Multi-field modelling of hydride forming metals Part II: Application to fracture

• A model for hydrogen behaviour in metals that form binary hydrides is presented.
• Multi-field PDEs for the involved phenomena are solved in a 3D FEM setting.
• A continuum material description with “smeared” hydrides is used.
• A cohesive zone fracture model caters for hydride induced cracking.
• The model is validated against experiments on Zr alloys.

In Part I of the present article, we formulated a continuum-based computational model for stress- and temperature-directed diffusion of hydrogen in metals that form brittle binary hydrides, such as Zr and Ti alloys. Among the space–time dependent parameters calculated by the model are the volume fraction and the mean orientation of hydride precipitates. These parameters are of importance for quantifying the embrittlement of hydrided materials. In this second part of the work, we use measured data for the strength and toughness of hydrided Zr alloys to correlate the local fracture properties of the two-phase (metal + hydride) material to the aforementioned parameters. The local fracture properties are used as space–time dependent input to a cohesive zone type submodel for fracture, which is fully integrated with the hydrogen transport model from Part I. The complete model is validated against fracture tests on hydrogen-charged Zr–2.5%Nb, a material used in nuclear reactor pressure tubes. More precisely, we study local embrittlement and crack initiation at a blunt and moderately stressed notch, resulting from gradual accumulation of hydrides at the notch during temperature cycling. We also simulate tests on crack initiation and growth by delayed hydride cracking, a subcritical crack growth mechanism with a complex temperature dependence. From the results of the simulations, we conclude that the model reproduces many observed features related to initiation and propagation of hydride induced cracks in the Zr–2.5%Nb material. In particular, it has the capacity to reproduce effects of the material’s temperature history on the fracture behaviour, which is important for many practical applications.