TY - JOUR

T1 - Direct inversion of the Longitudinal ray transform for 2D residual elastic strain fields

AU - Wensrich, C. M.

AU - Holman, S.

AU - Courdurier, M.

AU - Lionheart, W. R.B.

AU - Polyakova, A. P.

AU - Svetov, I. E.

N1 - This work is supported by the Australian Research Council through a Discovery Project Grant (DP170102324). Access to the RADEN and KOWARI instruments was made possible through the respective user access programs of J-PARC and ANSTO (J-PARC Long Term Proposal 2017L0101 and ANSTO Program Proposal PP6050). Contributions from W Lionheart and S Holman were supported by the Engineering and Physical Sciences Research Council through Grant EP/V007742/1. The authors would also like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the program Rich and Non-linear Tomography: A Multidisciplinary Approach when work on this paper was undertaken. This program was supported by EPSRC Grant Number EP/R014604/1. Contributions from Matias Courdurier were partially supported by ANID Millennium Science Initiative Program through Millennium Nucleus for Applied Control and Inverse Problems NCN19-161.

PY - 2024/7

Y1 - 2024/7

N2 - We examine the problem of Bragg-edge elastic strain tomography from energy resolved neutron transmission imaging. A new approach is developed for two-dimensional plane-stress and plane-strain systems whereby elastic strain can be reconstructed from its Longitudinal ray transform (LRT) as two parts of a Helmholtz decomposition based on the concept of an Airy stress potential. The solenoidal component of this decomposition is reconstructed using an inversion formula based on a tensor filtered back projection (FBP) algorithm whereas the potential part can be recovered using either Hooke’s law or a finite element model of the elastic system. The technique is demonstrated for two-dimensional plane-stress systems in both simulation, and on real experimental data. We also demonstrate that application of the standard scalar FBP algorithm to the LRT in these systems recovers the trace of the solenoidal component of strain and we provide physical meaning for this quantity in the case of 2D plane-stress and plane-strain systems.

AB - We examine the problem of Bragg-edge elastic strain tomography from energy resolved neutron transmission imaging. A new approach is developed for two-dimensional plane-stress and plane-strain systems whereby elastic strain can be reconstructed from its Longitudinal ray transform (LRT) as two parts of a Helmholtz decomposition based on the concept of an Airy stress potential. The solenoidal component of this decomposition is reconstructed using an inversion formula based on a tensor filtered back projection (FBP) algorithm whereas the potential part can be recovered using either Hooke’s law or a finite element model of the elastic system. The technique is demonstrated for two-dimensional plane-stress systems in both simulation, and on real experimental data. We also demonstrate that application of the standard scalar FBP algorithm to the LRT in these systems recovers the trace of the solenoidal component of strain and we provide physical meaning for this quantity in the case of 2D plane-stress and plane-strain systems.

KW - Longitudinal ray transform

KW - bragg edge

KW - neutron transmission

KW - strain tomography

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85196400053&origin=inward&txGid=28f532906422fdfa768a8b83f40e1aa3

UR - https://www.mendeley.com/catalogue/46645713-eaa3-35ab-8430-fa6d42751278/

U2 - 10.1088/1361-6420/ad52bb

DO - 10.1088/1361-6420/ad52bb

M3 - Article

VL - 40

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 7

M1 - 075011

ER -