Simulating the Growth of Dual-Phase Boride Layer on AISI M2 Steel by Two Kinetic Approaches

Abstract

Two kinetic approaches (integral method and Dybkov method) have been applied for simulating the boriding kinetics of AISI M2 steel in the range of 1173 to 1323 K, by including the effect of incubation periods. For the integral method, a peculiar solution of the resulting system of differential algebraic equations (DAE) has been employed for assessing the diffusivities of boron in FeB and Fe2B. The boron activation energies in FeB and Fe2B have been deduced from both approaches and compared with the data taken from the literature. Furthermore, to experimentally extend the validity of both approaches, four additional boriding conditions obtained on the boronized samples at 1173, 1223, 1273 and 1323 K for 10 h were then used. The predicted boride layers’ thicknesses were confronted to the experimental values. Consequently, a satisfactory concordance was obtained when comparing the simulated layers’ thicknesses to the experimental values derived from the literature.

Prediction models for the kinetics of iron boride layers on AISI 316L steel

“…The constant C up is the maximum content of boron in FeB (=16.40 wt.%) while C low denotes the minimum content of boron in the same phase (=16.23 wt.%) [10]. C up is the maximum boron concentraton Fe 2 B (=9.00 wt.%) whilst C low is the minimum boron concentration in Fe 2 B (8.83 wt.%) [10]. The variable v(t) denotes the position of (FeB/Fe 2 B) interface while v is the position of (Fe 2 B/substrate) interface.…”

“…By using the alternative diffusion model (ADM), the layers' thicknesses can be determined by solving numerically the following set of differential Equations (10) and (11) with the Runge-Kutta method [16]: (10) and…”

“…In terms of kinetic modelling of boriding process, a certain number of mathematical models was implemented and dedicated to the growth of FeB and Fe 2 B layers on some steels [7][8][9][10][11][12][13]. In the following mathematical models [7][8][9][10]12], the boride incubation periods were considered during the growth of both phases.…”

“…In terms of kinetic modelling of boriding process, a certain number of mathematical models was implemented and dedicated to the growth of FeB and Fe 2 B layers on some steels [7][8][9][10][11][12][13]. In the following mathematical models [7][8][9][10]12], the boride incubation periods were considered during the growth of both phases. Thus, all these models can be used as tools for searching for the optimized values of boride layers' thicknesses for the practical utilization of treated steels during the extreme working conditions.…”

“…For predicting the boriding kinetics of AIS 316 steel, the mean values of these two parameters were then considered to solve this diffusion problem. Keddam and Jurci [10] proposed two different approaches (the integral diffusion model and a modified version of the Dybkov model [13] with the inclusion of boride incubation periods) for the bilayer growth (FeB/Fe 2 B) onto the AISI M2 steel. Finally, Nait Abdelah et al [11] suggested a numerical treatment regarding the boriding kinetics of AISI H13 steel by employing the mean diffusion coefficient (MDC) method and ignoring the incubation periods for the formation of iron boride layers.…”