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Occurrence and effect of ironing in the hole-flanging process
Journal of Materials Processing Technology 211 (2011) 1606–1613
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Occurrence and effect of ironing in the hole-flanging process Ahmed Kacem a , Abdelkader Krichen a,∗ , Pierre-Yves Manach b a b
Laboratoire de Génie de Production Mécanique et Matériaux, National Engineering School of Sfax, University of Sfax, B.P. 1173, 3038 Sfax, Tunisia LIMATB, Université de Bretagne-Sud, Rue de Saint Maudé, B.P. 92116, 56321 Lorient Cedex, France
a r t i c l e
i n f o
Article history: Received 2 January 2011 Received in revised form 22 April 2011 Accepted 28 April 2011 Available online 11 May 2011 Keywords: Hole-flanging Ironing Metal forming Finite elements
a b s t r a c t The effect of the clearance-thickness ratio on the hole-flanging process was investigated to determine the occurrence of ironing. A 2 mm thick 1000 series aluminium alloy sheet was considered. An elasticplastic finite element model using remeshing option was developed. Experiments were conducted to verify the reliability of the developed finite element model. A critical clearance-thickness ratio which is a limit between two conditions of hole-flanging was found: hole-flanging with edge stretching and hole-flanging with ironing in which the metal is squeezed between the punch and the die. The effect of the hole-flanging condition on the punch load, the forming kinematics, the flange geometry and the boring quality was studied. The finite element results were validated by experimental results. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Hole-flanging is a sheet metal forming process which is often applied to produce a flange around holes. In the conventional holeflanging process, a blank-holding force is set to clamp firmly the sheet between the blank-holder and the die. Then, a punch forces the periphery of the hole into the die as shown in Fig. 1. In practice, hole-flanging process can be performed with or without ironing. Ironing is performed by setting a low value of the clearance between the punch and the die C. In this case, the metal is squeezed between the punch and the die leading to a longer flange. When the process is performed without ironing, the flange is formed by edge stretching leading to a thinner flange. In the literature, ironing was applied to the hole-flanging process for specific cases. Kumagai et al. (1999) have performed hole-flanging with ironing to study the forming of flanges for twoply sheet metal. Kumagai and Saiki (1998) have investigated the influence of the workpiece thickness on the punch load, the finished shape and the metal flow in the hole-flanging with ironing of thick sheet metal. Recently, Thipprakmas et al. (2007) have performed also the hole-flanging with ironing for thick sheet metal to study the effect of the quality of the initial hole on the flanged shape. In many industrial applications, the process is performed with ironing to obtain a long flanges that can be used for example to increase bearing surface or to increase the number of threads that will fit in a tapped hole.
∗ Corresponding author. E-mail address: [email protected] (A. Krichen). 0924-0136/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2011.04.017
Others techniques were proposed to produce a long flange. Lin et al. (2007) have adopted the cold extrusion to obtain a flange with more substantial lip thickness and greater height. In this case, the flange is formed by exerting a punch force on the rim of a preholed cup-shaped workpiece at the same time as a clamping force is applied to suppress dilation on the bottom of the cup. Lin and Tung (2007) showed that with sufficient clamping force, this technique could produce significant extruded flange height. This technique requires an accurate control of the clamping force and an additional step for preparing the cup-shaped workpiece. Thiruvarudchelvan and Tan (2007) have used the Maslennikov’s technique to produce a long flange. This technique is based on the use of flexible materials such as urethane in the design of forming tools. In this case, the flange is formed by means of an annular urethane pad instead of the rigid punch used in the conventional hole-flanging process. The used technique needs a higher press capacity and the flexible tool material has a short life expectancy as shown in the work of Thiruvarudchelvan (2002). Cui and Gao (2010) have performed hole-flanging operation using a multistage incremental forming process. Instead of the rigid punch employed in the conventional process, a CNC controlled rigid tool with a smooth ball end tip is traversed on a sheet metal blank. In this study, among three forming strategies, it was demonstrated that the forming strategy by increasing the part diameter in small steps during the forming process produces a relatively higher flange height and uniform wall thickness. This technique is mainly applied to make prototype parts or batches of small quantities. In the present work, the conventional hole-flanging process of thin sheet metal with and without ironing was used. For this purpose, hole-flanging was carried out by varying the clearance between the punch and the die C and keeping the other parameters unchanged. Finite element (FE) simulations were performed to
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Table 1 Tool geometry parameters used in the hole-flanging process.
Fig. 1. Conventional hole-flanging process with and without ironing.
identify the occurrence of ironing by the determination of a limit between the hole-flanging with ironing and the hole-flanging without ironing (i.e. with only edge stretching). Moreover, attention was paid to study the effect of the hole-flanging condition on the punch load, the forming kinematics and the final shape. In parallel, experiments were carried out to check the FE results.
Nomenclature
Symbol
Considered values
External radius of the workpiece Radius of the initial hole Workpiece thickness Punch radius Cone semi-angle of the punch Punch profile radius Die radius Die profile radius Clearance
Re Ri t Rp ˛ Rpp Rd Rdp C
15 mm 3 mm 2 mm 6 mm 30◦ 4 mm 6.82–9.04 mm 0.2 mm 0.82–3.04 mm
were also performed at 45◦ and 90◦ to the rolling direction. The measurement of both transverse and longitudinal strains leads to the plastic anisotropy coefficients r0 = 0.45, r45 = 0.55 and r90 = 0.89. The normal anisotropy coefficient r¯ = (r0 + r90 + 2r45 )/4 = 0.61 is significant and the planar anisotropy coefficient r = (r0 + r90 − 2r45 )/2 = 0.12 is rather weak. For the FE analysis, the aluminium alloy was assumed to have an elastic-plastic behaviour with an isotropic hardening rule. Despite the significant normal anisotropy observed on this material, the anisotropy was neglected in a first step. The material was assumed to be isotropic and to obey the von Mises yield criterion given by: f = J2 () − R
(1)
J2 denotes the second stress invariant that is defined as follows:
2. Materials and techniques
J2 () =
2.1. Material behaviour A 2 mm thick 1000 series aluminium alloy sheet was considered for this work. A monotonic tensile test was carried out on rectangular sample of gauge dimensions 150 mm × 20 mm × 2 mm under displacement control at a constant rate of 5 mm/min, according to a procedure defined in Laurent et al. (2009). The load was measured by a load cell of 50 kN capacity. The Cauchy stress is calculated by the ratio of the load over the current section of the sample. The current section is determined from the initial section of the sample by assuming both isochoric plastic deformation and a homogeneous distribution of strain along the gauge length of the sample. The logarithmic strain was measured by a field measuring system by 3D image correlation (Aramis) as defined in Zang et al. (2011). The obtained stress–strain curve in the rolling direction is shown in Fig. 2. As expected for such aluminium alloy, it is observed that the saturation of the tensile stress is reached for low strain values. The Young’s modulus (E= 68 GPa) was determined from the experimental stress–strain curve. The Poisson’s ratio was taken equal to 0.28. To determine the material anisotropy, tensile tests
3 S:S 2
(2)
where S is the deviatoric part of the Cauchy stress tensor . R denotes the isotropic hardening function, that is chosen with a saturation form of Voce (1948) type: R = R0 + Q (1 − exp(−b))
(3)
where R0 , Q and b are the initial yield stress, the hardening saturation and the rate at which saturation is achieved, respectively. The evolution of the plastic strain rate is obtained by using the normality rule: dp = d
∂f = dn ∂
(4)
where n gives the direction of the plastic strain increment and d, called the plastic multiplier, determines the magnitude of the plastic strain increment. The values of the model parameters (R0 = 65 MPa, Q = 53 MPa and b = 750) were obtained by the best fit to the experimental stress–strain curve in the rolling direction as shown in Fig. 2. 2.2. Hole-flanging parameters To succeed hole-flanging, some parameters have to be controlled, especially the tool geometry parameters. The nomenclatures of the tool geometry parameters are mentioned in Table 1 and they are illustrated in Fig. 3. Among this list, some of them determine whether the hole-flanging process is performed with or without ironing as shown in Fig. 1(b) and (a), respectively.
