Evaluation and prediction of hot rheological properties of Ti ... - NOPR

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Indian Journal of Engineering & Materials Sciences Vol. 21, December 2014, pp. 647-656

Evaluation and prediction of hot rheological properties of Ti-6Al-4V in dual-phase region using processing map and artificial neural network Tong Wen*, Yuan-Wang Yue, Lan-Tao Liu & Jian-Ming Yu College of Materials Science and Engineering, Chongqing University, Chongqing 400044, China Received 29 August 2013; accepted 5 March 2014 Isothermal compression tests of Ti-6Al-4V are conducted in the dual-phase region at different temperatures (1053-1203 K) and strain rates (0.01-10 s-1). Processing maps based on the principles of the dynamic material model are then constructed using the experimental data. Stable and unstable regions on the maps are distinguished to evaluate the hot forming performance of the alloy. The regions suitable for hot forming are validated by the microstructure evolutions. The domain with a high power dissipation efficiency η larger than 0.3 is found to be the optimal processing region on the map at a strain of 0.7, where the temperatures range from 1090 K to 1203 K and the strain rates from 0.01 s-1 to 0.1 s-1. Moreover, an artificial neural network model with a back-propagation algorithm was developed to predict the hot rheological properties of the alloy involving complex nonlinear intrinsic relationships between the processing parameters. Theoretical processing maps are drawn by using the predicted data and then compared with the experimental maps. The results indicate that the model can track the experimental data with sound precision, and the theoretical maps can definitely give guidance to the design of hot forming process of Ti-6Al-4V in the dual-phase region. Keywords: Ti-6Al-4V alloys, hot working, plasticity, compression test

Ti-6Al-4V is a two-phase (α+β) structure titanium alloy that is widely used in the fields of aeronautics and aerospace, medical equipment, chemicals machinery, etc., because of its excellent comprehensive properties, such as low density, high specific strength, good corrosion resistance, and metallurgical stability1,2. The hot working operations of Ti-6Al-4V, such as forging and rolling, are usually concentrated in the two-phase region rather than the β region, although it has a better plasticity in the β region. This is done to obtain defect-free and homogeneous fine microstructures after forming and consequently guarantee the desired mechanical properties of the products. When combined with the interaction of phase transformation from α→β at high temperature, where the strain-softening phenomenon articulates dynamic recrystallization (DRX) and dynamic recovery (DRV), Ti-6Al-4V possesses a complex deformation performance that varies with the processing status in the α+β region. Unlike in most steels, the subsequent heat treatment has comparatively less impact on the final performance of the titanium alloy. Thus, the hot forming process of Ti-6Al-4V is of great significance for the quality of products in terms of mechanical properties. Extensive __________ *Corresponding author (E-mail: [email protected])

testing has been performed on titanium alloy, and, in general, much knowledge on the deformation modes and mechanisms involved has been obtained3-6. Nonetheless, in the forming of Ti-6Al-4V, the thermoplastic-forming process must be controlled strictly and precisely because of the narrow range of forging temperature and the sensibility to the processing conditions, such as temperature and deformation velocity. Since there is dearth of fundamental understanding of the complex influence, the forming of Ti-6Al-4V is still hard work in practice. In recent years, following the pioneering work of Prasad et al.7,8, thermal processing maps have been employed more and more to study material formability under complex hot forming conditions in a wide variety of metals. Most of the maps are based on the principles of the dynamic material model (DMM), which is considered a bridge between large plastic deformation and the evolution of dissipative microstructures in the material9-12. Nowadays, the processing map is considered an effective tool that can provide a quantitative basis for shaping the design of the process parameters13,14. Nevertheless, so far almost all the constructions of processing maps are based on experimental data, for example, the results from compressive tests15,16. Because of the limitations of physical experiments, it is difficult to count on all

