Crystal plasticity FE modeling of Ti alloys for a range of strain-rates. Part I: A unified constitutive model and flow rule

Abstract

The deformation and failure response of many polycrystalline metallic materials is strongly dependent on the strain-rate. For an applied strain-rate, different points in the material microstructure can undergo strain-rates that differ by orders of magnitude depending on location and deformation history. Dislocation motion in metals is governed by the thermally-activated and drag-dominated processes under low and high rates of deformation, respectively. Commonly used flow rules, e.g the phenomenological power law or the linear viscous drag models are generally applicable to a limited range of strain-rates, without transcending these rates. To enable this transition in a seamless manner, this two part paper develops a unified constitutive model and an image-based crystal plasticity finite element model for polycrystalline hcp metals. The first part develops a dislocation density-based crystal plasticity constitutive relation with a unified flow rule by combining the thermally-activated and drag-dominated stages of dislocation slip, suitable for modeling deformation at a wide range of strain-rates. The model is explicitly temperature-dependent, making it appropriate for simulating high rate deformations, where temperature increases locally with plastic deformation due to the adiabatic heating. The unified model is used to study rate-sensitivity of flow stress in single crystal and polycrystalline titanium alloy, Ti-7Al. An elastic overshoot, followed by a stress relaxation is observed at high strain-rates in single crystals. For the polycrystalline simulations, the model effectively captures the increase in rate sensitivity at high strain-rates.