Sylvain Corveleyn

Frederic Lachaud
email: frederic.lachaud@isae-supaero.fr

Florentin Berthet

Claude Rossignol

Long-term creep behavior of a short carbon fiber-reinforced PEEK at high temperature: Experimental and modeling approach

Keywords:

In this work, the time-dependent mechanical behavior of a short carbon fiber-reinforced PEEK is investigated at temperatures near and above the glass transition temperature and for stresses below the damage threshold. An experimental procedure including creep/recovery tests and dynamic mechanical tests was carried out by varying stress levels, temperatures and fiber orientation. The mechanical behavior is shown to be linear viscoelastic below the damage threshold. Effect of the fiber orientation on elastic and viscoelastic behavior is similar. A procedure involving the time-temperature superposition principle (TTSP) is set to assess the long-term linear viscoelastic behavior and is shown to provide reliable results. A Maxwell Generalized model is used for unidirectional identification of the model's parameters. It is then implemented via a UMAT in Abaqus with failure criteria for viscoelastic materials from the literature for 3D calculation of industrial parts.

Introduction

Composite materials are increasingly used in the transport industry [START_REF] Aly | A review on utilization of textile composites in transportation towards sustainability[END_REF] as they possess high specific mechanical properties, fatigue properties compared to other materials such as metal alloys and are corrosion-free. As a result, the use of composite materials has grown over the past twenty years to lighten structures in the transport industry (for example, in aerospace with the A350, the Boeing 787 containing more than 50% by weight of composite materials or in the automotive industry with the BMW i3, whose body is entirely made of composite materials [START_REF] Jacob | Carbon fibre and cars -2013 in review[END_REF]). More specifically, thermoplastic based composites have sparked interest for some applications [START_REF] Dıáz | Developments to manufacture structural aeronautical parts in carbon fibre reinforced thermoplastic materials[END_REF] because they have a short cycle time [START_REF] Bessard | Matériaux Composites Structuraux à Base PEEK Élaborés Par Thermo-Compression Dynamique : Relation Procédé-Propriétés[END_REF], they are weldable [START_REF] Da Costa | A review of welding technologies for thermoplastic composites in aerospace applications[END_REF], have a better impact strength than thermoset based composites [START_REF] Shah | Impact resistance and damage tolerance of fiber reinforced composites: A review[END_REF] and are mostly recyclable [START_REF] Sarasua | Recycling effects on microstructure and mechanical behaviour of PEEK short carbon-fibre composites[END_REF]. They allow production time and cost reductions compared to thermoset composite materials: for example, Fokker claims 20% cost and 10% mass savings on the fully thermoplastic composite elevators and rudder of its Gulfstream G650 [START_REF] Van Ingen | Development of the Gulfstream G650 induction welded thermoplastic elevators and rudder[END_REF]. Some thermoplastics are considered as highperformance polymers (e.g. PPS, POM, PEI and PAEK) as they possess remarkable thermomechanical performance [START_REF] Campo | Polymeric Materials and Properties[END_REF]. Their composites allow the production of lighter and less expensive parts than those produced from aluminum alloys. Their chemical resistance also allows the production of parts without any surface treatment [START_REF] Villoutreix | [END_REF]. Among these materials, carbon fiber-reinforced PEEK is interesting for applications requiring high thermomechanical properties [START_REF] Bessard | Matériaux Composites Structuraux à Base PEEK Élaborés Par Thermo-Compression Dynamique : Relation Procédé-Propriétés[END_REF][START_REF] Chang | Effects of temperature and fiber orientation on the tensile behavior of short carbon fiber reinforced PEEK composites[END_REF]. Its physicochemical structure gives it chemical resistance over a broad range of fluids [START_REF] Villoutreix | [END_REF] and thermomechanical resistance with a high glass transition temperature (T g = 143 • C), melting temperature (T m = 343 • C) and high crystallization rate [START_REF] Berthet | Behaviour and damage of injected carbon-fibre-reinforced polyether ether ketone: From process to modelling[END_REF][START_REF] Gao | Cooling rate influences in carbon fibre/PEEK composites. Part 1. Crystallinity and interface adhesion[END_REF]. These properties make PEEK composites good candidates for use as structural materials, even for high temperatures [START_REF] Chang | Effects of temperature and fiber orientation on the tensile behavior of short carbon fiber reinforced PEEK composites[END_REF]. Even though continuous carbon fiberreinforced composites offer high mechanical performance, their manufacturing processes limit their use to simple geometries. The use of short carbon fiber-reinforced PEEK allows the design of complex geometries for semi-structural parts and the production of large series by injection molding.

At high temperatures however, typically higher than the glass transition temperature, semi-crystalline thermoplastic composites undergo creep (defined as time-dependent strain evolution under constant stress) [START_REF] Ferry | Viscoelastic properties of polymers[END_REF]. Continuous carbon fiber-reinforced PEEK composites do not undergo creep when fibers are oriented in the load direction (only transverse or in-plane shear creep occurs with this type of composites) [START_REF] Schieffer | Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effet du vieillissement thermique[END_REF][START_REF] Albouy | De la contribution de la visco-élasto-plasticité au comportement en fatigue de composites à matrice thermoplastique et thermodurcissable[END_REF][START_REF] D'amore | Viscoelastic effects in poly(ether ether ketone) (PEEK) and PEEK-based composites[END_REF]. This is not the case for short carbon fiber-reinforced thermoplastic composites where creep occurs even in the fiber direction [START_REF] Endo | Linear orthotropic viscoelasticity model for fiber reinforced thermoplastic material based on Prony series[END_REF][START_REF] Oseli | The effect of short fiber orientation on long term shear behavior of 40% glass fiber reinforced polyphenylene sulfide[END_REF]. This phenomenon can lead to failure over extended periods [START_REF] Miyano | Prediction of long-term fatigue life of quasiisotropic CFRP laminates for aircraft use[END_REF][START_REF] Guedes | Creep and fatigue lifetime prediction of polymer matrix composites based on simple cumulative damage laws[END_REF], or make the part too deformed to be suitable for its intended use. Long-term creep behavior at temperatures higher than the glass transition temperature must be taken into account during the design stage of the part. Little is known, however, of the long-term creep behavior of this kind of material.

