Developing A Crack Propagation Model in the Metallic Materials from A Self-consistent Coupled Atomistic-Continuum Model
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Date
2017-06-21
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Johns Hopkins University
Abstract
Understanding failure process in metallic materials is crucial to their engineering applications. The complexity of failure analysis origins from the intrinsic nature that failure process couples various mechanisms across multiple spatial and temporal scales. While crack propagation models at macroscopic level such as cohesive zone model have made substantial progress in crack propagation studies, these models performs poorly at micron and sub-micron scale. One major reason is the lacking of representation of microstructure dependence and interaction between cracks and plastic deformations such as dislocation and twinning. There is considerable need to develop a physical based crack propagation model addressing the evolution of deformation mechanisms and the impact on crack propagation.
In this dissertation, a novel computational framework is developed to explicitly model the process of crack propagation and associated deformation mechanisms evolution with atomistic resolution. The development starts with building a robust tool to characterize and quantify the evolution of deformation mechanisms in atomistic simulation. To overcome the length scale limitation of pure atomistic simulation methods such as molecular dynamics, a self-consistent atomistic and continuum coupling model is introduced using continuum model in the far field and atomistic model near crack tip. The coupling is achieved by enforcing geometric compatibility and force equilibrium condition in a weak sense at the interface region between two domains. The coupled model takes care of numerical error sources such as ghost-force and phonon-reflection and allows finite temperature applied in the atomistic domain in order to study the thermally activated processes. A nonlinear and nonlocal constitutive relation is used for the continuum domain to be consistent with inter-atomic potentials. The coupled model is solved iteratively using software package LAMMPS　as simulator of atomistic system and finite element code for continuum system, both efficiently implemented in parallel and communicating using message passing interface(MPI). \\
The developed characterization tool in atomistic simulation revealed the orientation dependence of nucleation and evolution　of crack tip deformation mechanisms, the analysis shows the change of dominated mechanism also has strong effect on the energy evolution. The coupled concurrent model is used to study the crack tip field and dynamic crack propagation. The simulation result shows a transition between crack propagation and dislocation nucleation for different orientations. Crack propagation is found to prefer low index $(100)$, $(110)$ planes than high index planes. A parametrized rate form of crack propagation law is extracted from the coupled concurrent model, and applied in a pure continuum model for validation. In the dislocation dominated scenario, a dislocation density based information passing method is introduced to incorporate the plastic deformation into the coupled model validated by correlating distribution of dislocation density with plastic deformation rate in the interface region.
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Keywords
Multi-scale modelling, Molecular dynamics, Crack propagation, Dislocation, Atomistic-continuum coupling