Solution of Singular Integrals in Mathematical Model of Mode I Crack near Strength Mismatched Interface

PDF (Size:259KB) PP. 156-162   DOI: 10.4236/ajcm.2012.22021

Author(s)

Characteristics of Mode I crack near the interface of elasticity matched but plasticity and strength mismatched materials differ from those of the crack in a homogenous body. Interface body of different strength influences the plastic or cohesive zone at the crack tip in parent body. The mathematical model for load line opening of the crack near the interface in linear elastic regime involves singular integrals. The paper presents explicit solution of these integrals with the help of Cauchy’s principal value theorem. Cases of thin and thick welds between the materials are investigated. Solutions of the integrals are well substantiated. Final results are provided in a consolidated form.

KEYWORDS

Crack Opening Displacement; Singular Integrals; Strength Mismatch; Weld Interface; Cauchy’s Principal Value Theorem

Cite this paper

S. Bhat and V. Ukadgaonker, "Solution of Singular Integrals in Mathematical Model of Mode I Crack near Strength Mismatched Interface," American Journal of Computational Mathematics, Vol. 2 No. 2, 2012, pp. 156-162. doi: 10.4236/ajcm.2012.22021.

 [1] G. T. Hahn and A.R. Rosenfield, “Local Yielding and Extension of a Crack under Plane Stress,” Acta Metallurgica, Vol. 13, No. 3, 1965, pp. 293-306. doi:10.1016/0001-6160(65)90206-3 [2] D. Wappling, J. Gunnars and P. Stahle, “Crack Growth across a strength Mismatched Bimaterial Interface,” International Journal of Fracture, Vol. 89, No. 3, 1998, pp. 223-243. doi:0.1023/A:1007493028039 [3] D. Porter and D. S. G. Stirling, “Integral Equations—A Practical Treatment, from Spectral Theory to Applications,” Cambridge University Press, Cambridge, 1990. [4] F. O. Reimelmoser and R. Pippan, “The J-Integral at Dugdale Cracks Perpendicular to Interfaces of Materials with Dissimilar Yield Stresses,” International Journal of Fracture, Vol. 103, No. 4, 2000, pp. 397-418. doi:10.1023/A:1007605224764