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Acta Metall Sin  2017, Vol. 53 Issue (9): 1110-1124    DOI: 10.11900/0412.1961.2016.00547
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Modeling of Strain Hardening Behavior and Mechanical Properties of Al-7Si-Mg Cast Aluminum AlloysDuring Tensile Process
Rui CHEN1, Qingyan XU1(), Huiting GUO2, Zhiyuan XIA2, Qinfang WU2, Baicheng LIU1
1 Key Laboratory for Advanced Materials Processing Technology (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
2 Mingzhi Technology Co. Ltd., Suzhou 215006, China
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Al-7Si-Mg alloy castings have extensive applications in automotive industries, and the tensile properties of these alloys including yield strength, ultimate tensile strength and elongation are commonly used to judge their mechanical properties. In this work, the modified precipitation kinetics model, yield strength model and strain hardening model have been proposed to predict the tensile properties of Al-7Si-Mg alloys. The precipitation kinetics model can be used to predict the precipitate microstructure parameters including the precipitate density, size, size distribution, volume fraction, and composition and so on in these alloys, combining which with the strength model, their yield strengths can be obtained. The strain hardening model can be applied to simulate the stress-strain curves during tensile process, and the ultimate tensile strengths and elongations can be obtained by combining this model with the experimental data fitted with the expression (σUTSY)=Y+n+f (Tss). First, the evolution of precipitate microstructure parameters and yield strengths as a function of ageing time were simulated, and then their comparisons with the experimental results were performed. The possible reasons resulting in the deviations between simulated and experimental yield strengths were analyzed. The stress-strain curves during tensile process of Al-7Si-0.36Mg alloy were simulated using strain hardening model, and the influences of ageing treatment and as-cast microstructure refining scale on the parameters of dislocation storage rate, dynamic recovery rate and the stress-strain curves were analyzed. Then, the ultimate tensile strengths and elongations of Al-7Si-0.4Mg alloy aged at different temperatures were predicted which are in better agreement with the experimental results, and the influence of secondary dendrite arm spacing on tensile properties was also analyzed. Finally, the limitation of present model and the factors influencing the prediction precision of tensile properties were outlined.

Key words:  Al-7Si-Mg alloy      tensile property      strain hardening      precipitate      ageing treatment      modeling     
Received:  05 December 2016     
ZTFLH:  TG146.2  
Fund: Supported by National Basic Research Program of China (No.2011CB706801) and National Natural Science Foundation of China (Nos.51374137 and 51171089)

Cite this article: 

Rui CHEN, Qingyan XU, Huiting GUO, Zhiyuan XIA, Qinfang WU, Baicheng LIU. Modeling of Strain Hardening Behavior and Mechanical Properties of Al-7Si-Mg Cast Aluminum AlloysDuring Tensile Process. Acta Metall Sin, 2017, 53(9): 1110-1124.

