Yield criteria for anisotropic polycrystals

Chapter 5 is devoted to modeling the elastic–plastic behavior of anisotropic polycrystalline metals. After introducing the only two rigorous methodologies for extending isotropic formulations such as to account for anisotropy, the most versatile three-dimensional orthotropic yield criteria for materials with the same response in tension and in compression are presented. While the need for analytic yield criteria that account for both anisotropy and tension–compression asymmetry in the plastic deformation of hexagonal materials such as magnesium, zirconium, and titanium alloys has been long recognized, only recently models that describe these key features have been developed. These contributions along with applications for a variety of loadings are discussed.