In this paper, the boundary element method (BEM) for two-dimensional contact mechanics analysis is applied to a number of angle crack problems involving crack surfaces in contact. The formulation employed is based on the quadratic isoparametric boundary element, and the near-tip fields for both open and closed crack tips are properly modelled in the analysis using special crack tip elements with mid-side nodes. Stress intensity factor solutions are presented for a range of geometries and coefficients of friction in each of the problems treated. Where possible, the BEM results are compared with those available in the literature and good agreement between them is obtained. The study shows that friction between the crack surfaces in contact can have a significant effect indeed on the magnitude of the stress intensity factors for all the problems considered.

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Journal Engineering Fracture Mechanics
Liu, S.B., & Tan, C. (1992). Two-dimensional boundary element contact mechanics analysis of angled crack problems. Engineering Fracture Mechanics, 42(2), 273–288. doi:10.1016/0013-7944(92)90218-4