Flow Behavior and Activation Energy Evolution of 7075-T6 Al Alloy During Hot Deformation

Abstract

In this paper, the hot deformation behavior of 7075-T6 aluminum alloy was studied by hot compression experiments. The results show that the flow stress exhibits a continuous decrease at low temperatures. At high temperatures, the flow stress exhibits a steady state. The softening at low temperatures is dominated by dynamic recovery (DRV), accompanied by coarsening of precipitates, resulting in a continuous decrease in flow stress. As the temperature increases, dynamic recrystallization (DRX) gradually strengthens, and the DRX mechanism gradually transforms from continuous dynamic recrystallization to geometric dynamic recrystallization. Compared to the strain-compensated Arrhenius-type model, the novel modified constitutive equation has a higher prediction accuracy, with a correlation coefficient as high as 0.9991 and an average relative absolute error as low as 2.0734%. The activation energy decreases with increasing temperature and strain rate. At low temperatures and low strain rates, the activation energy decreases with increasing strain but shows the opposite trend at high temperatures and high strain rates. Based on the activation energy maps, the optimum hot-working parameters for this alloy are temperature 653–733 K and strain rate 0.001–0.1 s⁻¹.

Introduction

The combination of high specific strength, fracture toughness and resistance to stress corrosion endows 7075 Al alloy with unique advantages in the manufacture of automotive and aerospace structural components.^1,2,3 The formation of 7075 Al alloy structural components typically necessitates hot plastic processing, and the processing parameters such as temperature, strain rate and strain exert a significant influence on its formability and mechanical properties at room temperature.^4,5 During the plastic processing, by manipulating the processing parameters, we can obtain structural parts possessing good microstructure and mechanical properties. However, devising an appropriate processing route necessitates a thorough comprehension of the deformation behavior of the alloy under different conditions.

The hot deformation behavior of alloys is always described using constitutive equations. Over a long period of time, numerous researchers have made numerous efforts in establishing constitutive equations, and some typical models have been proposed.^6,7 Among these models, the hyperbolic sine Arrhenius-type model proposed by Sellars and McTegart⁸ has become the most used because of its simple form and wide range of applicability. The original Arrhenius-type model does not contain strain, making it unable to describe the entire deformation process of alloys. To accurately describe the flow behavior of alloys at different strains, a strain compensation method was proposed to modify the original Arrhenius-type model, which has been widely applied to describe the thermal deformation behavior of many aluminum alloys, such as 1070,⁹ 7050,¹⁰ AA2030,¹¹ 6063,¹² AA5083¹³ and A356.¹⁴ The strain-compensation Arrhenius-type model considers the material constants (α, n and lnA) and deformation activation energy Q as polynomial relationships that vary with strain. Due to the consideration of strain, the accuracy of the model has been greatly improved.¹⁵ Although the strain-compensation Arrhenius-type model can improve the accuracy of predicting flow stress, it still has limitations. In fact, material constants and activation energy are not only a function of strain but are also affected by deformation temperature and/or strain rate, especially activation energy.^16,17,18 However, current research rarely considers the influence of deformation conditions on material constants and activation energy, which can lead to unrealistic predictions of alloy hot deformation behavior.

In addition, activation energy plays a crucial role in the process of hot deformation, which is closely related to the thermodynamic mechanism of dislocation movement. It can effectively reflect the processing properties of alloys.^18,19,20,21 Generally, under lower activation energy conditions, the processing properties of alloys can be improved.²¹ However, the activation energy of alloys during hot deformation is complex and varies, which is affected by deformation conditions and microstructure.¹⁷ Therefore, accurately describing the activation energy of alloys during thermal deformation and understanding the effects of deformation conditions and microstructure evolution on activation energy are crucial.

A hot compression experiment was conducted on 7075-T6 Al alloy between 573 K and 733 K and at strain rates of 0.001–1 s⁻¹ to gain a clear understanding of its flow behavior and processability during hot deformation. By analyzing the flow stress curves and characterizing the microstructure of the deformed specimens, the hot deformation flow behavior of the alloy was analyzed. A new modified Arrhenius-type constitutive equation was developed by considering material constants and activation energy as functions of the deformation conditions. This equation was compared with the traditional strain-compensated Arrhenius-type constitutive equation. Based on the new modified constitutive equation, activation energy maps were constructed, and the influence of deformation conditions on activation energy was studied. The alloy’s hot processing parameters were optimized accordingly. The research results provide guidance for understanding the hot deformation behavior of aluminum alloys and optimizing processing parameters.

