Investigations of The Hybrid Effects of The Operational Parameters In The Radial Forging Process Based On The Validation of The Hardness Test

In this study, considering all the parameters in radial forging and a three-dimensional model has been simulated using the finite element method. By implementing an elastoplastic state for the specimen tube, parameters such as friction type, residual stress distribution, effective strain distribution, material flow velocity and its effect on the neutral plate and the distribution of force in the die have been studied and analyzed. The effects of angle on the quality and characteristics of the specimen and the longevity of the die have also been obtained. Experimental results have been used to confirm the accuracy of the simulation. The results of the hardness test after forging were compared with the simulation results. Good agreement between the results indicates the accuracy of the simulation in terms of hardness. Therefore, this validation allows confirming the other obtained results for the analysis and prediction of various components in the forging process. After the validation and confirmation of the results through the hardness test, the hardness distribution was obtained by considering temperature changes and the effective strain on the specimen.


Introduction
Radial forging process (RFP) is a type of open die forging that the product has surrounded by four dies. Thus, this machine is designed for round products such as tubes, shafts, stepped shafts, axes, gun bars and rifle barrels. Reducing the diameter of specimens is the main purpose for using radial forging. Accordingly, the specimen is surrounded by four dies with special feed rates and rotational angles. Thus, when feeding stops, these dies reduce the diameter and deform the specimen via frequent strokes. Based on deformations, there are variations in specimen dimensions in both the radial and axial directions. In other words, geometry changes occur in both directions: in the radial direction, which changes the radius, and in the longitudinal direction, which changes the hollow shaft length.
Farahani et al. [3] found the optimum design profile of the die. Based on this study, they applied two methods of analysis (FEM and the slab method) and compared the results of these two methods for conical and curved specimens. In this comparison between the analytical and numerical methods, the results showed only a 6% difference. They also claimed that by enhancing the angle and plug angle up to 20°, the normalization of the die presser by plug pressure will decrease. In order to estimate of total load except for FEM, the upper bound method can calculate the total force within RFP. Thus, Ghaei et al. [4,5] investigated the effective parameters of RFP in terms of forging load in order to determine the upper boundary limit. The influence of die angle on loading deformation and other parameters of die geometry was demonstrated. Moreover, they studied RFP without a mandrel through FEM. Accordingly, they presented variations of thickness, axial feeding, die angle, percentage of reduction and amount of axial and hoop stress by using the mandrel in two directions. They illustrated that not using a mandrel increases stress in both directions. Finally, they claimed that by enhancing the percentage of reduction, the peak of axial stress decreases. At hardening, the parameters such as plastic deformation and temperature have direct affection. Therefore, Groche and Krech [6] expressed the relation between strain and hardening is one of the essential phenomena during the cold processes that can impact directly on the total load. Studies performed through the sensor element in the process with two separate mandrels have shown that neglecting the hardening zone for certain materials with a high hardness coefficient leads to a deviation in the residual stress up to 30%. In the aspect of designing of radial forging machine and its components. Hebdzyński and Herrmann et al. [7,8] designed a machine included 4 levers and one eccentric sleeve while a ball-andsocket joint supported the levers. Within the new design, they studied the effect of die angle and feed rate, claiming that the forging force decreased. As well as, the die surface in order to improve the reduction zone has been designed. It was shown that by increasing the amplitude factor, the axial forging force will decrease, also specified that the designed tools do not require lubricating material. Also, Kocich et al. [9] investigated the multiplier bar within an Al/Cu/Al structure. They analyzed the total force and microstructure behavior through simulation and experiments. According to the results, the total force depends on the length of the multiplier bar while the maximum force is located at the midpoint in the axial direction. The length of the specimen can affect friction between various layers. Due to the optimization of die geometry, Lahoti et al. [11] examined die parameters, illustrating the coordinates of the neutral plane relative to die geometry. They claimed that varying the die length can increase the metal flow by shifting the neutral plane to the die exit zone. In order to hardness study within RFP Lim et al. [12] presented the microstructure, hardness and diameters of the bar after the swaging process through an experimental study. Accordingly, they showed that the density of the material increased by decreasing the grain size and the hardness and diameter reduction have a direct relationship.
