Summary
A Zener-Stroh crack is initiated by dislocations pile-up. Due to this displacement loading mechanism, only one of the two crack tips is sharp, and crack propagation is possible along the sharp tip only. When such a crack is initiated near an interface, the crack faces behind the sharp crack tip may contact each other due to material mismatch and loading combination. In the present study, a subinterface Zener-Stroh crack is analyzed with contact zone consideration near the tip. The problem is formulated as a set of nonlinear Cauchy-type singular integral equations which are solved numerically using Erdogan and Gupta's method. The physically pathological features of interpenetration of the crack surfaces and oscillation of the near tip fields are eliminated in the solutions due to the presence of a contact zone near the crack tip. It is found that the normal traction is bounded at the crack tip where a contact zone exists; while the shear traction has square-root singularities at both the crack tips. This result, is totally different to the case of an interface crack where Mode I and Mode II stress intensity factors, are inter-related at the sharp crack tip.
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References
Zener, C.: The micro-mechanism of fracture. Fracturing of metals. Cleveland, American Society for Metals, 3–31 (1948).
Stroh, A. N.: The formation of cracks as a result of plastic flow. I. Proc. Roy. Soc. LondonA 223, 404–414 (1954).
Cottrell, A. H.: Theory of brittle fracture in steel and similar metals. Trans. Metall. Soc. AIME212, 192–203 (1958).
Kikuchi, M., Shiozawa, K., Weertman, J. R.: Void nucleation in astrology. Acta Met.29, 1747–1758 (1981).
Weertman, J. R.: Zener-Stroh crack Zener-Hollomon parameter, and other topics. J. Appl. Phys.60, 1877–1887 (1986).
Erdogan, F., Gupta, G. D.: On the numerical solution of singular integral equations. Quart. Appl. Math.30, 525–534 (1972).
Comninou M.: The interface crack. J. Appl. Mech.44, 631–636 (1977).
Comninou, M.: The interface crack in a shear field. J. Appl. Mech.45, 287–290 (1978).
Comninou M., Schusmueser, D.: The interface crack in a combined tension-compression and shear field. J. Appl. Mech.46, 345–348 (1979).
Hills, D. A., Kelly, P. A., Dai, D. N., Korsunsky, A. M.: Solution of crack problems. The distributed dislocation technique. Dordrecht: Kluwer 1996.
Dundurs, J., Comninou M.: Some consequences of the inequality conditions in contact and crack problems. J. Elasticity (1980).
Yang, M. F., Kim, K. S.: The behavior of subinterface cracks with crack-face contact. Eng. Fract. Mech.44, 155–165 (1993).
Dundurs, J.: Discussion. J. Appl. Mech.36, 650–652 (1969).
Fan, H., Sun, Y. M., Xiao, Z. M.: Contact zone in an interface Zener-Stroh crack. Mech. Mater.30, 151–159 (1998).
Dundurs, J.: Elastic interaction of dislocations with inhomogeneities. Mathematical theory of dislocations, pp. 70–115, New York: ASME 1969.
Muskhelishvili, N. I.: Singular integral equations. Groningen: Noordhoff 1953.
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Xiao, Z.M., Fan, H. & Suh, Y.M. On the contact zone of a subinterfacial Zener-Stroh crack. Acta Mechanica 142, 133–148 (2000). https://doi.org/10.1007/BF01190015
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DOI: https://doi.org/10.1007/BF01190015