Effect of Strain Gage Length When Determining Residual Stress by Slitting

This paper investigates the effect of strain gage length on residual stress estimated by the slitting (or crack compliance) method. This effect is quantified for a range of gage length normalized by sample thickness, $l∕t$⁠, between 0.005 and 0.100. For specific $l∕t$ values, compliance matrix elements are determined by finite element methods for a range of crack depth and polynomial basis functions for residual stress. Resulting compliance matrices are shown and used to determine error in residual stress that may arise due to differences in $l∕t$ assumed in data reduction and existing in the slitting experiment. Errors increase monotonically with increasing difference between assumed and actual $l∕t$ and reach a root-mean-square error of 14% of peak stress. In order to avoid such errors, a scheme is presented that allows compliance matrices to be computed for $0.005⩽l∕t⩽0.100$ from tabulated coefficients and limits root-mean-square error to $<2%$ of peak stress. An example is provided to illustrate the application of the data reduction scheme to laboratory data.