title: An atomistic J-integral at finite temperature based on Hardy estimates of continuum fields.
abstract: 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.
authors.affiliation: Sandia National Laboratories, Livermore, CA 94551-0969, USA. rjones@sandia.gov
authors.forename: R E
authors.initials: RE
authors.lastname: Jones
authors.forename: J A
authors.initials: JA
authors.lastname: Zimmerman
authors.forename: J
authors.initials: J
authors.lastname: Oswald
authors.forename: T
authors.initials: T
authors.lastname: Belytschko