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Predictive Modeling of 42CrMo4 Hardness after Two-Step Heat Treatment Using Symbolic Regression

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Abstract:

During a heat treatment, a material undergoes microstructural changes that result in an alterationof its hardness. In a two-step heat treatment, the material is first adjusted to an initial hardness viaa specified cooling rate. Subsequently, the hardness is reduced through a tempering process, whileits ductility is increased. Depending on the tempering duration, tempering temperature, and initialhardness, different resulting hardness values are obtained. The resulting hardness after a chosen heattreatment has thus far been difficult to predict. This work employs symbolic regression to develop amodel that predicts the hardness evolution of 42CrMo4 steel as a function of cooling rate, temperingduration, and tempering temperature. By describing the model with few parameters, it has alsobeen demonstrated that cooling rates and tempering temperatures leading to a target hardness canbe determined. The overall model achieves a coefficient of determination of R2 = 98.50 % for knownexperimental data and a combined coefficient of determination of R2 = 93.13 % for previouslyunknown cooling rates (forward) and previously unattained resulting hardness values (inverse).Our work shows that the resulting hardness of 42CrMo4 can be predicted using a small numberof parameters. This work is anticipated to establish a foundation for further research endeavors.For instance, the approach using symbolic regression can be further adapted to identify physicallyinterpretable constants. Furthermore, the model description offers the possibility of coupling witha simulation model to accurately predict the hardness of a component.

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Periodical:

Solid State Phenomena (Volume 390)

Pages:

121-135

DOI:

https://doi.org/10.4028/p-oDeJ6s

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Cite this paper

Online since:

April 2026

Authors:

Johann Albers*, Fabian Dittrich, Sebastian Härtel

Keywords:

42CrMo4, Heat Treatment, Material Hardness, Predictive Model, Symbolic Regression

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Creative Commons CC BY 4.0

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* - Corresponding Author

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