Finite Element Simulation of Process and Springback of ... Aided Deep Drawing Using Tapered Blank Holder ... and compared with four segments tapered blank holder technique by ABAQUS

Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer 2010

© 2010 IAU, Majlesi Branch

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Finite Element Simulation of Process and Springback of Friction Aided Deep Drawing Using Tapered Blank Holder Divided Into Eight Segments Mehran Kadkhodayan* Department of Mechanical Engineering, Ferdowsi University of Mashhad, Iran E-mail: [email protected] *Corresponding author

Rasoul Pourhasan Department of Mechanical Engineering, Ferdowsi University of Mashhad, Iran E-mail: [email protected]

Received 1 May 2010; Revised 30 August 2010; Accepted 17 September 2010

Abstract: In this paper, a novel technique on friction aided deep drawing using tapered blank holder divided into eight segments is proposed to overcome defect of friction aided deep drawing using four segments tapered blank holder technique. A taper blank holder is designed to be of two parts: stationary part with 5 degree taper angle and moving parts divided into eight tapered segments. The main function of this tapered blank holder device is adopting the frictional force between the blank and the blank holder segments to work in the useful drawing direction. At first, the drawing mechanism of eight segments tapered blank holder technique and inflow of material in the flange portion of blank are investigated and compared with four segments tapered blank holder technique by ABAQUS software to show the merits of the proposed process. Then, the finite element analysis of springback is investigated by the ABAQUS software. Effect of different process parameters such as initial blank thickness, punch profile radius, blank holder force, friction coefficient and hardening models on springback prediction are studied. A successful deep cup with drawing ratio up to 3.67 can be produced without any defect by using this new technique only in one die set. The cost and time of die fabrication in this technique are less than the conventional deep drawing.

Keywords: ABAQUS/explicit, Eight Segments Tapered Blank Holder, Friction Aided Deep Drawing.

Reference: M. Kadkhodayan and R. Pourhasan, (2010), "Finite Element Simulation of Process and Springback of Friction aided Deep Drawing Using Tapered Blank Holder divided into Eight Segments", Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4, pp. 1-11

Biographical notes: M. Kadkhodayan, Associate Professor in Mechanical Engineering in Ferdowsi University of Mashhad, Research area: sheet metal forming, plasticity. R. Pourhasan is M.Sc in Mechanical Engineering from Ferdowsi University of Mashhad, Iran. His current research interest includes material processing and plasticity.

Majlesi Journal of Mechanical Engineering, Vol. 3/ No. 4/ Summer - 2010


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1 INTRODUCTION

The forming limit in conventional deep drawing of sheet metals with a metal punch and die is confined by the fracture of a cup at the punch profile portion. The limiting drawing ratio (LDR) achieved by the first stage drawing in conventional deep drawing seldom exceeds about 2. Thus, if a cup of final proportion exceeding this limiting value is required, redrawing or ironing in one or more stages is necessary as subsequent operations. Since a pair of punch and die is needed for each stage, the cost and time for making tools increases particularly in small-lot production of deep cups. Many novel processes have been developed to overcome this problem in the small-lot production of deep cups [1].

Punchless deep drawing process was proposed by Maslennikov to obtain a deep cup [2]. In this process, a rubber ring is used instead of a metal punch in the conventional deep drawing. Unlike the conventional process, the drawing deformation of a blank is caused by the frictional force induced at the interface between the rubber ring and the flange portion of the blank. Because the drawing of the blank is done by the radial compressive force, the fracture at the punch profile portion can be avoided. Therefore, a very deep cup can be produced using only one rubber ring and metal die throughout the drawing process. However, the frictional force induced by the rubber ring is not large enough, and therefore the application of this process is limited to rather soft materials with small deformation resistance. In addition, other disadvantages of this process are the short life time of the rubber ring and circumferential fracture at the flange portion of thin sheets [3].

A new deep drawing process was proposed to overcome deficiencies of Maslennikov's process [4]. In this process a flat metal blank holder divided into four segments is used instead of the rubber ring in the Maslennikov's process. This metal blank holder is made by cutting a conventional steel blank holder into four segments which can move radially inward and outward under a certain blank holding pressure. Unfortunately, this process has one defect during the application of such proposed device which is occurrence of wrinkle due to flowing of flange material into the gaps between the blank holder segments.

To overcome this problem of the friction aided deep drawing process using four segments flat blank holder, a new eight segments flat blank holder device was proposed by Hassan et al. [5]. This device is made by fitting four flat small wedges in the gaps between the

four flat drawing segments. The only difference between these two techniques is in the number of blank holder segments. With using eight segments flat blank holder technique, good results were obtained. However, in the case of using thin sheets, a crack was observed due to the localized intensive shear deformation at the boundaries between the drawing segments and the wedges.

