Quantifying the uncertainty of synchrotron-based lattice strain measurements

Abstract

Crystallographic lattice strains -measured using diffraction techniques -are the same magnitude as typical macroscopic elastic strains. From a research perspective, the main interest is in measuring changes in lattice strains induced during in-situ loading: either from one macroscopic stress level to another or from one cycle to the next. The hope is to link these measurements to deformation-induced changes in the internal structure of crystals, possibly related to inelastic deformation and damage. These measurements are relatively new -little experimental intuition exists and it is difficult to discern whether observed differences are due to actual micromechanical evolution or to random experimental fluctuations. If the measurements are linked to material evolution on the size scale of the individual crystal, they have the potential to change the ideas about grain scale deformation partitioning processes and can be used to validate crystal-based simulation frameworks. Therefore, understanding the uncertainty associated with the lattice strain experiments is a crucial step in their continued development. If the measured lattice strains are of the same order as the random fluctuations that are part of the measurement process, documenting the strains can create more confusion than understanding. Often lattice strain error is quoted as 61 3 10 24 . This simple value fails to account for the range of factors that contribute to the experimental uncertainty -which, if not properly accounted for, may lead to a false confidence in the measurements. The focus of this paper is the development of a lattice strain uncertainty expression that delineates the contributing factors into terms that vary independently: (i) the contribution from the instrument and (ii) the contribution from the material under investigation. These aspects of uncertainty are described, and it is then possible to employ a calibrant powder method (diffraction from an unstrained material with high-precision lattice constants) to quantify the instrument portion of the lattice strain uncertainty. In these experiments, the instrument contribution to the uncertainty has been found to be a function of the Bragg angle and the intensity of the diffracted peaks. To develop a model for the instrument portion of the lattice strain uncertainty two datasets obtained using a MAR345 online image plate at the Cornell High Energy Synchrotron Source and a GE 41RT amorphous silicon detector at the Advanced Photon Source have been examined.

Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction

“…Because the bi-scale optimization scheme relies on the SPFs measured at individual diffraction volumes located throughout the sample to determine the 3D residual stress field in the sample, a sufficient number of grains needs to be present in a diffraction volume to obtain reliable orientation dependent stresses and strains [42]. In this work, the average grain size was 3 µm and having a sufficient number of grains in a diffraction volume was not an issue.…”

“…The lattice strain measurement uncertainty is determined by considering the systematic aberration of the detector and the geometry of the experimental setup [26]. Using the uncertainty estimation methodology proposed by Schuren et al [42], the lattice strain measurement uncertainty is on average 5 × 10 −5 for the three {hkl}s interrogated.…”

A rotational and axial motion system load frame insert for in situ high energy x-ray studies

“…The uncertainty in the stress components is estimated to be approximately ±12 Mpa (assuming an elastic strain uncertainty of ±10 −4 and neglecting uncertainty in the elastic constants). 53 From Figures 5 and 6, it can be seen that there is a significant degree of intergranular stress heterogeneity, which is seen to evolve with increasing load levels despite a minimal amount of plastic deformation. Of particular note are the noticeable changes in the distribution of grain level stress "hot spots."…”

Integrating experiments and simulations to estimate uncertainty in lattice strain measurements

“…The calibrant insert is used to quantify both the experiment geometry and the lattice strain uncertainty associated with the instrument itself. 9,23 Using the diffraction results from the CeO 2 calibrant insert, we determined the model parameters for equation (5) for each load step. The mean and the standard deviation of the dr min and S a for all the load steps measured were found to be 2:8460:05 mm and ð1:660:3Þ310 À8 , respectively.…”

“…9 The instrument portion of the lattice strain uncertainty is often quoted as the sole source of uncertainty and is typically on the order of 61310 À4 . However, the ability to quantify the material-specific contribution to the lattice strain uncertainty has remained elusive.…”