An Investigation on the Softening Mechanism of 5754 Aluminum Alloy during Multistage Hot Deformation

Isothermal interrupted hot compression tests of 5754 aluminum were conducted on a Gleeble-3500 thermo-mechanical simulator at temperatures of 350 °C and 450 °C, and strain rates of 0.1 s−1 and 1 s−1. To investigate the metadynamic recrystallization behavior, a range of inter-pass delay times (5–60 s) was employed. These tests simulated flat rolling to investigate how softening behaviors respond to controlled parameters, such as deformation temperature, strain rate, and delay times. These data allowed the parameters for the hot rolling process to be optimized. The dynamic softening at each pass and the effect of metadynamic recrystallization on flow properties and microstructural evolution were analyzed in detail. An offset yield strength of 0.2% was employed to calculate the softening fraction undergoing metadynamic recrystallization. A kinetic model was developed to describe the metadynamic recrystallization behaviors of the hot-deformed 5754 aluminum alloy. Furthermore, the time constant for 50% recrystallization was expressed as functions related to the temperature and the strain rate. The experimental and calculated results were found to be in close agreement, which verified the developed model.


Introduction
Different hot deformation processes of metals and alloys holds remarkable importance due to its direct effects on mechanical properties of final products.Therefore, the hot forming behavior of different materials has been a significant scientific issue [1].The hot rolling and forging processes of aluminum alloy consist of several continuous deformation passes such as inter-pass periods between deformations.Materials will subject to static recovery, static recrystallization, and metadynamic recrystallization during the inter-pass periods [2].Meanwhile, microstructural changes during multistage hot deformation render an effect on the mechanical characteristics of the metals and hence affect the deformation process.The manufacture of high quality products and optimization of pass schedules require a good knowledge of the relationships between hardening and softening behaviors.Modeling a kinetics equation necessitates a better understanding of the dynamic softening during hot deformation (simultaneous with straining) and the metadynamic or static softening between thermomechanical passes [3][4][5][6].The modeling results are critical for the optimization of process parameters [7].Generally, the degree of dynamic softening can be determined using relative softening (RS) or quasistatic softening, and four different methods, including offset-stress, back-extrapolation stress, strain-recovery, and average stress methods, are employed to evaluate the softening fraction at the inter-pass durations.
A set of two-pass hot compression tests with various parameters were conducted in this study.These tests were designed to simulate flat rolling and provide in-depth insight into the high-temperature deformation behavior of 5754 aluminum alloy.The dynamic and metadynamic recrystallization softening behaviors of this studied alloy during multistage hot deformation were analyzed by relative softening (RS) and 0.2% offset-stress, respectively.To date, numerous studies have been directed to clarify the dynamic and metadynamic recrystallization behaviors of alloys and metals, and related kinetics equations have been developed [8][9][10][11][12][13][14][15].No systematic work on, nor any fundamental knowledge of, multistage hot compression for this alloy has ever been reported.Accordingly, the present study has been designed to obtain 5754 aluminum alloys with good mechanical properties and to optimize its use for production.The purpose of this paper is mainly to focus on how metadynamic recrystallization softening behaviors respond to control parameters such as deformation temperature, strain rate, and delay time, thereby optimizing the hot rolling and forging process parameters.Moreover, a metadynamic recrystallization kinetics model of this aluminum alloy during two-pass deformation was established.Furthermore, the time constant for 50% recrystallization was expressed as functions related to the temperature and the strain rate.The experimental and calculated results were found to be in close agreement, which verified the developed model.

