On the predictive capabilities of anisotropic yield criteria for metals undergoing shearing deformations

In order to evaluate the predictive capabilities of 3-D anisotropic yield functions for cases when the material axes rotate with the deformation, a rectangular block subjected to constrained simple shearing deformations is considered. The ability of a constitutive model to predict negligible normal stress components, both in and normal to the plane of shearing (regardless of the specimen thickness), is adopted as a measure to test the accuracy of the yield functions employed. For the yield functions examined, if a high exponent is assigned to the yield function, the results indicate that even in the range of small-to-medium shearing strains, non-negligible normal stresses may not be obtained. When the plane strain condition is imposed normal to the plane of the applied shear, then the stress component along this direction can be unrealistically high. When the plane stress condition is imposed, even though the strain component in the thickness direction is negligibly small, the predicted normal stresses in the plane of the shearing are considerably different than those of the plane strain case. Due to the presence of in-plane anisotropy, the results evidently depend largely on the initial orientation of the material axes relative to the shear axes, which affects the sign as well as the magnitudes of the predicted normal stresses. A possible implication of these results for metal forming operations involving shear is obviously the need to verify the possibility of errors which can emerge due to the type of analysis (2-D versus 3-D) employed.