Stress Analysis for Kinematic Hardening in Finite-Deformation Plasticity.

Abstract

Abstract : Kinematic hardening represents the anisotropic component of strain hardening by a shift, alpha, of the center of the yield surface in stress space. The currently adopted approach in stress analysis at finite deformation accounts for the effect of rotation by using Jaumann derivatives of alpha and the stress. This analysis generates the unexpected result that oscillatory shear stress is predicted for monotonically increasing simple shear strain. Simple shear strain growing at constant rate gamma-dot = k yields a spin in the plane of shearing having the constant magnitude k/2. The effect of this on the evolution equation for the shift tensor alpha causes the latter to rotate continuously. In contrast, the kinematics of simple shear prescribe that no material directions rotate by more than pi radians. These two features seem inconsistant since the shift tensor has its origin embedded in the material, for example as rows of dislocations piled up against grain boundaries. By defining a modified Jaumann derivative based on the angular velocity of directions embedded in the body which characterize the effective resultant orientation of the micro-mechanisms responsible for the anisotropic hardening, a method of stress analysis is implemented which eliminates the inconsistency and yields a monotonically increasing shear stress. (Author)