Mode I stress intensity factors for edge cracks emanating from 2-D U-notches using composition of SIF weight functions

Abstract

The recently developed Composition Principle for SIF Weight Functions [Brennan FP, Teh LS. Determination of crack tip stress intensity factors in complex geometries by composition of weight function solutions. Fatigue Fract Eng Mater Struct 2004; 27:1–7.] has been applied to generate mode I stress intensity factor (SIF) solutions for an edge crack emanating from a single U-notched plate. While weight function coefficients for other constituents were well presented [Teh LS, Brennan FP. Stress intensity factors for 2-D semicircular notches using the superposition of SIF weight functions. Fatigue Fract Eng Mater Struct superposition 2005;28:423–435.], SIF solutions and the associated stress distributions for U-notches in semi-infinite strips are required for the composition model. These were obtained by finite element analysis (FEA) and details of the FEA modelling are presented. The FEA results were verified giving good agreement with analytical solutions. The weight function for cracks from U-notches in semi-infinite bodies presented here can also be used in any composition model requiring this geometry as one of its constituents. This paper also demonstrates the mathematical efficiency and reliability of the SIF weight function composition concept.