Abstract
We study the interaction between a radial matrix crack and a circular compressible liquid inclusion embedded in an elastic matrix under uniform remote in-plane normal stresses. The crack is simulated by a continuous distribution of climbing edge dislocations. A Cauchy-type singular integral equation is derived by imposing the traction-free condition on the crack surfaces. The singular integral equation is solved numerically using the Gauss-Chebyshev integration formula, resulting in the mode I stress intensity factors at the two crack tips and the internal uniform hydrostatic tension within the liquid inclusion. Our detailed numerical results indicate that the crack will propagate toward or away from the liquid inclusion depending on the inclusion-crack distance, the crack length, the compressibility of the liquid inclusion, the Poisson’s ratio of the matrix and the external loading. This fact implies that the liquid inclusion exhibits softening as well as stiffening effects.
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