A. Compressive deformation behavior

Figure 1 presents the true compressive stress–strain curves of the as-homogenized Mg–Zn–Ca–La alloy. The flow curves exhibited typical characteristics of dynamic recrystallization. The stress was increased with the increase of strain at the initial stage of deformation due to work hardening, then a peak stress was reached. With the further increase of strain, flow stress decreased because the strengthening effect caused by work hardening was weaker compared with the softening effect from dynamical recrystallization. Finally, a steady state was achieved when work hardening and dynamic softening reached a balance.

FIG. 1.

True compressive stress–strain curves of the samples compressed at the strain rate of (a) 0.001 s⁻¹, (b) 0.01 s⁻¹, (c) 0.1 s⁻¹, and (d) 1 s⁻¹.

The samples compressed with high temperatures and low strain rates exhibited a low flow stress, which was because high temperature supplied high dislocation mobility^{Reference Ou, Nie and Zheng30} and low strain rate provided enough time for the accumulation of activation energy.^{Reference Liao, Wu, Zhou and Yang31} It should be noticed that the samples deformed with the strain rate of 0.001 s⁻¹ exhibited an obvious serrated flow characteristic, which might be related to the dynamic strain aging effect.^{Reference Lu, Yin, Huang, Quan, Zeng, Zhou and Wang32} The solute atoms had enough time to diffuse to dislocation when deformed at low strain rate, which would exert a drag force for dislocation movement. Subsequent applied stress promoted the dislocation to overcome the drag force and move freely. Then the process repeated during deformation, leading to the serrations in the stress–strain curves. The sample deformed at 250 °C with the strain rate of 1 s⁻¹ showed a very rapid decline after the strain of 0.6, which was related to the formation of the crack during deformation.

During hot compression deformation, the relationship of deformation temperature and strain rate on flow stress can be described by a hyperbolic sine-type constitutive equation^{Reference Lv, Peng, Wang, An, Zhong, Tang and Pan33}:

(1)$$\dot{\varepsilon } = A{\left[ {\sinh \left( {\alpha \sigma } \right)} \right]^n}\exp \left( {{{ - Q} / {RT}}} \right)\quad ,$$

where $\dot{\varepsilon }$ is the strain rate (s⁻¹), A is the structure factor, α is the material constant, σ is the peak stress (MPa), n is the stress exponent, Q is the deformation activation energy (kJ/mol), R is the gas constant (8.314 J/mol), and T is the absolute temperature during hot deformation.

To calculate the value of α in Eq. (1), the other two conventional equations were used to describe the relationship between deformation parameters and flow stress. Normally, the power law was used at the low stress level [Eq. (2)], while exponential law was used at the high stress level [Eq. (3)].

(2)$$\dot{\varepsilon } = {A_1}{\sigma ^{{n_1}}}\exp \left( {{{ - Q} / {RT}}} \right)\quad ,$$

(3)$$\dot{\varepsilon } = {A_2}\exp \left( {\beta \sigma } \right)\exp \left( {{{ - Q} / {RT}}} \right)\quad ,$$

where n ₁ is the stress exponent and A ₁, A ₂, and β are the material constants. By taking the natural logarithm on both sides of Eqs. (2) and (3), simplified equations can be obtained as follows:

(4)$$\ln \dot{\varepsilon } = {n_1}\ln \sigma + \ln {A_1} - {Q / {\left( {RT} \right)\quad ,}}$$

(5)$$\ln \dot{\varepsilon } = \beta \sigma + \ln {A_2} - {Q / {\left( {RT} \right)}}\quad .$$

According to Eqs. (4) and (5), ${n_1} = {{\partial \ln \dot{\varepsilon }} / {\partial \ln \sigma }}$, $\beta = {{\partial \ln \dot{\varepsilon }} / {\partial \sigma }}$, and α = β/n ₁. The relationships of $\ln \dot{\varepsilon } - \ln \sigma$ and $\ln \dot{\varepsilon } - \sigma$ at different temperatures are plotted in Fig. 2. Therefore, the average values of n ₁ and β were determined to be 8.5538 and 0.0641, respectively. Then the average α value of the alloy is calculated as α = β/n ₁ = 0.0075 MPa⁻¹.

FIG. 2.

Relationship between strain rate and flow stress (a) $\ln \dot{\varepsilon } - \ln \sigma$ and (b) $\ln \dot{\varepsilon } - \sigma$.

