Investigation of the viscoplastic behaviour of alloys in the semi-solid state by homogenization
Résumé
The aim of this paper is to investigate the viscoplastic behaviour of alloys in the semi-solid state. Over a critical solid volume fraction, the metallic material is considered as a porous medium constituted by a viscoplastic skeleton and saturated by an incompressible Newtonian fluid. By using homogenization method of periodic structures, we determine the macroscopic equivalent medium. We show that the heterogeneous material displays three types of behaviour: biphasic, monophasic with fluid pressure effect and monophasic with fluid viscosity effect, according to the contrast of the mechanical properties of the two components. This contrast is measured by a small parameter var epsilon, ratio of the dimensions of pores or solid particles to the macroscopic characteristic length of the sample or of the excitation. The homogenization process applied to the viscoplastic saturated porous medium permits to validate the structure of constitutive laws already proposed in the phenomenological way to describe experimental data.