Assessment of the interaction between three collinear unequal straight cracks with unified yield zones

N. Akhtar; S. Hasan; N. Akhtar; S. Hasan

doi:10.3934/matersci.2017.2.302

AIMS Materials Science

2017, Volume 4, Issue 2: 302-316. doi: 10.3934/matersci.2017.2.302

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Research article Special Issues

Assessment of the interaction between three collinear unequal straight cracks with unified yield zones

N. Akhtar ^,,
S. Hasan

Department of Mathematics, Jamia Millia Islamia, New Delhi-110 025, India

Received: 04 December 2016 Accepted: 04 February 2017 Published: 10 February 2017

The Dugdale model has been modified in the paper to include the effect of linearly varying yield stress distribution. An isotropic infinite plate is considered with three collinear unequal straight cracks with coalesced yield zones. Muskhelishvili’s complex variable approach is used to solve the problem. Closed form analytical expressions for stress intensity factor and crack tip opening displacement at each crack tip are obtained when boundary of the plate is subjected to uniform stress distribution and developed yield zones are assumed variable stress distribution. Different yield zone lengths and crack tip opening displacements are observed at each crack tip. A comparative case with the solution of two equal cracks is studied to show that the problem considered in this paper is the predecessor of the two equal cracks problem.
- multiple-site damage,
- stress intensity factor,
- yield zone length,
- Dugdale strip yield model,
- crack-tip opening displacement
Citation: N. Akhtar, S. Hasan. Assessment of the interaction between three collinear unequal straight cracks with unified yield zones[J]. AIMS Materials Science, 2017, 4(2): 302-316. doi: 10.3934/matersci.2017.2.302

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Abstract

The Dugdale model has been modified in the paper to include the effect of linearly varying yield stress distribution. An isotropic infinite plate is considered with three collinear unequal straight cracks with coalesced yield zones. Muskhelishvili’s complex variable approach is used to solve the problem. Closed form analytical expressions for stress intensity factor and crack tip opening displacement at each crack tip are obtained when boundary of the plate is subjected to uniform stress distribution and developed yield zones are assumed variable stress distribution. Different yield zone lengths and crack tip opening displacements are observed at each crack tip. A comparative case with the solution of two equal cracks is studied to show that the problem considered in this paper is the predecessor of the two equal cracks problem.

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