Interfacial excess energy, excess stress and excess strain in elastic solids: Planar interfaces

Rémi Dingreville, Jianmin Qu

Research output: Contribution to journalArticlepeer-review

90 Scopus citations

Abstract

In this paper, interfacial excess energy and interfacial excess stress for coherent interfaces in an elastic solid are reformulated within the framework of continuum mechanics. It is shown that the well-known Shuttleworth relationship between the interfacial excess energy and interfacial excess stress is valid only when the interface is free of transverse stresses. To account for the transverse stress, a new relationship is derived between the interfacial excess energy and interfacial excess stress. Dually, the concept of transverse interfacial excess strain is also introduced, and the complementary Shuttleworth equation is derived that relates the interfacial excess energy to the newly introduced transverse interfacial excess strain. This new formulation of interfacial excess stress and excess strain naturally leads to the definition of an in-plane interfacial stiffness tensor, a transverse interfacial compliance tensor and a coupling tensor that accounts for the Poisson's effect of the interface. These tensors fully describe the elastic behavior of a coherent interface upon deformation.

Original languageEnglish
Pages (from-to)1944-1954
Number of pages11
JournalJournal of the Mechanics and Physics of Solids
Volume56
Issue number5
DOIs
StatePublished - May 2008

Keywords

  • Grain boundaries
  • Interface energy
  • Interface properties
  • Theory and modeling

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