Materials
5754 aluminum alloy is a common Al-Mg alloy.Its mechanical properties, such as its moderate strength, its good corrosion resistance, its weldability, and its easy forming characteristics, have made it the primarily used material in the manufacture of doors, platform floors, body frames, and other structural components in the automotive industry.The experimental 5754 aluminum alloy used for multistage hot deformation tests were machined from a warm rolled plane.The chemical composition (wt %) of the alloy used in the experiments is reported in Table 1.The size of all specimens was 20 mm in the transverse direction, 18 mm in the normal direction, and 10 mm in the rolling direction (20 mm × 18 mm × 10 mm).The geometric outline of the deformation zone is approximated for rolling simulations.Figure 1 is given to show the specimens before forming, after one step, and after a second step of forming.
including offset-stress, back-extrapolation stress, strain-recovery, and average stress methods, are employed to evaluate the softening fraction at the inter-pass durations.
A set of two-pass hot compression tests with various parameters were conducted in this study.These tests were designed to simulate flat rolling and provide in-depth insight into the high-temperature deformation behavior of 5754 aluminum alloy.The dynamic and metadynamic recrystallization softening behaviors of this studied alloy during multistage hot deformation were analyzed by relative softening (RS) and 0.2% offset-stress, respectively.To date, numerous studies have been directed to clarify the dynamic and metadynamic recrystallization behaviors of alloys and metals, and related kinetics equations have been developed [8][9][10][11][12][13][14][15].No systematic work on, nor any fundamental knowledge of, multistage hot compression for this alloy has ever been reported.Accordingly, the present study has been designed to obtain 5754 aluminum alloys with good mechanical properties and to optimize its use for production.The purpose of this paper is mainly to focus on how metadynamic recrystallization softening behaviors respond to control parameters such as deformation temperature, strain rate, and delay time, thereby optimizing the hot rolling and forging process parameters.Moreover, a metadynamic recrystallization kinetics model of this aluminum alloy during two-pass deformation was established.Furthermore, the time constant for 50% recrystallization was expressed as functions related to the temperature and the strain rate.The experimental and calculated results were found to be in close agreement, which verified the developed model.

Materials
5754 aluminum alloy is a common Al-Mg alloy.Its mechanical properties, such as its moderate strength, its good corrosion resistance, its weldability, and its easy forming characteristics, have made it the primarily used material in the manufacture of doors, platform floors, body frames, and other structural components in the automotive industry.The experimental 5754 aluminum alloy used for multistage hot deformation tests were machined from a warm rolled plane.The chemical composition (wt %) of the alloy used in the experiments is reported in Table 1.The size of all specimens was 20 mm in the transverse direction, 18 mm in the normal direction, and 10 mm in the rolling direction (20 mm × 18 mm × 10 mm).The geometric outline of the deformation zone is approximated for rolling simulations.Figure 1 is given to show the specimens before forming, after one step, and after a second step of forming.

Material Testing
A set of two-pass hot compression tests were conducted using a computer-controlled, servo-hydraulic Gleeble-3500 thermo-mechanical simulator.As can be observed in Figure 2, all specimens were heated at a rate of 10 • C/s to the specified temperature, then held at this temperature for 240 s to eliminate thermal gradients and to guarantee complete heating before compression.Tantalum foils were used to minimize the friction between the specimen and the indenter during compression.Two different forming temperatures (350 • C and 450 • C) and two strain rates (0.1 s −1 and 1 s −1 ) were used.The deformation degree is the same in the two deformation passes, and a height reduction of 35% was adopted at each stage.The specimens would be held for times ranging from 5 s to 60 s at the deformation temperature during the inter-pass periods.In order to calculate the softening fraction, a second deformation pass was acquired.
During the hot compression process, the variations in strain and stress were continuously controlled by a computer, which was equipped with an automatic data acquisition system.The true stress-strain data were recorded by the testing system.To preserve the deformed microstructure, the specimens were quenched by cold water immediately after each compression experiment.The samples were cut along the direction of compression for analysis, and then mounted, polished, and anode-coated at 20 V for 2 min using a solution of fluoroboric acid (10 mL) in water (400 mL) for observation by optical microscopy.The strain distribution was concentrated in the center of the plane specimen, which assists the optical observation of the microstructures in the deformed material.Figure 3 shows optical microscopy images of the initial microstructures.

