Modeling fracture and failure of material is a complex phenomenon that needs an atomic-scale understanding of the kinetics and energetics of different deformation mechanisms. Several efforts have been made over the years to model the fracture at continuum scale e.g., cohesive zone model. The success of these continuum scale fracture models relies on the appropriate incorporation of the interaction between the crack and the different deformation mechanisms within the material such as interatomic decohesion, dislocation nucleation, mobility of the dislocations, dislocation reaction, twining etc. Hence, there is a need to develop a systematic framework to quantify these interactions and develop physics-based constitutive laws that can be used in continuum scale fracture models. 
The present work develops a concurrent coupled atomistic-continuum model to capture the interaction between different deformation mechanisms on the propagation of the crack. The atomistic region is modeled using time-accelerated Molecular Dynamics (MD) and for the continuum region, the density-based Crystal Plasticity Finite Element (CPFE) model is used. The Hyperdynamics is used for the time acceleration of the MD. The atomistic-continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in the interface region. A sequence of steps is performed to characterize and quantify the dislocations at the interface and then transfer those dislocations from the atomistic to the continuum region in the density form. The propagation of the dislocations in the density form is modeled by solving the transport equation of a conserved quantity, also known as the advection equation. The meshless Reduced Kernel Particle Method (RKPM) is used to solve the advection equation over the continuum domain.
The developed concurrent coupled atomistic-continuum model is used to study the brittle and ductile propagation of a crack in a nickel single crystal.  From self-consistent homogenization, crack tip dislocation nucleation and evolution are determined for crystal plasticity models, as well as parametrized form of crack propagation laws. The concurrent model is also used to construct the free energy functional of the phase-field model where the evolution of different energy contributions during the fracture process is obtained.


Development of a Self-consistent Coupled Atomistic-Continuum Model to Study the Brittle and Ductile Fracture in Metallic Materials

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