The time-dependent mechanical behavior type of study depends on the final application [START_REF] Schieffer | Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effet du vieillissement thermique[END_REF]. For high-temperature forming of thermoplastic composites, viscoplastic behavior will be used. For strain evolution until failure of materials under constant mechanical load, viscoelastic behavior is used. In this work, viscoelastic behavior will be studied. Viscoelasticity can be linear if there exists a linear relationship between stress and viscoelastic strain, or non-linear if this is not the case [START_REF] Schieffer | Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effet du vieillissement thermique[END_REF][START_REF] Albouy | De la contribution de la visco-élasto-plasticité au comportement en fatigue de composites à matrice thermoplastique et thermodurcissable[END_REF][START_REF] Lévesque | Modélisation du comportement mécanique de matériaux composites viscoélastiques non linéaires par une approche d'homogénéisation[END_REF]. Viscoelasticity can be studied by dynamic mechanical testing [START_REF] Ferry | Viscoelastic properties of polymers[END_REF][START_REF] Cai | Simplified determination method of long-term viscoelastic behavior of amorphous resins[END_REF][START_REF] Guo | Isothermal physical aging characterization of Polyetherether-ketone (PEEK) and Polyphenylene sulfide (PPS) films by creep and stress relaxation[END_REF], with creep/recovery tests [START_REF] Schieffer | Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effet du vieillissement thermique[END_REF][START_REF] Albouy | De la contribution de la visco-élasto-plasticité au comportement en fatigue de composites à matrice thermoplastique et thermodurcissable[END_REF][START_REF] Lévesque | Modélisation du comportement mécanique de matériaux composites viscoélastiques non linéaires par une approche d'homogénéisation[END_REF][START_REF] Nordin | Nonlinear viscoplastic and nonlinear viscoelastic material model for paper fiber composites in compression[END_REF] (static tests with imposed load) or relaxation tests (static test with imposed strain) [START_REF] Guo | Isothermal physical aging characterization of Polyetherether-ketone (PEEK) and Polyphenylene sulfide (PPS) films by creep and stress relaxation[END_REF]. Temperature has a great influence on time-dependent mechanical behavior due to macromolecular chain mobility changes [START_REF] Chang | Effects of temperature and fiber orientation on the tensile behavior of short carbon fiber reinforced PEEK composites[END_REF][START_REF] Ferry | Viscoelastic properties of polymers[END_REF][START_REF] Albouy | De la contribution de la visco-élasto-plasticité au comportement en fatigue de composites à matrice thermoplastique et thermodurcissable[END_REF]. Methods linking time to temperature allow long-term behavior determination with short-term tests [START_REF] Ferry | Viscoelastic properties of polymers[END_REF][START_REF] Maksimov | Time and temperature dependent deformation of poly (ether ether ketone)(PEEK)[END_REF]. Moreover, the mechanical behavior of short carbon fiber-reinforced composites is anisotropic [START_REF] Chang | Effects of temperature and fiber orientation on the tensile behavior of short carbon fiber reinforced PEEK composites[END_REF][START_REF] Berthet | Behaviour and damage of injected carbon-fibre-reinforced polyether ether ketone: From process to modelling[END_REF] as is time-dependent mechanical behavior [START_REF] Endo | Linear orthotropic viscoelasticity model for fiber reinforced thermoplastic material based on Prony series[END_REF][START_REF] Oseli | The effect of short fiber orientation on long term shear behavior of 40% glass fiber reinforced polyphenylene sulfide[END_REF][START_REF] Staub | Multi-Scale Simulation of Viscoelastic Fiber-Reinforced Composites[END_REF].

To model the viscoelastic behavior of materials, an empirical model as power law, also called Findley's law, has been used and extended to non-linear viscoelasticity [START_REF] Hadid | Empirical nonlinear viscoelastic model for injection molded thermoplastic composite[END_REF]. Its time domain validity remains limited. Some rheological models based on assembly of springs and dashpots can be used for linear viscoelasticity behavior. The Zener model, also known as the standard generalized model, is a combination of a Maxwell model (consisting of a spring-dashpot in series) in parallel with a spring. As it possesses only one relaxation time, it is limited to simple cases and limited time periods. The Maxwell generalized model is a development of the Zener model with an unlimited number of Maxwell elements (spring-dashpot in series). It provides as many relaxation times as needed to take into account more precisely the complex mechanical behavior over a broader range of time [START_REF] Endo | Linear orthotropic viscoelasticity model for fiber reinforced thermoplastic material based on Prony series[END_REF][START_REF] Crochon | Modeling of the viscoelastic behavior of a polyimide matrix at elevated temperature[END_REF][START_REF] Vidal-Sallé | Constitutive equations for orthotropic nonlinear viscoelastic behaviour using a generalized Maxwell model Application to wood material[END_REF]. The spectral model is also used to model the time-dependent mechanical behavior of composite materials. Relaxation times are linked to their weigh in the mechanical behavior via a distribution function (Gaussian function for example). This allows modeling with a limited number of parameters and has been mostly used for laminated composites [START_REF] Schieffer | Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effet du vieillissement thermique[END_REF][START_REF] Albouy | De la contribution de la visco-élasto-plasticité au comportement en fatigue de composites à matrice thermoplastique et thermodurcissable[END_REF]. Introducing non-linear parameters adapts the model to nonlinear viscoelasticity. To take into account time-dependent failure, some failure criteria of viscoelastic materials have already been compared to experimental viscoelastic failure data obtained on glass/epoxy composites leading to good predictions [START_REF] Miyano | Prediction of long-term fatigue life of quasiisotropic CFRP laminates for aircraft use[END_REF][START_REF] Guedes | Creep and fatigue lifetime prediction of polymer matrix composites based on simple cumulative damage laws[END_REF][START_REF] Guedes | Mathematical Analysis of Energies for Viscoelastic Materials and Energy Based Failure Criteria for Creep Loading[END_REF].

The objective of this work is to study the time-dependent mechanical behavior of a short carbon fiber-reinforced PEEK over a very long time period (at least several decades) and at temperatures higher than T g for a potential industrial application at these high temperatures. The work is split into two parts:

-an experimental investigation of time-dependent mechanical behavior of the material to define its mechanical behavior and limits of its use -a modeling study intended to propose a mechanical model of the time-dependent behavior with associated failure criteria, to identify it and to simulate the behavior and time-dependent failure of structures at high temperatures.

