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

Energy selective neutron imaging for the characterization of polycrystalline materials

This multipart dissertation focuses on the development and evaluation of advanced methods for material testing and characterization using neutron diffraction and imaging techniques. A major focus is on exploiting diffraction contrast in energy selective neutron imaging (often referred to as Bragg edge imaging) for strain and phase mapping of crystalline materials. The dissertation also evaluates the use of neutron diffraction to study the effect of multi-axial loading, in particular the role of applying directly shear strains from the application of torsion. A portable tension-torsion-tomography loading system has been developed for in-situ measurements and integrated at major user facilities around the world. Promising applications for the Bragg edge technique are implemented at the neutron imaging facility CONRAD at the reactor source BER-II as well as at neutron time of flight instruments. Strain mapping is successfully demonstrated for all cases to yield quantifiable results, but is limited in practicality due to limitations in choice of the scattering vector (direction of probed strain tensor component) and the gauge volume selection. The use of Bragg edge imaging for crystalline phase mapping was explored and appears to be a very promising technique. The extension to three-dimensionally resolved tomography is presented for samples exhibiting the TRansfomation Induced Plasticity (TRIP) effect, while challenges with characterizing textured samples are discussed. Individual crystallites within a polycrystalline material exhibit elastic anisotropy which is significant as that can lead to stress concentrations and inhomogeneities during plastic deformation. Characterization of elastic anisotropy is important to understand the effects of texture on the macroscopic mechanical properties. Diffraction methods can do this, by probing the response of individual lattice planes to externally applied mechanical stress. Past experimental data using diffraction based methods have largely been limited to uni‑axial tensile and/or compressive loading conditions, even though shear dominates most common failure mechanisms for structural materials. Within this dissertation, experimental techniques have been established for the measurement of lattice strains under applied torsion (pure shear) and lattice specific shear moduli are reported. This is accomplished using a (traditional) neutron diffractometer instrument, in conjunction with special alignment procedures and the specifically designed axial-torsional loading system

A virtual world of paleontology

Computer-aided visualization and analysis of fossils has revolutionized the study of extinct organisms. Novel techniques allow fossils to be characterized in three dimensions and in unprecedented detail. This has enabled paleontologists to gain important insights into their anatomy, development, and preservation. New protocols allow more objective reconstructions of fossil organisms, including soft tissues, from incomplete remains. The resulting digital reconstructions can be used in functional analyses, rigorously testing long-standing hypotheses regarding the paleobiology of extinct organisms. These approaches are transforming our understanding of long-studied fossil groups, and of the narratives of organismal and ecological evolution that have been built upon them

Challenges in imaging and predictive modeling of rhizosphere processes

Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes

Histogram Tomography

In many tomographic imaging problems the data consist of integrals along lines or curves. Increasingly we encounter "rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors tensors and functions. The data can also be higher dimensional and in many cases consists of a one or two dimensional spectrum for each ray. In many such cases the data contain not just integrals along rays but the distribution of values along the ray. If this is discretized into bins we can think of this as a histogram. In this paper we introduce the concept of "histogram tomography". For scalar problems with histogram data this holds the possibility of reconstruction with fewer rays. In vector and tensor problems it holds the promise of reconstruction of images that are in the null space of related integral transforms. For scalar histogram tomography problems we show how bins in the histogram correspond to reconstructing level sets of function, while moments of the distribution are the x-ray transform of powers of the unknown function. In the vector case we give a reconstruction procedure for potential components of the field. We demonstrate how the histogram longitudinal ray transform data can be extracted from Bragg edge neutron spectral data and hence, using moments, a non-linear system of partial differential equations derived for the strain tensor. In x-ray diffraction tomography of strain the transverse ray transform can be deduced from the diffraction pattern the full histogram transverse ray transform cannot. We give an explicit example of distributions of strain along a line that produce the same diffraction pattern, and characterize the null space of the relevant transform.Comment: Small corrections from last versio

Resonant Elastic Soft X-Ray Scattering

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site, and valence specific probe to study spatial modulations of charge, spin, and orbital degrees of freedom in solids on the nanoscopic length scale. It cannot only be used to investigate single crystalline materials. This method also enables to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces