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Computer aided modelling of flexible forming process
Journal of Materials Processing Technology 148 (2004) 376–381
Computer aided modelling of flexible forming process M. Husnu Dirikolu∗ , Esra Akdemir Department of Mechanical Engineering, Kirikkale University, 71450 Kirikkale, Turkey Received 27 January 2003; received in revised form 23 February 2004; accepted 23 February 2004
Abstract Flexible forming enables the production of sheet metal parts with complex contours and bends by utilising a flexible medium, such as natural or synthetic rubber, as one half of a conventional die set. This study is concerned with simulation and investigation of the significant parameters associated with this process. The analyses were carried out on a commercially available finite element package with appropriate nonlinear material and frictional models. These investigations showed the effectiveness of finite element simulations in process design and exposed the rubber hardness and its advance, blank material type, contact friction, die design as crucial parameters that require adjustment before actual operations. © 2004 Elsevier B.V. All rights reserved. Keywords: Flexible forming; Sheet metal; Nonlinear analysis; Mooney–Rivlin
1. Introduction Minimisation of response times and costs and maximisation of the efficiency and quality in producing a product are imperative for survival in the competitive manufacturing industry. Sheet metal forming is a widely used and costly manufacturing process, to which these considerations apply. Many small companies in industry are recently required to manufacture curved products that are small in lot size, which means both a higher cost per detail and a necessity for multiple tools. A possible alternative forming method, which can reduce production costs for such companies, is flexible forming process (FFP). This process, also known as rubber pad forming or Guerin process, is schematically shown in Fig. 1. It involves a rubber filled chamber, a blank, and a form block and has been used as a sheet shaping method for metal as well as composite parts in the aerospace industry. The flexibility of operation, the capability for drawing, bending, and embossing of simple or moderately complex parts, the protection of sheet surface by rubber, and low tooling costs are the underlying advantages of the process [1]. Several studies have been carried out to analyse FFP. An experimental study by Browne and Battikha has shown the
∗ Corresponding author. Tel.: +90-318-357-3576; fax: +90-318-357-2459. E-mail address: [email protected] (M.H. Dirikolu).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.02.049
rate of rubber advance to be an important process parameter due to behaviour of rubber under sudden loading. They also analysed the use of different types of lubricants at the blank and its interfaces. Wax (Vestoplast 703) was found to be the best lubricant for the process, whereas the parts needed some cleaning for a while by immersion in a hot water and detergent bath. The dependence of the clamping force for the prevention of wrinkling and cracking on the type of blank material was also investigated [2,3]. In another study, Kwon et al. have investigated the flexible bending of a structural aluminium frame using rubber. From the experimentally bent profiles, a parametric study for process design was performed [4]. These mentioned studies are experimental and although helpful in understanding the basics of the process, they are limited in terms of time and cost. A more versatile way, which is supported by dramatic advances in computer processing power and software tools, is numerical analysis. However, few numerical investigations of FFP could be found in literature the most notable of which being that by Sala [5]. Sala used a specific finite element (FE) code to optimise FFP stamping of an aluminium alloy frame. His investigations included effects of bending radii, blank material type, stamping velocity, and rubber type and thickness. This study aims at simulating FFP by using ANSYS® , a commercial finite element package. The FE model on which the investigations were based was in 3D form. The modelling details are given in Section 2.
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
Fig. 1. Schematic representation of rubber pad forming process and the studied model (in mm).
