Vincent Renner
email: vincent.renner@univ-lyon2.fr

Structural borrowing in word-formation: An exploratory overview

Keywords: morphology, word-formation, contact linguistics, borrowing, language change

This exploratory overview of structural borrowing in word-formation discusses the multiformity of processes and patterns affected by language contact and then reviews linguistic and sociolinguistic indicators that may impact on the relative plausibility of scenarios of contact-induced change. A number of key features of this type of borrowing are highlighted: first, it is not a negligible phenomenon and should gain a more prominent position in the general contact linguistics literature; second, it is a manifold phenomenon and fine-grained descriptions, in both their qualitative and quantitative aspects, need to be considered; third, certifying the external causation of change is a challenge and the analysis should cautiously be limited to arguments of relative plausibility, which may combine and strengthen each other.

Introduction

Structural borrowing in word-formation seems to have been a relatively underresearched area within contact linguistics. Studies on morphological borrowing are numerous (see e.g. [START_REF] Gardani | Borrowed morphology: An overview[END_REF] for a recent overview), but specific discussions on the borrowing of abstract morphological schemata, or morphostructural borrowing, are noticeably rarer. This is especially so in the case of word-formation, a domain in which relevant examples and analyses are sparsely scattered in the linguistic literature. This scarcity may well be partially explained by an actual paucity of attested cases, but it is also likely to partly result from the relative difficulty of identifying structural (vs. material) innovations and of certifying the external (i.e. contact-induced) causation of linguistic change.

The concept of structural borrowing should not necessarily presuppose the nonexistence of the linguistic element under study in the recipient language of the contact situation. For instance, even though the conspicuous presence of lexical blends in present-day Polish is seen as a modern innovation, some morphological outputs of lexical blending have been occasionally attested for centuries (Konieczna 2012: 56-57). As Ad Backus (2014: 24) aptly remarks, "change [...] is often a matter of 'merely' increasing or decreasing frequency of use, rather than the adoption or complete loss of particular forms" and it seems advisable not to adopt a narrow focus that would be limited to structures previously completely unattested in the recipient language (structural borrowing sensu stricto), but to include the manifold forms of contact-induced change. Structural borrowing in word-formation is thus defined here as the increase or decrease in frequency of use of an abstract word-formation schema caused by language contact and includes the new availability of a virtually unknown schema (i.e. a change from a null to a non-null frequency, or structural borrowing sensu stricto).

The approach adopted for this research is cross-linguistic, but it is not of a typological nature. The article more modestly aims to gather together illustrations of a variety of contactinduced phenomena so as to put a number of key issues into a broader perspective. It is organized as follows: Section 2 reviews the multiformity of processes and patterns affected by language contact and presents a qualitative typology of structural borrowing in wordformation and Section 3 then discusses linguistic and sociolinguistic indicators that may impact on the relative plausibility of scenarios of contact-induced change.

A multiformity of structural changes

This section examines an illustrative sample of cases described in the literature, from the central, concatenative processes of word-formation, i.e. affixation and compounding, to peripheral, non-concatenative types of structure, i.e. clipping, blending and reduplication.

Affixation

According to R. L. Trask (1998: 322-323), Basque has historically made an extremely moderate use of the pattern of prefixation. Basque prefixes are claimed to result either from affixal borrowing from the neighboring Romance languages, as in the case of des-'dis-', or from structural calquing, i.e. the language-internal forging of a prefix on the basis of a Romance model pattern, as in the case of ez/ez-'no; non-'. This morphological development exemplifies the crossing of the line between material and structural borrowing: the appearance of a new exogenous prefix cannot be considered a simple case of material innovation if it occurs in a context where no pattern of prefixation was already commonly available in the word-formation system of the recipient language.

Compounding

Many patterns of compounding have migrated or varied in frequency of use under the influence of language contact. Berthold [START_REF] Forssman | Baltisch-finnische Sprachkontakte am Beispiel der Adposition[END_REF], cited in Heine & Kuteva 2005: 154) reports that nominal compounding was virtually non-existent in the Baltic languages until the 5 th -7 th centuries CE, when contact was established with the Finnic speakers of Estonian and Livonian, two languages making ample use of the pattern, and it is this event which is surmised to have led to the subsequent presence of noun compounds in Latvian. In presentday Slavic, the new prominence of the bare noun-noun construction is said to come from the heightened influence of English in Central and Eastern Europe [START_REF] Vakareliyska | An Anglo-americanism in Slavic morphosyntax: Productive [N[N]] constructions in Bulgarian[END_REF], which has led to an emerging dispreference for the canonical adjective-noun construction, as in Bulgarian for instance (Bagasheva 2016: 18), or to the appearance of a new interfixless construction, as is manifest in Polish (Konieczna 2012: 53;Jaworski 2014: 41-43 Contact-induced change can also become manifest through marked variations in frequency of use. The increased frequency of subordinative nominal noun-noun compounding in French under the influence of English has for instance been measured by Pierre Arnaud (2018 [in this volume]) and, conversely, language contact may also lead to a decrease in frequency of use. In Flemish, a variety of Dutch in contact with French, Johan [START_REF] Taeldeman | Französisch-flämische Sprachinterferenz in Flandern[END_REF], cited in Heine & Kuteva 2006: 55) notes that speakers are inclined to prefer the French-induced adjective-noun construct (3a) to the canonical noun-noun construct (3b):

(3a) administratieve kosten 'administrative costs' (3b) administratie.kosten 'administration costs'.

Similarly, in South Tyrol, where Italian and German are both official languages, the typically Romance noun-preposition-noun construction is developing at the expense of standard nounnoun compounding in the local variety of German (Riehl 2001, cited Another formal type of change in compound patterning is also attested. The lexical borrowing of English compounds is considered to have led to the increased presence of semantically right-headed nominal compounds in Romance, at the expense of the canonical left-headed constructions of the noun-noun and noun-preposition-noun types. This has, for instance, been noted for French [START_REF] Renner | Fan zone, webradio, infobulle: les noms composés ont-ils perdu la tête? Actes du colloque OPALE Les anglicismes: des emprunts à intérêt variable?[END_REF])for common nouns (5a-b) and commercial proper nouns (5c)and for Italian (5d-e) (Iacobini 2014: 196)

Clipping

Clipping can also be affected by contact-induced change. This is for example the case in Polish, a language in which this operation of subtraction used to be common only in specific lexical fields, i.e. first names (6a), place names (6b) and school subjects (6c), and is now widely applied in informal discourse, without any domain restrictions (6d-e), under the influence of English (Jaworski 2014: 35-38

): 2 (6a) Jolanta > Jola (6b) Warszawa 'Warsaw' > Wawa (6c) matematyka 'mathematics' > matma (6d) manifestacja 'manifestation' > manifa (6e) wykonanie 'performance' > wykon.
In Catalan, a Spanish-induced morphostructural change has also affected hypocoristic formation (Cabré Monné 2008: 900-907). First names were traditionally left-clipped, but they can now also be right-clipped:

(7a) Alexandre > Xandre vs Àlex (7b) Montserrat > Serrat, Rat vs Montse (7c) Santiago > Iago vs Santi.

Lexical blending

The influence of language contact on the frequency of use of lexical blending provides a salient cross-linguistic example of recent structural change in word-formation. This may be explained by the fact that the change dates back only a few decades and that it has affected a process which used to be extremely marginal, if not non-existent, in the languages in question. Several scholars have described a similar type and time of change in a variety of Balto-Slavic languages. In their overview of the current contact situation between Latvian and English, Gunta Ločmele and Andrejs Veisbergs (2011: 312) stress that "[g]rowth in the use of blends has also been noted. In the past, blending was a non-existent word formation pattern in Latvian". Christo Stamenov (2015: 175) also reports that "[a] couple of decades ago blending as a means of word-formation was non-existent in Bulgarian". Ewa Konieczna (2012: 57) claims that "never before has Polish witnessed such an upsurge of blends" and Gordana Lalić-Krstin (2008: 237) notes similarly that "[u]ntil fairly recently, blending was practically unknown in Serbian. In the past few years, however, it has skyrocketed, forming hundreds of new blends". Svitlana Filonik (2015: 188) remarks that "[e]ven though there are a few attestations of Ukrainian blends in works published before the 1990s, they are exceptionally rare" and Ievgeniia Karpilovska (2016: 2914) observes more generally that " [d]uring the last few decades, the Ukrainian lexicon has been characterized by an increased productivity of composition, blending and juxtaposition. This is facilitated by wide and intensive contacts of Ukrainian with other languages, primarily, English". Ada Böhmerová (2010: 112) states likewise that "[i]n Slovak the increase in the productivity of blending and the communicative frequency and penetration of blends beyond the category of nonce-words or occasionalisms is rather recent and could be ascribed to the last three decades". It emerges from these descriptions that a remarkable increase in frequency of use of the process of blending can be linked to the decades around the turn of the 21 st century and to heightened contact with English in a host of countries from Central and Eastern Europe. The phenomenon is to be tied to the sociolinguistic changes that followed the Revolutions of 1989 and the end of Communist rule in the region, in which the new embrace of the West in general, and of American culture in particular, came with a concomitant embrace of the English language.

Reduplication

Due to the influence of both Chinese and Malay, the use of reduplication is widespread in Colloquial Singapore English [START_REF] Wee | Reduplicated morphology in Colloquial Singapore English: Something to write home about?[END_REF]). First names and common nouns can be duplicated to encode a hypocoristic value (8a-d) and verbs can be either duplicated to indicate attenuation (8e-f) or triplicated to mark continuity (8g-h):

(8a) Henry > Ry-Ry As nominal evaluative duplication is attested in Chinese but not in Malay, and verbal continuative duplication is attested in Malay but not in Chinese (while verbal attenuative duplication is attested in both languages), it is assumed that the productive use of noun and verb duplication in Colloquial Singapore English originates from contact with not just one, but two languages. The existence of the formal pattern of triplication is, however, to be considered as an internal innovation as it is not attested in either Chinese or Malay (Wee 2004: 267-269).

