The creep of an elastoviscoplastic beam under a bending loading

Thermoplastics start to manifest a nonlinear mechanical behavior from relatively low loading levels. Under a bending solicitation, which generates a nonuniform stress field, the material behavior becomes more challenging. Indeed, a flexed specimen may have different behaviors from one point to another according to the local stress state. In the present work, a six-parameter rheological model is used to simulate the nonlinear behavior of an elastoviscoplastic beam, subjected to a three-point bending load. In the framework of Euler-Bernoulli theory, the mathematical formulation of a bent beam behavior involves the bending curvature function. This function allows the determination of the strain and stress fields along and through the beam. However, when the beam reaches the viscoplastic stage, the differential equation providing the bending curvature of the beam requires a numerical integration, which has been accomplished in this work. This theoretical modeling approach is supported by experimental creep tests carried out on polyamide specimens (PA6). The testing results are qualitatively consistent with the predictions of the proposed rheological model.