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Title: Comparative study on constitutive models for 21-4N heat resistant steel during high temperature deformation
Authors: Li, YM
Ji, HC
Cai, ZM
Tang, XF 
Li, YG
Liu, JP
Keywords: 21-4N
High temperature deformation
Constitutive models
Numerical simulation
Issue Date: 2019
Publisher: Molecular Diversity Preservation International (MDPI)
Source: Materials, 2 June 2019, v. 12, no. 12, 1893, p. 1-22 How to cite?
Journal: Materials 
Abstract: The Gleeble-1500D thermal simulation test machine was used to conduct the isothermal compression test on 21-4N at the strain rate (epsilon) of 0.01-10 s(-1), the deformation temperature (T) of 1273-1453 K and the maximum deformation is 0.916. The data of the stress-strain (sigma-epsilon) were obtained. Based on the sigma-epsilon data, the Johnson-Cook (J-C), modified J-C, Arrhenius and Back-Propagation Artificial Neural Network (BP-ANN) models were established. The accuracy of four models were verified, analyzed and compared. The results show that J-C model has a higher accuracy only under reference deformation conditions. When the deformation condition changes greatly, the accuracy of J-C model is significantly reduced. The coupling effect of T and epsilon of modified J-C model is considered, and the prediction accuracy is greatly improved The Arrhenius model introduces Zener-Hollomon (Z) to represent the coupling effect of T and epsilon, it has a fairly high prediction accuracy. And it can predict flow stress (sigma) accurately at different conditions. The accuracy of BP-ANN model is the highest, but its learning rate is low, the learning and memory are unstable. It has no memory for the weights and thresholds of the completed training. So, there are certain limitations of it in use. Finally, a Finite Element Method (FEM) of the isothermal compression experiment for four models were established, and the distribution of the equivalent stress field, equivalent strain field and temperature field with the deformation degree of 60% were obtained.
EISSN: 1996-1944
DOI: 10.3390/ma12121893
Rights: © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
The following publication Li, Y.; Ji, H.; Cai, Z.; Tang, X.; Li, Y.; Liu, J. Comparative Study on Constitutive Models for 21-4N Heat Resistant Steel during High Temperature Deformation. Materials 2019, 12, 1893, 1-22 is available at
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