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the variables in a wide scope. Furthermore, as mentioned above, the hot rheology behaviors of titanium alloy are affected remarkably by lots of factors, including the thermo-mechanical processing parameters (temperature, strain, and strain rate) and the microstructure evolution. The highly nonlinear relationships between these factors also make it hard to use the traditional regression method to deal effectively with the dispersed experimental data. Either the effect of the factors or their nonlinear relationships lead to a notable reduction in the accuracy of the analysis17. Under such circumstances, artificial neural networks (ANN) have recently been applied to describe the hot deformation processes18-22. The ANN model is a data-driven black-box model that is capable of solving highly nonlinear complex problems. It has good generalization ability. Unlike the constitutive models commonly used in finite element analysis, the ANN method does not need to derive a specific mathematical model or identify the parameters. To date, most studies have focused on predicting the flow stress for given deformation conditions based on the ANN method, with materials varying from steel18,19 to non-ferrous metals20-22. In the present study, efforts were made to obtain a comprehensive understanding of the hot rheological properties of the Ti-6Al-4V titanium alloy with a major primary microstructure of equiaxed α phase. The aim was not only to give significant experimentbased guidance to the design of hot working schedules, but also to establish an approach that can predict with reasonable precision the mechanical and workable performance of the alloy in a wide range of processing condition. First, based on a series of hot compression tests, the effects of temperature, strain, and strain rate on the hot deformation behavior of Ti-6Al-4V in the α+β zone were investigated. The observation of deformed microstructure was consulted to confirm the distribution of rheological safe and unsafe areas predicted by the processing map. Second, an ANN model was suggested to predict the flow behavior of Ti-6Al-4V using the experimental data from the hot compression tests. The theoretical processing maps were then constructed based on the predicted data. Finally, the processing maps constructed with experimental and predicted data (the former simplified as EPM, the latter simplified as PPM) were compared to verify the validity of the concept.

Experimental Procedure The as-received Ti-6Al-4V alloy had a nominal chemical composition of Ti-6.5Al-4.1V- 0.16O0.21Fe-0.03C-0.015N-0.002H. Figure 1 shows the original microstructure, which exhibits a uniform equiaxed grain with the majority of phase α. The β transus temperature was found to be at around 1260 K by thermal dilatation method. Cylinder-shaped compression specimens were cut using the wire-electrode cutting method. These specimens had a diameter of 10 mm and a length of 15 mm. The specimens were deformed compressively to a maximum reduction of 60% in height (with maximum true strain of about -0.9; the minus sign will be omitted hereafter) on a Gleeble-1500 thermo-mechanical simulator in a vacuumed environment. To reduce the friction between the surfaces of the anvils and specimens, a mixture of machine oil and graphite was lubricated on both sides of each sample. The compression conditions in the current research were Kelvin temperatures of 1053 K, 1103 K, 1153 K, and 1203 K, and the strain rates were 0.01 s-1, 0.1 s-1, 1 s-1, 3 s-1, and 10 s-1. All specimens were heated at a constant rate 10 K/s to the deformation temperature and held at that point for 90 s to ensure a uniform initial temperature and reduce the material anisotropy. As soon as correctly compressed, the samples were immediately cooled down with water to retain the deformed microstructure. Sections for optical microscopy observation were prepared by cutting the samples at the middle planes perpendicularly to the compression axis direction. These sections were then polished and etched using a standard procedure.

Fig. 1 – Primary microstructure of the as-received Ti-6Al-4V

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Fig. 2 – True strain-stress curves of Ti-6Al-4V at different compression temperatures: (a) 1053 K, (b) 1103 K, (c) 1153 K and (d) 1203 K

Construction and Identification of Experimental Processing Map of Ti-6Al-4V Hot isothermal rheological characteristics of Ti-6Al-4V

Figure 2 shows the experimental true stress-strain curves of Ti-6Al-4V at various temperatures and strain rates. Obviously, the alloy is sensitive to temperature and strain rate. The flow stress shows a complex nonlinear relationship with strain. It increases dramatically with the strain rate and decreases with the temperature. The results are in agreement with previous observations by other researchers4,5,9, with a slight deviation. This deviation is caused mostly by the diversity of the original microstructures of the specific material and the distinction of the experiment conditions, such as lubrication. Two phenomena usually occur simultaneously during the hot deformation of metals. One is the proliferation of dislocations and their interaction, which will lead to the hardening of the materials. The other is the decrease of dislocation density due to DRV and DRX, which will lead to softening. The hardening and the softening will reach a balance with the development of the deformation. It can be seen from the curves that at the earlier compressing stages beyond