Towards a qualitative typology of structural borrowing

The previous subsections have shown that a wide variety of changes is attested and it is helpful to observe that, from a qualitative standpoint, they do not affect the different recipient languages to the same extent. A qualitative cline of structural borrowing can be positedfrom "minimal" to "slight", "moderate" and finally "heavy" changedepending on the relative degree to which the core of the word-formation system is affected. There is heavy restructuring when a process which used to be virtually unavailable emerges in the wordformation system, as in the case of lexical blending for a number of languages of Central and Eastern Europe. There is moderate restructuring in case of, for instance, positional innovation. This includes the appearance of prefixation (alongside suffixation) in Basque and of right-headed compounding (alongside left-headed compounding) in French and Italian.

There is slight restructuring when the general form of a pattern is only marginally modified, as in Polish compounding, which now includes some new interfixless constructions. Finally, the change may be only minimal, when it does not have consequences on the forms of new outputs, as in the case of clipping in Polish. For a fine-grained measure of structural change in a word-formation system, the two dimensionsqualitative and quantitative (i.e. in terms of variation of frequency of use)should thus be taken into account.

Assessing the plausibility of contact-induced change

As Sarah Thomason (2001: 91) aptly puts it, "[e]stablishing the fact of contact-induced change is usually easy when the focus is on loanwords, but it can be much harder, and often impossible, with structural interference. Loanwords are easier to establish because they betray their origin directly". It is comparatively harder to spot structural borrowing because of its schematic nature. It is also hard to measure it because of the difficulty of building diachronic corpora tagged with word-formation information, and hard to fully authenticate it as the assessment is generally only probabilistic. These observations should, however, not be a deterrent to examining the issue and this section discusses various possible indicators that could be considered to enhance the relative plausibility of an external causation of change.

A correlation can first be posited between the form of language contact and the relative likelihood of external causation. Casual contact is expected to lead to lexical borrowing only (Thomason 2001: 70). A weak contact setting, characterized by a remote connection chiefly mediated by the broadcast and digital media (Onysko 2009: 58;Zenner & Van De Mieroop 2017: 77) as is the case of English in many parts of the world, including the countries of Continental Europe -, is hypothesized to be less prone to non-material (i.e. structural) borrowing than a situation of more intense contact, which may be indexed by widespread bilingualism and/or the co-officiality of the languages under consideration in a given territory, as in South Tyrol, Catalonia or Singapore. It also seems possible to link social, sociolinguistic and linguistic change under certain circumstances. The fact that a sudden social and sociolinguistic change such as the dissolution of the Eastern Bloc at the end of the twentieth century may be documented and tied to a new situation of language contact (see e.g. Przygoński 2016 on Poland) doubtlessly increases the plausibility of external causation. That an identical change is attested to have occurred concurrently in several languages tied to the same geopolitical event, from Latvian to Bulgarian, also strengthens the hypothesis.

Structural borrowing can also, in some cases, be tied to the presence of lexical precursors in the recipient language and the attestation of such linguistic cues could be deemed to be a factor boosting the plausibility of contact-induced change. This borrowing scenario has already been described for bound morphemes (see e.g. Bombi 2017: 273-275).

To take an example, the suffix -ing encountered in Spanish and French is not considered to have been straightforwardly borrowed from English. It was abstracted only after a number of lexical borrowings containing this formal ending (e.g. camping, karting, rafting) had entered each language, and after the form was assigned a stable core meaning ('leisure activity'), and thus a morphemic status. The integration into the recipient language is complete only when the new affix is attested to concatenate with native bases, as in (9a-b) for Spanish and (9c) for French:

(9a) balconing off a balcony, or between balconies' < balcón 'balcony' (9b) puenting 'bungee jumping' < puente 'bridge' (9c) ruisseling 'hiking up a stream' < ruisseau 'stream'.

In a parallel fashion, it could be argued that some instances of structural borrowing are not straightforwardly borrowed, but abstracted on the basis of a set of exogenous units integrated through lexical borrowing. This reasoning is surmised to at least apply to the morphological processes which combine two input words, i.e. compounding and lexical blending. For compounding, the lexical precursors are borrowed compounds which retain the morphostructure of the donor language, but whose morphological abnormality is backgrounded by the fact that they are fully integrated from a lexical standpoint as they display compounding elements which are already part of the lexicon of the recipient language. Examples of this type of compound borrowing from English include:4 For blending, the lexical precursors are borrowed blends which are not morphologically opaque in the recipient language because of the existence of formally similar source words in the recipient and the donor language. Examples of this type of lexical borrowing from English in Balto-Slavic include: 5 (11a) Ukr. obamánija 'Obamania' < Obáma + mánija 'mania' (11b) Ukr. sekspért 'sexpert' < séks 'sex' + ekspért 'expert' (11c) Latv. kaplete 'caplet (= capsule-shaped tablet)' < kapsula 'capsule' + tablete 'tablet' (11d) Bulg. glokalen 'glocal' < globalen 'global' + lokalen 'local'.

The presence of compounds like those in (10) and of blends like those in (11) can be regarded as mediating the appearance of native-born items such as the compounds in (5) and the blends in ( 12):

(12a) Ukr. akvás 'kvass diluted with water' < ákva 'aqua' + kvás 'kvass' (12b) Latv. atkritne 'trash folder' < atkritumu 'trash' + atvilktne 'drawer' (12c) Bulg. kljukini 'gossip news' < kljuki 'gossip' + novini 'news'.

The presence of lexical precursors in the recipient language makes a scenario of contactinduced change more likely and, more broadly, it should be pointed out that even though lexical borrowing might not necessarily always be a prerequisite for structural borrowing to occurit is for instance unclear that it is the case for reduplication in Section 2.5 above -, the two types of borrowing go hand in hand, the existence of structural borrowing being tied to non-casual language contact, and so to a substantial concurrent stream of lexical borrowing.

Conclusion

This exploratory overview has strived to highlight a number of key features of structural borrowing in word-formationfirst, that it is not a negligible phenomenon and should gain a more prominent position in the general contact linguistics literature; second, that it is a manifold phenomenon and that fine-grained descriptions, in both their qualitative and quantitative aspects, need to be considered; third, that certifying the external causation of change is a challenge and that the analysis should cautiously be limited to arguments of relative plausibility, which may combine and strengthen each other. Much remains to be done in order to obtain a deeply informed view of the field and future research in the area should aim to better document a wider variety of individual cases and to devise finer-tuned models of contact-induced change in word-formation.

  Italian: il grappolo d'uva 'the bunch of grapes' (4b) South Tyrolean German: das Bündel von Trauben 'the bunch of grapes' (4c) Standard German: das Trauben.bündel 'the grapes.bunch'.

( 8b )

 8b Jeffrey > Jeff-Jeff 3 (8c) buddy > buddy-buddy (8d) mummy > mummy-mummy (8e) stop > stop-stop 'make a short stop' (8f) cry > cry-cry 'cry a little bit' (8g) stop > stop-stop-stop 'keep on stopping' (8h) stare > stare-stare-stare 'keep on staring'.

(

  10a) Fr. webradio 'web radio' (10b) Fr. science-fiction 'science fiction' (10c) It. internet caffè 'Internet café' (10d) It. scuolabus 'schoolbus'.

For a discussion of the presence/absence of interfixes in Polish noun-noun constructs, see also[START_REF] Cetnarowska | Identifying (heads of) copulative appositional compounds in Polish and English[END_REF].

For a discussion of the increasing use of clipping in Polish, see alsoKonieczna (2012: 54-55).

For a discussion of name reduplication in Colloquial Singapore English, see also[START_REF] Wong | The reduplication of Chinese names in Singapore English[END_REF].

The French data are taken from Vincent[START_REF] Renner | Fan zone, webradio, infobulle: les noms composés ont-ils perdu la tête? Actes du colloque OPALE Les anglicismes: des emprunts à intérêt variable?[END_REF] and the Italian data from Claudio[START_REF] Iacobini | A constructionist account of the emergence of a new lexeme-formation pattern: Italian right-headed verbal compounds[END_REF].

[11][12], the Ukrainian data are taken from Svitlana[START_REF] Winters | Lexical blending in Ukrainian: System or sport? Calgary: University of Calgary[END_REF], the Latvian data from Gunta[START_REF] Ločmele | The other polysystem: The impact of translation on language norms and conventions in Latvia[END_REF] and the Bulgarian data from Christo[START_REF] Stamenov | Borrowing word-formation: -ing suffixation and blending in Bulgarian[END_REF].

Acknowledgements

I would like to express my thanks to three anonymous reviewers, Alexandra Bagasheva, Jesús Fernández-Domínguez and Akiko Nagano for their useful comments and suggestions on earlier drafts of this work. The usual disclaimers apply.


Nicolas Candau
email: nicolas.candau@epfl.ch

Oguzhan Oguz

Edith Peuvrel-Disdier

Jean-Luc Bouvard

Christophe Pradille

Noelle Billon

Strain-Induced Network Chains Damage in Carbon Black Filled EPDM

Keywords: Elastomers, Damage, Chains Network

This paper presents an experimental method to follow in-situ the chains network alteration of filled vulcanized rubbers induced by deformation. Macroscopic damage is first investigated on a series of EPDM by quantifying void fraction via Digital Image Correlation (DIC). In-situ DIC void fraction and the swollen pore fraction measured ex situ, i.e. on mechanically tested specimen, show analogous dependence on applied deformation. From such observation, Flory-Rehner equation is used by substituting fraction of swollen specimen by DIC void fraction to access to in-situ changes in network chains density, ν. Below the stretching ratio λ=3, reversible voids and accompanied by slight decrease of ν. Above λ=3, irreversible voids are associated with significant decrease of ν. Transition from reversible to irreversible voiding is finally ascribed to increased pore size of damaged elastically active chains network domains, as revealed by ex situ thermoporosimetry.

