Calculation of the yield strength of polycrystalline materials with a hexagonal close-packed lattice at a given texture

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For a polycrystalline material with a hexagonal close-packed lattice, a model is proposed that allows estimating the yield strength at a given texture. The plasticity properties of an individual grain are described by the generalized von Mises criterion. The most widespread averaging approaches are considered to determine the yield strength of a polycrystal. An original averaging method for a heterogeneous medium under plastic deformation conditions is proposed that takes into account the presence of undeformed grains whose share is determined by means of the percolation theory. Using each approach, the problem about tension/compression of a homogeneous rod of square cross-section is solved for two limiting cases: no texture and rigid basis texture. The calculation results are juxtaposed with the available literature data. The effect of the texture on the yield strength is considered. A qualitative explanation of generating a texture is given.