Multiphysics Simulation and Experimental Validation of Phase Transformation and Hardness in Jominy End-Quenched Low-Alloy Steels

Abstract High-volume industrial continuous hot-rolled steel heat treatment processes involve sophisticated multi-phase modeling. The performance of a given process can be optimized by coupling phase transformation kinetics with the cooling conditions of the process. This study develops a multiphysics model to simulate an intensive quenching process for steel, which is inherently transient and highly dependent on numerous parameters. The simulated object was a Jominy end-quenched specimen geometry using two commercial steels, AISI 4130 and AISI 4140, with the goal of transferring a verified methodology to the heat treatment process for industrial heavy-section products (bars, slabs). The simulation employs thermal, mechanical, and metallurgical models to estimate hardness, stress–strain response, and phase transformation, including martensite, bainite, pearlite, and retained austenite. The Johnson–Mehl–Avrami–Kolmogorov (JMAK) model is used for diffusional transformations, while the Koistinen–Marburger model is used for diffusionless transformations. Thermophysical properties were defined using JMATPro ® software. Validation against experimental thermal profiles, Rockwell hardness, and Materials Image Processing and Automated Reconstruction (MIPAR™) quantified martensite fractions showed strong agreement: hardness predictions achieved root-mean-square error (RMSE) of 2.57‐3.49 HRC, and martensite phase fractions correlated closely with microstructural measurements. The model successfully predicted the extended hardenability of AISI 4140 versus AISI 4130, with residual stress distributions following expected compression-tension-compression patterns.