Experiments and Methods

Materials

The material used in this study is a 7075 Al alloy thick plate (120 mm) provided by China Yunnan Aluminum Co., Ltd., which has undergone T6 treatment (7075-T6) after rolling. The chemical composition of the alloy is shown in Table I. At present, 7075-T6 aluminum alloy thick plates are utilized in die forging processes for automotive support arms because of their ability to provide uniform and stable initial stock. The stress direction in 7075-T6 aluminum alloy thick plates occurs in the thickness direction during the die forging formation of support arms. To better simulate real-world conditions, the compression specimens used in this study were cut along the direction of the thick plate. The microstructure of the 7075-T6 aluminum alloy plate is shown in Fig. 1 (TD and RD represent the thickness direction and rolling direction, respectively). As shown in Fig. 1, after rolling, the grains of the 7075-T6 aluminum alloy are elongated and distributed along the rolling direction. The original deformed grain boundaries are clearly visible. Additionally, many coarse particles are present near the original deformed grain boundaries. Due to rolling deformation, these particles have undergone a certain degree of breakage. Previous studies have shown that^22,23,24 Al-Zn-Mg-Cu alloys with coarse particles mainly consist of Al₇Cu₂Fe and Al₂CuMg phases, which usually form during solidification and are difficult to eliminate during subsequent processing, but they will break during deformation. EDS analysis was used to analyze the coarse particles in Fig. 1, and the results are shown in Table II. Al₇Cu₂Fe and Al₂CuMg phases exist in the studied alloy, and it was also observed that many fine precipitates are distributed in the grain interior and grain boundaries, which are MgZn₂ phases.²⁴

Table I Chemical composition of experimental alloys (wt.%)

Fig. 1

Microstructure of 7075-T6 aluminum alloy: (a) OM, (b) EBSD, (c) SEM of low magnification, (d) SEM of high magnification.

Table II EDS results of the marked areas in Fig. 1c and d

Hot Compression Tests

The hot compression experiment was carried out using TA DIL805 equipment under the deformation module. The deformation temperature was set at 573 K, 613 K, 653 K, 693 K and 733 K, and the selected strain rates were 0.001 s⁻¹, 0.01 s⁻¹, 0.1 s⁻¹ and 1.0 s⁻¹. The compressed test sample was cylindrical in shape with a diameter of 5 mm and height of 10 mm. Before the compression experiment, the sample was heated by induction heating at a rate of 5 K s⁻¹ to the deformation temperature and then maintained at the temperature for 3 min to ensure temperature stability. Then, each sample was compressed under pre-set deformation conditions until a true strain of 0.8 was reached. Subsequently, the sample was quenched in helium gas as the quenching medium with a cooling rate of 50 K s⁻¹ to retain the deformed microstructure. The hot compression experiment was carried out under vacuum conditions, and the computer system controlled and saved experimental data.

Microstructure Characterization

The compressed sample was cut along the axial direction to observe the microstructure features of the axial section. The observation of the microstructure of the deformed sample was completed by optical microscopy (OM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The SEM was equipped with energy-dispersive spectroscopy (EDS) and electron backscatter diffraction detector (EBSD), which can be used to analyze the composition of the second phase particles and grain structure information in the deformed sample. Before characterization, the polishing surface of the deformed sample was polished on sandpaper, polished to 3000 mesh and then polished with Al₂O₃ suspension. The samples for OM observation need to be corroded with Keller's reagent (2 mL HF, 3 mL HCl, 5 mL HNO₃, 190 ml H₂O). The samples for EBSD testing were prepared by electrolytic polishing, and the samples for TEM testing were prepared by electrolytic double spray.

Results and Analysis

Analysis of Flow Behavior

Through hot compression experiments, the stress-strain data of the alloy under different deformation conditions were obtained and plotted as curves in Fig. 2. Obviously, the flow stress is affected by the deformation temperature, strain rate and strain. At constant strain and strain rate, the flow stress decreases with increasing temperature, showing negative temperature sensitivity. Conversely, at constant strain and temperature, the flow stress increases with increasing strain rate, showing positive strain rate sensitivity. These observed phenomena are similar to the hot deformation characteristics of other aluminum alloy materials.^22,25,26,27 In addition, flow stress curves in the figure roughly exhibit two shapes: (1) The flow stress gradually decreases after reaching a peak, showing significant flow softening effect, which mainly occurs at relatively low temperatures (≤ 653 K), and this softening effect weakens with increasing strain rate; and (2) The flow stress shows almost stable flow after reaching a peak, mainly occurring under relatively high temperature conditions.

Fig. 2

True stress-strain curves of 7075-T6 aluminum alloy under different deformation conditions: (a) 0.001 s⁻¹, (b) 0.01 s⁻¹, (c) 0.1 s⁻¹, (d) 1 s⁻¹.

