arXiv subjects

Christopher Wensrich

Publications and source records attributed to Christopher Wensrich.

8 recordsLinked to original sources

arXiv2026

An essay on $d_0$ in neutron-based strain measurement techniques: equilibrium-based methods for non-destructive $d_0$ estimation

Determination of the stress-free reference lattice spacing, $d_0$, is a central and often underestimated difficulty in diffraction-based strain measurement. Although commonly treated as a material constant, $d_0$ often varies with position and measurement direction as a result of composition, phase, texture and residual stress at the sub-bulk scale. While direct measurement of $d_0$ from coupons is usually preferable, this is sometimes impractical or even impossible. This paper reviews the $d_0$ problem in general and develops a hierarchy of non-destructive alternatives based on mechanical equilibrium. This ranges from established techniques based on force-balance, to the application of boundary conditions and finally an approach based on point-wise equilibrium within a sample, implemented through eigenstrain analysis. In all cases, examples are provided in the form of real samples including an additively manufactured Inconel cube, ancient Roman bronze medical probes and an ancient bronze dagger of purported Persian origin. These latter examples demonstrate that equilibrium can provide a practical physical constraint for estimating $d_0$ when destructive reference measurements are entirely inappropriate.

cond-mat.mtrl-sci↗

arXiv2026

Single-axis high-energy X-ray diffraction tomography for elastic residual strain: uniqueness and stability of solutions in the presence of equilibrium constraints

It is well-established that single-axis Transverse Ray Transform tomography data from high-energy X-ray diffraction is insufficient for general reconstruction of three-dimensional elastic strain. In this paper we show that, when combined with the constraint of mechanical equilibrium, this problem becomes uniquely solvable for isotropic elastic samples with known elastic constants and non-zero Poisson's ratio. Building on the reconstruction framework of Desai and Lionheart [N.M. Desai, W.R.B. Lionheart, An explicit reconstruction algorithm for the transverse ray transform of a second rank tensor field from three axis data, Inverse Problems 32 (11) (2016) 115009], we formulate this constrained single-axis tomography problem in the Fourier domain and show that the resulting system is invertible everywhere outside a finite collection of measure zero characteristic planes. In the case of bounded samples, this is sufficient to establish uniqueness for reconstructions. We further derive conditional stability estimates that quantify the regularity requirements associated with reconstruction of the various strain components.

math.AP↗

arXiv2025

Uniqueness of solutions in high-energy x-ray based `eigenstrain tomography' and other inverse eigenstrain problems: Counter examples and necessary conditions for well-posedness

Eigenstrain tomography combines diffraction-based strain measurement with elasticity theory to reconstruct full three-dimensional residual stress fields within solids. Notwithstanding a number of recent examples, the uniqueness of such reconstructions has not yet been clearly established. In this paper, we examine the underlying inverse problem in detail and construct explicit counterexamples demonstrating non-uniqueness for a recent implementation of x-ray eigenstrain tomography involving reconstruction from a single measured component of strain. We follow on to explore minimum conditions for well-posedness and conclude that the full elastic strain tensor within an isotropic sample can be uniquely reconstructed from three measured components; specifically the three shear components, or the three diagonal components. We further prove two key results related to eigenstrain reconstruction in a general sense; 1. That any possible residual stress field can be generated by a diagonal eigenstrain and 2. That residual stress fields exist that cannot be generated by isotropic eigenstrains. Together, these findings establish rigorous minimum experimental and computational requirements for well-posed eigenstrain tomography techniques and inverse eigenstrain problems in general.

math.AP↗

arXiv2025

Well-posedness and trivial solutions to inverse eigenstrain problems

We examine the well-posedness of inverse eigenstrain problems for residual stress analysis from the perspective of the non-uniqueness of solutions, structure of the corresponding null space and associated orthogonal range-null decompositions. Through this process we highlight the existence of a trivial solution to all inverse eigenstrain problems, with all other solutions differing from this trivial version by an unobservable null component. From one perspective, this implies that no new information can be gained though eigenstrain analysis, however we also highlight the utility of the eigenstrain framework for enforcing equilibrium while estimating residual stress from incomplete experimental data. Two examples based on measured experimental data are given; one axisymmetric system involving ancient Roman medical tools, and one more-general system involving an additively manufactured Inconel sample. We conclude by drawing a link between eigenstrain and reconstruction formulas related to strain tomography based on the Longitudinal Ray Transform (LRT). Through this link, we establish a potential means for tomographic reconstruction of residual stress from LRT measurements.

math.GM↗

arXiv2020

Bayesian Non-parametric Bragg-edge Fitting for Neutron Transmission Strain Imaging

Energy resolved neutron transmission techniques can provide high-resolution images of strain within polycrystalline samples allowing the study of residual strain and stress in engineered components. Strain is estimated from such data by analysing features known as Bragg-edges for which several methods exist. It is important for these methods to provide both accurate estimates of strain and an accurate quantification the associated uncertainty. Our contribution is twofold. First, we present a numerical simulation analysis of these existing methods, which shows that the most accurate estimates of strain are provided by a method that provides inaccurate estimates of certainty. Second, a novel Bayesian non-parametric method for estimating strain from Bragg-edges is presented. The numerical simulation analysis indicates that this method provides both competitive estimates of strain and accurate quantification of certainty, two demonstrations on experimental data are then presented.

cs.CE↗

arXiv2018

Probabilistic modelling and reconstruction of strain

This paper deals with modelling and reconstruction of strain fields, relying upon data generated from neutron Bragg-edge measurements. We propose a probabilistic approach in which the strain field is modelled as a Gaussian process, assigned a covariance structure customised by incorporation of the so-called equilibrium constraints. The computational complexity is significantly reduced by utilising an approximation scheme well suited for the problem. We illustrate the method on simulations and real data. The results indicate a high potential and can hopefully inspire the concept of probabilistic modelling to be used within other tomographic applications as well.

physics.data-an↗

arXiv2018

Tomographic Reconstruction of Two-Dimensional Residual Strain Fields from Bragg-Edge Neutron Imaging

Bragg-edge strain imaging from energy-resolved neutron transmission measurements poses an interesting tomography problem. The solution to this problem will allow the reconstruction of detailed triaxial stress and strain distributions within polycrystalline solids from sets of Bragg-edge strain images. Work over the last decade has provided some solutions for a limited number of special cases. In this paper, we provide a general approach to reconstruction of an arbitrary system based on a least squares process constrained by equilibrium. This approach is developed in two- dimensions before being demonstrated experimentally on two samples using the RADEN instrument at the J-PARC spallation neutron source in Japan. Validation of the resulting reconstructions is provided through a comparison to conventional constant wavelength strain measurements carried out on the KOWARI engineering diffractometer within ANSTO in Australia. The paper concludes with a discussion on the range of problems to be addressed in a three-dimensional implementation.

physics.app-ph↗

arXiv2017

Deformation and Fabric in Compacted Clay Soils

Hydro-mechanical anisotropy of clay soils in response to deformation or deposition history is related to the micromechanics of plate-like clay particles and their orientations. In this letter, we examine the relationship between microstructure, deformation and moisture content in kaolin clay using a technique based on neutron scattering. This technique allows for the direct characterisation of the microstructure within representative samples using traditional measures such as the orientation density function and soil fabric tensor. From this information, evidence for a simple relationship between components of the deviatoric strain tensor and the deviatoric fabric tensor emerged. This relationship provides a physical basis for future anisotropic constitutive models based on the micromechanics of these materials.

cond-mat.soft↗