Analytical and computational modeling of the mechanical response of polycrystalline and nanocrystalline metals

Metallic materials with different grain sizes exhibit vasty differences in their mechanical behavior. For example, the mechanical strength of nanocrystalline materials is superior to those with coarse grain materials. In recent decades, many analytical and experimental efforts have been contributed to this new materials field.; In this research, a computational and analytical study of the grain size effect on the behavior of polycrystalline and nanocrystalline copper. A phenomenological constitutive description of this scaling response is discussed and adopted to build the numerical model. Both elastic and plastic anisotropy are included in this investigation. The material is envisaged as a composite, comprised of the grain interior, with flow stress sigmafG, and grain boundary layer, with flow stress sigmafGB. The hardening rates in the grain interior and grain boundary are different as a result of differences in dislocation source densities and interactions. The material is modeled as a monocrystalline core surrounded by a mantle grain boundary with a higher work hardening rate response.; The computational predictions of plastic flow as a function of grain size are made incorporating differences of dislocation accumulation rate in grain-boundary regions and grain interiors. To depict the deformation response of face-centered cubic copper, three material models are implemented into an Eulerian finite element hydrocode. In model I, three sets of crystals with hard, medium and soft orientations are randomly embedded in the computational domain; the flow stress is developed for isotropic von Mises plasticity from the experimental data of C23, C26 and C30. In model II, rate dependent crystal plasticity with planar double slip is implemented in the grain interiors to study the nonuniform deformation and localized plastic flow while the mechanical behavior of grain boundaries is defined as in model I. In model III, both the grain interior and grain boundary are modeled with crystal plasticity. For all the models, an implicit time integration scheme is adopted for the stress update algorithms.; The trends for the grain size effects is analyzed from the simulation results. At large grain sizes, the Hall-Petch response is observed, while in the nanocrystalline domain, the Hall-Petch slope gradually decreases until it asymptotically approaches the flow stress of the grain boundaries. These computational results are compared with the experimental Hall-Petch slopes for copper and stress-strain measurements from micro to nanocrystalline domains.