2. Modelling requirements One of the major requirements for computer simulations is the incorporation of material properties through realistic models. The rates of deformations in FFP are limited by the behaviour of the flexible medium as suggested in the above literature. As a result, a quasi-static nonlinear approach with negligible temperature effects can be assumed applicable for FFP simulations. Blank materials undergo large strain plastic deformation and therefore true stress–true strain test data up to failure are required in order to define the suitable blank material model in the simulations. This study considers multilinear isotropic hardening (MISO) material model existing in ANSYS to simulate large strain plastic deformation of the blank materials. MISO uses the von Mises yield criterion coupled with an isotropic work hardening assumption [6]. These considerations also apply to the flexible medium. Flexible materials have nonlinear stress–strain characteristics for relatively large deformations. Under such conditions, they are generally assumed as nearly incompressible. In this study, hyperelastic theory is used to describe the flexible medium. Hyperelasticity makes use of a strain energy function W, whose derivative with respect to a strain component determines the corresponding stress component as: ∂W σij = (1) ∂εij
the slope and the intercept of a plot of uniaxial stress versus stretch ratio for an incompressible material following the two-parameter Mooney–Rivlin model. In addition to nonlinearity associated with material properties, geometric nonlinearity arising from nonlinear strain–displacement relationships should also be associated with FFP simulations since during forming, the model exhibits large deformations and rotations and has frictional contacts at the blank and its interfaces. These effects are taken into account when geometric nonlinearity option is activated in the nonlinear solution procedure of ANSYS. The frictions at blank interfaces, i.e. flexible medium-blank and blank-form block, were assumed to follow Coulomb’s model. The friction coefficients at the former and latter interfaces were considered as 0.2 and 0.1 for lubricated conditions, respectively [8]. Interface elements were used to model the areas of potential contact. In this study, all potential contact surfaces were modelled as deformable and ANSYS handles these tasks by providing a contact wizard based on a contact–target surface scheme with an adjustable impenetrability constraint that assures contact compatibility. Based on the above considerations, the FFP model has been generated as shown in Fig. 2. The rubber has been modelled by using four-node HYPER158 10-node tetrahedral hyperelastic solid elements. The number of nodes and elements are 1052 and 554, respectively. HYPER158 is applicable to nearly incompressible rubber-like materials with arbitrarily large displacements and strains. The blank and the form block are modelled with SOLID92 3D 10-node tetrahedral structural solid elements that have plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. 2290 and 3473 elements, and 4932 and 6137 nodes are, respectively, employed for the former and the latter models.
where W=
n k+m=1
1 Ckm (I1 − 3)k + (I2 − 3)m + κ(I3 − 1)2 2
I1 , I2 and I3 are the strain invariants, which are expressed in terms of the principal stretch ratios λ1 , λ2 and λ3 . κ is the bulk modulus and I3 = 1 for incompressible material behaviour. The hyperelastic constants, Ckm , determine the material response. The hyperelastic description in this study is based on the two-parameter Mooney–Rivlin model (n = 1 in Eq. (1)) [7]. The Mooney–Rivlin constants, namely C01 and C10 , for any given hyperelastic material are determined from experiments. C01 and C10 , respectively, correspond to
377
Fig. 2. The finite element model.
378
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
True Stress (MPa)
600 500 400 300 200
0 0,00 Fig. 3. The contact–target elements at the interfaces.
Contact elements, namely CONTA174 and TARGE170, have been created at the interfaces as presented in Fig. 3. CONTA174 is used to represent contact and sliding between 3D “target” surfaces modelled with TARGE170 and a deformable surface, defined by this element. The element is applicable to 3D structural contact analysis. It has the same geometric characteristics as the solid element face with which it is connected. Contact occurs when the element surface penetrates one of the target segment elements (TARGE170) on a specified target surface. Here Coulomb friction is allowed [6]. 2780 elements and an impenetrability constraint of 0.1 have been used for this task. The forming loads were applied on the blank in terms of displacements on the top surface of the rubber pad. Hundred loadsteps and a substep value of 100 with limits varying from 10 to 200 have been employed during solution. The selection of these step numbers is critical since these affect the accuracy of the integrations carried out at successive numerical operations.
