (sulfur, accelerator, activator, and antioxidant)

with the blend obtained at step 1, using a two-roll mixing mill (Agila, roll dimensions: 300 × 700 mm 2 ) at 60 °C and 20 rpm for 5 min.

Step 3: Then, rubber slabs were vulcanized during press moulding at 200 bar and 170 °C for a duration equal to t98%, as reported in Table V-1.

Swelling measurement

The density of vulcanized chains can be calculated by a swelling experiment at equilibrium.

Swelling rates of cross-linked polymers are related to their degree of cross-linking, but their ability to swell also depends on the polymer-solvent affinity (0.43 for EPDM/p-xylene at 80 °C).

The study of EPDM swelling is used to characterize both the degree of crosslinking as well as to estimate the degradation of the crosslinking network after mechanical fatigue.

The procedure used for the swelling measurements is schematized in where EPDM = 0.86 g/cm 3 is the density of the EPDM matrix and solvent = 0.86 g/cm 3 is the density of p-xylene in our experiments. In the case of filled materials, the filler mass fraction is described by w and it must be subtracted because the fillers are considered to not participate in swelling.

Based on the assumption of additivity of the free energy of mixing and the free energy of elasticity, the Flory-Rehner theory [28] for the swelling of a rubber network gives the expression of the crosslink density as:(

In situ coupled mechanical fatigue/electrical investigations

The sinusoidal signal is the same that we have used in section 4.

Frequency

To study the impact of frequency (f) on the fatigue behavior, loading cycles have been performed

at different frequencies ranging from 0.1 to 3 Hz. The composite self-heating is related directly to the viscoelastic nature of the matrix and the dissipated energy during dynamic loadings. Since the test for EPDM 35LS at f = 3 Hz shows a sample temperature increase by 10 °C for a strain amplitude of 60% (detected by IR-camera), f = 3 Hz was defined as the upper limit for this investigation.

Loading ratio

The R-ratio, = is a useful descriptor of mechanical loading, and its value considerably affects the fatigue behavior. For R=0, i.e., the minimum loading quantity is min = 0 and the mechanical loading conditions are said to be "relaxing". Therefore, a buckling phenomenon is observed after a few deformation cycles. The impact of the R-ratio has been studied in both cases (with and without bucking phenomenon) for R ranging from 0 to 0.6.

Verification tests and analysis methodology of electrical and mechanical results

Data processing of electrical results

The strain/conductivity evolution with time for fatigue testing is presented in Figure V-9. Various parameters can be studied. For instance, the electrical conductivity at maximal strain ( ) shows an increase before fracture. Furthermore, the minimal and the maximal conductivity as well as the amplitude of the conductivity show a decrease with the number of cycles. The parameter selected for the fatigue analysis was the electrical amplitude . In our study, the electrical amplitude is normalized by using the 10th cycle as reference (corresponding to the "1st cycle after accommodation"): = . Similarly, the stress is also normalized using the 10th cycle as reference, = . As it can be seen in Figure V-12, while the mechanical property uniformly decreases before the failure of the specimen, the electrical property shows an increase during mechanical fatigue and then a plateau and a decrease before fracture. As it will be discussed in the following, the presence of the plateau can reveal the first damage mechanisms and could be a tool to predict failure. response is reported for EPDM-35LS as a function of fatigue cycles c) in linear scale d) in logarithm scale, for sample stretched at 60% at 1 Hz and with a loading ratio of R = 0.

Results and discussion

The evolution of the mechanical stress as a function of the number of fatigue cycles is similar for all 3 specimens that were investigated. The number of cycles at break are of the same order of magnitude for the 3 samples (Nf1= 602, Nf2= 551, and Nf3= 515).

The evolution of the amplitude of the electrical conductivity is repeatable for both CB/EPDM composite. Hence, the normalized amplitude of electrical conductivity, seems to be an efficient descriptor for fatigue tests.

For a damage-free test, a decrease in the conductivity amplitude is observed, whereas for tests performed in the endurance zone, first an increase in the conductivity amplitude, then a change of slope of vs. number of cycle and finally a decrease of are observed. For fatigue test in the endurance zone, distinct successive phenomenon is due to damages propagation.

The influence of various parameters has been studied to see the impact of the frequency and the strain amplitude on electrical and mechanical responses. for EPDM-25HS at 3 Hz and from 1 to 1.5 for EPDM-25HS at 1 Hz. increase from 1 to 2.0 for EPDM-35LS at 3 Hz and from 1 to 1.5 for EPDM-35LS at 1 Hz. The influence of frequency is also noticeable on the mechanical properties. Indeed, when the frequency is higher, the material stiffness undergoes a stronger decrease as can be seen in The normalized electrical amplitude, is therefore a suitable parameter to predict the fracture of filled elastomers. Indeed, two parameters can be used, the deviation from the electrical behavior law in fatigue (Eq 6) or the decrease over a few cycles before failure. In the following, the frequency is fixed at 1 Hz (unless otherwise specified), which will be a reference frequency for our fatigue tests. In order to investigate breaking effects of the rubber matrix swelling tests have been performed.

From the swelling measurement, the apparent cross-linking density can be determined. The The cross-linking density is called "apparent" because the crosslinking agent interacts with the CB and adsorb on the filler surface [33]. The decrease of the cross-linking density comes from the breakage between the filler/cross-linked network interactions, as the breakage energy of this type of bonds is lower than that of the covalent bonds. As it can be seen in Figure V-20, the apparent crosslinking density is decreasing between the sample in the initial state and the sample after the accommodation cycles, it can be explained by the damages of the interaction filler/crosslinked network. As reported in Figure V-20, is decreasing even more when the sample have undergone fatigue test in the endurance zone for both EPDM-25HS and EPDM-35LS. This result implies that, in addition to deteriorating the links between the filler and the vulcanized network, the crosslinked network itself is damaged during the fatigue tests. The comparison of the crosslinking density after a damage-free test and after the accommodation test was also performed. In Other techniques would also allow us to validate or not the apparition of cavity before rupture.

Indeed, Dinari et al. [35] studied the fatigue-induced damage in CB filled styrene-butadiene rubber and observed local inhomogeneities (voids and cracks) using mesoscale X-ray tomography. Environmental scanning electron microscopy observations showed relevant altered morphologies of elastomeric chains with a predominant effect of CB fillers. To fully understand the damage mechanisms in CB filled EPDM, X-ray tomography and SAXS could be used during the increase of as well as during the decrease of before failure.

Conclusion

In this work, we carried out in situ coupled mechanical/electrical investigations during uniaxial

NotationCB : ::

 : Carbon black CNT: Carbon nanotubes ENB: 5-ethylidene-2-norbornene HD: Hexa-1,4-diene DCPD: dicyclopentadiene EPDM: Ethylene Propylene Diene Monomer ZnO: zinc oxide CFRP: Carbon fiber-reinforced plastics NR: Natural rubber SBR: Styrene butadiene rubber NBR: nitrile butadiene elastomers SWCNT: Single walled carbon nanotubes MWCNT: Multiwalled carbon nanotubes SAXS: Small Angle X-ray Scattering USAXS: Ultra Small Angle X-ray Scattering SANS: Small Angle Neutron Scattering USANS: Ultra Small Angle Neutron Scattering WAXS: Wild Angle X-ray Scattering NDT: Non-destructive testing MDR: Moving Dye Rheometer mec : Mechanical stress elec : Electrical conductivity // : Electrical conductivity measured in parallel direction (in respect of the surface of the sample) Electrical conductivity measured in perpendicular direction True mechanical strain nom: Nominal mechanical strain : Mechanical elongation : Apparent crosslinking density fH: Hermans' factor R: Loading ratio or L: Small Angle Neutron Scattering I//: Scattering intensity in the meridional direction I : Scattering intensity in equatorial direction Q: Scattering invariant 2 : Scattering angle Tg: Glass transition temperature or : Crosshead displacement rate during unloading or loading

Figure I- 4 .

 4 Figure I-4. Three different domains can be distinguished on the stress-strain curve:

Figure I- 4 .

 4 FigureI-4. Hyperplastic characteristic response of an elastomer during a rupture test[28]

  Figure I-6. a) Illustration of the typical endurance curve where three fatigue zones are

  Figure I-8a is an example of the increase in electrical conductivity as a function of conductive fillers, in this case CB fillers. The creation of the continuous network occurs for a certain CB content which can be correlated with a plateau of conductivity at low frequency as seen in Figure I-8b for AEM 20

Figure I- 8

 8 Figure I-8. a) Variation of AC conductivity as a function of carbon black phr concentration b) AC conductivity as a function of frequency for a ethylene acrylic elastomer filled with carbon black.

  the most important parameter for the formation of a conductive network is not the volume of fillers itself, but the volume around such fillers in which the center of another object of similar shape cannot penetrate. This is defined as the excluded volume (FigureI-9).

Figure I- 9 .

 9 Figure I-9. Schematic representation of the excluded volume in a 2D representation. a) 25 spherical particles covering a squared area b) 5 cylindrical particles covering the same squared

A

  schematic representation in Figure I-9 is a 2D representation where the total area covered by 25 spherical particles (black solid circles) is approximately equal to the same area occupied by 5 cylinders particles. Moreover, as shown in Figure I-9a, there is still room to fit more spherical particles (these spaces are represented by empty circles with dashed lines) between the existent particles (schematized by solid lines) which allows one to obtain a very low excluded volume.

  nodules are linked together by covalent bonds and are organized in the form of a primary structure called aggregate, whose size is in the order of a hundred nanometers. These aggregates can assemble into clusters by the action of Van der Waals interactions to form agglomerates whose size can reach several tens of microns, as schematized in Figure I-10.

Figure I- 10 .

 10 Figure I-10. Multi-scale representation of the structure of carbon black composite[START_REF] Koga | New Insight into Hierarchical Structures of Carbon Black Dispersed in Polymer Matrices: A Combined Small-Angle Scattering Study[END_REF]

  as a function of strain for CB/elastomer composite (Figure I-11).

Figure I- 11 .

 11 Figure I-11. Typical electrical signature of CB filled elastomer (ethylene-octene elastomer) with

  Figure I-12.

Figure I- 12 .

 12 Figure I-12. Strain dependence of the electrical resistivity for natural rubber filled with 3 phr of MWCNTs. Labels in red: resistivity during unloading. The other colors represent the different loading cycles.

