# Thermomechanical characterization of the basic fatigue mechanisms at the inclusions' scale

Yann Marco, Isaure Masquelier, Vincent Le Saux, Bertrand Huneau, Philippe Heuillet, Pierre Charrier

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## To cite this version:

Yann Marco, Isaure Masquelier, Vincent Le Saux, Bertrand Huneau, Philippe Heuillet, et al. Thermomechanical characterization of the basic fatigue mechanisms at the inclusions' scale. Ninth European Conference on Constitutive Models for Rubber (ECCMR 2015), 2015, Prague, Czech Republic. pp.395-402, 10.1201/b18701-69. hal-05262810

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Submitted on 16 Sep 2025

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# Thermomechanical characterization of the basic fatigue mechanisms at the inclusions' scale

Y. Marco, I. Masquelier & V. Le Saux

ENSTA Bretagne—Laboratoire Brestois de Mécanique et des Systèmes, Brest, France

B. Huneau

Ecole Centrale de Nantes, Institut de Recherche en Génie Civil et Mécanique (GeM),
UMR CNRS 6183, Nantes, France

P. Heuillet

LRCCP, Vitry-sur-Seine, France

P. Charrier

Trelleborg Vibracoustic, Nantes, France

**ABSTRACT:** Because of the heterogeneous nature of these filled materials, the fatigue properties of elastomers are strongly connected to their microstructure. The goal of this study is to characterize the fatigue damage scenario at the inclusions' scale. In a companion paper (Huneau *et al.*, 2015) SEM tech-niques were applied to describe the early stages of initiation. Nevertheless, this description remains geo-metric and provides no local mechanical data. To overcome this limitation, thermal measurements at the microstructure scale are achieved and a specific protocol is applied to infer the dissipation fields from the temperature measurements. Formerly developed on a classical structural sample, this approach is applied to samples with well mastered typical flaws at the microscopic scale and then to samples exhibit-ing isolated carbon blacks agglomerates. The experimental results obtained are finally correlated to SEM observations, providing a precious database for the understanding and a quantitative evaluation of the initiation mechanisms induced by inclusions.

## 1 INTRODUCTION

The fatigue properties of elastomeric parts against fatigue are strongly related to the microstructure features because these reinforced materials are heterogeneous. The industrial development of materials resistant to fatigue is therefore very complex because the variable parameters are incredibly numerous, including the original ingredients and the processing parameters, from mixing to injection and curing. The understanding of the fatigue behaviour requires both the description of the thermo-mechanical response and of the microstructure. De-spite very interesting data, these approaches are usually considered separately, with accurate description of the microstructure and of the initiation sites' morphology on the one hand (Gent and Park 1984, Le Cam et al. 2013, Le Saux et al. 2011, Legorju-Jago 2012, Huneau et al. 2013) and of the thermo-mechanical response on the other hand (Mars 2001, Saintier et al. 2006, Le Saux et al. 2010, Marco et al. 2013). Some recent studies tried to

relate thermal measurements and micro-tomography analysis to characterize the fatigue properties of elastomeric materials (Le Saux et al. 2010, Marco et al. 2013) from an average point of view. But the links between the macroscopic mechanical criterion and the local failure mechanisms are still missing because the main failure mechanisms identified in the literature (Gent and Park 1984, Le Saux et al. 2011, Masquelier 2014) are only described from a geometric point of view.

The aim of this study is to improve the description of the fields of dissipated energy at low scales thanks to temperature measurements. A specific experimental set up and a dedicated protocol to characterize the local dissipation gradients have been developed and formerly validated on structural samples at the macro-scale (Marco et al. 2014, Masquelier et al. 2015). Here, this protocol is firstly applied at the microscopic scale on two specific geometric defects (a hole and a rigid area). Then the protocol is applied to describe the dissipation fields and the failure mechanisms for the three
typical microstructural cases, i.e. break of the inclusion, cavitation between two close inclusions and interface failure at the poles of the inclusion. Filled NR and SBR materials are considered.

# 2 EXPERIMENTAL SETTINGS

## 2.1 Materials and samples

The materials used in this study are NR and SBR compounds filled with respective amounts of 20 and 43 phr of carbon blacks. More data on the recipes can be found in Masquelier (2014).

