# Constitutive Modeling of 2024 Aluminum Alloy Based on the Johnson–Cook Model

• S. Rasaee
• A. H. Mirzaei
Technical Paper

## Abstract

In this paper, hot compression behavior of Al2024 in the temperatures range of 573–723 K and strain rate range of 0.001–0.6 s−1 was studied based on standard tests. The prediction of flow stress was performed using constitutive equations based on the basic and modified Johnson–Cook model, and the accuracy of the proposed models was estimated by statistical error analysis method. Based on the experimental results, flow stress got changed significantly with changes in the strain rate and temperature. Since the basic model could not examine the correlated effects of the parameters, it had inadequate exactness to estimate the flow stress especially at high temperatures. During calculation, the constants in the modified model, effects of hardening and softening behavior were included in addition to considering the correlated effects of the parameters, so the accuracy of the modified model was increased significantly.

## Keywords

2024 aluminum alloy Hot compression deformation Constitutive equation Johnson–cook model

## List of Symbols

σ

Flow stress

ε

Strain

T

Temperature

$$\dot{\varepsilon }$$

Strain rate

$$\dot{\varepsilon }^{*}$$

Dimensionless strain rate $$\dot{\varepsilon }^{ *} = \dot{\varepsilon }/\dot{\varepsilon }_{\text{r}}$$

$$T^{*}$$

$${\text{Homologous}}\;{\text{temperature:}}$$ $$T^{ *} = \left( {T - T_{\text{r}} } \right)/\left( {T_{\text{m}} - T_{\text{r}} } \right)$$

$$T_{\text{r}}$$

The temperature at the reference condition: $$T_{\text{r}} = 673\;{\text{K}}$$

$$\dot{\varepsilon }_{\text{r}}$$

The strain rate at the reference condition: $$\dot{\varepsilon }_{\text{r}} = 0.001\;{\text{s}}^{ - 1}$$

## References

1. 1.
Chen L, Zhao G, Gong J, Chen X, and Chen M. J Mater Eng Perform 24 (2015) 5002.
2. 2.
Chen L, Zhao G, and Yu J. Mater Des 74 (2015) 25.
3. 3.
Changizian P, Zarei-Hanzaki A, and Roostaei A A. Mater Des 39 (2012) 384.
4. 4.
Lin Y C, and Chen X -M. Mater Des 32 (2011) 1733.
5. 5.
Abbasi-Bani A, Zarei-Hanzaki A, Pishbin M H, and Haghdadi N. Mech Mater 71 (2014) 52.
6. 6.
Johnson G R, and Cook W H, in 7th International Symposium on Ballistics. The Hague, Netherlands (1983).Google Scholar
7. 7.
Akbari Z, Mirzadeh H, and Cabrera J -M, Mater Des 77 (2015) 126.
8. 8.
Ashtiani H R, Parsa M, and Bisadi H, Mater Sci Eng A 545 (2012) 61.
9. 9.
Chen L, Zhao G, Yu J, Zhang W, and Wu T, Int J Adv Manuf Technol 74 (2014) 383.
10. 10.
Zhang C, Zhao G, Chen H, Guan Y, Cai H, and Gao B, J Mater Eng Perform, 22 (2013) 1223.
11. 11.
Liu H, Bao J, Xing Z, Zhang D, Song B, and Lei C, J Mater Eng Perform, 20 (2011) 894.
12. 12.
He A, Xie G, Zhang H, and Wang X, Mater Des (1980–2015) 52 (2013) 677–685.Google Scholar
13. 13.
Li H Y, Wang X F, Duan J Y, and Liu J, J Mater Sci Eng A, 577 (2013) 138.
14. 14.
Lin Y C, and Chen X -M, Comput Mater Sci 49 (2010) 628.
15. 15.
Mirzadeh H, Mech Mater 85 (2015) 66.
16. 16.
Lin Y C, Li L T, Fu Y X, and Jiang Y Q, J Mater Sci, 47 (2012) 1306.
17. 17.
Song W, Ning J, Mao X, and Tang H, Mater Sci Eng A, 576 (2013) 280.
18. 18.
Bobbili R, and Madhu V, J Mater Eng Perform 25 (2016) 1829.
19. 19.
Hou Q Y, and Wang J T, Comput Mater Sci 50 (2010) 147.
20. 20.
Lin Y C, Chen X -M, and Liu G, Mater Sci Eng A, 527 (2010) 6980.
21. 21.
Samantaray D, Mandal S, Phaniraj C, and Bhaduri A, K Mater Sci Eng A, 528 (2011) 8565.
22. 22.
Deng Y, Yin Z, and Huang J, Mater Sci Eng A 528 (2011) 1780.
23. 23.
Lin Y C, Li Q F, Xia Y C, and Li L T, Mater Sci Eng A 534 (2012) 654.