Prediction of plastic anisotropy of textured polycrystalline sheets using a new single-crystal model

Abstract

In this paper, we predict the effect of texture on the plastic anisotropy and consequently the drawing performance of polycrystalline metallic sheets. The constituent grain behavior is modeled using the new single-crystal yield criterion developed by [1]. For ideal texture components, the yield stress and plastic strain ratios can be obtained analytically. For the case of strongly textured sheets containing a spread about the ideal texture components, the polycrystalline response is obtained numerically on the basis of the same single-crystal criterion. It is shown that for textures obtained with rotationally symmetric misorientations of scatter width of up to 35° from the ideal orientation, the numerical predictions have the same trend as those obtained analytically for an ideal texture, but the anisotropy is less pronounced. Furthermore, irrespective of the number of grains in the sample, Lankford coefficients have finite values for all loading orientations. Illustrative examples for sheets with textures containing a combination of few ideal texture components are also presented. The simulations of the predicted polycrystalline behavior based on the new description of the plastic behavior of the constituent grains capture the influence of individual texture components on the overall degree of anisotropy. The polycrystalline simulation results are also compared to analytical estimates obtained using the closed-form formulas for the ideal components present in the texture in conjunction with a simple law of mixtures. The analytical estimates show the same trends as the simulation results. Therefore, the trends in plastic anisotropy of the macroscopic properties can be adequately estimated analytically.