Modeling deformation induced textures in titanium using analytical solutions for constrained single crystal response

• Published in: Journal of the mechanics and physics of solids Vol. 43; no. 8; pp. 1283 - 1302
• Main Authors: Prantil, Vincent C., Jenkins, James T., Dawson, Paul R.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.08.1995; Elsevier
• Subjects: Cold working, work hardening; annealing, post-deformation annealing, quenching, tempering recovery, and crystallization; Cold working, work hardening; annealing, quenching, tempering, recovery, and recrystallization; textures; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Materials science; Physics; Treatment of materials and its effects on microstructure and properties; Strain rate sensitivity; Compressive stress; Monocrystals; Hexagonal crystals; Transition elements; Slip; Analytical method; Shear stress; Theoretical study; Titanium; Plastic deformation; Texture
• ISSN: 0022-5096
• DOI: 10.1016/0022-5096(95)00019-F

We present an efficient method for computing the large deformation behavior of hexagonal close-packed polycrystalline metals. Under slip-dominated deformation conditions, these crystals are often nearly inextensible along a direction perpendicular to the base of the lattice unit cell. We adopt a kinematic procedure introduced by Parks and Ahzi (1990) for partitioning the macroscopic deformation among these inextensible crystals and show that a decomposition of the crystal deformation is possible which decouples the basal and prismatic shearing. We use this decoupling to reduce the problem of determining the crystal stress components to a pair of simplified two-dimensional equations for the basal and prismatic components, respectively. We derive analytic solutions for prismatic slip and the corresponding components of the crystal stress. When the single crystal behavior is rate-insensitive, a similar solution for the basal components is a good approximation for the remainder of the crystal stress. We show how the decomposition also decouples the texture evolution into separate basal and prismatic contributions. In the limit of low rate sensitivity, this allows the orientation distribution of the inextensible axis to be computed from a consideration of basal slip alone. Simulations of polycrystalline response along various deformation paths indicate that the rate-insensitive results are a good approximation to the rate-sensitive regime over a broad range of the rate sensitivity parameter. This is a consequence of the very limited number of slip modes and their decoupling. As a result, the simplified stress solutions and the decoupled texture evolution can be used at higher rate sensitivities characteristic of processing at higher temperatures.