the elastic deformation, work hardening is dominant. The flow stress reaches its peak quickly with a small strain, and then with the increase of strain the hardening disappears and all the flow stresses decrease with the temperature at a given strain rate. As the curves show, the hardening stages at a higher strain rate, such as 10 s-1, last longer before the stress reaches its peak value. The stress then declines obviously at the same temperature. Curves at strain rates of 3 s-1 and 1 s-1 are closely adjacent, and it can be found that there is more softening at 3 s-1, as shown in Fig. 2 a and b. The influence of strain rate on stress increases with the temperature, hence intervals between the curves increase at higher temperature, as shown in Fig. 2 c and d. The flow softening behavior observed at fast strain rates may indicate the generation of deformation heat during hot compression testing. Meanwhile, the curves are smooth at a relatively lower strain rate, such as 0.01 s-1 and 0.1 s-1. Such a limited amount of flow softening at slow strain rates can be put down to the occurrence of dynamic spheroidization of phase α, or dynamic recovery rather than dynamic recrystallization 9.

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Fig. 3 – Microstructures deformed at

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of 1 s-1,

of 0.9, and different temperatures: (a) 1053 K, (b) 1103 K, (c) 1153 K and (d) 1203 K

Figure 3 shows the microstructures of Ti-6Al-4V formed at different temperatures with a strain rate of 1 s-1 and a strain of 0.9. It can be seen that the primary phase α had less change when the temperature was 1053 K or 1103 K. However, obvious phase transformations happened at 1153 K and 1203 K, presenting a mixed structure of α+β phases with an increased volume fraction of the β phase. In titanium alloy, the crystal texture of phase α is hexagonal close-packed (HCP); for phase β it is body-centered cubic (BCC)1,2. Thus, α is the major phase and HCP slip is the basal deformation mode when the temperature is below 1153 K. When the temperature is over 1153 K, phase α gradually transforms to β and then BCC slip is strengthened. It is commonly known that the HCP structure has fewer independent operative slip systems, so the alloy would exhibit lower deformation ability when the temperatures are in a low range. Construction of processing maps based on experimental data (EPM) Approach of processing map

By utilizing the true stress-strain curves from the hot compression test, the processing map can be constructed based on the DMM presented by Prasad

et al.7,8. According to DMM theory, the whole dissipative power P in plastic deformation could be divided into two parts. These are named G and J, where G stands for the power dissipation through plastic deformation, most of which is converted into viscoplastic heat, and J stands for the power dissipation through microstructure transition, such as phase transformations, dynamic recovery, and dynamic recrystallization. The equation can be given by P= σ ε& = G+J

… (1)

where represents the true stress and represents the strain rate. The dynamic response relationship between flow stress and strain rate could be expressed as . The strain rate sensitivity m is a characteristic parameter that has an intimate relationship with the microstructure evolution during the hot deformation process7. It can be calculated as: m=

∂ (lnσ ) ∂ (lnε )

… (2)

WEN et al.: HOT RHEOLOGICAL PROPERTIES OF Ti-6Al-4V

The efficiency of power dissipation η can then be defined as n=

J 2m = J max m + 1

…(3)

The power dissipation efficiency η also characterizes the rate of the microstructure evolution during hot working. A high η-value indicates that lots of energies were consumed to execute the microstructure evolution, including dynamic recovery and dynamic recrystallization. Consequently the domain is suitable for processing. On the other hand, it is not suitable for work when the deforming conditions belong to an unstable zone with a low η-value17. According to the principle of maximum entropy production rate, an instability criterion can be proposed to represent the larger plastic flow body based on the extremum principles of irreversible thermodynamics, given by 8 m ) m +1 +m ≤ 0 δ ln ε&

δ ln ( ξ (ε& ) =

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regularly according to the processing conditions. It can be seen that η is small in the domains with low temperature and high strain rate, while it becomes large at higher temperature. Regions with maximum η at high temperature and high strain rate shift to the right of the processing map with the increasing strain. This indicates that stable deformation with larger strain in a zone with a high strain rate needs higher temperature. The white domain in the map represents the safe region for processing. The shaded domain, which implies the negative instability parameter, represents the unstable region. The unstable region shifts with strain and locates mostly in the area with lower temperature, or in the area with moderate temperature and strain rate. Figure 5 presents the relationships between η-value and strain. The pictures show that the changes of η are not notable at strain rates of 0.1 s-1 and 1 s-1. On the other hand, there is an obvious change with the strain at strain rates of 0.01 s-1 and 10 s-1, implying that the microstructure evolution is severe under these situations. Verification of processing map with deformed microstructure

… (4)

where ξ (ε& ) is a dimensionless instability parameter that can be obtained with Eq. (4) under varied deformation temperatures and strain rates by using and m at different strain rates. A contour map of ξ (ε& ) , namely, the instability map, then can be drawn using the interpolation method.

