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# Prediction of the Work-Hardening Exponent for 3104 Aluminum Sheets with Different Grain Sizes

by 1,2,*, 1, 3,*, 1,2 and
1
Key Laboratory for Anisotropy and Texture of Materials, School of Materials Science &Engineering, Northeastern University, Shenyang 110819, China
2
Research Center for Metallic Wires, Northeastern University, Shenyang 110819, China
3
Department of Applied Science, University of Quebec at Chicoutimi, Chicoutimi, QC G7H2B1, Canada
*
Authors to whom correspondence should be addressed.
Materials 2019, 12(15), 2368; https://doi.org/10.3390/ma12152368
Received: 28 June 2019 / Revised: 20 July 2019 / Accepted: 23 July 2019 / Published: 25 July 2019
A practical approach to predict the yield strength and work-hardening exponent (n value) to evaluate the deep-drawing performance of annealed 3104 aluminum sheets is presented in the present work by only measuring and analyzing the grain size of the sheet. The various grain sizes were obtained through the different annealing treatment and then the evolution of the n value under different strains and the yield strength of annealed 3104 aluminum sheet were evaluated. Results showed that the n value and yield strength vary greatly with the grain size. A mathematical model relating grain size d, work-hardening exponent n, target strain ε, and yield strength Rp0.2 was developed in the present work. Within the studied grain size range d (12–29 μm), the n value generally increased with d in a strain-dependent manner, such that $n = 0.1875 − 85.03 × exp [ − d / 1.94 ]$ when the ε was less than 0.5%, but $n = 0.3 − 0.15 d − 1 / 2$ when the ε was greater than 2%. On the other hand, the n value was found to depend on the target strain ε as $n = 0.276 − A 1 × exp [ − e / 1.0435 ]$ , where A1 varies with d and its value is in the range of 0.132–0.364. In addition, the relationship between Rp0.2 and d followed the Hall-Petch equation ( $R p 0.2 = 36.273 + 139.8 × d − 1 / 2$ ). View Full-Text
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MDPI and ACS Style

Tian, N.; Yuan, F.; Duan, C.; Liu, K.; Wang, G.; Zhao, G.; Zuo, L. Prediction of the Work-Hardening Exponent for 3104 Aluminum Sheets with Different Grain Sizes. Materials 2019, 12, 2368. https://doi.org/10.3390/ma12152368

AMA Style

Tian N, Yuan F, Duan C, Liu K, Wang G, Zhao G, Zuo L. Prediction of the Work-Hardening Exponent for 3104 Aluminum Sheets with Different Grain Sizes. Materials. 2019; 12(15):2368. https://doi.org/10.3390/ma12152368

Chicago/Turabian Style

Tian, Ni; Yuan, Fei; Duan, Ceheng; Liu, Kun; Wang, Guangdong; Zhao, Gang; Zuo, Liang. 2019. "Prediction of the Work-Hardening Exponent for 3104 Aluminum Sheets with Different Grain Sizes" Materials 12, no. 15: 2368. https://doi.org/10.3390/ma12152368

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