Material Testing
A set of two-pass hot compression tests were conducted using a computer-controlled, servo-hydraulic Gleeble-3500 thermo-mechanical simulator.As can be observed in Figure 2, all specimens were heated at a rate of 10 °C/s to the specified temperature, then held at this temperature for 240 s to eliminate thermal gradients and to guarantee complete heating before compression.Tantalum foils were used to minimize the friction between the specimen and the indenter during compression.Two different forming temperatures (350 °C and 450 °C) and two strain rates (0.1 s −1 and 1 s −1 ) were used.The deformation degree is the same in the two deformation passes, and a height reduction of 35% was adopted at each stage.The specimens would be held for times ranging from 5 s to 60 s at the deformation temperature during the inter-pass periods.In order to calculate the softening fraction, a second deformation pass was acquired.
During the hot compression process, the variations in strain and stress were continuously controlled by a computer, which was equipped with an automatic data acquisition system.The true stress-strain data were recorded by the testing system.To preserve the deformed microstructure, the specimens were quenched by cold water immediately after each compression experiment.The samples were cut along the direction of compression for analysis, and then mounted, polished, and anode-coated at 20 V for 2 min using a solution of fluoroboric acid (10 mL) in water (400 mL) for observation by optical microscopy.The strain distribution was concentrated in the center of the plane specimen, which assists the optical observation of the microstructures in the deformed material.Figure 3 shows optical microscopy images of the initial microstructures.

Material Testing
A set of two-pass hot compression tests were conducted using a computer-controlled, servo-hydraulic Gleeble-3500 thermo-mechanical simulator.As can be observed in Figure 2, all specimens were heated at a rate of 10 °C/s to the specified temperature, then held at this temperature for 240 s to eliminate thermal gradients and to guarantee complete heating before compression.Tantalum foils were used to minimize the friction between the specimen and the indenter during compression.Two different forming temperatures (350 °C and 450 °C) and two strain rates (0.1 s −1 and 1 s −1 ) were used.The deformation degree is the same in the two deformation passes, and a height reduction of 35% was adopted at each stage.The specimens would be held for times ranging from 5 s to 60 s at the deformation temperature during the inter-pass periods.In order to calculate the softening fraction, a second deformation pass was acquired.
During the hot compression process, the variations in strain and stress were continuously controlled by a computer, which was equipped with an automatic data acquisition system.The true stress-strain data were recorded by the testing system.To preserve the deformed microstructure, the specimens were quenched by cold water immediately after each compression experiment.The samples were cut along the direction of compression for analysis, and then mounted, polished, and anode-coated at 20 V for 2 min using a solution of fluoroboric acid (10 mL) in water (400 mL) for observation by optical microscopy.The strain distribution was concentrated in the center of the plane specimen, which assists the optical observation of the microstructures in the deformed material.Figure 3 shows optical microscopy images of the initial microstructures.

