Abstract
The problem of constrained deformation of crystals based on the Bishop-Hill’s maximum work principle or Taylor’s minimum shear principle is interpreted as a constrained optimization problem for a process system consisting of many elementary processes such as simple glides on a crystallographic slip system. The mathematical method for analysis of crystal rotations under constrained deformation is introduced based on the consideration that when the plastic distortion components are prescribed, the corresponding stress and rotation vector components are the optimized responses of its process. The proposed method is applied to the simulation of rolling texture development in bcc metals deformed by the ⟨111⟩ pencil glide, using a function minimization program capable of dealing with multimodal function and non-linear constraints.
The predicted rolling textures of bcc metals are in good agreement with the experimentally determined ones of iron. Therefore, this computational method can be expected to yield realistic information about other deformation texture problems.
