Influence of the t33-stress on the 3-D stress state around corner cracks in an elastic plate

When an analysis of the 3-D crack behavior in LEFM is performed, usually only the first term of the Williams series expansion, which corresponds to the r(-1/2) singularity, is taken into account. However, it is well known that t(ij) stresses (second order terms) have still influence. Even when the t(ij) stresses are introduced, the only term usually taken into account corresponds to the t(11) factor, generally called T-stress. If a correct 3-D description has to be done, the t(33) term has also to be considered. In this work, the relevance of the t(33) stress term in the analysis of a mode 1 corner crack is shown in contrast to other approaches that use certain ad hoc parameters, such as the so called T-z-constraint factor proposed by Guo and co-workers. The analysis is carried out for elliptical corner cracks with different aspect ratios, showing that the introduction of the t(33) description avoids the approximations inherent to the T-z approach. (C) 2010 Elsevier Ltd. All rights reserved.