Experimental study

The purpose of the experimental study of the material's timedependent mechanical behavior is to investigate the effect of stress applied, temperature and fiber orientation. The experimental procedure described below will vary all these parameters in order to define a mechanical model and to identify its parameters.

Material and process

The material used in this study is an easy flow grade of PEEK reinforced with 40% by weight short high-modulus carbon fibers (with a mean length of 120 µm [START_REF] Berthet | Behaviour and damage of injected carbon-fibre-reinforced polyether ether ketone: From process to modelling[END_REF]) provided by Victrex® as pellets under commercial name PEEK 90HMF40 (Fig. 1). The samples used in this study are injection molded dumbbell samples according to ISO527 1A and dumbbell samples machined from injection molded plates according to ISO527 1BA (Fig. 2). Dumbbell samples and plates were injection molded with a DK 65/160 machine with parameters shown Table 1.

Fiber orientation in the material is checked by microscopic observations of a cut specimen (Fig. 3). The common core/shell structure is observed with fibers oriented along the direction of injection near the surface (shell) and a core, with fibers oriented perpendicular to the injection direction [START_REF] Vincent | Orientation des fibres courtes dans les pièces en thermoplastique renforcé[END_REF]. The shell is thicker than the core and fibers are mostly aligned in the injection direction. This is explained by the flow during injection: near to the mold surface, shear flow aligns fibers into the direction of injection, while far from the mold surface, elongational flow aligns fibers perpendicular to the injection direction [START_REF] Vincent | Orientation des fibres courtes dans les pièces en thermoplastique renforcé[END_REF]. To study the effect of fiber orientation on mechanical behavior, ISO527-1BA samples were machined from injected plates at 0 • , 45 • and 90 • from the injection direction. Shear flow occurring on mold cavity also explains why ISO527-1A samples have more fibers oriented in the injection direction than ISO527-1BA samples cut in the injection direction from plate (see Fig. 4).

Experimentation campaign

An experimental procedure including static tensile tests, creep/recovery tests and dynamic mechanical tests is carried out. The aim is to define the stress range (situated below the damage threshold), timedependent mechanical behavior and to provide long-term experimental data for the modeling study. The influence of stress, temperature and fiber orientation is investigated.

Short-term creep test

Prior to the creep tests, the stress range for material use must be determined and, specifically, the maximum stress defined here as stress value when damage begins to appear. The material is mechanically characterized in traction at room temperature, 150 • C and 250 • C with both monotonic and loading/unloading tests (an example of curves at 150 • C on an ISO527-1A sample is given Fig. 5) at strain rateε = 10 -4 s -1 . The machine used is an INSTRON 8862 and strain is measured with an extensometer 2620-601 having a 25 mm gauge length. In this manner, the engineering properties (elastic modulus, strain and stress at failure) as well as plasticity and damage can be measured. Plasticity is defined as the permanent strain after unloading (Fig. 5). Damage is defined as the drop in material rigidity and computed as Eq. ( 1).

d i = 1 - E i E 1 (1)
Where E i is the secant modulus obtained on the i th loading/unloading cycle and E 1 is obtained in the elastic part of the traction curve (graphical explanation is given Fig. 5).

At least 3 samples are tested, including at least 2 for loading/ unloading tests. Example of results obtained at 150 • C are shown in Fig. 5 (note that damage and plasticity are determined by the stress levels chosen) and some engineering properties are summarized in Table 2. The quasi-static mechanical behavior of the material is seen to be temperature-dependent: brittle below T g and softer and more ductile above. This behavior is linked to the semi-crystalline nature of the PEEK matrix.

From damage evolution (like that shown Fig. 5 for an ISO527-1A sample tested at 150 • C), a maximum stress for use of material for each type of configuration (temperature, fiber orientation) is set, as shown in Table 3. This value corresponds to the damage threshold of the material and stresses below this value are assumed to not damage the material.

Material creep is studied in traction at room temperature, 150 • C and 250 • C and under stresses below the damage threshold following the quasi-static mechanical characterization presented before. An MTS tensile machine is used, and strain is measured with either an extensometer 634.33F-01 having a 25 mm gauge length, or a strain gage which provides better results (no sliding and better accuracy). Viscoelastic behavior is identified with a multi-step creep/recovery test procedure including 5 creep/recovery steps with increasing load (Fig. 6) [START_REF] Lévesque | Modélisation du comportement mécanique de matériaux composites viscoélastiques non linéaires par une approche d'homogénéisation[END_REF]. Loading rate is set to 1 MPa.s -1 , creep steps are 4 h long and recovery steps are 8 h long.

Long-term creep test based on DMA

The aim is to identify long-term creep compliance by applying the time-temperature superposition principle (TTSP) to linear viscoelastic properties [START_REF] Ferry | Viscoelastic properties of polymers[END_REF][START_REF] Maksimov | Time and temperature dependent deformation of poly (ether ether ketone)(PEEK)[END_REF]. Tests are carried out with ISO527-1A sample in traction on a BOSE ELECTROFORCE 3330 A-T (Fig. 7). Strain is measured with strain gages.

A frequency and temperature sweep is used in the experiment. Frequency is varied from 0.02 Hz to 22 Hz and temperatures at 40 • C and from 100 • C to 310 • C every 10 • C. Amplitude is chosen as 0.05 mm in order to remain within the hypothesis of linear viscoelasticity. Vertical shift is applied to the storage modulus master curve to match the storage modulus at 40 • C to the modulus measured by tensile traction tests at

23 • C ISO527-1A ISO527-1BA cut at 0 • ISO527-1BA cut at 45 • ISO527-1BA cut at 90 • 150 • C ISO527-1A ISO527-1BA cut at 0 • ISO527-1BA cut at 45 • ISO527-1BA cut at 90 • 250 • C ISO527-1A ISO527-1BA cut at 0 • ISO527-1BA cut at 45 • ISO527-1BA cut at 90 •
room temperature [START_REF] Deng | Temperature-dependent elastic moduli of epoxies measured by DMA and their correlations to mechanical testing data[END_REF].

