A kinetic model for analyzing the growth kinetics of fe2 b layers in aisi 4140 steel

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Kovove Mater. 48 2010 285–290 DOI: 10.4149/km 2010 5 285


A kinetic model for analyzing the growth kinetics of Fe2 B layers in AISI 4140 steel
M. Ortiz-Domínguez1 , E. Hernández-Sánchez1 , J. Martínez-Trinidad1 , M. Keddam2 , I. Campos-Silva1 *

Instituto Politécnico Nacional, Grupo Ingeniería de Superficies, SEPI-ESIME, U.P. Adolfo López Mateos, Zacatenco, Mexico D.F., 07738,Mexico 2 Département de Sciences des Matériaux, Faculté de Génie Mécanique et Génie des Procédes, USTHB, B.P N◦ 32, 16111, El-Alia, Bab-Ezzouar, Algiers, Algeria Received 15 February 2010, received in revised form 6 July 2010, accepted 6 July 2010 Abstract A kinetic model based on the mass balance at the growing interface and the effect of the boride incubation time was used to evaluate the growth ofFe2 B layers. The parabolic growth constant obtained by the model was expressed as a function of boron content in the Fe2 B layer and the process temperature. The simulated values were compared with experimental data derived from the literature, basically, for the boriding of AISI 4140 steel in the temperature range of 1123–1273 K. In addition, an expression of the Fe2 B layer thickness was obtainedthat showed good agreement with the experimental results. Finally, the instantaneous velocity of the Fe2 B/substrate interface and the weight gain produced by the formation of the Fe2 B layer were evaluated. K e y w o r d s : boriding, kinetic model, diffusion, layers, simulation

1. Introduction The term “boriding” means the enrichment of the surface of a work piece with boron by thermochemicaltreatment. By means of thermal energy, the boron atoms are transferred into the lattice of the parent material and, together with the atoms in that material, form the respective borides [1]. The boriding treatment applies in the temperature range 1073–1273 K between 1 and 10 h and it can be carried out in gaseous, liquid and solid medium. Iron borides are mainly formed on steel, and there are twokinds of iron borides: FeB, which is rich in boron, and Fe2 B, which is poor in boron. The thickness of the layer formed (known as the case depth), which affects the mechanical and chemical behavior of borided steels, depends on the boriding temperature, the treatment time and the boron potential that surrounds the surface sample [2]. A monolayer Fe2 B with a particular morphology is suitable forpractical use due to the difference between the specific volume and coefficient of thermal expan-

sion of the Fe2 B layer and the substrate. Saw-tooth shaped morphology of the boride layer/substrate interface is observed in low-alloy steels whereas in high-alloy steels the interface tends to be flat [3]. During the last decades, the modeling of the growth kinetics of boride layers has attracted muchattention to understand the effect of process parameters (boron potential, temperature and time) on the kinetic behavior of boride layers. For this reason, various diffusion models [4–11] were proposed in the literature. These models do not take into account the effect of the boride incubation time on the kinetics. Recently, a certain number of published works have considered this fact [12–17]. Inthis work, a kinetic model was applied to simulate the growth kinetics of Fe2 B layer considering the effect of boride incubation time. In addition, the parabolic growth constant (k) was evaluated at the Fe2 B/substrate interface as a function of boron content in the Fe2 B layer and process temperature. As a fitting parameter of the model, the upper boron Fe content (Cup2 B ) in the Fe2 B layer wasestimated in

*Corresponding author: tel.: (+52) (55) 57296000 ext. 54768; fax: (+52) (55) 57296000 ext. 54589; e-mail address: icampos@ipn.mx


M. Ortiz-Domínguez et al. / Kovove Mater. 48 2010 285–290

CFe2 B [x(t > 0) = 0] = 0. The boundary conditions were set as:
Fe B CFe2 B [x(t = t0 ) = 0] = Cup2 B for Cads > 8.83 wt.% B, Fe2 B CFe2 B [x(t = t0 ) = u] = Clow B for Cads < 8.83...
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