It is well known that the significant changes in flow stress during deformation are the result of the competition between work hardening and dynamic softening.^18,19,20,28 When the dynamic softening rate is greater than the work hardening rate, the flow stress curve exhibits a shape like (1). When the dynamic softening rate is almost equal to the work hardening rate, it exhibits dynamic equilibrium flow, such as shape (2). When the dynamic softening rate is less than the work hardening rate, the flow stress will increase, which is not obvious in this study. According to previous research,^24,29 dynamic recovery (DRV), dynamic recrystallization (DRX) and thermal activation precipitation are the main mechanisms controlling the hot deformation flow stress of precipitation hardening alloys. Among them, DRV and DRX are typically used as typical softening mechanisms in the hot deformation process of precipitation hardening alloys, while thermal activation precipitation is used as a strengthening mechanism. Generally, during hot deformation, when DRV occurs in the alloy, the flow stress curve shows a smooth shape, while when the DRX mechanism occurs, the flow stress curve shows a significant decrease.³⁰ For aluminum alloys with high stacking fault energy, dislocation climb and cross-slip occur easily during hot deformation, resulting in the formation of equiaxed sub-grains through DRV.^24,29 In addition, even if DRX occurs in aluminum alloys, it is closely related to DRV.^24,30 Therefore, the hot deformation flow stress curve of aluminum alloys usually exhibits a stable or slightly decreasing trend. In addition, for precipitation strengthened aluminum alloys, during hot deformation, due to the growth and coarsening of precipitate particles, a large number of solute atoms are consumed, while the pinning effect of fine precipitate particles on dislocations is weakened, thus accelerating the occurrence of DRV.^31,32,33,34 The flow stress curve therefore shows a significant strain softening phenomenon. A more realistic analysis of hot deformation behavior requires combined microscopic tissue observations for confirmation.

Analysis of Microstructure

The IPF images of 7075-T6 samples under different hot deformation conditions are shown in Fig. 3. In the IPF image, low-angle grain boundaries (LAGBs, 2–5°), medium-angle grain boundaries (MAGBs, 5–15°) and high-angle grain boundaries (HAGBs, > 15°) are marked with white, gray and black lines, respectively. At a deformation temperature of 573 K, the microstructure of the sample is composed of further elongated grains and fine equiaxed grains. The LAGB content in the deformed grains is relatively low, and the number of complete grains connected by MAGBs is also very small. Fine equiaxed grains distribute along the boundaries of the original deformed grains, forming a “necklace-like” structure (as shown by the blue dashed lines in Fig. 3a and b), which is a typical feature of discontinuous dynamic recrystallization (DDRX).^30,35 Although DRX grains appeared in the deformed structure at 573 K, their content is relatively small, and the deformed grains are still the main component in the structure. Therefore, we consider DRV as the main softening mechanism during deformation at this temperature. Comparing the deformed structures under 573 K/0.001 s⁻¹ and 573 K/1 s⁻¹ conditions showed that when the deformation rate increases, the number of LAGBs significantly increases, indicating that the increase of strain rate results in an insufficient DRV process, and many LAGBs have not yet been transformed into MAGBs.

Fig. 3

IPF maps of the samples under different deformation conditions: (a) 573 K/0.001 s⁻¹, (b) 573 K/1 s⁻¹, (c) 653 K/0.01 s⁻¹, (d) 693 K/0.01 s⁻¹, (e) 733 K/0.001 s⁻¹, (f) 733 K/1 s⁻¹; (g) and (h) are identified in the figure.

Under the condition of deformation at 653 K/0.01 s⁻¹, the original deformation grain morphology of the long strip-shaped material still exists, but the number of MAGBs inside the deformation grains increases at this time, and complete sub-grains are formed at the grain boundaries, as shown by the blue arrows in Fig. 3c. At this time, the deformation grains simultaneously contain LAGBs, MAGBs and HAGBs, and some equiaxed grains are composed of MAGBs and HAGBs, indicating that the DRX mechanism formed under this condition is continuous dynamic recrystallization (CDRX).^30,35 However, since many deformation grains and a certain number of DRX grains are included in the deformation structure at this time, it is believed that the softening mechanism of deformation at 653K/0.01 s⁻¹ is DRV and DRX.

As the temperature increases further, the proportion of MAGBs and HAGBs increases, and the size of the formed (sub)grains becomes larger, as shown by the blue and black arrows in Fig. 3d and e. The (sub)grain size formed at 733 K/0.001 s⁻¹ is the largest, and the deformed grains are almost completely replaced by the formed (sub)grains, indicating a more complete DRX process. In addition, at this time, 1-2 layers of neatly stacked brick-like sub-grains appear inside the original deformed grains, as shown by the black dashed box in Fig. 3e, which is a characteristic of geometric dynamic recrystallization (GDRX).²⁴ Therefore, it is believed that at high temperature and low strain rates, the thermal deformation softening mechanism of 7075-T6 aluminum alloy is CDRX and GDRX. However, at 733 K/1 s⁻¹, because of the increase in strain rate shortening the deformation time, DRX is not sufficient. The number of DRX grains formed from sub-grains decreases and their size is also small, as shown in Fig. 3f, indicating partial DRX under this condition. Its dynamic softening mechanism includes DRV and DRX.

