Three-Dimensional Constraint Effects on the Slitting Method for Measuring Residual Stress

The incremental slitting or crack compliance method determines a residual stress profile from strain measurements taken as a slit is incrementally extended into the material. To date, the inverse calculation of residual stress from strain data conveniently adopts a two-dimensional, plane strain approximation for the calibration coefficients. This study provides the first characterization of the errors caused by the 2D approximation, which is a concern since inverse analyses tend to magnify such errors. Three-dimensional finite element calculations are used to study the effect of the out-of-plane dimension through a large scale parametric study over the sample width, Poisson's ratio, and strain gauge width. Energy and strain response to point loads at every slit depth is calculated giving pointwise measures of the out-of-plane constraint level (the scale between plane strain and plane stress). It is shown that the pointwise level of constraint varies with slit depth, a factor that makes the effective constraint a function of the residual stress to be measured. Using a series expansion inverse solution, the 3D simulated data of a representative set of residual stress profiles are reduced with 2D calibration coefficients to yield the error in stress. The sample width below which it is better to use plane stress compliances than plane strain is shown to be about 0.7 times the sample thickness; however, even using the better approximation, the rms stress errors sometimes still exceed 3% with peak errors exceeding 6% for Poisson's ratio 0.3, and errors increase sharply for larger Poisson's ratios. The error is significant, yet, error magnification from the inverse analysis in this case is mild compared to, e. g., plasticity based errors. Finally, a scalar correction (effective constraint) over the plane-strain coefficients is derived to minimize the root-mean-square (rms) stress error. Using the posed scalar correction, the error can be further cut in half for all widths and Poisson's ratios.