Acta Metallurgica Sinica (English Letters) ›› 2025, Vol. 38 ›› Issue (9): 1527-1544.DOI: 10.1007/s40195-025-01882-6
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													Shudong Yang1, Xiaoqian Guo1( ), Chao Ma2, Lu Shen1, Lingyu Zhao3, Wei Zhu3
), Chao Ma2, Lu Shen1, Lingyu Zhao3, Wei Zhu3
												  
						
						
						
					
				
Received:2024-10-31
															
							
																	Revised:2025-02-05
															
							
																	Accepted:2025-02-25
															
							
																	Online:2025-09-10
															
							
																	Published:2025-06-12
															
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								Xiaoqian Guo, Shudong Yang, Xiaoqian Guo, Chao Ma, Lu Shen, Lingyu Zhao, Wei Zhu. Anisotropic Mechanical Behavior in an Extruded AZ31 Magnesium Alloy: Experimental and Crystal Plasticity Modeling[J]. Acta Metallurgica Sinica (English Letters), 2025, 38(9): 1527-1544.
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																													Fig. 1 a Schematic of tensile and compressive samples with the typical grain orientation and b EBSD of initial sample in the extruded AZ31 Mg alloy bar
 
																													Fig. 2 Grain boundary and twin boundary (GB + TB) maps, inverse pole figures (IPF) maps, and pole figures (PF) maps of a T30, b T60, c C0 and d C90 at the plastic strain of 0.03, 0.03, 0.06 and 0.06, respectively
| Deformation mode | ${\tau}_{0}$ (MPa) | ${\tau}_{1}$ (MPa) | ${{h}}_{0}$ (MPa) | ${{h}}_{1}$ (MPa) | Latent hardening parameter | ${{A}}_{1}$ | ${{A}}_{2}$ | |||
|---|---|---|---|---|---|---|---|---|---|---|
| hsBa | hsPr | hsPy | hsET | |||||||
| Basal | 7 | 15 | 180 | 37 | 1.0 | 1.0 | 1.0 | 4.0 | ||
| Prismatic | 62 | 2 | 20 | 15 | 3.0 | 1.0 | 1.0 | 1.0 | ||
| Pyramidal < c + a > | 97 | 41 | 1000 | 0 | 1.0 | 1.0 | 1.0 | 4.2 | ||
| Extension twinning | 10 | 1 | 10 | 1 | 1.0 | 1.0 | 1.0 | 1.0 | 0.01 | 0.8 | 
Table 1 Values of the hardening parameters involved in the VPSC-TDT model
| Deformation mode | ${\tau}_{0}$ (MPa) | ${\tau}_{1}$ (MPa) | ${{h}}_{0}$ (MPa) | ${{h}}_{1}$ (MPa) | Latent hardening parameter | ${{A}}_{1}$ | ${{A}}_{2}$ | |||
|---|---|---|---|---|---|---|---|---|---|---|
| hsBa | hsPr | hsPy | hsET | |||||||
| Basal | 7 | 15 | 180 | 37 | 1.0 | 1.0 | 1.0 | 4.0 | ||
| Prismatic | 62 | 2 | 20 | 15 | 3.0 | 1.0 | 1.0 | 1.0 | ||
| Pyramidal < c + a > | 97 | 41 | 1000 | 0 | 1.0 | 1.0 | 1.0 | 4.2 | ||
| Extension twinning | 10 | 1 | 10 | 1 | 1.0 | 1.0 | 1.0 | 1.0 | 0.01 | 0.8 | 
 
																													Fig. 3 Experimental (symbols) and simulated (solid lines) true stress-true strain curves of the extruded AZ31 Mg alloy bar under different loading directions: a 0°, b 30°, c 60° and d 90°
 
																													Fig. 4 True stress-strain curves of the extruded AZ31 Mg alloy bar in a tension and b compression, and corresponding relative activities in different loading directions: (a1,b1) 0°, (a2,b2) 30°, (a3,b3) 60° and (a4,b4) 90°
 
