Crystalline plasticity and scale transition: the case of polycrystals

In the article , elastoviscoplastic behavior laws have been established for single crystals on the basis of changes in scale, from atomistics through dislocation dynamics to continuum mechanics. They are used in this second article to predict the mechanical response of polycrystals and the scaling effects observed in many metal alloys.

First, methods for simulating polycrystalline aggregates and the fundamental principles of homogenization methods are presented in detail. Applications include modeling the distortion of load-bearing surfaces, studying the behavior of polycrystals under multiaxial loading and the influence of grain boundaries on intragranular deformation heterogeneities.

Finally, we show the limits of the classical continuous approach when it comes to reproducing scale effects commonly observed in physical metallurgy. The dynamics of dislocations can account for many of these effects, notably the Hall-Petch effect. However, it is possible to describe some of these effects using a generalized continuous medium approach, for example by incorporating the notion of crystal lattice curvature and its effect on strain hardening.

Most of the quantities, notations and symbols used in this article were introduced and defined in the article