Abstract
In this work we apply a material-frame, kernel-based estimatorof continuum fields to atomic data in order to estimate theJ-integral for the analysis of an atomically sharp crack at finite temperatures.Instead of the potential energy appropriate for zero temperature calculations, weemploy the quasi-harmonic free energy as an estimator of the Helmholtz freeenergy required by the Eshelby stress in isothermal conditions. We employ thesimplest of the quasi-harmonic models, the local harmonic model of LeSar andco-workers, and verify that it is adequate for correction of the zero temperatureJ-integral expression for various deformation states for our Lennard-Jones test material. Weshow that this method has the properties of: consistency among the energy, stress anddeformation fields; path independence of the contour integrals of the Eshelbystress; and excellent correlation with linear elastic fracture mechanics theory.
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