Therefore, friction aided deep drawing process using a tapered blank holder divided into four segments was proposed to eliminate the defects of localized wrinkling and crack that was observed in the previous techniques [6]. A cup was produced without wrinkling and cracks by using this process. But, a non-uniform flow of material in the flange portion of cup was observed in this method, (Fig. 1). The figure shows this defect at the direction C after 50 times drawing operations. At this stage of drawing, the radial inflow of material in the C-directions is greater than those in the directions A and B. As a result, the material coming to the die opening buckles and makes craters in the clearance between the punch and die.

Springback is a phenomenon that occurs in many cold working processes. When a metal is deformed into the plastic region, the total strain is made up of two parts, the elastic part and the plastic part. During removing the load, a stress reduction will occur and accordingly the total strain will decrease by the amount of the elastic part, which results in springback [7]. Oliveira et al. [8] evaluated several work hardening models in order to determine their influences on the numerical prediction of the springback phenomenon. They investigated the effect of different constitutive models on the numerical simulation of mild (DC06) and dual phase (DP600) steels submitted to several bending/unbending strain-path changes, during which a high level of equivalent plastic strain resulted. Esat et al. [9] carried out springback analysis of different aluminium sheets with different thicknesses and explored a relation between the amount of springback and total equivalent plastic strain and also equivalent stress. They concluded that the material with higher yield strength and smaller equivalent plastic strain has higher amount of springback than the material with lower yield strength and higher equivalent plastic strain.

The finite element analysis (FEA) of springback is very sensitive to many numerical parameters, including the number of through-thickness integration points, type of element, mesh size, angle of contact per element on die shoulder, possible inertia effects and contact algorithm. Moreover, springback is also sensitive to many physical parameters including material properties,



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hardening laws, friction coefficient, blank holder force and punch profile radius. All those make springback simulation very cumbersome [10].

In this paper a novel process on friction aided deep drawing using eight segments tapered blank holder is proposed to overcome deficiency of four segments tapered blank holder technique. The deformation mechanism and the effects of drawing conditions are investigated by ABAQUS/Explicit software. In continuance, the springback occurred in the cup produced by this new technique is numerically studied. Influences of initial sheet thickness, punch profile radius, blank holder force, friction coefficient and hardening model on springback are investigated by means of the finite element software, ABAQUS.

Fig. 1 Crater defect observed in C- directions

2 DRAWING MECHANISM OF A TAPERED BLANK HOLDER DIVIDED INTO EIGHT SEGMENTS

Figure 2 shows schematically the proposed eight segments tapered blank holder device. This metal blank holder is made by cutting a tapered steel blank holder into eight segments. It can move radially inward and outward under a certain blank holding pressure. It consists of a stationary base and eight tapered drawing segments that have similar planes of 5 degree taper angle. All of these segments are level with each other and the base is tapered in the same direction. The drawing segments can slide in radial direction under a constant speed over the tapered surfaces of the stationary base. In the first drawing step, deformation starts when four facing segments move radially inward to the die opening in the A-direction as shown in Fig. 2 (a). The other four segments in the B-direction move in the reverse direction, i.e. downward and radially outward opposite to the drawing direction as shown in Fig. 2(c). Due to this action, the blank sheet and the die in the A-direction are lifted up as shown in Fig. 2(b), while in the B-direction; there is no contact between the

blank sheet and segments as shown in Fig. 2(c). At that time about 50% of the flange portion which is under drawing segments in the B-direction is not subjected to the blank holder force. On the other hand, the four segments in the A-direction are advancing to the die opening, so that they tightly contact with the blank sheet as shown in Fig. 2(b). As a result, the frictional force generated in the A-direction aids the blank to deform and move toward the die opening. While, the four segments in the B-direction do not generate outward frictional force opposing the blank deformation. Therefore, this technique successfully eliminates the localized intensive shear deformation observed when using the flat blank holder divided into eight segments. However, small wrinkles arise in the B-direction of the flange portion due to the circumferential compressive force. In the second drawing step, the blank holder segments in the B-direction move radially inward to the die opening, while the other four segments in the A-direction move in the reverse direction. Hence, the wrinkles generated in the B-direction in the first drawing step will be simultaneously corrected. Therefore, a complete and successful deep cup can be obtained by repeating these two steps to a certain number of drawings.

