Modeling of the hot deformation behavior of a high phosphorus steel using artificial neural networks

Accepted Manuscript Title: Modeling of the hot deformation behavior of a high phosphorus steel using artificial neural networks Authors: Kanchan Singh, S.K. Rajput, Yashwant Mehta PII: DOI: Reference:

S2352-9245(17)30007-8 http://dx.doi.org/doi:10.1016/j.md.2017.03.001 MD 24

To appear in: Received date: Revised date: Accepted date:

29-10-2016 16-3-2017 21-3-2017

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Modeling of the hot deformation behavior of a high phosphorus steel using artificial neural networks Kanchan Singha, S.K.Rajputa,*, Yashwant Mehtab a

Department of Mechanical Engineering Institute of Engineering and Technology, Jhansi

284128, India b

Department of Metallurgical and Materials Engineering, Indian Institute of Technology

Roorkee, 247667, India *Corresponding author. Tel.: +91-510-2320321: Fax: +91-510-2320349 E-mail address: [email protected] Graphical abstract

Fig. 1. Artificial neural network model

Fig. 2. CCT diagrams for high phosphoric steel

Fig. 3. True stress vs. true strain for high phosphorus steel obtained from hot compression at (a) 750 ºC, (b) 900 ºC, and (c) 1050 ºC, at different strain rates

ABSTRACT The hot deformation behavior of high phosphorus steels were investigated through thermomechanical simulations for temperatures ranging from 750 ºC to 1050 ºC and with strain rates of 0.001 s-1, 0.01 s-1, 0.1 s-1, 0.5 s-1, 1.0 s-1 and 10 s-1. Using a combination of temperature, strain and strain rate as input parameters and the obtained experimental stress as a target, a multi-layer artificial neural network (ANN) model based on a feed-forward back-propagation algorithm with ten neurons is trained, to predict the values of flow stress for a given processing condition. A comparative study of predicted stress using ANN and experimental stress shows the reliability of the predictions. A processing map for true strain of 0.7 was plotted with the help of the predicted values of flow stress, and the optimum processing conditions were investigated, at low

temperatures and moderate to high strain rates, as well as at moderate to high temperatures and low to moderate strain rates. Keywords: Hot workability; Dynamic material model; Feed forward back propagation; Artificial neural network; Processing map.

1. Introduction Delhi iron pillar shows an excellent corrosion resistance property due to the presence of relatively high amount of phosphorus. Phosphorus forms a protective layer on the surface of the pillar and resists further corrosion [1]. Phosphorus creates brittleness in the steel by segregating at grain boundaries. However adding a small quantity of carbon in phosphoric irons displaces phosphorus from the grain boundary due to a site competition effect and thus increases the cohesion. Additional heat treatment processes at high temperature in the dual phase region also remove phosphorus away from grain boundaries and result in improved ductility and toughness [2]. High phosphorus steel with small amounts of carbon (0.001 to 0.005 wt.%) show good ductility and strength [3]. Ductile-to-brittle transition temperature also increases due to the presence of phosphorus in steel [4]. In structural and salty marine environment applications, high phosphorus steel shows better corrosion resistance as compared to thermo-mechanical treatment (TMT). In a concrete environment, high phosphorus steel is not susceptible to stress corrosion cracking as compared to mild steel [5]. During the industrial processing of any metal and alloy, the hot deformation process is an important step. Many researchers performed hot working of different materials in order to determine the required load for the deformation process, to understand the dynamic material models (DMM), to explore the dynamic recrystallization (DRX) and also to develop a processing map to investigate the safe hot working domains [6]. Dynamic recrystallization provides better workability in materials by a simultaneous softening process and reconstructing the microstructures. The evaluation of the workability of materials includes both the measurement of the resistance to the deformation process and the limit of plastic deformation, before the occurrence of cracking and fracture. The initial performance

