Elasto-plastic analysis for a finite thickness rectangular plate containing a through-thickness central crack

Abstract

The objective of this work is to present a three-dimensional analysis of the elasto-plastic response of a center-cracked rectangular panel by using an alternate method, the method of lines (MOL). The problem of a finite thickness rectangular plate containing a through-thickness central crack under uniaxial tension is studied in detail. An incremental procedure is used to seek the 3-D elasto-plastic stress and strain distribution. The Prandtl-Reuss equations and the associated von Mises flow rule are employed. The material is assumed to be elastic-plastic with nonlinear work-hardening. Effective stress and effective strain concepts are used. The MOL is used to reduce the governing equations on displacements to a coupled set of ordinary differential equations (ODE) along x, y, z lines. These are integrated by Peano-Baker method. Since the ODE are of constant coefficient the coefficient matrix is diagonalized and the matrizon is easily evaluated. Numerical results on stresses, displacements, the growth of plastic zone and the crack surface opening displacements are reported and their variation along the thickness are presented in graphs. The variation of the stress intensity factor K 1, along the thickness direction is given. It is found that the computation time needed for determining the distribution of stresses and strains is much less than what has been reported by using other methods. A comparison of results on SIF with those obtained by other methods is also given.