Weight Functions of Radial Cracks in Hollow Disks

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 (K_I) for a given crack geometry under different loading conditions. An analytical expression, which relates the explicit crack-face weight functions to the radial distance (r_s) 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 (R_o) and inner disk radius (R_i) [0.01 ≤ a/(R_o − R_i) ≤ 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.