Results and discussion

Short-term creep tests

The raw results for creep/recovery tests of an injection molded dumbbell sample at 150 • C are shown Fig. 8. An average curve (arithmetic mean of all samples tested) is also shown. The results show that there is residual strain at the end of the recovery step which can be due to plastic deformation or material aging.

Another mechanical loading history was applied and shows (Fig. 9) that after having been stressed at the maximum stress, the residual strain after recovery does not change during the remainder of the test. This shows that residual strain is due to plasticity.

Viscoelastic strain during creep steps is extracted from raw results subtracting elastic and plastic strain from the total strain measured as viscoplastic strain is shown to not appear. It is then possible to determine whether viscoelasticity is linear or not. Fig. 10 shows creep compliance computed as Eq. ( 2) during each i th creep step for the test carried out at 150 • C and an average of the five curves smoothed with a moving average. Where C i (t) is the time-dependent creep compliance, ε visco (σ i , t) is the time-dependant viscous strain and σ i the stress applied during each i th creep step.

C i (t) = ε visco (σ i , t) σ i (2)
The five curves show a satisfactory overlap (Fig. 10). Hence, viscoelasticity can be considered linear below the damage threshold. The same observations are made with tests at room temperature and 250 • C.

Similar calculations can be performed on results obtained at room temperature and 250 • C. Creep compliance values for the three temperatures of interest are shown Fig. 11. Almost no creep occurs at room temperature: viscoelastic strain after 4 h creep is 10 -6 . However, at 150 • C and 250 • C, creep is greater and varies with temperature: the higher the temperature, the larger the creep strain (viscoelastic strain after 4 h creep is 1.5 10 -5 at 150 • C and 1.9 10 -5 at 250 • C). This can be explained because the glass transition temperature of PEEK is 143 • C: at room temperature, the material is in its glassy state and only little macromolecular movement can occur. At 150 • C and 250 • C, corresponding to the end of transition to the rubbery state, macromolecular chain movement is allowed in the amorphous phase of the polymer. Finally, creep compliance appears quite linear in the log(time) scale, which means that an exponential law can properly describe the creep compliance function of time within the test time.

Due to the molding process, fiber orientation leads to an anisotropic elastic behavior [START_REF] Berthet | Behaviour and damage of injected carbon-fibre-reinforced polyether ether ketone: From process to modelling[END_REF] and viscoelasticity should also be anisotropic. Creep compliances measured for the different material orientations are shown Fig. 12. Viscoelastic strain is smaller as the fibers are oriented in the load direction. More waviness for the 90 • and 45 • curves can be noticed as the stress involved to test these samples is smaller than for the 0 • and injection molded samples and considering the compliance definition shown Eq (2).

Fig. 13 shows that there is a linear relationship between creep compliance and elastic modulus: creep compliance divided by the elastic modulus function of the different fiber orientations appear similar given experimental uncertainties existing in stress/strain measurements. This is observed whatever the temperature (150 • C or 250 • C). Linear viscous mechanical behavior is due to the matrix and the influence of fibers is similar in elasticity and linear viscoelasticity [START_REF] Staub | Multi-Scale Simulation of Viscoelastic Fiber-Reinforced Composites[END_REF].

With short-term creep tests, the effect of stress level, fiber orientation and temperature were investigated. The time-dependent mechanical behavior of the studied material is shown to be linear viscoelastic below the damage threshold. There is almost no creep at room temperature, but above the glass transition temperature, viscous behavior is observed. Finally, fiber orientation has the same influence on viscoelasticity as on elasticity.

Long-term creep tests

The modulus function of frequency and temperature obtained by DMA tests is shown Fig. 14 aFigure 14. For temperatures below 120 • C, the effect of frequency on the modulus is limited (1.2% decrease in modulus). This can be explained by the reduced mobility of the macromolecular chains below Tg-30 • C for most polymers [START_REF] Hanay | Treatise on Solid State Chemistry: Volume 3 Crystalline and Noncrystalline Solids[END_REF]. At the glass transition temperature, the material undergoes the biggest decrease in modulus (19GPa drop between 120 • C and 190 • C).

A master curve of the modulus can be then obtained by horizontally shifting the curves from one reference curve. This is also known as the Time Temperature Superposition Principle (TTSP) [START_REF] Ferry | Viscoelastic properties of polymers[END_REF] and can be formalized as Eq. ( 3):

E(t, T) = E( t a T , T 0 ) ( 3
)
Where E is the modulus, t the time, T the temperature, T 0 the reference temperature and a T the shifting factor. The shifting factor experimentally obtained can be linked with temperature through Arrhenius' law [START_REF] Ferry | Viscoelastic properties of polymers[END_REF] as Eq. ( 4):

log(a T ) = E a 2, 3 × R × ( 1 T - 1 T 0 ) ( 4
)
Where R is the perfect gas constant and E a is the activation energy to be defined. This activation energy is the only parameter linking time and temperature in the viscous behavior.

The reference temperature is chosen to be 120 • C because it corresponds to the onset of the thermomechanical curve. By horizontally shifting the curves obtained for each other single temperature (higher temperatures to lower frequencies), the smooth master curve for a reference temperature of 120 • C shown Fig. 14 b. is created. The Arrhenius plot of the shift factor (Fig. 15) shows a satisfactory linearity R 2 = 0.98 and activation energy is calculated as 515 kJ.mol -1 .

Modulus as a function of frequency obtained by DMA (master curve shown Fig. 15.b) can lead to creep compliance as a function of time following equations by Cai et al. [START_REF] Cai | Simplified determination method of long-term viscoelastic behavior of amorphous resins[END_REF] reminded Eq. ( 5).

⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ E(t) = E ( 1 f
) [START_REF] Da Costa | A review of welding technologies for thermoplastic composites in aerospace applications[END_REF] In this way, the data obtained by both short-term and long-term creep tests can be compared. Fig. 16 shows satisfactory trends of those The TTSP applied in our study provides long-term creep data for the material and the link between time and temperature. Data of long-term and short-term creep tests are consistent and provide confidence in the method used.

D(t) = 1 E(t)

Modeling

The experimental study has provided data on the time-dependent mechanical behavior of short carbon fiber PEEK. Time-dependent mechanical behavior is linear viscoelastic below the damage threshold. The effects of temperature and fiber orientation have been determined. Finally, long-term data have been obtained as well as the relationship between time and temperature.

