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

R. E. Jones, J. A. Zimmerman, J. Oswald, T. Belytschko

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

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.

Original languageEnglish (US)
Article number015002
JournalJournal of Physics Condensed Matter
Volume23
Issue number1
DOIs
StatePublished - Jan 12 2011
Externally publishedYes

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics

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