Measurement of probability distributions for internal stresses in dislocated crystals

Abstract

In situ laser-based resonant ultrasound measurements of microstructure mediated mechanical property evolution

On the mechanistic basis of fatigue crack nucleation in Ni superalloy containing inclusions using high resolution electron backscatter diffraction

“…The methodology and application of the HR-EBSD technique have been well documented [37,[40][41][42][43]46] and recently reviewed by Wilkinson et al [52] and Britton et al [53], hence it is just briefly described here. Forty 128 pixel x 128 pixel regions of interest were randomly placed across each EBSD pattern and comparison of ROIs between test and reference EBSD patterns enables the calculation of displacements corresponding to zone axes shifts.…”

“…Measurement of rotation gradients can be used to evaluate the net curvature and an estimate of GND content [41]. Measurement of residual stress variations within each grain across a map has recently been used to calculate total dislocation measurement [37]. Its capability has been extended significantly from qualitative measurement on single or a few grains [30,[47][48][49][50] to quantitative analysis in thousands of grains [51].…”

“…The detailed mathematical framework for total dislocation density estimation can be found in the appendix according to Wilkinson et al [37]. Briefly in dislocated crystals the measured elastic stresses have some extreme values (tails) which do not follow a Gaussian normal distribution, unlike the majority of points towards the central region of the stress distribution.…”

“…not spatially resolved, but still quantitative) through calculations based upon distributions of stress associated with the statistics of probing close to a dislocation core within a dislocated crystal, using an analysis based upon the work of Groma and colleagues [38,39]. Wilkinson et al [37] validated with discrete dislocation dynamics calculations and demonstrated that this technique works with HR-EBSD based residual stress maps assessing a series of experimental samples in Cu deformed in tension to increasing levels of plastic strain. The mathematical framework to calculate total dislocation density from HR-EBSD measurement can be found in appendix of this current work.…”

“…While spatial resolution of SSDs is not currently possible with HR-EBSD based methods, recent work by Wilkinson et al [37] includes quantitative estimation of the total dislocation (i.e. SSD and GND) content for a map (i.e.…”