Diffraction tomography of strain

Lionheart, William R.B. and Withers, Philip J. (2014) Diffraction tomography of strain. [MIMS Preprint]

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Abstract

We consider whether it is possible to recover the three dimensional strain field tomographically from neutron and X-ray diffraction data for polycrystalline materials. We show that the distribution of strain transverse to a ray cannot be deduced from one diffraction pattern accumulated along that path, but that a certain moment of that data corresponds to the transverse ray transform of the strain tensor and so may be recovered by inverting that transform given sufficient data. We show that the whole strain tensor can be reconstructed from diffraction data measured using rotations about six directions that do not lie on a projective conic. In addition we give an inversion formula for complete data for the transverse ray transform. We also show that Bragg edge transmission data, which has been suggested for strain tomography with polychromatic data, cannot provide the strain distribution within the material but only the average along the ray path.

Item Type: MIMS Preprint
Additional Information: This version is revised after comments from referees for the journal Inverse Problems
Uncontrolled Keywords: x-ray diffraction, strain, tomography, tensor, Pascal's theorem
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 44 Integral transforms, operational calculus
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 41 Electromagnetism; electron and ion optics
PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 46 Continuum mechanics of solids
Depositing User: Prof WRB Lionheart
Date Deposited: 12 Jan 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2236

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