Experimental and Numerical Study of the Mechanical Behaviour of an Unfilled Silicone Rubber

In this contribution, the mechanical behaviour of an unfilled silicone rubber was analysed. Firstly, tensile and pure shear tests were carried out on silicone plates. During the tests, full-field measurements of the strain on the surface of deformed samples were obtained using a Digital Image Correlation technique. Results show that Mullins effects, hysteresis as well as strain rate sensitivity can be considered as negligible. Consequently, three hyperelastic models were fitted with the experimental data (Mooney, Gent and Haines & Wilson models). Secondly, a plate silicone sample containing holes was deformed in tension. In parallel, Finite Element simulation of this experiment was performed with the fitted hyperelastic models. The comparison of experimental and numerical results emphasizes the importance of the choice of the hyperelastic modelling in the simulation of strain fields. For example, this could be fundamental for crack tip analysis. 4M), using both an axial load cell of 125 daN and specially designed autoblocking grips (Fig. 1). During the tests, the deformation of samples and their superimposed pattern was recorded using a CCD camera (JAI, 1280×1024 pixels, 25Hz, see figure 1). Using the Digital Image Correlation Software 7D (Vacher 2003), it was then possible to determine the local strain field on the surface of the deformed samples. In order to analyse the mechanical behaviour of the silicone, samples were subjected to two types of homogeneous loadings and one heterogeneous one:  Simple tensile tests were performed on bone samples having an initial gauge length l0 of 60 mm and a gauge cross section S0 of 122 mm2 (Fig. 2(a)).  Pure shear strain state was approached by performing plane strain tensile tests (Fig. 2(b)). The height l0 as well as the width b0 of samples were 6 mm and 70 mm, respectively.  A tensile test was also performed on a plate (height l0  80 mm, width b0  70 mm) containing five holes (Fig. 3). The central hole has a diameter of 24 mm, whereas the four other hole’s diameter was set to 19 mm. Notice that the positions of the centres have not been positioned to produce a regular arrangement, so that the plate does not have any symmetry. For the two homogeneous tests, monotonic as well as cyclic loadings were performed at constant elongation rate 0 / l l  ranging from 2 10 s to 10s ( l being the current gauge length). The analysis of the local displacement field deduced from 7D also proved that the strain state in the gauge zones could fairly be considered as homogeneous. Moreover, the plate with holes was subjected to a monotonic loading at a constant crosshead velocity l =2 10 mm s. For this test, strong strain heterogeneities were recorded. 4 HOMOGENEOUS TEST 4.1 Tests and results Experiments were designed to evaluate different physical aspects of rubber materials. First, a cyclic tensile test has been performed. Two cycles are realized at six increasing stress levels (cf. timing diagram of figure 4) at 0.008 s elongation rate. This test was designed to evaluate the Mullins effect and hysteretic behaviour of the silicone. The curves of figure 4 show a perfect non linear elastic behaviour without Mullins effect or hysteretic behaviour since all loading and unloading curves are superimposed. Figure 4. Cyclic tensile test: (a) timing diagram of the load applied 0 / l l  = 0.008 s (b) nominal stress – elongation behaviour Figure 1. Testing machine with tensile test specimen and CCD camera Figure 2. (a) Simple tensile test specimen and (b) pure shear test specimen (a) 10 mm 10 mm (b)