A Bayesian approach to triaxial strain tomography from high‐energy X‐ray diffraction

Abstract

Diffraction of high-energy X-rays produced at synchrotron sources can provide rapid strain measurements, with high spatial resolution, and good penetrating power. With an uncollimated diffracted beam, through-thickness averages of strain can be measured using this technique, which poses an associated rich tomography problem. This paper proposes a Gaussian process (GP) model for three-dimensional strain fields satisfying static equilibrium and an accompanying algorithm for tomographic reconstruction of strain fields from high-energy X-ray diffraction. This method can achieve triaxial strain tomography in three dimensions using only a single axis of rotation. The method builds upon recent work where the GP approach was used to reconstruct two-dimensional strain fields from neutron-based measurements. A demonstration is provided from simulated data, showing the method is capable of rejecting realistic levels of Gaussian noise.

Bayesian non-parametric Bragg-edge fitting for neutron transmission strain imaging

“…This is because least-squares is equivalent to finding a maximum likelihood estimate with a Gaussian noise model. 10 As such, these methods can be interpreted as providing a maximum likelihood estimate of strain;…”

“…Several methods for strain tomography have been developed and an overview is given by Hendriks. 10 Methods for neutron strain tomography take as inputs a large number of strain images requiring many thousands of Bragg-edges to be analysed. Therefore, in order for strain tomography methods to be accurate, it is imperative that the methods used to produce these strain images are accurate and produce reliable estimates of confidence, which the strain tomography methods can take into account.…”

Extracting true stresses and strains from nominal stresses and strains in tensile testing

“…Among the many ways to measure flow curves, the tensile test still retains an important position because it offers the advantages of high precision and absence of friction. Although the best tensile test results are principally obtained by accurately measuring the geometry and/or strain of the test piece during straining, for example by digital image correlation (DIC) [ 1–4 ] or, in a completely different way, by strain tomography, [ 5,6 ] the ‘classical’ way of extracting the true stresses and true plastic strains from the easily measurable nominal stress–strain curve is still frequently used in practice.…”

Radial Basis Functions and Improved Hyperparameter Optimisation for Gaussian Process Strain Estimation

“…Over the past decade, a number of algorithms for fullfield elastic strain tensor reconstruction from neutron and X-ray measurements have been published [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. For the most part, these can be broadly classified as solutions to 'rich' tomography problems -the reconstruction of higher-order tensor fields from lower-order (average) measurements.…”

“…Amongst these are algorithms that operate on Braggedge neutron transmission images [3-11, 13, 14, 16], conventional diffraction strain scans [12], high-energy X-ray measurements [1,2,15], and most recently so-called 'diffraction tomography' profiles [17]. The particular details of these measurements and algorithms are described in detail in the provided references.…”