To better elucidate the microstructure evolution law of hot deformation for 7075-T6 aluminum alloy, TEM technology was employed to characterize the microstructure of deformed samples, and the results are shown in Fig. 4. At the condition of 573 K/0.001 s⁻¹, dislocation cells (red dashed region), sub-grains (yellow dashed region) and coarse precipitates (blue arrow) can be observed, as shown in Fig. 4a, indicating that sufficient DRV occurred at this time, which is consistent with the EBSD analysis results. Previous research³³ showed that coarsening of precipitates is more prone to occur during hot deformation process. This is because dislocation motion and “pipe diffusion” along dislocations increase the diffusion rate of atoms, so that the growth and diffusion of precipitates are accelerated. Once coarsening of precipitates occurs, a large number of solute atoms will be consumed, and the pinning effect of fine precipitates on dislocations will be weakened. Therefore, dislocation motion becomes easier, and sufficient dislocation motion enhances DRV, so that the phenomenon of flow softening is presented in the flow stress curve as shown in Fig. 2 at low temperature conditions.

Fig. 4

TEM images of the sample after deformation under different conditions: (a) 573 K/0.001 s⁻¹, (b) 573 K/1 s⁻¹, (c) 653 K/0.01 s⁻¹, (d) 733 K/0.01 s⁻¹.

At a temperature of 573 K, when the strain rate increases to 1 s⁻¹, the atomic diffusion is limited because of the short deformation time. Therefore, the precipitates in Fig. 4b have relatively small size. These small precipitates pin the dislocations and cause their accumulation and entanglement around them (red arrows), which hinder the dislocation movement and make it difficult for DRV to fully proceed. Therefore, the flow stress curve decreases only slightly as deformation progresses, corresponding to the curve in Fig. 2.

As the temperature increases, the number of precipitates decreases and their size increases at 653 K/0.01 s⁻¹ because dissolution and coarsening of precipitates occur simultaneously at this temperature. As a result, the flow stress curve shows a tendency to level off. In addition, dislocation cells and DRX grains were observed in TEM images, indicating that DRX occurred under this condition. Furthermore, DRX developed from dislocation cells, suggesting that the formation mechanism of DRX is CDRX.

As the temperature increased further, there was little precipitate at 733 K/0.01 s⁻¹, indicating that the original precipitate almost dissolved in the matrix. At this time, sub-grains and DRX grains were also observed. The DRX grains were ‘brick-like,’ indicating that CDRX and GDRX occurred at this time, which was consistent with the EBSD analysis results.

In summary, the dynamic softening mechanism of 7075-T6 aluminum alloy during thermal deformation is mainly DRV and DRX. At low temperatures, DRV is dominant. When the strain rate is low, the coarsening of precipitates accelerates DRV, resulting in a continuous decrease in flow stress. As the temperature increases, precipitates undergo dissolution and coarsening, while DRX is enhanced. At 653 K/0.01 s⁻¹, the DRX mechanism is CDRX. When the temperature further increases to 733 K/0.01 s⁻¹, the DRX grain size increases significantly, and the DRX mechanism is CDRX and GDRX.

Constitutive Equations

In current work, the Arrhenius-type constitutive equation is adopted to describe the relationship between the flow stress and the deformation temperature and strain rate in the hot deformation process of 7075-T6 aluminum alloy, and its basic form is as follows:^36,37

$$ \dot{\varepsilon } = AF(\sigma )\exp \left( { - \frac{{\text{Q}}}{RT}} \right) $$

(1)

$$ F(\sigma ) = \left\{ {\begin{array}{*{20}c} {\sigma^{{n_{1} }} \quad \quad \quad } & {(\alpha \sigma < 0.8)} \\ {\exp (\beta \sigma )} & {(\alpha \sigma > 1.2)} \\ {[\sinh (\alpha \sigma )]^{n} } & {({\text{for }}\;{\text{all}}\; \, \sigma )} \\ \end{array} } \right. $$

(2)

where $\dot{\varepsilon }$ and σ are the strain rate and flow stress, respectively, Q and T refer to the activation energy for deformation and temperature, R is the gas constant (8.314 J mol⁻¹ K⁻¹), and n₁, β, α, n, and A are material constants, with α = α = β/n₁. To calculate the value of each constant, we substitute Eq. 2 into Eq. 1 and take the natural logarithm of both sides of the new equation to obtain:

$$ \left\{ {\begin{array}{*{20}c} {\ln \sigma = \frac{1}{{n_{1} }}\ln \dot{\varepsilon } - \frac{1}{{n_{1} }}\ln C_{1} \quad \quad \quad \quad } & {(\alpha \sigma < 0.8)} \\ {\sigma = \frac{1}{\beta }\ln \dot{\varepsilon } - \frac{1}{\beta }\ln C_{2} \quad \quad \quad \quad \quad } & {(\alpha \sigma > 1.2)} \\ {[\sinh (\alpha \sigma )] = \frac{1}{n}\ln \dot{\varepsilon } + \frac{1}{n}\frac{Q}{RT} - \frac{1}{n}\ln A} & {({\text{for }}\;{\text{all}}\; \, \sigma )} \\ \end{array} } \right. $$