index during hot deformation is a flow stress. Therefore, during hot deformation of a material, a complete description of the workability is specified by its flow stress. The workability of the material depends on different working parameters (like temperature, strain, and strain rate). Different techniques have been proposed to evaluate the workability of a material in the form of processing maps [7]. The processing maps are developed by the superimposition of power dissipation efficiency and instability maps, and are plotted as a function of temperature and strain rate at a specific strain. These maps are utilized in industry for different metal working processes to improve the product quality, and the maximum efficiency domain is used to identify the optimum working parameters for hot deformation of a particular material [8]. Frost and Ashby plotted the material response in terms of a deformation mechanism map [9]. Raj extended the Ashby concept by constructing a processing map for two damage mechanisms, cracking at grain boundaries at triple junctions and generation of cavities at hard particles in a soft matrix [10]. Later, Prasad et al. overlapped two maps (i.e. power dissipation efficiency map and instability map) to the developed processing map with the dynamic materials model (DMM) approach. During plastic deformation of a material, the total applied power is the product of stress and strain rate. According to Prasad, the total applied power is a summation of G and J, and the physical interpretation of G (the power dissipation content in plastic deformation), and J (power dissipation co-content in microstructure transitions) are based on thermodynamic principles with the efficiency of power dissipation is confirmed by microstructural investigation [11]. The power dissipation per unit volume, P, can be expressed by Prasad et al. [12] and shown in Eq. (1). 



PT ,  G  J     d   d , 0

(1)

0

where  is flow stress and  is strain rate. The efficiency of power dissipation, η, is the ratio of J and the maximum possible value of J as expressed in Eq. (2), which shows the workability of a particular material for different processing conditions.



J J max



2J 2m  P m 1

(2)

The strain rate sensitivity parameter m is one of the most important control parameters and is tested for the lowest strain rate. For various alloy systems at given deformation conditions, m varies as a function of temperature and strain rate. The strain rate sensitivity (m) is calculated using Eq. (3).

  ln   m   ln    ,T

(3)

Eq. (4) expresses the approach developed by Ziegler et al. [13] according to which the flow instability occurs when,

D D   

(4)

D (  ) is the power dissipation function. The instability domain occurs during the plastic flow proposed by Prasad et al. [12] and is given by Eq. (5).

   

 ln m m  1 m0  ln 

(5)

where the instability parameter    is a dimensionless parameter. In order to develop the instability map,    is evaluated as a function of temperature and strain rate. Ji et al. performed hot compression tests on Aermet100 steel for the temperature ranging from 800 ºC to 1200 C with constant strain rates from 0.01 s-1 to 50 s-1 up to true stain of 0.9 and used artificial neural network (ANN) to predict the hot deformation behavior. Ji et al. observed that the ANN model predicts the deformation behavior, dynamic recrystallization (DRX), and dynamic recovery (DRV) accurately and efficiently [14]. Li et al. conducted hot compression tests on modified 2.25 Cr-1Mo steel for 60% height reduction using strain rates of 0.01 s-1 to 10 s -1

for the temperature range 1173 K to 1473 K. Based on experimental results, ANN and

constitutive equation models were compared [15]. Liu et al. conducted isothermal compression tests of 300M steel on a Gleeble® 3500 simulator machine for a wide range of strain rates from

0.1 s-1 to 25.0 s-1, temperature ranging from 1173 K to 1413 K and strain up to 0.69. ANN and regression methods were used for modeling of flow stress. The result shows that the ANN model is better than the regression model [16]. Li et al. studied the hot compressive behavior of 28CrMnMoV steel on a Gleeble-3500 thermo mechanical simulator with strain rates ranging from 0.01 s-1 to 10 s-1 and at temperatures ranging from 1173 K to 1473 K up to 60% height reduction. A comparative study shows that relative error for constitutive equations were -13.60% to 10.89% whereas for ANN model error is in the range of -3.66% to 3.46% [17]. Rajput et al. performed hot compression tests on plain carbon steel for wide strain rates ranging from 0.01 s-1 to 20 s-1 and temperature range from 750 ºC to 1050 ºC, and they observed that the maximum power dissipation efficiency regime lies in 750 ºC and 875 ºC for strain rates 0.01 s-1 to 0.1 s-1 [18]. Zhang et al. investigated hot deformation behavior of 9Cr-oxide dispersion-strengthened (ODS) steel for a temperature ranging from 1050 ºC to 1200 ºC and strain rates 0.001 s-1 to 1.0 s1

on a Gleeble 1500D simulator, and observed optimum processing domains with the help of a

processing map [19]. Rajput et al. performed uniaxial hot compression test on a low carbon TiNb micro-alloyed steel for the temperature ranging from 750 ºC to 1050 ºC and strain rates 0.01 s-1 to 80 s-1. Power dissipation maps were developed and correlate with the microstructures [20]. Rajput et al. studied the hot deformation behavior of AISI 1016 steel by hot compression on a Gleeble® 3800 thermomechanical simulator machine for a wide range of strain rates and temperatures and determined the workability zones with the help of a processing map using DMM and modified dynamic materials model [21]. Regarding the hot deformation behavior of high phosphorus steel limited data is available. In the present work, the isothermal compression tests of high phosphorus steel is conducted in the temperature ranging from 750 ºC to 1050 ºC at constant strain rates of 0.001 s-1 to 10 s-1 up to true strain of 0.7 using thermo-mechanical simulator Gleeble® 3800. The artificial neural network is trained with experimental data obtained from hot compression experiments to predict the deformation behavior of high phosphorus steel. Processing maps were constructed with the help of ANN predicted data to suggest the optimum hot working conditions for the material.

