Int J Fract DOI 10.1007/s10704-017-0232-0 IUTAM BALTIMORE Elastic crack propagation model for crystalline solids using a self-consistent coupled atomistic–continuum framework Somnath Ghosh · Jiaxi Zhang Received: 30 January 2017 / Accepted: 1 July 2017 © Springer Science+Business Media B.V. 2017 Abstract Deformation and failure processes of crys- talline materials are governed by complex phenom- ena at multiple scales. It is necessary to couple these scales for physics-based modeling of these phenomena, while overcoming limitations of modeling at individ- ual scales. To address this issue, this paper develops self-consistent elastic constitutive and crack propaga- tion relations of crystalline materials containing atomic scale cracks, from observations made in a concur- rent multi-scale simulation system coupling atomistic and continuum domain models. The concurrent multi- scale model incorporates a finite temperature atomistic region containing the crack, a continuum region repre- sented by a self-consistent crystal elasticity constitutive model, and a handshaking interphase region. Atom- istic modeling is done by the molecular dynamics code LAMMPS, while continuum modeling is conducted by the finite element method. For single crystal nickel a nonlinear and nonlocal crystal elasticity constitutive relation is derived, consistent with the atomic poten- tial function. An efficient, staggered solution scheme with parallel implementation is designed for the cou- pled problem. The atomistic–continuum coupling is S. Ghosh (B ) M. G. Callas, Departments of Civil Mechanical and Material Science Engineering, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218, USA e-mail: [email protected] J. Zhang Department of Civil Engineering, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218, USA achieved by enforcing geometric compatibility and force equilibrium in the interphase region. Quantita- tive analyses of the crack propagation process focuses on size dependence, strain energy release rate, crack propagation rate and degradation of the local stiffness. The self-consistent constitutive and crack propagation relations, derived from the concurrent model simula- tion results are validated by comparing results from the concurrent and full FE models. Excellent accuracy and enhanced efficiency are observed in comparison with pure MD and concurrent model results. Keywords Concurrent atomistic–continuum model · Crack propagation · Molecular dynamics · Finite element analysis · Self-consistent modeling · Multi- scale simulation 1 Introduction Damage and failure of structural materials like metals and alloys involve deformation and failure mechanisms than span multiple length and time scales. These mech- anisms can include bond-breaking or atomic separa- tion at the atomic-scale, evolution of dislocation struc- tures and other defects at the sub-micron scale, intra- and transgranular cracks in grains and grain bound- aries at the micron-scale, and fracture zones in struc- tural components at the macro-scale. While signifi- cant progress has been made in computational model- ing of polycrystalline materials to predict deformation 123
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