Creep model

In order to model the experimental mechanical behavior over a long time period, the Generalized Maxwell model is used (Fig. 17). It is a linear viscoelastic model comprised of springs and dashpots like other linear viscoelastic models such as the Maxwell model (comprised of a spring and a dashpot in series), the Voight model or the Zener model. The main advantage of the Generalized Maxwell model is that it considers relaxation times as necessary to describe the behavior of the material. The number of relaxation times is dependent upon the identification time considering that generally, one relaxation time per decade is used.

Hereditary equation for 1D modeling

To model the unidirectional behavior of a nonlinear viscoelastic material, Schapery's equation is commonly used [START_REF] Albouy | De la contribution de la visco-élasto-plasticité au comportement en fatigue de composites à matrice thermoplastique et thermodurcissable[END_REF][START_REF] Lévesque | Modélisation du comportement mécanique de matériaux composites viscoélastiques non linéaires par une approche d'homogénéisation[END_REF][START_REF] Nordin | Nonlinear viscoplastic and nonlinear viscoelastic material model for paper fiber composites in compression[END_REF][START_REF] Crochon | Modeling of the viscoelastic behavior of a polyimide matrix at elevated temperature[END_REF][START_REF] Golden | An Approach to Characterize Nonlinear Viscoelastic Material Behavior Using Dynamic Mechanical Tests and Analyses[END_REF]:

ε(t) = g 0 .D 0 .σ(t) + g 1 . ∫ t 0 ΔD(Ψ -Ψ ' ). d(g 2 σ) dτ dτ (6)
Where D 0 is the elastic compliance and ΔD the transient compliance and.

Ψ = ∫ t 0 dt' aσ and Ψ' = ∫ τ 0 dt'
aσ are the reduced times andg 0 ,g 1 , g 2 and a σ are non-linear parameters which depend on the stress applied. If the material behaves linear viscoelastically, non-linear parameters are reduced to 1 and the equation becomes:

ε(t) = D 0 .σ(t) + ∫ t 0 ΔD(t -τ). dσ dτ dτ (7)
Moreover, transient compliance is often described as a Prony series which considers relaxation times as necessary to properly describe the material's behavior:

ΔD(t) = ∑ D i ( 1 -exp ( -t τ i ) ) (8)
Where D i is the transient compliance associated with the relaxation timeτ i .

Eqs. ( 7) and ( 8) correspond to the Generalized Maxwell model and the relationship with the notations shown Fig. 17 are reminded Eq. ( 9).

⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ E j = 1 ∑ j-1 i=0 D i - 1 ∑ j i=0 D i ∑ N i=0 E i = 1 ∑ N i=0 D i τ i = η i E i (9)
To consider the effects of temperature, moisture and aging on viscoelastic behavior, reduced times are used and the previous equation (Eq. ( 7)) becomes:

ε(t) = D 0 .σ(t) + ∫ t 0 ΔD(Ψ -Ψ ' ). dσ dτ dτ ( 10
) With Ψ = ∫ t 0 dt '
aT .aH.ate and Ψ' =

∫ τ 0 dt '
aT .aH.ate the reduced times where a T is the horizontal shift factor due to temperature, a H the one linked to water uptake and a te the one for aging. In this study, only the effect of temperature will be taken into account [START_REF] Schieffer | Modélisation multiéchelle du comportement mécanique des composites à matrice organique et effet du vieillissement thermique[END_REF][START_REF] Crochon | Modeling of the viscoelastic behavior of a polyimide matrix at elevated temperature[END_REF][START_REF] Lai | 3-D schapery representation for non-linear viscoelasticity and finite element implementation[END_REF][START_REF] Tanks | Accelerated creep and creep-rupture testing of transverse unidirectionalarbon/epoxy lamina based on the stepped isostress method[END_REF].

Differential equation for 3D modeling

The model by Vidal-Sallé and Chassagnes is used for 3D modeling of the viscoelastic behavior [START_REF] Vidal-Sallé | Constitutive equations for orthotropic nonlinear viscoelastic behaviour using a generalized Maxwell model Application to wood material[END_REF]. The constitutive equations are reminded in Eq. [START_REF] Chang | Effects of temperature and fiber orientation on the tensile behavior of short carbon fiber reinforced PEEK composites[END_REF].

⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ σ = σ0 + ∑ N i=1 σi ε = C0 σ0 + ∑ N i=1 Ci σi + Γi σi ( 11
)
Where σ is the total stress applied, σ0 is the stress applied to the spring branch and σi is the stress applied to the i th Maxwell element, C0 is the instantaneous stiffness matrix and Ci and Γi are the stiffness and viscous matrices of the i th Maxwell element. Elastic and viscoelastic stiffness matrices have the same material symmetry, as shown in Eq. [START_REF] Berthet | Behaviour and damage of injected carbon-fibre-reinforced polyether ether ketone: From process to modelling[END_REF].

Γi = Ci : Θi = A i ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 1 E 1 - ν 21 E 2 - ν 31 E 3 0 0 0 - ν 12 E 1 1 E 2 - ν 32 E 3 0 0 0 - ν 13 E 1 - ν 23 E 2 1 E 3 0 0 0 0 0 0 1 G 12 0 0 0 0 0 0 1 G 13 0 0 0 0 0 0 1 G 23 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
τ 6 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (12)

Implementation and identification

1D model: Simplification for viscoelastic model parameter identification

Identification of the parameters for the viscoelastic model is carried out from the unidirectional tests presented below. Experimental results show that mechanical behavior is linear viscoelastic. Viscoelastic strain can be described as follows, combining Eqs. ( 7) and [START_REF] Van Ingen | Development of the Gulfstream G650 induction welded thermoplastic elevators and rudder[END_REF].

ε(t) = D 0 .σ 11 (t) + ∫ t 0 ∑ D i τ i .exp ( τ -t τ i ) .σ 11 (t)dτ (13)
Eq. ( 13) can be written as the dot product shown Eq. [START_REF] Ferry | Viscoelastic properties of polymers[END_REF].

