Modelling stress-dependent transformation strains of heterogeneous materials
Résumé
This paper aims at drawing attention to some difficulties which may arise when using the concept of “stress-free strain” or “transformation strain” for the prediction of the macroscopic behaviour of rate-independent or rate-dependent elastoplastic polycrystals and composite materials, especially in the context of the self-consistent homogenization procedure. These difficulties are due to the stress-dependence of plastic and viscoplastic strains, which can hardly be considered as true “stress-free strains”, contrary to other physically well-identified (thermal, magnetic...) eigenstrains: when omitting this stress-dependence within an elastic framework, a direct self-consistent-type derivation of the overall behaviour leads to an overestimation of the mechanical interphase interactions and of the resulting overall stiffness. An alternative treatment, based on a tangent-type linearization process, is proposed which leads to the introduction of fictitious “stress-free strains” that do not reduce to the plastic or the viscoplastic ones and consequently yield softer predictions. Nevertheless, the limits of Hill’s approximation of the nonlinear self-consistent modelling are acknowledged and discussed.