Weight Functions for $T$-Stress for Edge Cracks in Thick-Walled Cylinders

This paper presents $T$-stress solutions for an internal edge crack in thick-walled cylinders. Elastic fracture mechanics analysis using the boundary element method (BEM) is performed to determine the $T$-stress solutions for a wide range of radius ratios and relative crack lengths. The loading cases considered in the BEM analysis for the cracked cylinder are crack-face pressures with polynomial stress distributions acting on the crack face. $T$-stress results for the uniform and linearly varying crack-face pressure cases are subsequently used as the reference solutions to derive weight functions for $T$-stress. Boundary element results of $T$-stress for other stress distributions, namely, other nonlinear crack face loading, internal pressure, and steady-state thermal loading, are used to validate the derived $T$-stress weight functions. Excellent agreement between the results from the weight function predictions and those directly computed is shown to be obtained. The weight functions derived are suitable for obtaining $T$-stress solutions for thick-walled cylinders with an internal edge crack under any complex stress fields.