Acta Metallurgica Sinica (English Letters) ›› 2019, Vol. 32 ›› Issue (4): 452-460.DOI: 10.1007/s40195-018-0859-5
• Orginal Article • Previous Articles Next Articles
Hui Wang1(
), Cheng Lu1, Kiet Tieu1, Yu Liu1, Rui Wang1, Jintao Li1
Received:2018-08-30
Revised:2018-10-25
Online:2019-04-10
Published:2019-04-19
Contact:
Wang Hui
About author: Dr. Kun-Kun Deng was born in 1983 and was awarded Ph. D in Harbin University of Technology in 2011. After graduation, he worked in the College of Materials Science and Engineering, Taiyuan University of Technology. At the same time, he continued his research work on the design, fabrication and processing of advanced Mg-based material in. Now, he is the vice chairman of Youth Committee in Magnesium Alloy Branch of Chinese Materials Research Society. He was denoted as young academic pacemaker of Shanxi Province in 2018. He has held two projects of National Nature Science Foundation of China, one project of Specialized Research Fund for the Doctoral Program of Higher Education, one Project of International Cooperation in Shanxi and two projects of Natural Science Foundation of Shanxi. He has published more than 60 articles. The time cited is more than 840 (without selfcitations), and the H-index is 22. In addition, he has published one academic monograph and acquired eight Chinese patents. 
Hui Wang, Cheng Lu, Kiet Tieu, Yu Liu, Rui Wang, Jintao Li. Correlation Between Crystal Rotation and Redundant Shear Strain in Rolled Single Crystals: A Crystal Plasticity FE Analysis[J]. Acta Metallurgica Sinica (English Letters), 2019, 32(4): 452-460.
| Case A | Case B | Case C | Case D | |
|---|---|---|---|---|
| Initial orientation | roCube (00\(\bar{1}\))[ | Goss (011)[ | Copper (112)[11\(\bar{1}\)] | Brass (\(\bar{1}\)01)[1\(\bar{2}\)1] |
| Orientation stability | Unstable | Stable | Semi-stable | Stable |
| Activated slip systems | Symmetrical | Symmetrical | Asymmetrical | Asymmetrical |
| Deformation | Rolling | Rolling | Rolling | PSC |
| Reduction | 50% | 30% | 50% | 43% |
| Friction coefficient | 0.25 | 0.25 | 0.11 | 0.1 |
| Diameter of rolls | 75 mm | 75 mm | 310 mm | ∞ |
| Initial thickness | 3.0 mm | 2.8 mm | 4.0 mm | 7.0 mm |
| Reference | [ | [ | [ | [ |
Table 1 Simulation conditions of four simulation cases
| Case A | Case B | Case C | Case D | |
|---|---|---|---|---|
| Initial orientation | roCube (00\(\bar{1}\))[ | Goss (011)[ | Copper (112)[11\(\bar{1}\)] | Brass (\(\bar{1}\)01)[1\(\bar{2}\)1] |
| Orientation stability | Unstable | Stable | Semi-stable | Stable |
| Activated slip systems | Symmetrical | Symmetrical | Asymmetrical | Asymmetrical |
| Deformation | Rolling | Rolling | Rolling | PSC |
| Reduction | 50% | 30% | 50% | 43% |
| Friction coefficient | 0.25 | 0.25 | 0.11 | 0.1 |
| Diameter of rolls | 75 mm | 75 mm | 310 mm | ∞ |
| Initial thickness | 3.0 mm | 2.8 mm | 4.0 mm | 7.0 mm |
| Reference | [ | [ | [ | [ |
Fig. 1 a Rolling, b PSC model
Fig. 2 Distribution of activated slip systems in a roCube, b Goss, c Copper, d Brass [18]
| \(n\) | \(\dot{\gamma }_{0} \left( {{\text{s}}^{ - 1} } \right)\) | \(h_{0}\) (MPa) | \(h_{\text{s}}\) (MPa) | \(\tau_{1}\) (MPa) | \(\tau_{0}\) (MPa) | \(q\) |
|---|---|---|---|---|---|---|
| 300 | 1E-04 | 100 | 0.01 | 6.3 | 6 | 1 |
Table 2 Parameters used in the Bassani-Wu hardening model
| \(n\) | \(\dot{\gamma }_{0} \left( {{\text{s}}^{ - 1} } \right)\) | \(h_{0}\) (MPa) | \(h_{\text{s}}\) (MPa) | \(\tau_{1}\) (MPa) | \(\tau_{0}\) (MPa) | \(q\) |
|---|---|---|---|---|---|---|
| 300 | 1E-04 | 100 | 0.01 | 6.3 | 6 | 1 |
Fig. 3 Distrbiution of a TD-rotation in the experiment, b TD-rotation and \(- \;\gamma_{XY}\) in the simulation of roCube after a 50% reduction
Fig. 4 Distribution of a shear strain on slip system a1 (\(\gamma_{{{\text{a}}1}}\)) and b1 (\(\gamma_{{{\text{b}}1}}\)), b imbalance ratio between \(\gamma_{{{\text{a}}1}}\) and \(\gamma_{{{\text{b}}1}}\), \(\left( {\gamma_{{{\text{a}}1}} - \gamma_{{{\text{b}}1}} } \right)\)/max (\(\gamma_{{{\text{a}}1}}\), \(\gamma_{{{\text{b}}1}}\))
Fig. 5 Distribution of a TD-rotation in the experiment [3], b TD-rotation and \(- \;\gamma_{XY}\) in the simulation of Goss after a 30% reduction