The Zener–Hollomon (Z) parameter can integrate the effects of deformation temperature and strain rate on the flow stress during hot deformation, which can be expressed as follows^{Reference Nie, Kang, Deng, Wang, Guo and Wang34}:

(6)$$Z = \dot{\varepsilon }\exp \left( {{Q \over {RT}}} \right) = A{\left[ {\sinh \left( {\alpha \sigma } \right)} \right]^n}\quad .$$

By taking the natural logarithm on both sides of Eq. (6), the following equation could be obtained:

(7)$$n = {\left\{ {{{\partial \ln \dot{\varepsilon }} \over {\partial \ln \left[ {\sinh \left( {\alpha \sigma } \right)} \right]}}} \right\}_T}\quad ,$$

(8)$$Q = {\rm{Rn}}{\left\{ {{{\partial \ln \left[ {\sinh \left( {\alpha \sigma } \right)} \right]} \over {\partial \left( {{1 / T}} \right)}}} \right\}_{\dot{\varepsilon }}}\quad .$$

The relationships of $\ln \dot{\varepsilon } - \ln \left[ {\sinh \left( {\alpha \sigma } \right)} \right]$ under different temperatures and ln[sinh(ασ)] − 1/T under different strain rates are plotted in Fig. 3. Then the average activation energy Q was estimated to be 188.9 kJ/mol, which was higher than that for lattice diffusion of magnesium (135 kJ/mol^{Reference Mirzadeh, Roostaei, Parsa and Mahmudi35}). The high Q value for the Mg–Zn–Ca–La alloy might be attributed to the existence of precipitates and fine microstructure. Precipitates could effectively hinder dislocation motion during deformation and exerted resistant force for lattice self-diffusion, as pointed out in the SiC reinforced Al matrix.^{Reference Mirzadeh36} The fine dynamically recrystallized (DRXed) grains provided more grain boundaries acting as barriers to the movement of dislocations and lattice self-diffusion. Additionally, the addition of alloying elements had a significant effect on the activation energy, which was detected in steels and Al alloys.^{Reference Lino, Guadanini, Silva, Neto and Barbosa37,Reference Odoh, Mahmoodkhani and Wells38} 0.2 wt% Cr addition in the Al–Mg–Si alloy hinders the movement of dislocation, which led to the increase of flow stress and activation energy due to the effect of solution strengthening.^{Reference Odoh, Mahmoodkhani and Wells38} Therefore, Ca or La in the Mg–Zn–Ca–La alloys with slow diffusion velocity compared with the matrix would serve as barriers to dislocation movement. Meanwhile, Ca or La preferred to segregate to dislocation or grain boundaries due to the large atomic radius,^{Reference Zeng, Zhu, Xu, Bian, Davies, Birbilis and Nie39} which could exert extra force for the mobility of dislocation or grain boundaries. It might be another reason for the high activation energy in the Mg–Zn–Ca–La alloy.

FIG. 3.

Variation of (a) $\ln \dot{\varepsilon } - \ln \left[ {\sinh \left( {\alpha \sigma } \right)} \right]$ at different temperatures and (b) ln[sinh(ασ)] − (1/T) at different strain rates.

Then the Zener–Hollomon parameters were obtained, shown in Table I. According to Eq. (6), the values of the related parameters A and n of the constitutive equation can be determined by linear fitting curves of ln Z and ln[sinh(ασ)] (Fig. 4). By substituting activation energy Q into Eq. (6), the constitutive equation for the Mg–Zn–Ca–La alloy can be expressed as follows:

(9)$$\dot{\varepsilon } = 2.1807 \times {10^{15}}{\left[ {\sinh \left( {0.0075\sigma } \right)} \right]^{5.925}}\exp \left( { - {{188.9 \times {{10}^3}} \over {8.314T}}} \right)\quad .$$

TABLE I.

Zener–Hollomon parameters for the Mg–Zn–Ca–La alloy compressed at different conditions.

FIG. 4.

Relationship between Zener–Hollomon parameter and peak stress in hot compression tests.

As can be seen in Fig. 4, these data points were close to the center of the fit line obtained by linear fit. The corresponding 95% confidence band for this fit was plotted by two lines adjacent to the fitting line. Meanwhile, the data points fell within the prediction band (the outer lines) corresponding to the 95% confidence band.

B. Processing map

The processing map was usually used to investigate the workability of metal materials and to analyze the evolution of the microstructure using power dissipation efficiency during deformation. The efficiency of power dissipation (η) can be expressed as follows^{Reference Xu, Pan, Nakata, Qiao, Chi, Zheng and Kamado3}:

(10)$$\eta = {J \over {{J_{\max }}}} = {{2m} \over {m + 1}}\quad ,$$

where $m = {\left( {{{\partial \ln \sigma } \over {\partial \ln \dot{\varepsilon }}}} \right)_{\varepsilon {\rm{,}}T}}$ is the strain rate sensitivity coefficient. The value of η represented the energy of power dissipation used for dynamic recrystallization but could not characterize the ability of workability of materials because the energy of power dissipation located in the instability region of the material might have a large value. The instability region could be obtained by the instability criterion,^{Reference Sun, Liu, Wang, Shu-Bo, Xian and Wen-Bo40} which was described as follows:

