温度梯度对定向凝固<bold>Al-Zn-Mg-Cu</bold>合金微观组织和硬度的影响

王熠璇; 贾丽娜; 张虎; Wang Yixuan; Jia Lina; Zhang Hu

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Influence of Temperature Gradient on Microstructure and Microhardness of Directionally Solidified Al-Zn-Mg-Cu Alloy PDF

- ORCID：
Wang Yixuan
✉
- ORCID：
Jia Lina
✉
- ORCID：
Zhang Hu

Department of Materials Science and Engineering, Beihang University, Beijing 100191, China

Updated：2021-11-25

Abstract

The Al-Zn-Mg-Cu alloy with high Zn content was cast at different temperature gradients by directional solidification. The primary dendrite arm spacing λ₁, the secondary dendrite arm spacing λ₂, and the Vickers hardness of specimens were characterized. Based on the experiment results, the relationship among temperature gradient, dendritic arm spacing, and microhardness was determined by linear regression analysis and curve fitting analysis. The results are in agreement with the dendritic growth theoretical models, and the solidification parameters of Al-Zn-Mg-Cu alloy were obtained. In addition, the influence mechanism of temperature gradient on microhardness was analyzed. The results have a guidance function on the optimization of preparing methods of Al-Zn-Mg-Cu alloy with high zinc content.

Keywords

Al-Zn-Mg-Cu alloys; directional solidification; temperature gradient; dendrite arm spacing; theoretical model

Science Press

The age-hardening Al-Zn-Mg-Cu aluminum alloys (AA7XXX series) are widely used for aircraft structures and various critical military facilities due to their excellent combinations of high strength and lightweight^[

1-3]. The strength of AA7XXX series alloys can be obviously improved with increasing the Zn content^{[Reference 4-6}4-6]. However, when Zn content is more than 8wt%, the phenomenon of grain coarsening and serious macrosegregation occurs more likely. Moreover, due to the large temperature difference between liquid phase and solid phase during the solidification of Al-Zn-Mg-Cu aluminum alloys, the non-equilibrium solidified eutectic structures can be formed at the grain boundary. Therefore, hot cracking easily occurs in the casting, leading to poor casting performance and negative effect on the subsequent extrusion process^{[Reference 7

Baidu Scholar}7], which seriously restricts the application of Al-Zn-Mg-Cu aluminum alloys in industry.

To predict and control the solidification structure and to improve the properties of as-cast Al-Zn-Mg-Cu aluminum alloys, the formation mechanism of dendrite spacing and its relationship with the solidification conditions, especially the temperature gradient during cooling, should be investigated. However, since solidification is a complex process involving heat, mass, and momentum transfer, numerous experiments and theoretical studies on dendrite spacing were conducted using directionally solidified single-phase alloys, such as Al-Cu, Al-Mg, and Al-Fe alloys^[

8-17]. In addition, complete models of the relationship among solidification condition, microstructure, and mechanical properties were established. But similar models for solidified multi-phase alloys, such as Al-Zn-Mg-Cu alloys, were barely reported. In recent years, Xie^{[Reference 18

Baidu Scholar}18] and Yan^{[Reference 19

Baidu Scholar}19] et al studied the microstructure and microsegregation of solidified 7050Al alloy by directional solidification and modified the Scheil model, but the relationship between solidification condition and mechanical properties was still imprecise.

In this research, the relationship among primary dendrite arm spacing (λ₁), secondary dendrite arm spacing (λ₂), microhardness, and the temperature gradient (G, particularly the one caused by specimen diameter) of Al-8.9Zn-2.1Mg-1.8Cu-0.13Zr aluminum alloy was obtained and the related models were established. Moreover, the effect of temperature gradient on microhardness and related mech-anism were discussed. The results provide more information for the solidification process of Al-Zn-Mg-Cu aluminum alloys.

1 Experiment

The Al-Zn-Mg-Cu material used in this research was Al-8.9Zn-2.1Mg-1.8Cu-0.13Zr alloy ingot, and its chemical composition is presented in Table 1. In order to obtain different temperature gradients, Al₂O₃ tubes of high purity with inner diameter of 4, 7, 12, and 15 mm and length of 200 mm were used to load the specimens with different diameters for the directional solidification. The directional solidification of specimens was performed in the Bridgman-type directional solidification furnace using liquid Ga-In-Sn as the cooling medium, as shown in Fig.1. The specimens were superheated to 750 °C for 1 h before directional solidification, and then solidified at a drawing velocity of 100 μm/s. The solidified specimens were subsequently cut along longitudinal and transverse directions for further observation.