Dynamic Softening Behavior
Aluminum alloys undergo mechanism restoration of dynamic recovery and dynamic recrystallization during deformation, particularly at high temperature.The flow behaviors are very complex during hot deformation, and the parameters of hot deformation, such as temperature and strain rate, affect the flow stress significantly.Therefore, the control of deformation parameters is critical in optimizing the final mechanical properties [16][17][18][19][20]. Figure 4 indicates the true representative stress-stain curves of the studied alloy under various deformation conditions.The stress level decreases with an increasing temperature or with a decreasing strain rate.These typical curves exhibit a single peak at a small strain, then decrease to a steady state, and remain constant at 350 • C at a strain rate of 1 s −1 , showing the dynamic softening behavior after peak stress.Generally, the yield stress at the second deformation stage decreases with an increasing delay time under the same temperature and the same strain rate.Verlinden et al. [21,22] proposed relative softening (RS) to quantify dynamic softening.The equation can be expressed as where σ p is the value of peak stress and σ p+0.25 is the value taken at a strain of 0.25 beyond the peak (Figure 5).Dynamic hardening occurs as RS < 0, and dynamic softening occurs as RS > 0. The measured RS values (4.6%, 2.0%, 6.9%, and 5.2%) indicate that dynamic softening occurred here.The obtained stress-strain curves under all test conditions are single-peak without oscillation, which is an indication of softening behavior due to continuous dynamic recrystallization (CDRX) [23,24].Furthermore, the RS values at the second deformation stage are smaller than those at the first.The inhomogeneous deformation and friction at high strain (ε > 0.6) lead to smaller RS values and to little dependence on delay times during inter-pass periods at the same temperature and the same strain rate.Those results signify that a dynamic softening fraction may approach zero with further straining at the second deformation stage.
Metals 2017, 7, 107 4 of 11 Aluminum alloys undergo mechanism restoration of dynamic recovery and dynamic recrystallization during deformation, particularly at high temperature.The flow behaviors are very complex during hot deformation, and the parameters of hot deformation, such as temperature and strain rate, affect the flow stress significantly.Therefore, the control of deformation parameters is critical in optimizing the final mechanical properties [16][17][18][19][20]. Figure 4 indicates the true representative stress-stain curves of the studied alloy under various deformation conditions.The stress level decreases with an increasing temperature or with a decreasing strain rate.These typical curves exhibit a single peak at a small strain, then decrease to a steady state, and remain constant at 350 °C at a strain rate of 1 s −1 , showing the dynamic softening behavior after peak stress.Generally, the yield stress at the second deformation stage decreases with an increasing delay time under the same temperature and the same strain rate.Verlinden et al. [21,22] proposed relative softening (RS) to quantify dynamic softening.The equation can be expressed as where σp is the value of peak stress and σp+0.25 is the value taken at a strain of 0.25 beyond the peak (Figure 5).Dynamic hardening occurs as RS < 0, and dynamic softening occurs as RS > 0. The measured RS values (4.6%, 2.0%, 6.9%, and 5.2%) indicate that dynamic softening occurred here.The obtained stress-strain curves under all test conditions are single-peak without oscillation, which is an indication of softening behavior due to continuous dynamic recrystallization (CDRX) [23,24].Furthermore, the RS values at the second deformation stage are smaller than those at the first.The inhomogeneous deformation and friction at high strain (ε > 0.6) lead to smaller RS values and to little dependence on delay times during inter-pass periods at the same temperature and the same strain rate.Those results signify that a dynamic softening fraction may approach zero with further straining at the second deformation stage.

Modeling the Kinetics of Metadynamic Recrystallization
Softening mechanisms including static recovery, static recrystallization, and metadynamic recrystallization normally occur during inter-pass periods [25].The degree of softening depend on the deformation temperature, strain rate, and holding time.Metadynamic recrystallization occurs when εε  c , where ε is the strain at the interval and ε c is the critical strain.Following this, in the present study, the metadynamic recrystallization appears to be the dominant softening mechanism during the inter-pass holding.The optical microscopy images at the center of the specimens after various inter-pass durations are shown in Figure 6.Coarse equiaxed alloy grains are evident in the initial microstructure of the alloy (Figure 3), and the topography appears primarily to be isometrically crystalline with a large angle.By contrast, the fine equiaxed recrystallized grains can be found for the two-pass compressed alloy.As can be seen, the microstructural evolution after a 30 s inter-pass delay time indicated full recrystallization.This observation is due to the fact that metadynamic recrystallization does not require an incubation period, and the softening process is relatively speedy.In this study, the softening fraction (FS) caused by metadynamic recrystallization can be quantitatively examined using 0.2% offset stress.The equation can be expressed as where σ1 and σ2 are the offset stresses at the first and second deformation stage, respectively, and σm is the flow stress at the interval (Figure 5).
The softening fraction is plotted against the delay time with various test parameters in Figure 7.As can be seen, the softening fraction of metadynamic recrystallization is increased by the inter-pass delay time.The stress-strain curves of the second pass will be the same as those of the first pass if the materials are fully softened during the inter-pass time.While no softening occurs, the second compression yields a stress-strain curve that is in accordance with the extrapolated one of the first stage.The amount of recrystallization significantly depends on the inter-pass delay time, and the softening fraction of metadynamic recrystallization is increased by the inter-pass delay time.As the delay time is reduced, a smaller amount of recrystallization occurs, which leads to a small amount of work hardening on reloading [26].In addition, the softening fraction increases as the temperature increases due to the thermally activated softening mechanisms.The stored energy in the material at a high strain rate cannot be released as a consequence of lesser time being available at the first deformation stage, which can be released during the inter-pass periods and lead to the subsequent softening.

