Mechanical Properties and Constitutive Modeling of 6063-T5 Aluminum Alloy Over a Wide Range of Strain Rates and Temperatures

In this study, the stress–strain relationship of 6063-T5 aluminum alloy over a wide range of temperatures and strain rates was investigated. First, quasi-static tensile tests and high temperature split Hopkinson pressure bar (SHPB) tests were carried out for 6063-T5 aluminum alloy, where, the experimental temperature ranged from room temperature to 350 °C, and the dynamic strain rate was 500 s−1–6000 s−1. Second, the effects of temperature and strain rate on the mechanical properties of the materials were discussed. The results showed that the 6063-T5 aluminum alloy exhibited clear temperature softening and strain rate hardening effects, but the strain rate softening effect could also occur under certain temperature conditions. Third, the fracture morphology of the tensile specimen and the metallographic structure of the dynamic compression specimen under different temperatures and strain rates were analyzed. Finally, by improving the fitting method and constitutive model, the modified Johnson–Cook constitutive model for the 6063-T5 aluminum alloy was obtained. Compared to the traditional model, the modified Johnson–Cook constitutive model could predict the mechanical behavior of the 6063-T5 aluminum alloy accurately under high temperature and dynamic conditions.


Introduction
6063-T5 aluminum alloy is a heat-treatable alloy in the Al-Mg-Si series alloy with moderate strength, allowing it to be widely used in various industrial and civil construction profiles.However, engineering structures may be subjected to dynamic load and high-temperature effects, such as explosions or fire, during their service life.Therefore, to accurately predict and evaluate structural performance, it is critical to study the mechanical properties of materials under high strain rate and hightemperature conditions.
The mechanical properties of metal materials are closely related to the plastic strain, temperature and strain rate.The split Hopkinson pressure bar (SHPB) device is commonly used to assess the dynamic behavior of materials over a wide range of strain rates [1][2][3][4].Using a heating device, the SHPB device can also be used to investigate dynamic mechanical properties under different temperature conditions.
Xueling Fan et al. [5] studied the compressive stress-strain relationships of 6061 Al alloy over a wide temperatures range (293-673 K) and strain rates (1 × 10 −3 to 1 × 10 4 s −1 ).The results showed that the dynamic mechanical behavior was highly dependent on temperature under relatively low strain rates or on strain rate at relatively high temperatures.Liu et al. [6] also used an improved SHPB apparatus to investigate the mechanical behavior of Zr-based bulk metallic glass at elevated temperatures from 423 to 683 K under a high strain rate from 5000 s −1 to 10 4 s −1 .Experimental results revealed that the failure stress decreased with increasing temperature, and the strain rate dependency was relatively small.Visser et al. [7] carried out impact compression tests on low carbon steel specimens at temperatures between 293 K and 923 K and strain rates between 1000 s −1 and 5000 s −1 .The resulting stress-strain curves were partitioned into thermal and athermal stress components, and the role of twin boundaries was discussed in terms of their interaction relation with dislocation motion and grain subdivision.
Li et al. [8] conducted low, intermediate and high strain rates experiments on flat smooth and notched tensile specimens extracted from dual phase steel sheets, and an SHPB testing system with load inversion device was used to achieve high strain rates.Li et al. [9] designed experiments conducted on Ti700 alloy at strain rate of 10 4 s −1 and temperatures between 20 °C and 800 °C to determine the influence of cold-contact-time (CCT) on the temperature variations within the specimen.Niu et al. [10] investigated the dynamic compressive mechanical properties of 30CrMnSiNi2A steel at 30-700 °C and 3 × 10 3 -10 × 10 3 s −1 .The experimental results showed that the specimens had clear temperature sensitivity at 300 °C and the strain rate hardening effect at a high strain rate was not significant with increasing temperature.Lee et al. [11] compared the impact plastic behavior of three steels with different levels of carbon content under strain rates ranging from 1.1 × 10 3 s −1 to 5.5 × 10 3 s −1 and temperatures ranging from 25 to 800 °C.The effects of the carbon content, strain rate and temperature on the mechanical responses of steels were evaluated.
The Johnson-Cook (J-C for short) constitutive model has clear physical meaning, simple expression and strong versatility, and has been widely used to describe the mechanical behavior of metal materials in large strain, high strain rate and wide temperature ranges.While, J-C model is a purely phenomenological model that considers strain hardening, strain rate strengthening, and thermal softening to be independent microscopic mechanisms, and does not include the influence of strain history on the rate-temperature effect.Therefore, many scholars have proposed revised models based on J-C model to improve the limitations.Seo et al. [12] investigated the effects of temperature as well as the strain and strain-rate on Ti-6Al-4 V. Furthermore, a modified J-C constitutive equation were determined by adding a ratio of the flow stresses just prior to and following recrystallization.Rule et al. [13] modified the strain rate term by adding a fractional term to describe the strain rate strengthening effect of the segmented strain rate.Wang et al. [14] added the normal distribution function form to the temperature term of the J-C model based on the model of Rule [13], thus phenomenologically describe the abnormal stress peak phenomenon in a certain temperature range.Iqbal et al. [15] carried out a detailed investigation to study the constitutive behavior of Armox 500T steel under varying stress, strain rate and temperature conditions.The material parameters of J-C flow and the fracture model were calibrated and validated by numerical simulations.To obtain a more accurate J-C fracture model, Erice et al. [16] used ABAQUS/standard and LS-DYNA numerical codes to calibrate the experimental data of FV535 steel obtained from quasistatic tensile tests and dynamic compression tests.Wang et al. [17] investigated the dynamic behavior of Inconel 718 under an ultrahigh strain rate and high temperature during the cutting process.For the strain rate softening effect found at high strain rate, the values of C in the second bracket of J-C model were fitted as the function of temperature, then the modified J-C model was established.
In this study, 6063-T5 aluminum alloy was taken as the research object.Quasistatic tensile tests were first conducted under a strain rate of 0.035 s −1 and temperature range of 25 °C to 350 °C.Then dynamic compression experiments in the strain rate range of 500 s −1 to 6000 s −1 and the same temperature rang were performed using a high temperature SHPB device.The effect of temperature and strain rate on the mechanical properties of materials were discussed, and the fractures of the tensile and dynamic compression specimens under different working conditions were analyzed by scanning electron microscopy (SEM) and metallography, respectively.Based on the data obtained from the above experiments, a modified J-C constitutive model was established to describe the nonlinear mechanical behavior of the 6063-T5 aluminum alloy material over a wide range of strain rates and temperatures.

