Issue 49

Y. Saadallah et alii, Frattura ed Integrità Strutturale, 49 (2019) 666-675; DOI: 10.3221/IGF-ESIS.49.60 672 Stress-strain curves To evaluate the relevance of the rheological model taken into account, the stress-strain curves of the experiment and those of the simulation, at four strain-rates, are compared. Below the elastic limit, the stress is related to the strain by a linear function. The threshold of plasticity being reached, the curve takes another pace. Indeed the spring of the viscoplastic mechanism connecting the stress to the strain with a nonlinear function is at the origin of the nonlinearity observed on the curve. The error between the test-model results is almost insignificant. Sensitivity of the elastic limit to the strain-rate The stress corresponding to the elastic limit depends considerably on the strain-rate. Indeed, the higher the strain-rate, the greater the stress corresponding to the elastic limit. Fig. 4 illustrates the dependence of the elastic limit on the strain-rate. In the references [19, 20, 34-36], the authors extensively discussed the sensitivity of the elastic limit to the strain rate. Different functions have been established. It should be mentioned that the elastic limit also depends on the temperature, an aspect that is not considered in this study because the tests were conducted at constant room temperature. In the present work, the dependence can be expressed by a power law as illustrated in Fig. 4. In addition, Fig. 5 shows the elastic limit versus the logarithm of the strain-rate. There is a linear increase in the elastic limit as a function of the strain-rate. This is in perfect agreement with other work on polymers with references [35-37]. In another plane, the strain corresponding to the elastic limit is insensitive to the strain-rate. Figure 4 : Sensitivity of the elastic limit to the strain-rate. Figure 5 : Linearity of elastic limit at the logarithm of the strain- rate Sensitivity of the parameters to the strain-rate In order to verify the dependence of the viscoelastic and viscoplastic parameters of the strain-rate, four different speeds were taken into account in the tensile tests. Following the identification step, it turned out that the elastic modulus E is independent of the strain-rate while the other two viscoelastic parameters show non-linear dependency. Referring to Fig. 6, it is noted that the K module increases with the increase of the strain-rate while the viscosity parameter ve  decreases. On the viscoplastic plane, the work hardening coefficient n is independent of the strain rate whereas the other two viscoplastic parameters depend on it and are connected to it with nonlinear functions. Referring to Fig. 7, an analogy can be observed qualitatively between the viscoplastic parameters H and vp  on the one hand and the viscoelastic parameters K and ve  respectively on the other hand. Thus with the increase of the strain-rate, the module H increases while the parameter vp  decreases.