Three-dimensional thermo-elastic–plastic finite element modeling of quenching process of plain-carbon steel in couple with phase transformation

Abstract

This study focuses on finite element investigations of quenching process which is commonly applied to improve mechanical properties such as strength, hardness, and wear/fatigue resistances, etc. During the quenching process, various kinds of microstructures evolve depending on the cooling rate and temperature variation within the steel. This microstructural evolution has a significant effect on the final dimension and geometry of the mechanical parts. In order to investigate the effect of temperature variation and phase transformation on the dimensional change and stress distribution, thermo-elastic–plastic constitutive equation coupled with the mechanical strain, thermal strain, phase transformation strain, and transformation induced plasticity is described in detail. Using the constitutive equation introduced, a finite element program was developed and used to predict distributions of the temperature, volume fraction of each phase transformed, and stress and dimensional change of the cylindrical specimen, shaft with key groove, and cam-lobe made of carbon steel. It was found out that numerically obtained values such as temperature history and stress distribution were in good agreement with the data available in the literature for the cylindrical carbon steel specimen. The developed program can be used for better understanding of mechanics involved with the quenching process.

Introduction

Quenching is one of manufacturing processes to improve mechanical properties of mechanical components for automobiles, aircrafts, and machines subjected to high load and impact. The cooling rate and temperature variation within the steel during the quenching process results in microstructural evolution and have a significant effect on the final shape and dimension of mechanical parts. Effective control of such a phase transformation can lead to make these steel parts with better mechanical properties, microstructures, and final dimensional accuracies required. With increasing use of the finite element (FE) analysis as an effective controlling tool of phase transformation, mathematical modeling of phase transformation has been important for accurately analyzing the quenching process.

Johnson and Mehl [1] and Avrami [2], [3] proposed an analytical equation for diffusional transformation under the isothermal condition. Together with this equation, Scheil's additive rule [4] has been widely adopted to describe a non-isothermal cooling process like quenching by subdividing the cooling curve into various small isothermal steps. For handling a diffusionless transformation like an austenite–martensite transformation, Koistinen and Marburger [5] proposed an empirical model which can be used to predict the volume fraction of the martensite after rapid quenching. After these pioneering works, many investigations by Inoue and Raniecki [6], Rammerstorfer et al. [7], Fernandes et al. [8], Denis et al. [9], Agarwal and Brimacombe [10], Nagasaka et al. [11], Hawbolt et al. [12], Sjöström [13], and Kang and Im [14] have been made for modeling of the phase transformation to improve the accuracy of numerical simulations.

Due to the thermal strain resulted from the temperature variation during the quenching process, a dimensional change of the steel specimen takes place. However, it was well known that additional strains such as phase transformation strain and transformation-induced plasticity (TRIP) due to the difference and generation rate in the volume fraction of each phase and applied stress also have the significant effect on the final geometry of the mechanical part. Especially, microstructural plastic behavior, that is, TRIP occurs in the weaker phase, even though the external load lower than the yield strength of the weaker phase is applied. Some researchers such as Greenwood and Johnson [15], Leblond et al. [16], [17], Taleb et al. [18], [19], Fischer et al. [20], and Coret et al. [21] have analyzed this kind of microstructural transformation induced plasticity obtained from experimental or theoretical approaches in order to consider its effect in FE simulations.

In this study, the numerical phase transformation models such as Johnson–Mehl–Avrami–Kolmogorov (JMAK) model for the diffusional transformation and Koistinen and Marburger (KM) model for the diffusionless transformation were employed to investigate a dimensional change during the quenching process. During phase transformation, the volume fraction of each phase transformed and stress applied lead to the microstructural plasticity in the weaker phase as mentioned earlier. In order to consider the microstructural plasticity in the weaker phase according to the volume fraction of each phase transformed and stress applied during the quenching process, the numerical model proposed by Leblond et al. [16], [17] and modified by Taleb et al. [18], [19] was employed. Also, generation of the latent heat released due to the phase transformation inducing the temperature increase was considered in this work.

Even though the constitutive equation was introduced in many papers, most of these papers have offered no or a little information in the derivation procedure of the constitutive equation including the phase transformation effect. Using the constitutive equation in couple with the phase transformation, a FE program was developed and used to predict distributions of the temperature, volume fraction of each phase, and stress and dimensional change of the cylindrical specimen, shaft with key groove, and cam-lobe made of carbon steel. From this study, it was found out that numerically obtained values such as temperature history and stress distribution were in good agreement with the data available in the literature for the cylindrical carbon steel specimen and three-dimensional thermo-elastic–plastic FE program developed can be a useful tool in investigating design parameters for the quenching process.