Isotropic polycrystal yield surfaces of b.c.c. and f.c.c. metals: crystallographic and continuum mechanics approaches

Abstract

For the crystallographic approach, isotropic yield surfaces of b.c.c. metals with the ratio of critical shear stress on {112}〈111〉 slip systems to that on {110}〈111〉 slip systems in the range of ( √ 3 2 , 2 √3 ) have been simulated with the Taylor model. Isotropic yield surface f.c.c. metals is included as a special case where {112}〈111〉 slip systems are all removed out. All the yield surfaces considered are located between the Mises and Tresca criteria; and linear variations of the average size and the “shape” of the isotropic yield surface with the critical shear stress ratio were found. For the continuum mechanics approach, using a series of stress transformation functions proposed in the present work, the Hill and the Hershey, Hosford and Hill (HHH) yield function shave been developed to be new yield functions expressed in 6-dimensional stress space. The new yield function based on the HHH expression can include the Mises and the Tresca criteria, as well as the isotropic form of the Barlat and Lian (BL) yield function as special cases. By comparison of the new yield function with the isotropic yield behaviours of both b.c.c. and f.c.c. metals simulated with the Taylor model, very good agreements are obtained and the parameters in the new yield function are determined in the sense of crystallographic plasticity theory.