Integration algorithm for modeling the elasto- viscoplastic response of polycrystalline materials

摘要

An integration scheme is presented for modeling the texture evolution and stress strain response of elasto-viscoplastic polycrystalline materials. Single crystal kinematics based on a multiplicative decomposition of the deformation gradient is used to obtain an evolution equa- tion for the crystal elastic deformation gradient. An implicit scheme to integrate this equation is presented which is stable and efficient. The reorientation of the crystal as well as the elastic strain can then be obtained from a polar decomposition of the elastic deformation gradient. Numerical studies are presented using material parameters for aluminum (FCC crystals) and zircaloy (HCP crystals) to den1onstrate the general nature of the model. Predictions of the model are also compared with those obtained using a rigid-viscoplastic polycrystal mode1 which neglects the elastic response. Retaining the elastic response makes the model useful for large deformation analyses where both anisotropy due to texture as well as elastic effects such as springback and residual stresses are important.