Computational description of nanocrystalline deformation based on crystal plasticity

Abstract

The effect of grain size on the mechanical response of polycrystalline metals was investigated computationally and applied to the nanocrystalline domain. A phenomenological constitutive description is adopted to build the computational crystal model. Two approaches are implemented. In the first, the material is envisaged as a composite; the grain interior is modeled as a monocrystalline core surrounded by a mantle (grain boundary) with a lower yield stress and higher work hardening rate response. Both a quasi-isotropic and crystal plasticity approaches are used to simulate the grain interiors. The grain boundary is modeled either by an isotropic Voce equation (Model I) or by crystal plasticity (Model II). Elastic and plastic anisotropy are incorporated into this simulation. An implicit Eulerian finite element formulation with von Mises plasticity or rate dependent crystal plasticity is used to study the nonuniform deformation and localized plastic flow. The computational predictions are compared with the experimentally determined mechanical response of copper with grain sizes of 1 μm and 26 nm. Shear localization is observed during work hardening in view of the inhomogeneous mechanical response. In the second approach, the use of a continuous change in mechanical response, expressed by the magnitude of the maximum shear stress orientation gradient, is introduced. It is shown that the magnitude of the gradient is directly dependent on grain size. This gradient term is inserted into a constitutive equation that predicts the local stress–strain evolution.