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D. Porter and D. S. G. Stirling, “Integral Equations—A Practical Treatment, from Spectral Theory to Applications,” Cambridge University Press, Cambridge, 1990.

has been cited by the following article:

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

  AUTHORS: Sunil Bhat, Vijay G. Ukadgaonker

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

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.2 No.2, June 22, 2012

  ABSTRACT: 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.