Test Specimens
The test specimens had a cylindrical rod shape and were all processed from the same batch of 6063-T5 aluminum alloy bars.Table 1 shows the chemical composition of the 6063-T5 aluminum alloy.The sizes of the specimens conformed to the Chinese standard of GB/T 228.1-2010 [32] and GB/T 228.2-2015 [33], and the dimensions and physical drawings of the specimens are shown in Fig. 1.

Experimental Equipment and Methods
The quasi-static tensile tests were carried out on an MTS810 microcomputer control electronic testing machine, and the experimental equipment is shown in Fig. 2. The main body of the equipment was composed of a heat-insulated box, temperature controller and cross beam, with the temperature control precision of the equipment reaching ± 0.5 °C.The grips and specimen could be heated simultaneously by the electrothermal furnace, so a temperature gradient on the surface of the specimen can be avoided.Before the experiment, the specimen was installed on the test machine, and the installation of the specimen is shown in Fig. 3a.After the specimen was clamped by grips, the high-temperature extensometer buckle was placed in the middle of the specimen to measure the strain and elastic modulus during the tension process.In addition, copper wire was used to fix the working end of the thermocouple to the middle of the specimen to monitor the surface temperature of the specimen during testing.The remote end of the thermocouple was connected to a thermometer (Fig. 3b), which displayed the surface temperature of the specimen during the test in real time.Subsequently, the heating temperature was set by the temperature controller, and after the specified temperature was reached, the time of heat preservation was at least 20 min before loading.During force loading, the strain rate was controlled at 0.035 s −1 .Seven temperature conditions were used in the tests, namely room temperature, 100 °C, 150 °C, 200 °C, 250 °C, 300 °C, and 350 °C.Testing at each temperature was repeated three times, and the average value was adopted.

