Uncovering hidden bias in neutron diffraction residual strain measurements

Abstract

When calculating residual strain via neutron or X-ray diffraction, uncertainties propagated from the peak fit are often inadequate to describe the true scatter of measurements about a singular strain state, such as one that should describe a macroscopic continuum. Because diffraction is inherently a selective process, orientation dependent scatter arises from the sub-sampling of strong microstructure and strain gradients. This paper investigates the appropriateness of propagated uncertainties with reference to their original intention, i.e., noise about a mean value. Thirty-six unique orientations of strain measurements are taken at multiple locations within an additive friction-stir deposition component with fine-scale gradients (~200 um) of plastic strain, texture, and residual elastic strain. Multiple strain and stress calculation pathways are compared: direct substitution of three measurements into Hooke's law, direct inversion of any six unique orientations into the strain state tensor, and thirty-six measurement least-squares estimation. For the latter two cases, the appropriateness of the uncertainty interval is statistically evaluated based on a physical constraint: common agreement under the strain transformation law. For this sample, the direct inversion of six measurements retains a conservative estimate of the uncertainty. However, propagated uncertainties in the least-squares solution greatly underestimate the true experimental scatter. A simple pathway to estimate appropriate uncertainty intervals is suggested. These results demonstrate that interpretation of uncertainty in residual strain is strongly dependent on intrinsic, sample-dependent effects, and that oversampling orientations and statistical analysis can give more accurate results with realistic uncertainties.