Modeling the Kinetics of Metadynamic Recrystallization
Softening mechanisms including static recovery, static recrystallization, and metadynamic recrystallization normally occur during inter-pass periods [25].The degree of softening depend on the deformation temperature, strain rate, and holding time.Metadynamic recrystallization occurs when ε > ε c , where ε is the strain at the interval and ε c is the critical strain.Following this, in the present study, the metadynamic recrystallization appears to be the dominant softening mechanism during the inter-pass holding.The optical microscopy images at the center of the specimens after various inter-pass durations are shown in Figure 6.Coarse equiaxed alloy grains are evident in the initial microstructure of the alloy (Figure 3), and the topography appears primarily to be isometrically crystalline with a large angle.By contrast, the fine equiaxed recrystallized grains can be found for the two-pass compressed alloy.As can be seen, the microstructural evolution after a 30 s inter-pass delay time indicated full recrystallization.This observation is due to the fact that metadynamic recrystallization does not require an incubation period, and the softening process is relatively speedy.In this study, the softening fraction (FS) caused by metadynamic recrystallization can be quantitatively examined using 0.2% offset stress.The equation can be expressed as where σ 1 and σ 2 are the offset stresses at the first and second deformation stage, respectively, and σ m is the flow stress at the interval (Figure 5).The softening fraction is plotted against the delay time with various test parameters in Figure 7.As can be seen, the softening fraction of metadynamic recrystallization is increased by the inter-pass delay time.The stress-strain curves of the second pass will be the same as those of the first pass if the materials are fully softened during the inter-pass time.While no softening occurs, the second compression yields a stress-strain curve that is in accordance with the extrapolated one of the first stage.The amount of recrystallization significantly depends on the inter-pass delay time, and the softening fraction of metadynamic recrystallization is increased by the inter-pass delay time.As the delay time is reduced, a smaller amount of recrystallization occurs, which leads to a small amount of work hardening on reloading [26].In addition, the softening fraction increases as the temperature increases due to the thermally activated softening mechanisms.The stored energy in the material at a high strain rate cannot be released as a consequence of lesser time being available at the first deformation stage, which can be released during the inter-pass periods and lead to the subsequent softening.The kinetics model of metadynamic recrystallization softening behavior can be expressed by the following exponent-type equation [27,28], where mdrex X is the softening fraction, and n is the Avrami exponent.t0.5 is an empirical time constant for 50% recrystallization, which can be widely expressed as where a and m are material constants.R is the gas constant, which is equal to 8.314 J/(mol K).Qm is the activation energy for recrystalliation.ε and T are the strain rate and the deformation temperature, respectively.The kinetics model of metadynamic recrystallization softening behavior can be expressed by the following exponent-type equation [27,28],

Determination of n
where mdrex X is the softening fraction, and n is the Avrami exponent.t0.5 is an empirical time constant for 50% recrystallization, can be widely expressed as where a and m are material constants.R is the gas constant, which is equal to 8.314 J/(mol K).Qm is the activation energy for recrystalliation.ε and T are the strain rate and the deformation temperature, respectively.The kinetics model of metadynamic recrystallization softening behavior can be expressed by the following exponent-type equation [27,28],