  Figure I-13.

Figure I- 13

 13 Figure I-13. Continuous (dashed lines) and pseudocyclic (solid lines) resistivity-strain responses

Figure I- 15 .

 15 Figure I-15. SAXS curves for fluffy, pelletized, and depelletized N330 carbon black. The curves have been scaled to overlap at high q. The solid lines indicate least-squares power-law fits for

  Zhang et al. have detected nanocavitation for the first time in carbon black filled styrene-butadiene rubber (CB/SBR) under uniaxial loading by real-time small-angle X-ray scattering (SAXS) using synchrotron X-ray radiation. A three-phase model was developed to calculate the void volume fraction from the scattering invariant Q determined from the observed SAXS patterns. The schematic drawing of this mechanism is represented in Figure I-16.

Figure I- 16 .

 16 Figure I-16. Schematic drawing of the proposed mechanism for the opening of nanocavities and their arrangement under external loading[START_REF] Zhang | Nanocavitation in Carbon Black Filled Styrene-Butadiene Rubber under Tension Detected by Real Time Small Angle X-ray Scattering[END_REF]

Finally, the impact

  of mechanical fatigue on electrical properties for filled elastomer has been only studied by ex-situ measurement (post-mortem analysis) which exhibit a damage of the percolating network after fatigue test. As a general conclusion of the bibliographic study, a detailed understanding of the structural mechanisms involved under deformation is required to establish the origin of the percolation/depercolation mechanisms, as synthesized in Figure I-17.

Figure I- 17 .

 17 Figure I-17. Synthesis of the literature on the impact of mechanical deformation on the electrical properties for CB/elastomers composites by in situ investigations (cyclic and continuous stretching) and ex-situ investigations (fatigue test).

Figure II- 1 .

 1 Figure II-1. Schematic diagram of CB aggregates in rubber with different connective structures (a) low structured (b) highly structured.[1]

Figure II- 2 .

 2 Figure II-2. Schematic representation of the internal mixer used in step 1, of the roller mixer usedin step 2 and of the elastomer plates obtained after vulcanization under hot press in step 3.[3]

  Dielectric/Impedance Spectrometer (BDS) (Figure II-3a) and a Keysight B2980A multimeter (Figure II-3b).

Figure II- 3

 3 Figure II-3. a) Novocontrol Alpha Broadband Dielectric/Impedance Spectrometer used to measure the AC-conductivity of samples as a function of frequency b) Keysight B2980A Series of Femto/Picoammeters and Electrometers/High Resistance Meters for DC measurement.

  of the sample (Figure II-4a), where L represents the thickness of the sample, S the surface area between the electrodes, and R the electrical resistance. The electrical conductivity can be also measured in the parallel direction in respect to the surface of the sample (Figure II-4b), where L represents the length of the sample, S the surface area between the electrodes, and R the electrical resistance.

Figure II- 4 .

 4 Figure II-4. Schematic representation of electrical conductivity measurement in two different directions: a) perpendicular and b) parallel to the surface of the samples

Figure II- 5 .

 5 Figure II-5. Typical conductivity measurement by BDS for EPDM-35LS as a function of frequency.

  typical experiment is shown in FigureII-6, where the evolutions of the true strain and stress are investigated as a function time during a continuous deformation until sample breakdown.

Figure II- 6 .

 6 Figure II-6. Typical experiment of continuous strain as a function of time until failure

  50 cycles at true deformation amplitudes reaching max of 0.09, 0.18, 0.35, 0.47, 0.57, 0.69 and returning to min values corresponding to complete unloading (F = 0) are done. Typical curves showing true strain and stress evolutions with time for these types of experiments are presented in Figure II-7.

Figure II- 7 .

 7 Figure II-7. Typical experiment of cyclic strain between max and min and the corresponding stress evolution with time

Figure II- 8 .

 8 Figure II-8. Determination with a cathetometer of the true local displacement and the local deformation applied to the gauge length of the H2 specimen.

Figure II- 9 .

 9 Figure II-9. The principle of determination of the local displacement and deformation that is effectively applied to the gauge length of the specimen.

Figure II- 11 .

 11 Figure II-11. Evolution of displacement as a function of time for controlled fatigue tests with sinusoidally imposed displacement.

Figure II- 12 .

 12 Figure II-12. Setup used to determine the fatigue behavior (number of cycles before breakdown) of 5 specimens for an imposed strain.

Figure II- 13

 13 Figure II-13 illustrated the scheme of simultaneous WAXS/SAXS at the European Synchrotron Radiation Facility (ESRF) in Grenoble (France) on the D2AM beamline [8]. Four panels of WAXS 2D detectors are used, leaving an open space near the direct beam for a higher-resolution SAXS detector.

Figure II- 13 .

 13 Figure Scheme for simultaneous WAXS/SAXS beamline[9]

  1.23 × 10 -4 m 3 /mol is the molar volume of p-xylene and is the volume fraction of EPDM in the swollen network ( = 1/G).

Figure II- 14 .

 14 Figure Schematic representation of swelling test procedure.[11]

Figure II- 15 .

 15 Figure II-15. Picture (a) and schematical illustration (b) of the setup used for carrying out coupled mechanical/electrical investigations.

Figure II- 16

 16 Figure II-16. a) Typical experiment of continuous strain and stress and electrical conductivity as a function of time b) Typical experiment of cyclic strain and the corresponding stress and conductivity evolution with time.

  3.3.1 (the displacement increases progressively for the 5 first cycles). That is the reason why for fatigue experiments, the results are shown after the 10 first cycles. Setup used to do simultaneously electrical/mechanical measurement upon fatigue cycles is shown in Figure II-17.

Figure II- 17 .

 17 Figure II-17. The setup is used for coupled electrical and mechanical fatigue. Only one specimen is used for each fatigue tensile test, contrary to the setup for mechanical fatigue see section 4.3.3.2 (Figure II-12a).

Figure II- 18 .

 18 Figure II-18. Picture of the setup used for electrical/mechanical/structural investigation

  undeformed state) and R the electrical resistance measured by Keysight B2980A picoammeter at 5 V. The experimental setup presented in in Figure II-19 was used to characterize the evolution of the electrical, mechanical, and structural properties of EPDM/CB composites as a function of applied strain.

Figure II- 19

 19 Figure II-19. (a) Schematic representation of the coupled mechanical/electrical/structural investigations (b) 2D WAXS pattern, in which each pixel is characterized by an intensity I, a scattering angle 2(corresponding to a diffusion vector q) and an azimuthal angle (c) Analysis of a WAXS diffractogram obtained by azimuthal average of the intensity for each q. (d) The molecular orientation of polymer chains is observed by division of the WAXS pattern in azimuthal sectors. c) 2D SAXS pattern, in which each pixel is characterized by an intensity I, correspondingto a scattering vector q and an azimuthal angle . (f) SAXS curves obtained for EPDM filled with CB could be divided in two regions. (g) Scattering invariant Q evolution with elongation ratio ..

  correlate the evolution of electrical conductivity to the mechanical Mullins effect. This correlation opens the possibility of in situ monitoring the mechanical properties of elastomeric composite materials by coupled electrical measurements. The essential advantage brought by the electrical measurements is their capacity of being easily implementable for materials working under real functioning conditions in an industrial environment. This can have potential applications in monitoring in real-time the impact of fatigue, extreme deformations or damage on the material properties and functionality. In our study, we demonstrate the deep relationship linking the evolution of the electrical conductivity during mechanical deformation to the mechanical Mullins effect. To this purpose, EPDM composite materials filled with CB fillers of different low and high structures and at different concentrations have been investigated. A clear electrical signature of the mechanical Mullins effect is evidenced. This characteristic electrical signature reveals a different facet of the mechanical Mullins effect, arising from a kinetic reorganization of the CB fillers by competing mechanisms of de-percolation and re-percolation taking place parallel and perpendicular to the axial stretching direction. The evolution of the mechanical properties of elastomeric composite materials under mechanical strain can be thus correlated to the electrical conductivity, which can have potential applications in monitoring the impact of fatigue and damage of materials by in situ electrical measurements.

Figure III- 1 .

 1 Figure III-1. The specimens are fixed between a polycarbonate piece and brass electrodes by four screws. The polycarbonate piece is designed to fit into the tensile testing grip of the Shimadzu instrument. The electrical conductivity was determined by taking into account the variation of the geometry of specimens during the tensile test, using the formula = × , where L represents the sample length, S the sample cross-section and R the electrical resistance measured by the Keysight B2980A picoammeter at 5 V. The experimental setup presented in Figure III-1 was used to characterize the evolution of the electrical and mechanical properties of EPDM/CB composites as a function of strain.

Figure III- 1 .

 1 Figure III-1. Schematic representation of the setup used for carrying out coupled mechanical/electrical investigations

Figure III- 2 .

 2 Figure III-2. Definition of the Mullins ratio RM represents the energy fraction that is dissipated during one stress-strain cycle. Amec represents the area between the loading curve and the unloading curve which characterizes the dissipated energy. B represents the area under the unloading curve. The electrical hysteresis Aelec represents the area between the loading and the unloading conductivity curve.

  conductivity as a function of the CB content was measured in order to analyze the percolation curves. The comparison between the conductivity values measured in the parallel and perpendicular direction (in respect to the sample surface) is also reported, for each composite material studied in the current study. Then, the electrical conductivity is measured as a function of the sample size in order to quantify the distribution of local electrical properties. Additionally, the verifications for coupled electrical and mechanical measurements are realized by verifying that the home-made jaws used for the current study give equivalent mechanical results to the standard jaws employed with the classical dynamometer. Finally, a buckling test was performed to check if the sample handling changes the electrical properties before starting the coupled electrical/mechanical experiments2.6.1. Electrical measurementThe electrical properties of CB/EPDM composite materials in an equilibrated state were measured at room temperature after a thermal treatment of at least 1h at 140 °C under vacuum. The samples were cut in strips of 40 × 15 × 2 mm 3 . The electrical contacts were gold metallized by sputtering to eliminate the influence of the contact resistance. The electrical conductivity was measured using a Novocontrol Alpha Broadband Dielectric/Impedance Spectrometer (BDS) in the frequency range from 10 5 Hz to 10 0 Hz. measured for f = 100 Hz as a function of CB content is reported in Figure III-3. The initial conductivity and the conductivity after a thermal treatment of 1 h and 2 h at 140°C under vacuum is shown. The results indicate that 1 h of thermal treatment is sufficient to erase the impact of mechanical and ageing history and obtain rejuvenated samples.

