Constitutive Mechanics of Hexagonal Close-Packed Solids under Compression and Shear An Anisotropic Crystal-Plasticity Framework

Hexagonal close-packed (HCP) solids, including magnesium, titanium, and zirconium, can exhibit strongly orientation-dependent deformation, tension–compressionasymmetry, and markedly different resistance to competing slip and twinningmechanisms. These characteristics cannot generally be represented by a single,orientation-independent compressive-strength or shear-strength value. They arisefrom the crystal’s elastic anisotropy, the available crystallographic deformationsystems, the loading direction relative to the crystal axes, and the evolution of twinsand texture during deformation.This paper develops a continuum crystal-plasticity framework for analyzing HCPsolids under combined compression and shear. The formulation couples anisotropicelasticity to crystallographic slip, rate-dependent flow, hardening, deformationtwinning, and a phenomenological damage variable. It distinguishes hydrostaticpressure from deviatoric stress and resolved shear stress, which drive differentaspects of the mechanical response. The resulting equations provide a physicallyinterpretable framework for studying orientation-dependent behavior. They do notconstitute material-specific predictions: quantitative application requires calibrationfor the particular alloy, microstructure, temperature, and loading rate. The analysisalso clarifies that HCP metals are solids rather than fluids; “difficulty of shearing”is interpreted here as resistance to plastic shear, not as a fluid-like constitutiveresponse.