A fast efficient multi-scale approach to modelling the development of hydride microstructures in zirconium alloys

Abstract

A mechanistic understanding of hydrogen diffusion and hydride precipitation at the microscale underpins the prediction of delayed hydride cracking in zirconium alloy nuclear fuel cladding. We present a novel approach to modelling the microstructures created by hydride precipitation at loaded notches in polycrystalline Zr alloys. The model is multi-scale in that it includes the elastic dipole tensor of interstitial hydrogen in α-Zr, it treats the stressdriven diffusion of hydrogen at the meso-level (mm), it calculates the thermodynamically favourable spatial arrangement of microhydrides and their assembly into macrohydride colonies, in a textured polycrystalline sample, and it treats the full elastic field of the loaded notch and all the hydrides at a scale similar to the cladding thickness. A simplifying innovation is the representation of the elastic field of a microhydride by a dislocation dipole, where the Burgers vector is set to create the experimentally measured strain in the 〈1100〉 direction. The model provides a predictive framework for treating elastic anisotropy, a variety of potential nucleation sites, and different grain sizes. Simulated micrographs of hydride networks in polycrystalline samples with blunt and sharper loaded notches are compared with experimental micrographs obtained at the same scale. The simulations are extremely fast and calculations typically take around tens of seconds. This makes it possible to carry out detailed sensitivity studies with respect to several pertinent metallurgical variables, as well as conducting ensemble averaging of hydride microstructures.