A Computational Framework for Phase-field Modeling

Report No. ARL-MR-0760
Authors: Jaroslaw Knap and John Clayton
Date/Pages: January 2011; 28 pages
Abstract: As part of the Director's Research Initiative, phase-field theory and simulation software are developed. The theory addresses mechanical twinning in crystalline solids with equilibrium equations obtained via a variational principle in the null temperature limit. Numerical solutions to weak forms of governing equations are obtained via conjugate gradient energy minimization and the finite element (FE) method. Two fundamental problems in materials physics are considered. The first addresses homogeneous nucleation of a twin in a magnesium (Mg) single crystal. Critical shear strains for nucleation obtained numerically using the phase-field approach are in fair agreement with those obtained analytically in the sharp-interface limit. The second addresses twin nucleation in calcite (CaCO3) single crystals subjected to indentation loading. Long, thin, asymmetric twins with sharp cusp-like tips are observed in the numerical simulations and are in qualitative agreement with experiments. All results obtained are predictive; the model does not require calibration or fitting of material parameters.
Distribution: Approved for public release
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Last Update / Reviewed: January 1, 2011