Energy Resolved Neutron Imaging for Strain Reconstruction using the Finite Element Method

A pulsed neutron imaging technique is used to reconstruct the residual strain within a polycrystalline material from Bragg edge strain images. This technique offers the possibility of a nondestructive analysis of strain fields with a high spatial resolution. A finite element approach is used to reconstruct the strain using the least square method constrained by the conditions of equilibrium. The procedure is developed and verified by validating for a cantilevered beam problem. It is subsequently demonstrated by reconstructing the strain from experimental data for a ring-and-plug sample, measured at the spallation neutron source RADEN at J-PARC in Japan. The reconstruction is validated by comparison with conventional constant wavelength strain measurements on the KOWARI diffractometer at ANSTO in Australia. It is also shown that the addition of a simple Tikhonov regularization can improve the reconstruction

A comparison of triangular and quadrilateral finite element meshes for Bragg edge neutron transmission strain tomography

A wavelength resolved measurement technique used in neutron imaging applications is known as energy-resolved neutron transmission imaging. This technique of reconstructing residual strain maps provides high spatial resolution measurements of strain distribution in polycrystalline materials from sets of Bragg edge measurement images. Strain field reconstructions obtained from both triangular and quadrilateral finite element meshes are compared. The reconstruction is approached via a least square method and relies on the inversion of the longitudinal ray transform, which has uniqueness issues. References B. Abbey, S. Y. Zhang, W. J. J. Vorster, and A. M. Korsunsky. Feasibility study of neutron strain tomography. Proc. Eng., 1:185–188, 2009. doi:10.1016/j.proeng.2009.06.043. R. Aggarwal, M. H. Meylan, B. P. Lamichhane, and C. M. Wensrich. Energy resolved neutron imaging for strain reconstruction using the finite element method. J. Imag., 6(3):13, 2020a. doi:10.3390/jimaging6030013. R. Aggarwal, M. H. Meylan, C. M. Wensrich, and B. P. Lamichhane. Finite element approach to Bragg edge neutron strain tomography. In B. Lamichhane, T. Tran, and J. Bunder, editors, Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2018, volume 60 of ANZIAM J., pages C279–C294, June 2020b. doi:10.21914/anziamj.v60i0.14054. M. E. Fitzpatrick and A. Lodini. Analysis of residual stress by diffraction using neutron and synchrotron radiation. CRC Press, 2003. URL https://www.routledge.com/Analysis-of-Residual-Stress-by-Diffraction-using-Neutron-and-Synchrotron/Fitzpatrick-Lodini/p/book/9780367446802. A. W. T. Gregg, J. N. Hendriks, C. M. Wensrich, A. Wills, A. S. Tremsin, V. Luzin, T. Shinohara, O. Kirstein, M. H. Meylan, and E. H. Kisi. Tomographic reconstruction of two-dimensional residual strain fields from Bragg-edge neutron imaging. Phys. Rev. Appl., 10:064034, Dec 2018. doi:10.1103/PhysRevApplied.10.064034. J. N. Hendriks, A. W. T. Gregg, C. M. Wensrich, A. S. Tremsin, T. Shinohara, M. Meylan, E. H. Kisi, V. Luzin, and O. Kirsten. Bragg-edge elastic strain tomography for in situ systems from energy-resolved neutron transmission imaging. Phys. Rev. Mat., 1:053802, 2017. doi:10.1103/PhysRevMaterials.1.053802. E. H. Kisi and C. J. Howard. Applications of neutron powder diffraction, volume 15 of Neutron Scattering in Condensed Matter. Oxford University Press, 2012. URL https://global.oup.com/academic/product/applications-of-neutron-powder-diffraction-9780199657421. W. R. B. Lionheart and P. J. Withers. Diffraction tomography of strain. Inv. Prob., 31:045005, 2015. doi:10.1088/0266-5611/31/4/045005. C. C. Paige and M. A. Saunders. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software, 8:43–71, 1982. doi:10.1145/355984.355989. J. R. Santisteban, L. Edwards, M. E. Fitzpatrick, A. Steuwer, P. J. Withers, M. R. Daymond, M. W. Johnson, N. Rhodes, and E. M. Schooneveld. Strain imaging by Bragg edge neutron transmission. Nucl. Inst. Meth. Phys. Res., 481:765–768, 2002. doi:10.1016/S0168-9002(01)01256-6. T. Shinohara and T. Kai. Commissioning start of energy-resolved neutron imaging system, RADEN in J-PARC. Neut. News, 26(2):11–14, 2015. doi:10.1080/10448632.2015.1028271. T. Shinohara, T. Kai, K. Oikawa, M. Segawa, M. Harada, T. Nakatani, M. Ooi, K. Aizawa, H. Sato, T. Kamiyama, H. Yokota, T. Sera, K. Mochiki, and Y. Kiyanagi. Final design of the energy-resolved neutron imaging system RADEN at J-PARC. J. Phys., 746, 2016. doi:10.1088/1742-6596/746/1/012007. A. S. Tremsin, J. B. McPhate, W. Kockelmann, J. V. Vallerga, O. H. W. Siegmund, and W. B. Feller. High resolution Bragg edge transmission spectroscopy at pulsed neutron sources: proof of principle experiments with a neutron counting MCP detector. Nucl. Inst. Meth. Phys. Res., 633:S235–S238, 2011. doi:10.1016/j.nima.2010.06.176. R. Woracek, J. Santisteban, A. Fedrigo, and M. Strobl. Diffraction in neutron imaging—A review. Nucl. Inst. Meth. Phys. Res., 878:141–158, 2018. doi:10.1016/j.nima.2017.07.040

Direct inversion of the Longitudinal Ray Transform for 2D residual elastic strain fields

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 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 filtered back projection 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.Comment: 30 pages, 9 figure