predictive modeling and response surface method of operating …ijens.org/vol_20_i_01/200301-4747...

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:20 No:01 1

200301-4747-IJMME-IJENS © February 2020 IJENS I J E N S

Predictive Modeling and Response Surface

Method of Operating and Geometrical Parameters

for Bending Force and Spring Back in V-Bending

Process Hussein Zein1, 2, *

1 Mechanical Engineering Department, College of Engineering, Qassim University, Buraidah 51452, Saudi Arabia

2 Mechanical Design and Production Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt * [email protected]

Abstract-- The main objective of this work is to develop a 3D

predictive model of Finite Element Analysis (FEA) to simulate

and predict the bending force and the spring back behaviour

of yellow brass alloy sheets (ASTM B36) in the V-bending

process. To achieve this objective, the FEA program

(ABAQUS/EXPLICIT) is used to create this numerical

simulation for different values of the operating and the

geometrical parameters (friction coefficients, bend radius,

and opening die dimension). Furthermore, the effect of these

process parameters on the bending force and the spring back

behaviour is investigated by using the response surface

method (RSM) in the V-bending process. Finally, the

simulation results are shown that the investigated process

parameters had much influenced on the bending force and the

spring back angle in the V-bending process by finding the

optimum design points using the predictive model of the

response surface method.

Index Term-- Finite Element Analysis; Bending Force;

Spring Back; Response Surface Method; Bend Radius;

Friction Coefficients. 1. INTRODUCTION

Sheet metal forming is one of the oldest fabrication

processes identified to mankind, and bending can most likely be regarded as its most basic variant [1]. Bending is

a process by which metal can be deformed by plastically

deforming the material and changing its shape. The

material is stressed further than the yield strength but lower

than the ultimate tensile strength.

In a mission to enhance fuel economy, the automobile

manufacturers have been significantly looking at light

metals to light-weight their vehicles. Considerable weight

saving can be achieved by replacing parts made from mild

steel with those made from light-weight materials

(aluminum and magnesium alloys) and high specific

strength materials. Such materials are less formable than mild steel, and parts made from them absence dimensional

control because of the considerable amount of spring back

that they generate after forming [2].

The elastic recovery of material is one of the main

sources of shape and dimensional accuracy of drawpieces.

Springback cannot be removed, but there are several

techniques to minimize the elastic return of the stamped

part because of the elastic recovery of sheet metal after

forming. One of the techniques is an appropriate design of

the die which takes into consideration the amount of spring back. In addition, the change in selected bending process

variables can minimize the spring back. The concept of the

modification of the die shape contains extra overbending of

the material [3]. Between the many advanced techniques of

predicting the final profile of the drawpiece, the finite

element method (FEM) is the most often utilized [4]. FEM

is the main method utilized to simulate sheet metal forming

processes to be able to figure out the distribution of stresses

and deformations in the material, forming loads and

possible locations of the defects.

The measure of the spring back value is a spring back

coefficient or angle of spring back. The value of the spring back coefficient be determined by the value of bend angle

and bend radius, sheet metal thickness, and width of the

sheet metal, the mechanical properties of the sheet material,

the bending process temperature, and the strain rate [5].

The research of Caden et al. [6] demonstrated the influence

of the coefficient of friction on the spring back value.

These computer tools enable the design engineer to

study the process and material factors. The reliability of

predicted formability and the precision of the predicted

deformed geometry for a given part depend on the

predicted computational modeling approach [7]. In spite of the well-developed material behaviour models, metal

forming simulations often do not yield the correct results.

This is generally due to utilizing a very simplified friction

model. Coulomb friction model is a simple model

frequently utilized in simulations. In this model, the ratio

between friction force and normal force defined as the

coefficient of friction μ, that considered to be constant [8].

Nevertheless, especially in lubricated systems, friction

depends on a large number of parameters, e.g., the micro-

geometry, the macro-geometry, the lubricant and the

operational factors: velocity, temperature and normal load

[9]. Dametew and Gebresenbet [10] studied by using the mathematical method the influence of sheet metal

thickness, sheet metal type, friction, tool radius and tool

shape on spring back for different materials of sheet metal.