Figure III- 3 .

 3 Figure III-3. Conductivity before and after thermal treatment of 1 hour (pink) or 2 hours (blue) at 140°C under vacuum.

Figure III- 4 .

 4 Figure III-4. Electrical conductivity as a function of frequency for EPDM-25LS, EPDM-25HSand EPDM-35L at room temperature.

Figure III- 5 .

 5 Figure III-5. Electrical conductivity as a function of the CB concentration for low and highly structured CB fillers, measured a) in the parallel and b) in the perpendicular direction (in respect to the sample surface)

Figure III- 6 .

 6 Figure III-6. Electrical conductivity in parallel measured at 5 different places for each EPDM composite corresponding to a) 9%vol low structured CB b) 12%vol low structured CB c) 15%vol low structured CB d) 25%vol low structured CB and e) 9%vol high structured CB, f) 12%vol high structured CB, g) 15%vol high structured CB, h) 25%vol high structured CB

Figure III- 7 .

 7 Figure III-7. Schematic of the experiment performed to determine the distribution of electrical properties as a function of sample size. The size of a sample was progressively reduced (from 3 cm to 0.75 cm) and the conductivity was measured at each scale.

Figure III- 8 . 2 . 6 . 2 .

 8262 Figure III-8. Electrical conductivity at various sizes (3cm, 1.5cm, and 0.75 cm) for a) EPDM-25LS, b) EPDM-25HS, and c) EPDM-35LS

Figure-III- 9 .

 9 Figure-III-9. Comparison of mechanical data obtained using the standard Shimadzu grip withthe data obtained using the setup employed for the coupled electrical/mechanical measurements.

Figure III- 10 .

 10 Figure III-10. Electrical conductivity as a function of frequency for the virgin sample (black line),

  mechanical responses (stress-strain curves) are shown for various cycles Figure III-11 for EPDM-25LS, EPDM-25HS, and EPDM-35LS. Regardless of the filler concentration or structure, after the first cycle the maximum corresponding to decreases for the following cycles and reaches a constant after 4 cycles, as shown in Figure III-11.

Figure III- 11 .

 11 Figure III-11. Stress-strain responses at max = 0.69 for a) EPDM-25LS b) EPDM-25HS and c) EPDM-35LS at several selected cycles (1st, 2nd, 4th and 10th) carried-out to reach stabilization of the mechanical properties. Prior to the measurement at max = 0.69, the samples had been cyclically stretched at = 0.09, 0.18, 0.35, 0.47 and 0.57 (50 cycles per amplitude). The initial deformation rate was = 0.3 .

Figure III- 12 .

 12 Figure III-12. Continuous (cross lines) and cyclic (solid lines) stress-strain responses of a) EPDM filled with 25 %vol CB b) EPDM filled with 25 %vol CB HS c) EPDM filled with 35 %vol CB LS.

  Figure III-13 displays for the 1 st , 5 th and 50 th cycle and the mechanical dissipated energy corresponding to different applied strains for nanocomposites with various CB contents (EPDM-25LS and EPDM-35LS) and different structures (EPDM-25LS and EPDM-25HS). For EPDM-25LS (Figure III-13a), the Mullins ratio reaches 53.5 % at the first cycle for = 0.09 and then rapidly decreases with increasing the number of cycles. The difference in between the 5 th and 50 th cycle is only 3.8 %, attaining a rather steady value of ~30.8 % after the 5 th cycle. This is in agreement with the fast mechanical stabilization observed in Figure III-11. The relatively high during the 1 st cycle and its reduction during subsequent cycles suggest that a reorganization takes place, due to timedependent stress relaxation [19] or interphase damage between EPDM and CB [20]. Nonetheless, is almost constant for each 1 st cycle in the strain range 0.09 < < 0.69. = 53.7% for Chapter III. In situ coupled mechanical/electrical investigations of EPDM/CB composite materials: The electrical signature of the mechanical Mullins effect 100 = 0.69, which induces a variation of 0.2% between at =

  into account: the influence of the deformation amplitude and the impact of the unloading displacement rate. Typical true strain-time, stress-time and conductivity-stress curves of the composite materials investigated in our study are presented in Figure III-14. The measured curves during the first 5 cycles at each strain are shown. The true strain has been successively increased from 0.09 to 0.69 and 50 cycles have been carried out for each strain value. As shown in Figure III-14, the conductivity-strain curves exhibit a local maximum of conductivity both during loading and unloading. At high strains, the conductivity maximum is observed only during unloading for EPDM-25HS and EPDM-35LS (Figure III-14b/Figure III-15b and Figure III-14c/Figure III-15c). The impact of the maximum strain on the characteristic conductivity-strain response of EPDM/CB nanocomposites measured during cyclic loading is shown in Figure III-15, where the maximal strain was successively increased from 0.09, 0.18, 0.35, 0.47, 0.59 to 0.69. For EPDM-25LS, the electrical conductivity values during the mechanical cycles decrease with increasing . For a given cycle, the value of conductivity exhibits a maximum in the loading and unloading phase. Quantitatively comparing different cycles carried out for EPDM-25LS, it is observed that the conductivity peak during unloading from = 0.09 is close to = 1.2 10 S/cm, whereas = 4.1 10 S/cm for = 0.69 (Figure III-15a

Figure III- 14

 14 Figure III-14. 5 first loading-unloading cycles where strain, stress and conductivity vs. time are reported for a) EPDM-25LS b) EPDM-25HS and c) EPDM-35LS for max of 0.09, 0.18, 0.34, 0.47, 0.59 and 0.69. The inlets are a zoom of the electrical response for 2 cycles

Figure III- 15 .

 15 Figure III-15. 5 last cycles of loading/unloading for max of 0.09, 0.18, 0.34, 0.47, 0.59 and 0.69 are shown for a) EPDM-25LS b) EPDM-25HS and c) EPDM-35LS. 50 cycles are carried-out for each amplitude d) Aelec as a function of for the 1st cycle.

  different than in the following loading cycles (Figure III-17). This effect is more pronounced for EPDM-25LS, as compared to the other composites (Figure III-17a). The phenomenon of electrical hysteresis presented in Figure III-17 indicates that the percolation of the CB network is not the same during the loading and unloading steps. The non-monotonic and hysteresis effects can be thus related to a competing interplay of connecting/disconnecting electrical pathways occurring due to the axial and perpendicular deformation.

Figure III- 17

 17 Figure III-17. 5 first cycles out of 50 cyclic loadings a) Normalized conductivity according to the initial electrical conductivity 0 as a function of strain b) stress-strain response.

  Figure III-18a. Figure III-18c presents the subtraction between the SAXS pattern measured upon unloading down to a strain of 0.55 and the data corresponding to the virgin (undeformed) sample presented in Figure III-18a. In both Figure III-18b and Figure III-18c, a "butterfly" like pattern with a high-intensity perpendicular to the stretching direction is obtained during loading and unloading. This indicates a filler-to-filler distance that is becoming smaller in the direction perpendicular to stretching, in full agreement with the percolation/depercolation mechanism proposed in our study. The subtraction between Figure III-18b and Figure III-18c, both presenting SAXS patterns corresponding to the same mechanical strain (0.55) but obtained upon loading (Figure III-18b) and unloading (Figure III-18c), does not lead to null intensity values but gives an anisotropic pattern (Figure III-18e). This reveals the existence of a structural hysteresis, in full agreement with the mechanical and electrical hysteresis observed in our study. One can thus conclude that the origin of the electrical and mechanical hysteresis is related to a structural hysteresis occurring upon loading and unloading. As explained in our study, this is due to the kinetics of percolation and re-percolation taking place at different time scales.

Figure III- 18

 18 Figure III-18. a) Initial 2D patterns of the virgin specimen EPDM-25LS b) 2D difference patterns of EPDM-25LS where the virgin specimen is subtracted from the specimen stretched during loading (1) c) 2D difference patterns of EPDM-25LS where the virgin specimen is subtracted from the specimen stretched during unloading (2). The black zone observed in the subtracted 2D patterns corresponds to negative values. d) Loading and unloading stress-strain curve for EPDM-25LS e) 2D difference patterns of EPDM 25LS where the unloading pattern (2) is subtracted from the loading pattern (1) for a strain of 0.55 and the stretching axis is represented by the vertical arrow.

  electrical and mechanical cyclic loops, Figure III-19 reports the maximum stress amplitude , / , as a function of the cycle number N (Figure III-19a) and the conductivity at the unloading peak normalized by the initial amplitude of conductivity , / , as a function of N (Figure III-19b). As shown in Figure III-19a, the mechanical stabilization is reached in less than 10 cycles for all investigated materials. However, this is not the case for the electrical response, which needs a longer time to reach the equilibrium state (Figure III-19b).

Figure III- 19

 19 Figure III-19. a) Evolution of the maximum of stress amplitude , /

Figure III- 20

 20 Figure III-20. 5 last cycles (out of 50 strain cycles) showing a) stress-strain response b) conductivity-strain responses for EPDM-25LS at various : 0.5, 10, 50 and 500

  this work, in situ coupled mechanical/electrical investigations upon cyclic and continuous loading on EPDM-based composite materials prepared using CB fillers of different (low and high) structures and at different concentrations have been carried out. The coupled mechanical/electrical measurements have been performed in systematic dependence on the strain amplitude and unloading displacement rate. A clear electrical signature of the mechanical Mullins effect is revealed in the curves of electrical conductivity vs. mechanical strain. As in the mechanical Mullins effect, the electrical Mullins effect exhibits a strong dependence on the deformation history of the investigated materials. Non-monotonic electrical conductivity/mechanical strain curves accompanied by a phenomenon of electric hysteresis are observed, indicating a reorganization of the CB percolation upon loading and unloading. This reorganization of the CB fillers is driven by competing mechanisms of de-percolation and repercolation taking place parallel and perpendicular to the axial stretching direction. The electrical hysteresis depends on the applied strain but also on the relaxation kinetics of the polymer matrix.

Chapter IV.