Cauchy stress (MPa)
120 100 Experiment 80
Model
60
2.3. Ironing parameters
40 20 0 0
0.01
0.02
0.03
0.04
0.05
Logarithmic strain Fig. 2. Experimental and numerical stress–strain curves in the rolling direction.
Ironing occurs when the clearance between the punch and the die (C = Rd − Rp ) is set lower than a certain value from which the flange will be continuously in contact with the punch and the die during forming. Therefore, for a given workpiece thickness t, Rp and Rd are the two parameters that must be controlled to perform holeflanging with or without ironing. In the hole-flanging practice, to control the occurrence of ironing it is convenient to consider the
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Fig. 3. Tool geometry parameters of the conventional hole-flanging process.
clearance-thickness ratio Rc which is defined as the ratio of the clearance C to the workpiece thickness t. 2.4. Experiments The workpiece was an aluminium washer punched by the conventional punching process. The clearance between the punch and the die for the punching operation was set to 6 %t. The initial hole was punched from the side opposite the intended flange. This prevents splitting of the severely stretched edge of the flange as reported by ASM (1996). Conventional hole-flanging tools including die, truncated pilotpunch and blank-holder were used as shown in Fig. 4. A pilot was designed at the lower end of the hole-flanging punch for proper locating of the workpiece. The geometrical parameters of the workpiece are illustrated in Fig. 3 and the considered values of tool geometry parameters are mentioned in Table 1. In practice, the clearance-thickness ratio Rc was controlled by keeping the radius of the punch Rp constant and changing the radius of the die Rd . For this purpose, several dies with different Rd values were used. A range of clearance-thickness ratio Rc values between 0.41 and 1.52 was studied, the other geometrical parameters being kept constant. After centering the workpiece on the die, it was clamped between the die and the blank-holder by using four screws M10. The screws were slightly tightened in such a way to prevent the upward motion of the blank-holder and the workpiece as shown in the work of Krichen et al. (2011). Hole-flanging process was carried out with a universal tension-compression testing machine of maximum load 50 kN. It was performed under displacement control at a constant low rate of the punch equal to 5 mm/min. The output of the displacement gauge and of the load cell was continuously recorded in a data acquisition system. 2.5. FE modelling A FE model was developed to perform numerical analysis on the hole-flanging process. The analyses were performed using the standard version of the software ABAQUS. As shown in Fig. 3, the geometry of the tools, the workpiece and the loading are axisymmetric. Moreover, as the sheet metal was assumed to be isotropic, the material properties are also axisymmetric. Therefore, a 2D axisymmetric model was adopted. The tools (die, punch and blank-holder) were modeled as rigid surfaces. The workpiece was modeled as a deformable body with an elasticplastic material using the material properties specified in Section 2.1. A 3-nodes linear axisymmetric triangle element (CAX3) and 4nodes bilinear axisymmetric quadrilateral element with selective
Fig. 4. Experimental tool.
reduced integration (CAX4R) were used. The choice of a reduced integration element was made to speed up the computation as this element uses only one integration point per element instead of four. Note that a few triangular elements were used to avoid severe volume locking. An automatic mesh generator program was used to generate the initial FE mesh as shown in Fig. 5. Due to the large mesh distortions, remeshing techniques were used in order to compute an accurate solution. The adaptive remeshing process involves the iterative generation of multiple dissimilar meshes to determine a single, optimized mesh that is used throughout the analysis. The mesh size can be refined or coarsened according to an error indicator. The equivalent plastic strain error indicators were chosen to decide if the workpiece needs to be remeshed. A typical obtained FE mesh is shown in Fig. 5. Remeshing was applied for each case studied in this work. Coulomb’s friction law was used to solve the frictional effect of the tool–workpiece interfaces. To describe reasonable contact conditions between the tools and the workpiece, the friction coefficient was set to 0.2. FE simulations were performed in two steps. In the first step, the die and the blank-holder were rigidly clamped and the punch was constrained to move in the axial direction. In the second step, the blank-holder was removed to analyse the final shape after springback phenomenon. 3. Results and discussion 3.1. Punch load To investigate the effect of Rc on the punch load, the relationship between punch load and punch travel is plotted in Fig. 6 for different values of Rc . It was found that the change in Rc does not affect the punch load–punch travel relationship at the beginning of the process. After this stage, the punch load increases with decreasing Rc . After reaching the maximum punch load (Fmax ), for high values of Rc , the
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6 FE result
Punch load (kN)
5
Experiments
4 Rc=0.41
3 2
Rc=1.52
1 0 0
2
4
6
8
10
12
14
16
Punch travel (mm) Fig. 7. Punch load versus punch travel for Rc equal to 1.52 and 0.41.
mate the experimental punch load in some portions of the curve and underestimate it in other portions. For the entire curve, the difference does not exceed 17 % of the experimental value. In term of Fmax , a good agreement between experimental and numerical results is observed. To illustrate this observation, the evolution of the maximum punch load Fmax with Rc obtained experimentally and numerically is plotted in Fig. 8. It can be seen that as Rc decreases, Fmax increases. Fmax increases more sharply when the hole-flanging is performed with reduced values of Rc . From comparison between experimental and numerical results, it can be concluded that the developed FE model can be an appropriate tool to predict the punch load during hole-flanging process with an acceptable difference as shown in Fig. 7. Moreover, the FE model estimates precisely the maximum punch load and its evolution with Rc . This is more important from an industrial point of view. Fig. 5. FE model (a) initial mesh and (b) mesh after 3 adaptive remeshing iterations.