Introduction

Ethylene-propylene-diene-terpolymer rubber (EPDM) is one of the most attractive synthetic rubbers due to its outstanding resistance to aging and ozone combined with its strong ability to be extended with fillers and oil plasticizers. [START_REF] Noordermeer | Ethylene-Propylene Elastomers[END_REF] It provides mechanical performances adapted to a large number of industrial applications. In tire sidewall, EPDM plays a major role to prevent dynamic propagation of crack due to its ozone resistance. [START_REF] Young | Dynamic Property and Fatigue Crack Propagation Research on Tire Sidewall and Model Compounds[END_REF][START_REF] Sahakaro | Blending of NR/BR/EPDM by reactive processing for tire sidewall applications. I. Preparation, cure characteristics and mechanical properties[END_REF] In nuclear power plants, EPDM serves as insulation of electric cables owing their ability to resist irradiation. [START_REF] De Almeida | Influence of PE/PP ratio and ENB content on the degradation kinetics of γ-irradiated EPDM[END_REF] Recycling EPDM is then a crucial industrial challenge. [START_REF] Fisher | Method of devulcanizing a cross-linked elastomeric material U[END_REF] Because of weak penetration of devulcanization agents in the rubber matrix, mechanical devulcanization is a more promising route than chemical devulcanization. [START_REF] Diaz | Thermo-mechanical recycling of rubber: Relationship between material properties and specific mechanical energy[END_REF] Mechanical devulcanization is assumed to convert mechanical work into molecular debonding or into an increase in temperature able to break some covalent bonds. In any case, the first step consists of physical breakage and dispersion into small pieces. Understanding the mechanisms at molecular scale responsible for this macroscopic failure is hence of great importance. The understanding of elementary processes involved in the deformation of given rubbers can be partly achieved by a systematic study at intermediate mesoscale to investigate the relationship between macroscopic observation and molecular mechanisms.

One approach consists of in-situ characterization of temperature and strain field during mechanical tests that combine Infrared thermography (IR) and Digital Image Correlation (DIC) respectively. These two techniques are often coupled to give insights on thermomechanical behaviour of polymeric systems. [START_REF] Chrysochoos | Use of Full-Field Digital Image Correlation and Infrared Thermography Measurements for the Thermomechanical Analysis of Material Behaviour[END_REF][START_REF] Maurel-Pantel | A thermo-mechanical large deformation constitutive model for polymers based on material network description: Application to a semi-crystalline polyamide 66[END_REF][START_REF] Samaca Martinez | Thermomechanical analysis of the crack tip zone in stretched crystallizable natural rubber by using infrared thermography and digital image correlation[END_REF] However, their combination to access potential damage is not systematically discussed. Damage is a dilatational mechanism, associated with void creation and hence generates a raise of volumetric strain accessible by DIC. [START_REF] Le Cam | A review of volume changes in rubbers: the effect of stretching[END_REF][START_REF] Ramier | In situ SALS and volume variation measurements during deformation of treated silica filled SBR[END_REF] Part of mechanical dissipation originates from damage, and is further converted into heat. [START_REF] Montesano | Use of infrared thermography to investigate the fatigue behavior of a carbon fiber reinforced polymer composite[END_REF] In rubbery materials, energy dissipation has an essential role in fracture mechanisms [START_REF] Hamed | Energy Dissipation and the Fracture of Rubber Vulcanizates[END_REF] and damage can be distinguished from other dissipative contributions as proposed in ref. [START_REF] Samaca Martinez | Filler effects on the thermomechanical response of stretched rubbers[END_REF] At molecular scale, filled vulcanized rubbers contain various types of network bonds such as chemical cross-links, physical rubber-filler bonds, chains entanglements. The structure and heterogeneities of such complex network in carbon-black filled EPDM has been widely discussed. [START_REF] Valentin | Inhomogeneities and Chain Dynamics in Diene Rubbers Vulcanized with Different Cure Systems †[END_REF][START_REF] Litvinov | Rubber-Filler Interactions and Network Structure in Relation to Stress-Strain Behavior of Vulcanized, Carbon Black Filled EPDM[END_REF] The associated damage can find various origins: chains scission, sulphur-bond breakage, decohesion at filler-rubber interface, filler-filler rupture, [START_REF] Diani | A review on the Mullins effect[END_REF] molecules slippage at fillers surface. [START_REF] Houwink | Slipping of Molecules during the Deformation of Reinforced Rubber[END_REF] Fillers and vulcanization systems both have a dominant role in damage mechanisms in filled vulcanized rubber. Rigid fillers significantly accelerate voiding via strain amplification, and occurs at filler/rubber interface due to a high hydrostatic stress. [START_REF] Ramier | In situ SALS and volume variation measurements during deformation of treated silica filled SBR[END_REF][START_REF] Yannick | Effects of the amount of fillers and of the crosslink density on the mechanical behavior of carbon-black filled styrene butadiene rubbers[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] Vulcanization, by modifying the average end-to-end distance between chains, controls the local chains extension upon macroscopic strain which, in turn, tends to increase elastic strain energy associated with void nucleation that subsequently grows and transforms into cracks. [START_REF] Yannick | Effects of the amount of fillers and of the crosslink density on the mechanical behavior of carbon-black filled styrene butadiene rubbers[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] Le Cam | Mechanism of fatigue crack growth in carbon black filled natural rubber[END_REF] The relationship between chains network damage and macroscopic mechanical behaviour of filled vulcanized rubber is however difficult to clarify as it strongly depends on the filler system (nature, size, spatial distribution), the rubber system [START_REF] Dannenberg | Strain Energy as a Criterion for Stress Softening in Carbon-Black-Filled Vulcanizates[END_REF] (chemical nature, molecular weight, entanglements density), the filler-rubber interface, the vulcanization system (peroxide or sulphur vulcanized with mono, or poly sulfidic bonds), and the experimental conditions [START_REF] Kraus | Stress softening in carbon black-reinforced vulcanizates. Strain rate and temperature effects[END_REF] (temperature, strain rate). Mullins suggested that voids formed around Zn oxides clusters resulting from incomplete vulcanization are mainly responsible for voiding during loading at high strain rate. [START_REF] Mullins | Carbon-Black Loaded Rubber Vulcanizates: Volume Changes in Stretching[END_REF] Swelling of filled vulcanized Natural Rubber (NR) and Styrene-Butadiene Rubber (SBR) that undergo single loading reveal relative decrease of 15% of network chains density, ν, [START_REF] Dannenberg | Strain Energy as a Criterion for Stress Softening in Carbon-Black-Filled Vulcanizates[END_REF][START_REF] Kraus | Stress softening in carbon black-reinforced vulcanizates. Strain rate and temperature effects[END_REF] compare to the value for virgin rubber for a strain rate of 0.4 s -1 . More drastic thermo-mechanical solicitations like High Shear Mixing (HSM) yield in a decrease of ν by more than 70%, partially due to chemical crosslink breakage. [START_REF] Diaz | Thermo-mechanical recycling of rubber: Relationship between material properties and specific mechanical energy[END_REF] Due to the significant modification of chains network during the mechanical solicitation of rubber systems, many physically based models have been developed like mechanochemistry that incorporates strain induced network alteration. [START_REF] Melnikov | Damage of Cross-Linked Rubbers as the Scission of Polymer Chains: Modeling and Tensile Experiments[END_REF][START_REF] Govindjee | A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating Mullins' effect[END_REF][START_REF] Marckmann | A theory of network alteration for the Mullins effect[END_REF][START_REF] Hamed | Molecular Aspects of the Fatigue and Fracture of Rubber[END_REF] In spite of a large number of experimental studies and mechanical modelling, relationship between network chains damage and macroscopic damage in rubbers is still not systematically investigated and requires an adapted experimental methodology. To this aim, a multi-scale approach is used in this paper. Strain and thermal fields measured on the local surface of the specimens are tracked in situ, i.e. during tensile cycles. Three vulcanized EPDM and one unvulcanized EPDM are studied. Their network chain densities are measured ex situ by swelling.

We highlight an equivalence between void fraction obtained by DIC and swollen pores fraction measured by swelling and propose a method to identify the alteration of chains network in situ, i.e. during the rubber deformation. Chains network damage has been found to be associated with a transition from reversible to irreversible voiding mechanisms at a certain stretching ratio. We ascribed such transition to thermal stability of irreversible cavities consistent with an observed rise in size of damaged areas of rubber network measured by DSC thermoporosimetry.

Materials and experiments

Materials composition and processing

The materials are extended oil carbon black filled EPDM (Keltan 5470) obtained by sulphur vulcanization of the gum. They contain 70% in mass of Ethylene and 4.6% of ethylidene norbornene (ENB). The crystalline fraction estimated from Differential Scanning Calorimetry (DSC) is found less than 3% wt. for all materials. All materials contain 80 phr (80g per 100 g of rubber) of carbon black (N550), 65 phr of paraffin oil, 4 phr of calcium oxide, 5 phr of zinc oxide, 1 phr of stearine, 2 phr of PE 6 4000. The vulcanization components are the following:

Temperature and strain field measurement

Mechanical tests are performed on an electromechanical tensile test machine INSTRON 5960.

Rubber samples are stretched and unstretched at room temperature. The nominal tensile strain rate chosen for these tests is 1s -1 . The displacement fields on the front and side faces of the sample are recorded using a four-cameras system which consists of two-pairs systems (Figure 1).

Like for a single stereovision-system, each camera pair is set up independently of the other one.

