Closed-form solutions for a mode III radial matrix crack penetrating a circular inhomogeneity

Erdogan, 1972, On the numerical solution of singular integral equations, Q. Appl. Math., 29, 525, 10.1090/qam/408277 Erdogan, 1974, Interaction between a circular inclusion and an arbitrarily oriented crack, ASME J. Appl. Mech., 41, 1007, 10.1115/1.3423424 Luo, 1991, Matrix cracking in fiber-reinforced composite materials, ASME J. Appl. Mech., 58, 846, 10.1115/1.2897274 Xiao, 2001, Stress intensity factor for a Griffith crack interacting with a coated inclusion, Int. J. Fract., 108, 193, 10.1023/A:1011066521439 Wang, 2002, An edge dislocation in a three-phase composite cylinder model with a sliding interface, ASME J. Appl. Mech., 69, 527, 10.1115/1.1467090 Wang, 2003, A long crack penetrating a circular inhomogeneity, Meccanica, 38, 579, 10.1023/A:1024785726456 Wang, 2004, A long crack penetrating a transforming inhomogeneity, ASME J. Appl. Mech., 71, 582, 10.1115/1.1767166 Palaniappan, 2005, Classical image treatment of a geometry composed of a circular conductor partially merged in a dielectric cylinder and related problems in electrostatics, J. Phys.: Math. Gen., 38, 6253 W. Thomson (Lord Kelvin), Extrait D’une lettre de M. Liouville, Originally in J. Math. Pures Appl. 10 (1845) 364. Honein, 1992, On two circular inclusions in harmonic problems, Q. Appl. Math., 50, 479, 10.1090/qam/1178429 Palaniappan, 1999, Electrostatics of the conducting double sphere, J. Appl. Phys., 86, 3418, 10.1063/1.371223 Palaniappan, 2002, Electrostatics of two intersecting conducting cylinders, Math. Comput. Modell., 36, 821, 10.1016/S0895-7177(02)00229-7 Muskhelishvili, 1963 Yoon, 2006, Effect of a thin surface coating layer on thermal stresses within an elastic half-plane, Acta Mech., 185, 227, 10.1007/s00707-006-0353-4 Ru, 1997, A circular inclusion with circumferentially inhomogeneous interface in antiplane shear, Proc. R. Soc. Lond., A453, 2551, 10.1098/rspa.1997.0136 Erdogan, 1991, The Mode-III crack problem in bonded materials with a nonhomogeneous interfacial zone, ASME J. Appl. Mech., 58, 419, 10.1115/1.2897202 Wang, 1999, Screw dislocation near a slant edge crack, Mech. Mater., 31, 63, 10.1016/S0167-6636(98)00034-9 Chen, 1999, The behavior of screw dislocations emitted from a star crack with a central hole, Int. J. Fract., 99, 293, 10.1023/A:1018779503672 Wang, 2003, A circular inclusion with a nonuniform interphase layer in antiplane shear, Int. J. Solids Struct., 40, 881, 10.1016/S0020-7683(02)00644-3 C. Zener, The Micro-Mechanism of Fracture. Fracturing of Metals, American Society for Metals, Cleveland, 1948, pp. 3–31. Stroh, 1954, The formation of cracks as a result of plastic flow, I, Proceedings of the Royal Society of London A, 223, 404, 10.1098/rspa.1954.0124 Xiao, 2000, A Zener–Stroh crack in a fiber-reinforced composite material, Mech. Mater., 32, 593, 10.1016/S0167-6636(00)00021-1 Xiao, 2001, Stress analysis for a Zener–Stroh crack interacting with a coated inclusion, Int. J. Solids Struct., 38, 5007, 10.1016/S0020-7683(00)00335-8 Xiao, 2004, Electro-elastic stress analysis for a Zener–Stroh crack interacting with a coated inclusion in a piezoelectric solid, Acta Mech., 171, 29, 10.1007/s00707-004-0129-7 Chen, 2007, Singular integral equation method for multiple Zener–Stroh crack problems in antiplane elasticity, Eng. Anal. Bound. Elem., 31, 22, 10.1016/j.enganabound.2006.07.009