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Fig.1  Schematics of the engineering stress-engineering strain curve (σ-ε) during tensile process
(a) and the change of strain hardening rate (θ) with stress (b) of Al-7Si-Mg aluminum alloy (σY and σUTS—yield strength and ultimate tensile strength, respectively; e—elongation; εY—engineering strain corresponding to the yield strength; θ0—initial strain hardening rate)
Fig.2  Curve of Young's modulus of Al-7Si-Mg alloy vs yield strength (E—Young's modulus, R2—standard deviation)
Fig.3  Dimensions of flat shape (a) and cylindrical shape (b) tensile samples (unit: mm)
Sample shape ST temperature ST time Ageing Ageing
h temperature / ℃ time / h
Cylindrical 550 2 200 0~36
Cylindrical 550 2 180 0~72
Cylindrical 550 2 160 0~120
Cylindrical 535 2 180 0~72
Plat 550 2 180 0~72
Table 1  Parameters of solution treatment and artificial ageing for the tensile samples
Fig.4  TEM (a~c) and HRTEM (d~f) images of Al-7Si-0.4Mg alloy artificially aged at 180 ℃ for 20 min (a, d), 4 h (b, e) and 120 h (c, f) (Insets in Figs.4d and e show the cross section of needle-shaped precipitates)
Fig.5  Tensile properties of Al-7Si-0.4Mg alloy as a function of ageing time at 160 and 180 ℃
Fig.6  Curves of (σUTS-σY) vs σY for Al-7Si-0.36Mg cylindrical samples at different heat treatments (a) and with different secondary dendrite arm spacings (d) aged at 180 ℃ (b)
Ageing temperature / ℃ Ageing time / h Mean radius / nm Mean aspect ratio
160 8 1.46±0.167 7.4±2.12
160 24 1.76±0.188 7.8±2.31
160 120 1.91±0.290 8.0±3.08
180 0.33 1.07±0.085 -
180 1 1.40±0.240 7.1±2.20
180 4 1.75±0.271 7.5±2.88
180 24 2.01±0.320 7.8±2.36
180 120 2.28±0.274 6.8±1.98
200 2 1.89±0.274 8.2±3.16
Table 2  Measured mean radii and aspect ratios of β" precipitates of Al-7Si-0.4Mg alloy after different ageing treatments
Parameter Unit Value
Atomic fraction of Mg in β" precipitate xMgβ % 5/11[36]
Atomic fraction of Si in β" precipitate xSiβ % 6/11[36]
Aspect ratio of precipitate ? - 7
Interface energy γ Jm-2 0.35[38]
Shear modulus of matrix G Nm-2 2.7×1010[7]
Magnitude of the burgers vector b m 2.84×10-10[7]
Taylor factor M - 3.1[7]
Precipitate Young's modulus Ep GPa 59[16]
Ratio of volume fraction of matrix and β" precipitate ω - 1
Factor for adjusting the effective diffusion distance ξ - 1
Constant depends on the shape and nature of dislocation δ - 0.25[39]
Precipitate shearing/bypassing transition radius rpc nm 2.4
Precipitate coherency/incoherency transition radius rcl nm 4.0
Maximum number of loops around a precipitate np* - 9[16]
Parameter associated with the rate of dislocation storage k1 m-1 Varying
Parameter associated with the rate of dynamic recovery k20 - Varying
Parameter associated with dislocation loop k2p - 600
Table 3  Parameters used for the prediction of tensile properties and stress-strain curves in Al-7Si-Mg alloys
Fig.7  Densities (a) and mean radii (b) of β" precipitates as a function of ageing time for Al-7Si-0.4Mg alloy aged at 160, 180 and 200 ℃
Fig.8  Comparisons of predicted and measured yield strengths for Al-7Si-0.4Mg alloy aged at 160, 180 and 200 ℃
Ageing time / h xMgα / % k1 / m-1 k20 θ0 / MPa%-1 K
0 0.400 1.65 13 14.6 0.175
0.5 0.363 2.10 14 20.2 0.185
1 0.268 2.65 20 25.8 0.273
2 0.083 2.65 26 26.1 0.359
4 0.008 2.65 28 25.5 0.377
8 0.007 2.65 39 23.8 0.496
12 0.006 2.65 42 25.1 0.575
24 0.005 2.65 42 23.7 0.564
Table 4  Evolutions of xMgα, k1, k20, θ0 and K with ageing time at 180 ℃
Fig.9  Experimental and simulated stress-strain curves of Al-7Si-0.36Mg alloy (d=24.9 μm) after aged at 180 ℃ for different times
Fig.10  Influences of kinematic strain hardening (Δσkin_e) caused by grain boundary and eutectic silicon particles on the stress-strain curves (a) and strain hardening rate (b) in Al-7Si-0.36Mg alloy
d / μm k1 / m-1 k20 D / μm
53.2 2.38 26 5.8
43.0 2.46 26 5.5
36.7 2.55 26 5.0
24.9 2.65 26 5.0
Table 5  Parameters k1, k20 and D applied for calculating the stress-train curves of samples with different d values
Fig.11  Influences of d on the stress-strain curves (a) and strain hardening rate (b) in Al-7Si-0.36Mg alloy
Fig.12  Predicted engineering stress-engineering strain curves (a, b) of tensile samples of Al-7Si-0.4Mg alloy aged at 160 ℃ (a) and 180 ℃ (b) for 0~36 h, and the comparisons of predicted and experimental ultimate tensile strengths (c) and elongations (d)
Fig.13  Predicted yield strength, ultimate tensile strength (a) and elongation (b) of the tensile samples in Al-7Si-0.4Mg alloy with different secondary dendrite arm spacings after aged at 180 ℃ for 0~24 h (Solid lines and dash lines in Fig.13a represent the yield strength and ultimate tensile strength, respectively)
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