Chapter 4 - Dislocation-Based Single-Crystal Plasticity Model

Abstract

Various macroscopic continuum plasticity theories are given in Chapter 2, in which crystallographic details such as the anisotropy of the crystal lattice and the underlying dislocation microstructure evolution are not considered. In this chapter, conventional single-crystal plasticity theory and recent progress are introduced. First, the conventional constitutive model for single crystals, including the kinematics of single-crystal plasticity, dislocation density evolution, and stress updates, is described in detail. Then, a new dislocation-based crystal plasticity model is developed via the continuum description of the collective behavior of dislocations. Compared with conventional crystal plasticity models, a microforce balance equation is involved by combining the equation of dislocations motion and Orowan's law. The microforce balance equation contains back stress to consider the short-range interactions of dislocations. It is more convenient to deal with the complex interactions between dislocations and grain boundaries. As an application, the strong size effect and prominent Bauschinger effect in thin films with a passivation layer during loading and unloading are numerically studied using the proposed crystal plasticity model.