- Original Paper
- Open Access
Simulated and experimental investigation of the airfoil contour forming of 301 austenitic stainless steel considering the springback
© The Author(s). 2018
- Received: 28 September 2017
- Accepted: 6 December 2017
- Published: 5 January 2018
Metal forming has played a significant role in manufacturing development, thus investigations in the field of metal forming to improve the quality of the forming process are necessary. In the present study, the experimental and numerical analysis of airfoil contour forming of 301 austenitic stainless steel is examined in order to reduce the spring reversible ability under preheat temperature.
Considering the stress-strain properties of the preheat temperature; the body forming is simulated in ABAQUS software according to the theory of increasing the blank holder force during forming.
The obtained results of the spring-back for simulating the austenitic stainless steel airfoil are compared and investigated with the manufactured experimental sample results using deep tensile forming.
By comparing the results it can be seen that the control of blank holder force during forming cause to minimize the spring-back effects.
- Austenitic stainless steel
- Work hardening
Nowadays, the stainless steel is one of the most usable steels in automotive, military, and airborne industries. This is due to unique features such as high corrosion resistance and good formability (Bart et al. 2013). Other features of these steels such as ease of welding, soft and flexible for cold working, and to be non-magnetic are of interest to many researchers and industrialists (Luo 2013; Haghshenas 2016). The most outstanding of these steels are the ferritic stainless steels (400 series) (Henry and Maloy 2017; Löytty et al. 2016; Zhao et al. 2016), precipitation hardening stainless steels (Couturier et al. 2016; Silvestre et al. 2015), duplex stainless steels (austenitic-ferritic) (Schwarm et al. 2017; Mukherjee and Pal 2012; Samal et al. 2011), martensitic stainless steel alloys (Wiessner et al. 2017; Garrison and Amuda 2017), and austenitic stainless steels (200 and 300 series) (Tasker and Amuda 2017; Borgioli et al. 2016). Simulation of the springback depends on two main groups of parameters: the first group is the physical parameters such as mechanical properties, hardness, and friction coefficient rules, and the second group is numerical parameters such as the number of embedded points in the thickness direction, element type, mesh size, and the convergence tolerances that further are concerned with the simulating conditions of body.
Padmanabhan et al. (2002) examined the effect of the back force applied to the workpiece on the springback. The force applied by the hydraulic ram makes more tensile strain in the body and reduces the amount of springback. They showed that the increase of the applied back force in the sample causes the springback angle to reduce. Kuwabara et al. (2009) investigated the effect of the rolled direction on the springback. They evaluated the springback angle of the various steels with the different yield stress and found that the effect of springback in the tangential direction of rolling always is less than the perpendicular direction. Zhang et al. (2010) invented the multi-step compensation method to modify the springback direction. In this method, the die surface shape is compared with the actual piece based on the results of the simulation. After the first applied modification of the die, the die surface is simulated again and the results are compared with the actual piece. This is repeated until the deviation between simulation results and the actual piece is minimized. Uemori et al. (1998) studied the modeling type of the plastic hardening in the accuracy of the simulation. For this purpose, they examined the linear kinematic hardening and the combination of linear and nonlinear kinematic hardening model and it is concluded that the results of simulation in combined model is very similar to reality. The effect of simultaneous tension and pressure applied to the sheet during the forming process is investigated by Schilp et al. (2012). They studied springback factor using tensile pushing-bending, and stretch-bending for two bend angles 45° and 90°. They reported that the stretch-bending case is the best state to reduce the amount of springback. Sing and Agnihotri (2015) studied the parameters affecting the formation of deep stretch. They found that the blank holder force is the most important parameter that must be selected carefully in the deep tensile forming. They revealed that the blank holder force is the only parameter that alone directly affects the outputs such as material flow, variations of the thickness, and tear and shrinkage behavior. Liu et al. (2002) tried to minimize the amount of springback using the changing of the blank holder force. After a certain time, they exerted a large blank holder force on the walls to create a large plastic strain and thereby slowed down the flow of material into the die cavity. In this way, instead of reaching the blank holder force from zero to its maximum value in a short period of time of forming, and remaining constant during the forming period, it starts from an initial value and after a determined period of time, t1, progressively reaches to the second value and remains constant in the same amount of force up to the end of time of forming, t t . Then, they obtained the modified model of the technique that both of the primary and the secondary blank holder force can be calculated utilizing a mathematical algorithm. Accordingly, the primary blank holder force is computed as the force value that causes to lock the plate between the matrix and blank, and the secondary blank force is also estimated to be the maximum blank holder force.