3.2. Forming kinematics relationship is slightly affected. However, for reduced values of Rc , the relationship is strongly affected by the appearance of a second peak load. It was also found that no matter the value of Rc , Fmax is always found at the first peak load corresponding to the same punch travel value. In order to validate the obtained results, typical experimental and FE punch load–punch travel relationships for high and low values of Rc are plotted in Fig. 7. It can be seen that the shape of the numerical and experimental curves are broadly similar. However numerical results overesti-
To investigate the forming kinematics during the hole-flanging process, the evolution of the punch load–punch travel relationship and typical deformed shapes were analysed. Fig. 9 shows this relationship for a low and a high value of Rc . For the low value of Rc , numerical results show that hole-flanging exhibits six stages. In the first stage (I), the punch load increases at the beginning of the contact between the punch and the workpiece. This is followed by a linear evolution linked to the elastic deformation. At the end of this stage, a loss of linearity is observed indicating the onset 6
FE result
Maximum punch load (kN)
6
c
=0 .6
c
R
c= 0
.8
R
=0
.4 1 Rc 1
3
=1
4
R
Punch load (kN)
5
Rc
2 .5 =1
2 1
Experiment
5 4 3 2 1 0
0
0
0
2
4
6
8
10
12
14
Punch travel (mm) Fig. 6. Punch load versus punch travel for different Rc values.
16
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Clearance-thickness ratio (R c) Fig. 8. Evolution of the maximum punch load as a function of clearance–thickness ratio.
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Fig. 9. Punch load versus punch travel and typical deformed shape.
of the plastic deformation. The second stage (II) is characterized by stress concentrations in the close contact between the punch and the inner edge of the workpiece. This situation introduces a significant plastic deformation in this zone. Therefore, the major part of the second stage is achieved at a quasi constant load (i.e. load plateau). In the third stage (III), the deflection of the edge is the principal deformation. It occurs at the beginning of the contact between the truncated surface of the punch and the top surface of the workpiece. At this step, the punch load increases non-linearly with punch travel. The fourth stage (IV) is characterized by a flow forming process, in this stage the work material is pushed down towards the die cavity. Due to the significant plastic deformation induced in this step, the punch load reaches its maximum value then it decreases gradually. For low values of Rc , the thickness of the flange is higher than the gap between the punch and the die. Therefore, ironing occurs at the fifth stage (V). The motion of the punch forces the material to fill the narrow gap between the punch and the die. As a consequence, the punch load increases again to a secondary maximum. After ironing the major amount of the material, the punch load drops down. The final stage (VI) is characterized by a sliding between the die and the internal surface of the raised flange. The forming kinematics in the hole-flanging for high value of Rc was previously described in the work of Krichen et al. (2011). It was found that forming is achieved in only five stages. The three first stages (I, II and III) and the final stage are similar to that observed in hole-flanging with low value of Rc . Conversely, the fourth and the fifth stages (IV and V) are replaced by one stage in which the motion of the punch induces only the bending of the edge. 3.3. Final shape For all considered values of Rc , the finished products are obtained free from necking and fracture. Some typical examples are shown in Fig. 10.
To illustrate the dependence of the final shape to Rc , some sectional view of the finished product taken in the rolling direction are presented in Fig. 11. This figure shows also the simulated final deformed shape. Results are presented from low to high values of Rc . The progression of the final shape with Rc can be seen in this figure. To quantify this progression, the geometrical evolution of both the inner and the outer profiles of the flange are investigated in the next sections. 3.3.1. Inner profile For all values of Rc , hole-flanging leads to a flange with a curved profile followed by a straight profile as shown in Fig. 11. The curved profile leads to a round and the straight profile corresponds to the generatrix of a cylindrical boring as shown in Fig. 10. Conversely to the high values of Rc , a short curved profile and a long straight profile are obtained for low values of Rc . To investigate the effect of Rc on the characteristic dimensions of the inner profile, the evolution of the straight profile length (hs ) and the curved profile length (hc ) (see Fig. 11) with Rc are plotted in Fig. 12. It can be seen that for higher values of Rc , hs and hc are almost similar. When Rc decreases hs increases while hc decreases. hs increases more sharply for low values of Rc . Namely, hs becomes 13 times longer than hc for Rc equal to 0.41. For this value of Rc , hs is 3.4 times higher than the workpiece thickness that seems to be advantageous in the product design from an industrial point of view. In Fig. 12, the experimental values of hs and hc are superimposed. A good agreement between experimental and numerical values is observed. The average difference is about 6 % and 8 % of the numerical value for hs and hc , respectively. To investigate the quality and the dimensional accuracy of the obtained cylindrical boring, the numerical boring generatrix was analysed. In Fig. 13 the boring generatrix was compared to the nominal axis for different values of Rc . This figure shows the distribution of the radial error (Er ) along the boring generatrix for different val-
A. Kacem et al. / Journal of Materials Processing Technology 211 (2011) 1606–1613
Fig. 10. Typical examples of finished product.
Fig. 11. FE deformed shape and sectional view for different Rc values.
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7 ΔS S
hS
(hS) FE result
3
(hS) experiment (hc) FE result
2
0.075
0.05
hc
ΔS S (mm)
4
Hole-flanging with ironing
h
4
(h) FE result
3
(h) experiment 2
(hc) experiment
Hole-flanging without ironing
5
0.1
5
(te) , (h) (mm)
6 (hS) , (hc) (mm)
6
0.125
Workpiece thickness
0.025
1
te
1
0 0
0.2
0.4
0.6 0.8 1 1.2 Clearance-thickness ratio (Rc)
1.4
0 1.6
(te) FE result Rcc = 0.68
(te) experiment
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Clearance-thickness ratio (Rc)
Fig. 12. The straight profile length (hs ), the curved profile length (hc ) and the straightness error (S) versus Rc .
Fig. 14. The flange height (h) and the thickness at the flange extremity (te ) versus Rc .
ues of Rc . The radial error Er is defined as the deviation between the nominal and the obtained radius. It can be seen that the boring acquires either a positive or a negative radial error along the generatrix. The maximum radial error of about 0.1 mm is reached for a value of Rc equal to 1.52. This value corresponds to 1.6 % of the nominal radius. Moreover, the geometry of the obtained generatrix tends to the nominal axis as Rc decreases. To quantify this observation, the straightness error (S) of the boring generatrix is plotted versus Rc in Fig. 12. The straightness error S is the difference between the highest and the lowest radius of the obtained boring as shown in Fig. 13. It can be seen that the highest straightness error S of about 0.125 mm is obtained for a value of Rc equal to 1.52. It corresponds to 2 % of the nominal radius. The straightness error decreases as Rc decreases. It reaches a very low value of about 0.004 mm for low values of Rc . According to the evolution of the straightness error as shown in Fig. 12, two families of boring quality can be distinguished. The first includes the reduced values of Rc that leads to a good boring straightness. The second includes the high values of Rc that leads to an ordinary boring straightness. Accordingly, it is important to determine a critical value of Rc that limits these two families. This is investigated in the last section (Section 3.4).
of the flange has a straight shape as shown in Fig. 11. As Rc increases, the contact area between the flange and the die decreases. Consequently, the straight profile is reduced while a curved profile is developed in the lower part of the flange. For high values of Rc , the outer profile becomes entirely curved with a geometrical singularity in the die radius. In addition to the profile shape, Rc affects also the flange height (h) which is depicted in Fig. 11. The evolution of h versus Rc is plotted in Fig. 14. As Rc decreases from its highest value, the portion of the workpiece subjected to the deflection in the stage (III) decreases. As a consequence, a slight decrease of h is observed. However, for low values of Rc , ironing that occurs at stage (V) causes a sharp increases of h. Like the straightness error of the inner profile, the evolution of the flange height confirms the need of the determination of a critical value of Rc . This is investigated in the last section (Section 3.4). In Fig. 14, the experimental values of h are superimposed. A good agreement between experimental and numerical results is observed with a few exceptions where the difference reaches 12 % for low Rc values.
