Modeling the growth behavior of Fe ₂ B coatings using the inverse Stefan method

Abstract In this study, an innovative mathematical model based on the inverse Stefan approach was developed to predict the growth kinetics of Fe 2 B layers formed on ASTM A29 steel during boriding. Microstructural characterization and the determination of the average coating thickness were carried out using scanning electron microscopy (SEM) and optical microscopy (OM), providing an accurate description of the typical morphology of the borided phase. To evaluate the tribological behavior of both the substrate and the borided steel, pin-on-disk wear tests were conducted, revealing a significant reduction in the coefficient of friction (COF), from 0.61 for the untreated material to 0.27 after boriding, corresponding to an improvement of approximately 226 % in wear resistance. Furthermore, an analysis of variance (ANOVA) was performed to assess the influence of the process parameters on the coating thickness ( u ). The results indicated that both temperature ( T ) and treatment time ( t ) are highly significant factors, contributing 62.80 % and 24.75 %, respectively, while the T × t interaction accounted for 7.66 % of the variation.