Different researches were done to investigate the spring

back phenomenon numerically and experimentally for

diverse shapes, and process parameters [11]–[18]. The

majority of the analytical researches concentrated on air

bending despite the fact that minimal work was carried out

on the V-die bending process because of the characteristic

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problems as a result of the coining action related to this

process [19]. Earlier investigations [19]–[21] performed on

spring back in the V-bending process displayed that the

material’s grain size got minor impact, but surface

roughness experienced a reasonably greater impact on

spring back. The spring back was additionally discovered to be affected by the punch nose radius and the process

temperature along with the minor impact of the punch

velocity. Finite element methods were utilized to analyze

the impact of various process parameters and validate

numerical models in the V-bending process through several

researchers e.g. [22], [23]. These researchers presented that

the spring back was significantly influenced by bend

radius, punch angle and die shoulder radius. Leu [24]

studied the influences of process parameters, such as

material properties, lubrication, and process geometrical

parameters, on the position deviation and spring back of

high strength steel blanks, to be able to create process design recommendations for the asymmetric V-bending

process.

Wasif et al. [25] performed experimental and numerical

analysis for the spring back in high tensile strength steel

sheet metals at divers process parameters of the V-bending

process. Wasif and his team diagramed their experimental

results to investigate the influence of the process

parameters (sheet metal thickness and width, the bending

angle, and the tool geometry) on the spring back in the V-

bending process. The diagramed figures helped them to

obtain the optimal parameters for minimizing the spring back. In addition, they used their numerical models for the

forecasting of the spring back at various values of the

process parameters. They displayed that the spring back

decreased with increasing of the sheet metal width. Also,

they concluded that the spring back increased with

decreasing the bending angle.

Ramadass et al. [26] investigated the spring back

behavior of Ti-Grade (2) blanks in the V-bending process

by utilizing the finite element technique and the

experimental work. Ramadass and his associates used the

Taguchi and analysis of variance methods to classify the

significance of process parameters such as punch radius, sheet metal thickness and die opening dimension on the

spring back behavior. Finally, they validated the finite

element results by utilizing the Taguchi (L9) orthogonal

array. They determined the classification of the most

effective process parameters in minimizing the spring back

with the following influence ratios: 56.65% for sheet metal

thickness, 31.87% for the punch radius, and 9.73% for the

die opening.

Also, the bending force to perform the V-bending

process is an important factor in selecting the capacity of

the mechanical press and the geometries of the used tools. Mori et al. [27], Jiang et al. [28], Panthi et al. [29] and

Hakan et al. [30] came to the conclusion in their researches

on spring back that bending force rises with the rise in the

yield stress of the sheet metal. Narayanasamy and

Padmanabhan [31] studied the software of response surface

methodology for forecasting the bending force throughout

the air bending process for interstitial free steel sheets. The

researchers displayed that punch stroke is the dominating

factor identifying the bend force subsequently punch speed

and bend radius. Malikov et al. [32] studied the bending

force for air bending process by using numerical and

experimental calculations. Malikov and coworkers

demonstrate that bending position and structure location significantly affect bending force.

The experimental study of Srinivasan et al. [33] focused

on studying the effect of friction parameters on the spring

back and the bending force for electro-galvanized steel

sheets in the air-bending process. This study has shown that

the spring back increased and the bending force decreased

by reducing the friction coefficient. Srinivasan and Raja

[34] conducted an experimental analysis for the V-bending

process to comprehend the spring back, bending force and

thinning of bimetallic sheets (Al/Cu). Srinivasan and Raja

studied the influence of the process parameters like die

opening, punch radius, sheet thickness, and die angle on the spring back. They found that the spring back and the

bending force reduced with decreasing the punch radius

and rising the die angle. Also, they established that the

spring back increased and the bending force reduced with

the rising of the die opening. On the contrary, they figured

out that the spring back decreased and the bending force

increased with the rising of the sheet metal thickness.

In the present work, the V-bending process of yellow

brass alloy sheet metal (ASTM B36) is investigated

numerically and experimentally. The bending force is

studied at different values of the V-bending process parameters by using a numerical simulation of a

commercial finite element software ABAQUS/EXPLICIT.

Also, the spring back behaviour in the sheet metal is

investigated for these parameters. The effect of different

values of the operating and geometrical parameters

(friction coefficients, bend radius, and opening die

dimension) on the bending force and the spring back

behaviour are presented by using the 3D predictive model

of FEA and the response surface method.

