High resolution three-dimensional strain mapping: a new frontier in materials characterisation

Knowledge of the residual elastic strain in engineering components and materials is of primary importance for understanding and predicting deformation behaviour and fatigue lifetimes. There are a number of approaches for determining bulk residual elastic strain; however, many of these involve destructive sectioning or time-consuming pointwise scanning of the sample to map the spatially resolved strain distribution. Bragg-edge neutron transmission measurement is a new technique that provides a non-destructive two-dimensional map of the average strain profile through the sample volume by measuring the energy resolved transmission spectrum of thermal neutrons. Recently work has begun to enable tomographic three-dimensional reconstructions of the spatially varying strain fields within bulk materials and components from a series of average two-dimensional strain measurements. Characterising the strain state at a particular point in a sample requires knowledge of the six independent quantities that make up the second order strain tensor. Determination of the complete strain distribution throughout the sample therefore presents significant theoretical and practical challenges. Methods for determining strain generally only measure one component at a time, making mapping the entire strain tensor a laborious process. Bragg-edge neutron strain tomography seeks to recover the full three-dimensional strain distribution from a set of two-dimensional projections of the average strain profile. The successful implementation of this technique will greatly increase the speed with which data can be collected and, as demonstrated here, offers the potential for significantly improving the resolution of the imaged strain fields over previous diffraction based methods. This thesis demonstrates two methods of inverting Bragg-edge measurements. The first uses a numerical fitting technique to recover the two in-plane strain components. The second approach provides a direct inversion of the average measurement to recover the spatially resolved strain using the Radon transform, taken from conventional absorption tomography along with results from continuum mechanics. The work contained in this thesis represents a significant step towards the development of neutron strain tomography as a general tool for materials characterisation.

Submission note: A thesis submitted in total fulfilment of the requirements for the degree of Master of Science by published work to the Faculty of Science, Technology and Engineering, School of Engineering and Mathematical Sciences, Department of Physics, La Trobe University, Bundoora.

Thesis with publications.