Both systems are then placed in the same coordinate system using a calibration target. A low sampling rate of cameras (10 Hz) is chosen to ensure a low nominal strain increment between two images and make strain tracking more accurate. Front and side surfaces of the samples are coated with a white spray paint to generate a random speckle pattern. The series of images are post-processed using VIC-3D software package. [START_REF]®Software. Correlated Solutions Incorporated[END_REF] 3D DIC displacement data is converted into strain values with λ 1 the stretching ratio in the tensile direction, λ 2 and λ 3 are the transversal stretching ratios in the directions of the sample width and thickness respectively. More details on the choice of DIC parameters are provided in ref. The transversal and longitudinal strains are homogeneous in the center of the sample and significantly decrease close to the clamping zones (Figure 1c). The strain fields in both front and side surfaces are obtained from a region of interest (ROI) in the central part of the sample. The true stress is defined as the ratio between the applied force F and the specimen cross section:

𝜎 𝑇 = 𝐹 𝐿 0 𝑒 0 λ 2 λ 3 (1)
where L 0 is the initial length and e 0 the initial width. The volumetric strain ∆V/V 0 is defined as:

∆𝑉/𝑉 0 = λ 1 λ 2 λ 3 -1 (2)
For some tests performed at the highest stretching ratios, strain field in the thickness of the sample can be difficult to extract, due to strong reduction of thickness and too few pixels to be analysed. However, we found that the relationship ε 3 =1.1ε 2 between transverse deformations remains constant during the specimen axial deformation. Such weak transversal anisotropy is expected from processing conditions (calendaring), and consistent with previous observations. [START_REF] De Crevoisier | Volume changes in a filled elastomer studied via digital image correlation[END_REF] Volumetric strain can then be deduced for the highest stretching ratios assuming such relation being verified.

Trace of self-heating generated in the sample is recorded on its surface during the deformation using FLIR SC5000 camera. Temperature field is analysed on the front face of the specimen with ALTAIR software in the same ROI than for DIC analysis. Rubber samples stretched at different maximum strains are then stored after unloading at room temperature before performing ex situ swelling and thermoporosimetry.

Swelling

Swelling experiments using cyclohexane as a solvent are performed to determine the network chains density of the undeformed and mechanically tested EPDM specimens. Each sample is immersed in solvent for 72 h and the solvent is changed every 24 h. After 72 h the swollen mass of each sample (𝑚𝑠) is measured. Then, the samples are placed in an oven under vacuum at 70°C during 6 h to remove the solvent. The mass of the dry samples (𝑚𝑑) are then measured. The swelling ratio of the specimen Q is calculated as follows:

𝑄 = 𝑚 𝑠 -𝑚 𝑑 𝜌 𝑠𝑜𝑙𝑣 𝑚 𝑠 -𝑚 𝑑 𝜌 𝑠𝑜𝑙𝑣 + 𝑚 𝑑 𝜌 (3)
With ρ solv =0.778g.cm -3 is the density of the solvent and ρ the density of dry rubber specimen after de-swelling under vacuum. Like for DIC volumetric strain, volumetric strain for swelling experiments ∆Q/Q 0 is defined as:

∆𝑄(λ) 𝑄 0 = 𝑄(λ) -𝑄 0 𝑄 0 (4)
with 𝑄(λ) denotes the swelling ratio of a specimen mechanically tested up to λ and 𝑄 0 = 𝑄(λ = 1) the swelling ratio of a virgin specimen (undeformed). For filled compounds the Kraus correction [START_REF] Kraus | Swelling of filler-reinforced vulcanizates[END_REF] is used to account for the contribution of filler in swelling ratio. Q r is the swelling ratio of the rubber matrix defined as follows:

𝑄 𝑟 = 𝑄 -𝜑 1 -𝜑 (5)
with ϕ is the volume fraction of fillers calculated as:

𝜑 = 𝑚 𝑐 𝜌 𝑐 𝑚 𝑐 𝜌 𝑐 + 𝑚 𝑝𝑜𝑙 𝜌 𝑝𝑜𝑙 (6)
𝑚 c and ρc=1.87g.cm -3 are the dried mass and density of carbon black respectively. 𝑚 pol and ρ pol are the dried mass and density of polymer respectively measured after deswelling in vacuum.

Krauss correction in Equation 5assumes non-adhesion of the fillers to the rubbery matrix, hence creating vacuole. Such assumption is realistic in the frame of our study because swelling is performed on both virgin and mechanically tested specimen whose damage are partly ascribed to decohesion mechanisms, as will be discussed in the following. The average network chain density is then calculated from swelling experiments and the Flory-Rehner equation: 32

𝜐 = 𝑙𝑛(1 -𝑣 2 ) + 𝑣 2 + 𝜒 1 𝑣 2 2 𝑉 1 (-𝑣 2 1 3 + 2 𝑓 𝑣 2 ) (7)
With 𝑣 2 = 1/𝑄 𝑟 . V 1 =108 cm 3 /mol -1 is the molar volume of the solvent (cyclohexane), χ 1 is the Flory-Huggins polymer solvent dimensionless interaction term (χ 1 is equal to 0.353 for the EPDM-toluene system). The ratio 2/f is associated with the phantom model that assumes spatial fluctuation of crosslinks (non-affine) used for high deformation ratios. f, the crosslink functionality, is chosen equal to 4.

Thermoporosimetry

When crystallized, solvent molecules constrained to small volumes form relatively small crystallites and which therefore exhibit lower melting temperatures than the infinite crystal.

Practically, NR samples are put into a solvent (cyclohexane) during 72 h to reach the swelling equilibrium. They are then carefully extracted and put into an aluminium crucible. A Perkin Elmer Pyris diamond DSC is used. First, the sample is cooled down to -50°C at 10°C/min followed by an isothermal step at -50°C during 2 min. The sample is then heated at 10°C.min -1 up to 30°C. When temperature increases, the first peaks (or series of peaks) that appear corresponds to the melting of the cyclohexane entrapped in the network. The last peak (around 10°C) corresponds to the melting point of free cyclohexane (i.e. in excess). Melting peaks are deconvoluted by use of asymmetric Lorentzian functions (Figure S4a). After removal of free solvent melting peak (Figure S4b), the intensity is normalized by the swollen weight. The procedure is described in reference [START_REF] Candau | Strain-Induced Crystallization of Natural Rubber and Cross-Link Densities Heterogeneities[END_REF] . Based on Gibbs-Thompson equation, the pore size L is related to the melting temperature T m by:

𝑇 𝑚 °-𝑇𝑚 = 2𝜎 𝑆𝐿 𝑇 𝑚 °𝐿𝛥𝐻 𝑓 𝑓 (8)
With 𝜎 𝑆𝐿 is the solid-liquid surface energy, 𝑇 𝑚 ° is the melting temperature of the free solvent and 𝛥𝐻 𝑓 = 6.3 𝐽. 𝑔 -1 is the melting enthalpy of the solvent. The normalized pore size is given by:

𝐿 𝐿 𝑓 = 𝑇 𝑚 0 -𝑇 𝑓 𝑇 𝑚 0 -𝑇 (9)
With T f and L f correspond to the melting temperature and the size of the largest pores entrapped in the network respectively. It should be noted that the absolute value of L f is not accessible from thermoporosimetry. Hence in the following, the normalized pore size L/L f , instead the absolute pore size L, will be employed to discuss on the effect of both crosslink density and stretching ratio on pores size. After derivation of equation 9, the normalized intensity distribution of the pore size is given by:

𝐼 𝑛 = 1 𝑚 𝑑𝐻 𝑑𝑇 �𝑇 𝑚 0 -𝑇� 2 𝐿 𝑓 (10)
L f value being unknown, the intensity I=L f I n is hence plotted instead I n to account for the pore size distribution. An example of the plot I=f(L/L f ) is provided in Figure S4c. The average normalized pore size is then calculated as the L/L f value associated with half of the area under the normalized signal (denoted by the vertical line in Figure S4c).

Scanning electron microscopy (SEM)

Fractured surfaces of specimens subjected to tensile test were analysed by a Carl Zeiss AG SUPRA 40 electron scanning microscope. Electrons are collected by in-lens detector. A working distance of 5 mm and an acceleration voltage is 3keV are used. Samples are coated with carbon to avoid charging. Working distance of 9.9 mm is used for EDX analysis and the determination of the chemical composition.

Results and discussion

Macroscopic damage via strain-induced thermal and volume changes

Thermomechanical characterization of unvulcanized and vulcanized filled rubbers subjected to mechanical cycles up to various stretching ratios, λ, and at high strain rate (1 s -1 ) has been performed (Figure 2 and Supplementary Figures S1-S3). Stress-stretching ratio loadingunloading curves exhibit classical mechanical hysteresis (Figure 2a, Supplementary Figures S1a-S3a). Evidence for energy dissipation exists but strain appears to be mostly geometrically reversible. Such energy is converted into heat. Figures 2b and Supplementary Figures S1b-S3b display the evolution of self-heating with the stretching ratio. Self-heating, ∆T, gradually increases on the sample surface during loading and decreases during unloading with positive hysteresis. A negative loop is observed in all EPDM for λ>4.