  In situ coupled mechanical/electrical/WAXS/SAXS investigations on EPDM/CB composite materials: the mechanisms underlying the structure/properties relationship under uniaxial tensile stretching 124 obtained after normalization in respect to the exposure time, transmitted intensity, and subtraction of the image of the empty cell. For investigating potential anisotropic properties, radial averages have been calculated around the image center over 360° azimuthal angles, corresponding to 48 sectors of 7.5° width.

2 . 8 .

 28 in situ SAXS/WAXS and electrical conductivity measurements during a uniaxial tensile test are illustrated in Figure IV-2. Mechanical tests were performed using a homemade remotely controlled tensile test device at room temperature. It is composed of two crossheads, one of them being mobile and guided by two stainless steel guide bars and displaced Chapter IV. In situ coupled mechanical/electrical/WAXS/SAXS investigations on EPDM/CB composite materials: the mechanisms underlying the structure/properties relationship under uniaxial tensile stretching 125 with a threaded shaft, a DC electric motor and a LVDT sensor to control the crosshead position.The samples were stretched in the vertical direction with a crosshead speed of 10 mm/min, and the elongation was varied from 1 to the sample breakdown or to the maximal elongation max = The specimens were fixed between polycarbonate pieces and brass electrodes by four screws.The micromachine itself was mounted on a vertical displacement stage, and a position correction of -/2 was applied when the mobile crosshead was moved by . In this way, the center of the sample is maintained under the incident beam all through the elongation test, the same zone being measured at all times. At the same time, the electrical conductivity was determined by taking into account the variation of geometry of the specimens during a tensile test using = × = × where L is the sample length, S the sample cross-section (L0 and S0 are initial values in the undeformed state) and R the electrical resistance measured by a Keysight B2980A picoammeter by applying a voltage of 5 V. The experimental setup presented in Figure IV-2 was used to characterize the evolution of the electrical, mechanical, and structural properties of EPDM/CB composites as a function of the applied strain.

Figure IV- 1 .

 1 In the Porod region, the value of exponent b is always between -3.2 and -3.8 and the last term can be integrated.

Figure IV- 2 .

 2 Figure IV-2. (a) Schematic representation of the coupled mechanical/electrical/structural investigations (b) 2D WAXS pattern, in which each pixel is characterized by an intensity I, a scattering angle 2 (corresponding to a diffusion vector q) and an azimuthal angle (c) Analysis of a WAXS diffractogram obtained by azimuthal average of the intensity for each q. (d) The molecular orientation of polymer chains is observed by division of the WAXS pattern in azimuthal sectors. c) 2D SAXS pattern, in which each pixel is characterized by an intensity I, corresponding to a scattering vector q and an azimuthal angle . (f) SAXS curves obtained for EPDM filled with CB could be divided in two regions. (g) Scattering invariant Q evolution with elongation ratio .

Figure IV- 3

 3 Figure IV-3 displays the SAXS and WAXS patterns of both uncrosslinked matrices (E1 and E2) as well as both CB fillers (HS and LS). In Figure IV-3a, the SAXS profiles of E1 and E2 are shown: a peak is clearly visible for E1 while a broad shoulder can be seen for E2. In Figure IV-3c, two peaks are noticeable for the WAXS patterns of the uncrosslinked E1 and E2; the first one is located at = 1.36and the second one at 3 is broader. For E1, the peak at q = 1.36

Figure

  Figure IV-3a by the presence of a peak at the abscissa q*, from which a long period Lp could be calculated (Lp = 2 /q*). In Figure IV-3b, both CB are show similar SAXS profiles, the low-q power law exponent being slightly higher for CB HS compared to CB LS. For the WAXS pattern of both CB represented in Figure IV-3d, there is no difference in the graphitic nature of CB.

Figure IV- 3 .

 3 Figure IV-3. SAXS profiles of a) both matrix E1 and E2 (non-vulcanized) b) both CB HS and LS.

  identical for CB HS (Figure IV-4a) and CB LS (Figure IV-4b). Nonetheless, a change of exponent

Figure IV- 5 .

 5 Figure IV-5. DSC thermograms of unfilled composites for the (a) E2-0 and for (b) E1-0. Two heating/cooling/heating cycles comprised between -100 °C and 100 °C at 10 °C•min 1 were done for both composites. (c) DSC thermograms of filled composites from room temperature (25°C) to 100°C at 10 °C•min 1 for E2-0 (in black) and for E1-0 (in blue).

Figure IV- 6

 6 Figure IV-6 displays the comparison of WAXS patterns of (a) E1-0 and E2-0 and (b) the comparison between E1-25LS and E2-25LS. No significant changes in the diffraction diagrams in dependence on the EPDM nature were observed, neither for unreinforced matrices nor for the CB composites.

Figure IV- 6 .

 6 Figure IV-6. WAXS patterns of (a) unfilled E1-0 and E2-0 composites (b) filled E1-25LS and E2-25LS composites.

Figure IV- 7

 7 shows the 2D-WAXS patterns of E1-35LS and E1-25HS at various deformations.

Figure IV- 7 .

 7 Figure IV-7. 2D-WAXS patterns of E1-35LS at = 1.0 (a), 1.6 (b) and 2.0 (c). 2D-WAXS patterns of E1-25HS at = 1.0 (d), 1.6 and 2.0 (f) with a deformation rate of 10 mm/min.

Figure IV- 8 .

 8 Figure IV-8. E1-35LS WAXS diffractograms in the equatorial sectors ( =90°,270°) for an elongation of (a) =1.0, (b) =1.6 and (c) =2.0. E1-35LS WAXS diffractograms in the meridional sectors ( =0°,180°) for an elongation of (d) =1.0, (e) =1.6 and (f) =2.0.

Figure IV- 9 .

 9 Figure IV-9. The apparent Herman's factor fH was calculated for WAXS in situ during tensile testing at q=1.36 Å -1 for (a) E1-25LS, E1-25HS and E1-35LS (b) the comparison of EPDM orientation for composites with matrix 1 and matrix 2 and as a function of CB structure during stretching where E1-25LS is symbolized by dotted line (the orientation is superposed for the other composite as shown in Figure IV-9a).

  mechanical behavior of the EPDM-CB composites with CB fillers of different structure and volume fraction and for different EPDM matrices are reported in Figure IV-10, where the true stress is plotted as a function of the elongation parameter .

Figure IV- 10 .

 10 Figure IV-10. Influence of the EPDM matrix, CB content and CB structure on ( ) curves for: (a) E1-25LS and E2-25LS; (b) E1-25HS and E2-25HS; (c) E1-35LS. (d) Corresponding parameter C1 for each system is determined and normalized by the parameter C1 of E1-0 or E2-0

  conductivity. The latter offers a complementary view on our coupled experiments, specifically related to the CB network connectivity evolution that occurs during stretching. The plots of conductivity vs. elongation ratio are displayed in Figure IV-11 for the CB filers of different structure and volume fraction and for different EPDM matrices. The electrical behavior can be separated in three regimes with increasing elongation.

Figure IV- 11 .

 11 Figure IV-11. Influence of EPDM matrix, CB content and CB structure on the electrical properties under large elongation for (a) E2-25LS and E1-25LS (b) E2-25HS and E1-25HS (c) E1-35LS.

Figure IV- 12 .

 12 Figure IV-12.SAXS scattering diagrams were obtained by the azimuthal average of the intensity for (a) E1-25LS (b) E1-25HS and (c) E1-35LS during a tensile test.

Figure IV- 13 .

 13 Figure IV-13. (a) SAXS scattering diagrams obtained in the meridional region ( =0° and 180°) (b) SAXS scattering diagrams obtained in the equatorial region ( =90° and 270°) for E1-35LS during tensile test. (c) Data analyses are performed with a first Generalized Porod's law

  (c) Exponents a// and b// are determined in the meridional direction (d) Exponents a and b are determined in the equatorial direction

Figure IV- 14 .

 14 Figure

Figure IV- 14 .

 14 Figure IV-14. The exponent a in the equatorial direction is determined in the low-q region and b in the high-q region for (a) E1-25LS (b) E2-25LS (c) E1-25HS and (d) E2-25HS

  conductivity in regime II (see Figure. In a second step, for E1-25HS, the power law exponent a decreases for > 2.1, with a variation close to E1-35LS. Moreover, we can notice that in the equatorial direction, when a is decreasing, b is also decreasing, as shown in Figure IV-13b and Figure IV-14d. It appears that at high extension ratios, a change in the scattering regime gradually appears, possibly correlated to the decrease of conductivity observed in regime III for E1-25HS and E1-35LS in Figure IV-11. Chapter IV. In situ coupled mechanical/electrical/WAXS/SAXS investigations on EPDM/CB composite materials: the mechanisms underlying the structure/properties relationship under uniaxial tensile stretching 146 To confirm cavitation as the origin of the evolution of scattering regime and of the decrease in the conductivity occurring at high deformations, the scattering invariant Q was quantitatively analyzed. The invariant Q has been compared to the electrical conductivity upon increasing the elongation ratio , as reported in Figure IV-15a, b, c, d.

Figure IV- 15 .

 15 Figure IV-15. Correlation of electrical conductivity and the scattering invariant Q as a function of extension ratio for (b) E1-25LS (c) E1-35LS (d) E1-25HS and (e) E2-25HS. Breakage occurs before cavitation in E2-25HS system, and crosslinking is possibly too low to induce cavitation vs viscoelastic deformation. Cavitation occurs in E1-35LS and E1-25HS and manifestsas an increase of Q values at large extension ratios.

  In this work, in situ coupled mechanical/electrical/structural investigations upon uniaxial loading on EPDM-based composite materials prepared using CB of different (low and high) structure and different volume fractions have been carried out. The quantitative analysis of the apparent Herman's factor indicates orientation effects of the polymer chains, increasing with the mechanical strain. A correlation between electrical, mechanical, and structural properties have been carried out by an in-depth investigation of the composites structure by in situ SAXS measurements during tensile test. The role of aggregate interpenetration in the electrical behavior of CB/EPDM composites was clearly shown. The reorganization of CB aggregates drives the creation of new conductive pathway perpendicular to the axial stretching direction shown by the decrease of the intensity scattered at low-q. Furthermore, the apparition of nanocavitation effects at large deformation amplitudes proceeding the material breakdown has been evidenced by the analysis of the scattering invariant Q. It is reported that this phenomenon, accompanying the incipient phase of material damage, is clearly marked by the evolution of electrical conductivity which shows a significant decrease. Our study offers thus a comprehensive picture of the successive structural mechanisms underlying the structure /properties relationship under mechanical strain up to material breakdown, summarized as follows: chain orientation, reorganization of the CB aggregates and cavitation followed by mechanical failure. Our study could have thus potential applications in developing new smart rubber materials where microstructural changes proceeding the material breakdown can be in situ monitored by coupled electrical measurements.Acknowledgements:The financial support given by ANRT through the CIFRE project no. 0479-0065 is highly acknowledged. We acknowledge the European Synchrotron Radiation Facility for provision of synchrotron radiation facilities on the BM2-D2AM beamline (data DOI: . The Wideangle X-ray detector (WOS) was funded by the French National Research Agency (ANR) under the "Investissement d'Avenir" program (Grant no. ANR-11-EQPX-0010).