ε(t) = ( σ 11 (t) C 1 (t) ⋯ C i (t) ⋯ C N (t) ) ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ D 0 D 1 ⋮ D i ⋮ D N ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ (14)
The second vector is the one to be identified. The first one is fully defined as C i are time-dependent and can be written for each time step as follows:

C i (t + Δt) = τ i . [ Δt 2 .
( exp

( - Δt τ i
)

.σ 11 (t) + σ 11 (t

+ Δt) ) + C i (t).exp ( - Δt τ i ) ] (15)

3D model: Simplification and resolution for simulation

Once the parameters have been identified, carrying out any simulation on an industrial part needs to implement a 3D mechanical model. According to the literature on elastic behavior [START_REF] Berthet | Behaviour and damage of injected carbon-fibre-reinforced polyether ether ketone: From process to modelling[END_REF] and experimental results on time-dependent mechanics of the material, the following assumptions can be made:

Transverse isotropic symmetry:

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ E 2 = E 3 ν 21 = ν 31 ν 32 = ν 23 G 12 = G 13 G 23 = E 2 2 × (1 + ν 23 ) (16)
Shear modulus is calculated thanks to Eq. ( 17), considering an elastic modulus for 0 • , 45 • , 90 • and Poisson's ratio determined in the experimental study.

G 12 = 1 4 E 45 • -1 E1 -1 E2 + 2 ν12 E1 ( 17
)
Time dependency does not depend on the material direction (as shown Fig. 13), Eq. ( 18) can be assumed:

τ 1 = τ 2 = ⋯= τ 9 (18)
A i coefficients are defined from D i identified in unidirectional tests.

⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ A j = 1 ∑ j-1 i=0 D i - 1 ∑ j i=0 D i ∑ N i=0 A i = 1 ∑ N i=0 D i (19)
The problem's constitutive equations to be solved are as follows:

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Δσ = ∑ N i=0 Δσ i Δσ i = C-1 i ( Δε -Γi σi (t) × Δt ) ∂Δσ ∂Δε = ∑ N i=0 C-1 i ( 20
)
Incremental viscoelastic strain is solved like Eq. ( 21).

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ Δε an = ⎛ ⎜ ⎝ Γi -1 Ci Δt + 1 2 Ĩ⎞ ⎟ ⎠ ( ε(t) + Δε 2 -εan (t) ) εan (t + Δt) = εan (t) + Δε an (21)

Failure criteria to predict failure

Finally, to predict creep failure, two failure indices for viscoelastic materials from the literature are introduced. Those have been successfully employed by Guedes [START_REF] Guedes | Creep and fatigue lifetime prediction of polymer matrix composites based on simple cumulative damage laws[END_REF] on experimental results by Myiano on carbon fiber-reinforced epoxy composites [START_REF] Miyano | Prediction of long-term fatigue life of quasiisotropic CFRP laminates for aircraft use[END_REF] to assess long-term viscoelastic failure. They were chosen for their ability not only to best fit experimental data, but also because they are the most penalizing compared to other indices [START_REF] Guedes | Creep and fatigue lifetime prediction of polymer matrix composites based on simple cumulative damage laws[END_REF].

The first one is based on a maximum strain criterion Eq. ( 22). It is simple to use but does not consider stress triaxiality.

MS index = max i,j∈E1,3F ( ε ij ε ij rupt ) (22)
The second one is the Modified Reiner Weissenberg [START_REF] Tanks | Accelerated creep and creep-rupture testing of transverse unidirectionalarbon/epoxy lamina based on the stepped isostress method[END_REF] index based on stored energy into material which takes into account stress triaxiality.

M -RW index = W s 0, 5 × max i,j∈E1,3F ( ε ij rupt ×σ ij ) (23)
Where W s is the stored energy, equal to the energy contained in springs of the model [START_REF] Guedes | Creep and fatigue lifetime prediction of polymer matrix composites based on simple cumulative damage laws[END_REF][START_REF] Guedes | Mathematical Analysis of Energies for Viscoelastic Materials and Energy Based Failure Criteria for Creep Loading[END_REF] and can be assessed for a constant unidirectional creep loading σ 0 as follows [START_REF] Guedes | Mathematical Analysis of Energies for Viscoelastic Materials and Energy Based Failure Criteria for Creep Loading[END_REF][START_REF] Tanks | Accelerated creep and creep-rupture testing of transverse unidirectionalarbon/epoxy lamina based on the stepped isostress method[END_REF]:

W s = σ 0 2 [ D 0 2 + ∑ n i=1 D i 2 ( 1 -exp ( - t τ i ) ) 2 ] (24)
The algorithm for calculation of a 3D part is described Fig. 18:

Results and discussion

From the experimental data and model proposed previously, the model will be identified, then a 3D model will be first validated and then used for calculation of an industrial part.

Identification 1D

From the experimental data and with Eq. ( 14), identification of the transient compliances D i associated with the relaxation times τ i can be computed. The method used consists in assuming τ i = 10 i-1 and solving Eq. ( 14) with a linear least squares solver lsqlin contained in Matlab.

Relaxation times are chosen according to sampling rate (here 1 Hz, i.e. one datum is recorded every second) and experimental test duration (here, 4 h = 14400 s). The lowest relaxation time chosen must respect inequality τ min < Δt 3 as for smaller relaxation times, the associated maxwell element will be instantaneously relaxed. The highest relaxation time must be less than 3 times the total test duration: as for higher relaxation times, the associated Maxwell element will never be relaxed and will behave like a spring. In order to identify the model, the experimental data of the previously presented Fig. 10 are used. Results of the identification are shown in Fig. 19 and the parameters are summarized in Table 4. A very good description of the experimental data is obtained from the model. It can be observed that after 3 times the highest relaxation time (here, after 30000 s) the model saturates: evolution of creep compliance is no longer described. This is due to the fact that all of the model's Maxwell elements are then relaxed. If a longer simulation is carried out, transient compliances associated with longer relaxation times must be identified.

The model must therefore be identified over a long-time range, experimentally obtained by the time-temperature superposition principle (TTSP). The same procedure as previously on long-term experimental data shown Fig. 16 is computed, with relaxation times ranging from 10 -30 to 10 20 . The master curve is identified with less than 3.5% relative error (see Fig. 20).