Table 1 Composition of Al-Zn-Mg-Cu alloy (wt%)

Zn	Mg	Cu	Zr	Fe	Si	Al
8.9	2.1	1.8	0.13	≤0.15	≤0.15	Bal.

Fig.1 Schematic diagram of Bridgman-type directional solidifica-tion furnace

The longitudinal and transverse sections of the specimens were inlaid in bakelite powder at 130 °C. The specimens were then ground with 240#~3000# SiC paper, polished with diamond pastes of 0.5 μm, and etched by Keller's reagent (1.5 mL HCl, 1 mL HF, 2.5 mL HNO₃, and 95 mL H₂O) for 25 s. Because the secondary dendrite arms of specimens could not be observed clearly after corrosion by Keller's reagent, Weck's reagent (100 mL H₂O, 4 g KMnO₄, 1 g NaOH) was used to corrode the longitudinal section to measure the secondary dendrite arm spacing. The specimens were observed by Carl Zeiss optical microscope (OM). The dendritic arm spacings (λ₁ and λ₂) were measured using the Image J software, and the magnification factor was taken into consideration.

The values of λ₁ on the transverse sections were measured using the triangle method^[

20]. The triangle was formed by joining three neighbor dendrite centers, and the length of the triangle sides was referred as λ_1T, as shown in Fig.2. On the longitudinal section, the primary dendrite arm spacing along longitudinal direction λ_1L was obtained by measuring the distance between the nearest two dendrites tips. During the measurements, the values of λ_1T and λ_1L were measured 50~80 times for each specimen. The λ₁ value used in analysis was the average value of λ_1T and λ_1L.

Fig.2 Schematic diagrams of dendritic arm spacing measurement: (a) longitudinal and transverse sections; (b) measurement of λ_1L and λ₂ on longitudinal section; (c) measurement of λ_1T by triangle method and area counting method on transverse section

The values of λ₂ were measured by averaging the distances between adjacent side branches on the longitudinal section of primary dendrites, as shown in Fig.2. All the secondary dendrite arm spacing data used in this research were the average value of the initial λ₂ value of 25~40 primary dendrites in each specimen.

Microhardness was measured by a micro-Vickers sclerometer under a load of 200 g and a dwell time of 10 s. The microhardness was measured at least twenty times on transverse and longitudinal sections of each specimen. Due to the composition segregation, inhomogeneities in the microstructure, and error in judging indentation boundary, some errors were unavoidable. In order to reduce the error, the maximum and minimum values were removed and then the average of remaining values was calculated and used.

According to the heat balance equation of directional solidification and assuming that the radial heat flow in the melt is neglected, the temperature gradient of liquid phase (G_L) at the liquid-solid interface can be obtained as follows^[

12,21]:

G_{L} = \frac{1}{K_{L}} (K_{S} G_{S} - ρ L_{f} v) = \frac{1}{K_{L}} [\frac{2 h α (T - T_{0})}{v r} - ρ L_{f} v]

(1)

where K_L and K_S are the thermal conductivity of the liquid and solid phases, respectively; G_S is the temperature gradient of solid phase; ρ is density of the alloy; L_f is latent heat of crystallization; v is drawing velocity; h is the composite heat transfer coefficient between the casting and the cooling medium; α is thermal diffusivity; T is the casting temperature; T₀ is the temperature of the cooling medium; r is radius of the specimen.

Some parameter values calculated by JMatPro software are shown in Table 2. The temperature at which the alloy begins to solidify is substituted by the casting temperature T. The room temperature is taken as the temperature of cooling medium T₀.

Table 2 Parameters used in experiment

Parameter	Value
Casting temperature, T/K	903
Cooling medium temperature, T₀/K	298
Thermal conductivity of liquid phase, K_L/W·m^-1·K^-1	86.73
Latent heat of crystallization, L_f/J·g^-1	4.1
Thermal diffusivity, α/m²·s^-1	2.95×10^-9
Drawing velocity, v/μm·s^-1	100
Alloy density, ρ/g·cm^-3	2.55

For composite heat transfer coefficient h, the heat transfer coefficient of conduction, convection, and radiation can be set as h_c, h_f, h_R, respectively. Then h can be obtained by Eq.(2) as follows:

h=h_c+h_f+h_R

(2)

Since the specimen was directly inserted into the cooling medium during the directional solidification, h_R in the fluid is 0 and the thermal resistance between the specimen and the Al₂O₃ tube is very small. Then Eq.(3) can be obtained, as follows:

h≈h_f

(3)

When Ga-In-Sn liquid metal was used as cooling medium^[

22,23], Eq.(3) can be transformed as Eq.(4), as follows:

h≈h_f=14 122 W/m²‧K

(4)

The results of calculated temperature gradient are shown in Table 3.

