Residual stress solution extrapolation for the slitting method using equilibrium constraints

Established methods for calculating residual stresses from the strains measured when using the slitting method give results for the stresses that exist within the depth range of the slit. Practical considerations typically limit this range to about 90-95% of the specimen thickness. Force and moment equilibrium can provide additional information that may be used to estimate the residual stresses in the no-data region within the remaining ligament beyond the maximum slit depth. Three different numerical methods to calculate the residual stress profile over the entire specimen thickness are investigated. They are truncated Legendre series, regularized Legendre series, and regularized unit pulses. In tests with simulated strain data and with strain data measured on a cold compressed 7050-T7452 Aluminum hand forging, the three methods gave generally similar stress results in the central region of the specimen. At small depths, where the strain sensitivity to the residual stresses is low, the two regularized calculation methods tended to give more stable results. In the area of very large depth beyond the maximum depth of the slit, the regularized Legendre series solution generally gave the most realistic stress results.