A quantitative study on planar mechanical anisotropy of a Mg-2Zn-1Ca alloy

doi:10.1016/j.jmst.2021.07.051

Abstract

Abstract:

A TD-tilted basal texture in Mg alloys often generates a strong planar mechanical anisotropy. Unfortunately, there has been not a quantitative study on this issue. In the present study, the mechanisms for the anisotropy of tensile yield strength in RD-TD plane were quantitatively studied for a Mg-2Zn-1Ca alloy with different grain sizes and textures. Here, RD and TD refer to the rolling direction and transverse direction of the plate. The results show that there is a strong planar yield anisotropy (∼24 ± 5 MPa), regardless of grain size, while this yield anisotropy is absent in texture with a circular distribution of basal poles. The examination of microstructure and X-ray diffraction analysis reveals that, beside basal slip as the predominant mode under both RD-tension and TD-tension, prismatic slip in RD-tension and both prismatic slip and extension twinning in TD-tension are also important. The parameters of Hall-Petch relation are also used to further analyze the mechanism for yield anisotropy. The changeable intercept, ${{\sigma }_{0}}$, and invariant Hall-Petch slope, k, between RD-tension and TD-tension are rationalized accounting for this anisotropy. The reasons why there are different ${{\sigma }_{0}}$ and similar k between TD-tension and RD-tension are quantitively discussed. At last, a texture design for decreasing the planar yield anisotropy is given.

Key words: Mg alloy, Deformation, Yield strength, Anisotropy

Xinde Huang, Yunchang Xin, Yu Cao, Guangjie Huang, Wei Li. A quantitative study on planar mechanical anisotropy of a Mg-2Zn-1Ca alloy[J]. J. Mater. Sci. Technol., 2022, 109: 30-48.

Figures/Tables 23

Table 1. Recent reported tensile yield strength along rolling direction (RD) or extrusion direction (ED) and transverse direction (TD) in RE/Ca containing Mg alloys sheets with inclined off-basal texture.

Alloys	Loading direction	Yield strength (MPa)	Refs.
Mg-2Zn-1.2Ca (Rolling)	Tension // RD	111	[14]
Mg-2Zn-1.2Ca (Rolling)	Tension // TD	84	[14]
Mg-2Zn-1.2Ca (Cross-rolling)	Tension // RD	109	[14]
Mg-2Zn-1.2Ca (Cross-rolling)	Tension // TD	86	[14]
Mg-1.98Zn-1.93Gd (Rolling)	Tension // RD	112	[11]
Mg-1.98Zn-1.93Gd (Rolling)	Tension // TD	82	[11]
Mg-1.98Zn-1.93Gd (Cross-rolling)	Tension // RD	92	[11]
Mg-1.98Zn-1.93Gd (Cross-rolling)	Tension // TD	88	[11]
Mg-2Zn-2Gd (Rolling)	Tension // RD	114	[13]
Mg-2Zn-2Gd (Rolling)	Tension // TD	83	[13]
Mg-2Zn-2Gd (Cross-rolling)	Tension // RD	98	[13]
Mg-2Zn-2Gd (Cross-rolling)	Tension // TD	95	[13]
Mg-0.3Zn-0.1Ca (Rolling)	Tension // RD	92.5	[25]
Mg-0.3Zn-0.1Ca (Rolling)	Tension // TD	61	[25]
Mg-3Al-1Zn-3Li (Extrusion)	Tension // ED	177.6	[26]
Mg-3Al-1Zn-3Li (Extrusion)	Tension // TD	108.3	[26]
Mg-7.6Gd-2.46Y (Extrusion)	Tension // ED	157	[27]
Mg-7.6Gd-2.46Y (Extrusion)	Tension // TD	174	[27]
Mg-0.5Zn-0.2Ca-0.2Ce (Extrusion)	Tension // ED	83.9	[28]
Mg-0.5Zn-0.2Ca-0.2Ce (Extrusion)	Tension // TD	118.3	[28]
Mg-4.2Y-2.3Nd-0.6Zr (Rolling)	Tension // RD	419.9	[21]
Mg-4.2Y-2.3Nd-0.6Zr (Rolling)	Tension // TD	120	[21]
Mg-4.2Y-2.3Nd-0.6Zr (Cross-Rolling)	Tension // RD	397	[21]
Mg-4.2Y-2.3Nd-0.6Zr (Cross-Rolling)	Tension // TD	152.3	[21]
Mg-5.5Gd-4.4Y-1.1Zn-0.5Zr (Rolling)	Tension // RD	281	[29]
Mg-5.5Gd-4.4Y-1.1Zn-0.5Zr (Rolling)	Tension // TD	213	[29]
Mg-1.1Zn-0.76Y-0.56Zr (Rolling, LRR)	Tension // RD	152	[24]
Mg-1.1Zn-0.76Y-0.56Zr (Rolling, LRR)	Tension // TD	131	[24]
Mg-1.1Zn-0.76Y-0.56Zr (Rolling, FHRR)	Tension // RD	136	[24]
Mg-1.1Zn-0.76Y-0.56Zr (Rolling, FHRR)	Tension // TD	129	[24]
Mg-0.64Zn-0.41Sn-0.65Y (Extrusion)	Tension // ED	188.4	[30]
Mg-0.64Zn-0.41Sn-0.65Y (Extrusion)	Tension // TD	124.3	[30]
Mg-2Gd-3 Zn (Extrusion)	Tension // ED	172	[31]
Mg-2Gd-3 Zn (Extrusion)	Tension // TD	121	[31]
Mg-5.6Zn-0.2Ca-0.1Al-0.1Mn (Rolling + T5)	Tension // RD	264	[32]
Mg-5.6Zn-0.2Ca-0.1Al-0.1Mn (Rolling + T5)	Tension // TD	209	[32]