3. The experimental input data The necessary blank material mechanical properties for FFP simulations were obtained from tension tests. Flat tension specimens from 1 mm thick commercial aluminium and steel sheets along their rolling directions were prepared and tested in laboratory according to TS138/EN10002-1 standard. These experiments were carried out on Instron 8516+ universal testing machine [9]. The true stress–true strain diagrams from these tests are shown in Fig. 4. The elasticity moduli (E) and Poisson’s ratios (ν) are 71 and 200 GPa, and 0.334 and 0.3 for aluminium and steel specimens, respectively. The form block material is assumed to be steel with a modulus of elasticity of 200 GPa and a Poisson’s ratio of 0.3.
Steel specimen Aluminium specimen
100 0,05
0,10
0,15
0,20
0,25
0,30
True Strain (mm/mm) Fig. 4. True stress–true strain diagrams for aluminium and steel blank materials.
Natural rubber was originally used in FFP applications. Later, with the development of plastics, several elastomers were considered. Of these elastomers, polyurethane turned out to be the most suitable for FFP [10]. One of the strongest points of polyurethane is its ability to be moulded in a wide range of harnesses. Polyurethane also has the ability to withstand temperatures of up to 150 ◦ C and loading of up to 50,000 cycles before replacement. Waltz [11] has obtained experimental Mooney–Rivlin constants for polyurethane rubber with Shore A hardnesses ranging from 35 to 70◦ . From these data, two types with 55 and 70◦ hardness values (see Table 1) have been used as flexible medium in the simulations.
4. Results and discussion This study concentrates on the significant parameters associated with FFP process. The analyses are carried out by varying the process parameters during simulations. One of the parameters is the advancement of the polyurethane chamber. Since, polyurethane is assumed incompressible, its advance is directly proportional to the amount of free volume between the form block, which is accounted for springback, and the blank material. The simulations show the effect of excessive rubber advance by nonconvergence and necking behaviour in the blank. In this study, a 5 mm advancement has been calculated and applied for the polyurethane pad. Another parameter is the hardness of the pad. In order to determine the effect of hardness, the values listed in Table 1 have been incorporated in the simulations. The results are given Fig. 5a and b for the soft and hard polyurethane pads, respectively. The simulations revealed that as the Shore A
Table 1 Mechanical properties of rubber pad materials used in the simulations Polyurethane rubber
Hardness Shore A (◦ )
Mooney–Rivlin constant C10 (MPa)
Mooney–Rivlin constant C01 (MPa)
G (MPa)
E (MPa)
Poisson’s ratio (ν)
Type 1 Type 2
55 70
0.382 0.736
0.096 0.184
0.956 1.839
2.868 5.517
0.49997 0.49997
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
379
Fig. 6. von Mises stresses for steel blank materials using hard polyurethane pad.
the aluminium. With all parameters remaining the same and using the hard polyurethane, the von Mises stresses except those at the flanges of the steel and aluminium blanks (see Fig. 2) are seen to remain in the elastic region. The effect of friction at the pad-blank and blank-form block interfaces was studied by varying the friction coefficients. For example, raising the friction coefficient from 0.2 and 0.1 to 0.3 and employing the aluminium blank and the hard polyurethane reduced the von Mises stress from 220 to 215 MPa as shown in Figs. 5b and 7, respectively. Finally, the form block was observed to be highly stressed about the flange region during simulations. Such a situation is shown in Fig. 8a where the maximum von Mises stress at the flange of the form block reaches 181 MPa during forming
Fig. 5. The effect of rubber hardness on von Mises stresses in the aluminium blank: (a) soft rubber (Shore A 55◦ ); (b) hard rubber (Shore A 70◦ ).
hardness is increased from 55 to 70◦ , the maximum von Mises stress in the blank material is increased from 210 to 220 MPa. These values are observed to be at the flange, and comparing the two cases, the stresses are only slightly different in the remaining regions. The flange region has undergone plastic deformation, while the bottom is not deformed as can be seen from the figures. Blank material type will obviously affect the outcome of FFP operations due to different mechanical behaviour. Aluminium and steel blanks are considered in the simulations and the results are presented in Figs. 5b and 6, respectively. The maximum von Mises stress in the steel blank was calculated as 314 MPa, while it was found to be 220 MPa for
Fig. 7. von Mises stresses for a friction coefficient of 0.3.