2. Experimental methods 2.1. Material and methods

A solid plate casting containing ferro-silicon, Ferro-phosphorus, graphite, and aluminum shots (as a de-oxidizer) was prepared with dimensions 200 mm x 400 mm x 40 mm in a sand mold, and small pieces of 30 mm x 40 mm x 30 mm were cut from casting with the help of a power hacksaw. These small pieces were hot forged at 950 ºC and prepared with a 12 mm diameter rod which was used to prepare the hot compression specimens. Table 1 shows the chemical composition of high phosphorus steel.

Table 1 Chemical composition (in wt.%) for high phosphorus steel. Element

Si

Composition 0.26

P

C

Mn

Cr

Ni

Cu

Al

W

Fe

0.13

0.05

0.2

0.13

0.07

0.02

0.003

0.02

99.12

2.2. Phase transformation characterization The continuous cooling transformation (CCT) is used to determine the extent of transformation in terms of critical temperatures. The CCT test was performed using a Gleeble® 3800 thermo mechanical simulator machine. To perform CCT experiments, the specimen of 10 mm diameter and 85 mm length was used. The specimen was heated with the heating rate of 5 ºCs-1 to an austenitization temperature of 1050 ºC for a 10 s duration, followed by cooling with a cooling rate of 1 ºCs-1 to room temperature. Ar3 and Ar1 temperatures show the first and second deviation points during the cooling process and shown in the CCT diagrams, respectively. 2.3. Hot compression test Hot compression tests were carried out on specimens of dimension 15 mm length and 10 mm diameter with the help of a Gleeble® 3800 thermo-mechanical simulator at constant strain rates ranging from 0.001 s-1 to 10 s-1. The deformation temperature was in the range of 750 ºC to 1050 ºC in steps of 50 ºC and heated with the heating rate of 5 ºCs-1, up to austenitization temperature of 1050 ºC. The above processing parameters are used to simulate the rolling operations [22]. Ktype thermocouple was spot welded at the mid span of the specimens to control the temperature during the entire process. To minimize the friction and temperature gradient between the samples and ISO-T anvil, graphite foil and a nickel based lubricant were used. Each specimen was

deformed up to a true strain of 0.7. In-situ water quenched the specimen to preserve the deformed microstructure.

3. Modeling with artificial neural network To predict the material behavior at different processing conditions, artificial neural network (ANN) is a quite efficient computing tool. ANN can be used to solve complex problems efficiently like physical processes, and algebraic and optimization problems. Unlike the regression method, an ANN does not require any mathematical model. It has the capability to learn from a given set of data and recognizes patterns without any prior assumptions about their behavior, and generalize their performance for a new set of data to predict the whole hot deformation behavior [23]. Artificial neural networks consist of a number of small fundamental units known as neurons, which interact within the network through parallel weighted connections, and to minimize the target error to adjust its weights and biases. To investigate the flow behavior of high phosphorus steel ANN is developed by using feed-forward back propagation (BP) algorithm with Levenberg-Marquardt (L-M) training algorithm. The BP algorithm is an iterative gradient training algorithm which involves minimization of mean square error between predicted output and targeted output during the training network. LevenbergMarquardt (L-M) algorithm is an effective method for solving different non-linear optimization problems. To optimize the training process, the training function ‘Trainlm’ adjust weights and bias according to the Levenberg-Marquardt technique in the BP algorithm [24]. A total of 252 experimental input-output data points were employed to develop the present ANN model, consisting of three layers: input, output and hidden layers as shown in Fig. 1.