The experiments are achieved on very thin samples (0.2 mm of thickness), in order to spot the inclusions more easily and to get a consistent information on the thermal sources in the bulk from surface measurements. The dimensions of the samples are given on Figure 1 and the geometry is centred on the defect studied.

## 2.2 Experimental devices

All tests are achieved on a Bose electro-dynamical testing machine equipped with a 3.2 kN cell force and are displacement controlled. The thermal acquisition is performed thanks to a FLIR SC7600-BB infrared camera with a lens so-called “G1” with an analyzed zone identical to the Focal Plane Array detector, 7 mm*5 mm here). The spatial resolution is then of 15 µm.

In order to improve the thermal resolution a specific pixel-wise calibration including temperature dependency is used here. The calibration is performed thanks to a HGH DCN1000 N4 extended black body (emissivity of 0.98±0.02 and thermal stability ±0.02°C). The digital level of each pixel of the FPA is converted into temperature using its own function:

$$T(i,j) = \sum_{n=0}^{4} \left\{ \sum_{m=0}^{2} a_{n,m}(i,j) \cdot \left[ T_{cam} - T_{cam}^{0} \right]^{m} \right\} DL(i,j)^{n} \quad (1)$$

where $T_{cam}$ is the actual internal temperature of the camera, $T_{cam}^{0}$ is a reference internal temperature set

<figure><img src="image_3.png" /><figcaption>Figure 1. Global geometry of the samples.</figcaption></figure>

to 30°C, $a_{n,m}$ are the coefficients of the polynome. A bad pixel detection is then performed and its temperature is replaced by the value of one of its non-defective neighbours according to a specific research algorithm. After this specific calibration, a thermal resolution of about 10 mK is obtained for differential measurements.

## 2.3 Experimental protocol

The experimental protocol is illustrated on the Figure 3. After an accommodation stage to limit the Mullins effect, the sample is submitted to a sinusoidal loading between 0 and 12 mm (i.e. a max average strain of about 120% over the sample) and then kept at the maximal deformation during the cooling. A thermal acquisition using a rate of 100 images/s is performed during the loading step. This protocol is then followed by the same cyclic loading led to failure, with a lower thermal acquisition rate. A special attention was paid to the experimental conditions in order to limit as much as possible the influence of the environment on the measurement (see Fig. 2).

<figure><img src="image_4.png" /><figcaption>Figure 2. Experimental devices.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3. Mechanical protocol.</figcaption></figure>
## 3 ANALYSIS PROTOCOL

The evaluation of the thermal sources from the temperature measurements requires solving the heat equation (Lemaître & Chaboche 2004).

$$ \rho C \dot{T} + \text{div}(\bar{q}) = \Delta + r + C_T + C_E \quad (2) $$

where $\rho$ is the density, $C$ the specific heat, $T$ the temperature, $q$ the thermal flux, $\Delta$ the intrinsic dissipation, $r$ the contribution of external radiation, $C_T$ the couplings of the internal variables to the temperature and $C_E$ the thermo-elastic couplings. In our study, the temperature variations are considered to be small enough (under 3°C) to neglect the couplings of the internal variables to temperature.

Equation 2 therefore becomes:

$$ \rho C \dot{T} + \text{div}(\bar{q}) = \Delta + r + C_E \quad (3) $$

In recent papers (Marco et al. 2014, Masquelier et al. 2015) an experimental approach has been developed and validated. Only the main ideas are recalled here.

In order to neglect the diffusion, the principle is to consider two very close instants at the beginning of the cyclic loading (La Rosa & Risitano 2000) (Fig. 4). The characteristic time to reach the thermal equilibrium of our sample is evaluated from the cooling step to about 24 s. Considering two consecutive cycles at 10 Hz therefore leads to a ratio of 240 between the time considered to evaluate the temperature rate for two successive identical mechanical states and the characteristic thermal time. We therefore consider that the heat diffusion is negligible between the configurations considered and Equation 3 becomes:

$$ \rho C \dot{T} = \Delta + r + C_E \quad (4) $$

<figure><img src="image_6.png" /><figcaption>Figure 4. Protocol for dissipation mapping.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5. Example of dissipation mapping.</figcaption></figure>

