Asymptotic study of the interfacial crack with friction. (English) Zbl 0963.74048

Audoly, B.

J. Mech. Phys. Solids 48, No. 9, 1851-1864 (2000).

Summary: We study a model of interfacial crack in which contact of the crack faces obeys a Coulomb law of friction. For such cracks it is possible that the stress has a singularity stronger than \(r^{-1/2}\) near the tip. In this paper, we demonstrate that these strong singularities can, in fact, be discarded, because they would assume a backward propagation of the crack. In passing, we prove that near-tip slip is possible in one direction only, which is imposed by the sign of the elastic mismatch. The locking of the stress intensity factor during a nonmonotonic cycle of loading is pointed out, as well as the formation of a bubble near the tip under certain loading conditions.

MSC:

74R10	Brittle fracture
74M10	Friction in solid mechanics
74G70	Stress concentrations, singularities in solid mechanics
74G10	Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics

Keywords:

fracture; layered material; formation of bubble; interfacial crack; Coulomb law of friction; strong singularities; near-tip slip; stress intensity factor; nonmonotonic cycle of loading

References:

[1]	Audoly, B., 2000. Mode dependence and the delamination of thin films. J. Mech. Phys. Solids, to be published; Audoly, B., 2000. Mode dependence and the delamination of thin films. J. Mech. Phys. Solids, to be published · Zbl 0992.74051
[2]	Comninou, M., Interface crack with friction in the contact zone, Journal of Applied Mechanics, Transactions of the ASME, 44, 780-781 (1977)
[3]	Comninou, M.; Dundurs, J., An example for frictional slip progressing into a contact zone of a crack, Engineering Fracture Mechanics, 12, 191-197 (1979)
[4]	Comninou, M.; Dundurs, J., Effect of friction on the interface crack loaded in shear, Journal of Elasticity, 10, 203-212 (1980) · Zbl 0457.73098
[5]	Comninou, M.; Dundurs, J., On the behaviour of interface cracks, Res. Mechanica, 1, 249-264 (1980)
[6]	Deng, X., An asymptotic analysis of stationary and moving cracks with frictional contact along bimaterial interfaces and in homogeneous solids, International Journal of Solids and Structures, 31, 2407-2409 (1994) · Zbl 0946.74572
[7]	Dundurs, J.; Comninou, M., Some consequences of the inequality conditions in contact and crack problems, Journal of Elasticity, 9, 71-82 (1979) · Zbl 0393.73117
[8]	Hutchinson, J. W.; Suo, Z., Mixed mode cracking in layered materials, Advances in Applied Mechanics, 29, 63-191 (1991) · Zbl 0790.73056
[9]	Malyshev, B. M.; Salganik, R. L., The strength of adhesive joints using the theory of cracks, Int. J. Fract. Mech., 1, 114-128 (1965)
[10]	Rice, J. R., (Liebowtiz, H., Fracture: An Advanced Treatise, vol. 2 (1968), Academic Press: Academic Press New York), 191-311 · Zbl 0193.54701
[11]	Rice, J. R., A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of Applied Mechanics, 35, 379-386 (1968)
[12]	Rice, J. R., Elastic fracture mechanics concepts for interfacial cracks, Journal of Applied Mechanics, 110, 98-103 (1988)
[13]	Stringfellow, R. G.; Freund, L. B., The effect of interfacial friction on the buckle-driven spontaneous delamination of a compressed thin film, Int. J. Solids Structures, 30, 1379-1395 (1993) · Zbl 0775.73231
[14]	Suo, Z.; Hutchinson, J. W., Interface crack between two elastic layers, Int. J. Fract., 43, 1-18 (1990)