(a)

(b) (c)

Fig. 2 (a) Schematic of eight segments tapered blank holder, (b) and (c) Schematic of die in motion



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3 TEST MATERIAL

In the current study, soft aluminum (Al-O) blank of 0.5mm thickness is used as a testing material. Tool dimensions are listed in Table 1. The material constants F (strength coefficient of blank material), n (work-hardening exponent) and r (normal anisotropy) determined from the uniaxial tension test are listed in Table 2. The blank diameter is changed as 86 mm and 110 mm which give drawing ratios of 2.87 and 3.67. Dry friction condition between the blank sheet and blank holder segments is necessary to increase the induced frictional force.

die Outer diameter (mm) 120 Inner diameter (mm) 32 Profile radius(mm) 3 Tapered blank holder Outer diameter (mm) 116 Inner diameter (mm) 35 Blank holder force (kN) 60-100 Assistant punch Diameter (mm) 30 Profile radius (mm) 3-5 Punch force (kN) 5

Table 2 Mechanical properties and dimensions of

aluminum blank n-value 0.27 r- value 0.76 F-value (MPa) 220 Young modules (GPa) 70 Thickness (mm) 0.5-0.7 Blank diameter (mm) 86-110

4 NUMERICAL SIMULATION

Nowadays explicit models are widely utilized to analyze sheet metal forming processes since they allow fully 3-D geometry and complex contact conditions to be taken into account with relevant CPU savings with respect to the implicit algorithms [11-14]. Such models solve a set of independent dynamic equilibrium equations at each time increment in order to upgrade the geometry of the meshed structure. No inversion of the stiffness matrix and iterative procedure to get a satisfactory solution are required. In this way, CPU time is saved and the incidence of plastic instabilities can be described well since the analysis continues even if diagonal terms of stiffness matrix approach to zero.

However, as far as evaluation of the springback phenomenon is concerned, when the contact between the stamped part and the rigid dies is lost, the deformed sheet starts to oscillate around the new equilibrium position, until the accumulated kinetic energy is dissipated. As a consequence, the prediction of the elastic springback is a very time consuming step in explicit FEM analysis of sheet stamping processes. Actually a suitable amount of damping should be artificially introduced in order to accelerate the kinetic energy dissipation. Nevertheless, it is very difficult to evaluate the correct amount of applied damping.

The commercial ABAQUS code provides such combined approach, incorporating a procedure by which the stress state at the end of the loading phase is supplied to the implicit numerical code (ABAQUS/Standard) which performs a simple elastic step. This stress state was obtained through a dynamic explicit FEM simulation carried out with ABAQUS/Explicit.

The finite element model of friction aided deep drawing using eight segments tapered blank holder technique is shown in Fig. 3. Because of the symmetry, only one quarter of die is modeled. The type of element used in punch, die and blank holder is discreet rigid element (R3D4) and blank is modeled by using 4-node, shell element (S4R) with the symmetry boundary conditions along the X and Y axes. Twenty nine integration points through the thickness are used in the modeling. The mass scaling is applied to shorten analysis time; however, too much mass scaling causes an improper dynamic effect. Therefore, different mass scaling values are examined to achieve a favorite value. In the simulation, 1859 elements are used in one quarter of blank. In order to model friction at the tool-work piece interface, the coulomb friction model is used. Frictional condition of contact surface is one of the most important factors in this process. Dry friction condition between the blank sheet and blank holder segments is necessary to increase the induced frictional force. Therefore, with increasing friction coefficient between the blank and blank holder segments, frictional force in this region will be increased; as a result, the blank can move easier to the die opening. On the other hand, decreasing of frictional force between the blank sheet and die can cause easier moving of the blank; thus decreasing of friction coefficient between the blank and die is very important. Therefore, friction coefficient between the blank holder segments and blank and also between the blank and die are assumed to be 0.3 and 0.03, respectively. Algorithm of contact for this process is surface to surface contact with penalty method.

Table 1 Tool dimension

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technique is less than that for four segments blank holder technique. Also, an example of successful produced cup without any defect by friction aided deep drawing using eight segments tapered blank holder technique is shown in Fig. 9.

Fig. 5 Radial displacement of flange in A-direction of

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Fig. 6 Radial displacement of flange in B-direction of

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Fig. 7 Radial displacement of flange in C-direction of

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Fig. 9 An example of successful cup with drawing

ratio 3

5.1.2. Thickness strain distribution

Figure 10 shows the thickness strain distribution at longitudinal cross section through the C-direction of a drawn cup. Since a blank receives bending under tensile force, the thinnest portion is observed around

Number of drawing

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the punch profile radius. However, the bottom of cup becomes slightly thin and exhibits a uniform thickness strain distribution. At the sidewall of cup, the thickness strain decreases gradually, while the cup becomes thickener at the flange portion. At the die profile portion, the cup thickness changes rapidly which is almost the same as the one may be observed in the conventional deep drawing with metal punch and die.

