cycles: Competition between strain rates and memory effect

La cristallisation sous tension (SIC) du caoutchouc naturel (NR) est étudiée lors de cycles dynamiques à hautes fréquences. La procédure expérimentale est identique à celle présentée dans le chapitre précédent : les échantillons sont prédéformés, laissés à relaxer pendant cinq minutes et sollicités dynamiquement. Lors du chapitre précédent, nous avions étudié la SIC uniquement au maximum de déformation pendant le cycle. Dans ce chapitre, grâce à un réglage de l’obturateur du système stroboscopique sur différentes positions, son évolution est maintenant suivie sur l’ensemble du cycle pour différentes configurations d’essais dynamiques.

Deux cas de figure peuvent être distingués suivant que les cycles sont réalisés en partie ou en totalité au dessus de la déformation de fusion λm. Dans le premier cas, lorsque la déformation imposée au minimum du cycle λmin est inférieure à λm, la SIC est peu développée. Inversement, pour les cycles où λmin est supérieure à λm, la cristallisation est favorisée grâce à un effet mémoire de l’orientation des chaînes cristallisables. En revanche, dans ces conditions, la fusion semble accélérée puisqu’elle intervient à une déformation plus élevée que la fusion ayant lieu lors d’un cycle en traction lente. Cette accélération est probablement liée aux temps d’essais dynamiques trop courts, ne permettant pas à la phase amorphe de relaxer la contrainte et donc de favoriser la stabilité des cristallites. Enfin, en comparant les cycles dynamiques réalisés à température ambiante et 50°C, il apparait que l’effet de la température sur la SIC s’atténue à haute vitesses de sollicitations, i.e. lorsque la cristallisation est forcée de s’opérer à grande déformation. Cette observation est confirmée par ailleurs grâce à des essais mécaniques en traction monotone. Ce résultat semble cohérent avec la thermodynamique de cristallisation. En effet, lorsque la cristallisation a lieu à grandes déformations, la nucléation est principalement contrôlée par l’énergie de déformation alors que la contribution d’origine enthalpique a un impact plus limité.

Chapitre 8. Strain induced crystallization of

natural rubber during dynamic cycles:

Competition between strain rate and memory

effect

Nicolas Candau

, Laurent Chazeau

, Jean-Marc Chenal

, Catherine

Gauthier

, José Ferreira

, Etienne Munch

, Dominique Thiaudière

Submitted to Polymer

aUniversité de Lyon, CNRS

bMATEIS, INSA-Lyon, CNRS UMR5510, F-69621, France

cManufacture Française des Pneumatiques Michelin, Centre de technologies, 63040 Clermont Ferrand Cedex 9, France

dInstitut Lumière Matière, UMR5306 CNRS, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France

d Synchrotron SOLEIL - Ligne de lumière DIFFABS, L'orme des merisiers, Saint Aubin, 91192 Gif sur Yvette, France

Table of Contents

Abstract ... 197

1. Introduction ... 197

2. Materials and experiments ... 198

2.1. Materials ... 198

2.2. Mechanical characterization ... 199

2.3. In situ WAXS measurements at slow strain rate ... 199

2.4. In situ WAXS measurements in dynamic conditions ... 200

3. Experimental results ... 201

3.1. Crystallite morphology and orientation ... 201

3.2. Crystalline cycles at high strain rates ... 202

4. Discussion ... 206

4.2. Temperature and strain rate influence ... 208 5. Conclusion ... 210 6. Acknowledgements ... 211 7. Appendix... 211 8. References ... 212

Abstract

Strain-induced crystallization (SIC) of natural rubber (NR) is studied during cycles (between λmin and λm) at high frequency thanks to a recently designed homemade machine. Two cases can be distinguished: the cycle can be performed partly (λmin < λm) or totally (λmin > λm) above the melting stretching ratio λm. In the second case, a memory effect due to the crystallites orientation is observed during the loading. However, by increasing the frequency, this memory effect is suppressed due to (i) nucleation delay and (ii) self-heating, which becomes high enough to sufficiently delay λm, so that λmin < λm. During unloading, the melting is accelerated during the dynamic cycle compared to the cyclic test at slow strain rate (10-3 s-1). A possible explanation is that the amorphous chains surrounding the crystallites have not sufficient time to relax and thus decrease the thermal stability of the crystallites. Finally, cycles performed at room temperature and 50°C are compared. It appears that the effect of temperature on SIC kinetics vanishes at high strain rates, i.e. when crystallization is forced to occur at high stretching ratio. This is explained by the fact that nucleation is mainly controlled by strain energy while the enthalpic contribution has a limited role.

1. Introduction

Strain Induced crystallization (SIC) of Natural Rubber (NR) is currently of great interest for both industrial and academic communities. The excellent properties of NR are thought to be the consequence of its ability to crystallize under strain. In particular, there are ongoing works to understand the crack growth and fatigue behavior of NR 1-5.

The SIC of NR was for the first time evidenced by Acken and Long 6, 7, only few years after the discovery of SIC in 1925 8. The characteristic time of this phenomenon is in the range of the characteristic times of the loading of the material in usual applications. The problem is that such rapid SIC kinetics remains difficult to characterize.

In literature, the strategy to study SIC has been often indirect, by the use of thermal 9-11 or mechanical measurements 12. Unfortunately, these techniques provide only partial information, as they do not give access to the crystalline microstructure. The progressing ability of WAXS detectors has then been used to capture more and more rapidly a diffraction pattern. In particular, recent in situ WAXS experiments using impact tensile test 13, 14 allowed evaluating SIC process on a sample rapidly stretched and relaxed in the deformed state. Even if it gives interesting results

concerning the very first stage of the SIC process, no measure can be performed during the deformation of the sample.

