IJPAM: Volume 105, No. 2 (2015)

DUGDALE MODEL FOR THREE UNEQUAL COLLINEAR
STRAIGHT CRACKS WITH COALESCED YIELD ZONES:
A COMPLEX VARIABLE APPROACH

S. Hasan
Department of Mathematics
Jamia Millia Islamia (Central University)
New Delhi, 110 025, INDIA


Abstract. The paper aims to provide an analytical solution of the problem of three unequal collinear straight cracks with coalesced plastic/yield zones weakening an infinite elastic perfectly plastic plate. These cracks are located on the real axis in such a manner that the two cracks exist very close to each other. Cracks are open in mode-I type deformation on the application of uniform stresses at the infinite boundary of the plate. Hence, yield zones are developed at each crack tip. Stresses applied at the infinite boundary of the plate increased to such a limit that the yield zones developed between two closely located cracks are coalesced. Assume that the yield stress of the plate is enough to detain further opening of cracks. The problem is solved using complex variable method and analytical expressions are derived for stresses applied at infinite boundary of the plate, yield zone length. A comparative study is carried out for load bearing capacity with the results of two collinear straight cracks, which is the limiting case of the cracks configuration considered in this paper.

Received: Jule 3, 2015

AMS Subject Classification: 74R05, 74R10

Key Words and Phrases: crack opening displacement, Dugdale model, multiple cracks, stress intensity factor, Yield zone

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DOI: 10.12732/ijpam.v105i2.13 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 2
Pages: 311 - 323


CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).