The creep of UO2 doped with Nb2O5 and Cr2O3 has been assessed using a point defect model based on the law of mass action, and the diffusional creep according to the Nabarro-Herring mechanism, which relates the creep rate to the lattice self-diffusivity, the inverse of grain area and the applied stress. The self-diffusion coefficients of cation (U) and anion (O) are directly proportional to the concentrations of ions, which in turn are functions of dopant concentrations. The model has been used to evaluate past creep experiments on UO2 doped with Nb2O5 and Cr2O3 in concentrations up to about 1 mol%, with a varying grain size at different temperatures and applied stresses. The creep rate increases significantly with the dopant concentration and the putative model, after a modification of the creep rate coefficient, retrodict the measured data satisfactorily. A number of factors affecting creep rate and thereby our model computations are discussed.

A computational model for hydrogen transport, hydrogen induced deformation and fracture in metals that form binary hydrides, such as Zr and Ti alloys, is presented. The model uses a continuum description of the two-phase (metal + hydride) material, and solves the multi-field partial differential equations for temperature and stress-directed hydrogen diffusion together with mechanical equilibrium in a three-dimensional finite element setting. Point-kinetics models are used for metal-hydride phase transformation and stress-directed orientation of hydride precipitates, while a cohesive zone fracture model caters for initiation and propagation of cracks. The local fracture properties of the hydrided material are correlated to the calculated local concentration and orientation of the hydride precipitates, which have a strong embrittling effect on the material. In Part I of this two-part paper, we present sub-models applied for the aforementioned phenomena together with a detailed description of their numerical implementation. The applicability of the model is then demonstrated by simulating five independent experiments on hydrogen transport, metal-hydride phase transformation and stress-directed hydride orientation in zirconium alloys. Based on the results, we conclude that the model captures these phenomena over a wide range of thermo-mechanical loading conditions, including thermal cycling. Part II of the paper is focussed on fracture, and includes details on the fracture model and its validation against tests and experiments on initiation and propagation of hydride induced cracks.

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.

Metal oxides added to UO2 to improve material performance during irradiation, or as burnable absorbers to control reactor energy output, affect point defect processes in UO2. The oxygen and uranium Frenkel pairs and the uranium-oxygen Schottky defects regulate the O/U ratio, which in turn influence diffusion processes in UO2. The dopants considered here include Cr2O3 and Gd2O3. Using the law of mass action to the Frenkel and Schottky defects in doped UO2, we relate O/U to the dopant concentration. Also, we find relationships between the oxygen and uranium vacancies and dopant concentration. The uranium self-diffusion coefficient is proportional to concentration of uranium vacancies in the hyper-stoichiometric region, whereas to that of uranium interstitials in hypo-stoichiometric region. We relate this to the creep rate and diffusion coefficient of fission gases in UO2. We use the model to evaluate creep rate and gas diffusivity in doped UO2 in light of experimental data.

This work deals with a computational model for hydrogen transport, hydrogen induced deformation, embrittlement and fracture in hydride forming metals, notably Ti and Zr. The model uses a continuum description of the two-phase (alpha-phase metal plus delta-phase hydride) material, and solves the multi-field partial differential equations for temperature- and stress-directed hydrogen diffusion together with mechanical equilibrium in a three-dimensional finite element setting. Point-kinetics models are used for metal-hydride phase transfor¬mation and stress-directed orientation of hydrides, while a cohesive zone fracture model caters for initiation and propagation of cracks. The model as a whole is versatile and can be used to study a wide range of problems and conditions involving transport of hydrogen by directed diffusion in combination with hydride precipitation and fracture. The applicability of the model is demon-strated by simulations of fracture tests on a hydrogen-charged Zr-Nb alloy.

A model for precipitation of the plate-shaped second-phase under applied stress is presented. The precipitates in the matrix-precipitate system are represented by their local volume fraction and an orientation parameter that defines the alignment of a precipitate platelet in a given direction. Kinetic equations, based on diffusion theory and classical nucleation theory, are used to describe the time evolution of these two parameters. The model is used to describe the stress orientation of hydrides in Zr-alloys in light of experiments.

The overall solid-to-solid phase transformation kinetics under non-isothermal conditions has been modeled by means of the differential equation method. The method requires provisions for expressions of the fraction of the transformed phase in equilibrium condition and the relaxation time for transition as functions of temperature. The thermal history is an input to the model. We have used the method to calculate the time/temperature variation of the volume fraction of the favored phase in the α ⇔ β transition in a zirconium alloy under heating and cooling, in agreement with experimental results. We also present a formulation that accounts for both additive and non-additive phase transformation processes. Moreover, a method based on the concept of path integral, which considers all the possible paths in thermal histories to reach the final state, is suggested.