The stroboscopic approach can be used to solve this problem. It allows recording WAXS patterns by accumulation of the diffracted intensity thanks to a stroboscopic acquisition. The advantages of such a technique are first to avoid any averaging over an elongation domain (since a stroboscopic device selects the desired elongation level), secondly to enable in situ WAXS measurements in a frequency range never reached before. With this technique, the pioneering work of Kawai clearly evidenced that crystalline fraction measured during the dynamic cycles decreases when frequency increases from 0.1 Hz to 10 Hz 15. More recently, Albouy 16 used same approach but in a larger frequency range (from 0.01 Hz to 50 Hz) and evidenced the coexistence of both crystallization and melting kinetics which are found in the range of several decades of milliseconds. We also presented preliminary results and showed that SIC kinetics increases when stretching ratio increases 17. However, these studies only focused on the minimum and maximum stretching ratio reached during the dynamic cycle.

This paper is thus dedicated to the study of SIC during of a whole dynamic cycle at high frequency thanks to the improvement of our stroboscopic device. A complete analyze of the crystalline features such as the crystallinity index (CI), the size of the crystallites (Lhkl), their orientation (ψhkl) is proposed. Several loading and thermal conditions are explored with various pre-stretching values, dynamic amplitude and temperature. This last parameter is known to be a major one that control SIC in NR at relatively slow strain rate 12, 18, 19. Its effect on SIC at high strain rates is especially studied in a last section.

2. Materials and experiments

2.1. Materials

The samples composition is the following: NR rubber gum (Technically Specified Rubber TSR20) provided by Michelin Tire Company, stearic acid (2 phr, i.e. 2 g per 100 g of rubber), ZnO (1.5 phr), 6PPD (3 phr), CBS (1.9 phr) and sulfur (1.2 phr). The material has been processed following the Rauline patent 20. First, the gum is introduced in an internal mixer and sheared for 2 min at 60°C. Then, the vulcanization recipe is added and the mix is sheared for 5 min. The material is afterward sheared in an open mill for five minutes at 60°C. Sample sheets are then obtained by hot pressing at 170°C during 13 min. Dumbbell-shaped samples, with a 6 mm gauge length (l0) and 0.8 mm thickness, are machined. The number density of the elastically effective subchains (so-called hereafter average network chain density ν) was estimated from the swelling ratio in toluene and from the Flory – Rehner equation 21 and found equal to 1.4 × 10-4 mol.cm-3. This density is tuned so that (i) it promotes the development of strain-induced crystallization 22

and (ii) it is high enough to avoid an inverse yield effect 23. In order to avoid microstructure modification during the different mechanical tests, i.e. an uncontrolled Mullins effect, the samples are stretched four times up to stretching ratio (λ = 7) higher than the maximum stretching ratio reached during the in situ cyclic tests (λ = 6).

2.2. Mechanical characterization

The EPLEXOR® 500 N of Gabo Qualimeter society (Ahlden, Germany) is used in order to carry out mechanical characterization at different temperatures. Mechanical tests consist of a monotonic stretching at various strain rates, and from the relaxed state up to the maximum stretching ratio λ = 6. Before each tensile test, a soak time of five minutes guarantees that the desired temperature, obtained by air circulation, is homogeneous in the oven. For all the mechanical tests, the tensile force is converted into nominal stress σ = F/S0. Stress is then plotted as a function of the nominal stretching ratio λ = l/l0. λ is accurately measured tanks to a video extensometer.

When NR crystallizes, its stress strain curves exhibits a relaxation followed by a stress hardening. This is better visualized by plotting the tangent modulus Et, defined as the derivative dσ/dλ, as a function of λ. It has been widely shown in literature that the stretching ratio at the beginning of the mechanical relaxation gives a good estimate of the crystallization onset c 3, 12, 23-25. Hence λc will be estimated as the stretching ratio at which dEt/dλ is equal to zero.

2.3. In situ WAXS measurements at slow strain rate

The in situ WAXS experiments are carried out on the D2AM beamline of the European Synchrotron Radiation Facility (ESRF). The X-ray wavelength is 1.54 Å. Tests are performed in a temperature-controlled chamber, which enables to submit the samples to more or less complex thermo-mechanical history. The following tests are performed: (i) stretching at a constant strain rate (4.2 × 10-3 s-1) and heating in the deformed state, (ii) stretching after pre-heating (from room temperature to 80°C), (iii) thermal cooling in the deformed state after stretching at high temperature (above room temperature). Cooling rate is measured but not controlled. It can be roughly estimated equal to 2°C. min-1.

The two-dimensional (2D) WAXS patterns are recorded by a CCD camera (Princeton Instrument). The beam size is small enough (300 µm × 300 µm) to avoid superimposition with the scattered signal. The background, (i.e. air scattering and direct beam intensities) is properly measured in absence of any sample. It can then be subtracted to the total intensity scattered in the presence of the rubber sample. The corrected scattering intensity is finally normalized by the thickness and the absorption of the sample. Each scattering pattern is integrated azimuthally. The deconvolution of the curve I=f(2θ) enables the extraction of the intensity at the peak top and the width at half height of each crystalline peak and the intensity at the peak top of the amorphous phase. The crystallinity index CI is then determined as follows 26:

(1) where Ia0 and Iaλ are the intensity of the amorphous phase at the peak top in the unstretched state and the stretched state, respectively. The average crystallite sizes Lhkl (L200, L102 and L002) in the direction normal to the (hkl) planes, are estimated from the Scherrer equation:

(2) where λw is the wavelength and θ is the Bragg angle. In this study, each crystalline peak is fitted with a Lorentzian function in which the width at half-height is β1/2. According to the parameters chosen for the fit of the experimental peak, the K value is 0.64 27. In order to measure the average crystallite size in the stretching direction L002 (c1), the tensile test machine