Modelo estatístico de regressão para estimar a microdureza vickers em um aço 1020 cementado

Abstract

The present work aimed at the statistical regression modeling to estimate Vickers microhardness, for an AISI 1020 steel that has gone through the case-hardening thermochemical process. This modeling was used to measure the dimensions of the carburized layers on the steel surface, by calculating the carbon concentration, obtained from its diffusion. The diffusion model used was physically supported by Fick’s laws and Boudouard’s thermochemical reactions. Once applied to steels, this model describes the growth kinetics of the layers. The analytical model was used to perform calculations of carbon concentrations related to time and depth in relation to the surface of the part. Consequently, the carbon concentration was used as a variable, which together with the carburizing processing time, the depth and the proportion of charcoal, allowed a modeling of the Vickers microhardness of AISI 1020 steel. This modeling made use of the statistical tools of regression analysis, more specifically, non-linear regression, of the polynomial type of order 2. The model presented, met all the presuppositions imposed for a regression model. An excellent fit of the proposed model was found, since approximately 97.0% of the variation in Vickers microhardness is explained by the variation in the model. Therefore, the model will be able to analyze the relationships between the variables depth, time and the proportion of charcoal, thus making it possible to predict future values for Vickers microhardness. The applicability of the proposed model will allow a reduction in costs, as well as an increase in the efficiency and quality of the samples.