To the analysis of RS, strain, the effect of friction coefficient, Liu et al. [13,14] investigated RFP through 2D FEM simulation. The most variations in RS occurred in the axial direction when increasing the feed rate while the hoop stress criteria are very sensitive to variations in the reduction rate. At first, the final strain is reduced by enhancing the friction value and then enhanced after the extreme point. Due to the nature of RFP, the optimal value of each parameter should be adjusted according to the material and other parameters, but the changing trend is almost constant. Accordingly, the drawing force is decreased by increasing the die angle; after an increase of almost 6°-8°, the drawing force will increase through the drawing bar, Mahdavi and Haghighat [15]. As well as, the maximum reduction on the bar and strain hardening are directly proportional. While most scientists have studied through the 2D mathematical model that cannot cover all variations during the process.
In this regard Moumi et al. [16] studied the material flow of the swaging process via FEM. The neutral plate was subjected to a variety of friction and feed velocities. Moreover, this simulation, which was based on a 2D dimension cloud, describes various process parameters. By increasing the velocity of feeding, the rate of neutral plate location change decreases. One of the essential boundary conditions in order to the simulation of RFP is the assumed flow material within the process. Therefore, Pantalé and Gueye [17] investigated the Ludwik and Johnson-Cook laws of 2D material behavior. The elastoviscoplastic equation is unable to describe the strain rate in cold forging, while the Johnson-Cook law can describe material behavior for cold forging in terms of the strain rate. They show that the maximum thickness occurs with a 17% reduction in specimen diameter when operating without a mandrel.
The investigation of the microstructure of forged tube can present the impressive criteria during the process, such as die geometry. Besides, the analysis of micro hardness can be used as a validation method. Thus, Sanjari et al. [19,20] claimed through a microstructural investigation, by increasing the friction coefficient, the homogeneity of deformation will increase. Moreover, they showed that increasing the friction factor can increase the effective strain plus the variations of strain range will also increase. On the other hands, to obtain minimum inhomogeneity and radial force, they used FEM results for optimization via Taguchi neural networks and validated by experimental hardness tests. They thus showed that high friction on the inner side is the cause of high inhomogeneity. The die angle makes the most contributions to the optimized parameters.
The material displacement is simulated through three approaches: parallel velocity, continuous velocity and FEM. Based on the results, FEM has the highest accuracy and the parallel method has the lowest when describing the distribution of displacement. Also, the calculation of the field velocity of material continuously through the upper band method can provide more accurate predictions than the parallel velocity field while showing the material's streamline, Wu et al. [22,23]. They also illustrated the location and movement of the neutral plane with different diameter reductions via the upper bond method. Also, the convex value at the end of the model increases if the reduction rate and feed rate increase and also, the material flow more than the feed rate depends on the reduction rate.
While the FEM have fewer errors than the upper bound method based on validation by experimental outcomes, Yang et al. [24] analyzed radial forging with rectangular die and specimens through the upper bound method and FEM. They showed that by increasing the die angle, the axial flow of the material will decrease. Due to the wide range of RFP applications, Zhang et al. [24] utilized RFP to join tubular parts. They showed that the length of overlapping can increase the connecting strength; however, if the necking for aluminium increases by more than 45%, the aluminium will fail.
Although in the previous investigation, the FEM and parameters impact have been considered, they have neglected the interaction of the parameters with each other or the implementation of the most accurate model and method. Therefore, it is necessary to examine this complex process through variations in the essential parameters that influence the process and to take a comprehensive view of the effects of these changes on the specimen. Therefore, a 3D visco-elastoplastic model was chosen, as it predicts and characterizes this process and all factors affecting it with high accuracy. In addition, the results were validated through the two parameters of total load and micro hardness. The experimental and simulation results are in agreement, indicating the accuracy of the simulation and prediction process.