Results Analysis
Figure 4 illustrates the fracture of tensile specimens at different temperatures.It can be found intuitively that the size of the fracture cross-section did not continue to decrease with an increase in temperature.Figure 5 shows the variation trend of the reduction of area with temperature.The reduction of area was defined as the percentage of the change in cross-sectional area of the necking area at the time of specimen fracture compared to the original cross-sectional area.With an increase in temperature, the reduction area firstly increased, then decreased, increased again, and finally reached minimum value at 200 °C.It is related to intermediate temperature embrittlement [34].In the tensile test, temperature changes could generate uncertainty in the material test.According to the high-temperature tensile test under each determined strain rate, material brittleness reached its maximum at a certain temperature.
Figure 6 shows the fracture surface morphologies of the tensile specimens at different temperatures and magnifications by SEM.A large number of dimples were distributed on the fracture surface at room temperature and 150 °C, and the dimple sizes were larger in some positions.By contrast, a greater number of dimples and deeper dimples were observed at 150 °C than at room temperature, which indicated that the plasticity of the material increased with temperature.However, when the temperature reached 200 °C and 250 °C, the dimple size became smaller and shallower and no extra-large dimples appeared.Figure 6c and e shows that the dimples were mostly distributed on the grain boundaries.Figure 6d and f illustrates noticeable torn edges on the fracture surface, where both sides of the torn edge were relatively smooth and the dimples were not apparent, which conformed to the characteristics of quasi-cleavage fracture.This also indicated a relative increase in brittleness.In addition, secondary cracks appeared at some locations, which was partly due to intergranular fracture, and the fragmentation of the inclusion phase or separation from the matrix could also result in the generation of cracks.The appearance of cracks resulted in a decrease in matrix continuity, and the plasticity of the material was further reduced.Macroscopically, this was consistent with the variation trend of reduction area.As the temperature further increased to 350 °C (Fig. 6g), the morphology of dimples differed from that of those at room temperature.At low temperatures, there were many dimples with a dense distribution; while at high temperatures, the number of dimples was relatively small and the size was relatively large.The appearance of larger dimples indicated that the material plasticity increased again to its maximum plasticity.
Through conversion, the true stress-strain curves at different temperatures under quasi-static conditions were obtained, as shown in Fig. 7.It can be seen that 6063-T5 aluminum alloy exhibited a significant temperature softening phenomenon, where the strength of the material decreased with the increase of temperature, including mechanical properties such as yield strength and tensile strength.In addition, the elastic modulus also slightly decreased.During the process of temperature increase, the difference in flow stress between 200 °C and 250 °C was significant, which indicated that when the temperature was increased to 200 °C, the material was more sensitive to temperature.The material stress-strain curves had no yield platform, and when the temperature did not exceed 150 °C, a clear strain hardening phenomenon could be observed.At room temperature, when the strain were 0.02, 0.04 and 0.06, the stress were 238 MPa, 252 MPa, 262 MPa, respectively; and at 100 °C, the true stresses at strains of 0.02, 0.04, 0.06, 0.08 and 0.10 were 219 MPa, 228 MPa, 235 MPa, 238 MPa, 240 MPa, respectively.And the stress-strain curve could be expressed approximately by a linear hardening material model.However, when the temperature exceeded 150 °C, the strain hardening phenomenon disappeared, and the stress-strain curve could be approximated by an ideal plastic model.
According to the stress-strain curve, the yield strength (R p0 ) and reduction factors (ratio of yield strength at different temperatures to the ratio at room  2. It can be seen that the yield strength at 350 °C was only 11% of the value at room temperature, indicating a significant temperature softening effect.
Figure 8 presents the histogram and fitting curve of yield strength of the 6063-T5 aluminum alloy with temperature changes.According to the histogram, a more significant reduction in yield strength occurred when with the temperature exceeded 200 °C, and based upon research by Summers [35] on the variation trend of aluminum alloy yield strength with temperature, the Farazdaghi Harris functions can be well used to characterize the nonlinear stress-strain process, thus, this function was selected to fit the yield strength under different temperature conditions, and the following functional relation was obtained: 3 High Temperature SHPB Tests

