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The flexion solicitation induces in a bent beam a non-uniform stress field. The problem becomes more challenging when the material has a complex behavior, because the material may have different response from one area to another according to the local stress state. In the present work, it is considered, a six parameters rheological model to simulate the behavior of an elastoviscoplastic material. The mathematical law of the behavior is established; thereafter one must determine the beam bending curvature which is an essential and capital parameter for the flexion. Indeed, the bending curvature allows knowing the stress field in the beam. In viscoelastic step, the curvature is obtained by an analytical integration. While in the elastoviscoplastic step, two zones of different behaviors coexist which are namely viscoelastic and elastoviscoplastic, then a numerical integration is required. The numerical integration is achieved, and then the stress field is obtained through the beam and over the time.

The behavior of thermoplastics depends on several factors, mainly time and temperature. The present work is the a study of the dependence of these materials on time. The material considered in this study is a polyamide 6. The applied behavior model is represented by the Kelvin-Voigt viscoelastic mechanism. the mathematical formulation of the equations of the model is put in place and tensile tests at different strain rates are conducted. The parameters model are then identified. These being sensitive to the strain-rate, the relation which links them with it is established by means of an exponential regression. The results test-model are presented and dicussed.

The behavior of thermoplastics depends on several factors, mainly time and temperature. The present work is focused on an analysis of the time sensitivity of the viscoelastic and viscoplastic parameters of a rheological model. The material considered in this study is a polyamide 6. The analogical model is represented by the Kelvin-Voigt viscoelastic mechanism mounted in series with a viscoplastic branch of Bingham. After a mathematical formulation of the equations governing the model, tensile tests at different strain rates are conducted. The model parameters are then identified by inverse analysis. The technique of genetic algorithms has been favored. A nonlinear dependence of these parameters on the rate of strain has been observed. The dependence function has been established by a nonlinear regression technique. The comparison of the experimental results with those obtained by the model reveals a satisfactory agreement, hence the validation of the approach adopted.