Table 3 Temperature gradients G of different specimens

Specimen diameter/mm	G/K·mm^-1
4	2.91
7	1.66
12	0.97
15	0.77

2 Results and Discussion

2.1 Effect of temperature gradient on dendritic arm spacings

Fig.3 and Fig.4 show the OM images of longitudinal and transverse sections of Al-Zn-Mg-Cu alloys after directional so-lidification at the steady-state conditions under different tem-perature gradients with a constant growth rate of V=100 μm/s.

Fig.3 OM images of transverse (a~d) and longitudinal (e~h) sections of directionally solidified Al-Zn-Mg-Cu alloys with different diameters etched in Keller's reagent: (a, e) 4 mm, (b, f) 7 mm, (c, g) 12 mm, and (d, h) 15 mm

Fig.4 OM images of longitudinal sections of directionally solidified Al-Zn-Mg-Cu alloy with different diameters etched in Weck's reagent: (a) 4 mm, (b) 7 mm, (c) 12 mm, and (d) 15 mm

For the calculation of primary dendrite arm spacing λ₁, Hunt^[

23] firstly established the function of solidification parameters (V, G, C₀). Assuming that the front dendrite can be regarded as a sphere, which is determined by the minimum undercooling, the Hunt model can be expressed by Eq.(5) as follows:

λ_{1} = 2.83 {[m (k - 1) D Γ]}^{0.25} C_{0}^{0.25} V^{- 0.25} G^{- 0.5}

(5)

where m is liquidus slope, k is partition coefficient, D is diffusion coefficient in liquid, Γ is the Gibbs-Thomson coefficient, and C₀ is the initial concentration of solute.

Trivedi^[

24] modified the Hunt model by introducing marginal stability criterion, and λ₁ was obtained as follows:

λ_{1} = 2.83 {[m (k - 1) D Γ L]}^{0.25} C_{0}^{0.25} V^{- 0.25} G^{- 0.5}

(6)

where L is a constant depending on harmonic perturbation.

The theoretical model developed by Kurz et al^[

25] assumed that the shape of the dendrite can be regarded as ellipsoid, and used the marginal stability criterion for the isolated dendrite. Then the model can be expressed by Eq.(7) as follows:

λ_{1} = 4.3 {[m (k - 1) D Γ / k^{2}]}^{0.25} C_{0}^{0.25} V^{- 0.25} G^{- 0.5}

(7)

When the parameters except temperature gradient are fixed, all the models based on single-valued selection can be simplified as Eq.(8), indicating that λ₁ is a function of temperature gradient G, which can be expressed as follows:

λ_{1} = k_{1} G^{- 0.5}

(8)

In semi-analytic computation, the relationship between λ₂ and the local solidification time τ_f is generally used to describe the secondary dendrite arm coarsening process, which ultimately leads to the equation between λ₂ and τ_f or the cooling rate c_R^[

8,26]:

λ_{2} = B {c_{R}}^{- l}

(9)

λ_{2} = M {τ_{f}}^{p}

(10)

where the coefficients M and B are related to the alloy composition; the local solidification time τ_f=(T_L-T_S)/VG (T_L is the liquidus temperature and T_S is the solidus temperature); the exponent p is equal to 1/3 in general, depending on the chosen coarsening model; the exponent l is obtained from experiment.

For the exponent p in Eq.(10), it does not always remain at 1/3, and can be affected by other factors such as the liquidus and the distribution coefficient. The exponent p is increased with increasing the slope of the liquidus, and decreased with increasing the distribution coefficient^[

27]. Then the model can be simplified as follows:

λ_{2} = k_{2} G^{- p}

(11)

The relationship between microstructure parameters (λ_1L, λ_1T, and λ₂) and temperature gradient was determined by a curve fitting analysis. The fitting results are shown in Table 4. As shown in Table 4 and Fig.5, with increasing the tempera-ture gradient, the dendrite arm spacings (λ₁, λ₂) are decreased. The relationships between microstructure parameters (λ₁, λ₂) and the diameter of specimen are λ_1T=193G^-0.51, λ_1L=204G^-0.41, λ₁=199G^-0.45, and λ₂=57G^-0.18. The experiment data are reasonably in agreement with the derived formulas.