(11)$${\xi _{\left( {\dot{\varepsilon }} \right)}} = {{\partial \ln \left[ {{m / {\left( {m + 1} \right)}}} \right]} \over {\partial \ln \dot{\varepsilon }}} + m \lt 0\quad ,$$

where ${\xi _{\left( {\dot{\varepsilon }} \right)}}$ is the instability parameter related to strain rate and deformation temperature. An instability map defined instability domains with ${\xi _{\left( {\dot{\varepsilon }} \right)}} \lt 0$. In general, stability domains corresponded to dynamic recrystallization, which reflected better workability. Therefore, the stability domains were selected to be deformation window. However, the instability domains corresponded to adiabatic shear band and crack propagation.^{Reference Xu, Pan, Nakata, Qiao, Chi, Zheng and Kamado3} Therefore, the processing map could be constructed through the overprinting of the dissipation map and an instability map.

Figure 5 shows the processing map obtained at a compressive true strain of 0.8. The counter number signified the efficiency of power dissipation and the shaded area corresponded to the flow instability. It could be seen that the instability region was mainly distributed at temperature ranging from 250 to 300 °C and the strain rate ranging from 0.001 to 1 s⁻¹. The power dissipation efficiency was high and no flow instability was detected when the deformation was at a temperature of 300–350 °C and a strain rate of 0.001–0.01 s⁻¹. This was related to the stable microstructure of the alloy after hot deformation. The increase fraction of DRX would decrease dislocation density and reduce the stress concentration because high temperature enhanced the diffusion rate and thermal agitation of atoms and low strain rate provided enough time for dislocations to move.^{Reference Liu, Liu, Zhao, Huang and Chen41}

FIG. 5.

Processing map of the Mg–Zn–Ca–La alloy compressed to a strain of 0.8 (the efficiency of power dissipation in percent is indicated by the contour values).

The optimum processing parameter domains for magnesium alloys were generally located at a high power dissipation efficiency between 35 and 45%, in which stable flow gave rise to a stable microstructure and improved workability via dynamic recrystallization.^{Reference Wang, Xu, Wang, Zheng, Cui and Yang42} However, the peak efficiency values obtained for the Mg–Zn–Ca–La alloy were approximately 30%, which indicated that incomplete dynamic recrystallization occurred during hot compression. Considering both the power dissipation efficiency and stability, the optimum hot working window was suggested to be the temperature of 350 °C and the strain rates between 0.001 and 0.01 s⁻¹.

C. Microstructure analysis

Grain refinement could affect the mechanical properties of the magnesium alloys significantly, which was commonly achieved by dynamic recrystallization during hot deformation processing. Therefore, it is of significance to investigate the effects of deformation conditions on dynamic recrystallization. The kinetics of dynamic recrystallization can be expressed by the Avrami equation^{Reference Yu, Zhang, Wang, Yin, Cui and Qi43}:

(12)$${X_{{\rm{DRX}}}} = 1 - \exp \left[ { - k{{\left( {{{\varepsilon - {\varepsilon _{\rm{c}}}} \over {{\varepsilon ^ * }}}} \right)}^{{n_{\rm{m}}}}}} \right]\quad ,$$

where X _DRX is the DRX volume fraction; ε_c is the critical strain of the initiation of DRX, which is the strain of the minimum point of −(∂²σ/∂σ∂ε); ε* is the strain for the maximum softening rate, which corresponds the strain of the lowest work hardening rate; k and n _m are the material constants.

In addition, the relationship between X _DRX and flow stress can be expressed as follows:

(13)$${X_{{\rm{DRX}}}} = {{{\sigma _{\rm{p}}} - \sigma } \over {{\sigma _{\rm{p}}} - {\sigma _{{\rm{ss}}}}}}\quad ,$$

where σ_p is the peak stress and σ_ss is the steady-state stress. According to Eqs. (12) and (13), the mean values of k and n under different conditions are obtained to be 0.7267 and 2.1365, respectively. Thus, the kinetic model of DRX evolution of the Mg–Zn–Ca–La alloy can be expressed as follows:

(14)$${X_{{\rm{DRX}}}} = 1 - \exp \left[ { - 0.7267{{\left( {{{\varepsilon - {\varepsilon _{\rm{c}}}} \over {{\varepsilon ^ * }}}} \right)}^{2.1365}}} \right]\quad .$$

Then the variation of volume fraction of the DRXed region with deformation parameters can be theoretically predicted, as shown in Fig. 6. It is observed that the volume fraction of DRX increased with increasing strain. Moreover, the DRX volume fraction also strongly depended on the deformation temperatures and strain rates.

FIG. 6.

Predicted evolution of DRX volume fraction for samples deformed under different strain rates: (a) 0.001 s⁻¹, (b) 0.01 s⁻¹, (c) 0.1 s⁻¹, and (d) 1 s⁻¹.

