Multiscale modelling of delayed hydride cracking
Creators: name: Patel, Mitesh
Publisher: name: Imperial College London
Year: 2020

description: A mechanistic model of delayed hydride cracking (DHC) is crucial to the nuclear industry as a predictive tool for understanding the structural failure of zirconium alloy components that are used to clad fuel pins in water-cooled reactors. Such a model of DHC failure must be both physically accurate and computationally efficient so that it can inform and guide nuclear safety assessments. However, this endeavour has so far proved to be an unsurmountable challenge because of the seemingly intractable multiscale complexity of the DHC phenomenon, which is a manifestation of hydrogen embrittlement that involves the interplay and repetition of three constituent processes: atomic scale diffusion, microscale precipitation and continuum scale fracture. This investigation aims to blueprint a novel multiscale modelling strategy to simulate the early stages of DHC initiation: stress-driven hydrogen diffusion-controlled precipitation of hydrides near loaded flaws in polycrystalline zirconium. Following a careful review of the experimental observations in the literature as well as the standard modelling techniques that are commonplace in nuclear fuel performance codes in the first part of this dissertation, the second and third parts introduce a hybrid multiscale modelling strategy that integrates concepts across a spectrum of length and time scales into one self-consistent framework whilst accounting for the complicated nuances of the zirconium-hydrogen system. In particular, this strategy dissects the DHC mechanism into three interconnected modules: (i) stress analysis, which performs defect micromechanics in hexagonal close-packed zirconium through the application of the mathematical theory of planar elasticity to anisotropic continua; (ii) stress-diffusion analysis, which bridges the classical long-range elastochemical transport with the quantum structure of the hydrogen interstitialcy in the trigonal environment of the tetrahedral site; and (iii) diffusion-precipitation analysis, which translates empirical findings into an optimised algorithm that emulates the thermodynamically favourable spatial assembly of the microscopic hydride needles into macroscopic hydride colonies at prospective nucleation sites. Each module explores several unique mechanistic modelling considerations, including a multipolar expansion of the forces exerted by hydrogen interstitials, a distributed dislocation representation of the hydride platelets, and a stoichiometric hydrogen mass conservation criterion that dictates the lifecycle of hydrides. The investigation proceeds to amalgamate the stress, stress-diffusion and diffusion-precipitation analyses into a unified theory of the mesoscale mechanics that underpin the early stages of DHC failure and a comprehensive simulation of the flaw-tip hydrogen profiles and hydride microstructures. The multiscale theory and simulation are realised within a bespoke software which incorporates computer vision to generate mesoscale micrographs that depict the geometries, morphologies and contours of key metallographic entities: cracks and notches, grains, intergranular and intragranular nucleation sites as well as regions of hydrogen enhancement and complex networks of hydride features. Computer vision mediates the balance between simulation accuracy and simulation efficiency, which is completely novel in the context of DHC research as a paradigm at the intersection of computational science and computer science. Preliminary tests show that the simulation environment of the hybrid model is significantly more accurate and efficient in comparison with the traditional finite element and phase field methodologies. Due to this unprecedented simulation accuracy-efficiency balance, realistic flaw-tip hydrogen profiles and hydride microstructures can be simulated within seconds, which naturally facilitates statistical averaging over ensembles. Such statistical capabilities are highly relevant to nuclear safety assessments and, therefore, a systematic breakdown of the model formulation is presented in the style of a code specification manual so that the bespoke software can be readily adapted within an industrial setting. As the main contribution to DHC research, the proposed multiscale model comprises a state-of-the-art microstructural solver whose unrivalled versatility is demonstrated by showcasing a series of simulated micrographs that are parametrised by flaw acuity, grain size, texture, alloy composition, and histories of thermomechanical cycles. Direct comparisons with experimental micrographs indicate good quantitative agreement and provide some justification to the known qualitative trends. Furthermore, the overall hybrid methodology is proven to scale linearly with the number of hydrides, which is computationally advantageous in its own right because it allows the bespoke software to be extended without compromising its speed. Several possible extensions are outlined which would improve the phenomological accuracy of the multiscale model whilst retaining its efficiency. In its current form, however, this hybrid multiscale model of the early stages of DHC goes far beyond existing methodologies in terms of simulation scope.