This note presents the stress intensity factors of a long crack penetrating a circular transforming inhomogeneity. Using the Greens functions of dislocations interacting with a circular inhomogeneity experiencing an isotropic (free expansion) eigenstrain, the elasticity solution is reduced to a system of singular integral equations representing the traction boundary condition along the crack surfaces. The normalized stress intensity factor, obtained through a numerical solution of the integral equations, has a strong dependence on the elastic mismatch, and can be either negative or positive depending on the crack-tip location. The formulation and results generalize a previously published transformation-toughening model that assigns equal elastic moduli to the inhomogeneity and the surrounding medium.
A Long Crack Penetrating a Transforming Inhomogeneity
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Sept. 25, 2002; final revision, Feb. 6, 2004. Associate Editor: K. Ravi-Chandar.
Wang and , Y., and Ballarini , R. (September 7, 2004). "A Long Crack Penetrating a Transforming Inhomogeneity ." ASME. J. Appl. Mech. July 2004; 71(4): 582–585. https://doi.org/10.1115/1.1767166
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