380
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
Fig. 8. (a) von Mises stresses in the form block. (b) Strains in the polyurethane pad.
of the aluminium specimen with the soft polyurethane. The strain values predicted in the soft rubber pad are given in Fig. 8b. Therefore, considering the pressure applied by the pad material, it should be designed such that its dimensional stability could be preserved during operations.
5. Conclusions The use of finite-element simulation in the better understanding of forming operations is becoming more important as it provides a cheap and efficient way to determine important process parameters. This paper presents, a 3D finite element simulation study concerning the flexible forming process. Conclusions in relation to certain process parameters can be given as follows. One of the outcomes of this study is that a polyurethane pad with a hardness range varying from 55 to 70◦ Shore A can be considered appropriate for flexible forming applications. The advancement of the pad, in other words, the volume swept by the pad, is another important parameter that needs adjustment. The simulation results showed that a variation in pad hardness would not impart a big change on forming stresses in the blank.
The stress distribution trends for different blank materials (such as steel and aluminium in this study) show a resemblance, i.e. reaching their maximum at the flange region. Springback due to blank material type will affect the design of the form block, even if the FFP operation is carried out in one stroke. Changing the lubrication conditions at the contact surfaces shows itself as resulting in slightly lower stresses in the deformed blank. However, the surface finish is known to be affected by these conditions. Finally, the prevention of the form block from being deformed plastically becomes an important issue due to extremely high pressures endured during flexible forming operations.
References [1] S. Kalpakjian, Manufacturing Processes for Engineering Materials, 2nd ed., Addison-Wesley, Wokingham, UK, 1991. [2] E. Battikha, D.J. Browne, Experimental rubber-pad forming of aluminium sheet, in: Proceedings of the Ninth Conference Irish Manufacturing Committee, University College, Dublin, September 1992, pp. 479–487.
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381 [3] D.J. Browne, E. Battikha, Optimisation of aluminium sheet forming using a flexible die, J. Mater. Process. Technol. 55 (1995) 218–223. [4] H.C. Kwon, Y.T. Im, D.C. Ji, M.H. Rhee, The bending of an aluminium structural frame with a rubber pad, J. Mater. Process. Technol. 113 (2001) 786–791. [5] G. Sala, A numerical and experimental approach to optimise sheet stamping technologies. Part II. Aluminium alloys rubber-forming, Mater. Design 22 (2001) 299–315. [6] ANSYS Theory Manual for Release 5.6, 11th Edition, ANSYS Inc., November 1999.
381
[7] M. Mooney, A theory for large elastic deformation, J. Appl. Phys. 11 (1940) 582–597. [8] E.M. Mielnik, Metalworking Science and Engineering, McGraw-Hill, New York, 1991. [9] E. Akdemir, Computer aided modelling of rubber pad forming process, MSc Thesis, Kirikkale University, 2002. [10] S. Thiruvarudchelvan, The potential role of flexible tools in metal forming, J. Mater. Process. Technol. 122 (2002) 293– 300. [11] M. Waltz, Private communication. [email protected].