Parameters and Methodology of Radial Forging Process
RFP is one of the basic tools for metal deformation. This machine includes four dies, which surround the specimen and make consecutive strokes on it in order to increase material strength. There are many types of radial machines with different work functions, such as hot or cold forging, hydraulic or mechanical stroking and rotary swaging. The radial forging equipment implemented in the simulation is shown in Fig. 1. The mandrel is fixed to the specimens and then four dies deform the product with consecutive strokes. The quality and dimension precision depend heavily on the process parameters. These parameters directly affect the longevity of the die and forging machine by helping to calculate the residual stress and principal stress on the other components. As such, investigating die geometry through 3D finite element simulation, which can present all interactions between the equipment during operation, is essential. Moreover, regardless of the geometric characteristics of the workpiece, other end-product features, such as residual stress and microstructure, can be affected by the design criteria of the radial forging machine. The geometry parameters of the die are presented in Fig. 2.
In this figure, the three sections of the die are shown. These have three duties: sinking, forging and sizing. The die angle has direct effects on sinking and forging. It can also change the coordinates of the neutral plane according to the material flow. The section of the die has a direct relationship with the feed rate and homogeneity deformation of the specimen's surface. The important factors in RFP such as total force, die angle, type of friction and value of the coefficient friction can have a principal role in microstructure hardness, material flow, residual stress and the amount of increased strength of the specimen. Therefore, these factors are discussed below via a comparison between different types of friction and the value of parameters.
Two types of friction are considered: coulomb (sliding) and constant shear (sticking). The coulomb law describes the contact forces between two objects under elastic deformation. However, these objects can be elastic-plastic: one is elastic and the other is rigid during elastic deformation. Moreover, the simulation of sheet forming has been recommended for this type. The frictional stress is calculated to describe the contact of two plastic or porous objects by the flow stress of the object. The frictional force in the coulomb law model is defined by: = where is frictional stress, P is the interface pressure between two bodies and is the friction factor. (1) Constant shear friction includes highly precise measurement and modeling of bulk-forming simulations. The frictional force in the constant shear law is defined as follows: where m is the frictional coefficient and is the normal yield stress of the material. This states that friction is a function of the yield stress of the deforming body.
The material used in the simulation was DIN-16CrMo4 steel. The material parameters are shown in Table 1.
The initial forging temperature was 900°C. In the current study, the flow stress was obtained through the Johnson-Cook equation:  As mentioned, parameters such as residual stress can have a direct impact on the strength of the specimen and its longevity. Residual stress is a function of multiple factors such as temperature, die angle, total force and friction that the effect of these factors has presented and analyzed separately. Thus, material flow velocity, one of the factors used for calculating the microstructure of the material and the amount of hardness, is examined in the following sections. Moreover, the effect of die angle on the neutral plane coordinates via material velocity and the location of the neutral plane relative to the die zone is presented. In terms of the friction, the effects of different values of coefficient friction on temperature, residual stress and specimen quality are shown. The most accurate and most suitable types of friction have been determined by comparing the simulation results for two types of friction and their effect on forging force. It is worth mentioning that the type of friction has been determined via using the simulation results closest to the actual results. In this investigation, the simulation has been validated by comparing the experimental hardness values and the simulated hardness values. Specimen hardness itself is a function of different parameters however it is expressed here using temperature and effective strain. For this purpose, a hardness test was designed to measure hardness at several points along the specimen. Sonmez and Demir [21] measured the effective strain values at several points along with the specimen. Therefore, the hardness was calculated via the hardness function and measured values. Finally, as simulation verification, the experimental and measured graphs were compared. Other outcomes of the simulation could be cited, such as residual stress and the analysis of other influences on specimen quality. In general, due to the complex nature of the process, which is a function of overlapping multiple factors, there is no explicit concept of optimization for the whole process. When expressing an optimal value for die angle, total force or feed rate, other parameters may be neglected.
Thus, it seems that the best way to study this process is a comprehensive analysis of the effects of the parameters on each other. Due to the wide potential application of this process, it is worthwhile attempting to increase the quality of the specimen and meet working conditions.

Numerical analysis and experimental method
There are several methods for analyzing the forging process, such as the upper bounds methods, the slab method and others investigated and implemented by previous authors, but the most accurate results are obtained by FEM. This method provides a comprehensive view of all the phenomena and conditions during forging.
