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

Abstract

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.

An Investigation of Radial Basis Function Method for Strain Reconstruction by Energy-Resolved Neutron Imaging

“…The complicated meshing rules are not required while performing RBF, and here lies the advantage of the proposed method over the framework of finite elements. The use of meshless methods over the finite-element approach for reconstruction tensor strain field [39][40][41] has many other benefits. We can quickly increase the support domain, change basis functions, adopt nodal densities, and many more.…”

Geometrically Flexible and Efficient Numerical Solution Technique for Bragg Edge Neutron Transmission Strain Tomography

“…The descriptions of the algorithms, the comparison of approaches and the improvements in the resolution of the images are intended to serve as an entry-point guide for researchers wishing to continue this work further. Some of this research has been published in [1][2][3][4].…”