Simulation of the incubation time for the formation of (FeB/Fe₂B) bilayer on pure iron

Abstract

In this work, a mathematical model was used in order to study the growth kinetics of (Fe2B/FeB) bilayer during bori-ding process basing on the second Fick’s law and mass balance equation. The run of the numerical simulation allowed calculating the incubation time (τ) of each boronized layer (Fe2B or FeB), and estimating the effect of this parameter on the growth of the boronized layer. The boride incubation time for forming the FeB or Fe2B layer on the pure iron substrate was incorporated into the present mathematical model. To simulate the value of the growth rate constant and the incubation time for the bilayer configuration, the experimental data available in the literature concerning the boronizing of pure iron were considered. Based on the experimental and simulation results, it was shown that the incubation time decreases with increasing temperature in the FeB and Fe2B phases. It was concluded from this study that the thickness of each boride layer depended on its growth rate constant and on another parameter kτ which was the rate constant of incubation time.The obtained results confirmed the validity of the present mathematical model and gave a good estimate of the incubation time during the formation of each boride layer as well as formulated the variation of this parameter with a mathematical equation. Furthermore, the comparison of experimental data with the simulated results of boronized layer thickness allowed to validate the present model.

Confrontation of linear versus nonlinear approach in Fe2B boridelayer thickness predictions

“…The linear approach can be of use from an engineering point of view and is validated through comparison with another nonlinear approach, the diffusion model, published previously by Mebarek et al [27]. Both approaches use the same experiment results obtained from boronizing substrates of XC38 steel [29].…”

“…Specific models were developed by researchers, and further investigations were carried out. Presenting a few, the parabolic growth law model [22], the alternative diffusion model [23], the Dybkov model [24], the integral model [25,26] and the diffusion model that is based on the second law of Fick [26][27][28][29][30]. All these models are nonlinear and have a common goal: to analyze the diffusion data by studying the kinetics of boride layer thicknesses.…”

Dybkov model for the estimation of boron diffusion in the FeB/Fe2B bilayer on AISI 316 steel

“…where erf the Gauss errorfunction; and are constants to be determined according to the boundary conditions. The interfaces(FeB/Fe 2 B) and (Fe 2 B/Fe), shift by an infinitely small distance dx, which results from the flows in and out of the surface concerned, and is expressed by the following formulae: (10) with .…”

“…The boride layer can be either mono-phased or bi-phased [9]. Themorphology of the layers can be tooth shaped or planar depending on the alloying elements present in the steel [1,10]. For carbon steel, the diffusion of boron atoms into the substrate gives rise to the formation of a (boride layers/substrate) interface with saw-tooth morphology [2].…”