As the evaluation is done over a mechanical cycle, the contributions of elastic coupling compensate. Finally, by considering the subtraction of the temperature $\theta$ and as the radiation contribution is assumed constant for two close instants, equation 4 writes:

$$ \rho C \dot{\theta} = \Delta \quad (5) $$

This equation can be used to evaluate the mean temperature over a given zone but the most interesting output is of course to use it to evaluate directly the field of the mean dissipated energy over a cycle, by direct subtraction of the thermal fields measured for configuration A and B (see Fig. 4). To ease the understanding, this is illustrated on Figure 5 for a sample with a hole (Masquelier et al. 2015).

If this protocol is quite obvious from a theoretical point of view, the difficulties come from the very low thermal and spatial resolutions needed to catch temperature variations within microscopic distances.

# 4 APPLICATION TO MICROSCOPIC GEOMETRIC FLAWS

## 4.1 Sample with a hole

### 4.1.1 Geometry

The protocol described previously is applied to a sample with a hole created with a pin. The diameter of the hole is about 300 µm.

### 4.1.2 Dissipation field

Figure 6 illustrates the subtraction of the temperature fields to obtain the dissipation fields. In order to illustrate better the resolution obtained on the energy gradient, the profile of dissipated energy along a given area (black rectangle) is plotted. The results obtained are fully consistent with the expected fields, with a maximum dissipation located at the equator of the hole and a minimum dissipation at the poles.
<figure><img src="image_8.png" /><figcaption>Figure 6. Temperature, dissipation fields and dissipation profile for the sample with a micro-hole.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 7. Temperature, dissipation fields and dissipation profile for the sample with a spot of glue.</figcaption></figure>

## 4.2 Sample with a spot of glue

### 4.2.1 Geometry

A sample with a hole was quite simple to obtain but this case is not representative of the most common failure case for inclusions, i.e. the initiation at the poles, induced by a strong interface between the inclusion and the matrix. To generate a testing case closer to this configuration, we had the idea to put a small spot of an epoxy-based glue on the surface of the film. The result turned out to be very good and generates a failure at one pole before the crack propagation. The diameter of the spot is 750 µm.

### 4.2.2 Dissipation field

The same protocol is applied to this sample and Figure 7 illustrates the temperature fields and the

field of dissipated energy. Here again, a profile along the vertical direction (black rectangle) is plotted in order to illustrate better the energy gradients.

The results obtained appear fully consistent with this mechanical case of a strong interface and strong cohesion of the spot surrounded by a flexible matrix. The areas of maximum dissipation are located at the poles, which is well correlated to the failure location observed.

# 5 APPLICATION TO INCLUSIONS

In this section, we consider several films obtained from “badly” mixed compounds, i.e. with bigger inclusions than the ones classically found for industrial applications. This allows for spotting them more easily and for keeping a relevant spatial resolution.

## 5.1 NR rubber with a big inclusion

### 5.1.1 Geometry

The sample considered was cut from a film of NR with 20 phr of carbon blacks, around a CB inclusion of 400 µm diameter. The nature of the inclusion was assessed by an EDS analysis. The geometry of the inclusion is given on Figure 8 and one can see that the geometry is not circular and present an irregular contour. The SEM observations are obtained on the already tested specimen (this is why a crack is visible), and observed for several elongations using a specific in situ tensile device (Beurrot et al. 2010).

### 5.1.2 Dissipation field

The analysis protocol is applied to this sample and Figure 9 illustrates the field of dissipated energy obtained.

The obtained dissipation fields are comparable to the ones measured with the artificial inclusion, with maximum dissipation at the poles of the inclusion and a low dissipation of the inclusion. This is pleading for both a strong cohesion of the inclusion and a good interface connection to the surrounding matrix. This is also consistent with the crack initiation classically observed at the poles.

<figure><img src="image_10.png" /><figcaption>Figure 8. SEM photo of the CB inclusion after testing.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 9. Dissipation fields for the NR sample with a CB inclusion.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 10. Evolution of the temperature fields around the inclusion.</figcaption></figure>

### 5.1.3 *Failure mechanism*

The sample was cycled 40 cycles until a crack was observed. This crack was expected to appear at one pole of the inclusion but actually, two hot spots appeared on the edges of the inclusion, leading in less than one cycle to the break of the inclusion and the creation of a hole (the dark zone on Fig. 10 on the right). The explanation comes from the shape of the inclusion (see Fig. 8), that exhibits an irregular contour with sharp radii near the initiation locations.

