The OxCM contour method solver for residual stress evaluation

Abstract

This paper introduces the OxCM contour method solver, a console application structured based on the legacy version of the FEniCS open-source computing platform for solving partial differential equations (PDEs) using the finite element method (FEM). The solver provides a standardized approach to solving linear elastic numerical models, calculating residual stresses corresponding to measured displacements resulting from changes in the boundary conditions after minimally disturbing (non-contact) cutting. This is achieved through a single-line command, specifically in the case of availability of a domain composed of a tetrahedral mesh and experimentally collected and processed profilometry data. The solver is structured according to a static boundary condition rule, allowing it to rely solely on the cross-section occupied by the experimental data, independent of the geometric irregularities of the investigated body. This approach eliminates the need to create realistic finite element domains for complex-shaped, discontinuous processing bodies. While the contour method provides highly accurate quantification of residual stresses in parts with continuously processed properties, real scenarios often involve parts subjected to discontinuous processing and geometric irregularities. The solver’s validation is performed through numerical experiments representing both continuous and discontinuous processing conditions in artificially created domains with regular and irregular geometric features based on the eigenstrain theory. Numerical experiments, free from experimental errors, contribute to a novel understanding of the contour method's capabilities in reconstructing residual stresses in such bodies through a detailed error analysis. Furthermore, the application of the OxCM contour method solver in a real-case scenario involving a nickel-based superalloy finite-length weldment is demonstrated. The results exhibit the expected distribution of the longitudinal component of residual stresses along the long-transverse direction, consistent with the solution of a commercial solver that was validated by neutron diffraction strain scanning.