Theoretical latent hardening in crystals—I. General equations for tension and compression with application to F.C.C. crystals in tension

Abstract

E quations for latent strengths in single slip, based upon the simple theory of finite distortional crystal hardening introduced by K.S. Havner and A.H. Shalaby (1977), are derived for both tensile and compression tests without restriction as to crystal class. Detailed comparisons between theoretical results and the experiments of P.J. Jackson and Z.S. Basinski (1967) on copper crystals in tension are presented. There is good qualitative agreement between theory and experiment regarding the diversity of anisotropic hardening among slip systems. Moreover, there is satisfactory quantitative agreement between the theory and the extrapolated experimental data in the stage III, large-strain range. It is suggested that further experimental investigation of latent hardening at large prestrains would be desirable. The simple theory predicts anisotropic hardening and the perpetuation of single slip in axial loading of cubic crystals initially oriented for single slip, but predicts symmetric, isotropic hardening of specimens initially oriented in positions of 4, 6 or 8-fold multiple-slip. These predictions are in general accord with experimental observations from tests of f.c.c. and b.c.c. crystals.