Fig. 10 Thickness strain distribution in C-direction

6 SPRINGBACK INVESTIGATION OF CUP

In order to measure the springback of the cup, two parameters are considered, i.e. mean radius of the cup edge and bottom angel of the cup (theta), as shown in Fig. 11. On the best knowledge of the authors, this process has not been carried out experimentally yet; hence, the results could not be compared with any data.

Fig. 11 Springback definition parameters

6.1. Effect of initial blank thickness

Initial blank thickness is one of the parameters that clearly affects on springback in sheet metal forming

which in fact may be utilized to control it. On the other hand, increasing the initial blank thickness causes rising of required punch load and weight of the blank that are undesirable factors in design parameters. Therefore, finding the optimum value for initial blank thickness is vital for the purpose of using suitable values in the design stage. Three different values of sheet thickness are considered for this purpose, i.e. 0.5 mm, 0.6 mm and 0.7 mm. Fig. 12(a) shows the relation between the value of initial blank thickness and the springback of mean radius of cup edge and Fig. 12(b) displays the relation between the value of initial blank thickness and the springback of cup bottom. It is found that with increasing the initial blank thickness, the springback amount is decreased. Since, with raising the initial blank thickness, the amount of equivalent plastic strain is increased; as a result, the springback amount will be decreased. In other words, springback phenomenon is due to elastic portions of variable strains in work piece. So, the amount of springback reduction with increasing of initial blank thickness depends on formation of larger plastic region in a definite deformation. This fact demonstrates the sensitivity of springback to the value of initial blank thickness in sheet metal forming.

(a) Mean radius of the cup edge

(b) Theta.

Fig. 12 Influence of initial blank thickness on springback

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Figure 13 illustrates the relation between the equivalent plastic strain and initial blank thickness from center to edge of the blank. It can be observed that points near the cup edge have more equivalent plastic strain. Besides, it is observed that with increasing the initial blank thickness, amount of equivalent plastic strain is increased. As a result, the springback amount is reduced.

Fig. 13 Equivalent plastic strain for different blank

thickness.

6.2. Effect of blank holder force

The influence of blank holder force on springback is studied in this part. Three different values of blank holder force are considered for this purpose. The relation between the value of blank holder force and springback is shown in Fig. 14. It is observed that the springback amount decreases as the blank holder force increases. This phenomenon can be explained by this fact that under sufficiently large value of blank holder force more plastic deformation will happen, hence, the amount of springback is reduced. On the other hand, excessive increasing of blank holder force may cause tearing of the sheet. As a result, an optimum amount of blank holder force has to be found in order to lessen the springback and avoid the sheet tearing.


(b) Theta

Fig. 14 Influence of blank holder force on springback.

6.3. Effect of punch profile radius

Simulation performed under different punch profile radii (Rp: 3, 4 and 5 mm). From Fig. 15, it may be observed that the springback increases as the punch profile radius increases which can be justified by the amount of plastic deformation. It has to be noted that the stress over the punch corner (punch profile radius) is the most significant factor governing the magnitude of springback. Figure 16 shows the amount of equivalent plastic strain in central layer of the cup from center to edge for different punch profile radius. It can be noticed that with increasing the punch profile radius, the amount of equivalent plastic strain is decreased.


(b) Theta

Fig. 15 Influence of punch profile radius on spring back

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Fig. 16 Equivalent plastic strain for different punch profile radius

6.4. Effect of friction coefficient

In order to investigate the effect of friction coefficient between the blank and blank holder on springback prediction, this process is simulated for different friction coefficients, i.e. 0.25, 0.3 and 0.4. The effect of friction coefficient on springback is displayed in Fig. 17. As it may be seen, with increasing the friction coefficient the springback is decreased. In fact, raising the friction coefficient can increase sheet drawing during forming process. It means that the plastic deformation region is enlarged under definite deformation in sheet and as a result, springback amount is decreased with increasing plastic region.


(b) Theta

Fig. 17 Influence of friction coefficient on springback

6.5. Effect of hardening model

One of the important factors in FE simulation of sheet metal forming is the hardening model type utilized in finite element code. In other words, accurate prediction of springback in finite element method depends on hardening model of the material. Isotropic hardening rule, linear kinematic hardening, non-linear kinematic hardening and combined isotropic/ kinematic hardening (ISO-KIN) models can be used during modeling of material behavior. The classic isotropic hardening model does not consider the Bauschinger effect. The linear kinematic hardening proposed by Prager [15] can only be applied into materials with linear stress-strain curve and it usually underestimates the springback.


