Elastic–plastic property closures for hexagonal close-packed polycrystalline metals using first-order bounding theories

Property closures delineate the complete set of theoretically feasible combinations of macroscale (homogenized) properties in a given material system. A novel spectral framework called microstructure sensitive design (MSD) was recently formulated and demonstrated to be capable of delineating elastic–plastic property closures in a number of composite material systems. In particular, it was successfully applied to cubic polycrystals, where it was assumed that the crystallographic texture had a dominant influence on the macroscale properties of interest. Application of these procedures to hexagonal polycrystals posed significant computational difficulties, because of the need to represent the texture in the hcp polycrystals in a much larger number of dimensions in the Fourier space compared with what was needed for the cubic polycrystals. This paper reports new computational schemes for delineating elastic–plastic closures for hcp polycrystals using the spectral framework of MSD. The primary focus of this paper continues to be on the influence of the crystallographic texture (in the hcp polycrystal) on the components of the macroscale anisotropic elastic stiffness, macroscale anisotropic tensile yield strength, and the macroscale R ratios (ratio of the transverse strains in tensile deformation mode) exhibited by the material.