Three-dimensional model of strength and ductility of polycrystalline copper containing nanoscale twins

Recent studies have shown that strength values similar to those observed in nanocrystalline metals can be obtained without a severe deterioration in ductility. This is achieved by introducing controlled, nanoscale, growth twins within ultrafine-grained metals. In this work, we present a continuum description of the effective response of nanotwinned ultrafine crystals. The model is based on a finite element formulation of the continuum three-dimensional problem. The deformation of polycrystal grains is described explicitly and the contribution of the twins is considered through a homogenized representation of the twin planes in the crystal lattice in each grain. A phenomenological three-dimensional model extending the two-dimensional model of Dao et al. [Dao M, Lu L, Shen YF, Suresh S. Acta Mater 2006;54:5421–32] is constructed to describe both the orientation-dependent dislocation blocking action and absorption at the twin boundaries, and its anisotropic influence on the intrinsic lattice properties. Simulations of tensile tests using this model capture the increased level of strength with increasing twin densities. The fracture initiation criterion proposed by Dao et al. is shown to provide a good description of the experimentally observed failure trends with respect to twin spacings, but to overpredict the failure strain initiation for the smallest twin spacing. Other possible failure mechanisms not considered in the model that could explain the discrepancies observed are discussed. In addition, a study of the influence of crystallographic texture on the effective response is presented. Overall, the proposed model captures the salient three-dimensional features of the deformation of nanotwinned ultrafine crystals and provides a modeling framework for predicting the transition from intragrain to intergrain mechanisms of failure.