Finally, the processing map can be constructed by superimposing the instability map over the power dissipation map7. Experimental processing maps

Figure 4 shows the processing maps of Ti-6Al-4V with strains at 0.3, 0.5, and 0.7. The numbers on the contour lines represent values of η, which change

As an example, the processing map of Ti-6Al-4V at the strain of 0.7 in Fig. 4(c) is roughly divided into two instability domains, i.e., A and B, and three stability domains, i.e., C, D, and E. Local plastic flow, adiabatic shear band, and wedge crack, among others, are known to be the major unstable phenomena in the hot deformation of metal12,16. To interpret, validate, and confirm the hot processability predicted by the processing map, a series of detailed metallographic observations at different processing regions are employed. In domain A of Fig. 4(c), the temperature ranges from 1060 K to 1153 K and the strain rate from 1.78 s-1 to 10 s-1. The power dissipation efficiency η reaches the minimum of 0.07. Figure 6(a) shows the metallographic microstructure corresponding to this domain with a temperature of 1103 K and a strain rate of 10 s-1. Areas that are densely populated with a fine

Fig. 4 – Experimental processing maps of Ti-6Al-4V under different strains: (a) ε=0.3, (b) ε=0.5 and (c) ε=0.7

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α phase can be found among the regions where nodulizing α phase appears. At a high strain rate, the heat generated by the plastic deformation cannot transmit to the lower temperature region in time. A

transient sharp rise of local temperature occurs, leading to deformation instability characterized by the occurrences of localized dynamic recrystallization, etc. A similar observation was made by Park et al.9,

Fig. 5 – Variation of η with ε at different deformation temperatures: (a) 1053 K, (b) 1103 K, (c) 1153 K and (d) 1203K

Fig. 6 – Microstructures of Ti-6Al-4V under different deformation conditions: (a) 1103 K/10 s-1, (b) 1103 K/1 s-1, (c) 1153 K /0.1 s-1, (d) 1053 K/10 s-1

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Fig. 7 – Microstructures of Ti-6Al-4V under different deformation conditions: (a) 1153 K/0.01 s-1, (b) 1203 K/0.01 s-1 and (c) 1203 K/10 s-1

who found that distortions in microstructure become severe with increasing strain rate and that local plastic deformation can be promoted due to the low thermal conductivity of the alloys. As to the unstable domains of B, the temperature ranges from 1053 K to 1085 K and the strain rate from 0.01 s-1 to 1.78 s-1, or the temperature ranges from 1085 K to 1160 K and the strain rate from 0.1 s-1 to 1 s-1. Figures 6(b) and 6(c) show the microstructures in these domains. It can be seen that a small amount of phase transformation occurs and the grains size decreases with increasing temperature. However, there is some elongated α within the balled grains and the structure is much uneven, indicating that part of the areas is not good at spheroidization due to the combination of forming speed and medium temperature. There is a narrow stable region C in the vicinity of temperature at 1053 K and strain rate of 10 s-1, as shown in Fig. 4(c). In this domain, the power dissipation efficiency η increased in lower temperature and higher strain rate, which is contrary to the manner of that when the strain is 0.3. The possible reason is that under the conditions in this domain there are apparent appearances of microstructure defects associated with the instability, which would result in an abnormal value of η. Such a domain is usually considered a metastable region that is not suitable for processing10. It can be seen from Fig. 6(d) that local deformation appears. Therefore, in terms of the microscopic deformation structure, poor forming quality exists when the deforming conditions belong to such an unstable zone with low power dissipation efficiency. In Fig. 4(c), there are two stable domains with the highest η-value on the processing map, namely, D and E. Domain D has the peak η-value of about 0.5. The temperature ranges from 1090 K to 1203 K and the strain rate from 0.01 s-1 to 0.1 s-1. Figure 7(a) (1153 K/0.01 s-1) and Fig. 7(b) (1203 K/0.01 s-1) show the microstructures of this domain. In Fig. 7(a), the nodulizing and refinement of phase α is prominent