By applying appropriate boundary conditions and simulation parameters, simulation accuracy can be significantly increased. Therefore, conditions such as friction in all process components (the back spring pressure of manipulators and mandrel and their impacts on material flow) are considered. Using specimen temperature, the heat transfer between the mandrel and the specimen has been calculated whilst this can have a direct effect on specimen hardness. Therefore, the viscoplastic model has been used for a more accurate examination of the material flow rate. Therefore, the Von Mises yield criterion has been implemented in order to flow rules. The relation between the essential matrices of FEM has been presented by Darki et al. [1].
Although other models such as rigid plastic or elastoplastic ones have been used in most previous studies, these do not have the necessary precision to determine neutral plate coordinates. In other words, it can be stated: (i) the material has viscoplastic behavior during the process; (ii) there is heat transfer during the forging process; and (iii) the dies and mandrel are assumed to be made from a rigid material. For the calculations and observations, RS has been defined as the final stresses on the product and residual stresses during the process. In most RFP simulations, the effects of die cooling are ignored due to the relatively short contact time between the die and the product.
In order to investigate the effects of the die angle, six different specimens are considered: these are described in the following table. Other geometrical dimensions of the components are listed in Table 2. It should be noted that all measurements in the simulation after each stroke on the specimen have been taken to show that stroke effect remains the same over the length of the tube. The length of the specimen is 200 mm. Also, the simulation dynamic parameters such as rate of stroking (stroke per min), Rotating feeds, Axial feed (mm), Number of strokes, Number of passes, Rotation per pass are respectively: 400, 36°, 20, 12, 2, 10°.
To validate the simulation, the hardness criterion is measurable. For this purpose, two auxiliary criteria, effective strain and temperature, have been used. These two criteria have an impact on the hardness of the specimen as illustrated in figure 4. For this reason, a tube with the geometry of the simulated specimen was used. The length, radius and thickness of the sample were measured by a hardness tester. The following is a view of the measured sample.
The experiment used standard temperature conditions and a portable hardness tester to measure the hardness in different sections at random points. According to the dimensions of the tube, the impact device type D has been considered to measuring the hardness of the tube in different section through the variations of effective strain. For this purpose, about 50 points were marked and measured. It should be noted that the die angle for this test was 5°. After measuring the radius variations and calculating the effective strain on the sample, the hardness-strain curve was obtained. The effective strain equation is given below [2]: where 1,2,3 are the principal strains and is the effective strain. By measuring the different strains on the specimen through simulation and placing them into the hardness function, the hardness value of the specimen is shown. To apply the temperature effects to other types of die and to show the distribution of hardness in all sections of the specimen, the hardness-temperature curve was defined by the hardness values obtained for different strains and temperature values. The hardness distribution is thus rendered visible by the temperature and strain effects. After comparing the experimental and Outer diameter (mm) -Reduction rate 30 -20% Inner diameter (mm) -Reduction rate 10 -60 % Outer diameter for mandrel (mm) 4 Length of die (mm) 70 Length of die land (mm) 25 Die angle 5°,10°,12.5°,15°,20°,90° Table 2. Geometry parameters of the mandrel, specimen and die.
simulation results and verifying the accuracy of the simulation, the same method of the simulation was used to analyze the other parameters. Sonmez and Demir [21] expressed the following equation as the hardness function, where ( ) is hardness and ( ̅ ) is effective strain.

Results and Discussion
In regard to the comparison between the error percentage of the simulation and experimental results; the current simulation procedure can be used for developing and expanding the investigation of parameters such as coefficient friction and die geometry. This simulation has been verified by comparing it with experimental results for cold RFP, which is presented in Table 3 [1].
In Table 3 has been illustrated the dimensions of experimental and mathematical model for a cold forging sample. According to the obtained results there is a good correspondence between the experimental and simulation results in the peak contact force through FEM simulations. In Figure 5 has been displayed a radial forging machine to obtain the experimental contact force. due to the obtained results, the difference is less than 5%, which might be due to a thermal effect.  Figure 5. Radial forging machine with a feeding system during the practical test.
