Anisotropic yield criterion for polycrystalline metals using texture and crystal symmetries
The authors make an attempt to bridge continuum and crystallographic approaches by exploiting the symmetries found in each grain of a polycrystalline metal, and by making use of isotropic plasticity equivalent (IPE) method of \textit{A. P. Karafillis} and \textit{M. C. Boyce} [J. Mech. Phys. Solids 41, No. 12, 1859-1886 (1993; Zbl 0792.73029)]. Using some linear transformation, this method allows to operate with a stress state of isotropic plasticity equivalent material instead of the actual stress state existing in an anisotropic material. Usually, in the continuum approach a phenomenological yield criterion, which is a function of the stress, is used to define the yield surface in stress space. At the same time, in crystallographic approaches the yield surface of a polycrystalline aggregate is determined from the yielding behavior of each grain in the aggregate. In this paper, using the IPE method, the authors obtain a continuum yield function for fcc polycrystalline metals. In order to bring microstructural information into the continuum model, they use two Taylor's assumptions, namely: (i) each grain has the same yield surface, and differs from the others only in its orientation, and (ii) each grain undergoes the same homogeneous deformation as the macroscopic deformation. To avoid theoretical difficulties, the present work is limited by modeling weakly-textured materials (the crystallographic yield theory of Bishop and Hill is used to determine the parameters for the IPE linear transformation tensor for a single fcc crystal). By assuming that the rates of work in anisotropic and IPE materials are equal, the authors find the IPE transformation tensor for a polycrystal by using only polycrystalline texture data. Thus, the developed IPE criterion can be viewed as a generalizaton of the Hill's anisotropic criterion, adding to him the abilities to describe non-quadratic yielding behavior, to account for microstructural texture, and to choose the number of data points used to calibrate the model. The obtained yield predictions are compared with results of another crystallographic and continuum criteria. For some commonly observed textures, the R-value (the ratio of the transverse plastic strain increment to the thickness strain increment during a uniaxial tensile stress) predicted by the present modernized IPE method is investigated through comparison with experimental data. Moreover, the authors give computations and comparisons of yield surfaces of fcc polycrystals for the same textures.
Bishop-Hill crystallographic yield theory
scientific article; zbMATH DE number 1340825