Determination of n
where X mdrex is the softening fraction, and n is the Avrami exponent.t 0.5 is an empirical time constant for 50% recrystallization, which can be widely expressed as where a and m are material constants.R is the gas constant, which is equal to 8.314 J/(mol K).Q m is the activation energy for recrystalliation.
. ε and T are the strain rate and the deformation temperature, respectively.Taking the logarithm of Equation (3) of both sides, substituting the softening fraction mdrex X and the related inter-pass delay time into Equation ( 5).
Figure 8 shows the plot of versus lnt.The average value of material constant n can be obtained by linear fitting, which is equal to 0.763.substituting the value t0.5 and strain rate ε into the above equation.Material constant m and activation energy for metadynamic recrystallization Q can be obtained via linear fitting.Figure 9 shows a relationship between lnt0.5 and ln ε , as well as lnt0.5 and 1/T.The activation energy for metadynamic recrystallization Q is 18.045 KJ/mol.Much previous investigation has been focused on softening mechanisms during the inter-pass period of different aluminum alloys [2,29,30].The exponent n and the present study is lower than that obtained for Al-5Mg Al-9Mg alloy, i.e., n = 3.6 [30].The variation of Avrami exponent n and activation energy Q values may be found for several reasons such as a decreasing growth rate or due to more planar growth morphology.In addition, the content of Mg will also lead to different activation energy for recrystallization.substituting the value of t 0.5 and strain rate .ε into the above equation.Material constant m and activation energy for metadynamic recrystallization Q can be obtained via linear fitting.Figure 9 shows a relationship between lnt 0.5 and ln .ε, as well as lnt 0.5 and 1/T.The activation energy for metadynamic recrystallization Q is 18.045 KJ/mol.Much previous investigation has been focused on softening mechanisms during the inter-pass period of different aluminum alloys [2,29,30].The exponent n and the present study is lower than that obtained for Al-5Mg and Al-9Mg alloy, i.e., n = 3.6 [30].The variation of Avrami exponent n and activation energy Q values may be found for several reasons such as a decreasing growth rate or due to more planar growth morphology.In addition, the content of Mg will also lead to different activation energy for recrystallization.Taking the logarithm of Equation (3) of both sides, substituting the softening fraction mdrex X and the related inter-pass delay time into Equation (5).
Figure 8 shows the plot of versus lnt.The average value of material constant n can be obtained by linear fitting, which is equal to 0.763.
substituting the value of t0.5 and strain rate ε into the above equation.Material constant m and activation energy for metadynamic recrystallization Q can be obtained via linear fitting.Figure 9 shows a relationship between lnt0.5 and ln ε , as well as lnt0.5 and 1/T.The activation energy for metadynamic recrystallization Q is 18.045 KJ/mol.Much previous investigation has been focused on softening mechanisms during the inter-pass period of different aluminum alloys [2,29,30].The exponent n and the present study is lower than that obtained for Al-5Mg and Al-9Mg alloy, i.e., n = 3.6 [30].The variation of Avrami exponent n and activation energy Q values may be found for several reasons such as a decreasing growth rate or due to more planar growth morphology.In addition, the content of Mg will also lead to different activation energy for recrystallization.

Verification of the Developed Kinetic Equation
The softening behavior induced by metadynamic recrystallization during the two-pass hot deformation of 5754 aluminum alloy was investigated.The developed kinetic model has been verified by comparing the experimental and predicted metadynamic recrystallized fraction.Figures 10 and 11 illustrate the fitted experimental results using regression analysis, and most of the experimental and predicted softening fraction have a linear relationship and show good agreement with each other.Furthermore, the statistical parameters such as the correlation coefficient (R) and the average absolute relative error (AARE) were calculated to quantitatively verify the accuracy of developed kinetic model.The correlative expressions are shown in Equations ( 9) and (10).
where E i and P i are the measured and calculated softening fraction, respectively.E and P are the average values of E i and P i , and N is the total number of the tested samples.The correlation coefficient is a reflection of the linear relationship between the experimental and predicted data.The AARE is an unbiased statistical parameter used to evaluate the predictability of a model that can be calculated through a term-by-term comparison of relative error [31,32].The values of R and AARE were calculated to be 0.974 and 9.306%.The results indicate the model developed here is shown to provide accurate predictions for 5754 aluminum alloy.
To conclude, the metadynamic recrystallization kinetic equation of two-pass hot-compressed 5754 aluminum can be assumed as:

Verification of the Developed Kinetic Equation
The softening behavior induced by metadynamic recrystallization during the two-pass hot deformation of 5754 aluminum alloy was investigated.The developed kinetic model has been verified by comparing the experimental and predicted metadynamic recrystallized fraction.Figures 10 and 11 illustrate the fitted experimental results using regression analysis, and most of the experimental and predicted softening fraction have a linear relationship and show good agreement with each other.Furthermore, the statistical parameters such as the correlation coefficient (R) and the average absolute relative error (AARE) were calculated to quantitatively verify the accuracy of the developed kinetic model.The correlative expressions are shown in Equations ( 9) and (10).
where Ei and Pi are the measured and calculated softening fraction, respectively.E and P are the average values of Ei and Pi, and N is the total number of the tested samples.The correlation coefficient is a reflection of the linear relationship between the experimental and predicted data.The AARE is an unbiased statistical parameter used to evaluate the predictability of a model that can be calculated through a term-by-term comparison of relative error [31,32].
The values of R and AARE were calculated to be 0.974 and 9.306%.The results indicate the model developed here is shown to provide accurate predictions for 5754 aluminum alloy.