These dissipative mechanisms can find several origins. First, it should be noted that the contribution of crystal plasticity to dissipative mechanisms is negligible due to the weak crystalline fraction (less than 3% wt.) and strain-induced crystallization is unlikely due to paraffin oil that impedes molecular ordering, as shown in polyisoprene [START_REF] Ren | Effects of plasticizers on the strain-induced crystallization and mechanical properties of natural rubber and synthetic polyisoprene[END_REF] and cis-1,4 polybutadiene [START_REF] Mark | The effect of strain-induced crystallization on the ultimate properties of an elastomeric polymer network[END_REF] . Dissipative mechanisms are hence rather ascribed to a high viscosity owing the presence of fillers [START_REF] Ramier | Mechanical behaviour of filled elastomers, the influence of filler adhesion to polymer and the influence of morphology[END_REF][START_REF] Kost | Resistivity behavior of carbon-black-filled silicone rubber in cyclic loading experiments[END_REF] as well as the damage associated with voiding. [START_REF] Samaca Martinez | Filler effects on the thermomechanical response of stretched rubbers[END_REF] Damage can occur due to strain amplification and stress concentration in the vicinity of fillers and filled rubbers generally exhibit large amount of voids. [START_REF] Le Cam | Cyclic volume changes in rubber[END_REF][START_REF] Le Cam | Mechanism of fatigue crack growth in carbon black filled natural rubber[END_REF] Digital Image Correlation (DIC) is used to measure volumetric strain that characterizes voiding volume fraction depending on applied deformation (Figure 2c, Figures S1c-S3c). Below λ =1.5, the absence of volumetric strain attests for rubber incompressibility in the elastic regime (ν = 0.499). [START_REF] Omnès | Effective properties of carbon black filled natural rubber: Experiments and modeling[END_REF] However, above λ =1.5, volumetric strain significantly increases as a function of stretching ratio, proving nonisochoric deformation. For λ <3, increase in volumetric strain could be reversible, though not elastic. For λ >3, volumetric strain is not recovered within the duration of test. This suggests the appearance of irreversible deformation mechanisms is likely associated with voids, which could not be closed upon unloading. Studying the relationship between mechanical energy and self-heating is required to identify viscous and damage contributions to dissipative mechanisms (Figure 3). Thermomechanical coupling describes reversible and irreversible deformation processes. The integration of reversible mechanisms to time over one cycle is zero. If adiabatic conditions prevail, as in the case of high-strain rate loading, and the thermo-elastic coupling is neglected, the heat equation integrated with time can be written as:

𝜌𝐶 𝑝 ∆𝑇 = 𝐸 𝑑𝑖𝑠𝑠 = 𝐸 1 + 𝐸 2 (11)
where C p , is the heat capacity (J.g -1 °C-1 ) and ρ is the bulk density (g.cm -3 ) of EPDM materials.

E diss is the energy dissipated over a cycle, measured as the difference of area under the loading and unloading curves. E 1 and E 2 are the heat production due to mechanical irreversibility, bulk viscosity and damage respectively. E diss and ∆T both increase with stretching ratio and network chains density (Figure 3a-b). In a certain energy range (from 0 to 15 MJ.m -3 ), relationship between ∆T and E diss follows a unique curve regardless of the network chains density,ν (Figure 3c). Assuming similar C p , and ρ for all tested materials, this means that the same quantity of mechanical energy is transferred into heat, and that respective contributions of viscosity and damage to dissipation do not depend on the network chains density for this energy range. For a higher energy range (above 15 MJ.m -3 ), slight upturns of self-heating are observed for the vulcanized EPDM (Figure 3c). This attests for a predominance of one of the two main contributions to heat dissipation, which is accelerated with increased network chains density.

This contribution should be damage because of higher stress concentration in the rubbery matrix due to higher density of sulphur-bonds and trapped entanglements. Contrarily, such upturn is prevented in the unvulcanized EPDM which can accommodate the stress up to very large deformation owing strong viscosity contribution to mechanical dissipation, via disentanglement or filler network deformation. Dissipated energy is calculated from the area under the curve of the cyclic tests (Figure 2a, Supplementary Figures S1a-S3a).

Relationship between damage mechanisms and network chains density,ν, is investigated by comparing volumetric strain behaviour for all EPDM. True stress, volumetric strain, tangent modulus and volumetric strain rate are plotted in Figure 4. Expectedly, tensile strength increases with ν (Figure 4a), obtained by increasing curing temperature: no vulcanization (EPDM-0), vulcanization at 140°C (EPDM-1) and vulcanization at 170°C (EPDM-2). However, tensile strength levels off for the rubber with the highest crosslink density (EPDM-3). This can be explained by polysulfidic bonds, that favour chains mobility yielding higher tensile strength, [START_REF] Hertz | Theory & Practice Of Vulcanization[END_REF] predominant at low curing times (EPDM-1 and EPDM-2) but which transform into mono and disulfidic bonds [START_REF] Dijkhuis | The relationship between crosslink system, network structure and material properties of carbon black reinforced EPDM[END_REF] with increasing curing time (EPDM-3) yielding in decreased tensile strength.

The tangent modulus provides an estimate of stiffness at a given stretching ratio (Figure 4b). It first decreases with stretching ratio which is consistent with Gaussian behaviour, 𝜎 = 𝐸/3 (𝜆 -1/𝜆 2 ), E being the elastic modulus. At an inflexion point around λ=1.5, experimental trend deviates from the Gaussian theory. The stretching ratio at inflexion point can be interpreted as the macroscopic stretching ratio associated with the limit extensibility of the shortest chains that contribute to the elastically active network. [START_REF] Kucherskii | New characteristic of tensile stress-strain properties in rubbers[END_REF] This stretching ratio being close for all materials, similar length of the shortest chains between bonds of the network is expected. While swelling provides an average value of chains length, network heterogeneities are expected in sulphurcured filled EPDM due to numerous macromolecular interactions, [START_REF] Valentin | Inhomogeneities and Chain Dynamics in Diene Rubbers Vulcanized with Different Cure Systems †[END_REF][START_REF] Litvinov | Rubber-Filler Interactions and Network Structure in Relation to Stress-Strain Behavior of Vulcanized, Carbon Black Filled EPDM[END_REF] justifying a certain distribution of chains length as also shown in our materials by thermoporosimetry experiments (see section 2.4, Figure 10 and Supplementary Figure S4). In the case of unvulcanized EPDM-0, the chains network elasticity is activated via trapped entanglements and rubber-filler interactions.

Volumetric strain onset (Figure 4d) is concomitant to stretching ratio at inflexion point (Figure 4b). Onset of volumetric strain is hence assumed to be associated with breakage of short chains domains due to their high level of stress concentration. Voiding onset occurs at early stage of deformation for unvulcanized EPDM-0. Due to the absence of moulding and curing step in hot-press, pre-existing stable micro-voids before mechanical testing is expected to favour void growth in that material.

Above the stretching ratio at inflexion point, volumetric strain increases faster with increased average network chains density (Figure 4c-d). Such trend is consistent with previous findings from the literature. [START_REF] Yannick | Effects of the amount of fillers and of the crosslink density on the mechanical behavior of carbon-black filled styrene butadiene rubbers[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] Increased volumetric strain up to failure traduces damage that involves domains containing longer and longer chains successively stretched up to breakage. Hence, as suggested above, contrarily to volumetric strain onset dominated by local short chains damage, damage at larger strains is more dominated by the alteration of the average network chains density (Table 1). One might note that the maximum volumetric strain is observed for the unvulcanized EPDM (EPDM-0) owing its ability to undergo large strain without macroscopic failure. Total void volume fraction in that material is even likely underestimated because voids that pre-exist to stretching are not counted in volumetric strain.

Strain to failure decreases by increasing the network chains density, ν. In the strain range preceding macroscopic failure of vulcanized EPDM, tangent modulus upturn indicates strain hardening (arrows in Figure 4b) while unvulcanized EPDM is subjected to strain softening.

These upturns are concomitant with volumetric strain rate upturns observed in vulcanized EPDM (arrows in Figure 4d) indicating a dramatic acceleration of damage. Such acceleration can partly explain previously observed heat upturns that occur at same deformation levels (Figure 3c). The permanent longitudinal and volumetric strain obtained after loading-unloading tests are presented in Figure 5. Fully reversible volumetric strain is observed for an applied stretching ratio λ <3 independently of the tested EPDM specimens (Figure 5a). For λ>3, volumetric strain becomes irreversible within the experimental time suggesting that voids remain open. The transition from reversible to irreversible voiding mechanisms is associated with a change in the slope of permanent longitudinal deformation at λ≈ 3 (Figure 5b) and can be explained by the contribution of deformed domains containing voids to the macroscopic longitudinal deformation.

The following section will provide an interpretation of such transition at network chains scale.

Damage at micro and molecular scale

Damage at micro and molecular scales are accessible via the observation of fractured surface (Figure 6) and solvent swelling behaviour (Figure 7-10). SEM images of fractured surface of mechanically tested specimen (EPDM-2) show fracture lines propagated in the rubbery matrix (Figure 6a). Observations at high magnitude reveal hundred nanometre sized carbon black fillers well dispersed in the rubbery matrix (Figure 6b). Fracture propagation lines are somewhat deviated by the fillers, that mostly remain attached to the rubber matrix while a few of them are debonded. Rigid micro-particles of ZnO and CaO (Figure 6a,c) are residual components resulting from the incomplete vulcanization. Micro-voids in the vicinity of these clusters can result from their decohesion to the rubbery matrix and have been suggested to be initiators of macroscopic failure in filled rubber when subjected to fatigue. [START_REF] Le Cam | Mechanism of fatigue crack growth in carbon black filled natural rubber[END_REF] Decohesion of fillers and rigid clusters partly contribute to voiding mechanisms quantified by volumetric strain (Figure 4c). Decohesion creates vacuoles surrounding rigid clusters or fillers which would then grow into larger voids.

