Generalized Methods for Computing Residual Stress

  • Title: Residual Stress

  • Sponsor: Sandia National Laboratories

  • Period: 2017-2020

  • PI: Wilkins Aquino

  • IOMechLab Students: Mark Chen

In this project, we develop a generalized residual stress inversion technique capable of being applied on any arbitrary geometry. Manufacturing processes often induce these unobservable internal “locked-in” stresses. If not properly accounted for, high residual stress may cause unexpected performances including premature failure. As such, it is of paramount importance to effectively quantify residual stress within a body of interest.

We solve this problem by first formulating it as an inverse problem and then employing PDE-constrained optimization. By appealing to the relaxation principle, we note that residual stresses can be released when the body is physically cut. Then, given the measured displacements (e.g. experimentally recorded using digital image correlation), we formulate the inverse problem as finding the tractions on the cut surface that caused the measured displacements. By employing Cauchy’s stress principle, once the tractions on the cut surface are found, the (residual) stresses released by the cut can be determined. We solve this inverse problem by turning it into a PDE-constrained optimization problem. We use gradient-based optimization methods, and we accordingly derive the necessary gradient and Hessian information in a matrix-free form to allow for parallel, large-scale operations.