Uncertainty quantification of residual stress evaluation by the FIB–DIC ring-core method due to elastic anisotropy effects

Abstract

• Compact matrix formulation is presented for residual stress calculation from residual strains using Voigt's 6-vector notation. • By performing the calculation for 8000 randomly selected crystal orientations, Uncertainty Quantification is obtained of residual stress evaluation for cubic materials with different anisotropy factors. Elastic anisotropy can have a significant effect on the reliability and precision of residual stress evaluation, due to the uncertainty in the elastic constants multiplied by the measured strains. For the focused ion beam – digital image correlation (FIB–DIC) ring-core method taken as an example, a Mathematica package was developed to evaluate the complete in-plane residual stress state from the measured strain relief values using known material orientation and anisotropic elastic properties for materials displaying cubic symmetry. However, in many practical situations the underlying material orientation is unknown, and nominal isotropic continuum elastic constants are used. This leads to a systematic error in the stress calculation. The present analysis focuses on the statistical evaluation of the uncertainty in stress evaluation due to the unknown material orientation as a function of its degree of anisotropy. We demonstrate an experimental application of this procedure to a real case of micron scale residual stress analysis in a nickel-base superalloy.