The paper presents the airfoil contour forming of a helicopter tail rotor with specific dimensions and material that is studied and analyzed to reduce the springback after forming and to prevent work hardening process. Then, the blank holder force is calculated based on the technique used by Liu et al. and the austenitic stainless steel of class 301 with a surface pressure of 0.163 MPa is employed. The feature of this kind of steel, the high springback after the forming process, and work hardening during forming can be mentioned so that the forming during the process is faced with the problems in conventional methods of forming. On the other hand, the very low thickness of the steel sheet can be noted that causes forming the deep drawing process require very precise dimensional tolerances of the die. Another important point is that the length of the piece and very small bandwidth leads to remove many forming techniques such as explosive forming. Finally, the obtained results of experimental and numerical analysis of finite element method (FEM) are compared and evaluated. In order to prevent the strain hardening during the process, the sheet is formed under the temperature of 350 °C without importing the fine pieces into the structure-phase variations and changing its mechanical properties. Furthermore, the mechanical properties such as stress-strain required for simulating are considered based on the mechanical properties of this temperature.
In this section, geometry and material characteristics of the helicopter tail rotor are expressed. Then, the specifications of aerodynamic forces and operating conditions of ballet are determined. The base of determination of the material is required for the production of the ballet.
Geometrical characteristics of the fin tail rotor
The width of the largest outfall
The width of the smallest outfall
The height of the largest outfall
The height of the smallest outfall
Approximate dimensions of the spreadsheet
350 × 1397
Fixed length of the largest cross section
Fixed length of the smallest cross section
Point-to-point characteristics of the cross-section A-A
Point-to-point characteristics of the cross-section B-B
The fin warp
Since the lift force due to circulating wind flow is different around the fin, the warp must be considered for the fin firstly to minimize the stress applied to the fin and secondly to distribute the lift force over the surface, uniformly (Fig. 1). The pitch angle (the angle between the chord line and horizontal line) is the most value at closest to the rotor mast, which the fin has a lowest linear velocity, and it is lowest value at the farthest point to the fin that has a highest linear velocity. Thus, the velocity of the forced air and applied loads to the center of the rotor mast, reaches to the minimum value (Federal Aviation Administration 2014).
The fin material
The mechanical properties of austenitic stainless steels of 301 at 25 °C (AK Steel Corporation 2007)
Various states of the work hardening of stainless steel 301 (AK Steel Corporation 2007)
Yield stress (PSI)
Tensile stress (PSI)
Elongation percent for 2 in. (as sample)
Hardness (Rockwell C)
In order to recognize that the hot or cold forming is allowed for the piece, under different temperatures, the hardness and tensile tests are taken place on the various samples of austenitic stainless steel grade 301.
Based on the theoretical and experimental documentaries, an abrasion coating method or process for forming the fin tail rotor is considered and then, using the results of paragraph (I) and the earlier geometrical and mechanical properties listed, the appropriate boundary conditions is utilized in the simulation.
The results of tensile and hardness test
Results of the tensile test
Metal temperature (°C)
Yield stress (Mpa)
Ultimate stress (Mpa)
Hardness (Rockwell C-HRC)
The results of Table 6 shows that before the crystallization temperature of the metal (i.e., 400 °C), the metal mechanical properties have the better conditions than the ambient temperature, while the increasing elongation percentage is also reached to stable conditions up to the crystallization temperature of the metal. Therefore, based on the obtained results of this test, it can be invoked that if the hot forming conditions of the austenitic stainless steel of 301 are provided up to the temperature of 350 °C, the destructive effects of work hardening during the process and springback after the process can be controlled. Herein, the temperature of 350 °C is considered to define the boundary conditions for practical forming and simulating the piece.
where E is Young’s modulus, and Y s is the yield stress.
To compensate the springback, the strategies such as over bending workpiece (2 to 8% more bending angle is considered), bottoming, and the bending tensile or dilation are used (Andersson 2007). It should also be noted that the effective parameters in springback and forming process under conditions of loading and unloading are the matrix geometric characteristics, plastic deformation of the workpiece, the workpiece geometry, boundary conditions, and the blank holder force (Liu et al. 2002). According to Tables 1 and 2, the R/t for the cross-section A-A ratio is higher than the cross-section B-B, so if the springback at this cross section be controlled, it could be reasoned that the springback of the whole piece have been controlled. Therefore, the simulation is considered based on the cross-section A-A and then, the springback is investigated.