Figure V- 1

 1 and detailed as follows: a sample with an initial mass Mi is introduced into p-xylene for 24 h at 80 °C to reach its equilibrium swelling, then it is weighed in its swollen state (corresponding to the mass Ms). It is then dried under vacuum at 80 °C for 1 day and weighed again, where its mass is Md. The swelling G of the polymer and the soluble fraction is deduced from the relationships (

  1.23 × 10 -4 m 3 /mol is the molar volume of p-xylene and is the volume fraction of EPDM in the swollen network ( = 1/G).

Figure V- 1 . 1 .

 11 Figure V-1. Schematic representation of swelling test procedure.[29]

Figure V- 2 .Figure V- 3 .

 23 Figure V-2. Determination with a cathetometer of the local displacement and deformation applied to the useful area of the H2 specimens.

Finally, the local 3 Figure V- 4 .

 34 Figure V-4. Correlation between crosshead displacement and local deformation of the specimens, after 5 loading/unloading cycles at the displacement of the test at room temperature

Figure V- 5 .

 5 Figure V-5. Evolution of displacement as a function of time for controlled fatigue tests with sinusoidally imposed displacement.

Figure V- 6 .

 6 Figure V-6. Setup used to determine the endurance curve.

  3.3.1 (the displacement increases progressively for the 5 first cycles). That is the reason why for fatigue experiments, the results are shown after the 10 first cycles. The setup used to carry out simultaneously electrical and mechanical measurements upon fatigue cycles is shown in Figure V-7.

Figure V- 7

 7 Figure V-7. a) Schematic representation of the setup used for carrying out coupled mechanical/electrical investigations. b) The setup is used for coupled electrical and mechanical fatigue. Only one specimen is used for each fatigue tensile test [30].

during a fatigue test 2 . 6 . 1 .

 261 Data processing of mechanical resultsDuring fatigue tensile tests, contrary to cyclic or monotonic uniaxial tensile tests, the mechanical properties cannot be continuously measured at various displacements for each cycle. Therefore, several relevant mechanical parameters such as the minimal stress, , maximal stress, , and the amplitude of stress, , have been selected to study. Typical evolutions of these parameters are represented in Figure V-8.

Figure V- 8

 8 Figure V-8. a) Typical mechanical parameters for one fatigue cycle b) mechanical parameters which are recorded during fatigue testing vs. fatigue cycles.

Figure V- 9 .

 9 Figure V-9. Typical measurement of the in situ electrical/mechanical fatigue test.

Figure V- 10

 10 Figure V-10. a) Electrical parameters which can be used to monitor mechanical damages b) Cyclic electrical signature evolution at various fatigue cycles (after 50, 150, and 330 fatigue cycles) where normalized conductivity vs. nominal strain is shown (Rupture is observed at cycle

Figure V- 11 .

 11 Figure V-11. Electrical descriptors a) , , ( ), and parameters as a function of cycles b) Area represents the area between the loading and the unloading curve of electrical conductivity vs. nominal strain.

Figure V- 12 .

 12 Figure V-12. Typical measurement of electrical properties (normalized amplitude of conductivity, in blue) and mechanical properties (normalized strength, in black) as a function of mechanical fatigue cycles. The inlet is a zoom of the electrical response corresponding to the plateau and to the decrease before fracture.

  Endurance classical fatigue tests were performed with EPDM-25HS and EPDM-35LS at 5 different levels of deformation. The endurance curves of both composites are reported in Figure V-13.

Figure V- 13 .

 13 Figure V-13. Maximal applied strain vs number of cycles at rupture (Nf) for a) EPDM-25HS and b) EPDM-35LS. The fatigue limit, represented by circles for unbroken specimens, was fixed to 5 × 10 5 cycles.

Figure V- 14 .

 14 Figure V-14. Evolution of the normalized conductivity amplitude, and normalized stress amplitude, as a function of fatigue cycles for a maximal applied strain of 0.25.

Figure V- 15 .

 15 Figure V-15. variations with the number of fatigue cycles: a) in linear representation. The inlet is a zoom of the electrical response showing a decrease before fracture. b) in semilogarithmic representation. The inlet is a zoom of the deviation of the electrical response in respect to behavior law (Eq 6). response is reported for EPDM-25HS as a function of the number of fatigue cycles. c) in linear representation and d) in logarithm representation for samples stretched at 140% at 1 Hz and with a loading ratio of R = 0.3.

Figure V- 16 .

 16 Figure V-16. variations with fatigue cycle, a) in linear scale. The inlet is a zoom of the electrical response showing a decrease before fracture. b) in semilogarithmic scale. The inlet is a zoom of the deviation of electrical response is respect to the electrical behavior law (Eq 6).

Conductivity and stress evolutions for a fatigue test in the endurance zone: frequency dependence

 dependence The normalized amplitude of conductivity, was measured for various frequencies of the loading/unloading cycles: 0.1 Hz, 1 Hz, and 3 Hz (Figure V-17).For both composites, as the frequency increases from 0.1 Hz to 3 Hz, the conductivity amplitude increases faster with the fatigue cycle number (Figure V-17a, c). increases from 1 to 2.8

  Figure V-17b,d. The decrease of the stiffness can be related to the rising temperature by self-heating at higher frequencies [16]. The following zones can be distinguished (Figure V-15a,b, and Figure V-16a,b): First an increase of which follows the electrical behaviour law (Eq 6) reported in Figure V-17a,c for both composites and for all investigated frequencies. Then a deviation from this law is observed as it can be seen in the inlet of the Figure V-17a,c for both composites and for all investigated frequencies. Finally, a rapid decrease of is observed, as shown in the inlet Figure V-17a,c.

Figure V- 17

 17 Figure V-17. a) Electrical response, . b) Mechanical response, at different frequencies for EPDM-25HS at maximal strain of 140% and with R = 0.4. c) Electrical response, d) Mechanical response, at different frequencies for EPDM-35LS at maximal strain of 60% and with R = 0. The inlet is a zoom of the electrical response where the electrical deviation from the modelling law (Eq 6) is observed at 0.1 Hz.

7

 7 in endurance curves for R-loading = 0 presented in Figure V-13. Moreover, for EPDM-25HS tested at max = 100%, it can be noticed that there is a stabilization and then a decrease of between cycle 6000 and the cycle at break(20 570). Electrical properties are intrinsic properties that can reveal a state of damage of the material by the decrease of before rupture. The electrical deviation and the decrease of is shown in the inlet in Figure V-18a;c. On one hand, the electrical deviation is observed over a larger number of cycles when the amplitude of deformation decreases. On the other hand, the evolution of does not exhibit any change with the strain amplitude and neither a particular evolution before fracture. Mechanical response vs. number of cycles didn't show any change before fracture whatever the frequency or the amplitude used in our study. All mechanical fatigue curves fall on a similar pattern. By monitoring the conductivity for damage-free fatigue test and tests performed in the endurance zone, the following conclusions can be drawn on the evolution of : Unlimited endurance test was performed at max = 25%: is decreasing with the number of fatigue cycle test. Endurance fatigue test: the increase of at low number of fatigue cycle and decrease before fracture is due to cumulative damage inducing with loading/unloading cycles. The increase in during damage may be due to breaking of the cross-linking nodes. Indeed, CB aggregates can be constrained by the crosslinking nodes, and, once the mono-or poly-sulfide bonds are damaged, the movement of aggregates becomes then possible. The change in slope and the drop in is probably due to the introduction of a new damage mechanism. For continuous uniaxial deformation tests (Chapter IV, Figure IV-15), a decrease in conductivity has been correlated to the apparition of nanocavities into the material. A parallel can be drawn with the fatigue tests and the change in slope followed by the decrease of is probably due to apparition of nanovoids.To use the electrical properties as an in situ measurement of damage, a more precise end-of-life criterion should be defined.Conductivity and stress evolutions for a fatigue test in the endurance zone:Quantitative analysesAs it can be seen in the previous part (see Figure V-18a), the change in the fatigue regime for EPDM-25HS at = 100% and 1 Hz with R = 0.3 is marked as a change in slope. Analysis using equation Eq 6 has been performed in Figure V-19. The typical modelling parameters are reported in Table V-2. The electrical behavior can be modelled by a linear mathematical function in semi-log curve (Eq 6), a deviation is observed for a certain cycle and this for the two tests performed (at 1 Hz and 0.1 Hz). The derivative of is calculated using the following equation: = The mean derivative is calculated using moving-average model over 50 fatigue cycles by using the adjacent-averaging formula in Origin software. The mean derivative vs. number of fatigue cycle is reported in Figure V-19b. The use of a criterion defined by a deviation from the electrical behavior law (Eq 6), such as a deviation between 1/2 to 1 decade between the derivative of the semi-log law (defined using Eq 6) and the derivative of the electrical behavior of the material (represented in Figure V-19b by an arrow between the modelling and actual electrical behavior). could allow the development of real-time damage monitoring. The deviation from the mathematical law is observed for all the fatigue experiments and the results with various amplitude of deformation for both EPDM-25HS and EPDM-35LS are represented in the Appendix 4. The definition of an end-of-life criterion by real-time monitoring of the evolution of the electrical conductivity shows the interest of in situ measurement for smart rubber applications.

Figure V- 19

 19 Figure V-19. a) Electrical response, for EPDM-25HS at = 100% and 1 Hz or 0.1 Hz and with R = 0.3 with their respective modelling curves b) study of the derivative of and their modelling curves.

  apparent cross-linking density is calculated for the sample in its initial state, after 10 cycles of deformation at 100% (representative of the accommodation cycles) and after the mechanical fatigue tests in both zones (unlimited endurance and limited endurance), as reported in Figure V-20.