High Temperature SHPB Apparatus and Experimental Techniques
The high temperature SHPB apparatus used in this study mainly consisted of a strike bar, incident bar, transmission bar, heating apparatus, and data processing system, as  shown in Fig. 9.The strike bar driven by high pressure gas impacted on the incident bar at a certain velocity and an incident wave (ε i ) formed in the incident bar.When the incident wave was transmitted to the end face of the specimen, the entire specimen was compressed due to the inertia effect.At this point, a portion of the incident wave was reflected back to the incident bar, forming the reflected wave (ε r ), while the remainder of the wave passed through the specimen to become a transmission wave (ε t ) and continued to propagate in the transmission bar.All waves were measured by a strain gauge attached to the corresponding bar.
The SHPB principle should meet the assumption of a one-dimensional elastic wave and the assumption of stress uniformity within the specimen, where the strain ε, strain rate ε , and stress σ could be obtained from the following formulas: A physical diagram of the high temperature SHPB device is shown in Fig. 10.The cylindrical specimens (ϕ5 × 3mm) used in the test were also processed from 6063-T5 aluminum alloy bars, as shown in Fig. 10b.To avoid the influence of temperature on the bar, a sleeve was designed.The specimen was fixed on the sleeve by an iron wire, as shown in Fig. 10c, and then the sleeve was arranged on the end of the bar.In this manner, only the specimen was heated during the heating process, avoiding the influence of temperature on the bar.An electrothermal furnace was used for heating, and its temperature was controlled by a temperature controller, as shown in Fig. 10d and e.In addition, a thermocouple was inserted into the furnace to monitor the surface temperature of the specimen, as shown in Fig. 10f.After the specimen was heated to the required temperature and maintained for 20 min, an impact test was performed, and the waveform data were measured by the strain gauges (Fig. 10g) affixed to the incident and transmission bar.By recording and processing the data using the strain meter (Fig. 10h) and special software, then the dynamic stress-strain curves could be obtained.

High Temperature SHPB Tests Results and Analysis
Figure 11 shows the specimens after impact compression at ′ = 2000 s −1 and ′ = 6000 s −1 ( ′ denotes the strain rate).After compression, the section of the specimen increased, while the height decreased.By contrast, the degree of compression deformation of the specimen at a higher strain rate is obviously greater.Additionally, the section of the specimen essentially increased with increasing temperature, but this trend was not constant.At the strain rate of 2000 s −1 , the cross section of the specimen reached the minimum value at 200 °C, and the same situation occurred at 150 °C under the strain rate of 6000 s −1 .This indicated that intermediate temperature embrittlement also occurred in the specimen under dynamic conditions.These deformed specimens were sectioned parallel to the compression axis for microstructure observations, and a schematic diagram of the microstructure observation location is shown in Fig. 12. Figure 13 shows the metallographic micrographs of the specimens under different dynamic compression conditions, where the upper and lower directions of the figures consisted of the dynamic 133 Page 12 of 23 compression direction.As shown in Fig. 13a, the material was composed of an α matrix phase and strengthening phase (black particles), and the strengthening phase particles were randomly distributed on the matrix.Under the condition of dynamic compression, metal streamline is generated inside the material, as shown in Fig. 13b-d.The metal streamline was the fibrous tissue formed by the elongation or compression of inclusions or second-phase particles in the metal whose direction was generally aligned with the direction of the maximum principal strain.Figure 13b shows that the particles of the strengthening phase were linearly distributed along the compression direction, and some particles were refined.When the temperature increased to 350 °C, as shown in Fig. 13c, the metal streamline became denser, and was not entirely parallel to the compression direction, but bent toward the radial side.This indicated that the plastic flow of the material increased and the middle of the specimen expanded slightly to the radial side.When the strain rate was 6000 s −1 and the temperature was 28 °C, as shown in Fig. 13d, metal streamline bending was more noticeable than that in the other images.It can be seen from Fig. 11b that the specimen was compressed into a flat piece and plastic deformation was more severe.Figure 14 presents the true stress-strain relationships of the 6063-T5 aluminum alloy at different temperatures under a certain strain rate.Under dynamic conditions, the 6063-T5 aluminum alloy also showed significant temperature softening effect, where Figure 15 shows the true stress-strain relationships of the 6063-T5 aluminum alloy at different strain rates under a certain temperature.It can be seen that the difference in flow stresses at different strain rates under the same temperature condition was  relatively minor, indicating that the material was more sensitive to temperature.Nevertheless, the material illustrated strain rate hardening effect, namely the strength of the material increased with the increasing of strain rate.However, at 350 °C, the flow stress at 4000 s −1 strain rate was greater than that at 6000 s −1 .It can be preliminarily inferred that at higher temperatures, the 6063-T5 aluminum alloy potentially showed a strain rate "softening" effect.Table 3 presents the yield strength of the 6063-T5 aluminum alloy at different strain rates and temperatures.Because the dynamic stress-strain curve greatly fluctuated, the original stress-strain curve was converted into a bilinear model by linear fitting, the intersection point was made perpendicular downwards, and the stress value at the intersection point with the original stress curve can be used as the yield strength value.Figure 16 shows the variation trend of yield strength with changing of temperature and strain rate.In Fig. 16a, It can be seen that temperature had a certain influence on the strain rate effect of materials, the yield strength of the material at different strain rate decreased with the increase of temperature, namely when the temperature increased, the strain rate effect weakened.Additionally, the trend lines of yield strength variation at strain rates of 4000 s −1 and 6000 s −1 were very close, which indicates that the sensitivity of the material to strain rate decreased with increasing of strain rate.Under the condition of high strain rate, the change in yield strength with further increase in strain rate was reduced, and even the yield strength was reduced.The effect of ratetemperature coupling effect on material yield stress could be more intuitively observed in Fig. 16b, and there was a significant strain rate effect below 300°C.When the temperature was above 300 °C (under the condition of strain rate > 4000 s −1 ), the strain rate effect showed the opposite pattern.It could be preliminarily inferred that under high temperature and high strain rate conditions, the strain rate effect was not obvious or even disappeared.

