Analytical Inverse Solution of Eigenstrains and Residual Fields in Autofrettaged Thick-Walled Tubes

Abstract

The smoothed inverse eigenstrain method is revisited for the reconstruction of residual fields and eigenstrains from limited strain measurements within axially symmetric tubes. The application of the present approach is successfully demonstrated for two cases of analytical solution and experimental measurements. The well-known advantage of the smoothed inverse eigenstrain approach is that it not only minimizes the deviation of measurements from the model predictions but also will result in an inverse solution satisfying all of the continuum mechanics requirements. As a result, less number of experimental measurements is required to reconstruct the complete residual fields. Consequently, the distribution of residual stresses is obtained without requiring the details of the hardening behavior of the material. Furthermore, the eigenstrain field is inversely determined satisfying the total strain compatibility equations, and a closed form analytical solution is presented for the distribution of eigenstrains.