3.3.2. Outer profile For reduced values of Rc , hole-flanging is performed with a full contact between the die and the flange. As a result, the outer profile
The analysis of the punch load, the forming kinematics and the final shape reveals that Rc affects much the obtained results. In particular, by allowing for the influence of Rc on some parameters such
3.4. Limit between hole-flanging with and without ironing
Fig. 13. Boring generatrix for different Rc values.
A. Kacem et al. / Journal of Materials Processing Technology 211 (2011) 1606–1613
as S, h and Fmax , it is shown that two families of hole-flanging can be distinguished. In the first the hole-flanging was performed with ironing whereas in the second the hole-flanging was performed without ironing (i.e. by only edge stretching). Therefore, it is important to determine the critical value (Rcc ) that limits between hole-flanging with and without ironing. Considering the geometrical conditions of the appearance of ironing in the hole-flanging process mentioned in Section 2.3, the thickness at the flange extremity (te ) (see Fig. 11) is the most suitable parameter to determine exactly Rcc . Fig. 14 shows the evolution of te versus Rc . It can be clearly observed that there are two families of Rc limited by the critical value Rcc which is equal to 0.68. When Rc is higher than 0.68, thinning of the flange occurs. Namely, te remains at a constant value of about 1.35 mm (thinning is about 32 %t). When Rc becomes equal or lower than Rcc , ironing begins and consequently te becomes equal to the clearance C. The critical value is depicted in Fig. 8 and Fig. 12. It can be seen that a significant change is observed at this value, in particular for the parameters S, h and Fmax . The critical value Rcc can also be determined analytically as the geometrical configuration for Rcc is in agreement with the assumptions proposed by Asnafi (1999) relating te to t, in the case of isotropic material, by: te = t
Ri Rd − te /2
(5)
Taking into account that te =C and Rd =Rp +te in this case, and by using Eq. (5), we obtain the following relationship:
Rcc =
Ri Rp + 0.5 Rcc t
(6)
Therefore, Rcc can be determined analytically by resolving the following equation: 3 2 0.5tRcc + Rp Rcc − Ri = 0
(7)
The obtained value of Rcc , that is in agreement with that predicted by the FE models is 0.67. 4. Conclusion FE simulations and experiments were carried out to study the effect of the clearance-thickness ratio on the hole-flanging process. For high values of the clearance-thickness ratio, hole-flanging was performed by edge stretching in which the flange gets thinner. For low values of the clearance-thickness ratio, hole-flanging was performed with ironing in which the metal is squeezed between the punch and the die. A critical value of the clearance-thickness ratio which is about 0.68 was found as a limit between the two hole-flanging conditions: hole-flanging with edge stretching and hole-flanging with ironing. This critical value was determined by
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analysing the thickness at the flange extremity and it was confirmed by analysing both the forming kinematics and the maximum punch load. Moreover, the effect of hole-flanging conditions on the final shape was quantified. It can be concluded that edge stretching leads to a short flange with a curved outer profile and a short boring with an ordinary quality. In addition, edge stretching leads to a boring with a wide rounded entrance and it causes the thinning of flange whose value was about 32 %t. However, when hole-flanging was performed with ironing, a long flange with a straight outer profile and a long boring with a high dimensional accuracy were obtained. Ironing leads also to a boring with a short rounded entrance and a flange with a constant cross section. The comparison between FE simulations and experiments shows that the developed FE model can be an appropriate tool to predict the punch load, the forming kinematics and the final shape with an acceptable agreement. Finally, it seems interesting to study the effect of the initial anisotropy of the sheet on the FE results. This will be done in future works. References ASM, 1996. ASM Handbook, vol. 14: Forming and Forging, fourth printing. ASM International. Asnafi, N., 1999. On stretch and shrink flanging of sheet aluminium by fluid forming. Journal of Materials Processing Technology 96, 198–214. Cui, Z., Gao, L., 2010. Studies on hole-flanging process using multistage incremental forming. CIRP Journal of Manufacturing Science and Technology 2, 124–128. Krichen, A., Kacem, A., Hbaieb, M., 2011. Blank-holding effect on the hole-flanging process of sheet aluminum alloy. Journal of Materials Processing Technology 211, 619–626. Kumagai, T., Saiki, H., 1998. Deformation analysis of hole flanging with ironing of thick sheet metals. Metals and Materials 4, 711–714. Kumagai, T., Saiki, H., Meng, Y., 1999. Hole flanging with ironing of two-ply thick sheet metals. Journal of Materials Processing Technology 89–90, 51–57. Laurent, H., Grze, R., Manach, P., Thuillier, S., 2009. Influence of constitutive model in springback prediction using the split-ring test. International Journal of Mechanical Sciences 51, 233–245. Lin, H.S., Lee, C.Y., Wu, C.H., 2007. Hole flanging with cold extrusion on sheet metals by FE simulation. International Journal of Machine Tools and Manufacture 47, 168–174. Lin, H.S., Tung, C.W., 2007. An investigation of cold extruding hollow flanged parts from sheet metals. International Journal of Machine Tools and Manufacture 47, 2133–2139. Thipprakmas, S., Jin, M., Murakawa, M., 2007. Study on flanged shapes in fineblanked-hole flanging process (FB-hole flanging process) using finite element method (FEM). Journal of Materials Processing Technology 192–193, 128–133. The Seventh Asia Pacific Conference on Materials Processing (7th APCMP 2006). Thiruvarudchelvan, S., 2002. The potential role of flexible tools in metal forming. Journal of Materials Processing Technology 122, 293–300. Thiruvarudchelvan, S., Tan, M., 2007. Investigations into collar drawing using urethane pads. Journal of Materials Processing Technology 191, 87–91. Advances in Materials and Processing Technologies, July 30th–August 3rd, Las Vegas, Nevada 2006. Voce, E., 1948. The relationship between stress and strain for homogeneous deformation. Journal of the Institute of Metals 74, 537–562. Zang, S., Thuillier, S., Port, A.L., Manach, P., 2011. Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension. International Journal of Mechanical Sciences, doi:10.1016/j.ijmecsci.2011.02.003.