																													Fig. 5 Yield strength (YS), ultimate strength (US) and yield strength asymmetry ratio of uniaxial tension and compression with the increase of oblique angle (ϕ)
 
																													Fig. 8 Predicted texture evolutions under uniaxial tension along different loading directions (ϕ) of a 0°, b 30°, c 60° and d 90° at the strain (ε) of 0.05, 0.10 and 0.15
 
																													Fig. 9 Predicted texture evolutions under uniaxial compression along different loading directions (ϕ) of a 0°, b 30°, c 60° and d 90° at the strain (ε) of 0.05, 0.10 and 0.15
 
																													Fig. 10 Measured (symbols) and simulated (lines) volume fraction of $\left\{{10}\stackrel{{-}}{1}{{2}}\right\}$ extension twin in a tension and b compression
 
																													Fig. 11 SF frequency distributions of a {0002} < 11$\stackrel{{-}}{2}$0 > basal slip and b {1$0\stackrel{{-}}{1}0$} < 11$\stackrel{{-}}{2}$0 > prismatic slip, and corresponding c1 table and c2 figure of average Schmid factor in different oblique angles (φ)
 
																													Fig. 12 EBSD analyses of IGMA on the AZ31 Mg alloy samples: a T30, b T60, c C0 and d C90 at the plastic strain of 0.03, 0.03, 0.06 and 0.06, respectively, and e SF of typical grains in the basal slip and prismatic slip
 
																													Fig. 13 SF distribution in polar projection maps of $\{{{10}\stackrel{{-}}{1}{{2}}}\}$ extension twin compared with initial texture (black dots) under uniaxial a–d tension and e–h compression along loading directions of 0°, 30°, 60° and 90°
 
																													Fig. 14 SF frequency distributions of $\{{{10}\stackrel{{-}}{1}{{2}}}\}$ extension twin under uniaxial a tension and b compression along loading directions of 0°, 30°, 60° and 90°
 
																													Fig. 15 a EBSD {0001} pole figures of full regions, b IPF maps and c {0001} pole figures of typical grains (G1-G4) and responding extension twin variants (V1-V6) in T30 and C90 at the strain of 0.03 and 0.06, respectively. G-grain, M-matrix, T-twin, V-variant
| Typical grain | Schmid factor of each variant | ||||||
|---|---|---|---|---|---|---|---|
| V1 | V2 | V3 | V4 | V5 | V6 | ||
| T30 | G1 | 0.1441 | 0.2037 | 0.3039 | 0.2713 | 0.3164 | 0.2894 | 
| G2 | 0.3466 | 0.3893 | 0.4187 | 0.3907 | 0.4174 | 0.4321 | |
| C90 | G3 | 0.0998 | 0.0977 | 0.4934 | 0.4982 | 0.1522 | 0.1495 | 
| G4 | 0.0174 | 0.0170 | 0.4454 | 0.4434 | 0.2870 | 0.2854 | |
Table 2 SF of $\{{{10}\stackrel{{-}}{1}{{2}}}\}$ twin variants corresponding to typical grains of T30 and C90. (The active variant is highlighted in bold.)
| Typical grain | Schmid factor of each variant | ||||||
|---|---|---|---|---|---|---|---|
| V1 | V2 | V3 | V4 | V5 | V6 | ||
| T30 | G1 | 0.1441 | 0.2037 | 0.3039 | 0.2713 | 0.3164 | 0.2894 | 
| G2 | 0.3466 | 0.3893 | 0.4187 | 0.3907 | 0.4174 | 0.4321 | |
| C90 | G3 | 0.0998 | 0.0977 | 0.4934 | 0.4982 | 0.1522 | 0.1495 | 
| G4 | 0.0174 | 0.0170 | 0.4454 | 0.4434 | 0.2870 | 0.2854 | |
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