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Solution of Singular Integrals in Mathematical Model of Mode I Crack near Strength Mismatched Interface
School of Mechanical and Building Sciences, VIT University, Vellore, India
Department of Mechanical Engineering, Indian Institute of Technology, Mumbai, India
- 1 School of Mechanical and Building Sciences, VIT University, Vellore, India
- 2 Department of Mechanical Engineering, Indian Institute of Technology, Mumbai, India
American Journal of Computational Mathematics·Volume 02 (2012)·Pages 156–162·Published 21 June 2012·DOI10.4236/ajcm.2012.22021
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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.
KeywordsCrack Opening DisplacementSingular IntegralsStrength MismatchWeld InterfaceCauchy’s Principal Value Theorem
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