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Occurrence and effect of ironing in the hole-flanging process Ahmed Kacem a , Abdelkader Krichen a,∗ , Pierre-Yves Manach b a b
Laboratoire de Génie de Production Mécanique et Matériaux, National Engineering School of Sfax, University of Sfax, B.P. 1173, 3038 Sfax, Tunisia LIMATB, Université de Bretagne-Sud, Rue de Saint Maudé, B.P. 92116, 56321 Lorient Cedex, France
a r t i c l e
i n f o
Article history: Received 2 January 2011 Received in revised form 22 April 2011 Accepted 28 April 2011 Available online 11 May 2011 Keywords: Hole-flanging Ironing Metal forming Finite elements
a b s t r a c t The effect of the clearance-thickness ratio on the hole-flanging process was investigated to determine the occurrence of ironing. A 2 mm thick 1000 series aluminium alloy sheet was considered. An elasticplastic finite element model using remeshing option was developed. Experiments were conducted to verify the reliability of the developed finite element model. A critical clearance-thickness ratio which is a limit between two conditions of hole-flanging was found: hole-flanging with edge stretching and hole-flanging with ironing in which the metal is squeezed between the punch and the die. The effect of the hole-flanging condition on the punch load, the forming kinematics, the flange geometry and the boring quality was studied. The finite element results were validated by experimental results. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Hole-flanging is a sheet metal forming process which is often applied to produce a flange around holes. In the conventional holeflanging process, a blank-holding force is set to clamp firmly the sheet between the blank-holder and the die. Then, a punch forces the periphery of the hole into the die as shown in Fig. 1. In practice, hole-flanging process can be performed with or without ironing. Ironing is performed by setting a low value of the clearance between the punch and the die C. In this case, the metal is squeezed between the punch and the die leading to a longer flange. When the process is performed without ironing, the flange is formed by edge stretching leading to a thinner flange. In the literature, ironing was applied to the hole-flanging process for specific cases. Kumagai et al. (1999) have performed hole-flanging with ironing to study the forming of flanges for twoply sheet metal. Kumagai and Saiki (1998) have investigated the influence of the workpiece thickness on the punch load, the finished shape and the metal flow in the hole-flanging with ironing of thick sheet metal. Recently, Thipprakmas et al. (2007) have performed also the hole-flanging with ironing for thick sheet metal to study the effect of the quality of the initial hole on the flanged shape. In many industrial applications, the process is performed with ironing to obtain a long flanges that can be used for example to increase bearing surface or to increase the number of threads that will fit in a tapped hole.
∗ Corresponding author. E-mail address: [email protected] (A. Krichen). 0924-0136/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2011.04.017
Others techniques were proposed to produce a long flange. Lin et al. (2007) have adopted the cold extrusion to obtain a flange with more substantial lip thickness and greater height. In this case, the flange is formed by exerting a punch force on the rim of a preholed cup-shaped workpiece at the same time as a clamping force is applied to suppress dilation on the bottom of the cup. Lin and Tung (2007) showed that with sufficient clamping force, this technique could produce significant extruded flange height. This technique requires an accurate control of the clamping force and an additional step for preparing the cup-shaped workpiece. Thiruvarudchelvan and Tan (2007) have used the Maslennikov’s technique to produce a long flange. This technique is based on the use of flexible materials such as urethane in the design of forming tools. In this case, the flange is formed by means of an annular urethane pad instead of the rigid punch used in the conventional hole-flanging process. The used technique needs a higher press capacity and the flexible tool material has a short life expectancy as shown in the work of Thiruvarudchelvan (2002). Cui and Gao (2010) have performed hole-flanging operation using a multistage incremental forming process. Instead of the rigid punch employed in the conventional process, a CNC controlled rigid tool with a smooth ball end tip is traversed on a sheet metal blank. In this study, among three forming strategies, it was demonstrated that the forming strategy by increasing the part diameter in small steps during the forming process produces a relatively higher flange height and uniform wall thickness. This technique is mainly applied to make prototype parts or batches of small quantities. In the present work, the conventional hole-flanging process of thin sheet metal with and without ironing was used. For this purpose, hole-flanging was carried out by varying the clearance between the punch and the die C and keeping the other parameters unchanged. Finite element (FE) simulations were performed to
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Table 1 Tool geometry parameters used in the hole-flanging process.
Fig. 1. Conventional hole-flanging process with and without ironing.
identify the occurrence of ironing by the determination of a limit between the hole-flanging with ironing and the hole-flanging without ironing (i.e. with only edge stretching). Moreover, attention was paid to study the effect of the hole-flanging condition on the punch load, the forming kinematics and the final shape. In parallel, experiments were carried out to check the FE results.
Nomenclature
Symbol
Considered values
External radius of the workpiece Radius of the initial hole Workpiece thickness Punch radius Cone semi-angle of the punch Punch profile radius Die radius Die profile radius Clearance
Re Ri t Rp ˛ Rpp Rd Rdp C
15 mm 3 mm 2 mm 6 mm 30◦ 4 mm 6.82–9.04 mm 0.2 mm 0.82–3.04 mm
were also performed at 45◦ and 90◦ to the rolling direction. The measurement of both transverse and longitudinal strains leads to the plastic anisotropy coefficients r0 = 0.45, r45 = 0.55 and r90 = 0.89. The normal anisotropy coefficient r¯ = (r0 + r90 + 2r45 )/4 = 0.61 is significant and the planar anisotropy coefficient r = (r0 + r90 − 2r45 )/2 = 0.12 is rather weak. For the FE analysis, the aluminium alloy was assumed to have an elastic-plastic behaviour with an isotropic hardening rule. Despite the significant normal anisotropy observed on this material, the anisotropy was neglected in a first step. The material was assumed to be isotropic and to obey the von Mises yield criterion given by: f = J2 () − R
(1)
J2 denotes the second stress invariant that is defined as follows:
2. Materials and techniques
J2 () =
2.1. Material behaviour A 2 mm thick 1000 series aluminium alloy sheet was considered for this work. A monotonic tensile test was carried out on rectangular sample of gauge dimensions 150 mm × 20 mm × 2 mm under displacement control at a constant rate of 5 mm/min, according to a procedure defined in Laurent et al. (2009). The load was measured by a load cell of 50 kN capacity. The Cauchy stress is calculated by the ratio of the load over the current section of the sample. The current section is determined from the initial section of the sample by assuming both isochoric plastic deformation and a homogeneous distribution of strain along the gauge length of the sample. The logarithmic strain was measured by a field measuring system by 3D image correlation (Aramis) as defined in Zang et al. (2011). The obtained stress–strain curve in the rolling direction is shown in Fig. 2. As expected for such aluminium alloy, it is observed that the saturation of the tensile stress is reached for low strain values. The Young’s modulus (E= 68 GPa) was determined from the experimental stress–strain curve. The Poisson’s ratio was taken equal to 0.28. To determine the material anisotropy, tensile tests
3 S:S 2
(2)
where S is the deviatoric part of the Cauchy stress tensor . R denotes the isotropic hardening function, that is chosen with a saturation form of Voce (1948) type: R = R0 + Q (1 − exp(−b))
(3)
where R0 , Q and b are the initial yield stress, the hardening saturation and the rate at which saturation is achieved, respectively. The evolution of the plastic strain rate is obtained by using the normality rule: dp = d
∂f = dn ∂
(4)
where n gives the direction of the plastic strain increment and d, called the plastic multiplier, determines the magnitude of the plastic strain increment. The values of the model parameters (R0 = 65 MPa, Q = 53 MPa and b = 750) were obtained by the best fit to the experimental stress–strain curve in the rolling direction as shown in Fig. 2. 2.2. Hole-flanging parameters To succeed hole-flanging, some parameters have to be controlled, especially the tool geometry parameters. The nomenclatures of the tool geometry parameters are mentioned in Table 1 and they are illustrated in Fig. 3. Among this list, some of them determine whether the hole-flanging process is performed with or without ironing as shown in Fig. 1(b) and (a), respectively.