Figure V- 20 .

 20 Figure V-20. Apparent cross-linking densities for a) EPDM 25HS for the undeformed state, after 10 loading/unloading cycles representative of the accommodation of the sample and after mechanical fatigue in the endurance zone. The cycle number at failure for endurance test are reported in Table V-3. Apparent cross-linking densities for b) EPDM 35LS for the undeformed state, after 10 loading/unloading cycles, after fatigue in the unlimited endurance zone (stop after 8. 10 4 cycles) and after mechanical fatigue in the endurance zone. The cycle number at failure for endurance test are reported in TableV-3

Figure V-

  Figure V-20b, it can be seen that both values are very close, which validates the difference in the electrical behavior observed during a fatigue test with damage and "damage-free" tests.

Figure V- 21 .

 21 Figure V-21. Evolution of the scattering invariant Q with maximal strain for EPDM-35LS.For the 1 st cyclic loading/unloading for = 50% and the cyclic loading/unloading for = 100% . Cavitation occurs for = 100% and manifests as an increase of Q values at large extension ratios.

Figure V- 22 .

 22 Figure V-22. Selected 2D-SAXS scattering where the initial 2D-SAXS scattering pattern of EPDM-35LS was subtracted at different values of (b) = 1.3, (c) = 1.6, and (d) = 1.9 as indicated in each frame title together with the corresponding Q value. Cavitation manifest as a large excess of anisotropic 2D scattering at large strains and a structural hysteresis upon unloading.

  mechanical fatigue on EPDM-based composite materials prepared with CB fillers of different structures (low and high structure CB) and at different concentrations. The damage of the crosslinked network has been highlighted by an in-depth investigation of the structure of the composites by swelling measurements after fatigue tests. The damage of the vulcanized network was correlated by an increase of the amplitude of the electrical conductivity due to a rise of the freedom of movement of fillers. Furthermore, our study brings new strategy for the detection of damage in CB-filled elastomers by DC conductivity measurements. First, the electrical behavior can be modelled using a semi-logarithm law, a deviation from this law can be estimated. To estimate this deviation, the derivation of both the modelled law and the electrical behavior with the number of fatigue cycles is calculated. We propose a new criterion it is based on the deviation between the derivative of the modelled law and the electrical behavior with the number of fatigue cycle and the criterion correspond to a deviation of ½ to 1 decade to estimate the end of life of an EPDM-based composite material. In situ electrical measurements allow thus real-time monitoring of damages in EPDM based composite materials filled with CB which could have numerous applications, in particular, in the field of smart rubber material. mechanical/electrical/WAXS/SAXS investigations have been carried out. Real-time correlation could be drawn between the electrical conductivity and the microstructural evolution of the composite morphology. Different mechanisms governing the structure/properties relationship are revealed: (1) Lost of CB contact at really low strain then (2) orientation of the EPDM chains and reorganization of the CB network taking place upon increasing the mechanical strain, and (3) at large deformations, the apparition of cavitation effects. The latter were determined as the main phenomenon inducing the depercolation of fillers. In particular, our work is original in correlating the decrease of the conductivity at high strain with the phenomenon of nanocavitation revelated by structural investigations. This result appears as a major advance in the field of smart rubbers, since it shows that electrical monitoring can detect nanocavitation effects, which are the first events appearing during material damage. It was necessary to verify that electrical measurement shows early sign of breakdown for mechanical fatigue tests which are more representative of the real conditions of filled rubber in an industrial environment.The third objective of this thesis is to develop a methodology to determine accurate electrical descriptor of mechanical damage which could be used at an end-of-life criterion. In situ coupled mechanical/electrical investigations upon uniaxial mechanical fatigue on EPDM-based composite have been carried out. A correlation between electrical amplitude evolution and damage of the cross-linked network has been carried out by an investigation of the structure of the composites by swelling measurements after fatigue tests. Our study brings new light into understanding the detection of damage by electrical measurement. Nanocavitation and decrease of the amplitude of conductivity during several cycles before fracture have been correlated. This correlation could be of potential interest in numerous applications, e.g. for in-service damage assessment of elastomeric materials by in situ electrical measurements. Our study shows the structural state of the CB network can be characterized by electrical monitoring and may be associated with evolutions of the crosslinking network or the formation of cracks. Understanding the electrical evolution with a structural evolution is generally a difficult challenge. This thesis shows the importance of using the intrinsic properties of elastomeric materials, especially electrical properties for the development of preventive maintenance (intrinsic properties and easily implemented). To sum-up, electrical properties were probed in situ and ex-situ during various mechanical tests (cyclic loading, uniaxial tensile stretching, and fatigue test). The combination of different techniques offered a clear comprehensive picture of the mechanisms underlying the coupling between the electrical/mechanical and structural properties of CB-filled EPDM as schematized in the figure below. L'objectif principal de la thèse est de déterminer l'état de vieillissement d'un caoutchouc chargé par une mesure de la conductivité électrique et ainsi réaliser des caoutchoucs intelligents qui seront « auto-capteur ». La formulation de tels matériaux permettrait d'éviter des problèmes rencontrés dans l'industrie où l'endommagement des pièces en caoutchouc est inconnu. Ainsi, la mesure de conductivité électrique en tant que méthode in situ non destructive permettrait de changer uniquement les pièces qui le nécessitent et passer d'une maintenance standardisée (remplacement des composants à fréquence constante) à une maintenance préventive. Une compréhension plus approfondie de l'évolution des propriétés électriques des matériaux composites élastomères subissant des déformations mécaniques représente une condition essentielle au développement des méthodes couplées in situ non-destructives, dont l'objectif est de détecter les endommagements. Afin de relever ce défi, des études électriques / mécaniques couplées in situ sur des matériaux composites à base d'EPDM (à différentes concentrations en monomère diène) chargé en noir de carbone, de structure différente (N326 basse structure et N347 haute structure) et à différentes concentrations (15% vol, 25% vol et 35% vol) ont été systématiquement réalisées. Pour atteindre cet objectif, la conductivité électrique a été mesurée en continu au cours de cycles mécaniques d'amplitudes et de vitesses différentes. Afin de comprendre les mécanismes microscopiques sous-jacents à l'évolution de la conductivité électrique, la diffusion des rayons X couplée in situ aux essais mécaniques/électriques ainsi que le taux de gonflement ont été caractérisés. Tout d'abord, l'évolution mécanique/électrique couplées in situ lors de chargements cycliques sur des composites à base d'EPDM a été étudiée. Les essais mécaniques/électriques couplées ont été réalisées à différentes amplitudes de déformation et avec des vitesses de déplacement différentes. Une corrélation entre la signature électrique et celle de l'effet Mullins mécanique est révélée dans les courbes de conductivité électrique en fonction de la déformation mécanique. Comme pour l'effet Mullins mécanique, l'effet électrique présente une forte dépendance de l'historique mécanique de l'échantillon étudié. Des courbes non monotones de la conductivité électrique en fonction de la déformation mécanique sont observées et elles sont accompagnées d'un phénomène d'hystérèse électrique. Cela démontre l'apparition d'une réorganisation du réseau percolé du noir de carbone lors du chargement et du déchargement. Cette réorganisation est pilotée par des mécanismes concurrents de « dépercolation » et de re-percolation qui ont lieu parallèlement et perpendiculairement à la direction d'étirement. L'hystérèse électrique dépend de l'allongement appliqué mais aussi de la cinétique de relaxation de la matrice polymère. Ceci est clairement démontré en réalisant des expériences de déchargement à différentes vitesses de décharge entre 0,5 mm/min et 500 mm/min. Il est démontré que, contrairement à l'effet Mullins mécanique, l'effet Mullins électrique dépend fortement de la vitesse de déplacement à la décharge. Ceci est dû à une cinétique de re-percolation qui devient trop lente par rapport à la vitesse de déchargement. Notre étude met en lumière une nouvelle approche sur la compréhension de l'effet Mullins, en révélant, par des investigations mécaniques/électriques couplées in situ, une facette différente de ce phénomène liée à une réorganisation cinétique des charges lors d'une déformation mécanique.Cela pourrait présenter un intérêt potentiel dans des nombreuses applications de suivi de l'évolution des propriétés mécaniques des matériaux élastomères par des mesures électriques couplées in situ.L'objectif a ensuite consisté à apporter un point de vue microstructural aux investigations électriques/mécaniques couplées in situ. Les mêmes types de matériaux élastomères ont été utilisés et, pour simplifier la compréhension des mécanismes mis en jeu, notre étude s/WAXS/SAXS couplées in situ ont été réalisées pour une corrélation en temps réel entre la conductivité électrique et l'évolution microstructurale de la morphologie du composite. Des mécanismes successifs et distincts régissant la relation structure/propriétés en fonction de l'amplitude de déformation sont révélés. On observe en premier lieu l'orientation des chaînes EPDM, suivie, lors de l'augmentation de la déformation mécanique, par la réorganisation du réseau de noir de carbone et qui, à de grandes amplitudes de déformation, voit apparaître des phénomènes de cavitation. Il est démontré que cette séquence de différents phénomènes microstructuraux se produisant sous étirement uniaxial en traction offre une image complète des mécanismes sous-jacents à l'évolution non monotone de la conductivité électrique avec la déformation mécanique.Le dernier axe de la thèse a été de développer une méthodologie pour corréler le suivi de la conductivité électrique avec un endommagement mécanique pour des essais de fatigue qui simule la durée de vie d'une pièce caoutchoutique. Une étude mécanique/électrique couplées in situ lors de la fatigue mécanique uniaxiale sur un composite à base d'EPDM a été réalisée. Une corrélation entre l'évolution de l'amplitude électrique et l'endommagement du réseau réticulé a été effectuée par une étude approfondie de la structure des composites par des mesures de gonflement après les tests de fatigue. En outre, notre étude apporte une nouvelle lumière dans la compréhension de la détection par une mesure électrique des endommagements sévères avant rupture. La nanocavitation et la diminution de l'amplitude de la conductivité pendant plusieurs cycles avant la rupture ont été corrélées, ce qui pourrait présenter un intérêt potentiel dans de nombreuses applications, par exemple, pour évaluer la durée de vie en service des matériaux élastomères par des mesures électriques couplées in situ.Clémentine Beutier-2022RÉSUMÉ EN ANGLAISdeeper understanding of the evolution of the electrical properties of elastomeric composite materials undergoing mechanical deformations represents an essential prerequisite for developing non-destructive in situ coupled approaches to detect the impact of fatigues effects leading to material damage. This can have numerous applications in the field of in situ monitoring, preventive maintenance, smart rubber materials etc. In order to address this challenge, in situ coupled electrical/structural/mechanical investigations on EPDM based composite materials (with different diene monomer contents) filled with carbon black of different structure (low structured and highly structured) and at different concentrations have been systematically carried-out. To this purpose, the electrical conductivity has been continuously measured during mechanical cycles of different amplitudes and velocity at constant strain or stress. In order to unravel the microscopic mechanisms underlying the evolution of the electrical conductivity, in situ coupled structural investigations by X-Ray scattering have been performed.Our study brings evidence for a characteristic electrical signature of the classical mechanical Mullins effect. A sequence of different microstructural phenomena taking place under uniaxial tensile stretching or fatigue test is also reaveled. This offers a comprehensive picture of the mechanisms underlying the non-monotonic evolution of the electrical conductivity with the mechanical strain.Two applications of potential impact employing the electrical/mechanical coupling will be presented and discussed in detail: (i) monitoring fatigues effects by in situ coupled electrical measurements and (ii) quantifying the impact of extreme deformations on material properties. Keywords: Smart materials, Mechanical properties, Electro-mechanical behavior, Polymer-matrix composites (PMCs) RÉSUMÉ EN FRANÇAIS ne meilleure compréhension de l'évolution des propriétés électriques des matériaux composites élastomères soumis à des déformations mécaniques représente un prérequis essentiel pour le développement des méthodes non-destructives couplées in situ pour détecter l'impact d'un endommagement. Ceci peut avoir des nombreuses applications dans le domaine de la maintenance préventive in situ, ou bien dans le domaine des caoutchoucs intelligents. Afin de relever ce défi, des études électriques/mécaniques couplées in situ sur des matériaux composites à base d'EPDM (à concentrations différentes en monomère diène) chargés en noir de carbone de différentes structures (basse structure et haute structure) et à différentes concentrations ont été systématiquement réalisées. Le but a été d'étudier l'évolution de la conductivité électrique en continu pendant des cycles mécaniques de différentes amplitudes et vitesses de déformation. Afin d'élucider les mécanismes microstructuraux qui déterminent l'évolution de la conductivité électrique, des études structurales couplées in situ par diffusion des rayons X ont été réalisées. Notre étude met en évidence une signature électrique caractéristique de l'effet Mullins. De plus, une séquence de différents phénomènes microstructuraux se produisant lors d'essais de traction uniaxial ou de fatigue offre une image complète des mécanismes sous-jacents à l'évolution non monotone de la conductivité électrique avec la déformation mécanique. Deux applications d'impact potentiel utilisant le couplage électrique/mécanique seront présentées et discutées en détail : (i) le suivi en temps réel des effets de la fatigue mécanique par des mesures électriques couplées in situ et (ii) la quantification de l'impact des déformations extrêmes sur les propriétés des matériaux. Mots clés : Matériaux intelligents, Propriétés mécaniques, Comportement électro-mécanique, Composites à matrice polymère A U

