This paper addresses the problem of theoretically predicting the evolution of void for a single crystal in ductile material accounting to the size and orientation effects. In this paper, a new damage model is derived based on the theory of mechanism-based strain gradient crystal plasticity (MSG-CP). By imposing the Taylor dislocation model into a widely used Gurson model (1), we extend the Gurson model to account for the void size effect. Meanwhile, we consider the crystal orientation effect by using MSG-CP to describe the behavior of matrix. Numerical simulation has been conducted under axisymmetric loading condition for cylindrical void and under spherical symmetric tension for spherical void. It reveals that the damage of a ductile porous material has strong orientation-dependence and size-dependence on microscale level. The traditional conclusion that the larger the void size is the faster it grows is also verified by the new model. Additionally, we add a kinematic hardening law to the MSG-CP theory, and have analyzed a hysteresic response of a single crystal under cyclic loading.

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