Determination of weight functions for elastic T‐stress from reference T‐stress solutions

This paper presents the application of the weight function method for the calculation of elastic T-stress. First, the background of the weight function method for the calculation of T-stress is summarized. Then an analysis of known weight functions for T-stress revealed that it is possible to approximate them with one universal mathematical form with three unknown parameters with high accuracy. The existence of this weight function form significantly simplified the determination of weight functions for T-stress. For any particular crack geometry, the unknown parameters can be determined from reference T-stress solutions. The general weight function expression, with suitable reference T-stress solutions, was used to derive the weight functions for single edge cracked plate, double edge cracked plate and center cracked plate specimens. These weight functions were then further used to calculate the T-stress solutions for cracked specimens under several nonlinear stress fields and were compared to available numerical data.

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