A Comparative Study on Johnson–Cook, Modified Johnson–Cook, Modified Zerilli–Armstrong and Arrhenius-Type Constitutive Models to Predict Hot Deformation Behavior of TA2

Bing Zhang,Xiaodi Shang,Jun Cai,Qiuyu Wang,Su Yao,Xiaokang Yang,Zhijuan Zhang,Kuaishe Wang

doi:10.1515/htmp-2019-0026

Abstract

Abstract The true strain data and true stress data are obtained from the isothermal compression tests under a wide range of strain rates (0.1–20 s−1) and temperatures (933–1,133 K) over the Gleeble-3500 thermomechanical simulator. The data are employed to generate the constitutive equations according to four constitutive models, respectively, the strain-compensated Arrhenius-type model, the modified Zerilli–Armstrong (ZA) model, the modified Johnson–Cook (JC) model and the JC model. In the meanwhile, a comparative research was made over the capacities of these four models and hence to represent the elevated temperature flow behavior of TA2. Besides, a comparison of the accuracy of the predictions of average absolute relative error, correlation coefficient (R) and the deformation behavior was made to test the sustainability level of these four models. It is shown from these results that the JC model is not suitable for the description of flow behavior of TA2 alloy in α+β phase domain, while the predicted values of modified JC model, modified ZA model and the strain-compensated Arrhenius-type model could be consistent well with the experimental values except under some deformation conditions. Moreover, the strain-compensated Arrhenius-type model can be also used to track the deformation behavior more precisely in comparison with other models.

Highlights

There are broad applications of TA2 industrial pure titanium, such as chemical, ship building and aviation industry due to its strong welding property, good mechanical performance and outstanding corrosion resistance [1, 2]
The deformation behavior of TA2 is sensitive to the processing parameters, such as the strain rate, strain and deformation temperature
The material flow behavior can be represented through the constitutive equation, which is input into finite element method (FEM) to trigger the deformation behavior of the material in certain loading conditions [6,7,8]

Summary

Introduction

There are broad applications of TA2 industrial pure titanium, such as chemical, ship building and aviation industry due to its strong welding property, good mechanical performance and outstanding corrosion resistance [1, 2]. The Johnson–Cook (JC) model has been widely employed in different commercial FEMs among these models to illustrate the high-temperature deformation behavior of alloys with its rapid calculation speed, small calculation quantity and simple form [16]. It is decided by five major material constants. Hongyi Zhan et al [20] proposed the modified ZA model to estimate the flow behavior of Ti–6Cr–5Mo–5V–4Al alloy in β-phase over a wide range of high strain rates and temperatures. The suitability of these three models was assessed through the comparison of the correlation coefficient (R) and the average absolute relative error (AARE)

Experimental procedures

Result and discussion

Conclusions