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Applications of modified Dugdale model to multiple collinear straight cracks with coalesced yield zones

Naved Akhtar, Shehzad Hasan and Sudhanshu Shekhar

Vol. 19 (2024), No. 4, 541–560
DOI: 10.2140/jomms.2024.19.541
Abstract

In this paper, the load-carrying capacity of an infinite elastic-perfectly plastic plate containing five collinear straight cracks with coalesced yield zones was studied using a modified Dugdale model. Important parts of this study are the coalescence of yield zones developed at the internal tips of closely located outer pairs of cracks and the influence of quadratically varying yield stress distribution on the load-bearing capacity and crack-tip opening displacement. Traditional concepts of Muskhelishvili’s complex variable method have been used to obtain analytical expressions for complex potential functions, stress intensity factors (SIFs), yield zone length, and crack-tip opening displacements (CTODs). Numerical results are obtained and shown graphically for yield zone length, applied load ratio, and CTODs. A good agreement of the results is seen with previously published work as limiting cases.

Keywords
multiple cracks, stress intensity factor, Dugdale model, load ratio, intercrack distance
Mathematical Subject Classification
Primary: 74A10, 74B05, 74B10
Milestones
Received: 4 October 2023
Revised: 19 December 2023
Accepted: 28 February 2024
Published: 5 May 2024
Authors
Naved Akhtar
Department of Mathematics
Jamia Millia Islamia
New Delhi 110 025
India
Shehzad Hasan
Department of Mathematics
Jamia Millia Islamia
New Delhi 110 025
India
Sudhanshu Shekhar
Department of Mathematics
Jamia Millia Islamia
New Delhi 110 025
India