Effective strain in simple shear deformation considering material anisotropy

The effective strain in simple shear was explored with material anisotropy by providing its mathematical expression. Based on large deformation theory, the kinematics of simple shear was analyzed with discretization of the deformation process and decomposition of the deformation gradient, from which expressions that can be practically utilized for evaluating effective strain were derived for simple shear. Material anisotropy was considered by using the quadratic anisotropic yield function with Lankford values. It was found that the effective strain in simple shear can be accurately estimated as the number of the discretized deformation steps approaches infinity. It was verified that the derived expression can also be obtained from other approaches based on the co-rotational rate of deformation tensor and the plastic work equivalence, respectively. To demonstrate its application, the effective strains of several anisotropic metals made of steel alloys and aluminum alloys were evaluated using the developed expression. It was found that the effective strain of the extruded aluminum profile differs significantly from those of the other metals due to its strong planar anisotropy. This result demonstrates that the effective strain in simple shear can be significantly influenced by material anisotropy. Further investigations were conducted on the evaluation of effective strain in cases where simple shear is approximated by a finite number of increments, deriving relevant expressions for effective strain. Effective strains calculated from these expressions showed good correlations with those obtained from the incremental computations using the commercial finite element software Abaqus/Standard.