because of the low strain rate and long deforming time at 1153 K. Phase transformation will lead to a certain number of lamellar structures in the phase boundary. The emergence of the lamellar structure suggests that part of phase α with HCP-type crystals is transformed into phase β with BCC-type crystals, which have better plasticity compared with the HCP type. Thus, these transformations can improve the formability of the material. In Fig. 7(b) the higher volume fraction of the lamellar structure at higher temperature (1203 K) will degrade the softening effect of globularization and lead to more sluggish subsidence of the flow stress, as shown in Fig. 2. The duplex microstructures comprising lamellar structure and primary phase α have good mechanical properties. Therefore, the domain can be considered an optimal processing region. Figure 7(c) shows the deformed microstructure of domain E at 1203 K/10 s-1. The η-value in this domain increases from 0.26 to 0.42. At the same temperature, the transformation from primary phase α to α+β at a high deforming rate is less than that at the lower rate. Simultaneously, the dislocations within some regions are difficult to offset under such condition. The distortion energies increase, which leads to a more obvious nodulizing and refinement effect of phase α. Nevertheless, as shown in Fig. 2, the flow stress of Ti-6Al-4V increases dramatically with the strain rate. Meanwhile there might be potential defects such as adiabatic shear band at a high strain rate8. Thus, conducting the processing at a high deformation velocity is usually not recommended. In the processing map of Ti-6Al-4V at a strain of 0.6 constructed by Luo et al.5, the instability region concentrated mainly in the area of temperature varying from 1090 K to 1185 K and strain rate varying from 0.01 s-1 to 1.0 s-1. In the map constructed by Park et al.9, at a strain of 1.0, the recommended optimum condition for thermo-mechanical processing comprises a temperature of 1123 K and a strain rate of

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Fig. 8 – Correlation between experimental and predicted flow stress by the ANN model -3

-1

Fig. 9 – Statistical analysis of the relative error by the ANN model

10 s . These conclusions are close to that of the current study and agree with the recommended conditions of the so-called isothermal forging that is suitable for the forming of titanium alloy.

correlation between the experimental and the predicted data had to be assessed. The correlation coefficient (R) is introduced as an evaluator, which is expressed by

Construction and Evaluation of Processing Maps based on ANN Modeling

R R=

Development of the ANN model

The back-propagation (BP) algorithm uses the known input-output pairs to adjust the weights and biases for the purpose of minimizing the error by utilizing gradient descent during the training procedure. More details about the ANN can be found in corresponding literatures18-21. In the present study, the inputs of the model are strain (ε), strain rate ( ), and deformation temperature (T), and the output of the model is flow stress (σ). A three-layer BP ANN architecture was used. Before the model was constructed, 20 experimental true stress-strain curves as shown in Fig. 2 were employed, and 31 sets of data on each curve were collected. The total 620 data sets were then divided into training data sets and testing data sets. Of these, 480 data sets were used to train the model. The other 140 data sets at true strain from 0.2 to 0.8 with an interval of 0.1 were used to test network performance. To determine the best number of neurons in the hidden layer that can be further implemented, a trial-and-error procedure with two neurons in the hidden layer at the beginning was employed. The hidden layer consisting of 14 neurons, which gave a minimum mean square error (MSE)18, was considered the optimal structure for the prediction of the flow stress of Ti-6Al-4V. Evaluation of the ANN model

To evaluate whether the trained model has good fault tolerance and generalization ability, the linear

