An analytical expression for the J2-integral of an interfacial crack in orthotropic bimaterials

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    This paper presents a new analytical expression relating the J2-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 Jk-integrals and SIFs. Although an analytical equation relating J1-integral or strain energy release rate and SIFs is available, a similar relation for J2-integral in debonded anisotropic solids is non-existent. Using this new analytical expression, in conjunction with the values of Jk, 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 J2-integral near the crack tip of a bimaterial orthotropic plate. Different bimaterial combinations are considered, and the effect of material mismatch on Jk is demonstrated.
    Original languageEnglish
    Pages (from-to)1443–1458
    Number of pages16
    JournalFatigue & Fracture of Engineering Materials and Structures
    Issue number9
    Early online date1 Feb 2017
    Publication statusPublished - 4 Sept 2017


    • bimaterial interface crack; debonded dissimilar anisotropic materials; Jk-integral;mixed mode fracture; orthotropic materials; stress intensity factor


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