Dislocation-informed Crystal Plasticity Modelling of Hydrides in Zr-alloy Materials

About the Project

This project is part of cohort 3 of the EPSRC CDT in Developing National Capability for Materials 4.0, with the Henry Royce Institute.

Hydride precipitation and irradiation damage in Zr-alloy fuel cladding materials are longstanding issues for water-cooled fission reactors. During oxidation of Zr-alloys, hydrogen (H) is produced and absorbed by the material. In operation, the H concentration may become sufficiently high as to precipitate Zr hydrides. Hydride precipitation and dissolution depend strongly on microstructure, stress state, and temperature. Hydrides induce localised plasticity through transformation strains [1] and can promote crack initiation via delayed hydride cracking (DHC) [2]. In parallel, intense neutron irradiation drives microstructural evolution and property degradation [3].

Current design codes and industry standards rely on simple approximations, such as empirical correlations for H pickup, H distribution and isotropic material behaviour. These approaches neglect local stresses, irradiated microstructures, anisotropy, thermal transients, and associated property evolution. Hence, to reliably predict the structural integrity of fuel cladding, high-fidelity microstructural models (crystal plasticity [4]) are required. In practise, however, crystal plasticity models are far too computationally expensive for industry to adopt. Herein lies the role of physics-based machine learning: to provide digital twins that retain the essential physics, while enabling efficient, component-scale predictions of cladding behaviour across relevant time- and lengthscales. This challenge aligns directly with the Materials 4.0 vision: integrating data-rich simulation, experimental calibration, and physics-based machine learning to deliver deployable digital twins for safety-critical materials systems.

The project involves three parts:

A. Mechanistic model development. This will involve enriching existing crystal plasticity finite element models [4] with hydride precipitation and irradiation damage capabilities. It will be essential to develop models to enable a phase transformation (Zr to hydride), accounting for orientation relationships, property evolution, and transformation strains. Maintaining thermodynamic consistency, hydride precipitation criteria will be developed and the irreversible transformation strain energy. The code will also incorporate irradiation damage via the formation of dislocation loops, accounting for their thermal and mechanical annihilation.

B. Calibration and procurement of training data. The enriched multiphysics framework will be calibrated against experimental measurements, with emphasis on EBSD measurements of hydride location, morphology, orientation, and volume fraction. Given the large number of coupled parameters required to describe hydride precipitation and irradiation-induced microstructure evolution, conventional trial-and-error calibration is not feasible. Instead, physics-informed Bayesian neural networks will be employed for parameter identification and validation. This ensures that the framework remains physically interpretable and grounded by experimental measurements. The calibrated model will then be treated as a high-fidelity “ground truth” and used to generate mechanical response training data across a wide range of conditions.

C. Development of a digital twin. The final stage of the project will focus on the development of a reduced-order, physics-based digital twin to predict the long-term mechanical integrity of Zr-alloy cladding at the component scale. This digital twin will be trained using data generated in B. Neural networks will be employed to learn constrained, physics-informed constitutive representations of the effective material response as a function of temperature, stress state, H concentration, irradiation dose and microstructure. Allowing rapid predictions of cladding behaviour under realistic operating conditions, including transient thermal-mechanical loading and evolving H and irradiation fields, at a computational cost orders of magnitude lower than crystal plasticity.

Funding Notes

This project is funded by Rolls-Royce. It is desirable that the candidate can obtain UK SC clearance in line with standard vetting procedures. If this is not possible, Rolls-Royce will not be able to provide access to further detailed information to support the DPhil project.

Enquiries

For general enquiries, please contact doctoral-training@royce.ac.uk.

For application-related queries, please contact the University of Oxford (graduate.studies@materials.ox.ac.uk).

For project-related queries, please contact the lead supervisor, Ed Tarleton (edmund.tarleton@eng.ac.uk)

Application Process

Please note that each partner of the CDT in Materials 4.0 will have its own application process. Applications to CDT projects will have two stages: the local application form (https://eng.ox.ac.uk/study/research-studentships) and the standard questionnaire which applicants will need to complete by the application deadline and send to the email address for application-related queries above.

The Materials 4.0 CDT is committed to Equality, Diversity and Inclusion. We strongly encourage applications from underrepresented groups.

Application Webpage

Please follow the link to apply, https://eng.ox.ac.uk/study/research-studentships.