Analytical expressions for the yield stress and Lankford coefficients of polycrystalline sheets based on a new single crystal model

Among processes involving plastic deformation, sheet metal forming requires a most accurate description of plastic anisotropy. One of the main sources of mechanical anisotropy is crystallographic texture. In this paper, using the new single crystal yield criterion developed by Cazacu et al. (Int J Solids Struct, 2017), we provide analytical expressions for the variation of the uniaxial flow properties of polycrystalline sheets. It is shown that irrespective of the ideal texture component, Lankford coefficients exist and have finite values for all loading directions. The illustrative examples presented show that using this approach, the anisotropy in polycrystalline behavior can be estimated accurately in a very efficient manner. Another added advantage is that once the single crystal behavior is known, no additional calibration or macroscopic mechanical tests are needed in order to predict the effect of different texture components on the polycrystalline behavior.