Continuum Models of Deformation Mechanisms in Nanocrystalline Metals

Nanocrystalline metals are polycrystalline metals with grain sizes in the nanometer range. They have attracted significant interest in recent years due to their unique mechanical and electrical properties. The main objective of this thesis is to develop continuum-scale descriptions of nanoscale deformation and failure mechanisms in nanocrystalline metals. The research has focused on three specific aspects: the influence of grain boundary mechanisms on the grain-size dependence of the yield stress, the influence of grain boundary friction on the response to shock loading and the increased ductility accompanied by increased strength observed in ultrafine crystals with embedded growth nanotwins. A phenomenological model considering grain boundary sliding and accommodation as uncoupled dissipative deformation mechanisms is proposed to describe the constitutive behavior of grain boundaries. In agreement with atomistic models and experiments, tensile test simulations using the numerical model predict the inverse Hall-Petch effect, i.e. a dependence of the yield stress on the inverse square root of the grain size with a negative slope. In addition, the model suggests that the observed discrepancy between atomistic and experimental results may be partially related to rate dependence effects. Recent atomistic simulation results suggest that high states of compression inhibit grain boundary sliding, which causes a reactivation of intragrain dislocation activity, leading to much higher material strength. We extend the continuum model to account for these frictional effects inhibiting deformation at the grain boundary. The extended model captures the salient features of the shock response of nanocrystalline copper observed in atomistic simulations, including the shock propagation and jump conditions, as well as the peak and trailing values of the deviatoric stress profile. One of the limitations of nanocrystals is their low ductility. It has been shown recently that the high strength of nanocrystals without a compromise in ductility can be achieved by growing ultrafine crystals with embedded nano-twins. Twin boundaries provide equivalent barriers to dislocation motion as grain boundaries do in nanocrystals, but without their associated low ductility. A model for describing the strengthening and toughening role of nanotwins is developed and calibrated to experiments. The model captures the dependence of the stress-strain response on twin density including the onset of fracture observed in experiments. Part of the legacy of this thesis work is a computational framework for large-scale simulation of the continuum-level response of nanocrystalline metals. This parallel computing framework was developed in order to address the necessity of describing the full three-dimensional response of large number of grains subject to a wide range of loading conditions. Thesis Supervisor: Rafil Radovitzky Associate Professor of Aeronautics and Astronautics Committee Member: Jaime Peraire Professor of Aeronautics and Astronautics Committee Member: Christopher Schuh Associate Professor of Materials Science and Engineering Committee Member: Subra Suresh Professor of Materials Science and Engineering