Weight Functions of Radial Cracks in Hollow Disks

Abstract

Explicit nodal weight functions for both bore and rim radial cracks in a hollow disk are presented with special emphasis on the load independent characteristics of the weight functions that can eliminate the repeated finite element computations of the Mode I stress intensity factors (KI) for a given crack geometry under different loading conditions. An analytical expression, which relates the explicit crack-face weight functions to the radial distance (rs) from the crack tip along the crack face, is also provided for wide range ratios of crack length (a) to the difference between outer disk radius (Ro) and inner disk radius (Ri) [0.01 ≤ a/(Ro − Ri) ≤ 0.8]. The accurate explicit weight functions of any crack length can be obtained easily with a cubic spline interpolation technique from an adequate set of explicit crack-face weight functions of discrete crack lengths. With the availability of the explicit crack-face weight functions for both the bore and rim cracks, the Mode I stress intensity factors under any complex loading conditions can be calculated accurately and inexpensively by a sum of worklike products between the equivalent “un-cracked” stress field and the interpolated crack-face weight functions. This equivalent uncracked stress field could include the body force loading of a rotating disk, thermal loading, complex residual stresses, the applied tractions at the crack face and other locations, and any combinations of these loading conditions.