Dissolution of particles in binary alloys: part I. computer simulations

Tundal, Ulf; Ryum, N.

doi:10.1007/bf02801160

Cited by 52 publications

(37 citation statements)

References 18 publications

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“…Some papers that study particle dissolution and growth by determination of the solution of a Stefan problem are due to, among many others, Whelan, 15) Aaron and Kotler, 16) and Tundal and Ryum. 17) In these papers it is assumed that the interface moves due to diffusion of one alloying element only, i.e. binary alloys.…”

Section: Introductionmentioning

confidence: 99%

A Model of the β-AlFeSi to α-Al(FeMn)Si Transformation in Al-Mg-Si Alloys

Kuijpers¹,

Vermolen

Vuik

et al. 2003

Mater. Trans.

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During the homogenisation process of Al-Mg-Si extrusion alloys, plate-like -Al 5 FeSi particles transform to multiple roundedAl 12 (FeMn) 3 Si particles. The rate of this to transformation determines the time which is required to homogenise the aluminium sufficiently for extrusion. In this paper, a finite element approach is presented which model the development of fraction transformed with time, in the beginning of the transformation, as a function of homogenisation temperature, as-cast microstructure and concentration of alloying elements. We treat the to transformation mathematically as a Stefan problem, where the concentration and the position of the moving boundaries of the and particles are determined. For the boundary conditions of the model thermodynamic calculations are used (Thermo-Calc). The influence of several process parameters on the modelled transformed fraction, such as the temperature and initial thickness of the plates, are investigated. Finally the model is validated with experimental data.

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Section: Introductionmentioning

confidence: 99%

A Model of the β-AlFeSi to α-Al(FeMn)Si Transformation in Al-Mg-Si Alloys

Kuijpers¹,

Vermolen

Vuik

et al. 2003

Mater. Trans.

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“…Such behavior has been observed in the case of the formation of precipitates during age hardening of aluminum alloys. [33][34][35][36] Therefore, only the particles that had sufficiently large sizes could survive and continue to grow, which resulted in a narrow size distribution of particles. In addition, due to the very short time to reach the homogenization temperature, the fraction of the particles that formed during heating might not be significant.…”

Section: A Effective Parameters On the Recrystallization Resistance mentioning

confidence: 99%

“…For example, the effect of the size distribution of dispersed particles on the mechanical properties and the growth and dissolution of these particles in structures were investigated. [31][32][33][34][35][36] Myhr et al [33] generated a special control volume formulation of the classical precipitation model for coupled nucleation, growth, and coarsening to describe the evolution of the particle size distribution with time during thermal processing of Al-Mg-Si alloys, including both isothermal and nonisothermal transformation behavior. The size distribution of particles was found to be effective on the precipitation behavior.…”

Section: Introductionmentioning

confidence: 99%

“…Myhr and Grong [34] studied the nonisothermal transformations in alloys containing a distribution of particles and found that the memory of a past process step, i.e., the previous particle sizes, is likely to have an effect on the overall transformation behavior. In addition, Tundal and Ryum [35,36] investigated the effect of size distribution of dispersed particles on their dissolution during homogenization. It was demonstrated that the size distribution of particles is an effective parameter on the model predictions and, therefore, should be considered in the model if an accurate prediction of the dissolution kinetics is to be achieved.…”

Section: Introductionmentioning

confidence: 99%

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Effect of the Size Distribution of Nanoscale Dispersed Particles on the Zener Drag Pressure

Eivani

Valipour

Ahmed

et al. 2010

Metall Mater Trans A

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In this article, a new relationship for the calculation of the Zener drag pressure is described in which the effect of the size distribution of nanoscale dispersed particles is taken into account, in addition to particle radius and volume fraction, which have been incorporated in the existing relationships. Microstructural observations indicated a clear correlation between the size distribution of dispersed particles and recrystallized grain sizes in the AA7020 aluminum alloy. However, the existing relationship to calculate the Zener drag pressure yielded a negligible difference of 0.016 pct between the two structures homogenized at different conditions resulting in totally different size distributions of nanoscale dispersed particles and, consequently, recrystallized grain sizes. The difference in the Zener drag pressure calculated by the application of the new relationship was 5.1 pct, being in line with the experimental observations of the recrystallized grain sizes. Mathematical investigations showed that the ratio of the Zener drag pressure from the new equation to that from the existing equation is maximized when the number densities of all the particles with different sizes are equal. This finding indicates that in the two structures with identical parameters except the size distribution of nanoscale dispersed particles, the one that possesses a broader size distribution of particles, i.e., the number densities of particles with different sizes being equal, gives rise to a larger Zener drag pressure than that having a narrow size distribution of nanoscale dispersed particles, i.e., most of the particles being in the same size range.

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“…To describe this particle dissolution in rigid media several physical models have been developed, incorporating the effects of long-distance diffusion [9], [2], [6] and non-equilibrium conditions at the interface [3], [1]. The long-distance diffusion models imply that the processes at the interface between particle and matrix proceed infinitely fast.…”

Section: Introductionmentioning

confidence: 99%

A conserving discretization for a Stefan problem with an interface reaction at the free boundary

2000

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The dissolution of an Al 2 Cu particle is considered. A characteristic property is that initially the particle has a non-smooth boundary. Furthermore the dissolution may be controlled by an interface reaction. The mathematical model of this dissolution process contains a description of the particle interface, of which the position varies in time. Such a model is called a Stefan problem. We use the finite element method to solve this problem numerically. The displacement of the free boundary is computed by a method based on the balance of atoms. This method leads to good results, also for non-smooth boundaries. Some numerical experiments are given for the dissolution of an Al 2 Cu particle in an Al-Cu alloy, with a varying rate of the interface reaction.1991 Mathematics Subject Classification: 35A35, 35R35, 65M06, 80A22

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Dissolution of particles in binary alloys: part I. computer simulations

Cited by 52 publications

References 18 publications

A Model of the β-AlFeSi to α-Al(FeMn)Si Transformation in Al-Mg-Si Alloys

A Model of the β-AlFeSi to α-Al(FeMn)Si Transformation in Al-Mg-Si Alloys

Effect of the Size Distribution of Nanoscale Dispersed Particles on the Zener Drag Pressure

A conserving discretization for a Stefan problem with an interface reaction at the free boundary

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Dissolution of particles in binary alloys: part I. computer simulations

Cited by 52 publications

References 18 publications

A Model of the &beta;-AlFeSi to &alpha;-Al(FeMn)Si Transformation in Al-Mg-Si Alloys

A Model of the &beta;-AlFeSi to &alpha;-Al(FeMn)Si Transformation in Al-Mg-Si Alloys

Effect of the Size Distribution of Nanoscale Dispersed Particles on the Zener Drag Pressure

A conserving discretization for a Stefan problem with an interface reaction at the free boundary

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A Model of the β-AlFeSi to α-Al(FeMn)Si Transformation in Al-Mg-Si Alloys

A Model of the β-AlFeSi to α-Al(FeMn)Si Transformation in Al-Mg-Si Alloys