(3)

As shown in Eq. 3, at the same temperature, the slope obtained by linear fitting of lnσ−ln $\dot{\varepsilon }$ and σ−ln $\dot{\varepsilon }$ relationships is equal to 1/n₁ and 1/β, respectively. By using the relationship α = β/n₁, the α value can be calculated. Notably, the equation does not contain strain. In other words, the stress data used for solving n₁ and β values are from the same strain condition. Taking the data fitting at 0.3 strain as an example, the fitting results of lnσ−ln $\dot{\varepsilon }$ and σ−ln $\dot{\varepsilon }$ are shown in Fig. 5a and b. The mean values of n₁ and β obtained from the fitting are 0.08866 and 6.50093, respectively, resulting in an α value of 0.01364. Next, the parameters n, Q and lnA need to be solved, which are contained in the third equation of Eq. 3. When the temperature is constant, the slope obtained by linear fitting of the ln[sinh(ασ)]−ln $\dot{\varepsilon }$ relationship is equal to 1/n. When the strain rate is constant, the slope obtained by linear fitting of ln[sinh(ασ)]− 1000/T relationship is equal to S = Q/nR, which can be used to calculate Q = SnR. At 0.3 strain, the fitting results of ln[sinh(ασ)]−ln $\dot{\varepsilon }$ and ln[sinh(ασ)]− 1000/T are shown in Fig. 5c and d, resulting in a mean value of n of 4.5695 and a mean value of Q of 164.0534 kJ/mol. Similarly, the value of lnA can be calculated from the intercept F in Fig. 5c using the equation lnA = Q/RT−nF, with a mean value of 26.2410.

Fig. 5

Linear fitting of (a) lnσ−ln $\dot{\varepsilon }$, (b) σ−ln $\dot{\varepsilon }$, (c) ln[sinh(ασ)]−ln $\dot{\varepsilon }$ and (d) ln[sinh(ασ)] −1000/T when the strain is 0.3.

After obtaining the parameters in Eqs. 1 and 2 through the above method, the constitutive equation at 0.3 strain can be obtained. Since the strain rate during plastic deformation is controlled by thermal activation energy and deformation temperature, their coupling relationship can be represented by the Zener-Hollomon (Z) parameter, as shown in Eq. 4. Therefore, the flow stress can be solved using a constitutive equation that includes the Z parameter, as shown in Eq. 5.^24,38

$$ Z = \dot{\varepsilon }\exp (Q/{\text{RT}}) $$

(4)

$$ \sigma = (1/\alpha )\ln \left\{ {\left( {Z/A} \right)^{1/n} + \left[ {\left( {Z/A} \right)^{2/n} + 1} \right]^{1/2} } \right\} $$

(5)

Strain-Compensation Arrhenius-Type Constitutive Equation

The original Arrhenius-type constitutive equation considers the influence of temperature and strain rate on flow stress but ignores the influence of strain on flow stress. To accurately predict the hot deformation behavior of aluminum alloys, many researchers have used strain compensation methods to predict the high-temperature flow behavior of many aluminum alloys and achieved good results.^{9,10,11,12,13,14,15} The strain-compensated Arrhenius-type (SCA) constitutive equation is a polynomial relationship considering material constants (α, n and lnA) and deformation activation energy Q as a function of strain. In this study, the selected strain range was 0.05–0.775 with an interval of 0.025. By using the fitting method shown in Fig. 5, the values of α, n, Q and lnA at each strain can be solved, and these parameters are then fitted to a polynomial relationship with strain using Eq. 6. As shown in Fig. 6, the determination coefficient is > 0.99 for all parameters, indicating that these polynomial relationships are reliable fits.

$$ \left\{ \begin{gathered} \alpha (\varepsilon ) = 10^{ - 3} \times \left( {{12}{\text{.7235}} + {0}{\text{.9129}}\varepsilon + {9}{\text{.3602}}\varepsilon^{2} - {7}{\text{.3629}}\varepsilon^{3} } \right) \hfill \\ {\text{n}}(\varepsilon ) = 5.0062 - 5.4004\varepsilon + 26.0312\varepsilon^{2} - 58.3181\varepsilon^{3} + 58.1431\varepsilon^{4} - 22.2232\varepsilon^{5} \hfill \\ Q(\varepsilon ) = 190.3176 - 273.25\varepsilon + 1150.721\varepsilon^{2} - 2400.9\varepsilon^{3} + 2380.445\varepsilon^{4} - 913.586\varepsilon^{5} \hfill \\ \ln A(\varepsilon ) = 31.3927 - 52.8848\varepsilon + 221.677\varepsilon^{2} - 464.376\varepsilon^{3} + 463.2665\varepsilon^{4} - 178.918\varepsilon^{5} \hfill \\ \end{gathered} \right. $$

(6)

Fig. 6

Variation of material parameters with strain (a) α, (b) n, (c) Q and (d) lnA.

