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Local Buckling Analysis of a Cracked Plate Subjected to Tension Using a Hybrid Method of FEM and BFM

Local buckling characteristics of a centrally cracked plate subjected to a uniaxial tensile load are analyzed by the finite element method based on the linear bifurcation theory. An analysis of two-dimensional stress distribution of the plate in the pre-buckling state is required in the process of buckling analysis. The stress distribution is analyzed by the body force method that guarantees high precision solution for a cracked plate. The predicted buckling load and mode agree well with the experimental results. Introduction A region of compressive stress may develop near a crack in a plate subjected to tensile load. As a consequence, local buckling in the vicinity of the crack may occur when tensile loading progresses. This phenomenon, so-called crack-buckling, complicates the fracture problem of the cracked plate even more. Many investigators have already reported undesirable effects due to the crack buckling on residual strength and fatigue characteristics of cracked plates. For instance, in static strength tests, reductions of the residual strength after buckling were observed by Dixson and Strannigan [1], Walker [2], Forman [3], and others. In acoustic fatigue tests [4-5], it was also found that the rate of crack propagation might be considerably increased after buckling. It is necessary, therefore, preliminarily to know a buckling load in any study of these fields. As regards the theoretical studies, the first to elucidate the qualitative nature in this problem was Cherepanov [6] who treated buckling of membranes. The theoretical analyses for buckling of cracked plates have been consecutively developed by Soviet workers [7-8]. On the other hand, some remarkable contributions on the quantitative nature have been made by Petyt [9] and by Markstroem and Storakers [10], using the finite element method. However, the theoretical studies have met some difficulties, because it is virtually impossible to obtain an exact solution and also because the numerical approach are often inaccurate. This paper deals with a typical problem of a rectangular plate with a central crack perpendicular to a uniaxial tensile load. The characteristics of the crack buckling are analyzed by use of the finite element method based on the linear bifurcation theory. The analysis of two dimensional stress fields of the plate in the pre-buckling state is also required in the buckling analysis. In view of the fact that the crack buckling behavior is predominantly affected by the in-plane stress distribution around the crack, the stress field is analyzed by the body force method [11] suited well for high precision stress analysis of a cracked plate. The predicted buckling load and mode are compared with the experimental results and the accuracy of analysis is also discussed. Graduate student, Mechanical Engineering Department Professor, Mechanical Engineering Department Key Engineering Materials Online: 2003-07-15 ISSN: 1662-9795, Vols. 243-244, pp 541-546 doi:10.4028/www.scientific.net/KEM.243-244.541 © 2003 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-13/03/20,21:06:05) 2 Title of Publication (to be inserted by the publisher) Buckling Analysis A problem to be solved is a centrally cracked plate illustrated in Figure 1. The boundaries at the loading edges are clamped with respect to deflection and are free at the others. In the classical stability problem in which the plate is assumed to be flat until buckling occurs, nonlinear behavior due to bending can be neglected. It follows that the in-plane stresses are linearly proportional to the applied tensile load. This implies that the in-plane stress analysis can be separated from the eigenvalue analysis for the crack-buckling problem.