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An analytical expression for the J 2 ‐integral of an interfacial crack in orthotropic bimaterials
Author(s) -
Tafreshi A.
Publication year - 2017
Publication title -
fatigue and fracture of engineering materials and structures
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.887
H-Index - 84
eISSN - 1460-2695
pISSN - 8756-758X
DOI - 10.1111/ffe.12587
Subject(s) - orthotropic material , stress intensity factor , integral equation , fracture mechanics , strain energy release rate , materials science , j integral , mathematical analysis , traction (geology) , singular integral , anisotropy , expression (computer science) , mathematics , mechanics , structural engineering , composite material , physics , finite element method , optics , engineering , computer science , mechanical engineering , programming language
Abstract This paper presents a new analytical expression relating the J 2 ‐integral and stress intensity factors (SIF) in an in‐plane traction‐free crack between two orthotropic elastic solids using the complex function method. The singular oscillatory near tip field of a bimaterial interfacial crack is usually characterized by a pair of SIFs. In linear elastic interfacial fracture mechanics, the majority of numerical and experimental methods rely on the analytical equations relating J k ‐integrals and SIFs. Although an analytical equation relating J 1 ‐integral or strain energy release rate and SIFs is available, a similar relation for J 2 ‐integral in debonded anisotropic solids is non‐existent. Using this new analytical expression, in conjunction with the values of J k , the SIFs can be computed without the need for an auxiliary relation. An example with known analytical solutions for SIFs is presented to show the variation of the J 2 ‐integral near the crack tip of a bimaterial orthotropic plate. Different bimaterial combinations are considered, and the effect of material mismatch on J k is demonstrated.