Combining Eqs. 4 and 5 with Eq. 6 forms the SCA constitutive equation, and the comparison of the calculated results with experimental results is shown in Fig. 7. It can be seen that the SCA constitutive equation can well reflect the trend of flow stress. However, under some deformation conditions, such as low temperature of 573 K or high strain rate of 1 s⁻¹, the model shows some deviation in predicting the flow stress, indicating that there is still room for improvement in the prediction accuracy of the model. A more detailed discussion on the accuracy of the model will be given in the following section.

Fig. 7

Comparison of stress predicted by SCA constitutive equation and experimental stress: (a) 0.001 s⁻¹, (b) 0.01 s⁻¹, (c) 0.1 s⁻¹ and (d) 1 s⁻¹.

Novel Modified Arrhenius-Type Constitutive Equation

The previous section showed that the strain compensation into the material parameters did not result in satisfactory prediction performance of the model. This was attributed to the fact that the activation energy for thermal deformation and material constants are not only strain-dependent but also depend on other deformation conditions such as deformation temperature and strain rate.^{16,17,18,19,20} Especially the activation energy should be simultaneously considered as a variable related to strain, strain rate and deformation temperature.^{16,17,18,19,20,21} In this section, the constitutive equation construction includes considering the material constants and activation energy as a function of strain, strain rate and/or deformation temperature. The activation energy is denoted as Q(ε, $\dot{\varepsilon }$, T), and the constructed constitutive equation is called the novel modified Arrhenius-type (NMA) constitutive equation. According to the previous discussion, the activation energy is related to n and S, so n and S should also be correspondingly changed to functions of strain, deformation temperature and/or strain rate. In fact, as shown in Fig. 5, n and S are not unique values, n changes with temperature, and S changes with strain rate. Therefore, in this study, n is considered a function of strain and temperature, denoted as n(ε, T), and S is considered a function of strain and strain rate, denoted as S(ε, $\dot{\varepsilon }$). Therefore, Q(ε, $\dot{\varepsilon }$, T) = S(ε, $\dot{\varepsilon }$) n(ε, T) R. Correspondingly, lnA(ε, $\dot{\varepsilon }$, T) can be solved, and lnA(ε, $\dot{\varepsilon }$, T) =  = Q(ε, $\dot{\varepsilon }$ T)/RT-n(ε, T)F(ε, T), where F(ε, T) is the intercept corresponding to solving n(ε, T).

The linear fitting method in Fig. 5 was adopted to obtain the n, F and S values under various deformation conditions. The scatter plot is shown in Fig. 8. Based on the distribution patterns of each parameter, use the rational 2D function to fit the surfaces of n(ε, T), F(ε, T) and S(ε, $\dot{\varepsilon }$) as shown by the green surface in Fig. 8. The determination coefficients R² of each fit are > 0.98, indicating that the fitting achieved a good result. The obtained fitting equation is:

$$ \left\{ \begin{gathered} {\text{n}}(\varepsilon ,T) = \frac{{ - 381.5093 + 3.015\varepsilon + 1.7487T - 0.0027T^{2} + 1.3851 \times 10^{ - 6} T^{3} }}{{1 + 0.7598\varepsilon - 0.5618\varepsilon^{2} + 0.873\varepsilon^{3} - 0.0088T + 1.2704 \times 10^{ - 5} T^{2} }} \hfill \\ F(\varepsilon ,T) = \frac{{936.4738 - 18.0521\varepsilon - 1.2791T - 0.0027T^{2} + 3.5593 \times 10^{ - 6} T^{3} }}{{1 - 10.219\varepsilon - 1.9463\varepsilon^{2} + 5.1031\varepsilon^{3} + 0.5605T - 9.8434 \times 10^{ - 4} T^{2} }} \hfill \\ S(\varepsilon ,\dot{\varepsilon }) = \frac{{3.073 + 7.1706\varepsilon + 0.6772(\ln \dot{\varepsilon }) - 0.0233(\ln \dot{\varepsilon })^{2} - 0.0128(\ln \dot{\varepsilon })^{3} }}{{1 + 1.559\varepsilon + 0.3197\varepsilon^{2} - 0.4829\varepsilon^{3} + 0.3484(\ln \dot{\varepsilon }) + 0.0348(\ln \dot{\varepsilon })^{2} }} \hfill \\ \end{gathered} \right. $$

(7)

Fig. 8

Rational 2D surface fitting results of (a) n(ε, T), (b) F(ε, T) and (c) S(ε, $\dot{\varepsilon }$) under different deformation conditions.

