Debonding of a circular inclusion: Asymmetric propagation of a pair of cracks

Abstract

Crack propagation associated with two initially symmetrical cracks located at the interface between an inclusion and the surrounding matrix, subjected to remote traction, is studied by means of Griffith's energy criterion within the framework of Linear elastic fracture mechanics. Using Muskhelishvili's method of complex potentials, we derive semi-analytical expressions of the stress intensity factor and energy release rate at the crack-tip. Finally, the discussion of the crack propagation mode is investigated. Based on these results, we discuss the mode of propagation of the cracks. Our analysis points at the possibility of a single-sided, rather than simultaneous, symmetric crack growth, even if both initial configuration and loading are symmetric.

Direct evaluation of stress intensity factors and T-stress for bimaterial interface cracks using the extended isogeometric boundary element method

“…Figures 22a and 22b also present the semi-analytical and numerical SIF solutions provided by Le et al [69]. In general, when compared to the FEM solutions given by the reference, the present results better approximate the semi-analytical responses, which demonstrates the efficiency of the proposed direct XIGABEM to determine the SIFs for interface cracks.…”

“…For each crack geometry, two material combinations are considered: the first contains a hard inclusion (E 2 = 10E 1 , ν 1 = 0.3 and ν = 0.2), while the second has a soft inclusion (E 1 = 10E 2 , ν 1 = 0.3 and ν 2 = 0.2). Le et al [69] derived semi-analytical expressions of the SIFs for this problem, which are used for comparison against our direct XIGABEM solutions. The isogeometric boundary element mesh considered in the numerical analysis is composed of 184 elements: 10 at each side of the plate and 72 along the perimeter of the inclusion.…”

“…The results obtained by XIGABEM for the normalised SIFs of tips A and C with the variation of γ 1 are shown in Figs 22a and 22b for the cases of a hard inclusion and a soft inclusion, respectively. For comparisons with the solutions given by Le et al [69], the normalised SIFs are computed by K * 1 + iK * 2 = (K 1 + iK 2 ) / σ 0 √ 2R 0.5+iε . For tip A, in both material combinations, the value of…”

Theoretical analysis of two cracks in sandstone under the simultaneous action of pressure and shear stress

“…Millwater 15 proposed a simple approximate technique to evaluate the SIFs of collinear cracks with arbitrary lengths and spacing under the action of tensile loading. Le et al 16 examined the SIFs of two symmetrical cracks located at the interface of inclusion and the surrounding matrix. Yi et al 17 extended the mixed‐mode Dugdale model to investigate an interface crack problem.…”