2. THE NUMERICAL SIMULATION MODEL

In this research, a Finite Element Analysis (FEA) 3D

model is created to simulate the V-Bending process

by utilizing a Finite Element Analysis (FEA) program

(ABAQUS/EXPLICIT). Figure 1 shows the geometric

arrangements were utilized in these simulations. Figure 2

displays all dimensions of the V-bending die which used in

the simulation model. The tooling components (punch and

die) were considered as 3D discrete rigid and represented by the movement of a single node, identified as

the reference node of the rigid body. The die and the punch

were meshed by using the type of R3D4 elements. The

sheet metal is modeled as a deformable and meshed by

using 3D stress, eight-node, and C3D8R elements. The

dimension for each initial blank is (80 mm x 30 mm x 1

mm). Coulomb friction coefficients of 0.01, 0.05, 0.125,

0.2 are considered for the sheet metal contact surfaces with

oily lubrication for sheet metal with die and sheet metal

with a punch, respectively [35].



Fig. 1. The assembly of the 3D finite element model in ABAQUS.

Fig. 2. All dimensions of the die in the V-bending process.

The sheet metal is created from yellow brass alloy. The material is modeled as an elastic-plastic material with isotropic

properties. Table 1 displays the material properties of the used sheet metal in the FEA simulation. Figure 3 shows the

plastic true stress, plastic true strain curve of the material behaviour for the used yellow brass alloy sheet metal.

Table I

The material properties of the used yellow brass alloy sheet metal (ASTM B36) sheet metal

Material Density

(g.cm-3)

Elastic modulus

(GPa)

Poisson’s

ratio

Yield stress

(MPa)

Thickness

(mm)

Yellow Brass ASTM B36 8.47 97 0.31 140 1



Fig. 3. Plastic True Stress vs. Plastic True Strain curve of yellow brass ASTM B36.

3. VALIDATION OF THE FEA MODEL

Since the sheet metal bending is about applying a force

on sheet metal to deform it, the universal testing machine

was used in the experiment work as shown in Figure 4.

Additional parts were needed to be installed on the

universal testing machine to prepare the machine, those

parts are the punch and the V-die; presented in Figure 5.

Fig. 4. Universal testing machine.



Fig. 5. Installation for the punch and the V-die on the universal testing machine.

Figure 6 describes the using of a universal testing

machine in the V-bending process. While Figure 7, and

Figure 8 illustrate the brass sheet metal before and after the bending process. By comparing the experimental result

with the FEA result using the same dimensions, it was

found that there was a convergence in the value of the

spring back angle (Δθ).

Fig. 6. The V-bending process

Fig. 7. Brass sheet metal before and after the V-bending process



Fig. 8. The measuring tool for measuring the final bending angle after the V-bending process

Figure 9 displays a comparison of the predictable

bending force change with punch travel distance (present

FEA work) with the experimental work data (by using a

universal testing machine). Note that the present FEA work

is even closer to the experimental work.

Fig. 9. The change of the bending force with punch travel distance.

4. RESULTS AND DISCUSSION Figure 10 shows the simulation of the spring back

action in the V bending process. Figure (10.a) displays the

V bending process during the bending process. While

Figure (10.b) shows the V bending process after the spring

back action.



(a) (b)

Fig. 10. The FEA simulation of the V bending process (a) During the bending process, (b) After the spring back action

The measure of the spring back value is an angle of spring

back (Δθ); as shown in Figure 11. The bend radius (rb)

affects on the spring back. Also, the main purpose of

lubrication is to accomplish the smallest value of the

friction coefficient with the least possible wear. Avery

useful design optimization tool is a response surface method (RSM) tool. In the following section, it will be

studied the spring back (Δθ) as the first response in the

RSM model. Figure 12 describes RSM for the variation of

the spring back angle (Δθ) with diverse values of the bend

radius (rb) of the final bending workpiece and the different

values of the friction coefficients at sheet metal interfaces

with die and punch. It is displayed that the spring back

angle (Δθ) increases with the rising of the bend radius (rb)

which is in good agreement with published results in [22 -

23], [26], and [34]. On the other hand, the spring back angle

(Δθ) decreases with an increase in the friction coefficient value (μ) which is consistent with the published results in

[33]. Figure 12 and Figure 13 display the design points

above and below the predicted value of the RMS to get the

minimum value of the spring back angle (Δθ).

