Machine Learning and Crystal Plasticity Modelling of Hydrides in Zr-alloy Materials for Nuclear Fuel Cladding

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:

1. 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.
2. 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.
3. 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.

This studentship is jointly funded by Rolls-Royce and the Materials 4.0 CDT and is open to Home and overseas students.

Course fees are covered at the level set for UK students (at least £10,470 p.a.). Please note that Overseas students are responsible for paying the difference in Home fees and Overseas fees, for the first year this difference is expected to be £24,230 and is likely to be at least this amount for a further three years. The stipend (tax-free maintenance grant) is at least £21,805 p.a. for the first year, and at least this amount for a further three years.”

Prospective candidates will be judged according to how well they meet the following criteria:

• A first class or strong upper second-class undergraduate degree with honours (or equivalent) in Engineering, Physics, Materials Science or Maths
• Excellent English written and spoken communication skills

The following skills are desirable but not essential:

• Ability to program in Matlab, Python or Fortran
• Knowledge of machine learning

Informal enquiries are encouraged and should be addressed to Professor Ed Tarleton (edmund.tarleton@eng.ox.ac.uk).

Candidates must submit a graduate application form and are expected to meet the graduate admissions criteria. Details are available on the course page of the University website.

1. D.J. Long, T. Dessolier, T.B. Britton, S. Pedrazzini, F.P.E. Dunne, Int. J. Plas., vol. 190, 2025.
2. S. Sunil, A. Gopalan, R.K. Sharma, T.N. Murty, R.N. Singh, J. Nuc. Mat., vol. 542, 2020.
3. C.D. Hardie, R. Thomas, Y. Liu, F.P.E. Dunne, Acta Mat., vol. 241, 2022.
4. Tarleton Group, Abaqus subroutine code, GitHub: https://github.com/TarletonGroup