A Finite Element Method for Simulation of Coupled Dynamics of Dislocations and Fracture

TL;DR

This paper introduces a finite element method that simulates the coupled evolution of dislocations and cracks in crystalline materials, accurately reproducing atomistic results and capturing size-dependent brittle and ductile behaviors.

Contribution

The paper presents a novel finite element approach that models dislocation and crack dynamics simultaneously, validated against molecular dynamics simulations and capable of capturing size effects.

Findings

Method accurately reproduces atomistic simulation results.

Captures size-dependent brittle and ductile behaviors.

Demonstrates crack initiation and propagation in various materials.

Abstract

This work presents a finite element method for simulating dynamic processes that involve the coupled evolution of dislocation motion and crack propagation. The method numerically solves the Concurrent Atomistic-Continuum (CAC) formulation of the conservation of linear momentum. A crystalline material is discretized at the unit-cell level using 6-node prism elements whose geometry allows dislocations and cracks to nucleate and propagate along element facets. Nanoscale simulations of single-crystal Cu, Fe, and Si demonstrate the initiation and propagation of dislocations and cracks, and these results are reproduced by the finite element method in excellent agreement with fully atomistic molecular dynamics simulations. Mesoscale simulations of single-crystal Cu further demonstrate the ability of the method to capture size-dependent brittle and ductile behavior. Under plane-strain conditions the Cu model fractures in a brittle manner, while a fully three-dimensional model exhibits curved and intersecting dislocations that blunt the crack tip and prevent crack propagation, resulting in ductile behavior. The accuracy, efficiency, and applicability of the method are discussed.