Fig. 11. Measuring of spring back angle (Δθ) and bend radius (rb)



Fig. 12. RSM for the different values of the bend radius (rb) and the coefficients of friction (μ) with Spring back angle (Δθ, Degree)

Fig. 13. Contour for the diverse values of the bend radius (rb) and the coefficient of friction (μ) with spring back angle (Δθ, Degree)

The horizontal distance between two centers of die

shoulder radius is known as opening die dimension (W);

shown in Figure 2. Figure 14 shows RSM for the change of

the spring back angle (Δθ) with different values of the bend

radius (rb) and diverse values of the opening die dimension

(W). The results of the predictive model display that the

spring back angle (Δθ) rises with the increasing of the bend

radius (rb) and the opening die dimension (W) which is in

good matching with published results in [34]. Figure 14 and

Figure 15 presents the design points above and below the

predicted value of the RSM to obtain the minimum spring

back angle (Δθ).



Fig. 14. RSM for the different values of the bend radius (rb) and the opening die dimension (W) with spring back angle (Δθ, Degree)

Fig. 15. Contour for the diverse values of the bend radius (rb) and the opening die dimension (W) with spring back angle (Δθ, Degree)

Figure 16 demonstrates RSM for the variation of the

spring back angle (Δθ) with dissimilar values of the friction

coefficients at sheet metal interfaces and various values of

the opening die dimension (W). From the FEA and RSM

results, it is shown that the spring back angle (Δθ)

decreases with increase in the friction coefficient value (μ).

On the other hand, the spring back angle (Δθ) increases

with the rising of the opening die dimension (W). Figure

16 and Figure 17 show the design points above and below

the predicted value of the RSM model.



Fig. 16. RSM for the diverse values of the opening die dimension (W) and the coefficients of friction (μ) with spring back angle (Δθ, Degree)

Fig. 17. Contour for the various values of the opening die dimension (W) and the coefficients of friction (μ) with spring back angle (Δθ, Degree)

In the same way, In the remaining part of this paper, it

will be investigated the bending force (Fb)as the second

response in the RSM model. Figure 18 and Figure 19

explain RSM and Contour for the variation of the bending

force (Fb) with punch travel distance at different values of

the bend radius (rb) and the dissimilar values of the friction

coefficients at sheet metal interfaces. It clear that the

bending force (Fb) decreases with increasing the bend

radius (rb). Nevertheless, the bending force (Fb) has a lower

value when the value of the friction coefficient (μ) is used

between 0.14 to 0.3. On the other hand, the bending force

(Fb) rises at lower and higher values of the friction

coefficient (μ=0.05 or μ=0.5).



Fig. 18. RSM for the various values of the bend radius (rb) and the coefficients of friction (μ) with bending force (Fb, ton)

Fig. 19. Contour for the several values of the bend radius (rb) and the coefficients of friction (μ) with bending force (Fb, ton)

Figure 20 and Figure 21 display RSM and Contour for

the variant of the bending force (Fb) with punch travel

distance at diverse values of the bend radius (rb) and the

different values of the opening die dimensions (W). The

predictive model of the RSM shows that the bending force

(Fb) decreases with increasing the bend radius (rb). On the

other hand, the bending force (Fb) reduces with the rising

of the opening die dimension (W) which is in good

agreement with published results in [34].



Fig. 20. RSM for the various values of the bend radius (rb) and the opening die dimension (W) with bending force (Fb, ton)

Fig. 21. Contour for the several values of the bend radius (rb) and the opening die dimension (W) with bending force (Fb, ton)

Figure 22 and Figure 23 show RSM and Contour for the

variation of the bending force (Fb) with punch travel

distance at varied values of the opening die dimensions (W)

and the diverse values of the friction coefficients at sheet

metal interfaces. The results of FEA and RSM demonstrate

that the bending force (Fb) increases with decreasing the

opening die dimension (W). While the bending force (Fb)

reduces with rising of the friction coefficients at sheet metal

interfaces.



Fig. 22. RSM for the various values of the opening die dimension (W) and the coefficients of friction (μ) with bending force (Fb, ton)

Fig. 23. Contour for the several values of opening die dimension (W) and the coefficients of friction (μ) with bending force (Fb, ton)

5. CONCLUSION

Simulation outcomes can essentially reduce the

manufacture expenses of high quality bending workpiece

by decreasing the lead time to manufacture and gives the

designers the ability to react quicker to market

modifications. Moreover, with the present FEA model and

RSM model, the smaller the bend radius is less spring back will be there with greater bending force. The fluid lubricant

with a higher value of the friction coefficient is more

suitable to apply between die/punch and sheet metal to

reduce the spring back action, on the other hand, the

bending force is to be high. Finally, the small die opening

dimensions are preferred to decrease the amount of the

spring back angle conversely the bending force will be

increased. As a final point, FE simulation and RSM results

in the present paper provide useful information to address the feasibility of the actual production process. Product

quality can also be improved. The risks of tool redesign and

modifications are minimized.



