  In this paper, we predict the effect of texture on the anisotropy in plastic
properties of polycrystalline metallic sheets. The constituent grain behavior
is modelled using the new single crystal yield criterion developed by Cazacu,
Revil, and Chandola (2017). 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 with misorientation
scatter width up to 25 degrees, the numerical predictions are very close to
those obtained analytically for an ideal texture. 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.
