Analysis for twinning and slip in face-centered cubic crystals under axisymmetric co-deformation

Abstract

The maximum work principle of Bishop-Hill was developed to analyze the axisymmetric co-deformation in face-centered cubic crystals (f.c.c.) for twinning on {111}〈112〉 and slip on {111}〈110〉 systems. The influence of ξ, the ratio of critical resolved shear stress for twinning to slip, on the yield stress states and corresponding active slip or/and twinning systems for orientations in the standard stereographic triangle of cubic crystal was investigated systematically. The Taylor factors and the anisotropy of yield strength for three important orientations [100], [110] and [111] in orientation space were analyzed. It is found that the yield strength asymmetry for the case of axisymmetric deformation of tension and compression can be explained based on the microscopic theory of crystal plasticity. The concept of orientation factor for twinning ability was proposed and the deformation mechanism map in the orientation space was established for the case of axisymmetric deformation. The deformation texture formation and development of f.c.c. crystals with low stacking fault energy for axisymmetric tension can be explained qualitatively on the basis of analyzed results.