This article outlines several polycrystal formulations commonly applied for the simulation of plastic deformation and the prediction of deformation texture. It discusses the crystals of cubic and hexagonal symmetry that constitute the majority of the metallic aggregates used in technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the homogeneous effective medium (HEM). The article analyzes the anisotropy predictions of rolled face-centered-cubic and body centered-cubic sheets and presents simulations of the axial deformation of hexagonal-close-packed zirconium. The applications of polycrystal constitutive models to the simulation of complex forming operations, through the use of the finite element method, are also presented.

This article provides a background of the complex relationship between titanium and its alloys with aqueous environments, which is dictated by the presence of a passivating oxide film. It describes the corrosion vulnerability of titanium and titanium oxides by the classification of oxide failure mechanisms. The mechanisms are spatially localized oxide film breakdown by the ingress of aggressive anions; spatially local or homogenous chemical dissolution of the oxide in a strong reducing-acid environment; and mechanical disruptions or depassivation such as scratching, abrading, or fretting. Titanium alloys can be classified into three primary groups such as titanium alloys with hexagonal close-packed crystallographic structure; beta titanium alloys with body-centered cubic crystallographic structures; and alpha + beta titanium alloys including near-alpha and near-beta titanium alloys. The article also illustrates the effects of alloying on active anodic corrosion of titanium and repassivation behavior of titanium and titanium-base alloys.