REFERENCES [1] J. R. Duflou, J. Váncza, and R. Aerens, “Computer aided

process planning for sheet metal bending: A state of the art,”

Comput. Ind., vol. 56, no. 7, pp. 747–771, 2005.

[2] M. Ramezani, Z. M. Ripin, and R. Ahmad, “Modelling of

kinetic friction in V-bending of ultra-high-strength steel sheets,”

Int. J. Adv. Manuf. Technol., vol. 46, no. 1–4, pp. 101–110,

2010.

[3] X. A. Yang and F. Ruan, “A die design method for springback

compensation based on displacement adjustment,” Int. J. Mech.

Sci., vol. 53, no. 5, pp. 399–406, 2011.

[4] P.-A. Eggertsen and K. Mattiasson, “On constitutive modeling

for springback analysis,” Int. J. Mech. Sci., vol. 52, no. 6, pp.

804–818, 2010.

[5] H.-L. Dai, H.-J. Jiang, T. Dai, W.-L. Xu, and A.-H. Luo,

“Investigation on the influence of damage to springback of U-

shape HSLA steel plates,” J. Alloys Compd., vol. 708, pp. 575–

586, 2017.

[6] W. D. Carden, L. M. Geng, D. K. Matlock, and R. H. Wagoner,

“Measurement of springback,” Int. J. Mech. Sci., vol. 44, no. 1,

pp. 79–101, 2002.

[7] M. Firat, “U-channel forming analysis with an emphasis on

springback deformation,” Mater. Des., vol. 28, no. 1, pp. 147–

154, 2007.

[8] M. Ramezani, Z. M. Ripin, and R. Ahmad, “Computer aided

modelling of friction in rubber-pad forming process,” J. Mater.

Process. Technol., vol. 209, no. 10, pp. 4925–4934, 2009.

[9] A. Matuszak, “Factors influencing friction in steel sheet

forming,” J. Mater. Process. Technol., vol. 106, no. 1–3, pp.

250–253, 2000.

[10] A. W. Dametew and T. Gebresenbet, “Study the Effects of

Spring Back on Sheet Metal Bending using Mathematical

Methods,” J. Mater. Sci. Eng., vol. 6, no. 5, pp. 22–2169, 2017.

[11] C. A. Queener and R. J. DeAngelis, “Elastic springback and

residual stresses in sheet metal formed by bending,” ASM Trans.

Q., vol. 61, no. 4, pp. 757-+, 1968.

[12] W. F. Hosford and R. M. Caddell, Metal forming: mechanics

and metallurgy. Cambridge University Press, 2011.

[13] D.-K. Leu, “A simplified approach for evaluating bendability

and springback in plastic bending of anisotropic sheet metals,”

J. Mater. Process. Technol., vol. 66, no. 1–3, pp. 9–17, 1997.

[14] J. Hu, Z. Marciniak, and J. Duncan, Mechanics of sheet metal

forming. Elsevier, 2002.

[15] T. D. S. Botelho, E. Bayraktar, and G. Inglebert, “Comparison

of experimental and simulation results of 2D-draw-bend

springback,” J. Achiev. Mater. Manuf. Eng., vol. 18, no. 1–2,

2006.

[16] F.-K. Chen and S.-F. Ko, “Deformation analysis of springback

in L-bending of sheet metal,” Adv. Sci. Lett., vol. 4, no. 6–7, pp.

1928–1932, 2011.

[17] A. Gnatowski, P. Palutkiewicz, and E. Bociąga, “Numerical

analysis of stress state during single point bending in DMTA

examinations,” J. Achiev. Mater. Manuf. Eng., vol. 28, no. 1,

pp. 47–50, 2008.

[18] T. Ohashi, H. Chiba, and H. Takano, “Employment of

Concentrated-Hard Sphere-Suspension Pad for V-bending of

Thin Strip,” J. Achiev. Mater. Manuf. Eng., vol. 31, no. 2, pp.

