Ali R Massih

Simulation of hydrogen embrittlement in zirconium alloys under stress and temperature gradients

Abstract A finite element model is presented for hydrogen embrittlement of zirconium alloys. The model takes into account the coupled processes of hydrogen diffusion, non-mechanical energy flow, hydride precipitation, hydride/solid solution deformation and fracture.The model has been tested successfully against the Sawatzky experiment and exact analytical solutions on hydrogen diffusion and hydride precipitation under a temperature gradient. Based on this model, the hydrogen embrittlement of a Zircaloy-2 cracked plate, is studied under tensile stress and temperature gradient. The initial and boundary conditions are according to those encountered in the fuel cladding of light water reactors during operation. The strong effect of crack tip stress intensification on hydrogen diffusion and initial hydride precipitation is shown. The problem is also studied by considering near-tip material damage which affects hydride precipitation significantly.

Hydride-induced embrittlement and fracture in metals—effect of stress and temperature distribution

Abstract A mathematical model for the hydrogen embrittlement of hydride forming metals has been developed. The model takes into account the coupling of the operating physical processes, namely: (i) hydrogen diffusion, (ii) hydride precipitation, (iii) non-mechanical energy flow and (iv) hydride/solid-solution deformation. Material damage and crack growth are also simulated by using de-cohesion model, which takes into account the time variation of energy of de-cohesion, due to the time-dependent process of hydride precipitation. The bulk of the material, outside the de-cohesion layer, is assumed to behave elastically. The hydrogen embrittlement model has been implemented numerically into a finite element framework and tested successfully against experimental data and analytical solutions on hydrogen thermal transport (in: Wunderlich, W. (Ed.), Proceedings of the European Conference on Computational Mechanics, Munich, Germany, 1999, J. Nucl. Mater. (2000a) 279 (2–3) 273). The model has been used for the simulation of Zircaloy-2 hydrogen embrittlement and delayed hydride cracking initiation in (i) a boundary layer problem of a semi-infinite crack, under mode I loading and constant temperature, and (ii) a cracked plate, under tensile stress and temperature gradient. The initial and boundary conditions in case (ii) are those encountered in the fuel cladding of light water reactors, during operation. The effects of near-tip stress intensification as well as of temperature gradient on hydride precipitation and material damage have been studied. The numerical simulation predicts hydride precipitation at a small distance from the crack-tip. When the remote loading is sufficient, the near-tip hydrides fracture. Thus a microcrack is generated, which is separated from the main crack by a ductile ligament, in agreement with experimental observations.

Dynamic stability of weakly damped oscillators with elastic impacts and wear

The dynamics of non-linear oscillators comprising of a single-degree-of-freedom system and beams with elastic two-sided amplitude constraints subject to harmonic loads is analyzed. The beams are clamped at one end, and constrained against unilateral contact sites near the other end. The structures are modelled by a Bernoulli-type beam supported by springs using the finite element method. Rayleigh damping is assumed. Symmetric and elastic double-impact motions, both harmonic and sub-harmonic, are studied by way of a Poincare mapping that relates the states at subsequent impacts. Stability and bifurcation analyses are performed for these motions, and domains of instability are delineated. Impact work rate, which is the rate of energy dissipation to the impacting surfaces, is evaluated and discussed. In addition, an experiment conducted by Moon and Shaw on the vibration of a cantilevered beam with one-sided amplitude constraining stop is modelled. Bifurcation observed in the experiment could be captured.

Vibro-impact dynamics of a periodically forced beam

The vibration and impact dynamics of a periodically forced loosely supported beam are analyzed. The wear work rates at impact points are evaluated. The considered beam is clamped at one end, and co ...

Kinetics of fission product gas release during grain growth

A theoretical framework for the calculation of fission product gas release by diffusion, irradiation-induced re-solution, grain boundary saturation and grain growth in ceramic nuclear fuel (UO2) under time-varying loads is presented. The diffusion equation is subjected to boundary conditions, which account for the aforementioned effects. Analytical solutions to the equation are obtained. The theory is applied to calculate fission gas release and grain growth as functions of temperature and time. Correlation between grain growth and gas release is calculated and the results are discussed in the light of experimental data.

Transformation kinetics of alloys under non-isothermal conditions

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.

An effective method for calculation of diffusive flow in spherical grains

The accuracy of a numerical fission gas release algorithm developed by Forsberg and Massih for solving the problem of diffusive flow to a spherical grain boundary is analysed. Estimates of numerical errors are derived for both steady-state and time varying conditions. We also present a method through which the accuracy of the algorithm can be improved or optimised for most applications.

High-temperature creep and superplasticity in zirconium alloys

High-temperature (≈ 900−1400 K) steady-state creep test data on as-received zirconium alloys, Zr-1wt%Nb and Zircaloy-4 used as fuel cladding materials in light water reactors are evaluated by employing two sets of models. In particular, the focus of the paper is on the former alloy and in the two-phase coexistence region, i.e. the (α+β)-domain of the alloy. In one modeling approach, the constitutive relations for the two single phase regions (α and β) are combined through a phase transition kinetic model and a phase mixing rule; in another, a superplasticity model is used directly to calculate the creep deformation rate as a function of stress and temperature in the (α+β)-domain. The results show that the former approach is inadequate in retrodicting the experimental data, while the latter one gives a fair overall agreement. The paper describes the details of the models, the data, and derivations of the constitutive laws.

Phase transformations near dislocations and cracks

A generic model for nucleation of oriented second-phase in alloys in the vicinity of cracksand dislocations, is considered. The model employs the Ginsburg-Landau approach, which accountsfor the elasticity of crystalline solid and the interaction of structure/composition with the elastic fieldin the vicinity of the defect and in the crystalline bulk. We examine the nature of the structural phasetransition and construct its phase diagram.

Second-phase nucleation on an edge dislocation

A model for nucleation of second phase at or around a dislocation in a crystalline solid is considered. The model employs the Ginzburg–Landau theory of phase transitions comprising the sextic term in the order parameter (η6) in the Landau free energy. The ground state solution of the linearised time-independent Ginzburg–Landau equation is derived, through which the spatial variation of the order parameter is delineated. Moreover, a generic phase diagram indicating tricritical behaviour near and away from the dislocation is depicted. The relation between classical nucleation theory and the Ginzburg–Landau approach is discussed, for which the critical formation energy of the nucleus is related to the maximum of the Landau potential energy. A numerical example illustrating the application of the model to the case of nucleation of hydrides in zirconium alloys is provided.