(b) Theta

Fig. 18 Influence of hardening model type on springback

Some researches have already studied the effect of using hardening model on springback. It has been shown that a combination of non-linear kinematic hardening rule and isotropic hardening can well predict the material behavior. In the current study, two hardening models are utilized in simulations, i.e. isotropic hardening model (ISO) and combined isotropic/ kinematic hardening (ISO-KIN). Figure 18 shows the springback of the cup for two hardening models. It is observed that isotropic model has predicted the springback of mean radius of cup edge more than that for the combined model. But, the amount of bottom angle of cup has been predicted less

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than that for the combined model. In overall, the combined hardening model has predicted the larger springback than the isotropic model.

7 CONCLUSION

A newly developed tapered blank holder divided into eight segments was used to obtain successful deep cups. This was achieved by overcoming the defect of non-uniform flow of material in the flange portion of cup observed when using four segments tapered blank holder technique. The drawing mechanism and inflow of material in the flange portion of blank were investigated in detail. It was concluded that flow of material in eight segments tapered blank holder technique is much more uniform than that for four segments tapered blank holder technique. Also, distortion of grids in the cup wall for eight segments technique was less than that for four segments technique. The obtained successful cup of 3.67 drawing ratio confirmed the possibility of the present technique in producing deep cups and showed that this process can noticeably increase the drawing ratio. On the other hand, in these techniques only one set of rigid tools was used throughout the drawing process; therefore, the cost and time of die fabrication was less than that for the conventional deep drawing.

Moreover, springback of friction aided deep drawing process was studied numerically by means of ABAQUS software. The influence of some important factors such as initial blank thickness, blank holder force, punch profile radius, friction coefficient and type of hardening model on springback of the cup produced by means of friction aided deep drawing process were investigated. The obtained numerical results show that increasing the value of the initial blank thickness reduces the springback of the deformed sheet. Also, with increasing blank holder force, the springback will be decreased. On the other hand, excessive increasing of blank holder force may cause tearing of sheet. As a result, an optimum amount of blank holder force should be selected to reduce the springback and avoid the sheet tearing simultaneously. The same result obtained for the effect of friction coefficient, i.e. with increasing friction coefficient between the blank and blank holder, springback of the deformed sheet was decreased. Furthermore, with the rising of punch profile radius, the springback increases. Finally, comparing different hardening models revealed that the combined hardening model predicted the larger springback than the isotropic model.

REFERENCES

[1] Yamaguchi, K., Nihara, M., Takakura, N., and Shirakawa, N., “Production of Deep Cups from Developed Blank,” Advanced Technology of Plasticity III, 1999, pp. 2039-2044.

[2] Hassan, M. A., Takakura, N., and Yamaguchi, K., “Fiction Aided Deep Drawing Using Polyurethane Ring and Metal Punch, Part 1: Experimental Observations on the Deep Drawing of Aluminum Thin Sheets and Foils,” Int. J. Machine Tools Manuf., Vol. 42, No. 5, 2002, pp. 625-631.

[3] Hassan, M. A., Takakura, N., and Yamaguchi, K., “Fiction Aided Deep Drawing Using Polyurethane Ring and Metal Punch, Part 2: Analysis of Drawing Mechanism and Process Parameters,” Int. J. Machine Tools Manuf., Vol. 42, No. 5, 2002, pp. 633-642.

[4] Hassan, M. A., Takakura, N., and Yamaguchi, K., “A Novel Technique of Friction Aided Deep Drawing Using a Blank-Holder Divided Into Four Segments,” Journal of Materials Processing Technology, Vol. 139, 2003, pp. 408-413.

[5] Hassan, M. A., Takakura, N., and Yamaguchi, K., “Friction Aided Deep Drawing Using Newly Developed Blank-Holder Divided into Eight Segments,” International Journal of Machine Tools and Manufacturing, Vol. 43, 2003, pp. 637-646.

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[7] Carden, W. D., Geng, L. M., Matlock, D. K., and Wagoner, R. H., “Measurement of Springback”, Journal of Mechanical Sciences, Vol. 44, 2002, pp. 79-101.

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Finite Element Simulation of Process and Springback of ... Aided Deep Drawing Using Tapered Blank Holder ... and compared with four segments tapered blank holder technique by ABAQUS