J-C Constitutive Equation
The J-C model comprehensively described the work hardening effect of metal materials, the strain rate effect, and the temperature softening effect, as expressed by [36]: where σ is the flow stress; represents the plastic strain; ε * =ε′/ ε 0 denotes dimen- sionless strain rate (ε′ is strain rate and ε 0 is a user defined reference strain rate); T * = (T − T 0 )/(T m − T 0 ) indicates the dimensionless homologous temperature (T denotes the current absolute temperature.T 0 refers to the reference temperature, gen- erally taken as the ambient temperature, and T m represents the melting temperature).
Traditionally, the strain rate of quasi-static tests can be taken as the reference strain rate (0.001 s −1 in this work).According to the actual experimental and material situation, the ambient temperature and melting temperature of the material are 25 °C and 660 °C respectively.The five material constants (A, B, n, C, Fig. True stress-strain curves at different strain rates under a certain temperature m) were obtained by fitting experimental data.The parameters A, B and n were generally obtained according to the material yield strength and strain hardening curve fitting under quasi-static conditions ( ε * = 1) at room temperature (T* = 0).Then Eq. 5 could be transformed as follows: where A corresponds to the yield strength value of the material at this point of time, and B and n could be obtained by fitting the strain strengthening stage curve with Eq. 6.
Parameter C could be obtained by fitting the yield strength values of materials under different strain rates at room temperature.Through transformation of the equation, Eq. 5 finally became: where according to Eq. 7, the slope of the curve obtained by fitting is the value of parameter C.   Parameter m could be acquired by fitting the yield strength corresponding to different temperatures under quasi-static conditions.Similarly, Eq. 5 could be transformed into the following equation: where, the left side of Eq. 8 has a linear relationship with ln(T * ), and the slope of the curve obtained by fitting is the parameter m value According to the above parameter calibration method, the five parameters of the J-C material model were determined and are listed in Table 4, under a reference strain rate of ε 0 =0.001 s −1 .

Comparison Between the J-C Model and Experimental Results
The stress-strain curves of the J-C model and experimental results were compared, as shown in Fig. 17 with strain rates of 2000 s −1 and 4000 s −1 taken as examples.As shown in figure, the J-C model had difficulty accurately predicting the experimental data, with a significant difference between the results.Specifically, with an increase in strain, the stress in the plastic stage of the J-C model continuously increased, which was quite different from the experimental curve where the stress remained unchanged in the plastic stage.
The reasons for the above differences were related to the fitting method.The morphology of the J-C model curve was mainly related to the first term of the J-C constitutive equation (Eq.5), and the constitutive parameters in the first term, namely A, B and n, which were obtained by fitting the room temperature stress-strain data under  quasi-static conditions.However, as mentioned above, under quasi-static conditions, and when the temperature did not exceed 150 °C, the stress-strain curve showed an clear strain hardening stage, which was not found in the stress-strain curve under dynamic conditions.Therefore, it was difficult to predict the dynamic mechanical behavior of the 6063-T5 aluminum alloy using the J-C model fitted by traditional methods.