By solving Eq. 7, Q(ε, $\dot{\varepsilon }$, T) and lnA(ε, $\dot{\varepsilon }$, T) can be obtained, and by combining Eqs. 4 and 5, the flow stress can be calculated. The comparison of the flow stress calculated by the NMA constitutive equation with experimental values is shown in Fig. 9. Compared to the SCA constitutive equation, the modified constitutive equation predicts the flow stress better in agreement with experimental values. It is clear that the novel modified constitutive equation in this study is more suitable for describing the hot deformation behavior of 7075-T6 aluminum alloy.

Fig. 9

Comparison of stress predicted by NMA constitutive equation and experimental stress (a) 0.001 s⁻¹, (b) 0.01 s⁻¹, (c) 0.1 s⁻¹ and (d) 1 s⁻¹.

Evaluation and Comparison of Constitutive Equations

To quantitatively evaluate and compare the accuracy of the SCA and NMA constitutive equations established in this article, the correlation coefficient (R) and average relative absolute error (AARE) were used to assess the predictive ability of the two models for flow stress. The calculation formulas for these metrics are given by Eqs. 8 and 9.^39,40

$$ R = \frac{{\sum\limits_{i = 1}^{N} {\left( {\sigma_{\exp }^{i} - \overline{\sigma }_{\exp } } \right)\left( {\sigma_{{{\text{pre}}}}^{i} - \overline{\sigma }_{{{\text{pre}}}} } \right)} }}{{\sum\limits_{i = 1}^{N} {\left( {\sigma_{\exp }^{i} - \overline{\sigma }_{\exp } } \right)^{2} } \sum\limits_{i = 1}^{N} {\left( {\sigma_{{{\text{pre}}}}^{i} - \overline{\sigma }_{{{\text{pre}}}} } \right)^{2} } }} $$

(8)

$$ {\text{AARE}} = \frac{1}{N}\sum\limits_{i = 1}^{N} {\left| {\frac{{\sigma_{\exp }^{i} - \sigma_{{{\text{pre}}}}^{i} }}{{\sigma_{\exp }^{i} }}} \right|} \times 100\% $$

(9)

The correlation analysis results of the flow stress calculated by SCA and NMA constitutive equations with experimental flow stress are shown in Fig. 10a and b. As is well known, the closer the stress data points are to the best match line, the more accurate the model is. The flow stress calculated by NMA constitutive equation is closer to the best match line in general, with an R value of 0.9991. However, for SCA constitutive equation, the R value is relatively lower, at 0.9936, and its predicted flow stress deviates slightly throughout the entire stress range, especially for the prediction performance at high stress levels, which can also be clearly observed in Fig. 7. To better analyze the error distribution of the two constitutive equations in predicting the flow stress, the residual distribution is plotted, as shown in Fig. 10c and d. The error distribution of the flow stress calculated by SCA constitutive equation is relatively scattered, with a distribution range of –16–14 MPa, while for the flow stress calculated by NMA constitutive equation, its error distribution is relatively concentrated, only distributed in – 4.5–4.0 MPa. In addition, the AARE value of the flow stress calculated by NMA constitutive equation is relatively small, at 2.0734%, while that of the flow stress calculated by SCA constitutive equation is relatively large, at 4.7168%. Therefore, it is concluded that among the two constitutive equations built in this article, NMA constitutive equation has higher prediction accuracy for the hot deformation flow stress of 7075 aluminum alloy and is more suitable for describing the hot deformation behavior of this alloy.

Fig. 10

Correlation analysis and residual distribution of flow stress calculated by SCA and NMA constitutive equations with experimental flow stress. (a, b) Correlation analysis results, (c, d) residual distribution.

Evolution of Activation Energy

It is well known that the activation energy Q describes the energy barrier that dislocation motion needs to overcome and can represent the ease of deformation of an alloy. Therefore, Q is often used as a measure to evaluate the machinability of alloys and optimize their processing conditions. Based on the solution presented in the previous section of this article, the variation of Q with temperature and strain rate under different strains is obtained and plotted in Fig. 11, which shows that Q varies between 111.0–240.0 kJ/mol under different temperatures, strain rates and strains (0.2–0.75). The maximum and minimum values are found in the low-temperature, low-strain rate region and the high-temperature, high-strain rate region, respectively. Under constant strain, Q decreases with increasing strain rate and temperature, with the rate of decrease gradually decreasing with increasing strain.

Fig. 11

Q evolutions under different strains of (a) 0.2, (b) 0.3, (c) 0.4, (d) 0.5, (e) 0.6 and (f) 0.75.

The thermal plastic deformation of alloys is primarily caused by dislocation slip through the activation processes. Increases in temperature and strain rate facilitate dislocation mobility, thereby reducing Q.^18,19,20 Specifically, as the temperature increases, dislocations can move with higher kinetic energy, making dislocation movement easier. Additionally, the increase in temperature enhances DRV and DRX, resulting in a decrease in dislocation density and a reduction in the resistance to dislocation movement. Therefore, Q decreases with increasing temperature. From the perspective of increasing strain rates, the applied external stress and resolved shear stress increase, providing higher kinetic energy for dislocation movement. Therefore, increasing strain rates are favorable for dislocation movement and promote Q reduction. However, increases in strain rates also have unfavorable effects on dislocation movement, as strain rate increases can lead to dislocation multiplication and entanglement, and the shortening of deformation time may result in incomplete DRV and DRX. These factors are detrimental to dislocation movement and lead to an increase in Q. Clearly, in this study, Q decreases with increasing strain rates, indicating that applied external stress and the increase in resolved shear stress has a greater impact on Q than dislocation multiplication and entanglement.

