MODELING DEFORMATION-INDUCED TEXTURES IN TITANIUM USING ANALYTICAL SOLUTIONS FOR CONSTRAINED SINGLE-CRYSTAL RESPONSE

We present an efficient method for computing the large deformation beh avior of hexagonal close-packed polycrystalline metals. Under slip-dom inated deformation conditions, these crystals are often nearly inexten sible along a direction perpendicular to the base of the lattice unit cell. We adopt a kinematic procedure introduced by Parks and Ahzi (199 0) for partitioning the macroscopic deformation among these inextensib le crystals and show that a decomposition of the crystal deformation i s possible which decouples the basal and prismatic shearing. We use th is decoupling to reduce the problem of determining the crystal stress components to a pair of simplified two-dimensional equations for the b asal and prismatic components, respectively. We derive analytic soluti ons for prismatic slip and the corresponding components of the crystal stress. When the single crystal behavior is rate-insensitive, a simil ar solution for the basal components is a good approximation for the r emainder of the crystal stress. We show how the decomposition also dec ouples the texture evolution into separate basal and prismatic contrib utions. In the limit of low rate sensitivity, this allows the orientat ion distribution of the inextensible axis to be computed from a consid eration of basal slip alone. Simulations of polycrystalline response a long various deformation paths indicate that the rate-insensitive resu lts 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 ca n be used at higher rate sensitivities characteristic of processing at higher temperatures.