Table 4 Relationships between microstructure parameters and temperature gradient

Dendrite arm spacing	Relationship	Square of correlation coefficient, R²
λ₁	λ_1T=193G^-0.51	0.99
	λ_1L=204G^-0.41	0.93
	λ₁=199G^-0.45	0.97
λ₂	λ₂=57G^-0.18	0.90

According to the reports about the relationships between the temperature gradient and microstructures (λ₁, λ₂) in previous works^[

8,10-16], it can be seen that even if the experiment is conducted under similar conditions (similar composition of specimen, drawing rate, or temperature gradient), the results vary and are distributed in dispersion. Besides, the results can be influenced not only by the drawing rate, temperature gradient, or the specimen composition, but also by the anisotropy of the solid-liquid interfacial energy, molecular attachment kinetics^{[Reference 28

Baidu Scholar}28], convections^{[Reference 29

Baidu Scholar}29,30], change of growth direction^{[Reference 31

Baidu Scholar}31], impurities, ripening process, and heating and cooling rate on the specimen. Compared with the results in this research, the relationship between λ₁ and temperature gradient is in agreement with that in previous works^{[Reference 8

Baidu Scholar}8,10-16]. Though there are some differences in relationship between λ₂ and temperature gradient, it still conforms to the exponential function.

2.2 Effect of dendritic arm spacings on microhardness

The Hall-Petch type equation^[

32,33] describes the relationship between yield strength σ or microhardness HV and grain size of a polycrystalline material, indicating that grain refinement is an effective way to improve the mechanical properties of polycrystalline materials in the conventional grain size range of micrometer. Hence, the relationship between microhardness and the grain size can be described as follows:

H V = H V_{0} + k_{3} d^{- 0.5}

(12)

where HV₀ is the initial microhardness of equilibrated phase; d is the average grain diameter; k₃ is a constant depending on materials. Xie et al^[

18] replaced the grain size with the primary dendrite arm spacing λ₁ and the secondary dendrite arm spacing λ₂. Then the equation can be expressed as follows:

H V = H V_{0} + k_{4} {λ_{1}}^{- 0.5}

(13)

H V = H V_{0} + k_{5} {λ_{2}}^{- 0.5}

(14)

where k₄ and k₅ are constants depending on materials. HV₀, k₄, and k₅ can be determined by experiments.

Based on the previous analysis, the relationship between microhardness and λ_1L, λ_1T, and λ₂ was determined by a linear regression analysis. As shown in Table 5 and Fig.6, with increasing the dendrite arm spacings (λ₁, λ₂), the micro-hardness is decreased. The fitting results are in agreement with the inferences deduced from Hall-Petch type equation, namely, Eq.(13) and Eq.(14). Therefore, increasing the temperature gradient results in finer dendritic microstructures, thereby increasing the microhardness HV. The relationships between microhardness HV, microhardness along transverse direction HV_T, microhardness along longitudinal direction HV_L and dendrite arm spacing λ_1L, λ_1T, λ₁, and λ₂ are HV_T= 69+733λ₁_T^-0.5, HV_L=53+1050λ₁_L^-0.5, HV=61+883λ₁^-0.5, and HV=-36+1201λ₂^-0.5.

Table 5 Relationships between microhardness and microstruc-ture parameters

Dendrite arm spacing	Relationship	Pearson correlation coefficient, r
λ₁	HV_T=69+733λ₁_T^-0.5	0.97
	HV_L=53+1050λ₁_L^-0.5	0.99
	HV=61+883λ₁^-0.5	0.97
λ₂	HV=-36+1201λ₂^-0.5	0.99

2.3 Effect of temperature gradient on microhardness

The Hall-Petch relation is derived from the dislocation stacking model^[

24,25]. Due to different orientations of atomic arrangement of adjacent grains and sub-grains on both sides of grain boundary, the grain boundary is in a distorted state. The dislocation density at grain boundary is large, which hinders the metal slip and dislocation movement, and therefore the grain boundary strengthening occurs. In addition, as for the as-cast Al-Zn-Mg-Cu aluminum alloy, the hard precipitation phase at the grain boundary also contributes to improving the microhardness of the alloy. The crystal structure of the second phase particles is different from that of the matrix. When the dislocation breaks through the particles, it will inevitably cause the mismatch of atomic arrangement on the slip surface, thus increasing the slip resistance.