The phenomenon can be further explained by referring to Fig. 11f, which shows that under the same strain rate, Q decreases with increasing temperature. At a strain rate of 0.001 s⁻¹ and a temperature of 573 K, Q is 175.8 kJ/mol, but it decreases to 126.0 kJ/mol at a temperature of 733 K. The microstructure analysis (Figs. 3 and 4) provides an explanation. This is because DRV occurs at low temperatures while DRX occurs and the DRX grains grow at high temperatures. At the same temperature, Q decreases with increasing strain rate. At 573 K, when the strain rate increases to 1 s⁻¹, Q decreases to 141.2 kJ/mol. According to the analysis of Figs. 3 and 4, under the condition of 573 K/1 s⁻¹, DRV is not sufficient, and there are many intertwined dislocations in the deformation structure, which should lead to an increase in Q. However, Fig. 11f shows the opposite trend, indicating that the increase in applied external stress and resolved shear stress with increasing strain rate is the dominant effect in the process of hot deformation, leading to a decrease in Q. This is consistent with the conclusions obtained by Liu et al.¹⁷ and Shi et al.¹⁹

The influence of strain on Q is also observed in Fig. 11. The significant change in Q with increasing strain is mainly observed in the low-temperature and low-strain rate region (such as 573 K/0.001 s⁻¹) and the high-temperature and high-strain rate region (such as 733 K/1 s⁻¹). In the low-temperature and low-strain rate region, Q decreases significantly with increasing strain, while Q gradually increases in the high-temperature and high-strain rate region. To better understand the evolution of Q with strain, the deformation conditions of 573 K/0.001 s⁻¹ and 733 K/1 s⁻¹ were selected for analysis, and the evolution of Q was plotted as Q curves shown in Fig. 12. Clearly, Q gradually decreases during deformation at 573 K/0.001 s⁻¹ but shows the opposite trend at 733 K/1 s⁻¹. This can be explained by referring to the microstructure evolution shown in Figs. 3 and 4. Previous analysis has shown that sufficient DRV and coarsening of precipitates occurred at 573 K/0.001 s⁻¹, indicating that dislocations had relatively easy slip and climb during deformation, resulting in a decrease in Q. At 733 K/1 s⁻¹, DRX occurred in the deformed structure, which refined the grains. Due to the strengthening effect of refined grains, Q increased with increasing strain.

Fig. 12

Change of Q with strain under typical deformation conditions.

By analyzing activation energy maps, the hot working parameters of alloys can be optimized. Generally, a region where the Q value remains stable can be considered as an ideal region for hot working of alloys.^19,41 Figure 11 shows that in the temperature range of 653–733 K and strain rate range of 0.001–0.1 s⁻¹, the Q value of 7075-T6 aluminum alloy remains stable at around 140.0–170.0 kJ/mol during the entire deformation process, making this range an optimal hot working window for the alloy.

Conclusion

The study deciphered the hot deformation behavior of 7075-T6 aluminum alloy via flow stress and microstructural analysis, developed a novel constitutive equation for hot deformation, compared it with traditional methods and utilized activation energy maps to refine hot-working parameters. The main conclusions obtained are as follows:

• (1) The alloy exhibits significant flow softening after reaching its peak stress at low temperatures (≤ 653 K), which weakens with increasing strain rate. At higher temperatures, the alloy exhibits a near-steady-state flow behavior.

• (2) Dynamic recovery (DRV) and dynamic recrystallization (DRX) occur concurrently during hot deformation. At lower temperatures, the flow stress experiences a continuous decrease as precipitates grow coarser, with DRV playing a dominant role. As the temperature increases, DRX gradually becomes predominant, and the DRX mechanism transitions from continuous to geometric dynamic recrystallization. Concurrently, the size of the recrystallized grains increases.

• (3) A novel modified Arrhenius-type constitutive equation is proposed, which considers material constants and activation energy that depend on deformation conditions. This equation shows superior performance compared to the traditional modified method in predicting flow stress. The correlation coefficient (R) is 0.9991, and the average absolute relative error (AARE) is only 2.0734%.

• (4) The activation energy decreases as temperature and strain rate increase. At low temperatures and slow strain rates, the activation energy decreases with strain. However, at high temperatures and rapid strain rates, the opposite trend is observed. From the activation energy maps, the optimal hot-working parameters for the studied alloy are determined to be in the temperature range of 653–733 K and the strain rate range of 0.001–0.1 s⁻¹.