Figure 7 shows the optical microstructures of the as-compressed Mg–Zn–Ca–La alloys. When the samples were deformed at low temperature and high strain rate, large amounts of deformed microstructure were detected, as shown in Figs. 7(a) and 7(b). With the increase of deformation temperature from 250 to 350 °C and decrease of strain rate from 1 to 0.001 s⁻¹, the fraction of dynamic recrystallization was increased. When the sample was deformed at the temperature of 350 °C and the strain rate of 0.001 s⁻¹, dynamic recrystallization almost completed [Fig. 7(l)]. Figure 8(a) shows the relationship between Zener–Hollomon parameter and DRX volume fraction (V _DRX), the black and red data points represented the experimental data and the predicted data according to the DRX kinetic model of the Mg–Zn–Ca–La alloy, respectively. It could be seen that the experimental data were basically consistent with the predicted data. Thus, the DRX kinetic model for the Mg–Zn–Ca–La alloy could be used to predict the DRX volume fraction of the Mg–Zn–Ca–La alloy.

FIG. 7.

OM images of the Mg–Zn–Ca–La alloy compressed with different deformation parameters: (a) 250 °C, 1 s⁻¹; (b) 250 °C, 0.1 s⁻¹; (c) 250 °C, 0.01 s⁻¹; (d) 250 °C, 0.001 s⁻¹; (e) 300 °C, 1 s⁻¹; (f) 300 °C, 0.1 s⁻¹; (g) 300 °C, 0.01 s⁻¹; (h) 300 °C, 0.001 s⁻¹; (i) 350 °C, 1 s⁻¹; (j) 300 °C, 0.1 s⁻¹; (k) 300 °C, 0.01 s⁻¹; (l) 300 °C, 0.001 s⁻¹. (CD represents compression direction).

FIG. 8.

Effect of Zener–Hollomon parameter on (a) recrystallized volume fraction and (b) DRX grain size of the Mg–Zn–Ca–La alloy.

The above microstructural observations indicated that the deformation temperature and the strain rate affect the evolution of dynamic recrystallization. Additionally, the DRXed grain size varied when deformed with different Zener–Hollomon parameters. Figure 8(b) shows the relationship between Zener–Hollomon parameter and DRX grain size. It could be seen that the DRXed grain size was decreased with the increase of Zener–Hollomon parameters. A linear exponential equation was proposed to describe the relationship between the DRX grain size and Z parameters, which could be expressed as follows^{Reference Fatemi-Varzaneh, Zarei-Hanzaki and Beladi44}:

(15)$${D_{{\rm{DRX}}}} = A{Z^{ - n}}\quad ,$$

where A is a material constant and n is the power law exponent. Prediction of grain size could be evaluated by power law exponent n. High n value indicated the fine DRX grain size against Z. Beer^{Reference Barnett, Keshavarz, Beer and Atwell45} reported a range of 0.09–0.13 for n in the AZ31 alloy after various deformation modes. The n value of the Mg–Zn–Ca–La alloy in the present study was almost double (0.27) compared with the maximum value of n in AZ31, which indicated that the DRXed grains had a low growth rate for the Mg–Zn–Ca–La alloy. It should be related to the existence of the second phase.

The distribution of the precipitates played an obvious role in the microstructure after dynamic recrystallization. The SEM images of the Mg–Zn–Ca–La alloy specimens compressed with the Zener–Hollomon parameter of 6.97 × 10¹⁴ to true strain of 1 are shown in Fig. 9. It could be seen that the coarse second phases were broken into small particles, which was covered by DRXed grains. This indicated that the second phase stimulated nucleation of dynamic recrystallization. Moreover, part second phases were fragmented to be small particles, which could act as obstacles for grain boundary mobility. Therefore, the existence of second phases in the Mg–Zn–Ca–La alloy was beneficial for grain refinement, which resulted in a small grain growth tendency by contrast to the AZ31 alloy.^{Reference Fatemi-Varzaneh, Zarei-Hanzaki and Beladi44}

FIG. 9.

SEM images of the samples compressed with Zener–Hollomon parameters of 6.97 × 10¹⁴ to the true strain of 1: (a) low magnification and (b) high magnification.

According to the above discussion, it could be found that deformation parameters had a significant effect on the microstructure of the Mg–Zn–Ca–La alloy. The optimum hot working window was established at the temperature of 350 °C and the strain rate between 0.001 and 0.01 s⁻¹. However, the DRXed grains size was large under this deformation condition, which might result in the deterioration of strength. The samples deformed with other deformation parameters such as low temperature exhibited fine DRXed grains, but the workability would be reduced. Therefore, the optimization of deformation parameters was of great significance to the improvement of the microstructure and mechanical properties of the Mg–Zn–Ca–La alloy.