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Acta Metall Sin  2018, Vol. 54 Issue (6): 950-958    DOI: 10.11900/0412.1961.2017.00398
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Theoretical Calculation of Schmid Factor and Its Application Under High Strain Rate Deformation in Magnesium Alloys
Yanyu LIU, Pingli MAO(), Zheng LIU, Feng WANG, Zhi WANG
School of Materials Science and Engineering, Shenyang University of Technology, Shenyang 110870, China
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As an important parameter, the Schmid factor has been widely applied to analyze the deformation modes in metals. In order to analyze the deformation mechanisms of magnesium alloys under high strain rate, the Schmid factors of four slip modes (basal, prismatic, pyramidal <a> and pyramidal <c+a> slips) and two twinning systems ({101?2} tension and {101?1} contraction twinnings) were systematically calculated in this work. The experimental values of Schmid factor of as-received AZ31 rolling magnesium alloy sheets were obtained by electron backscatter diffraction (EBSD) technique, and then the theoretical calculated values were compared with those values. The high strain rate compression test of AZ31 rolling magnesium sheets was conducted by using split Hopkinson pressure bar at the strain rate of 1600 s-1, and the microstructures after compression were observed by optical microscopy. The Schmid factors and microstructures are combined to discuss the predominant deformation mechanisms for different orientation samples under different loading directions. The results showed that the theoretical calculated values of Schmid factors are in good agreement with their experimental values. Therefore, the Schmid factor, owing to its simplicity and conveniene, could be used to analyze the predominant deformation mechanism and interpret the unique characteristics of "true stress-true strain" curves in magnesium alloys. Furthermore, since the Schmid factor and its variation trend associated with deformation behavior in magnesium alloys are related, the calculation result of Schmid factor can provide a theoretical analytic approach to understand anisotropic phenomena caused by strong texture in magnesium alloys.

Key words:  Schmid factor      magnesium alloy      deformation mechanism      EBSD     
Received:  22 September 2017     
ZTFLH:  TG146.2  
Fund: Supported by the Shenyang Science and Technology Plan 2017 Project (No.17-9-6-00)

Cite this article: 

Yanyu LIU, Pingli MAO, Zheng LIU, Feng WANG, Zhi WANG. Theoretical Calculation of Schmid Factor and Its Application Under High Strain Rate Deformation in Magnesium Alloys. Acta Metall Sin, 2018, 54(6): 950-958.

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Fig.1  Schematic relationships of loading direction with c-axis, a-axes, normal direction of slip (or twinning) plane and slip (or twinning) direction (? is the angle between the loading direction and the slip (or twinning) plane normal, λ is the angle between the loading direction and slip (or twinning) direction, θ is the angle between c-axis and the loading direction, α is the angle between a-axis and the projection of loading direction on the basal plane)
Fig.2  Counter map of Schmid factor (SF) of basal slip
Fig.3  Counter maps of SF of prismatic slip(a) Pr1 (b) Pr2 (c) Pr3
Fig.4  Counter maps of SF of pyramidal <a> slip(a) Py1 (b) Py2 (c) Py3 (d) Py4 (e) Py5 (f) Py6
Fig.5  Counter maps of SF of pyramidal <c+a> slip
Pyr1 (b) Pyr2 (c) Pyr3 (d) Pyr4 (e) Pyr5 (f) Pyr6
Fig.6  Counter maps of SF of {1012} tension twinning
(a) ET1 (b) ET2 (c) ET3 (d) ET4 (e) ET5 (f) ET6
θ / (°) Basal <a> Prismatic slip Pyramidal Pyramidal {1012} {1011}
slip <a> slip <c+a> slip twinning twinning
0 0 0 0 0.446 0.499* -
15 0.218 0.025 0.110 0.499* 0.475 -
47 0.499* 0.238 0.390 0.292 0.260 0.259
70 0.354 0.425 0.498* 0.474 0.073 0.490
80 0.201 0.478 0.490 0.499* 0.021 0.492*
90 0 0.499* 0.441 0.446 - 0.470
Table 1  The maximum SF for basal slip, prismatic slip, pyramidal <a> slip, pyramidal <c+a> slip and twinning at different load directions
Fig.7  Counter maps of SF of {1011} contraction twinning(a) CT1 (b) CT2 (c) CT3 (d) CT4 (e) CT5 (f) CT6
Fig.8  Initial microstructure and corresponding micro pole figures in the normal direction (ND) of AZ31 rolling sheet (RD—rolling direction, TD—transverse direction)
Fig.9  SF maps of basal slip (a), prismatic slip (b), pyramidal <a> slip (c), pyramidal <c+a> slip (d), {10\({\bar{1}}\)2} tension twinning (e) and {10\({\bar{1}}\)1} contraction twinning (f)
Fig.10  True stress-true strain curves of different AZ31 Mg alloys rolling sheet samples with different directions at the strain rate of 1600 s-1
Fig.11  Microstructures of TD (a), RD (b) and ND (c) samples at the strain of 0.05
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