Abstract
We consider the perturbation problem of a Mode III interfacial crack. The perturbation is of geometrical type and can be both perturbation of the crack faces and perturbation of the interface, which can deviate from the initial straight line configuration. Asymptotic formulae are derived for the first-order perturbation of the stress intensity factor. It is shown that, due to the unsymmetrical nature of the problem, the Mode III skew-symmetric weight function derived in Piccolroaz et al. (J Mech Phys Solids 57:1657–1682, 2009) is essential for the derivation of the correct asymptotic formulae. To illustrate the method, we present the numerical results for different geometrical perturbations of a half-plane interfacial crack in an infinite bimaterial structure. Discussion on the extension of the method to finite bodies is also presented.
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References
Antipov YA (1999) An exact solution of the 3-D-problem of an interface semi-infinite plane crack. J Mech Phys Solids 47: 1051–1093
Bercial-Velez JP, Antipov YA, Movchan AB (2005) High-order asymptotics and perturbation problems for 3D interfacial cracks. J Mech Phys Solids 53: 1128–1162
Bueckner HF (1985) Weight functions and fundamental fields for the penny-shaped and the half-plane crack in three-space. Int J Solids Struct 23: 57–93
Bueckner HF (1989) Observations on weight functions. Eng Anal Bound Elem 6: 3–18
Gradshteyn IS, Ryzhik IM (2007) Table of integrals, series, and products. Academic Press, London
Hutchinson JW, Mear ME, Rice JR (1987) Crack paralleling an interface between dissimilar materials. ASME J Appl Mech 54: 828–832
Lazarus V, Leblond JB (1998) Three-dimensional crack-face weight functions for the semi-infinite interface crack - I: Variation of the stress intensity factors due to some small perturbation of the crack front. J Mech Phys Solids 46: 489–511
Movchan AB, Movchan NV (1995) Mathematical modeling of solids with nonregular boundaries. CRC-Press, Boca Raton
Piccolroaz A, Mishuris G, Movchan AB (2007) Evaluation of the Lazarus-Leblond constants in the asymptotic model of the interfacial wavy crack. J Mech Phys Solids 55: 1575–1600
Piccolroaz A, Mishuris G, Movchan AB (2009) Symmetric and skew-symmetric weight functions in 2D perturbation models for semi-infinite interfacial cracks. J Mech Phys Solids 57: 1657–1682
Willis JR, Movchan AB (1995) Dynamic weight functions for a moving crack. I. Mode I loading. J Mech Phys Solids 43: 319–341
Willis JR (1971) Fracture mechanics of interfacial cracks. J Mech Phys Solids 19: 353–368
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Piccolroaz, A., Mishuris, G. & Movchan, A.B. Perturbation of mode III interfacial cracks. Int J Fract 166, 41–51 (2010). https://doi.org/10.1007/s10704-010-9484-7
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DOI: https://doi.org/10.1007/s10704-010-9484-7