Fig. 6 Distribution of a shear strain on slip system c2 (\(\gamma_{{{\text{c}}2}}\)) and a2 (\(\gamma_{{{\text{a}}2}}\)), b imbalance ratio between \(\gamma_{{{\text{c}}2}}\) and \(\gamma_{{{\text{a}}2}}\), \(\left( {\gamma_{{{\text{c}}2}} - \gamma_{{{\text{a}}2}} } \right)\)/max (\(\gamma_{{{\text{c}}2}}\), \(\gamma_{{{\text{a}}2}}\))
Fig. 7 Distribution of a TD-rotation and deformed FE mesh, b TD-rotation and \(- \;\gamma_{XY}\), c shear strain on slip system a1 (\(\gamma_{{{\text{a}}1}}\)) and c3 (\(\gamma_{{{\text{c}}3}}\)) along the thickness
Fig. 8 Sample shape changes and {111} pole figures in the a experiment [4], b simulation
Fig. 9 Evolution of shear strain on slip system c1 (\(\gamma_{{{\text{c}}1}}\)) and b3 (\(\gamma_{b3}\)) in one representative element
| Orientation | Matrix band | Shear strain on slip systems | \({\varOmega}_{\text{TD}}^{\text{P}}\) | \({\varOmega}_{\text{TD}}^{ *}\) | Macroscopic shear strain \(\gamma_{XY}\) | \({\varOmega}_{\text{TD}}\) | Relation \({\varOmega}_{\text{TD}} ={\varOmega}_{\text{TD}}^{\text{P}} +{\varOmega}_{\text{TD}}^{ *}\) |
|---|---|---|---|---|---|---|---|
| roCube | M1 | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} < \gamma_{{{\text{b}}1 - {\text{b}}2}}\) | -?TD | +TD | - | -?TD | (-?)?=?(-?)?+?(+), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) |
| M2 | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} > \gamma_{{{\text{b}}1 - {\text{b}}2}}\) | +?TD | -?TD | + | +?TD | (+)?=?(+)?+?(-), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) | |
| Goss | M1 | \(\gamma_{{{\text{c}}2 - {\text{c}}3}} < \gamma_{{{\text{a}}2 - {\text{a}}3}}\) | -?TD | +?TD | - | -?TD | (-)?=?(-)?+?(+), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) |
| M2 | \(\gamma_{{{\text{c}}2 - {\text{c}}3}} > \gamma_{{{\text{a}}2 - {\text{a}}3}}\) | +?TD | -?TD | + | +?TD | (+)?=?(+)?+?(-), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) | |
| Copper | M2 | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} > \gamma_{{{\text{c}}3 - {\text{d}}3}}\) | +?TD | -?TD | + | +?TD | (+)?=?(+)?+?(-), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) |
| M1a | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} > \gamma_{{{\text{c}}3 - {\text{d}}3}}\) | +?TD | +?TD | + | +?TD | (+)?=?(+)?+?(+) | |
| M1b | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} < \gamma_{{{\text{c}}3 - {\text{d}}3}}\) | -?TD | +?TD | + | +?TD | (+)?=?(-)?+?(+), \({\varOmega}_{\text{TD}}^{\text{P}}\)?<?\({\varOmega}_{\text{TD}}^{ *}\) |
Table 3 Deformation in matrix bands of roCube, Goss, and Copper
| Orientation | Matrix band | Shear strain on slip systems | \({\varOmega}_{\text{TD}}^{\text{P}}\) | \({\varOmega}_{\text{TD}}^{ *}\) | Macroscopic shear strain \(\gamma_{XY}\) | \({\varOmega}_{\text{TD}}\) | Relation \({\varOmega}_{\text{TD}} ={\varOmega}_{\text{TD}}^{\text{P}} +{\varOmega}_{\text{TD}}^{ *}\) |
|---|---|---|---|---|---|---|---|
| roCube | M1 | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} < \gamma_{{{\text{b}}1 - {\text{b}}2}}\) | -?TD | +TD | - | -?TD | (-?)?=?(-?)?+?(+), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) |
| M2 | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} > \gamma_{{{\text{b}}1 - {\text{b}}2}}\) | +?TD | -?TD | + | +?TD | (+)?=?(+)?+?(-), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) | |
| Goss | M1 | \(\gamma_{{{\text{c}}2 - {\text{c}}3}} < \gamma_{{{\text{a}}2 - {\text{a}}3}}\) | -?TD | +?TD | - | -?TD | (-)?=?(-)?+?(+), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) |
| M2 | \(\gamma_{{{\text{c}}2 - {\text{c}}3}} > \gamma_{{{\text{a}}2 - {\text{a}}3}}\) | +?TD | -?TD | + | +?TD | (+)?=?(+)?+?(-), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) | |
| Copper | M2 | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} > \gamma_{{{\text{c}}3 - {\text{d}}3}}\) | +?TD | -?TD | + | +?TD | (+)?=?(+)?+?(-), \({\varOmega}_{\text{TD}}^{\text{P}}\)?>?\({\varOmega}_{\text{TD}}^{ *}\) |
| M1a | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} > \gamma_{{{\text{c}}3 - {\text{d}}3}}\) | +?TD | +?TD | + | +?TD | (+)?=?(+)?+?(+) | |
| M1b | \(\gamma_{{{\text{a}}1 - {\text{a}}2}} < \gamma_{{{\text{c}}3 - {\text{d}}3}}\) | -?TD | +?TD | + | +?TD | (+)?=?(-)?+?(+), \({\varOmega}_{\text{TD}}^{\text{P}}\)?<?\({\varOmega}_{\text{TD}}^{ *}\) |
Fig. 10 Ratios between crystal rotation and redundant shear strain
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