Implementation and validation

Once identified on unidirectional experimental data, the model parameters are introduced into a user material subroutine (UMAT) developed for Abaqus simulation. In order to validate the model, some preliminary tests were conducted on a single hexahedral element (with 8 nodes, 3 degrees of freedom and 8 Gauss points -C3D8 in Abaqus) unidirectionally loaded (Fig. 21). An implicit algorithm is used in Abaqus. Loading is done within 1 s at 40 MPa under 150 • C and is maintained for 20 years or for 100 s before unloading.

Dependency upon the time increment is checked by changing it from 10 -4 s to 10 4 s. The conclusion is that the results are only weakly dependent on the time increment (less than 5%). Nevertheless, attention must be paid for complex loading paths including different loading steps. Simulation of the creep / recovery test shows poor results with the automatic increment. This can be explained by the inability of the model to take into account mechanical step change when it occurs between 2 times increments. Solution is to make time increment match the mechanical step change (i.e. to split time in as many steps as the mechanical path). The model leads then to satisfactory results (Fig. 22).

Application of the model to structures

Once the model has been identified and the methodology for calculation set, some simulations on structures can be carried out. We propose here to make some comparisons between simulation and experimental results on a dumbbell sample with different temperatures and fiber orientations. The sample is clamped at one of its ends and loaded with a point force on the other (Fig. 23 a.). Strain is measured inside the central zone of the sample where strain is homogeneous (Fig. 23 b.).

Simulations at 150 • C and 250 • C with material orientations of 0 • , 45 • and 90 • for a stress equal to the damage threshold are carried out. Stress is applied within 1 s and maintained for 20 years (~6.3 10 8 s). The increment is set to automatic, with a first increment value of 10 -4 s and a maximum value of 10 7 s.

Fig. 24 shows a comparison of experimental elastic modulus and elastic modulus obtained at the end of the loading step by the model. Both values are quite similar, leading mostly to an error of approximately 6%.

For long-term time-dependent behavior, Fig. 25 shows a comparison between simulation results and experimental data. The model identified from DMA data can now simulate material behavior whatever the temperature and whatever the fiber orientation as differences between simulations and experimental data remain limited. At 150 • C and for the longest times model tends to underestimate strain. This can be due to time-dependent damage or other non-linear behavior appearing during creep. At 250 • C, trends are consistent and results coherent. At 250 • C, trends are consistent and results coherent. However, simulation results at 250 • C show a decrease in strain rate, which reaches 0 s -1 after 4.95 10 7 s (equivalent to 2.2 years). This is due to relaxation of all Maxwell elements. The model identified is limited by finite experimental data obtained.

The results of Maximum Strain (MS) and Modified Reiner Weissenberg (MRW) failure indices according to time, temperature and fiber orientation are shown in Fig. 26 for stress equal to the damage threshold. It is interesting to note that both failure indices are proportional to strain evolution. The unidirectional stress state leads to similar values of MS and M-RW failure indices and is consistent with the work of Miyano [START_REF] Guedes | Creep and fatigue lifetime prediction of polymer matrix composites based on simple cumulative damage laws[END_REF]. We note that for 45 • sample, MS and M-RW failure criterion give not the same values; M-RW criterion is higher than MS criterion. This is due to the fact that for this test, transverse and in-plane shear stresses are similar. So as the transverse strain at failure is lower than shear strain at failure, M-RW criterion is activated for transverse component although for MS criterion it is the shear strain. In fact MS criterion concern only strains, by M-RW is a coupled criterion between the strains and stresses corresponding then to a more predictive criterion. Finally, it is noted that for stresses below the damage threshold, failure indices do not predict part failure within 20 years, whatever the temperature and whatever the fiber orientation.

With the model identified and knowing the shift factor due to temperature, the validity of the model can be assessed as 3 times the maximum relaxation time of the model. As shown Fig. 27, the model can provide long-term calculation for a wide range of temperatures (more than 2 years at 250 • C, 25 years at 240 • C) which is good enough for most industrial applications.

Conclusion

In this study, very long-term creep behavior of an injection molded short carbon fiber-reinforced PEEK was investigated for stresses below the damage threshold, even for temperatures above glass transition temperatures. An experimental procedure, including creep/recovery tests and dynamic mechanical tests, was carried out to identify the timedependent mechanical behavior and allow the choice of a model. The model parameters were identified thanks to experimental data obtained and some cross-tests were performed to demonstrate the confidence of the model obtained. Finally, the model was successfully used to simulate the time-dependent mechanical behavior of 3D parts.

Due to lack of large macromolecular movements, almost no creep appearings for temperatures below 120 • C. For higher temperatures, time-dependent mechanical behavior is linear viscoelastic for stresses below the damage threshold, even though little plasticity appears. Fiber orientation shows similar effects on linear viscoelasticity and on elasticity. Very long-term linear viscoelastic experimental data are obtained via dynamic mechanical analysis and the time temperature superposition principle, leading to satisfactory comparison with short-term creep data.

The Maxwell generalized model is suitable for unidirectional and three-dimensional calculation. Viscoelastic parameters are identified with experimental data and used as inputs for structure simulation. The model is implemented in Abaqus as a UMAT and simulation strategies were validated for long-term creep calculation and applied to a dumbbell sample by varying temperature and material orientations. Simulation results were compared with experimental data and provide satisfactory results. Failure criteria integrated into the model allow prevision of creep failure of structures. Finally, time/temperature limits for use of the model were defined.

Some experiments however, such as long-term creep, must be carried out to check the development of time-dependent damage or other timedependent phenomena occurring over a long duration (viscoplasticity, aging etc.). These complementary data should provide a better time to failure estimation.

Fig. 1 .

 1 Fig. 1. Pellets of Victrex® PEEK 90HMF40.

Fig. 2 .

 2 Fig. 2. Injection molded samples used for the tensile creep study.

Fig. 3 .

 3 Fig. 3. Microscopic observations made on the ISO527 1A sample.

Fig. 4 .

 4 Fig. 4. Experimental setup for monotonic, loading/unloading traction tests.

Fig. 5 .

 5 Fig. 5. Monotonic and loading/unloading at 150 • C on an ISO527-1A sample.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Multi-step creep/recovery test procedure (example for test on ISO257-1A sample at 150 • C).

Fig. 8 .

 8 Fig. 8. Experimental results obtained for several creep/recovery tests on ISO527-1A samples.

Fig. 9 .