699–704, 2008.

[19] D.-K. Leu and C.-M. Hsieh, “The influence of coining force on

spring-back reduction in V-die bending process,” J. Mater.

Process. Technol., vol. 196, no. 1–3, pp. 230–235, 2008.

[20] Z. Tekıner, “An experimental study on the examination of

springback of sheet metals with several thicknesses and

properties in bending dies,” J. Mater. Process. Technol., vol.

145, no. 1, pp. 109–117, Jan. 2004.

[21] Ö. Tekaslan, U. Şeker, and A. Özdemir, “Determining

springback amount of steel sheet metal has 0.5 mm thickness in

bending dies,” Mater. Des., vol. 27, no. 3, pp. 251–258, 2006.

[22] A. Nilsson, L. Melin, and C. Magnusson, “Finite-element

simulation of V-die bending: a comparison with experimental

results,” J. Mater. Process. Technol., vol. 65, no. 1–3, pp. 52–

58, 1997.

[23] W. M. Chan, H. I. Chew, H. P. Lee, and B. T. Cheok, “Finite

element analysis of spring-back of V-bending sheet metal

forming processes,” J. Mater. Process. Technol., vol. 148, no.

1, pp. 15–24, 2004.

[24] D.-K. Leu, “Position deviation and springback in V-die bending

process with asymmetric dies,” Int. J. Adv. Manuf. Technol.,

vol. 79, no. 5–8, pp. 1095–1108, 2015.

[25] M. Wasif, S. A. Iqbal, M. Tufail, and H. Karim, “Experimental

Analysis and Prediction of Springback in V-bending Process of

High-Tensile Strength Steels,” Trans. Indian Inst. Met., pp. 1–

16, 2019.

[26] R. Ramadass, S. Sambasivam, and K. Thangavelu, “Selection

of optimal parameters in V-bending of Ti-Grade 2 sheet to

minimize springback,” J. Brazilian Soc. Mech. Sci. Eng., vol.

41, no. 1, p. 21, 2019.

[27] K. Mori, K. Akita, and Y. Abe, “Springback behaviour in

bending of ultra-high-strength steel sheets using CNC servo

press,” Int. J. Mach. Tools Manuf., vol. 47, no. 2, pp. 321–325,

2007.

[28] Z. Q. Jiang, H. Yang, M. Zhan, X. D. Xu, and G. J. Li,

“Coupling effects of material properties and the bending angle

on the springback angle of a titanium alloy tube during

numerically controlled bending,” Mater. Des., vol. 31, no. 4, pp.

2001–2010, 2010.

[29] S. K. Panthi, N. Ramakrishnan, M. Ahmed, S. S. Singh, and M.

D. Goel, “Finite element analysis of sheet metal bending

process to predict the springback,” Mater. Des., vol. 31, no. 2,

pp. 657–662, 2010.

[30] D. Hakan, Ö. Mustafa, and S. Murat, “Effects of material

properties and punch tip radius on spring-forward in 90 V

bending processes,” J. Iron Steel Res. Int., vol. 20, no. 10, pp.

64–69, 2013.

[31] R. Narayanasamy and P. Padmanabhan, “Application of

response surface methodology for predicting bend force during

air bending process in interstitial free steel sheet,” Int. J. Adv.

Manuf. Technol., vol. 44, no. 1–2, pp. 38–48, 2009.

[32] V. Malikov, R. Ossenbrink, B. Viehweger, and V. Michailov,

“Experimental investigation and analytical calculation of the

bending force for air bending of structured sheet metals,” in

Advanced Materials Research, 2012, vol. 418, pp. 1294–1300.

[33] R. Srinivasan, D. Vasudevan, and P. Padmanabhan, “Influence

of friction parameters on springback and bend force in air

bending of electrogalvanised steel sheet: An experimental

study,” J. Brazilian Soc. Mech. Sci. Eng., vol. 36, no. 2, pp. 371–

376, 2014.

[34] R. Srinivasan and G. K. Raja, “Experimental study on bending

behaviour of aluminium-copper clad sheets in V-bending

process,” Mech. Ind., vol. 20, no. 6, p. 618, 2019.

[35] H. Zein, M. El Sherbiny, and M. Abd-Rabou, “Thinning and

spring back prediction of sheet metal in the deep drawing

process,” Mater. Des., vol. 53, pp. 797–808, 2014.

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