Bivariate Fourier-series-based prediction of surface residual stress fields using stresses of partial points

Abstract

Surface residual stresses are critical parameters for evaluating the surface quality and can have an influence on many mechanical properties of solids. These stresses inevitably arise in almost all engineering components during manufacturing. However, most experimental and finite element approaches cannot obtain a complete surface residual stress field in a mechanical part. In this study, we propose a predictive method to determine surface stress fields, depending on residual stresses being self-equilibrating. The effectiveness of the approach is verified using a numerical surface of a beam example with ideal measurements and a casting–milling surface with experimental data. Using the proposed method, surface residual stress fields can be obtained from the stresses of a limited number of points including boundary points to solve the governing equations via a Fourier series bivariate polynomial as an Airy stress function with the Tikhonov regularization method. Our method does not require simulations of the residual stress generation process. This method is suitable for complex engineering parts where the manufacturing process is difficult to recreate in detail. The predicted stress field can be imported into a finite element solver as initial stresses to promote the design, manufacturing, and assessment of mechanical components.