Fig. 1. Artificial neural network model To train the network temperature, strain rate and strain are assumed as input data and experimentally recorded flow stress as output data. Among these data sets, 80% of data are used in training and remaining is used in testing and validation. Training is performed by taking ‘Trainlm’ as training function and ‘tan sigmoid’ and ‘pure linear’ as transfer function for input and output layers, respectively. The learning rate was 0.5, and momentum was 0.7 during the training of the network. Since the network’s performance depends on the learning rate, momentum and number of iterations. At lower learning rates, the predictions are in lower agreement with the experimental values. The parameter momentum does not have a considerable effect on the accuracy of prediction but it affects the learning rate [25]. The optimal architecture of the ANN is found to be 3-10-1, where ten shows the number of neurons in a hidden layer. The number of neurons in the hidden layer is decided by the hit and trail method. There is no rigid rule to find the number of neurons in the hidden layer. But from Nworks Professional II Plus, the number of neurons in the hidden layer is calculated using Eq. (6). h

Numberoftr ainingset 10m  n 

(6)

Where h shows the number of neurons in the hidden layer, n is the number of neurons in the output layer and m is the number of neurons in the input layer. Thus, the ANN network with a single hidden layer with three input parameters and with 252 training data requires approximately seven neurons in a single hidden layer. After repeated trials by changing the

number of neurons in the hidden layer from 5 to 12, it was found that a network with one hidden layer consisting of ten hidden neurons gives a minimum RMS error. The performance converged to a final acceptable solution, and thus considered as the optimal configuration to predict the flow stresses of high phosphorus steel. Further, the predictability of the ANN model is expressed in the form of relative error and correlation coefficient (R2). For efficient training of the network before training both the input data sets and output data sets were normalized in the range of 0 to 1 using Eq. (7), because small and large magnitude mixed experimental data will confuse the learning process [26].     min   0.1  0.8     max   min

  

(7)

where X is the original value and Xʹ is the normalized value. Xmax and Xmin are maximum and minimum values of quantity X, respectively. Since, the values of experimental true strains are already in the range of 0 to 1, therefore there is no need to normalize.

4. Results and discussion 4.1. Phase transformation A CCT curve for high phosphorus steel was obtained after the CCT test with the help of a Gleeble® 3800 machine. The values of Ar3 and Ar1 temperatures are investigated as 965 ºC and 790 ºC respectively, from corresponding CCT diagrams (Fig. 2).

Fig. 2. CCT diagrams for high phosphoric steel. 4.2. Flow behavior The sample flow curves at deformation temperatures of 750 ºC, 900 ºC and 1050 ºC for strain rates ranging from 0.001 s-1 to 10 s-1 of high phosphorus steel are shown in Fig. 3. These flow curves are plotted from the data obtained during hot compression tests at different deformation temperatures. It has been observed from the flow curves of high phosphorus steel that at a particular strain rate the flow stress decreases with the increasing temperature. Also, for a constant temperature, the flow stress decreases with decreasing strain rate (Fig. 3). The true stress-strain curves initially show the strain hardening followed by softening at the deformation temperatures of 750 ºC for strain rates of 0.001-0.01 s-1, 900 ºC for strain rates of 0.001-0.5 s-1 and 1050 ºC for strain rates of 0.001-1.0 s-1. The softening (decrease in flow stress) is due to the dynamic recrystallization (DRX) mechanism. The peak stress shows the start of the DRX process followed by a decrease in the value of flow stress. As the strain rate increases or decreases with deformation temperature, the stress peak shifted towards the higher strain. That is because, at higher strain rates and/or at lower deformation temperatures, the work hardening rate increases as compared to the work softening rate. In general, with the increase in strain rate or decrease in deformation temperature, the flow stress gradually increases for the entire strain range for testing of specimens. At higher temperature and low strain rate (1050 ºC at 0.001 s-1), the multiple dynamic recrystallizations (MDRX) peaks were observed. This is due to developing new grains at the cost of old grains.

(a)

(b)

(c) Fig. 3. True stress vs. true strain for high phosphorus steel obtained from hot compression at (a) 750 ºC, (b) 900 ºC, and (c) 1050 ºC, for different strain rates. 4.3. ANN result For different strain rates, ANN predicts the value of flow stress with good correlation coefficient for BP algorithm of high phosphorus steel as shown in Figs. 4a and b. The predicted flow stress values were compared with experimental flow stress, and corresponding relative error (RE) are calculated using Eq. (8).  E  Pi    100% RE   i  Ei 

(8)

where Pi and Ei are predicted and experimental value for a given conditions. Calculated relative errors are in the range of ±3.5%.