Cauchy stress (MPa)
120 100 Experiment 80
Model
60
2.3. Ironing parameters
40 20 0 0
0.01
0.02
0.03
0.04
0.05
Logarithmic strain Fig. 2. Experimental and numerical stress–strain curves in the rolling direction.
Ironing occurs when the clearance between the punch and the die (C = Rd − Rp ) is set lower than a certain value from which the flange will be continuously in contact with the punch and the die during forming. Therefore, for a given workpiece thickness t, Rp and Rd are the two parameters that must be controlled to perform holeflanging with or without ironing. In the hole-flanging practice, to control the occurrence of ironing it is convenient to consider the
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Fig. 3. Tool geometry parameters of the conventional hole-flanging process.
clearance-thickness ratio Rc which is defined as the ratio of the clearance C to the workpiece thickness t. 2.4. Experiments The workpiece was an aluminium washer punched by the conventional punching process. The clearance between the punch and the die for the punching operation was set to 6 %t. The initial hole was punched from the side opposite the intended flange. This prevents splitting of the severely stretched edge of the flange as reported by ASM (1996). Conventional hole-flanging tools including die, truncated pilotpunch and blank-holder were used as shown in Fig. 4. A pilot was designed at the lower end of the hole-flanging punch for proper locating of the workpiece. The geometrical parameters of the workpiece are illustrated in Fig. 3 and the considered values of tool geometry parameters are mentioned in Table 1. In practice, the clearance-thickness ratio Rc was controlled by keeping the radius of the punch Rp constant and changing the radius of the die Rd . For this purpose, several dies with different Rd values were used. A range of clearance-thickness ratio Rc values between 0.41 and 1.52 was studied, the other geometrical parameters being kept constant. After centering the workpiece on the die, it was clamped between the die and the blank-holder by using four screws M10. The screws were slightly tightened in such a way to prevent the upward motion of the blank-holder and the workpiece as shown in the work of Krichen et al. (2011). Hole-flanging process was carried out with a universal tension-compression testing machine of maximum load 50 kN. It was performed under displacement control at a constant low rate of the punch equal to 5 mm/min. The output of the displacement gauge and of the load cell was continuously recorded in a data acquisition system. 2.5. FE modelling A FE model was developed to perform numerical analysis on the hole-flanging process. The analyses were performed using the standard version of the software ABAQUS. As shown in Fig. 3, the geometry of the tools, the workpiece and the loading are axisymmetric. Moreover, as the sheet metal was assumed to be isotropic, the material properties are also axisymmetric. Therefore, a 2D axisymmetric model was adopted. The tools (die, punch and blank-holder) were modeled as rigid surfaces. The workpiece was modeled as a deformable body with an elasticplastic material using the material properties specified in Section 2.1. A 3-nodes linear axisymmetric triangle element (CAX3) and 4nodes bilinear axisymmetric quadrilateral element with selective
Fig. 4. Experimental tool.
reduced integration (CAX4R) were used. The choice of a reduced integration element was made to speed up the computation as this element uses only one integration point per element instead of four. Note that a few triangular elements were used to avoid severe volume locking. An automatic mesh generator program was used to generate the initial FE mesh as shown in Fig. 5. Due to the large mesh distortions, remeshing techniques were used in order to compute an accurate solution. The adaptive remeshing process involves the iterative generation of multiple dissimilar meshes to determine a single, optimized mesh that is used throughout the analysis. The mesh size can be refined or coarsened according to an error indicator. The equivalent plastic strain error indicators were chosen to decide if the workpiece needs to be remeshed. A typical obtained FE mesh is shown in Fig. 5. Remeshing was applied for each case studied in this work. Coulomb’s friction law was used to solve the frictional effect of the tool–workpiece interfaces. To describe reasonable contact conditions between the tools and the workpiece, the friction coefficient was set to 0.2. FE simulations were performed in two steps. In the first step, the die and the blank-holder were rigidly clamped and the punch was constrained to move in the axial direction. In the second step, the blank-holder was removed to analyse the final shape after springback phenomenon. 3. Results and discussion 3.1. Punch load To investigate the effect of Rc on the punch load, the relationship between punch load and punch travel is plotted in Fig. 6 for different values of Rc . It was found that the change in Rc does not affect the punch load–punch travel relationship at the beginning of the process. After this stage, the punch load increases with decreasing Rc . After reaching the maximum punch load (Fmax ), for high values of Rc , the
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6 FE result
Punch load (kN)
5
Experiments
4 Rc=0.41
3 2
Rc=1.52
1 0 0
2
4
6
8
10
12
14
16
Punch travel (mm) Fig. 7. Punch load versus punch travel for Rc equal to 1.52 and 0.41.
mate the experimental punch load in some portions of the curve and underestimate it in other portions. For the entire curve, the difference does not exceed 17 % of the experimental value. In term of Fmax , a good agreement between experimental and numerical results is observed. To illustrate this observation, the evolution of the maximum punch load Fmax with Rc obtained experimentally and numerically is plotted in Fig. 8. It can be seen that as Rc decreases, Fmax increases. Fmax increases more sharply when the hole-flanging is performed with reduced values of Rc . From comparison between experimental and numerical results, it can be concluded that the developed FE model can be an appropriate tool to predict the punch load during hole-flanging process with an acceptable difference as shown in Fig. 7. Moreover, the FE model estimates precisely the maximum punch load and its evolution with Rc . This is more important from an industrial point of view. Fig. 5. FE model (a) initial mesh and (b) mesh after 3 adaptive remeshing iterations.
