Abstract
Accurate residual lattice strain measurements are highly dependent upon the precision of the diffraction peak location and the underlying microstructure suitability. The suitability of the microstructure is related to the requirement for valid powder diffraction sampling statistics and the associated number of appropriately orientated illuminated. In this work, these two sources of uncertainty are separated, and a method given for both the quantification of errors associated with insufficient grain sampling statistics and minimization of the total lattice strain measurement uncertainty. It is possible to reduce the total lattice strain measurement uncertainty by leveraging diffraction peak measurements made at multiple azimuthal angles. Lattice strain measurement data acquired during eight synchrotron X-ray diffraction experiments, monochromatic and energy dispersive, has been assessed as per this approach, with microstructural suitability being seen to dominate total measurement uncertainty when the number of illuminated grains was <106. More than half of the studied experimental data fell into this category, with a severe underestimation of total strain measurement uncertainty being possible when microstructural suitability is not considered. To achieve a strain measurement uncertainty under 10−4, approximately 3×105 grains must be within the sampled gauge volume, with this value varying with the multiplicity of the family of lattice planes under study. Where additional azimuthally arrayed data are available an in-plane lattice strain tensor can be extracted. This improves overall strain measurement accuracy and an uncertainty under 10−4 can then be achieved with just 4×104 grains.
Highlights
Accurate evaluation of the development and distribution of residual lattice strain is a key consideration in structural integrity assessment procedures, such as R6 [1] and BS7910 [2,3]
The fit of a Gaussian profile to this diffraction peak is shown in Figure 4b, with the peak center being found to lie at Q = 5.365 A−1 which corresponds to a lattice spacing, d = 1.171 A
The fit of a Gaussian profile to this diffraction peak is shown in Figure 4b, with the peak center being found to lie at Q = 5.365 Å−1 which corresponds to a lattice spacing, d =
Summary
Accurate evaluation of the development and distribution of residual lattice strain (and the associated quantification of residual stress) is a key consideration in structural integrity assessment procedures, such as R6 [1] and BS7910 [2,3]. Experimental measurement of lattice strain is typically achieved through either X-ray or neutron diffraction and the associated determination of Bragg diffraction peak locations, with these measurements routinely being made at large scale synchrotron X-ray or neutron facilities. In both cases accurate strain measurement is typically dominated by (a) the accurate location of the diffraction peak center and (b) microstructure suitability. While the former has been covered in great depth by Withers et al [4], the latter has not been systematically explored to the best of authors’ knowledge. This level of accuracy is reliant upon precise diffraction peak definition and high microstructure suitability, these rely upon good counting and powder diffraction sampling statistics, respectively
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