(a)

(b)

Fig. 4. Correlation between the experimental flow stress and predicted flow stress for the (a) Training data, (b) Testing data. The artificial neural network model is developed to simulate the effect of different deformation temperatures and strain rates on flow behavior of high phosphorus steel. The variations of predicted and experimental values of flow stress for deformation temperatures 750 ºC, 900 ºC, and 1050 ºC are clearly shown in Figs. 5a, b, and c. It is found that the developed predicted flow curves using fully trained ANN follow the experimental flow curves very closely.

(a)

(b)

(c)

Fig. 5. Comparisons between the experimental (colored lines) and predicted (dotted points) flow curves with the help of ANN at different strain rates for deformation temperatures (a) 750 ºC, (b) 900 ºC, and (c) 1050 ºC, of high phosphorus steel. 4.4 Sensitivity Analysis Sensitivity analysis is used to further validate each model, and examine the contribution of each input variable to the output for each individual case in the trained data. Different methods were available to determine the relative importance of the various inputs. One of the methods is the Weights method as proposed by Garson [27]. L

Qik

N

 ((w  w ) )   ( ((w  w )

Where

ij

j 1

N

L

i 1

j 1



N r 1

wrj

rj

r 1

ik

N

ij

r 1

rj

ik

))

(9)

denotes the sum of connection weights between input neurons N and hidden

neurons j. Qik represents the percentage of impact of the input variable xi on the output variable yk in relation to the rest of the input variables. Table 2. Relative importance of the different input parameters. Input

Temperature (°C)

Strain rate (s-1)

Strain

Relative importance (%)

42.41%

33.33%

24.26%

Since the relative importance of temperature is 42.41%, thus the temperature is the most important parameter among all input parameters. 4.5. Processing map and microstructural evolutions Optical micrographs of undeformed high phosphoric steel are shown in Fig. 6. The microstructure mainly consists of ferritic grains. For metallographic preparation, the hot deformed specimens were cut along the vertical compression axis. For optical light microscopy, the specimens were polished using different grades of polishing papers and cloth. The specimens were etched with 2% nital etchant to reveal the microstructures and Leica DMI 5000M microscope was used for light optical microscopy.

Fig. 6. Initial microstructure of high phosphorus steel. The microstructures of the water quenched hot deformed specimens at different deformation temperatures and strain rates up to true strain of 0.7, after austenization at 1050 ºC for 10 s are shown in Fig. 7. Microstructure mainly consists of ferrite grains which may be formed before, during and after hot deformation along with a little ferrite-carbide mixture. Austenite grains with higher percentage of carbon were converted into martensite after quenching which results in increase in hardness of the specimen. The average hardness of the specimen consists of ferritecarbide mixture phase (compressed at 750 ºC for a strain rate of 0.001 s-1) is found to be 490 HV, which is equivalent to plain carbon steel containing martensite phase with 0.2% carbon. This is due to the site competition effect of phosphorus in steel, as the amount of carbon content in

austenite grains exceed the average value of 0.05% C in the bulk [28]. The hot deformations were performed in ferritic, duplex phase and austenite regions. At higher temperature, the hardness of ferrite grains is less than austenite grains. It is observed from the microstructures that at high temperature and low strain rate, DRX is occurring. At 750 ºC (lower than Ar1), ferrite exists before the onset of deformation. At 900 ºC, proeutectoid ferrite exists before the onset of deformation and ferrite is also formed after deformation. At 1050 ºC, ferrite is formed after deformation. Hot deformation at high strain rate (10 s-1) in the ferrite region (below 900 ºC) produces elongated and recovered grain structures. The microstructure obtained at deformation temperature of 900 ºC is in the duplex phase region. The amount of ferrite in the specimen deformed at 900 ºC is less than that of the specimen deformed at 750 ºC. The microstructure of specimen deformed at 750 ºC and strain rate of 10 s-1 shows the dynamic recovery (Fig. 7), whereas the specimen deformed at 900 ºC and strain rate of 10 s-1 shows the complete recrystallized grain structure as shown in Fig. 7. The microstructures obtained at deformation temperatures of 1050 ºC for all strain rates show the recrystallized grains (Figs. 7). The microstructural studies advocate that dynamic recovery (DRV) takes place at low temperatures and/ or high strain rates, whereas dynamic recrystallization (DRX) takes place at low strain rate and/ or high temperature regions.