Fig. 1. EBSD inverse pole figures with respect to ND, corresponding (0002) pole figures and inverse pole figures along RD of the (a) UR-300 °C, (b) UR-350 °C, (c) UR-400 °C and (d) CR-350 °C samples.

Fig. 2. (a-1) Schematic illustration of grain orientation in macroscopic sample basis and texture components classification based on the distribution of (a-2) c-axis in the rolling plane and (a-3) a-axis to RD. (b) Grain number fraction of different texture components for the present four samples. Distribution of tilt angle of basal poles (ψ angle) in each BR and BT texture component for (c) UR-300 °C, (d) UR-350 °C, (e) UR-400 °C and (f) CR-350 °C samples.

Fig. 3. Tensile true stress vs. true strain curves of (a) UR-300 °C, (b) UR-350 °C and (c) UR-400 °C samples, and (d) corresponding work hardening rate, $\text{d}\sigma /\text{d}\varepsilon $. The abrupt slope changes in UR-400 °C sample are due to an intermediate pause of loading to remove the mechanical extensometer, which leads to an additional hardening during reloading.

Table 2. Mechanical properties of Mg-2Zn-1Ca alloys with varying rolling methods, annealing temperatures and test directions.

Sample	Tension direction	Yield strength (MPa)	Planar yield difference along RD and TD (MPa)	Ultimate strength (MPa)	Elongation to failure (%)
UR-300 °C	RD	182 ± 5	∼21	294 ± 15	13 ± 5
UR-300 °C	TD	161 ± 6	∼21	263 ± 3	12 ± 2
UR-350 °C	RD	134 ± 5	∼29	222 ± 6	7 ± 5
UR-350 °C	TD	108 ± 3	∼29	226 ± 5	9 ± 3
UR-400 °C	RD	107 ± 2	∼21	223 ± 5	10 ± 2
UR-400 °C	TD	86 ± 3	∼21	196 ± 8	9 ± 3
CR-350 °C	RD	124 ± 3	∼2	217 ± 5	8 ± 5
	TD	122 ± 4	∼2	243 ± 3	13 ± 3
	45°	121 ± 3		240 ± 2	12 ± 7

Fig. 4. (a) Tensile true stress vs. true strain curves of CR-350 °C sample showing the reduced in-plane yield anisotropy, and (b) corresponding strain hardening rate when loaded along RD, TD and 45° to RD.

Fig. 5. Microstructure of UR-350 °C sample after TD-tensioned to true strain of 1.0%. (a) EBSD Euler mapping, (b) misorientation profile and distribution of rotation axis with rotation angle ranging from 80° to 90° The inset table lists six extension twin variants characterized by rotation axis. (c) SF analysis of three representative twined grains. (d) Bright field TEM micrograph.

Fig. 6. XRD analysis and dislocation density calculation of the UR-350 °C sample after RD-tension and TD-tension at 1.0%. (a) The measured diffraction profile, (b) modified Williamson-Hall plot, quadratic relation of (ΔK-α)2/K2 as a function of χ, and frequency distribution of possible fractions of different dislocation slip systems in (c) RD-tension and (d) TD-tension. (e) Modified Williamson-Hall plot, linear relation of ΔK as a function of ${{K}^{2}}\overline{{{C}_{hk.l}}{{b}^{2}}}$. (f) Dislocation density of basal <a>, prismatic <a> and screw <a> dislocations for RD-tensioned and TD-tensioned samples (For interpretation of the references to color in this figure, the reader is referred to the web version of this article).

Fig. 7. (a) Variations of yield stress vs. grain size-1/2 during tension along RD and TD for UR-rolled samples. (b) Schematic diagram of slip/twining system characterized by normal of slip/twining plane (${\overset{\scriptscriptstyle\rightharpoonup}{n}}$) and slip/twin shear direction (${\overset{\scriptscriptstyle\rightharpoonup}{b}}$) in sample basis. (c) Schematic diagram of deformation mode transfer between two adjacent grains.

Table 3. The critical resolved shear stress of different deformation modes used for calculation of CRSS/SF ratio.