Table I -

 I 5. Value of Herman's orientation factor calculated for various strains.[START_REF] Munch | Molecular mobility of crosslinked elastomers stretched above Tg[END_REF]

	Strain (%)	Hermans' factor for SBR	Hermans' factor for NBR
	0	0.084	0.116
	100	0.112	0.165
	200	0.15	0.252
	250	0.164	0.284

Table II -

 II 1. Typical properties of the carbon black used in the current study.

	Properties	N326	N347
	Specific Surface Area	77 m²/g	83 m²/g
	DBP absorption	72 g/kg	124 g/kg
	Primary particle size	20-50 nm	20-50 nm
	Aggregates size	100-200 nm	100-200 nm

Table II -

 II 2. List of the composites used for the experimental part.

	Compounds	E1-0 E1-	EPDM	EPDM	E1-	EPDM	E2-0 E2-	E2-
			15LS	25LS or	35LS or	15HS	25HS or		25LS	25HS
				E1-25LS	E1-35LS		E1-25HS
	Matrix	5470 5470	5470	5470	5470	5470	9650 9650	9650
	(Keltan)
	CB	-	N326 N326	N326	N347 N347	-	N326 N347
	EPDM (phr) 100	100	100	100	100	100	100	100	100
	CB (phr)	0	45	90	140	45	90	0	90	90
	CB (%vol)	0	15	25	35	15	25	0	25	25
	Oil (phr)	20	20	20	20	20	20	20	20	20
	ZnO (phr)	5	5	5	5	5	5	5	5	5
	Stearic acid	1	1	1	1	1	1	1	1	1
	(phr)
	TMQ (phr)	1.5	1.5	1.5	1.5	1.5	1.5	1.5	1.5	1.5
	Sulphur	1.7	1.7	1.7	1.7	1.7	1.7	1.7	1.7	1.7
	(phr)
	Accelerators	4.6	4.6	4.6	4.6	4.6	4.6	4.6	4.6	4.6
	(phr)

In situ coupled mechanical/electrical investigations of EPDM/CB composite materials: The electrical signature of the mechanical Mullins effect

  cellulose fibres from the X-ray fibre diagram, Recueil Des Travaux Chimiques Des Pays-Bas. 65 (1946) 427-447. https://doi.org/10.1002/recl.19460650605. [15] G. Guenoun, N. Schmitt, S. Roux, G. Régnier, Crystalline orientation assessment in transversely isotropic semicrystalline polymer: Application to oedometric compaction of PTFE, Polymer

	Engineering & Science. 61 (2021) 107-114. https://doi.org/10.1002/pen.25561.
	electrical signature of the mechanical Mullins effect, Composites Science and Technology. (2021)
	109144. https://doi.org/10.1016/j.compscitech.2021.109144. The section: verification tests is
	added

CHAPTER III.

From: C. Beutier, L. David, G. Sudre, P. Cassagnau, P. Heuillet, B. Cantaloube, A. Serghei, In situ coupled mechanical/electrical investigations of EPDM/CB composite materials: The

  Experiments were carried out using Keltan EPDM rubber (Arlanxeo, Geleen, Netherlands) which is a semi-crystalline ethylene propylene diene monomer rubber with a density of 0.86 g.cm -3 and a Mooney viscosity ML(1+4) of 55 at 125 °C. The EPDM was cross-linked using different amounts of low structured (LS) carbon black (N326) or highly structured (HS) carbon black (N347) fillers with sulfur bridges. CB N326 and N347 were provided by Orion (Frankfurt, Germany). Elastomer composites of different compositions were obtained, as specified in TableIII-1. The processing oil selected as plasticizer was Torilis 6200, provided by Total (Ferrybridge, UK).

	2. Experimental
	2.1. Materials
		Density	EPDM-25LS EPDM-25HS EPDM-35LS
	EPDM	0.86	60.0	60.0	52.5
	CB	1.8	25.5	25.5	35
	Oil Torilis 6200	0.89	11.5	11.5	10
	ZnO / stearic acid	5.57 / 0.85 1.1	1.1	0.5
	Accelerators	-	0.5	0.5	0.5
	Sulfur	2.1	0.7	0.7	1
	Antioxidant: TMQ	1.1	0.7	0.7	0.5
	Vulcanization: t98% (min) -	16	15

Table III-1. Composition of EPDM in %vol where LS mean low structured (N326) and HS highly structured (N347) CB fillers. The vulcanization time t98% (determined by MDR) and the density of the composite compounds are also reported.

  Table III-2.

	Table III-2. Mechanical properties of EPDM25-LS, EPDM-25HS and EPDM-35LS. The Young's
	modulus E* is calculated from Hooke's law at	= 0.09. The mechanical stress at 100% of
	elongation is	_	.	_	corresponds to the nominal deformation at break and is the
	nominal stress at break. The initial electrical properties of each composite material after
	equilibration by thermal treatment are reported as
						EPDM-25LS	EPDM-25HS	EPDM-35LS
	E* (MPa)				18.2 ± 0.5	20.5 ± 1.0	36.1 ± 2.7
	_	% (MPa)			5.4 ± 0.1	10.8 ± 0.3	14.9 ± 0.2
	_	(%)				266 ± 17	201 ± 14	153 ± 6
	_	(MPa)				20.2 ± 1.2	24.0 ± 1.4	21.3 ± 1.6
	(S/cm)				1.3 x 10 -3	1.6 x 10 -2	3.4 x 10 -2

Table IV

 IV

		-1. The monomer contents of ethylene and 5-ethylidene 2-norbornene (ENB) are reported
	for Keltan 5470 (matrix 1, E1) and Keltan 9650 (matrix 2, E2). EPDM were filled with different
	CB fillers, where LS means low structure (N326) and HS high structure (N347). The oil and the
	filler content are reported in "part for hundred of rubber" (phr). The content of CB is reported
	in phr but also in %vol. The volume fraction of CB in %vol is the one used for the composite
	nomenclature in this work.
	Name EPDM	[Ethylene]	[ENB]	Fillers	Oil part	CB part	[CB]
		matrix	(wt%)	(wt%)	CB	(phr)	(phr)	(%vol)
	E1-0	5470	66	4.6	-	20	-	0%
	E1-25	5470	66	4.6	N326	20	90	25%
	LS
	E1-35	5470	66	4.6	N326	20	140	35%
	LS
	E1-25	5470	66	4.6	N347	20	90	25%
	HS
	E2-0	9650	54	6.5	-	20	-	0%
	E2-	9650	54	6.5	N326	20	90	25%
	25LS
	E2-	9650	54	6.5	N347	20	90	25%
	25HS

Table IV

 IV

	-2. C1 using Neo-Hookean law for each system determined from linear fitting
	from =1 ( ²--1 =0) to =1.2 ( ²--1 =0.61) with the coefficient of determination R².
	Name	EPDM matrix [CB] (%vol) Fillers CB C1composite R²
	E1-0	5470	0%	-	1.094	0.994
	E1-25 LS 5470	25%	N326	3.276	0.969
	E1-35 LS 5470	35%	N326	6.085	0.974
	E1-25 HS 5470	25%	N347	4.650	0.993
	E2-0	9650	0%	-	0.679	0.962
	E2-25LS 9650	25%	N326	2.042	0.982
	E2-25HS 9650	25	N347	3.988	0.991

Table V -

 V

	2. Modelling parameters for EPDM-25HS at	= 100% and 1 Hz or 0.1 Hz and
	with R = 0.3.
	1 Hz	0.1 Hz
	A 0.678 ± 0.003 0.711 ± 0.002
	b 0.405 ± 0.001 0.319 ± 0.001
	R² 0.99469	0.99587

A change in slope of the electrical response as a function of number of fatigue cycles is observed, irrespective of the nature of sample, frequency or amplitude of deformation. When fatigue tests are performed in the endurance zone, an increase of is observed as a function of the number of fatigue cycles. The opposite trend is observed for unlimited fatigue test, the amplitude of the normalized conductivity is decreasing with the number of fatigue cycles. The elastomeric composites used are composites with a high degree of cross-linking (complete vulcanization is estimated at 98%), which means that every bond of the cross-linking network is linked by covalent mono-or polysulfide bounds. The covalent bounds prevent the movement of CB aggregates. If the chains are broken, then the aggregates can 'move' more easily, allowing the creation of new percolation paths. This freedom of movement is visible by the increase in during fatigue.