In this section, based on the mechanical properties of austenitic stainless steel of 301 under temperature of 350 °C and the blank boundary conditions, the prototype die is modeled in ABAQUS software and then, the forming process is simulated.
The die and workpiece modeling
The purpose of the simulation is to estimate two parameters: the point of changing the blank holder force from the minimum mode to maximum, and the maximum blank holder force value in the state of transition loading.
q factor for aluminum and steel
Blank holder force is varied according to Fig. 5.
According to relation (5), the initial pressure on the clamp is calculated equal to 0.163 (Mpa).
By defining the path at the entrance nodes and defining the logarithmic strain output as an intended strain criterion (Δεmin) in Fig. 6, (in percentage terms), all the possible states for loading and unloading could be simulated and then, the best case for the point of change the loading from the minimum to maximum mode can be predicted.
Trial and error related to the blank pressure change between two phases and variations of the logarithmic strain
Pressure of phase 1 (Mpa)
Pressure of phase 2 (Mpa)
Logarithmic strain (%)
Trial and error related to dividing the submergence depth between the two phases and the logarithmic strain changes
Phase 1 depth (mm)
Phase 2 depth (mm)
Logarithmic strain (%)
In this section, the piece prototype is extracted from the deep tensile die and then, the results are compared with the simulation results.
Manufacturing the tensile forming die and extracting the sample piece
The sheet is controlled along the perpendicular to the forming using the dynamic feeders.
When the sheet surface gets contact with the punch, the blank is involved to the sheet and the initial force is applied.
During moving the punch in the matrix, the sheet feeders conduct the sheet into the mouth of the channel matrix by controlling the sheet velocity, and at this stage, the blank force is reached to its maximum value.
The deviation percentage of the measured values to the values inserted on the plot
The obtained springback simulation results under the optimum boundary conditions showed that the logarithmic strain percent is approximately equal to 8% and using these conditions where the minimal springback is yielded, the tensile forming die is designed and manufactured. In addition, the prototype piece was achieved with a maximum deviation of 0.9% compared to the nominal value indicated in the plot. This means that the theory criterion used in this study (i.e., control of the blank force and its value) is the correct criterion and on the basis of it, the piece die can be designed and constructed in the terms of the combinational contour of symmetric-asymmetric.
In this study, we have tried that the forming approach of the austenitic stainless steels as well as forming the helicopter tail rotor piece of steel grade 301 to be examined. Herein, based on the theory of Liu et al., the blank holder force is ascendant varied in during the forming. The flowchart of the secondary blank holder force is used to simulate the forming of the austenitic stainless steel sheet. In addition, to reduce the work hardening during the forming process, the initial preheat conditions were considered. Some sheet samples were placed under the various temperature conditions, and their mechanical properties were compared with the sheet tested under the ambient conditions. The result of this comparison showed that to prevent the work hardening during the process and to prevent the structure-phase changes, the preheated temperature that equal to 350 °C has closest and most optimal properties with respect to the environment temperature. The mechanical properties such as stress-strain curve required for the simulation were considered based on the abovementioned temperature. Secondly, the forming boundary condition set in such a way that when the punch goes down to 30 mm at the mouth of the die, the blank holder force is progressively shifted from the initial amount of 30,000 to 350,000 N. In order to form the intended steel group 301, the forming tensile die was designed and built based on the critical section and a sample length of 200 mm. Also, the primary and secondary blank forces are obtained using trial and error by design and construction of PLC system to control the speed of the punch relative to the velocity of movement of the plate holder jaw carriage. The hydraulic lifting jack pressure and the driver jack of the holder jaw carriage were considered based on the forming required tonnage, and then the prototype was built. Finally, by point to point controlling the resulting piece with the nominal dimensions contained in the plot, and based on the obtained results, it was concluded that the most piece deviation in the critical sections to the nominal dimensions is 0.9% that is acceptable based on the simulated logarithmic strain. Hence, it can be concluded that the piece springback has decreased. Meanwhile, by preheating the piece and cooling it under conditions of the ambient temperature, the amount of work hardening during the process is reached to its minimum value.
RB performed the analysis on all samples, interpreted the data, wrote the manuscript, and acted as the corresponding author. AG supervised the development of the work, helped in the data interpretation and manuscript evaluation. Both authors read and approved the final manuscript.
No funding has been received for the conduct of this study and/or preparation of this manuscript.
The authors declare that they have no competing interests.
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