Additionally, void nucleation is also expected to occur in the rubber matrix constrained between the filler aggregates due to high hydrostatic stress. [START_REF] Gent | Internal Rupture of Bonded Rubber Cylinders in Tension[END_REF] Regarding large voids fractions (Figure 4c), voiding does not remain localized at filler/rubber interface, but void growth should occur necessarily accompanied by alteration of chains network of the rubber matrix as discussed in the following. Increased DIC volumetric strain with applied deformation should translate voiding mechanisms at molecular and network chains scale. To assess this, the fraction of porosities at network chains scale is quantified by swelling (Figures 78) and DSC thermoporosimetry (Figures 910) performed on vulcanized materials mechanically tested up to different λ. Swelling ratio first slightly increases up to a critical value λ=3 for all vulcanized EPDM (Figure 7a). Above such critical value, slopes break-down indicates higher increase of Q traducing an overall increase of volume fraction of swollen areas in the specimens with applied deformation. The slopes change coincides with transition from reversible to irreversible voiding (Figure 5a). Q tends to level off for EPDM-1 and EPDM-3 and even decrease for EPDM-2 for the higher deformations. To further evaluate the relationship between DIC volumetric strain and swelling behaviour, we define a volumetric strain for swelling experiments, ∆Q/Q 0 , as defined in equation 4 in section 2.3, with Q the swelling ratio of a specimen that experiences mechanical testing and Q 0 the swelling ratio of un-tested material. ∆Q/Q 0 is plotted versus ∆V/V 0 obtained at various λ (unfilled data points, Figure 7b). ∆Q/Q 0 follows ∆V/V 0 regardless of the tested materials up to a value around 10%. For values of ∆V/V 0 higher than 10%, ∆Q/Q 0 reaches a threshold. Several sources of error can be identified when measuring swelling ratio on stretched specimen. First, decohesion between clusters and rubbery matrix (Figure 6c) can yield to an overestimate of rubber swelling due to creation of vacuoles at cluster interface. [START_REF] Valentín | Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber[END_REF] Regarding their low volume fraction, their impact on Q(λ) and ∆Q/Q 0 is negligible here. More important is the presence of voids in specimens stretched up to λ >3 (figure 5a) that are maintained when unloaded.

Assuming that solvent first fills these stable cavities but does not participate in rubber swelling, the corrected swelling that accounts for the presence of pre-existing voids is given by:

𝑄 𝑐𝑜𝑟𝑟 (λ) = 𝑄(λ) - ∆𝑉 𝑉 0 � 𝑟𝑒𝑠 1 - ∆𝑉 𝑉 0 � 𝑟𝑒𝑠 (12)
∆Q corr /Q 0 is then calculated with equation 4 (see section The network chains density ν(λ) shown in Figure 8a (unfilled data) is estimated from Q(λ) (Figure 7a) by using equations 3-7. ν progressively decreases and stabilizes or even increases in the case of EPDM-2. Using the previously described equivalence between DIC voiding and swollen pores, an estimate of ν(λ) via ∆V/V 0 obtained by DIC can be provided by substituting Q by V in equations 3-7 and assuming 𝑣 2 = 1/𝑉 𝑟 , with V r is the "dry" volume of rubber that contain porosities (instead of swollen volume for the calculation of Q r ) at a given deformation.

The obtained ν is found to regularly decrease with applied stretching ratio (Figure 8a, continuous trends) and well followsν estimated by swelling up to values indicated by arrows. For deformations above arrows, trends deviate because permanent voids are not considered in the calculation of ν by swelling. The correction proposed in eq. 10 is applied by using Q corr instead of Q and the corrected ν are plotted in Figure 8b (filled data) and found consistent with ν obtained by DIC (trend lines, Figure 8b).

From both approaches, namely DIC and swelling, network chains density, ν, is found to significantly decrease with applied deformation up to failure with a maximum relative decrease of -40%, -35% and -23% for EPDM-1, EPDM-2 and EPDM-3 respectively, consistent with void fraction of 24%, 17% and 11% for the same materials (Figure 4c).

In addition to loss of chemical and physical bonds at filler/rubber interface, large decrease in ν is necessarily accompanied by sulphur-bond breakage and/or chains scission in the rubbery matrix.

The entanglement density of EPDM being equal to 2-2.4.10 -4 mol.cm -3 , [START_REF] Litvinov | The Density of Chemical Crosslinks and Chain Entanglements in Unfilled EPDM Vulcanizates as Studied with Low Resolution, Solid State 1H NMR[END_REF] EPDM-2 and EPDM-3 are over-crosslinked. It means that their average network chains densities which comprise both chemical crosslinks and trapped entanglements mostly occurs by sulphur bond breakage. In specific case of EPDM-2, average network chains density decreases down to entanglement density, suggesting more entanglement breakage to be activated at large deformation for such material. Contrarily, EPDM-1 is under-crosslinked and damage of chains network is mostly associated with chain scission.

In conclusion, the chains network alteration upon stretching is accompanied by sulphur bond breakage and chain scission that induce the creation of reversible voids in the first stages of deformation (λ<3) and irreversible voids at higher deformation (λ>3). Such transition should be interpreted via more quantitative analysis of void size. with corrections (b). Calculations of ν are described in section 2.3 and corrections performed with the use of equ. 12. ν calculated by DIC volumetric strain is plotted with continuous lines. Arrows indicate deviation between swelling and DIC methods. Corrections to measure Qc orr using equation 12 can only be applied for specimen cyclically stretched, i.e. for which permanent volumetric strain is measured. Hence, such method is not applicable for specimen stretched up to failure (data at highest stretching ratios in figure 8a).

DSC thermoporosimetry is used to provide an analyse of the size of damaged domains independently of previously described swelling experiments. Such method is based on the principle that solvent molecules crystallized in a rubber matrix are constrained to small volumes and form only relatively small crystallites. Owing to a decrease of the chemical potential of solvent molecules in polymer solution [START_REF] Flory | Principles of Polymer Chemistry[END_REF] , they exhibit melting temperature depression.

Crystallized swollen EPDM previously stretched at different λ are heated to access the melting behaviour as shown in Figure 9. Heating of EPDM-2 and EPDM-3 specimens is characterized by three endothermic peaks: T m,1 and T m,2 due to trapped solvent and 𝑇 𝑚 0 = 10°𝐶 the melting temperature of infinite pores (free solvent). As expected, the melting temperature of trapped solvent decreases with average network chains density, i.e. from EPDM-1 to EPDM-3, as previously shown for a series of vulcanized Natural Rubber (NR). [START_REF] Candau | Complex dependence on the elastically active chains density of the strain induced crystallization of vulcanized natural rubbers, from low to high strain rate[END_REF] The two peak maxima of melting temperatures T m,1 and T m,2 slightly increase with applied stretching ratio, for EPDM-2, while only T m,2 is increased for EPDM-3. A single peak maximum of the melting temperature in EPDM-1 is observed below 𝑇 𝑚 0 , but rapidly merges with free solvent melting because pore sizes reach the size of free solvent crystals, hence not possible to deconvolute. More strikingly, the intensity of the peak maximum at T m,2 increases in detriment to the one of T m,1 in both EPDM-2 and EPDM-3 with increased stretching ratio. These observations suggest an increase of pore size with applied deformation. However, their quantitative interpretation requires a deconvolution of melting profiles as discussed in the following. DSC thermoporosimetry profiles in Figure 9 are translated into pore size distribution for EPDM-1, EPDM-2 and EPDM-3 via equations 9 and 10 detailed in section 2.4 (see also Supplementary Figure S4). The deduced normalized pore size L/L f shows large distribution (Figure 10), consistent with previous NMR observations of network heterogeneities in filled vulcanized EPDM. [START_REF] Valentin | Inhomogeneities and Chain Dynamics in Diene Rubbers Vulcanized with Different Cure Systems †[END_REF][START_REF] Litvinov | Rubber-Filler Interactions and Network Structure in Relation to Stress-Strain Behavior of Vulcanized, Carbon Black Filled EPDM[END_REF] Moreover, the higher the average network chain density, the smaller the pore size distribution.

This traduces a homogenization of the network chains density, occurring by crosslinking of largest pore domains while small pore domains remain unchanged. The latter observation confirms similitude of local network densities in domains made of shortest chains (right side of the curves in Figure 10) in all vulcanized EPDM samples while average network chain density obtained by swelling (Table 1) or thermoporosimetry (dotted lines in Figure 10) varies. The averaged L/L f is calculated for different specimens that have experienced loading at various stretching ratios (Figure 11a) and is found to follow different regimes: in the initial steps of deformation (λ<3) only weak pore size modification is observed. At higher deformation (λ>3), the pore size increases with λ. Such transition is concomitant to transition in rise of swelling ratio upon loading (Figure 7a), and with transition from reversible to irreversible volumetric strain (Figure 5a) that might indicate the large voiding size contributing to their irreversibility.

Finally, like for swelling experiments (Figure 7a and Figure 8a), the pore size levels off for the highest λ. This is due to the presence of pre-existing stable voids that are initially filled by the solvent without being swollen which underestimates the average values of pore size. Assuming equiaxial re-opening of cavities upon swelling, the characteristic distance of chains network r in the un-swollen state can be deduced from the pore size L through the relation:

𝐿 = 𝑄 1/3 𝑟 (13)
In vulcanized rubber, r is the root-mean-square end-to-end distance �〈𝑅 2 〉 between nodes of the chains network. Assuming Gaussian chains statistics for the calculation of r, it comes:

〈𝑅 2 〉 = 𝐶 ∞ 𝑛𝑙 2 (14)
with 𝐶 ∞ = 6.62 [START_REF] Richter | On the origins of entanglement constraints[END_REF] is the number of backbone bonds in one EPDM statistical segment, n is the average number of backbone bonds per monomer unit and l =2 Å is the average main-chain bond length. 𝑛 = 𝑀/𝑀 0 with 𝑀 = 𝜌/𝜈 and M 0 =35 g.mol -1 the weight-average molar mass of the network chains and of the monomer respectively. ρ =0.865 g.cm -3 is the bulk rubbery density and ν (mol.cm -3 ) is the network chains density (Table 1). The average distance between nodes of the chains network is then written:

𝑟 = � 𝐶 ∞ 𝜌 𝜈𝑀 0 � 1/2 𝑙 (15)
Calculated distances between nodes of the elastic network in the relaxed state are 4.2, 4.7 and 6.9 nm for EPDM-3, EPDM-2 and EPDM-1 respectively. From Eq. 11 and 13, the average swollen normalized pore size, deduced from the method proposed in section 2.4 and Figure S4, depends on the average crosslink density, following the relation:

𝐿 𝐿 𝑓 𝑄 -1/3 = 𝐾𝜈 -1/2 (16)
with K a constant equal to (𝐶 ∞ 𝜌/𝑀 0 ) 1/2 𝑙/𝐿 𝑓 . One might note that Gaussian approximation is used for developing Equation 16. Gaussian chains can be disturbed by the non-deformable filler particles dispersed in the elastomer matrix. [START_REF] Heinrich | Reinforcement of elastomers[END_REF] Here, assuming equiaxial reopening of the cavities upon swelling, Equation 2 adapted to swelling gives ∆𝑄/𝑄 0 = 𝜆 3 -1. Hence, the maximum value of Q r = 3.6 (Figure 7a) corresponds to λ = 1.66, which is close to λ range of Gaussian behaviour [1;1.5] as discussed in Figure 4b, suggesting the Gaussian assumption to be adapted to describe L-ν relationship. Equation 16 fits experimental data, with slope K defined in equation 16, in the full strain range of stretched EPDM-1 and EPDM-2 (Figure 11b) and thus verifies the increased damage with stretching ratio to be associated with increased void size at network chains scale. To sum up, various deformation regimes corresponding to strain-induced damage mechanisms have been described for a series of carbon-black filled vulcanized/unvulcanized EPDM and related to damage at network chains scale.