According to the relationships in Table 4 and Table 5, the relationships between temperature gradient and microhardness can be directly obtained, as listed in Table 6. After directional solidification, the transverse grain boundary which is perpendicular to the temperature gradient direction of the alloy is mainly eliminated. In microhardness measurement, the probability of indenter pressing on dendrites with the same orientation in longitudinal section is higher than that in cross section. The effect of grain boundary strengthening on the longitudinal section is weaker than that on the cross section. However, the effect of primary dendrite arm spacing in the longitudinal section on the temperature gradient is slightly stronger than that in the cross section, as shown in Fig.7, which proves that the second phase strengthening makes a major contribution to the improvement of microhardness of the alloy. The Hall-Petch relationship can still fit well because the second phase of as-cast Al-Zn-Mg-Cu alloy is concentrated at grain boundary. Three relationships between the primary dendrite arm spacing and microhardness are close to each other, while the relationship between the secondary dendrite spacing and microhardness is quite different. This may be because the second phase between the secondary dendrites is mostly spherical with dispersive distribution, which has little effect on the microhardness.

Table 6 Relationships between temperature gradient and microhardness

Dendrite arm spacing	Relationship
λ₁	HV_T=69+52.76G^0.255
	HV_L=53+73.51G^0.205
	HV=61+59.05G^0.225
λ₂	HV=-36+159.08G^0.09

The diffusion time of elements in dendrites is decreased with increasing the temperature gradient, which causes serious segregation and the fact that more continuous non-equilibrium solidification phases with network structure are formed at the grain boundary. The relation between HV and G can be obtained by synthesizing the above relationships: HV=61+59.05G^0.225. When the temperature gradient increases, the grain size becomes smaller, but the non-equilibrium phase between grain boundaries is increased. The presence of continuous non-equilibrium solidification phase between grain boundaries enhances the microhardness, but it also becomes the origin of defects. If the solidification phase is too much, it will not be easily eliminated by subsequent homogenization treatment, thus affecting the quality of extruded products. According to the relationship in Table 6, controlling the appropriate temperature gradient and avoiding excessive non-equilibrium solidification phase on the premise of forming finer grains are beneficial to the improvement of properties of as-cast Al-Zn-Mg-Cu aluminum alloy.

3 Conclusions

1) The values of primary dendrite arm spacing λ₁ and the secondary dendrite arm spacing λ₂ are decreased with increasing the temperature gradient G. The relationships between microstructure parameters (primary dendrite arm spacing along transverse direction λ_1T, primary dendrite arm spacing along longitudinal direction λ_1L, λ₁, λ₂) and the diameter of specimen are λ_1T=193G^-0.51, λ_1L=204G^-0.41, λ₁=199G^-0.45, and λ₂=57G^-0.18.

2) Increasing the temperature gradient results in finer dendritic microstructures, thereby increasing the micro-hardness HV. The relationships between microhardness HV (microhardness along transverse direction HV_T, microhardness along longitudinal direction HV_L, HV) and λ_1L, λ_1T, λ₁, and λ₂ are HV_T=69+733λ₁_T^-0.5, HV_L=53+1050λ₁_L^-0.5, HV=61+883λ₁^-0.5, and HV=-36+1201λ₂^-0.5. The fitting results are in good agreement with the Hall-Petch type equation.

3) The relation between HV and G can be obtained by synthesizing the above relationships: HV=61+59.05G^0.225. When the temperature gradient increases, the grain size becomes smaller, but the non-equilibrium phase between grain boundaries is increased, which easily becomes the crack origin. According to the relationship, selecting a proper temperature gradient can optimize the properties of as-cast Al-Zn-Mg-Cu aluminum alloy.

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Influence of Temperature Gradient on Microstructure and Microhardness of Directionally Solidified Al-Zn-Mg-Cu Alloy PDF

Abstract

Keywords

1 Experiment

2 Results and Discussion

2.1 Effect of temperature gradient on dendritic arm spacings

2.2 Effect of dendritic arm spacings on microhardness

2.3 Effect of temperature gradient on microhardness

3 Conclusions

References

首 页

期刊简介

编委会

投稿指南

过刊浏览

联系我们

English

Influence of Temperature Gradient on Microstructure and Microhardness of Directionally Solidified Al-Zn-Mg-Cu Alloy PDF

Abstract

Keywords

1 Experiment

2 Results and Discussion

2.1 Effect of temperature gradient on dendritic arm spacings

2.2 Effect of dendritic arm spacings on microhardness

2.3 Effect of temperature gradient on microhardness

3 Conclusions

References

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