∑iN=1 ( Ei − E )( Pi − P ) N

Σ i =1 ( Ei − E ) 2 ( Pi − P )2

… (6)

where Ei and Pi are the experimental and predicted value, respectively; and are the mean values of Ei and Pi, respectively; and N is the number of strain-stress samples. Other parameters for evaluating the performance of the model include average relative error (AARE), root mean square error (RMSE) and relative error19. Figure 8 illustrates the correlation of experimental and predicted data. With regard to perfect prediction, all the data points should be located in the line of inclination angle of 45°. It can be seen that most of the data points are closely gathered in the fitting line. The correlation coefficient R reaches 0.99951. The AARE is 1.45% and the RMSE is 2.80 MPa. The high R-value indicates a good correlation of the experimental and the predicted data sets, suggesting that the ANN model has excellent learning ability and can describe the heat rheological properties of the alloy. Figure 9 shows the relative error of the experimental and the predicted values. It follows a typical normal distribution, with the values changing from -5.12% to 4.45% and mainly concentrated in the range of -3% to 2%. Predicted flow stress

Figure 10 compares the experimental strain-stress curves with the flow stress predicted by the ANN model under different conditions. The relative errors obtained by the model vary from 4.45% to -4.5%. It can be observed that the predicted results can accurately track

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the experimental data involving the complex nonlinear relationship between the processing parameters and the phenomena of hardening and softening. Predicted processing maps

Taking into account the hot deformation features of Ti-6Al-4V in the hardening stage before stress reaches the peak, and the softening stage while stress remains relatively stable, theoretical processing maps

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were drawn based on the predicted data with strains of 0.3 and 0.7 at different temperature and strain rates, respectively, as shown in Fig. 11. A comparison of the maps in Fig. 11 and Fig. 4 shows that the η of EPM and PPM have a similar variation, either in work hardening or strain softening areas. It starts to increase from the low-temperature/high-rate area to the high-temperature/high-rate and high-temperature/ low-rate areas until it reaches the maximum. When

Fig. 10 – Comparison of the predicted and experimental stress of Ti-6Al-4V at deformation temperature: (a) 1053 K, (b) 1103 K, (c) 1153 K and (d) 1203 K

Fig. 11 – Predicted processing map of Ti-6Al-4V at different strain: (a) ε=0.3 and (b) ε=0.7

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the strain is 0.3, the minimum η of PPM and EPM are approximately 0.08 and 0.09, while the two maxima of PPM and EPM are about 0.37, 0.46, and 0.39, 0.47, respectively. When the strain is 0.7, the minimum PPM and EPM η are approximately 0.08 and 0.07, while the two maxima of PPM and EPM are about 0.31, 0.43, and 0.38, 0.5, respectively. Moreover, the instability regions in PPM and EPM are basically at the same position. Nevertheless, the instability area on the PPM is slightly larger, whereby it is more conservative or safer in terms of avoiding the vandalism behavior of material in practice.

predicting the processability of the alloy in various conditions, first by employing a limited group of experimental data to construct the ANN model, which can predict the macroscopic mechanical properties even outside of the experiment conditions, and then constructing the processing maps with the combination of experimental and predicted data.

Conclusions (i) The experimental true stress-strain curves of Ti-6Al-4V clearly indicate that the alloy is sensitive to temperature and strain rate. The flow stress shows a complex nonlinear intrinsic relationship with strain, temperature, and strain rate as well. This relationship is essentially correlated with the microstructures evolution, such as the α→β phase transformation and the strain-softening phenomenon articulating DRX and DRV. (ii) Experimental processing maps at 0.3, 0.5, and 0.7 of logarithmic strain were constructed. The stable and unstable deformation domains were determined to evaluate the forming performance of the alloy. In the map at a strain of 0.7, domain D with a high power dissipation efficiency η larger than 0.3 is considered the optimal processing region, where the deformation temperature ranges from 1090 K to 1203 K and the strain rate from 0.01 s-1 to 0.1 s-1. The predicted domains of flow instabilities, namely, domains A, B, and C, were also validated by the microstructures involving local DRX, elongated phase α, or local deformation. (iii) The predictability of the BP ANN model on the flow stress of Ti-6Al-4V was evaluated in terms of several statistical parameters. The evaluations are of the characteristic of small fluctuations and high correlation between the predicted and the experimental data, suggests that the ANN model has a strong prediction performance on the complex nonlinear hot rheological behavior of Ti-6Al-4V. (iv) A comparison of the processing maps based on experimental and predicted data showed them to have similar distribution and congenial extremum of η, and almost the same position of instability regions. To recapitulate, it is possible to create a pattern for

References

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