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.
Highlights
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
The material behaviour at the tip of the Mode I crack in a homogenous body is in general very complex and difficult to describe by continuum mechanical models
Cohesive zone is considered as the crack extension under the action of closing cohesive stress generated by elastic constraint exerted by surrounding non-yielded material over the cohesive zone
Summary
The material behaviour at the tip of the Mode I crack in a homogenous body is in general very complex and difficult to describe by continuum mechanical models. This zone is called as the plastic or cohesive zone. Qualitative characteristics of the cohesive zone were experimentally verified by Hahn et al [1] They conducted experiments on cracked steel specimens and found the cohesive zone, as shown, by etching the polished surface in front of the crack tip. In a bimaterial comprising elasticity identical but plasticity and strength mismatched constituents (like steels), the Mode I crack near the interface has the characteristics similar to the one in homogeneous parent body as long as the cohesive zone is in the parent body alone. The part of cohesive zone in the interface body is subjected to cohesive stress different from that acting over its portion in the parent body that triggers the effect of strength mismatch across the interface over the crack tip. The parent body, the weld and the interface body have similar elastic properties but variable strengths of comparable magnitudes
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