Stress intensity factors and T-stress for an edge interface crack by symplectic expansion

• Published in: Engineering fracture mechanics Vol. 102; pp. 334 - 347
• Main Authors: Zhou, Zhenhuan, Xu, Xinsheng, Leung, Andrew Y.T., Huang, Yi
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-04-2013
• Subjects: Adjoints; Boundary conditions; Complex stress intensity factor; Conjugates; Fracture mechanics; Interface crack; Mathematical analysis; Mathematical models; Orthogonality; Stress intensity factor; Symplectic method; T-stress; Interface crack; Symplectic method; T-stress; Complex stress intensity factor
• ISSN: 0013-7944; 1873-7315
• DOI: 10.1016/j.engfracmech.2013.03.007

•Established a Hamilton system for fracture analysis of an edge interface crack.•Derived symplectic eigenfunctions which compose a complete space.•Obtained exact solutions for both displacements and stresses simultaneously.•Represented the formulae of Mode I, II SIFs and T-stress by the eigenfunctions.•Analyzed the variations of SIFs with various influencing factors.
An analytical method is presented for finding the complex stress intensity factors (SIFs) and T-stress at an edge bi-material interface crack. A Hamiltonian system is first established by introducing dual (conjugate) variables of displacements and stresses whose solutions are expanded in terms of the symplectic series. With the aid of the adjoint symplectic orthogonality, coefficients of the series are determined by the boundary conditions along the crack faces and along the external geometry. Analytical solutions of SIFs and T-stress are obtained simultaneously. Numerical examples including the complex mixed boundary conditions are given. Factors influencing the SIFs are discussed.