- Title
- Probabilistic modelling and estimation of elastic strain from diffraction-based measurements
- Creator
- Hendriks, Johannes
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2020
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Stress is a physical quantity that describes the distribution of force within a solid and is widely regarded as the primary cause of failure in engineering components. As such, the measurement and analysis of stress induced by manufacturing or subsequent use is of great interest. In practice, stress cannot be measured directly and instead is inferred from secondary quantities such as elastic strain; which is directly related to stress. This thesis deals with the modelling and estimation of elastic strain from diffraction-based measurements and presents a unified framework. In particular, the problem of strain tomography is considered where the full distribution of strain in two- or three-dimensions is reconstructed (i.e. estimated) from lower dimensional projected images of the strain. This is analogous to conventional computed tomography where a map of the linear attenuation inside an object is reconstructed from lower dimensional tomographic slices. However, strain is a second order tensor quantity while density is a scalar quantity making strain tomography a significantly more complex task. Recent advances in detector technology, allow high-resolution strain images to be acquired using Bragg-edge neutron transmission. These provide measurements of the strain field that can be modelled by the longitudinal ray transform (LRT). If the components of strain are considered independent, then the mapping from the elastic strain field to the strain measurement via the LRT has a null space. Hence, additional a prior information is required in order to solve the inverse problem and reconstruct the strain field from a set of strain images. This a prior information could be physical constraints on the strain field, such as assuming the strain field satisfies compatibility or equilibrium. An approach based on Gaussian processes that allows the natural inclusion of these physical constraints is presented. In this approach, the unknown strain field components are modelled as random functions, and we can learn the shape of these functions from the data using Gaussian processes. Correlation between the random functions is designed to ensure that the represented strain field satisfies equilibrium. This is achieved by modelling the strain field components as partial derivatives of specific potential functions known as the Airy stress function in two- dimensions and the Beltrami stress function in three-dimensions. Estimation of strain using these models can be performed based on measurements that are modelled by linear operators; this includes line and volume integrals. Hence, this allows the estimation (or reconstruction) of elastic strain from Bragg-edge neutron strain images and the inclusion of equilibrium reduces the null space to the trivial one. Further, a method for the inclusion of boundary constraints is given and demonstrated to improve the estimates. This approach is demonstrated on synthetic and real data for both two- and three-dimensional strain fields and validated by comparison with finite element analysis and neutron diffraction measurements. The framework is extended to include the estimation of elastic strain from neutron diffraction and high-energy X-ray strain measurements. Estimation from neutron diffraction measurements is performed using a volume integral measurement model and is demonstrated on synthetic and real data to provide more accurate strain maps than conventional interpolation. High-energy X-ray strain measurement can also pose a tomography problem, and the presented method is capable of reconstructing the triaxial strain from measurements taken using only a single axis of rotation.
- Subject
- stress; probabilistic modelling; engineering; elastic strain; diffraction-based measurements
- Identifier
- http://hdl.handle.net/1959.13/1411479
- Identifier
- uon:36341
- Rights
- Copyright 2020 Johannes Hendriks
- Language
- eng
- Full Text
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 198 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 4 MB | Adobe Acrobat PDF | View Details Download |