(5) Table 3. Specimen geometry and contact force via the experimental and simulation results of process. [1] Since the contact force is one of the principal criteria of RFP in order to analyse of process, the examination of contact force vs radius reduction leads to an estimate of the quality of forged tube and dimensions of the radial machine. Therefore, Fig 6 displayed the contact force of experimental results [10] and FEM results vs reduction outer radius of tube and on the other hand, the function of this issue has been obtained to estimate applied force vs reduction radius for the used material. According to this comparison, the current simulation results have less error rather than other methods and previous investigation. [18] 4.1 Friction impacts -It is necessary to determine the most appropriate type of friction for the simulation before examining the effect of friction on temperature, forge force and material flow velocity. Hence, two types of friction (coulomb and shear) were simulated. In this case, the simulated forging force was measured and the most appropriate type of friction determined by comparing it with the experimental value. Given the higher values of the forging force for coulomb friction and the inconsistency with experimental values, it can be concluded that this type of friction is incapable of describing this process. On the other hand, due to shear friction's low error percentage, it can be claimed that the shear friction has a higher accuracy for the simulation of RFP. Thus, this friction model will be used to analyze this process with the assumption of a 0.4 friction coefficient. The comparison of both types of friction is shown in Figure 7. -As shown in Fig. 8, as the friction coefficient increases, the forging force increases sharply with each stroke. Thus, the friction coefficient has a direct relationship with the forging force. Moreover, the total time increases as the friction coefficient increases.   1  14  27  40  53  66  79  92  105  118  131  144  157  170  183  196  209  222  235  248  261  274  287  300  313  326  339  352  365  378  391   -Material flow velocity is one case where friction can have a direct and significant impact. For this reason, three different friction coefficient values, 0.4, 0.6 and 0.8, were considered. It should be noted that a die angle of 15° was assumed and the velocity was measured in the axial direction after the neutral plane. All values belong to the first pass. As shown in Fig. 9, as the friction coefficient increases, the material flow velocity decreases. The highest axial flow velocity of the material is produced by the lowest friction value.
- Fig. 10 shows temperature variations based on different shear friction values. As expected, with increasing friction, the temperature increases, which in itself can be a confirmation of the correct simulation method. The temperature distribution is also considered on the outer surface of the specimen. Calculating the temperature distribution and the maximum temperature for different friction values is needed to estimate specimen hardness. This analysis will be a criterion for controlling specimen temperature with respect to maximum allowable temperature. - Fig 11 illustrates the residual stress variations based on different friction values. The highest residual stress distribution values are produced by the highest friction value while the lowest is for the 0.4 shear friction coefficient. However, the non-uniformity of this stress distribution throughout the specimen can be considered a factor in reducing specimen quality. The 0.6 coefficient has a uniform RS distribution, which leads to higher specimen stability under critical loads.

4.2
Die angle impacts -As mentioned, one of the purposes of this simulation is to investigate the effects of die geometry on the specimen. Fig. 12 presents the effects of the (α) angle on density changes. Assuming that mass is constant throughout the process and the volume is reduced during operations, density will increase. The increase in density reflects the improvement of the specimen's microstructure. Fig. 12 shows that an angle of 10° leads to the highest density.
After 10°, the gradient of the density curve declines and the lowest value density is produced by an angle of 20°. - Fig. 13 shows the forging load along the workpiece per stroke. The shear friction coefficient is 0.4. As the chart shows, the highest forging load is 5° and the lowest 20°. There are more oscillations at 20° than at 5°, which can produce additional vibrations in the forging machine. Therefore, it is necessary to study the oscillations of the applied force when considering the maximum amount of force required.
-Due to the importance of the surface smoothness of the specimen and in order to avoid complicated operations, it is important to examine the dimension changes of the specimen and its deformation from a strain perspective. For this reason and given the inhomogeneity factor defined by equation (6), the presentation of effective strain distribution should be a measure of surface quality after forging: ̅ is effective strains on the surfaces contacting the specimen and the die and is the minimum strain on the radial direction of the specimen.
--In Fig. 15, the temperature distribution along the specimen is shown at different angles. As is clear, the lowest average temperature upon each stroke is at 15° and the highest at 90°. As the angle increases up to 10°, the temperature increases while for the angles over than 10° the temperature decreases. It is worth mentioning the die with the 90° doesn't follow these variations due to a lack of all section of geometry. 15° leads to the lowest temperature distribution. The temperature distribution increases for angles above 15°.