Table V -

 V 3. Recapitulative results of swelling rates (G) and apparent cross-linking densities ( app) after various fatigue tests for EPDM-25HS and EPDM-35LS

	Fatigue conditions EPDM-25HS		Fatigue conditions EPDM-35LS
		G	app (mol/m 3 )			G	app (mol/m 3 )
	R=0.3-100%-1 Hz-Nf=19,672	3.105	340.9		R=0.3-60%-1 Hz-Nf=3,870	3.031	344.3
	R=0.3-140%-3 Hz-Nf=382	3.203	312.7		R=0.3-80%-1 Hz-Nf=1,879	3.249	307.9
	R=0.4-140%-0.1 Hz-Nf=230	3.116	337.5		R=0-60%-1 Hz-Nf=4,650	3.088	346.0
	R=0.3-140%-1 Hz-Nf=4,100	3.168	322.4		R=0-60%-3 Hz-Nf=7,200	3.116	338.7
	mean	3.154 ± 0.070	328.4 13.2	±	mean	3.121 ± 0.092	334.2 17.9	±

Vulcanization: t98% (min)-15

Remerciements

Abstract

In situ coupled mechanical/electrical investigations on EPDM-based composite materials prepared using CB fillers of different (low and high) structure and at different concentrations have been carried-out by cyclic and continuous loading, with simultaneous measurements of stress, strain, and electrical conductivity. By investigations in dependence on the strain amplitude and unloading rate, the relationship linking the evolution of the electrical conductivity during mechanical deformation to the mechanical Mullins effect is demonstrated. A characteristic electrical signature accompanying the mechanical Mullins effect is revealed, originating from a kinetic reorganization of the CB fillers by competing mechanisms of de-percolation and repercolation. Notable differences between the electrical and the mechanical Mullins effect are also found, in particular, in relation to the kinetics of the stabilization of properties after the first mechanical deformation cycle. Our study brings new light into understanding the coupled evolution of mechanical and electrical properties of elastomeric composite materials, with possible applications in monitoring the material properties under mechanical deformation by in situ electrical measurements. scattering plots, in the form of different power laws. In the range of larger q values, a first generalized Porod's law I(q)=C/q a accounts for (rough) surface scattering from the primary particles but other power law regions at lower q values may be due to scattering from the CB aggregates and agglomerates with different fractal exponents (S(q)) as represented in Figure

Keywords

EPDM/CB composite materials: the mechanisms underlying the structure/properties relationship under uniaxial tensile stretching 147 scatterers. Nanovoids exhibit a large contrast with the surrounding matrix and impact the evolution of the scattering invariant. Since EPDM chains do not crystallize under strain, as it can be deduced by the WAXS analysis, crystallite formation cannot be invoked for the evolution of Q, whereas nanovoids cavitation was already reported for similar rubber composites [30,[47][48][49].

Furthermore, it can be observed that the onset of cavitation at c coincides with the maximum of electrical conductivity, and regime III of decreasing conductivity superimposes in the same elongation range where the invariant is increasing. Thus, it can be inferred that the appearance of nanovoids in the composites reduces the electrical conductivity because the nanovoids increase the non-conducting volume fraction in the material and contribute as well to a partial fragmentation of the percolated network. Furthermore, they limit the transverse contraction that is responsible for aggregate interpenetration under isochoric deformation conditions.

In order to further analyze the SAXS patterns, the ratio between the equatorial intensity ( ) and the initial intensity (Iini(q) at =1) and the ratio // ( ) ( ) corresponding to the normalized meridional intensity have been evaluated. Indeed, if the initial isotropic CB network is decomposed into elementary particles, then the scattered intensity can be written as Iini(q)=N.Ip(q).S(q), where N is the number of irradiated elementary particles (considered constant during an isochoric deformation), Ip(q) is the mean scattered intensity by elementary particles and S(q) is the apparent structure factor accounting for the spatial distribution of elementary particles within aggregates and agglomerates [24]. Since the elementary particles are rigid and not deformed by stretching, the ratios

and // ( ) ( ) can thus be phenomenologically interpreted as

. In a particular q range, an increase of this apparent structure factor (ASF) ratio is likely to reflect an ordering or an increase of spatial periodicity in the particle density at a characteristic distance d~2 /q. The ratios During the early stages of stretching, i.e., before cavitation, the ASF ratios are only impacted by deformation in the low q range at q < 0.02 Å -1 . As expected, a higher CB fraction induces higher structural evolutions. In the meridian direction, stretching induces an increase of the ASF ratio evidencing the establishment of larger inter-aggregate distances (i.e., a broader distribution of inter-aggregate distances extending to large values). Still, for the stretching ratios before cavitation, a broad local minimum appears at about q~0.012 Å -1 . On the contrary, in the equatorial direction, deformation is characterized by a decrease of the ASF ratio in the low-q range associated with inter-aggregate ordering and packing. This correlation evolution is efficient up to q~0.012 Å -1 corresponding to a characteristic distance 2 /q around 60 nm which is the typical size of CB aggregates. Thus, such structural reorganization could reveal the transverse compaction of CB aggregates leading to a minimum inter-aggregate distance of about 60 nm, and a separation or disentanglement along the meridional direction. For E1-35LS during the cavitation, the volume and the contrast of scatterers are no longer constant and the high q values of this ratio significantly exceed unity. However, a clear maximum appears in the equatorial direction, again close to q~0.012 Å -1 . This evolution results from nanocavitation, as deduced from the invariant calculations, but in the length-scale corresponding to aggregate sizes. Thus, nanovoid-nanovoid correlation (distance between adjacent nanocavities) should preferentially reflect inter-aggregate vs. intra-aggregate cavitation.

The presence of nanocavities can also be inferred from the change in the 2D scattering patterns. In order to highlight the changes in the microstructure, the initial 2D SAXS pattern ( = 1) is subtracted from the 2D SAXS pattern measured upon stretching ( > 1). At small elongation ratios, before nanocavitation occurs (Figure IV-17b), a "butterfly" like pattern [50] is observed:

the scattered intensity is higher in the direction parallel to the stretching direction, while is decreasing in the orthogonal direction (negative values appear after subtraction). As described above, these changes are due to the reorganization of the CB aggregates. At higher elongations, the scattered excess intensity becomes positive on the whole detector and an additional anisotropic scattering develops with a lozenge shape extended in the equatorial direction. Such anisotropic additional scattering was previously described to be due to elongated nanovoids with their major axis lying along the tensile direction [47] (see the schematic drawing in For both composites EPDM-25HS and EPDM-35LS, when the amplitude of deformation is higher, the number of cycles before fracture decreases. This result agrees with the results obtained

Correlation between electrical conductivity variations and material properties:

SAXS investigations

However, how to explain the decrease of the amplitude of before fracture? It is possible to correlate these observations with the ones obtained in Chapter IV. Indeed, a continuous tensile test until fracture can be considered as an "accelerated" fatigue test. In Chapter IV, the conductivity before fracture decreased and this observation was related to the apparition of nanovoids in the CB/EPDM composites. Fatigue specimens were studied post-mortem, i.e., after mechanical fatigue tests. We hypothesize that between the time the fatigue tests were performed (several months before) and the time structural investigations were carried out, the samples relaxed, and these cavities "healed". Deformation cycles on virgin samples were performed to The first objective of the thesis was to study the relationship of the evolution of electrical conductivity under strain in percolating CB-filled elastomers. As reported in the literature, a nonmonotonic response of the electrical conductivity is observed under cyclic deformation. A deeper comparison of the classical mechanical Mullins effect and electrical conductivity is realized. The electrical "Mullins" effect is studied, and an electrical hysteresis is observed depending on the maximum strain applied, similarly to the mechanical hysteresis usually observed. Additionally, the electrical hysteresis strongly depends on the relaxation kinetics of the polymer matrix whereas the mechanical hysteresis is less impacted. Thus, the electrical properties seem to probe different information of the material state, in comparison to the mechanical properties. Electrical and mechanical behaviors do not occur at the same microstructural scale. This opens the important question about the microstructural mechanisms involved in the deformation of such complex systems.

Subsequently, the study focused on bringing microstructural information to the mechanical and electrical investigations with several complementary techniques. Thus, in situ coupled Scheme of microstructural mechanisms observed with Electrical/Mechanical/X-Ray coupling for the three parts of the study.

The development preventive maintenance will avoid industrial waste by optimizing the lifetime of filled rubbers, leading as well to a reduction of the general costs (the elastomer pieces will be replaced not regularly, as in the preventive maintenance, but only when indications of damage are detected). However, to develop such method, a detailed study of the effect of processing could be done to define the best composites. The following lines of research could be carried out:

Impact of the matrix: type of elastomers (unsaturated, or saturated elastomers), type of cross-liking agent (sulfur, or peroxide)

Impact of the conductive fillers: CB, CNT, carbon fibers, or metallic fillers etc.

Impact of the geometry of the sample: approaching the geometry of the working pieces used in industry)

Impact of the mechanical test performed: compression, bending, or multiaxial fatigue to simulate all the type of mechanical damage that elastomers composites undergo in the industrial environment.

In addition to the analysis on the influence of processing, the complete