3.2. Forming kinematics relationship is slightly affected. However, for reduced values of Rc , the relationship is strongly affected by the appearance of a second peak load. It was also found that no matter the value of Rc , Fmax is always found at the first peak load corresponding to the same punch travel value. In order to validate the obtained results, typical experimental and FE punch load–punch travel relationships for high and low values of Rc are plotted in Fig. 7. It can be seen that the shape of the numerical and experimental curves are broadly similar. However numerical results overesti-
To investigate the forming kinematics during the hole-flanging process, the evolution of the punch load–punch travel relationship and typical deformed shapes were analysed. Fig. 9 shows this relationship for a low and a high value of Rc . For the low value of Rc , numerical results show that hole-flanging exhibits six stages. In the first stage (I), the punch load increases at the beginning of the contact between the punch and the workpiece. This is followed by a linear evolution linked to the elastic deformation. At the end of this stage, a loss of linearity is observed indicating the onset 6
FE result
Maximum punch load (kN)
6
c
=0 .6
c
R
c= 0
.8
R
=0
.4 1 Rc 1
3
=1
4
R
Punch load (kN)
5
Rc
2 .5 =1
2 1
Experiment
5 4 3 2 1 0
0
0
0
2
4
6
8
10
12
14
Punch travel (mm) Fig. 6. Punch load versus punch travel for different Rc values.
16
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Clearance-thickness ratio (R c) Fig. 8. Evolution of the maximum punch load as a function of clearance–thickness ratio.
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Fig. 9. Punch load versus punch travel and typical deformed shape.
of the plastic deformation. The second stage (II) is characterized by stress concentrations in the close contact between the punch and the inner edge of the workpiece. This situation introduces a significant plastic deformation in this zone. Therefore, the major part of the second stage is achieved at a quasi constant load (i.e. load plateau). In the third stage (III), the deflection of the edge is the principal deformation. It occurs at the beginning of the contact between the truncated surface of the punch and the top surface of the workpiece. At this step, the punch load increases non-linearly with punch travel. The fourth stage (IV) is characterized by a flow forming process, in this stage the work material is pushed down towards the die cavity. Due to the significant plastic deformation induced in this step, the punch load reaches its maximum value then it decreases gradually. For low values of Rc , the thickness of the flange is higher than the gap between the punch and the die. Therefore, ironing occurs at the fifth stage (V). The motion of the punch forces the material to fill the narrow gap between the punch and the die. As a consequence, the punch load increases again to a secondary maximum. After ironing the major amount of the material, the punch load drops down. The final stage (VI) is characterized by a sliding between the die and the internal surface of the raised flange. The forming kinematics in the hole-flanging for high value of Rc was previously described in the work of Krichen et al. (2011). It was found that forming is achieved in only five stages. The three first stages (I, II and III) and the final stage are similar to that observed in hole-flanging with low value of Rc . Conversely, the fourth and the fifth stages (IV and V) are replaced by one stage in which the motion of the punch induces only the bending of the edge. 3.3. Final shape For all considered values of Rc , the finished products are obtained free from necking and fracture. Some typical examples are shown in Fig. 10.
To illustrate the dependence of the final shape to Rc , some sectional view of the finished product taken in the rolling direction are presented in Fig. 11. This figure shows also the simulated final deformed shape. Results are presented from low to high values of Rc . The progression of the final shape with Rc can be seen in this figure. To quantify this progression, the geometrical evolution of both the inner and the outer profiles of the flange are investigated in the next sections. 3.3.1. Inner profile For all values of Rc , hole-flanging leads to a flange with a curved profile followed by a straight profile as shown in Fig. 11. The curved profile leads to a round and the straight profile corresponds to the generatrix of a cylindrical boring as shown in Fig. 10. Conversely to the high values of Rc , a short curved profile and a long straight profile are obtained for low values of Rc . To investigate the effect of Rc on the characteristic dimensions of the inner profile, the evolution of the straight profile length (hs ) and the curved profile length (hc ) (see Fig. 11) with Rc are plotted in Fig. 12. It can be seen that for higher values of Rc , hs and hc are almost similar. When Rc decreases hs increases while hc decreases. hs increases more sharply for low values of Rc . Namely, hs becomes 13 times longer than hc for Rc equal to 0.41. For this value of Rc , hs is 3.4 times higher than the workpiece thickness that seems to be advantageous in the product design from an industrial point of view. In Fig. 12, the experimental values of hs and hc are superimposed. A good agreement between experimental and numerical values is observed. The average difference is about 6 % and 8 % of the numerical value for hs and hc , respectively. To investigate the quality and the dimensional accuracy of the obtained cylindrical boring, the numerical boring generatrix was analysed. In Fig. 13 the boring generatrix was compared to the nominal axis for different values of Rc . This figure shows the distribution of the radial error (Er ) along the boring generatrix for different val-
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Fig. 10. Typical examples of finished product.
Fig. 11. FE deformed shape and sectional view for different Rc values.
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7 ΔS S
hS
(hS) FE result
3
(hS) experiment (hc) FE result
2
0.075
0.05
hc
ΔS S (mm)
4
Hole-flanging with ironing
h
4
(h) FE result
3
(h) experiment 2
(hc) experiment
Hole-flanging without ironing
5
0.1
5
(te) , (h) (mm)
6 (hS) , (hc) (mm)
6
0.125
Workpiece thickness
0.025
1
te
1
0 0
0.2
0.4
0.6 0.8 1 1.2 Clearance-thickness ratio (Rc)
1.4
0 1.6
(te) FE result Rcc = 0.68
(te) experiment
0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Clearance-thickness ratio (Rc)
Fig. 12. The straight profile length (hs ), the curved profile length (hc ) and the straightness error (S) versus Rc .
Fig. 14. The flange height (h) and the thickness at the flange extremity (te ) versus Rc .
ues of Rc . The radial error Er is defined as the deviation between the nominal and the obtained radius. It can be seen that the boring acquires either a positive or a negative radial error along the generatrix. The maximum radial error of about 0.1 mm is reached for a value of Rc equal to 1.52. This value corresponds to 1.6 % of the nominal radius. Moreover, the geometry of the obtained generatrix tends to the nominal axis as Rc decreases. To quantify this observation, the straightness error (S) of the boring generatrix is plotted versus Rc in Fig. 12. The straightness error S is the difference between the highest and the lowest radius of the obtained boring as shown in Fig. 13. It can be seen that the highest straightness error S of about 0.125 mm is obtained for a value of Rc equal to 1.52. It corresponds to 2 % of the nominal radius. The straightness error decreases as Rc decreases. It reaches a very low value of about 0.004 mm for low values of Rc . According to the evolution of the straightness error as shown in Fig. 12, two families of boring quality can be distinguished. The first includes the reduced values of Rc that leads to a good boring straightness. The second includes the high values of Rc that leads to an ordinary boring straightness. Accordingly, it is important to determine a critical value of Rc that limits these two families. This is investigated in the last section (Section 3.4).
of the flange has a straight shape as shown in Fig. 11. As Rc increases, the contact area between the flange and the die decreases. Consequently, the straight profile is reduced while a curved profile is developed in the lower part of the flange. For high values of Rc , the outer profile becomes entirely curved with a geometrical singularity in the die radius. In addition to the profile shape, Rc affects also the flange height (h) which is depicted in Fig. 11. The evolution of h versus Rc is plotted in Fig. 14. As Rc decreases from its highest value, the portion of the workpiece subjected to the deflection in the stage (III) decreases. As a consequence, a slight decrease of h is observed. However, for low values of Rc , ironing that occurs at stage (V) causes a sharp increases of h. Like the straightness error of the inner profile, the evolution of the flange height confirms the need of the determination of a critical value of Rc . This is investigated in the last section (Section 3.4). In Fig. 14, the experimental values of h are superimposed. A good agreement between experimental and numerical results is observed with a few exceptions where the difference reaches 12 % for low Rc values.
