Simulating the Interactions Between Microstructure and Deformation

The microstructure of a material can profoundly affect its mechanical properties, and deformation can in turn induce changes to the microstructure. For example, in a polycrystalline metal the yield stress is generally dependent on the grain size, and deformation can lead to recrystallization and a subsequent change in the microstructure and properties. Since the processing and fabrication of metal components generally involves thermomechanical treatments, understanding the interplay between deformation and microstructure is important in a broad range of engineering applications. We will attempt to address a selection of specific phenomena in which microstructure and deformation affect one another. Namely, we will focus on three topics: strain-induced grain boundary migration [1], recrystallization [1], and the effects of microstructural length scales on mechanical response [2]. Strain-induced boundary migration occurs when energy stored during deformation drives the motion of internal interfaces. To simulate this process, we couple an interface tracking model for grain growth with a polycrystal plasticity model for deformation. The inherent heterogeneity of the microstructure induces spatially nonuniform local stresses that can lead to grain morphologies and growth behavior that differ significantly from normal grain growth, as depicted in Fig 1. Deformation not only affects the existing microstructure, but can also create new ones. Dislocations generated during plastic deformation can organize into subgrain networks of (relatively) strain-free cells, and recrystallization occurs when these subgrains grow abnormally to create new strain-free grains. To gain insight into the origins and behavior of the recrystallization process, we use Potts Monte Carlo simulations of the evolution of subgrains based on experimentally derived interface properties [3]. These simulations suggest a model for the characteristics of recrystallized microstructures as functions of the deformation state, as demonstrated in Fig 2 by the dependence of recrystallized grain size on von Mises Strain. Deformation can influence microstructure in a variety of ways, but conversely the microstructure can greatly impact a material’s mechanical (and many other) properties. For example, grain size influences yield stress because dislocation motion is impeded by internal interfaces. However, many models for the mechanical response of a metal are independent of the size of the microstructural features, and a variety of approaches exist to address this issue [4,5]. We will present a polycrystal plasticity model that uses nonlocal integration to estimate the density of non-redundant dislocations and an evolution equation to model the redundant dislocations. This approach not only accounts for the geometrically necessary dislocations required for strain compatibility, but also produces dislocation pileup at internal interfaces because of the nonlocal treatment of non-redundant dislocations. Figure 3 shows the pileup of dislocations at grain boundaries in an idealized polycrystal, and Fig 4 contains the associated dependence of the structure’s yield stress as a function of the grain size. We will discuss our approaches for simulating strain-induced grain boundary migration, recrystallization, and scale-sensitive mechanical response. We will then present simulation results for 1) the roles of both elastic and plastic stored energy in driving grain boundary motion, 2) the onset of recrystallization from subgrain networks, and 3) the dependence of mechanical response on grain size.