A model to predict carburization profiles in high temperature alloys

Bongartz, K.; Lupton, D. F.; Schuster, H.

doi:10.1007/bf02655105

Cited by 61 publications

(23 citation statements)

References 12 publications

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“…The first explanation could be the slow diffusion of carbon released by CO(g) away from the interface which would induce an enrichment at the scale/alloy interface and would prevent reaction (2) from continuing. Nevertheless, as Bongartz et al [12] measured high values of the carbon diffusion coefficient in a Ni-25Cr-12Co-10Mo alloy (about 10 À8 cm 2 /s at 850 8C), carbon accumulation might not be the proper assumption at 900 8C. The other and more likely reason for explaining the slowing of CO(g) consumption is the decrease of the activity of the oxidizable elements M at the oxide/alloy interface vicinity as well as at the gas/oxide interface.…”

Section: Discussionmentioning

confidence: 93%

Oxide-Layer Formation and Stability on a Nickel-Base Alloy in Impure Helium at High Temperature

et al. 2007

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International audienceThe corrosion behavior in impure helium of Haynes 230, a nickel base alloy candidate for heat exchangers in Very High Temperature Reactors (VHTR), has been investigated. The study focused on the formation and the subsequent destruction of the surface oxide layer at 900 °C and 980 °C. In-situ gas-phase analysis coupled to post-exposure surface analyses showed that a chromium-rich surface oxide formed on Haynes 230 at 900 °C but was unstable above a critical temperature T A : the chromium-rich oxide reacted with carbon in solution in the alloy to produce chromium and CO(g). The effect of carbon monoxide partial pressure in the gas phase as well as the influence of chromium and carbon activities in the alloy on T A are discussed taking thermodynamics and kinetics aspects into account

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Section: Discussionmentioning

confidence: 93%

Oxide-Layer Formation and Stability on a Nickel-Base Alloy in Impure Helium at High Temperature

et al. 2007

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“…(13) These works generally used analytical methods to solve the equations of the model. Although numerical solutions have been provided for instance by Bongartz et al, (14) Christ et al, (5) Rank and Weinert (15) and Fortunier et al, (16) it seems that use of numerical methods to solve this type of problems has remained comparatively marginal. In contrast, the focus of this work is on numerical methods and their applications.…”

Section: Introductionmentioning

confidence: 98%

Numerical Simulation of Internal Oxidation of Steels during Annealing Treatments

Huin¹,

Flauder²,

Leblond

2005

Oxid Met

117

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This paper presents a new model for simultaneous diffusion and precipitation of chemical elements in metallic matrices, a scheme for its numerical solution, and several applications to problems of internal oxidation. The model basically stands as an extension of the classical Wagner model for internal oxidation of steels, but is more much general in that it allows for an arbitrary number of diffusing chemical elements, an arbitrary number of precipitate phases with arbitrary compositions, dependence of diffusion coefficients and solubility products upon (time-dependent) temperature, etc., thus allowing for a much broader range of applications. As a counterpart, it is generally impossible to solve the complex, non-linear equations of the model analytically, but this can be done numerically. The simple but efficient numerical scheme proposed is based on explicit 1D finite differences. Experience has shown that this scheme, in spite of its rusticity and the restrictions it imposes on the time-step, is more efficient than more elaborate strategies based on the finite-element method. The applications presented are concerned with internal oxidation of steels during annealing processes. The model and associated numerical scheme allow for evaluation of the amounts of the various oxide precipitates in the external layer of the sheet. This opens the way, through numerical parametric studies of the influence of the process parameters and the chemical composition, to the improvement of existing treatments and the development of new steel grades. INTRODUCTIONMany processes in the metallurgical industry involve simultaneous diffusion and precipitation of chemical elements: internal oxidation of a steel sheet during some annealing treatment is just one example. The aim of such a treatment is to prevent formation of superficial iron oxides or to eliminate them if they are already present. This is achieved by using a reducing atmosphere consisting mainly of hydrogen and nitrogen. During the process, oxygen, traces of which are present in the annealing atmosphere, diffuses inwards, the oxidizable elements diffuse outwards and various oxide precipitates are formed in the sub-surface alloy region.The aim of this paper is to present a new model for the simultaneous diffusion and precipitation of chemical elements in metallic matrices, its numerical implementation and several applications related to internal oxidation of steel sheets during annealing treatments. Emphasis will be placed on the last topic. The applications envisaged will notably include a study of the influence of the oxygen content of the annealing atmosphere upon the amounts of internal oxides formed, and a systematic investigation, for a given process, of the types of oxides formed for a wide range of steel grades.The first model for internal oxidation was proposed in the seminal work of Wagner. (1) Although it made several severely restricting hypotheses, such as the presence of a single oxidant, consideration of binary alloys only, oxidation of the sole most-react...

