TY - JOUR

T1 - An atomistic J-integral at finite temperature based on hardy estimates of continuum fields

AU - Jones, R. E.

AU - Zimmerman, J. A.

AU - Oswald, J.

AU - Belytschko, T.

PY - 2011/1/12

Y1 - 2011/1/12

N2 - In this work we apply a material-frame, kernel-based estimator of continuum fields to atomic data in order to estimate the J-integral for the analysis of an atomically sharp crack at finite temperatures. Instead of the potential energy appropriate for zero temperature calculations, we employ the quasi-harmonic free energy as an estimator of the Helmholtz free energy required by the Eshelby stress in isothermal conditions. We employ the simplest of the quasi-harmonic models, the local harmonic model of LeSar and co-workers, and verify that it is adequate for correction of the zero temperature J-integral expression for various deformation states for our Lennard-Jones test material. We show that this method has the properties of: consistency among the energy, stress and deformation fields; path independence of the contour integrals of the Eshelby stress; and excellent correlation with linear elastic fracture mechanics theory.

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

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U2 - 10.1088/0953-8984/23/1/015002

DO - 10.1088/0953-8984/23/1/015002

M3 - Article

C2 - 21406817

AN - SCOPUS:78651492009

VL - 23

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 1

M1 - 015002

ER -