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Weight function for an edge crack in an infinite orthotropic strip under normal point loading
Author(s) -
Das S.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900363
Subject(s) - orthotropic material , stress intensity factor , weight function , mathematical analysis , crack tip opening displacement , mathematics , materials science , harmonic function , structural engineering , geometry , finite element method , fracture mechanics , composite material , engineering
In this paper, the problem of an edge crack of finite length, situated in an orthotropic infinite strip of finite thickness h, under normal point loading has been considered. The displacements and stresses for orthotropic elasticity in plane strain condition are expressed in terms of two harmonic functions. The problem is resolved in a simplistic manner by seeking the solution of a pair of simultaneous integral equations with Cauchy type singularities which have finally been solved through finite Hilbert Transform technique. For large h, the analytical expression of the stress intensity factor (SIF) at the crack tip is obtained, which corresponds to the weight function of a crack under normal point loading. The numerical results of the normalized stress intensity factor at different arbitrary locations of the crack surface and various values of crack length have been computed for a particular orthotropic material (Steel‐Mylar composite) and the results are depicted graphically.