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“…Then the nucleation and growth (including coarsening) of M y N z (i.e., (N i ) k j and (R i ) k j for each class i of M y N z at every depth) are calculated as described in Eqs. [7] through [17]). Classes with (R i ) k j less than the radius corresponding to the size of one M y N z molecular unit are removed from the PSD and the M and N components are added to the solutes content of the matrix.…”

Section: A Numerical Methodsmentioning

confidence: 99%

“…Therefore, it would be highly beneficial to have at one's disposal a model that links the inward diffusion of I with the (depth-and time-dependent) precipitation state (volume fraction, number density, and size distribution) of the M y I z particles so that the microstructure of the alloys can be predicted and optimized. [1] Until now a series of attempts have been made to simulate inward diffusion of I and simultaneous precipitation of M y I z , [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] usually focusing on one specific (extreme) case of inward diffusion and precipitation. A simple model of coupled diffusion and precipitation was thus developed for the case of internal oxidation [2,3] and later applied to nitriding [4] and carburizing.…”

Section: Introductionmentioning

confidence: 99%

“…[5] This model assumes that the solubility of I in the matrix is negligible in the presence of dissolved M. The component I is thus instantaneously consumed by (internal) precipitation of M y I z , which leads to a sharp reaction front between the (completely precipitated) case and the (unreacted, I-free) core and to a reaction rate controlled by the diffusion of I through the M-depleted matrix. The model was generalized by considering a finite solubility of I, leading to some amount of dissolved I ahead of the reaction front during the precipitation; [6] in this variant, the model has been widely applied to carburizing [7][8][9] and nitriding. [10][11][12][13][14][15][16][17][18][19] A serious shortcoming of the type of models introduced earlier [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] is the disregard of the kinetics (the time and temperature dependencies) of the precipitation reaction.…”

Section: Introductionmentioning

confidence: 99%

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Coupling Inward Diffusion and Precipitation Kinetics; the Case of Nitriding Iron-Based Alloys

Jung

Meka

Rheingans

et al. 2016

Metall Mater Trans A

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A model that describes the inward diffusion of an element I into a solid substrate and the simultaneous precipitation of a compound M y I z , with M as the alloying element initially dissolved in the substrate matrix, is presented for the case of nitriding iron-based alloys. The model was developed by coupling the diffusion kinetics and the precipitation (nucleation and growth) kinetics. Additionally, the role of excess nitrogen and the kinetics of ammonia dissociation at the iron surface were incorporated into this coupled model. The model was successfully applied to the case of nitriding an Fe-2.23 at. pct V alloy; the simulation results are in good agreement with the measured data and allow for detailed understanding of the evolution of the nitride precipitates (volume fraction, number density, and size distribution) as a function of both nitriding time and depth in the specimen. The present model exposed the pronounced effects of the precipitation kinetics, of excess nitrogen, and of the surface-reaction kinetics on the overall nitriding kinetics and demonstrated a striking, nonmonotonous change with time of precipitate particle size at a distinct depth in the specimen.

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A model to predict carburization profiles in high temperature alloys

Cited by 61 publications

References 12 publications

Oxide-Layer Formation and Stability on a Nickel-Base Alloy in Impure Helium at High Temperature

Oxide-Layer Formation and Stability on a Nickel-Base Alloy in Impure Helium at High Temperature

Numerical Simulation of Internal Oxidation of Steels during Annealing Treatments

Coupling Inward Diffusion and Precipitation Kinetics; the Case of Nitriding Iron-Based Alloys

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