3.3.2. Outer profile For reduced values of Rc , hole-flanging is performed with a full contact between the die and the flange. As a result, the outer profile
The analysis of the punch load, the forming kinematics and the final shape reveals that Rc affects much the obtained results. In particular, by allowing for the influence of Rc on some parameters such
3.4. Limit between hole-flanging with and without ironing
Fig. 13. Boring generatrix for different Rc values.
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as S, h and Fmax , it is shown that two families of hole-flanging can be distinguished. In the first the hole-flanging was performed with ironing whereas in the second the hole-flanging was performed without ironing (i.e. by only edge stretching). Therefore, it is important to determine the critical value (Rcc ) that limits between hole-flanging with and without ironing. Considering the geometrical conditions of the appearance of ironing in the hole-flanging process mentioned in Section 2.3, the thickness at the flange extremity (te ) (see Fig. 11) is the most suitable parameter to determine exactly Rcc . Fig. 14 shows the evolution of te versus Rc . It can be clearly observed that there are two families of Rc limited by the critical value Rcc which is equal to 0.68. When Rc is higher than 0.68, thinning of the flange occurs. Namely, te remains at a constant value of about 1.35 mm (thinning is about 32 %t). When Rc becomes equal or lower than Rcc , ironing begins and consequently te becomes equal to the clearance C. The critical value is depicted in Fig. 8 and Fig. 12. It can be seen that a significant change is observed at this value, in particular for the parameters S, h and Fmax . The critical value Rcc can also be determined analytically as the geometrical configuration for Rcc is in agreement with the assumptions proposed by Asnafi (1999) relating te to t, in the case of isotropic material, by: te = t
Ri Rd − te /2
(5)
Taking into account that te =C and Rd =Rp +te in this case, and by using Eq. (5), we obtain the following relationship:
Rcc =
Ri Rp + 0.5 Rcc t
(6)
Therefore, Rcc can be determined analytically by resolving the following equation: 3 2 0.5tRcc + Rp Rcc − Ri = 0
(7)
The obtained value of Rcc , that is in agreement with that predicted by the FE models is 0.67. 4. Conclusion FE simulations and experiments were carried out to study the effect of the clearance-thickness ratio on the hole-flanging process. For high values of the clearance-thickness ratio, hole-flanging was performed by edge stretching in which the flange gets thinner. For low values of the clearance-thickness ratio, hole-flanging was performed with ironing in which the metal is squeezed between the punch and the die. A critical value of the clearance-thickness ratio which is about 0.68 was found as a limit between the two hole-flanging conditions: hole-flanging with edge stretching and hole-flanging with ironing. This critical value was determined by
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analysing the thickness at the flange extremity and it was confirmed by analysing both the forming kinematics and the maximum punch load. Moreover, the effect of hole-flanging conditions on the final shape was quantified. It can be concluded that edge stretching leads to a short flange with a curved outer profile and a short boring with an ordinary quality. In addition, edge stretching leads to a boring with a wide rounded entrance and it causes the thinning of flange whose value was about 32 %t. However, when hole-flanging was performed with ironing, a long flange with a straight outer profile and a long boring with a high dimensional accuracy were obtained. Ironing leads also to a boring with a short rounded entrance and a flange with a constant cross section. The comparison between FE simulations and experiments shows that the developed FE model can be an appropriate tool to predict the punch load, the forming kinematics and the final shape with an acceptable agreement. Finally, it seems interesting to study the effect of the initial anisotropy of the sheet on the FE results. This will be done in future works. References ASM, 1996. ASM Handbook, vol. 14: Forming and Forging, fourth printing. ASM International. Asnafi, N., 1999. On stretch and shrink flanging of sheet aluminium by fluid forming. Journal of Materials Processing Technology 96, 198–214. Cui, Z., Gao, L., 2010. Studies on hole-flanging process using multistage incremental forming. CIRP Journal of Manufacturing Science and Technology 2, 124–128. Krichen, A., Kacem, A., Hbaieb, M., 2011. Blank-holding effect on the hole-flanging process of sheet aluminum alloy. Journal of Materials Processing Technology 211, 619–626. Kumagai, T., Saiki, H., 1998. Deformation analysis of hole flanging with ironing of thick sheet metals. Metals and Materials 4, 711–714. Kumagai, T., Saiki, H., Meng, Y., 1999. Hole flanging with ironing of two-ply thick sheet metals. Journal of Materials Processing Technology 89–90, 51–57. Laurent, H., Grze, R., Manach, P., Thuillier, S., 2009. Influence of constitutive model in springback prediction using the split-ring test. International Journal of Mechanical Sciences 51, 233–245. Lin, H.S., Lee, C.Y., Wu, C.H., 2007. Hole flanging with cold extrusion on sheet metals by FE simulation. International Journal of Machine Tools and Manufacture 47, 168–174. Lin, H.S., Tung, C.W., 2007. An investigation of cold extruding hollow flanged parts from sheet metals. International Journal of Machine Tools and Manufacture 47, 2133–2139. Thipprakmas, S., Jin, M., Murakawa, M., 2007. Study on flanged shapes in fineblanked-hole flanging process (FB-hole flanging process) using finite element method (FEM). Journal of Materials Processing Technology 192–193, 128–133. The Seventh Asia Pacific Conference on Materials Processing (7th APCMP 2006). Thiruvarudchelvan, S., 2002. The potential role of flexible tools in metal forming. Journal of Materials Processing Technology 122, 293–300. Thiruvarudchelvan, S., Tan, M., 2007. Investigations into collar drawing using urethane pads. Journal of Materials Processing Technology 191, 87–91. Advances in Materials and Processing Technologies, July 30th–August 3rd, Las Vegas, Nevada 2006. Voce, E., 1948. The relationship between stress and strain for homogeneous deformation. Journal of the Institute of Metals 74, 537–562. Zang, S., Thuillier, S., Port, A.L., Manach, P., 2011. Prediction of anisotropy and hardening for metallic sheets in tension, simple shear and biaxial tension. International Journal of Mechanical Sciences, doi:10.1016/j.ijmecsci.2011.02.003.