Stochastic Mesoscale Modeling of Elastic-Plastic Deformation
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ABSTRACT Plastic response of a solid under stress depends on its crystallographic structure and morphology. Two of the major mechanisms of plasticity in metals are crystallographic slip and twinning. The purpose of this work is to analyze the influence of local stress distribution on slip and twin nucleation and propagation and to examine how this behavior depends on the interaction among slips, twins, and grain boundaries. We formulate a simple model in which slip and twin systems are defined at appropriate angles to each other. Plastic flow is treated as a Markovian stochastic process consisting of a series of local inelastic transformations (LITs) in the representative volume elements (RVE). The probabilities of LITs per unit time are defined in the framework of transition-state theory. By varying the types of allowed LITs and/or the scale of RVE, plastic deformation is modeled at different structural levels, from a small volume of single crystal to the aggregate response of an isotropic polycrystalline solid. An important feature of this model is that evolution of the internal stress distribution is traced explicitly throughout the simulation run. This allows us to examine conditions of slip and twinning in considerable detail. In particular, we observe that twinning occurs through a nucleation-and-growth mechanism whose rate is controlled by the size of the critical nucleus of the new phase.
INTRODUCTION The character of the plastic response of different solids depends on their morphology and crystallographic structure as well as on loading conditions. Quantitative details of plastic flow in different solids may differ significantly, but general trends, if we consider the influence of some particular factor on plastic behavior, are quite often the same for different solids. Plasticity models based on the averaged response of continuum material have been advanced [1,2] based on the assumption that plastic strain is locally homogeneous. At the same time, it is well known that crystal plasticity is often locally heterogeneous introducing major uncertainties in the constitutive laws. In this paper we examine the effects of localized plasticity in single crystals using a 2D stochastic model incorporating, in an idealized way, slip and twinning behaviors. The overall plastic deformation is considered to be inhomogeneous at the mesoscale associated with shear bands, slip or twinning. Following the original isotropic model developed by V. Bulatov and A. Argon [3], plastic flow is considered here to be a cumulative result of stochastic local inelastic transformations (LIT) in the representative volume elements (RVE) of the material. The superposition principle is applied to solve for heterogeneous elastic stress field building up in response to the misfit (plastic) strain produced by LITs[4]. Since the purpose of this work is to examine the influence of local stress distribution on shear bands, slip and twin nucleation and propagation, we represent slips and twins by LITs of different types oriented at special angles
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