In the low strain regime (λ<3), materials undergo reversible damage mechanisms. It is accompanied by reversible volumetric strain (Figure 5a), low permanent longitudinal deformation (Figure 5b), weak variation in swelling ratio (Figure 7a) and slow rise of swollen pore size (Figure 10a). Conformational changes that occur upon deformation can be argued to partly explain reversible volumetric strain. However, in the swollen state, polymer solvent interaction strongly influences chains conformation and might partially suppress the remaining chains conformation induced by mechanical loading, especially given the high swelling ratio values (Figure 7a). Slight increased swelling fraction and pore size are hence more related to localized, small and reversible voids which contribute to a slight increase in volumetric strain in the low deformation regime. Such voiding might be reflected by the damage of elastic network, as shown by a slight decrease in the network chains density in the initial steps of deformation (Figure 8). At such low deformations, pores sizes remain in the range of undamaged crosslinks distances (4-6 nm, cf. comments below equation 15). The chains the creation of dangling chains.

Within the frame of the tube 51 reduced topological constraints and eased relaxation of dangling chains during unloading favour reversible closing small cavities via re-entanglement.

In higher strain regime irreversible damage is accompanied by permanent volumetric strain (Figure 5a), rise in permanent longitudinal deformation (Figure 5b), large increase of swelling ratio (Figure 7a) and large rise of pore size (Figure 10a). Plastic deformation in filled rubber might favour voiding stability. However, quite low absolute value of permanent deformation upon unloading especially for the series vulcanized EPDM samples (Figure 5b), suggests plasticity not being the major cause for permanent voiding. The asymmetrical shape of the volumetric strain curves and high hysteresis (Figure 2c, Figure 4c, Supplementary Figure S1c-S3c) suggest opening and closing cavities to kinetic mechanism which depends on experimental time. A void nucleus spontaneously grows up to a critical size upon stretching so that elastic strain energy is high enough to compensate newly created surface energy [START_REF] Fond | Cavitation criterion for rubber materials: A review of void-growth models[END_REF] and makes them thermally stable, even after the load release. [START_REF] Diani | Irreversible growth of a spherical cavity in rubber-like material: A fracture mechanics description[END_REF] Kinetics of closing cavities contrarily relates to a return to equilibrium state between existing surface tension and strain energy. Thermoporosimetry does not provide absolute values for pore sizes and only average pore sizes have been analysed for sake of simplicity. However, such unambiguous transition at λ=3 in pore size is expected to ease transition from reversible to irreversible voids occurring at same λ.

At higher deformations, λ >5, both swelling ratio (arrows in Figure 7a, Figure 8a) and pore size (arrows in Figure 10a) reach threshold values, that we ascribe to the predominance of irreversible large voids that do not contribute to swelling behaviour. For surface energy of about 0.03 J/m 2 and for cavities of 100 nm, the effect of surface tension is negligible. [START_REF] Fond | Cavitation criterion for rubber materials: A review of void-growth models[END_REF] This size corresponds to the range of filler particles size observed by SEM (Figure 6b). Hence, such particle decohesion would yield in stable voiding. We thus suggest that, for λ >5, additionally to voiding occurring in the rubber matrix constrained between filler aggregates, damage is also expected to be accelerated by the nucleation of large cavity sites initiated by the decohesion of rigid filler and cluster that grow into the rubber matrix before yielding to macroscopic failure.

Conclusion

Due to strain amplification in rubber matrix and stress localization at filler/rubber and filler/cluster interfaces, vulcanized filled rubbers exhibit significant damage mechanisms when deformed up to failure, as shown in this paper on a series of EPDM samples. The observation of large voiding volume fraction however suggests such damage being not only localized at the interfaces but also to develop into the rubber matrix, necessarily accompanied by a significant modification of the rubber chains network. To account for this, we developed an experimental method to identify the relationship between damage classically observed at macro-scale and alteration of elastically active chains network. Voids fraction measured via Digital Image Correlation (DIC) and Flory-Rehner equation have been combined to estimate in situ, i.e. during mechanical testing, the modification of network chains density,ν. From this approach, two strain regimes have been identified: (i) at λ <3, reversible voiding is accompanied with slight decrease of ν and (ii) at λ >3 voiding becomes irreversible and ν significantly decrease with strain. We propose then, as revealed by ex situ thermoporosimetry, the transition from reversible to irreversible regime to be dominated by increased void sizes of rubber network domains ensuring their thermal stability. It could be of interest in future works to corroborate this by in situ measurements combining micro-computed tomography (µCT) and Small Angle X-Ray Scattering (SAXS) to access the full pore size distribution. We finally show that DIC can be easily used to monitor the progress of network chains damage during the uniaxial deformation of rubber systems. It could be profitable to generalize the understanding of molecular mechanisms at the origin of macroscopic damage in rubber systems, not only under single uniaxial tension, but in more industrially processes such as mechanical devulcanization, irradiation of electric cables, dynamic crack propagation in tires.

30

 30

Figure 1 .

 1 Figure 1. (a) Experimental thermomechanical set-up based on two independent stereo-vision systems to measure simultaneously strain fields on front and side surfaces of specimen and infra-red camera to measure temperature field on the front face of same specimen, (b) temperature field measured on the front face at various strains (white area indicates highest temperature), (c) longitudinal and transverse strain fields analysed on front and side faces of the specimen for a given macroscopic deformation.

Figure 2 .

 2 Figure 2. True stress (a), self-heating (b) and volumetric strain (c) during uniaxial cyclic test performed on EPDM-2 at room temperature and at the strain rate 1s -1 .

Figure 3 .

 3 Figure 3. (a) dissipated energy vs. stretching ratio, (b) self-heating accumulated at maximum strain during loading, λ,vs. stretching ratio, (c) self-heating vs. dissipated energy for EPDM-0, EPDM-1, EPDM-2 and EPDM-3.

Figure 4 .

 4 Figure 4. (a) True stress, (b) tangent modulus (calculated as the derivative of stress over strain) vs. stretching ratio, (c) volumetric strain vs. stretching ratio and (d) rate of volumetric strain (calculated as the derivative of volumetric strain over strain) vs. stretching ratio. Arrows indicate upturns related to slope changes of stress and volumetric strain.

Figure 5 .

 5 Figure 5. (a) Volumetric strain and (b) Stretching ratio measured right after unloading for EPDM-0, EPDM-1, EPDM-2 and EPDM-3 showing a transition from reversible to irreversible damage at λ=3 within the experimental time.

Figure 6 .

 6 Figure 6. (a),(b) SEM images of cross-section of fractured EPDM-2 sample, (c) SEM-EDX images on sample EPDM-2. In red are highlighted the principal zones showing cavities. Zinc, Calcium and Oxygen have been identified with EDX mapping in zones containing cavities.

2 . 3 )

 23 by substituting Q(λ) by Q corr (λ), (or permanent) volumetric strain provided in Figure 5a. Corrected values of volumetric strain ∆Q corr /Q 0 reasonably follow ∆V/V 0 . (filled data points, Figure 7b), showing DIC voids fraction and swollen pores fraction to comparably describe voiding mechanisms.

Figure 7 .

 7 Figure 7. (a) Swelling ratio measured on EPDM-1, EPDM-2 and EPDM-3, versus maximum stretching ratio that specimens have undergone during mechanical testing, (b) relative swelling ratio calculated from figure 7a versus relative volumetric strain estimated from DIC for EPDM-1, EPDM-2 and EPDM-3. The continuous line is a plot of ∆Q/Q 0 =∆V/V 0 . Dotted line is a guide for the eyes and follows the experimental trend (unfilled data).

Figure 8 .

 8 Figure 8. Network chain density, ν, estimated by swelling (data points) versus stretching ratio for EPDM-1, EPDM-2 and EPDM-3 mechanically tested at different maximum strain, without residual volumetric strain correction (a),

Figure 9 .

 9 Figure 9. Heat flow versus temperature during heating for EPDM-1 (a), EPDM-2 (b) and EPDM-3 (c). Blue dotted lines represent the maximum peak intensity corresponding to melting of trapped solvent (T m,1 and T m,2 ) and red dotted lines show the free solvent melting peak.

Figure 10 .

 10 Figure10. Normalized intensity versus normalized pore size giving access to pore size distribution in undeformed EPDM-1, EPDM-2 and EPDM-3. The procedure and equations used are detailed in section 2.4 of the manuscript. Dotted lines show the average normalized pore size equal to 0.070, 0.055, 0.048 for EPDM-0, EPDM-1 and EPDM-2 respectively. The average normalized pore sizes obtained for EPDM-1 and EPDM-2 are reported on Figure11at the corresponding axis value λ=1.

Figure 11 .

 11 Figure 11. (a) Normalized average pore size deduced from the methodology detailed in Supplementary Figure S4 versus stretching ratio for EPDM-2 and EPDM-3. The series of thermoporosimetry experiments performed on EPDM-1 has too low network chain density so that associated pore sizes are in the range of pore sizes of the free solvent and melting peaks cannot be deconvoluted properly. (b) L/L f Q -1/3 versus ν -1/2 for EPDM-2 and EPDM-3. The dotted line is a regression fit y=Kx of experimental data with a slope K=0.0637 and R squared value of 0.898.