Modification of the J-C Constitutive Equation and Fitting Method for the 6063-T5 Aluminum Alloy
Considering the differences in the stress-strain curve characteristics of the 6063-T5 aluminum alloy under dynamic and quasi-static conditions, the constitutive parameters were calibrated with a strain rate of 500 s −1 as the reference strain rate.Of note, dynamic impact consisted of an adiabatic process, in which the impact compression work was partially converted into heat energy, causing the temperature of the specimen to increase.The temperature increase caused by this process could be calculated by the following formula [17]: where the parameters η, ρ, and C v denote the coefficient of heat conversion, density and specific heat, respectively.Under the influence of adiabatic temperature increase, the material further softened, so in the plastic stage, the slope of the curve decreased with the increase of strain, and the curve showed a convergence trend.
It is a fact that the adiabatic temperature increase calculation formula in Eq. 9 involves many parameters, which is inconvenient to calculate.To simplify the calculation, the temperature change caused by impact insulation was written in linear form with equivalent plastic strain, i.e.ΔT = K .Considering the softening of the material caused by a temperature increase in Eq. 9, the traditional J-C constitutive equation was modified as follows: The third term of the modified J-C model had an extra parameter K. Therefore, when 500 was taken as the reference strain rate, the parameters of the modified J-C constitutive model are shown in Table 5.
Figure 18 shows the comparison between the modified J-C model and the experimental curve when the reference strain rate was 500 s −1 .According to the

Conclusion
A series of static/dynamic experiments and microscopic inspections were conducted on the response behavior of 6063-T5 aluminum alloy under wide temperature (room temperature to 350 °C) and strain rate (500 s −1 -6000 s −1 ) conditions, and exploring the influence of rate-temperature coupling effects on the mechanical properties of aluminum alloy from the macro and micro levels.On the basis of the classical J-C constitutive model, the modified J-C constitutive equation model coupling the strain rate and temperature effect was constructed by considering the effect of adiabatic temperature increase.The conclusions could be summarized as follows: 1.The 6063-T5 aluminum alloy showed an evident temperature softening effect under quasi-static and dynamic conditions.With an increase in temperature, the flow stress of the material gradually decreased.Under the quasi-static condition, the material sensitivity to temperature increased when the temperature reached 200 °C, while under the dynamic condition, the flow stress relatively uniformly decreased with the increase of temperature.2. The 6063-T5 aluminum alloy exhibited an overall strain rate hardening effect.However, temperature had an influence on the strain rate effect.When the temperature reached 300-350 °C or higher, the material flow stress dropped with the strain rate increased from 4000 s −1 to 6000 s −1 , and the strain rate showed softening effect.In addition, when the strain rate reached 4000 s −1 , the continuous increase in strain rate had limited change effect on material strength.3. The fracture morphologies of the tensile specimens at different temperatures showed that numerous dimples were distributed on the fracture surface.When the temperature of the 6063-T5 aluminum alloy was 200 °C -250 °C, the dimple size decreased and secondary cracks appeared, indicating that the plasticity of the material decreased and brittleness increased.Under dynamic compression, metal streamlines parallel to the compression direction appeared in the specimen.With an increase in temperature and strain rate, the compression deformation of the specimens intensified, and the metal streamline became more compact and bent in the radial direction.4. In terms of stress-strain curve morphology, the stress-strain curve of the 6063-T5 aluminum alloy under dynamic conditions showed no clear strain hardening stage, and this stage could still be observed under quasi-static conditions when the temperature did not exceed 150 °C.Therefore, by selecting the dynamic strain rate as the reference strain rate and considering the adiabatic temperature increase effect, the modified J-C model could more accurately describe and predict the mechanical behavior of the 6063-T5 aluminum alloy under high temperature and dynamic conditions.

Fig. 4 Fig. 5
Fig. 4 Fracture of the specimens after tensile tests

Fig. 12 1 Page 14 of 23 Fig.
Fig. 12 Schematic diagram of the microstructure observation location

Fig. 16
Fig. 16 Variations in the yield strength of 6063-T5 aluminum alloy with temperature and strain rate.(a) Variation trend of yield strength with temperature; (b) Variation trend of yield strength with strain rate

( 11 ) 9 Fig. 18
Fig.18 Comparison of the true stress-strain curves between modified the J-C model and experimental results

Table 1
Chemical compositions of the 6063-T5 aluminum alloy (wt%) Dimensions of the tensile specimens and physical drawing (mm)

Table 3
The yield strength (R p0 ) of the 6063-T5 aluminum alloy at different strain rates and temperatures

Table 4
Comparison of the true stress-strain curves between the J-C model and experimental results

Table 5
The constitutive parameters of the modified J-C model with 500 s −1 as the reference strain rate