Mode	Basal (B)	Prismatic (Pr)	Pyramidal I (PyI)	Pyramidal II (PyII)	{10-12} twin (ET)	{10-11} twin (CT)
CRSS (MPa)	27	46	117	96	15	153

Fig. 8. Maps showing favored deformation modes of each grain for the sample annealed at (a, b) 300 °C, (c, d) 350 °C and (e, f) 400 °C when tension along (a, c, e) RD and (b, d, f) TD. The double-sided arrow refers to tension direction.

Table 4. Number fraction of grains favoring basal, prismatic, pyramidal I, II slips, extension and contraction twinning during tension along RD and TD.

Empty Cell	Tensile direction	Basal	Prismatic	{10-12} twin
300 °C	RD	56.5%	40.4%	3.1%
300 °C	TD	58.6%	25.8%	15.6%
350 °C	RD	59.2%	37.1%	3.7%
350 °C	TD	59.0%	22.7%	18.3%
400 °C	RD	57.9%	38.1%	4.0%
400 °C	TD	58.9%	22.6%	18.5%

Fig. 9. Distribution of CRSS/SF ratio for all grains, and for grains favoring basal slip (CRSS/SF)B, grains favoring prismatic slip (CRSS/SF)Pr, grains favoring extension twining (CRSS/SF)ET: (a) UR-300 °C, (b) UR-350 °C and (c) UR-400 °C. The superscript RD/TD refers to tension direction.

Fig. 10. Grain boundaries maps showing adjacent grain pairs with varying favored deformation modes in typical regions for the sample annealed at (a, b) 300 °C, (c, d) 350 °C and (e, f) 400 °C when tension along (a, c, e) RD and (b, d, f) TD. The double-sided arrow refers to tension direction.

Table 5. Number (fraction) of adjacent grain pairs with varying favored deformation modes during tension along RD and TD.

Empty Cell	B-B	B-Pr	B-ET	Pr-Pr	Pr-ET	ET-ET
300 °C RD	3657 (31.23%)	5482 (46.81%)	359 (3.07%)	1960 (16.74%)	244 (2.08%)	8 (0.07%)
300 °C TD	4126 (35.24%)	3551 (30.32%)	2089 (17.84%)	682 (5.82%)	939 (8.02%)	323 (2.76%)
350 °C RD	5205 (33.44%)	6905 (44.36%)	855 (5.49%)	2056 (13.21%)	514 (3.31%)	30 (0.19%)
350 °C TD	5541 (35.60%)	4195 (26.95%)	3249 (20.87%)	743 (4.77%)	1313 (8.44%)	524 (3.37%)
400 °C RD	905 (31.09%)	1225 (42.08)	210 (7.22%)	387 (13.29%)	172 (5.91%)	12 (0.41%)
400 °C TD	996 (34.22%)	751 (25.80%)	657 (22.57%)	137 (4.70%)	262 (9.00%)	108 (3.71%)

Fig. 11. Distribution of ∆Stress for all adjacent grain pairs, and B-B, B-Pr, B-ET, Pr-Pr, Pr-ET and ET-ET grain pairs in UR-rolled samples annealed at (a) 300 °C, (b) 350 °C and (c) 400 °C. The superscript RD/TD refers to tension direction, while the subscript refers to specific grain pairs.

Fig. 12. Distribution of ${m}'$ for all adjacent grain pairs, and B-B, B-Pr, B-ET, Pr-Pr, Pr-ET and ET-ET grain pairs in UR-rolled samples annealed at (a) 300 °C, (b) 350 °C and (c) 400 °C. The superscript RD/TD refers to tension direction, while the subscript refers to specific grain pairs.

Fig. 13. Distribution of (a) CRSS/SF ratio, (b) ∆Stress and (c) ${m}'$ during RD and TD tension of the CR-350 °C sample. The superscript RD/TD refers to tension direction.

Fig. 14. (a-1) Average CRSS/SF ratio when tension along RD and (a-2) average |Δ(CRSS/SF)| when tension along RD and TD as a function of distribution of basal poles in (0002) PF. Prismatic orientation was defined to be evenly distributed and the average CRSS/SF was calculated in this case. Grains with |Δ(CRSS/SF)| ≤ 15 MPa in (b) UR-300 °C, (c) UR-350 °C, (d) UR-400 °C and (e) CR-350 °C samples.

Fig. 15. Microstructure with different number fractions of BR/BT and PR/PT texture components.

Fig. 16. Variations of |Δ(CRSS/SF)|, ∆Stress and m′ as a function of number fraction of (a, b) BR component with the same weight of PR/PT components, and (c, d) PR texture component with of the same weight of BR/BT components.

Fig. 17. Microstructures with (a-d) varying max. ψ angles in BR/BT texture component but same number fraction of BR/BT and PR/PT component, and (e, f) with the same max. ψ angle in BR/BT texture component but different fractions of BR/BT components.

Fig. 18. Variations of |Δ(CRSS/SF)|, ΔStress and m′ as a function of maximum ψ angles in microstructures with 50%/50% of BR/BT and PR/PT texture components.

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