TY - JOUR
T1 - Interfacial excess energy, excess stress and excess strain in elastic solids
T2 - Planar interfaces
AU - Dingreville, Rémi
AU - Qu, Jianmin
PY - 2008/5
Y1 - 2008/5
N2 - 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.
AB - 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.
KW - Grain boundaries
KW - Interface energy
KW - Interface properties
KW - Theory and modeling
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U2 - 10.1016/j.jmps.2007.11.003
DO - 10.1016/j.jmps.2007.11.003
M3 - Article
AN - SCOPUS:41749105767
SN - 0022-5096
VL - 56
SP - 1944
EP - 1954
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 5
ER -