-Material flow velocity can express the position of the neutral plate and the form of the microstructure particles. The coordinates of the neutral plate can change the stress distribution on the die and thus can be used to estimate die longevity. The flow velocity has a direct influence on the quality and shape of microstructures. Due to the pattern of material velocity distribution, as the die angle increases up to 15° the material flow velocity decreases while for over than 15° the range of velocity increases. Fig. 16 illustrates this trend. -Sanjari et al. [18] claimed that at an angle of 5°, the neutral plate is in the forging section. According to the obtained results, as the angle increases, the position of the neutral plate moves from the size section to the forging section. Similarly, as the angle decreases, the distance of the neutral plate from the edge of the pipe increases. On the other hand, as the die angle increases, the angle of the distribution of velocity zones in the material increases (β), which in turn can affect the shape of the granular material, thereby establishing a criterion for describing the microstructure. Figure 17 illustrates this phenomenon, the variation of the angles of the material flow layers and the position of the neutral plate. -Residual stress is one of the parameters which can determine the longevity of the specimen after forging. Hence, residual stress distribution was measured after each stroke. Based on examining the effect of die angle on residual stress, Fig. 18 shows the lowest value of residual stress was produced by an angle of 15°. Thus, by increasing the angle to 15°, residual stress decreases and then increases again for angles above 15°. It can also be claimed that an angle of 15° leads to the most uniform stress distribution. This can be a strong indicator of quality.
(c) Figure 17. a, b and c. 5, 15,20 die angles, respectively, vs. the distribution of velocity and the distance between the end of the specimen, the neutral plane and the angle of velocity.
(b) -Just as angle changes have different effects on the specimen, these changes can also occur in the forging machine. Residual stress is an important parameter in die analysis. For this purpose, the maximum stroke amplitude for different angles in the first pass was considered and the residual stress in the same motion range calculated. These variations are displayed in Fig. 19.
According to the results, the lowest value is produced by an angle of 12.5 °. After this angle, the residual stress on the die increases significantly while there are no drastic changes for angles lower than 12.5 °.

4.3
Hardness -Tube hardness analysis consists of two parts: analysis of the experimental results and analysis of the simulation results. In the experimental section, after calculating the effective strain value and measuring the hardness of the specimen with a hardness tester, the curves of the effective strain and hardness were obtained. Fig. 20 expresses the strain-hardness curve obtained via 4 approximated polynomials. Similarly, Fig 21 shows the measured values by hardness tester between 0.2-0.3 [mm/mm] effective strain. Finally, the investigation and analyses have been validated by comparing the hardness-strain curve obtained through the simulation and the experiment. Given the strong agreement between the simulation and experimental results, it can be claimed that other simulation results are reliable for analyzing radial forging in industrial conditions.   Fig. 22 shows the hardness distribution on the specimen's surface along the longitudinal line. According to the results, the lowest value for hardness distribution on the surface is related to an angle of 15 °. On the other hand, this angle leads to the highest hardness uniformity. The uniformity of the hardness distribution can be a criterion of microstructure quality and the uniformity of granularity in the surface layers.

Conclusion
In this research, a three-dimensional model of a radial forge was simulated and subjected to numerical analysis based on FEM. The simulation and experimental results were compared to each other and the strong agreement of the obtained results indicates the accuracy of the simulation for analyzing and predicting the characteristics of specimens based on the required conditions. In this research, an attempt has been made to analyze all the parameters affecting this process in order to provide the specimen with the required characteristics. Therefore, the results can be summarized as follows:  Results based on shear friction are more accurate and valid than those based on coulomb friction. As friction increases, residual stress in the specimen will increase;  A die angle (α) of 10° produces the highest density in the specimen while above10°, other angles lead to lower densities;  As the die angle increases, the angle of the velocity layers (β) in the material increases. This can reduce the distance between the neutral plate and the end of the specimen, transferring it to the sizing area. As a result, the radial force increases;  Increasing the die angle increases residual stress in the die. Thus, for angles above 12.5°, residual stress in the die increases considerably, which indicates a decrease in the longevity of the die and an increase in die fatigue;  The highest hardness is obtained at an angle of 20°, which creates uniform hardness along the entire length of the specimen. The amount of hardness changes greatly at other angles.