Thermally activated defect processes in metallic materials : from rate theory to mechanical properties
Keywords: Mechanical Engineering.

Understanding the mechanical strength of metals and alloys under different temperatures is essential in materials design for modern technology applications. Predicting temperature-dependent mechanical properties requires detailed knowledge of the elementary thermally activated defect processes governing plasticity. These microstructural mechanisms contribute to the plastic flow stress through (a) the 'intrinsic energy barrier' due to unfavorable atomic structures; (b) the long-range elastic interactions between these defects and other obstacles. Both aspects provide crucial inputs to mesoscale modeling methods for plasticity, such as dislocation dynamics (DD). This thesis includes three major projects. The first two focus mainly on (a), in which we combine atomistic simulation with statistical mechanical analysis to develop predictive kinetic theories of defect dynamics under stress. The third project focuses on (b), in which we develop a fast elasticity solver for solving long-range dislocation-void interactions. The first part of the thesis discusses the cross slip of screw dislocations in fcc metals, an essential mechanism for the temperature-dependent stage-III strain hardening. Cross slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic deformation, including dislocation pattern formation, strain hardening, and dynamic recovery. Molecular dynamics (MD) simulation has played an important role in determining the microscopic mechanisms of cross slip, but due to its limited timescale, predicting cross slip rate from MD is only possible at high-stress or high-temperature conditions. The transition state theory (TST) can predict the cross-slip rate over a wide range of stress and temperature conditions, but its predictions have been found to be several orders of magnitude too low in comparison to MD results. This discrepancy can be expressed by a large activation entropy whose physical origin remains unclear. Here we resolve this discrepancy by showing that the large activation entropy results from anharmonic effects, including thermal softening, thermal expansion, and soft vibrational modes of the dislocation. We expect these anharmonic effects to be significant when determining the rate of a wide range of stress-driven thermally activated processes in solids. The second part investigates how shear-transformation (ST) events respond to applied stress and thermal activation in CuZr metallic glasses. Understanding how shear transformation (ST) events respond to applied stress and thermal activation remains challenging for glassy materials due to their amorphous structure. Using MD simulation of early-stage deformation of CuZr metallic glasses, we find an anomalous temperature dependence of the elastic limit. We present the energy-strain landscape (ESL) based on high-throughput NEB calculations to probe the strain dependence on activation energies of multiple competitive ST events. A quantitative description is obtained from ESL analyses for the ST dynamics in metallic glasses, which reveals that the reversibility of ST events governs the elastic limit. We discover a strain-independent quantity eigen barrier that characterizes the reversibility of ST events and thus predicts the elastic limit of metallic glasses. We believe that the ESL picture brings a new perspective to understanding ST events' dynamics in glassy materials under external loading. Finally, we introduce a fast numerical methods we developed based on spherical harmonics for solving elasticity problems with any arbitrary boundary conditions defined on a sphere. We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials, and applied the method to dislocation-void interactions. The method is constructed based on a complete set of basis functions for the displacement potential of the elastic boundary value problem for a spherical hole, as well as the corresponding displacement, stress, and traction fields, all in terms of linear combinations of spherical harmonics. Using the fast transformation between the real and spherical-harmonics spaces provided by the {\it SHTOOLS} package, the method is more efficient than other image stress solvers such as the finite-element method. This method can be readily extended for solving elasticity problems involving inclusions and inhomogeneities, as well as contact between spheres. The tools developed here can also be useful for fast solution of differential equations with spherical boundaries beyond elasticity. The method is applied to long-range elastic interactions between dislocations and voids in crystalline solids and a biomechanical application in the force microscope for measuring immune cell-target interactions