 9 Fig. 9. Mechanical history shows plasticity is the cause of permanent strain on an ISO527-1A sample.

Fig. 10 .

 10 Fig. 10. Creep compliance during creep steps for the different magnitude of stress on ISO527-1A samples.

Fig. 11 .

 11 Fig. 11. Creep compliance obtained at room temperature, 150 • C and 250 • C on an injection molded ISO 527-1A sample.

Fig. 12 .

 12 Fig. 12. Effect of fiber orientation on creep compliance.

Fig. 13 .

 13 Fig. 13. Creep compliance normalized to tensile modulus shows that there is a similar effect of the fiber orientation on elastic and viscoelastic behavior at 150 • C and 250 • C.

Fig. 14 .

 14 Fig. 14. Raw results of DMA test and master curve.

Fig. 15 .

 15 Fig. 15. Arrhenius plot of the shift factor for a reference temperature of 120 • C.

Fig. 16 .

 16 Fig. 16. Effect of temperature on the creep compliance master curve.

Fig. 17 .

 17 Fig. 17. . Generalized Maxwell model.

Fig. 18 .

 18 Fig. 18. Algorithm for calculation of a 3D part.

Fig. 19 .

 19 Fig. 19. Short-term identification of the model.

Fig. 20 .

 20 Fig. 20. Long-term identification.

Fig. 21 .

 21 Fig. 21. Loading and limit conditions on a single element for model validation.

Fig. 22 .

 22 Fig. 22. Validation of model with pure creep (a.) and creep/recovery (b.).

Fig. 23 .

 23 Fig. 23. Boundary conditions (a.) and tensile stress result (b.).

Fig. 24 .

 24 Fig. 24. Experimental and simulation comparison of elastic modulus for different temperatures and orientations.

Fig. 25 .

 25 Fig. 25. Comparison of experimental data and simulation results according to fiber direction and temperature on a dogbone sample undergoing unidirectional creep for 20 years.

Fig. 26 .

 26 Fig. 26. Comparison of failure indices according to fiber direction and temperature on a dogbone sample undergoing unidirectional creep for 20 years.

Fig. 27 .

 27 Fig. 27. Model validity according to temperature applied.

Table 1

 1 Injection parameters used for injection molding the samples of this study.

		420
		200
	P hold (MPa)	80
	t hold (s)	12
	t cool (s)	55

T melt ( • C) T mold ( • C)

Table 2

 2 Engineering

	Test	Elastic modulus	Stress at failure	Strain at failure (%)
	temperature	(MPa)		(MPa)
		Mean	Standard	Mean	Standard	Mean	Standard
			deviation		deviation		deviation
	25 • C	40,937	1470	295	6,00	1.08	0.03
	150 • C	19,825	1137	141.4	3.5	2.13	0.31
	250 • C	13,322	1942	85.0	1.88	2.85	0.23

properties measured on 4 samples at room temperature, 150 • C and 250 • C on ISO527-1A samples.

Table 3

 3 Damage threshold function of sample type and temperature.

	Temperature	Sample	Damage threshold (MPa)

Table 4

 4 Parameters identified.

	τi(s)	Di(1/MPa)
	0	3,57E-05
	1	2,04E-07
	10	9,87E-07
	100	3,09E-06
	1000	3,92E-06
	10,000	7,50E-06

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Roy Chaaya

Stephane Gaboreau

Hugues Raimbourg

Joachim Tremosa

Impact of temperature on mechanical and geochemical behavior of swelling clay minerals

Impact of temperature on mechanical and geochemical behavior of swelling clay minerals

Abstract submitted for a Poster in Topic 6: Temperature-induced effects (Thermal-Hydraulic-Mechanical and Chemical coupled processes).

Roy CHAAYA* 1,2 , Stéphane GABOREAU 1 , Hugues RAIMBOURG 2 , Joachim TREMOSA 1 1 : BRGM, 45060 Orléans, France.

2 : ISTO, UMR 7327 -Université d'Orléans, CNRS, BRGM, 45071 Orléans, France. *Corresponding and presenting author (r.chaaya@brgm.fr)

The ubiquity of swelling clay minerals in surface and sub-surface geoscience systems, in sedimentary deposits, in fault zones or in their potential application in the context of nuclear waste disposal make the effect of temperature (> 60°C) on their hydrological, mineralogical and mechanical behaviour a major scientific issue. Therefore, we aim to assess the swelling behavior of clays when hydrated at temperature (≥ 60°C) under confined conditions. The swelling result from water-mineral interactions at different scales, from interlayer space within crystallite to pore space between particles, depending on the charge compensating cations. We are tackling these physical and chemical issues using a combined approach of experiments and geochemical modelling in order to apprehend the osmotic and crystalline contributions. Miniaturized oedometers were designed to acquire in-situ Xray data (SAXS/WAXS, tomography) according to hydration and the swelling pressure monitoring over time (Figure 1). Such new devices allow to analyze both the evolution of the hydration state of clay and the swelling pressure over time, from dry to saturated state, under drained and confined conditions. Experiments were performed with homo-ionic clays with different solutes (cations and ionic strength) and at different dry densities from 1.4 to 1.6 g.cm -3 . Preliminary results were acquired at temperatures ranging from 25 to 80°C for Na and Ca-form (Figure 2). Complementary data of water adsorption gravimetry isotherms, in confined conditions, were obtained in the same conditions. This set of data will contribute to evaluate the effect of temperature on the swelling pressure and the water retention capacity of swelling clays. All of these results contribute to a better understanding of the thermo-hydro-mechanical-chemical behavior of bentonites and help in the parametrization of geochemical modelling by quantifying the different contributions of watermineral interactions.

Figure 1 :

 1 Figure 1: SAXS analysis performed on a Kunipia-Na of density 1.5 g.cm -3 hydrated by a NaCl solution of concentration 10 -4 M.

Figure 2 :

 2 Figure 2: The swelling test results of a Kunipia-Na of density 1.5 g.cm -3 hydrated by a NaCl solution of concentration 10 -1 M at temperatures of 25; 60 and 80°C.

  Clay Conference 2022, 13-16 June, Nancy, France 8 th International Conference on Clays in Natural and Engineered Barriers for Radioactive Waste Confinement