Quantum Technologies AB

Uppsala, Sweden

Quantum Technologies AB

Uppsala, Sweden

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Bjerken C.,Malmö University | Massih A.R.,Malmö University | Massih A.R.,Quantum Technologies AB
Philosophical Magazine | Year: 2014

The time-dependent Ginzburg-Landau (TDGL) equation for a single component non-conservative structural order parameter is used to study the spatio-temporal evolution of a second phase in the vicinity of an edge dislocation in an elastic crystalline solid. A symmetric Landau potential of sixth-order is employed. Dislocation field and elasticity modify the second-order and fourth-order coefficients of the Landau polynomial, respectively, where the former makes the coefficient singular at the origin. The TDGL equation is solved numerically using a finite volume method, where a wide range of parameter sets is explored. Computations are made for temperatures both above and below the transition temperature of a defect-free crystal Tc0. In both cases, the effects of the elastic properties of the solid and the strength of interaction between the order parameter and the displacement field are examined. If the system is quenched below, a steady state is first reached on the compressive side of the dislocation. On the tensile side, the growth is held back. The effect of thermal noise term in the TDGL equation is studied. We find that if the dislocation is introduced above Tc0, thermal noise supports the nucleation of the second phase, and a steady state will be attained earlier than if the thermal noise was absent. For a dislocation-free solid, we have compared our numerical computations for a mean-field (spatially averaged) order parameter versus time with the late time growth of the ensemble-averaged order parameter, calculated analytically, and find that both results follow upper asymptotes of sigmoid curves. © 2013 Taylor & Francis.


Massih A.R.,Malmö University | Massih A.R.,Quantum Technologies AB
Journal of Nuclear Science and Technology | Year: 2013

High-temperature (→ 90071400 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 twophase 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. © 2013 Atomic Energy Society of Japan.


Bjerken C.,Malmö University | Massih A.R.,Malmö University | Massih A.R.,Quantum Technologies AB
PTM 2015 - Proceedings of the International Conference on Solid-Solid Phase Transformations in Inorganic Materials 2015 | Year: 2015

General properties of directed ordering near line defects in elastic crystals undergoing phase transition are studied using the two-component time-dependent Ginzburg-Landau equation. Upon quenching the system below its transition point, the temporal evolution of the order parameter in the vicinity of the defect is evaluated. The development of vortices is explored and their interaction with the structural defect is examined. Finally, phase transitions in improper ferroelectrics in the context of the model are discussed.


Massih A.R.,Malmö University | Massih A.R.,Quantum Technologies AB
Solid State Phenomena | Year: 2011

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. © (2011) Trans Tech Publications.


Massih A.R.,Quantum Technologies AB | Jernkvist L.O.,Malmö University
Computational Materials Science | Year: 2015

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. © 2015 Elsevier B.V. All rights reserved.


Jernkvist L.O.,Quantum Technologies AB | Jernkvist L.O.,Malmö University | Massih A.R.,Quantum Technologies AB | Massih A.R.,Malmö University
Computational Materials Science | Year: 2014

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. © 2013 Elsevier B.V. All rights reserved.


Jernkvist L.O.,Quantum Technologies AB | Jernkvist L.O.,Malmö University
Computational Materials Science | Year: 2014

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. © 2013 Elsevier B.V. All rights reserved.


Manngard T.,Quantum Technologies AB | Massih A.R.,Quantum Technologies AB | Massih A.R.,Malmö University
Journal of Nuclear Science and Technology | Year: 2011

We present a unified model for calculation of zirconium alloy fuel cladding rupture during a postulated loss-of-coolant accident in light water reactors. The model treats the Zr alloy solid-to-solid phase transformation kinetics, cladding creep deformation, oxidation, and rupture as functions of temperature and time in an integrated fashion during the transient. The fuel cladding material considered here is Zircaloy-4, for which material property data (model parameters) are taken from the literature. We have modelled and simulated single-rod transient burst tests in which the rod internal pressure and the heating rate were kept constant during each test. The results are compared with experimental data on cladding rupture strain, temperature, and pressure. The agreement between computations and measurements in general is satisfactory. The effects of heating rate and rod internal pressure on the rupture strain are evaluated on the basis of systematic parameter variations of these quantities. In the β-phase of Zr, the burst strain decreases with increasing heating rate, whereas in the two-phase coexistence (α + β) domain and °-phase, the situation is more complex. Also, the mechanism for creep deformation in the (α + β) domain is not well understood; hence, its mechanistic constitutive relation is presently unknown. © Atomic Energy Society of Japan.

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