### 5.1.4 *Comparison to SEM measurements*

In order to correlate the thermal fields measured to the microstructure, a comparison is performed with SEM measurements performed while elongating the sample for the same displacement. Figure 11 shows the good correlation (even with the restriction to white and black figures here).

## 5.2 *Natural rubber with two close inclusions*

### 5.2.1 *Geometry*

The sample considered was cut from a film of NR with 20 phr of carbon blacks, around two CB inclusion of about 300 µm diameter with a space of 200 µm between them. This geometry was measured by optical microscope observations.

<figure><img src="image_13.png" /><figcaption>Figure 11. Comparison of SEM and thermal views.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 12. Dissipation fields obtained for two close inclusions.</figcaption></figure>

### 5.2.2 *Dissipation field*

Figure 12 shows the field of dissipated energy obtained. One can see on this figure two low dissipation areas standing for the inclusions response and an important dissipation zone located between the inclusions.

### 5.2.3 *Failure mechanism*

As the test goes by, the temperature rise is more and more intense between the inclusions, up to cycle 1340 where a cold spot appears, meaning that a crack was generated. This crack developed then progressively up to cycle 1692 where a sudden break of the sample occurred. Figure 13 illustrates the evolution of the temperature field.

## 5.3 *SBR with circular inclusion*

### 5.3.1 *Geometry*

The sample considered was cut from a film of SBR with 43 phr of carbon blacks, around a CB inclusion of 500 µm diameter. The nature of the inclusion was assessed by an EDS analysis. The geometry of the inclusion is given on Figure 14 and one can see that the geometry is almost circular and present a very regular contour. The SEM observations are obtained after the accommodation step tested specimen and exhibits two clear interface failures around the poles.
<figure><img src="image_15.png" /><figcaption>Figure 13. Evolution of the thermal fields before failure.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 14. SEM observation of the inclusion (SBR sample).</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Figure 15. Dissipation fields (SBR with a CB inclusion).</figcaption></figure>

### 5.3.2 Dissipation field

Figure 15 shows the field of dissipated energy obtained. It should be understood that these dissipation fields are obtained on the inclusion as shown on Figure 14, i.e. with voids already created at the poles, probably during the accommodation step. One can distinguish the low dissipation areas at the equator of the inclusion and the two holes at the poles. The maximum dissipation is observed for this case on the edges of the holes.

### 5.3.3 Failure mechanism

Figure 16 illustrates the evolution of the thermal fields around the inclusion. One can see that the

<figure><img src="image_18.png" /><figcaption>Figure 16. Evolution of the thermal fields before failure.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Figure 17. Comparison of SEM and thermal views.</figcaption></figure>

crack propagates around the interface between the inclusion and the matrix in the area where the maximum dissipated energy is visible on Figure 15. One can also observe on the last picture that the interface between the inclusion and the matrix is strong enough to keep the inclusion in contact despite an interface almost completely cracked.

### 5.3.4 Comparison to SEM measurements

Figure 17 shows the comparison between SEM measurements and the dissipated energy field for the same global elongation. One can observe that a very good correlation is obtained, here again.

## 6 CONCLUSION

The goal of this study was to provide an experimental way to deduce the dissipated energy field involved at the microstructure scale. A specific protocol was applied on very thin samples (0.2 mm of thickness) for artificial flaws and natural inclusions. The very low thermal and spatial resolutions (15 µm and 10 mK, respectively) allows for exhibiting very well resolved gradients at the inclusions scales. The comparison of the SEM to the fields of temperature and of dissipated energy, achieved on the same samples illustrates clearly the very strong interest of the technique to understand the basic dissipation and fatigue mechanisms at the microstructure scale.
## ACKNOWLEDGEMENT

The authors would like to thank the ANR for its financial support (ANR-2010-RMNP-010-01) and all the partners of the PROFEM project, TBVC, GeM, UBS and LRCCP.

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