Table 1 .

 1 Recipes and network chain density, ν, of elastically active chains estimated from swelling measurements (in 10 -4 mol.cm -3 ). ν has not been measured in the case of EPDM-0 as it is transforms into a gel soluble in cyclohexane during swelling experiments.

	1.2phr of sulfur (75%), 1 phr of mercaptobenzothiazole (MBT 75%), 0.8% phr of
	mercaptobenzothiazole	disulfide	(MBTS	75%),	1.2	phr	of	N-cyclohexyl-2-
	benzothiazolesulfenamide (CBS 75%), 1.5 phr of zinc dialkyl dithiophosphate (ZDTP 70%). The
	rubbers are processed in an internal mixer. Sample sheets are then obtained by curing in a hot

press at high temperature. As shown in table 1, different curing conditions are used to obtain vulcanized rubbers with different network chain densities, ν. EPDM-1 and EPDM-3 have been cured at 140°C for 15 minutes and 255 minutes respectively so that the torque reaches 50% and 100% of maximum RPA. EPDM-2 has been cured at 170°C for 15 minutes so that the torque reaches 100% of maximum RPA. The ratio of accelerators over sulphur corresponds to efficient vulcanization system (EV), where the proportion of mono and disulfidic crosslinks is higher than for conventional vulcanization systems (CONV). Dumbbell-shaped samples, with a 15 mm gauge length (L 0 ), 6 mm thickness and 10 mm width, are then machined for mechanical testing.

Acknowledgements

The authors are indebted to the company SACRED for providing and processing of the rubber gum and to the laboratory GEPEA of the University of Nantes for the detailed set up of the curing procedure of rubber materials. This work was performed within the framework of the project ECOTHER supported by BPiFrance.


Cécile Faure
email: cecilefaure2203@gmail.com

Olivier Hue
email: olivier.hue@univ-ag.fr

Stéphane Henri
email: stephanehenri7@hotmail.com

Dr Sophie Antoine -Jonville

Ambient temperature-related exaggerated post-prandial insulin response in a young athlete: a case report

Keywords: environment, heat, diabetes, case study, exercise training

and implications for climate change

Odd post-prandial insulin response in a young athlete: a case report INTRODUCTION

Insulin resistance is a metabolic condition known to be associated with diabetes and its macro-and microvascular complications. Although exact causes are not completely understood, experimental and epidemiological evidence incriminates excess weight and physical inactivity as major contributors to insulin resistance development. [START_REF] Roberts | Metabolic syndrome and insulin resistance: underlying causes and modification by exercise training[END_REF] Here we divulge the unexpected case of a fit middle-distance runner considered as healthy who presented nonphysiological insulinemia.

CASE REPORT

An athlete who had been included in one of our nutrition studies presented exaggerated post-prandial insulin response (1162pmol/l; electrochemiluminescence immunoassay method; sample double-checked) during his participation in a protocol research in nutrition with published results. [START_REF] Faure | Impaired glucose tolerance after brief heat exposure: a randomized crossover study in healthy young men[END_REF] Plasma glucose remained normal (6.6mmol/l). After approximately 10 hours of fasting, he arrived at 6.45AM at the lab deliberately heated (30.3°C) for the purpose of the experiment. He had to rest down in a semi-recumbent position during 90 minutes. Then, he sat 30 minutes alone in a non-stimulating environment for an ad libitum meal of small ham and cheese sandwiches (799kcal, 25.7% proteins, 33.2% carbohydrates, 41.0% lipids), widely appreciated in Guadeloupe. He finished his meal within 20 minutes. The food was proposed in abundant quantity, on a plate weighted before and after the meal, the participant being unaware of the fact that food intake was a study outcome.

The water intake during the meal was 275mL (4ml/kg). He had blood sampling at different time points of the session before the meal, and 35 minutes after starting the meal.

The patient is a healthy 21-yr-old Afro-Caribbean middle-distance runner (800m-1500m) performing at the regional level. He is 1.84m tall, 68.8kg body mass and 9.5% body fat mass (Multi-frequency bioelectrical impedance analysis: InBody S10®, Biospace Inc, Japan). He had met all eligibility criteria of the study: absence of identified chronic or acute pathology, any other limitation to exercise, absence of any food allergy or eating disorder (normal score at the three-factor eating questionnaire), acclimation to tropical climate, regular physical activity (3650METs/min/week), normal birth weight, <2kg body mass variation in the previous 6 months. For the purpose of the study, he underwent a cardiopulmonary exercise test and a general dietary investigation. He had been training regularly and his maximal oxygen uptake is normal (52.3mlO 2 /min/kg, 108.3% of the predicted maximal in sedentary) with excellent endurance objectivized by the ventilatory threshold (67.3% of the maximal oxygen uptake). His dietary pattern is characterized by a daily intake of processed energy-dense food high in fat and low in fiber, and large amounts of carbohydratesin particular with a high glycemic index.

Further biological and clinical explorations were performed. All values for blood pressure, fasting glucose, insulin, lipid profile, lactate, CRPus, cortisol, IL6, glucagon, leptin, ghrelin, CCK, PP, body water distribution were normal. There was no evidence of acanthosis nigricans nor any hepatic or thyroid disease. The athlete reported no episode of hypo or hyperglycemia. He denied doping and was not aware of direct ascendant with diabetes. Other markers and determinants of insulin and glucose metabolism and function such as serum cpeptide or HbA1c were not evaluated and the athlete was not interested in undergoing an oral glucose tolerance test to further investigate potential metabolic disturbance. However, he was re-interviewed 2 years later and declared good health and performance status.

Interestingly, a few weeks after the occurrence of the odd post-prandial response, the athlete performed the same session with 21.0°C ambient temperature (similar time pattern, similar food intake for the last meal of the day preceding the test). His post-prandial response was completely normal in terms of insulin (416pmol/l) and blood glucose (5.5mmol/l), despite the ingestion of a larger quantity of sandwiches (1182 kcal) during the meal.

DISCUSSION

Fitness and leanness are considered as protective against insulin resistance. Here is described a counterexample, in which post-prandial insulinemia is not physiological in a young well-trained athlete with low percent body fat.

None of the criteria used to define the metabolic syndrome were met, whatever the chosen definition. [START_REF] Parikh | Changing definitions of metabolic syndrome[END_REF] In this patient, the exaggerated post-prandial insulin response does not occur concomitantly with isolated hypoglycemia. Hypoglycemia is listed in the differential diagnosis of most insulin-secreting islet cell tumors and other pathological conditions leading to hyperinsulinism. Acute and chronic diseases that affect the pancreas, liver, kidneys, thyroid and adrenal glands would be compatible with transient exaggerated post-prandial insulinemia. In particular, insulinoma and other endocrinopathies could be suspected.

However, none of the conditions to consider their diagnosis was present given the convergence of normal values for the biomarkers and the absence of symptom. For example, fasting glycaemia and insulinemia was measured at rest 12 times on 4 separate days. Only physiological values were observed (minimum and maximum were 3.7 and 4.6 mml/l and 34 and 179pmol/l for glucose and insulin, respectively). Based on available data and on the absence of development of later observable disease, our interpretation is to discard underlying pathology. We are not aware of any bias that would explain the observation. Subsequently, environmental temperature is the only identified factor likely to contribute to the abnormal profile described here. Increased glycaemia and/or insulinemia, specifically in ambient temperature above 25°C have been previously reported in healthy subjects [START_REF] Dumke | The effect of environmental temperature on glucose and insulin after an oral glucose tolerance test in healthy young men[END_REF][START_REF] Akanji | Oral glucose tolerance and ambient temperature in non-diabetic subjects[END_REF] and pregnant women. [START_REF] Schmidt | Iochida LC Variation in glucose tolerance with ambient temperature[END_REF] Also, this athlete participed in a study which evidenced higher postprandial glucose and insulin levels with heat exposure. [START_REF] Faure | Impaired glucose tolerance after brief heat exposure: a randomized crossover study in healthy young men[END_REF] Although he was the only one to present a quasi-pathological insulin response in the session performed in a warm environment, the increase in insulin and glucose was observed in most subjects. In the same study but with another group of participants performing a standard glucose tolerance test, the glucose load elicited an exaggerated increase in blood glucose in a warm environment. We therefore suggest that this case is an additional piece of evidence supporting that a warm environment is likely to impair glucose metabolism. This point is of potentially wide clinical relevancy since it could contribute to explain the diabetes burden in warm regions like India or the Pacific islands, where the overprevalence of metabolic pathologies is mostly attributed to genetic factors, jointly with poor diet and physical activity behaviors. Also, if confirmed, this phenomenon calls for better standardization of environmental temperature to improve the accuracy of the analyses of glucose tolerance. It furthermore has to be considered in the context of climate change that has been conceptualized as a risk multiplier as well as a trigger of primary effects on global health. [START_REF] Butler | Climate change and global health: a new conceptual framework -Mini Review[END_REF] Disturbance of glucose metabolism is a putative additional piece in the burden of disease of climate change.

In conclusion, in light of the present case, fitness and leanness appears as not systematically protective against acquired glucose metabolism impairment. The eventuality that high ambient temperature contributes to transient or even chronic glucose intolerance and/or insulin resistance deserves to be seriously explored.

  FIGURE LEGENDS

ACKNOWLEDGEMENTS: This case study was made possible by the recruitment and data collection from a project supported by grants from the European Social Fund (European Commission), Region Guadeloupe (No CR/12-116), the French Ministry of Overseas Territories (No 0123-C001-D971/2013) and from the European Regional Development Fund (PO No 1/1.4/-31793).

We warmly thank Chiraz Agrebi for her excellent revision.