Conclusions
The current study was conducted to investigate the metadynamic recrystallization behavior of 5754 aluminum alloy via employing isothermal interrupted hot compression tests.
The degree of dynamic softening is quantified by relative softening, while the softening fraction due to metadynamic recrystallization is examined using the 0.2% off-stress method.A kinetics model of the studied alloy was developed here.A fundamental understanding of the metadynamic recrystallization allows for the processing variables to be controlled carefully in tandem hot rolling.The conclusions can be drawn as followed: (1) The relative softening values under different test conditions signify the occurrence of dynamic softening at each stage, and the softening fraction may approach zero with further straining at the second deformation stage.(2) For the two-pass hot compressed 5754 aluminum alloy, the restoration mechanism is governed by metadynamic recrystallization.The softening fraction attributed to metadynamic recrystallization increases with increasing deformation temperature, delay time, and strain rate.(3) The predicted results were highly consistent with the experimental ones, which indicates that the developed kinetics equation can accurately describe the metadynamic recrystallization behaviors of 5754 aluminum alloy.

Figure 1 .
Figure 1.Specimens before forming, after one step, and after a second step of forming.

Figure 1 .
Figure 1.Specimens before forming, after one step, and after a second step of forming.

Figure 2 .
Figure 2. Experimental procedure for the two-pass hot compression tests.

Figure 2 .
Figure 2. Experimental procedure for the two-pass hot compression tests.

Figure 2 .
Figure 2. Experimental procedure for the two-pass hot compression tests.

Figure 4 .
Figure 4. Typical true stress-strain curves of two-pass hot deformation under (a) delay time of 5 s; (b) delay time of 30 s; (c) delay time of 60 s; (d) temperature 450 °C and strain rate 0.1 s −1 .

Figure 4 .Figure 5 .
Figure 4. Typical true stress-strain curves of two-pass hot deformation under (a) delay time of 5 s; (b) delay time of 30 s; (c) delay time of 60 s; (d) temperature 450 • C and strain rate 0.1 s −1 .

Figure 5 .
Figure 5. Determination of the characteristics stresses used to calculate softening fraction.

Figure 6 .
Figure 6.The optical microstructures after two-pass hot deformation for various inter-pass delay time of (a) 5 s, (b) 30 s, and (c) 60 s.

Figure 7 .
Figure 7.The curves of the softening fraction and the delay time.

Figure 6 .Figure 6 .
Figure 6.The optical microstructures after two-pass hot deformation for various inter-pass delay time of (a) 5 s, (b) 30 s, and (c) 60 s.

Figure 7 .
Figure 7.The curves of the softening fraction and the delay time.

Figure 7 .
Figure 7.The curves of the softening fraction and the delay time.

1 .
Determination of nTaking the logarithm of Equation (3) of both sides, ln ln1 1 − X mdrex = C + n ln t (5)substituting the softening fraction X mdrex and the related inter-pass delay time into Equation (5).

Figure 8
Figure 8 shows the plot of ln ln 1 1−X mdrex versus lnt.The average value of material constant n can be obtained by linear fitting, which is equal to 0.763.

3. 2 . 2 .
Determination of the Dependence of t0.5 on Deformation Parameters Taking the logarithm of Equation (4) of both sides,

3. 2 . 2 .
Determination of the Dependence of t 0.5 on Deformation Parameters Taking the logarithm of Equation (4) of both sides, ln t 0.5 = ln X + m ln.

3. 2 . 2 .
Determination of the Dependence of t0.5 on Deformation Parameters Taking the logarithm of Equation (4) of both sides,

Figure 10 .
Figure 10.The comparison of the experimental and the calculated metadynamic softening fraction at different deformation temperatures.

Figure 10 .
Figure 10.The comparison of the experimental and the calculated metadynamic softening fraction at different deformation temperatures.

Figure 11 .
Figure 11.Comparison between the experimental and predicted softening fraction.