Fig. 7. Microstructures of high phosphorus steel specimens deformed at different processing conditions. The power dissipation efficiency map of high phosphorus steel is shown in Fig. 8. Predicted data obtained from the ANN model are utilized to plot the processing map. This map is plotted in the axis of temperature and log strain rate and the iso-efficiency (η) lines indicate the power dissipation efficiency. During hot deformation, the efficiency shows the relative rate of entropy production, which characterizes the dissipative microstructure at different strain rate and temperatures. The domains of dynamic recrystallization and power dissipation in material through microstructural changes are initially represented by these power dissipation maps. DRX domains are favorable for the hot deformation of the material since the intrinsic workability is enhanced by the process of softening [29]. Positive values η are shown in the entire testing range of these power dissipation maps. Maximum dissipation efficiency in the stable domains represents better processing condition. Thus power dissipation maps can help in the optimizing process.

Variations of the instability parameter ξ in the axis of temperature and log strain rate are used to generate the instability map as proposed by Prasad et al. [12]. To show the unstable region in the instability map, instability criteria ξ < 0 is applied. The instability map for true strain of 0.7 (shaded area) are shown in Fig. 9. For safe hot working, the instability domains are avoided. The processing map is generated by superimposing the power dissipation efficiency map and instability map (Fig. 10). The safe workable regions of the high phosphorus steel are as follows: at low temperatures and moderate to high strain rates; and moderate to high temperatures and low to moderate strain rates. At low temperatures and high strain rates, the DRX of austenite takes place. Furthermore, the flow stress curves show softening towards a steady state region after the approaching peak, which represents DRX behavior (Fig. 3). At the beginning of deformation, the flow stress increases rapidly due to rapid multiplication of dislocation and work hardening dominates over the dynamic softening. The tendency of nucleation and growth of new grains is increased at low strain rates and/or high temperatures (i.e. at low Zener-Hollomon parameter) [21]. Under these conditions, the value of η is moderate to high and predicted the flow stability. The processing map gives a view of deformation mechanisms along with the workable window (processing conditions), that can be useful for the industrial applications.

Fig. 8. Power dissipation efficiency map of high phosphorus steel.

Fig. 9. Instability map of high phosphorus steel.

Fig. 10. Processing map of high phosphorus steel for true strain 0.7.

5. Conclusions In present work, the isothermal hot compression tests of high phosphorus steel were conducted in wide range of temperatures and strain rates. These experimental data were utilized to develop

multi-layer artificial neural network (ANN) models based on a feed forward back propagation algorithm. The following conclusions are drawn from this work. 1. The optimal configuration of developed ANN model is 3-10-1 and the relative error is in the range from ±3.5%. A predicted result from ANN model shows close agreement with the experimental data. 2. The flow curves of high phosphorus steel shows dynamic recrystallization at low strain rate and/or high temperatures, whereas hardening is shown at low temperatures and/or high strain rates and also correlate with microstructural study. 3. Processing maps are developed and the optimum processing condition were investigated, at low temperatures and moderate to high strain rates; and moderate to high temperatures and low to moderate strain rates.

Acknowledgement The authors wish to thank to Indian Institute of Technology, Roorkee for its support received to complete the whole work.

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Fig. 1. Artificial neural network model. Fig. 2. CCT diagrams for high phosphoric steel. Fig. 3a. True stress vs. true strain for high phosphorus steel obtained from hot compression at 750 ºC, for different strain rates. Fig. 3b. True stress vs. true strain for high phosphorus steel obtained from hot compression at 900 ºC, for different strain rates. Fig. 3c. True stress vs. true strain for high phosphorus steel obtained from hot compression at 1050 ºC, for different strain rates. Fig. 4a. Correlation between the experimental flow stress and predicted flow stress for the training data. Fig. 4b. Correlation between the experimental flow stress and predicted flow stress for the testing data. Fig. 5a. Comparison between the experimental (colored lines) and predicted (dotted points) flow curves with the help of ANN at different strain rates for deformation temperature 750 ºC, of high phosphorus steel. Fig. 5b. Comparison between the experimental (colored lines) and predicted (dotted points) flow curves with the help of ANN at different strain rates for deformation temperature 900 ºC, of high phosphorus steel. Fig. 5c. Comparison between the experimental (colored lines) and predicted (dotted points) flow curves with the help of ANN at different strain rates for deformation temperature 1050 ºC, of high phosphorus steel.

Fig. 6. Initial microstructure of high phosphorus steel. Fig. 7. Microstructures of high phosphorus steel specimens deformed at different processing conditions. Fig. 8. Power dissipation efficiency map of high phosphorus steel. Fig. 9. Instability map of high phosphorus steel. Fig. 10. Processing map of high phosphorus steel for true strain 0.7.