Computer aided modelling of flexible forming process M. Husnu Dirikolu∗ , Esra Akdemir Department of Mechanical Engineering, Kirikkale University, 71450 Kirikkale, Turkey Received 27 January 2003; received in revised form 23 February 2004; accepted 23 February 2004
Abstract Flexible forming enables the production of sheet metal parts with complex contours and bends by utilising a flexible medium, such as natural or synthetic rubber, as one half of a conventional die set. This study is concerned with simulation and investigation of the significant parameters associated with this process. The analyses were carried out on a commercially available finite element package with appropriate nonlinear material and frictional models. These investigations showed the effectiveness of finite element simulations in process design and exposed the rubber hardness and its advance, blank material type, contact friction, die design as crucial parameters that require adjustment before actual operations. © 2004 Elsevier B.V. All rights reserved. Keywords: Flexible forming; Sheet metal; Nonlinear analysis; Mooney–Rivlin
1. Introduction Minimisation of response times and costs and maximisation of the efficiency and quality in producing a product are imperative for survival in the competitive manufacturing industry. Sheet metal forming is a widely used and costly manufacturing process, to which these considerations apply. Many small companies in industry are recently required to manufacture curved products that are small in lot size, which means both a higher cost per detail and a necessity for multiple tools. A possible alternative forming method, which can reduce production costs for such companies, is flexible forming process (FFP). This process, also known as rubber pad forming or Guerin process, is schematically shown in Fig. 1. It involves a rubber filled chamber, a blank, and a form block and has been used as a sheet shaping method for metal as well as composite parts in the aerospace industry. The flexibility of operation, the capability for drawing, bending, and embossing of simple or moderately complex parts, the protection of sheet surface by rubber, and low tooling costs are the underlying advantages of the process [1]. Several studies have been carried out to analyse FFP. An experimental study by Browne and Battikha has shown the
∗ Corresponding author. Tel.: +90-318-357-3576; fax: +90-318-357-2459. E-mail address: [email protected] (M.H. Dirikolu).
0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.02.049
rate of rubber advance to be an important process parameter due to behaviour of rubber under sudden loading. They also analysed the use of different types of lubricants at the blank and its interfaces. Wax (Vestoplast 703) was found to be the best lubricant for the process, whereas the parts needed some cleaning for a while by immersion in a hot water and detergent bath. The dependence of the clamping force for the prevention of wrinkling and cracking on the type of blank material was also investigated [2,3]. In another study, Kwon et al. have investigated the flexible bending of a structural aluminium frame using rubber. From the experimentally bent profiles, a parametric study for process design was performed [4]. These mentioned studies are experimental and although helpful in understanding the basics of the process, they are limited in terms of time and cost. A more versatile way, which is supported by dramatic advances in computer processing power and software tools, is numerical analysis. However, few numerical investigations of FFP could be found in literature the most notable of which being that by Sala [5]. Sala used a specific finite element (FE) code to optimise FFP stamping of an aluminium alloy frame. His investigations included effects of bending radii, blank material type, stamping velocity, and rubber type and thickness. This study aims at simulating FFP by using ANSYS® , a commercial finite element package. The FE model on which the investigations were based was in 3D form. The modelling details are given in Section 2.
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
Fig. 1. Schematic representation of rubber pad forming process and the studied model (in mm).
2. Modelling requirements One of the major requirements for computer simulations is the incorporation of material properties through realistic models. The rates of deformations in FFP are limited by the behaviour of the flexible medium as suggested in the above literature. As a result, a quasi-static nonlinear approach with negligible temperature effects can be assumed applicable for FFP simulations. Blank materials undergo large strain plastic deformation and therefore true stress–true strain test data up to failure are required in order to define the suitable blank material model in the simulations. This study considers multilinear isotropic hardening (MISO) material model existing in ANSYS to simulate large strain plastic deformation of the blank materials. MISO uses the von Mises yield criterion coupled with an isotropic work hardening assumption [6]. These considerations also apply to the flexible medium. Flexible materials have nonlinear stress–strain characteristics for relatively large deformations. Under such conditions, they are generally assumed as nearly incompressible. In this study, hyperelastic theory is used to describe the flexible medium. Hyperelasticity makes use of a strain energy function W, whose derivative with respect to a strain component determines the corresponding stress component as: ∂W σij = (1) ∂εij
the slope and the intercept of a plot of uniaxial stress versus stretch ratio for an incompressible material following the two-parameter Mooney–Rivlin model. In addition to nonlinearity associated with material properties, geometric nonlinearity arising from nonlinear strain–displacement relationships should also be associated with FFP simulations since during forming, the model exhibits large deformations and rotations and has frictional contacts at the blank and its interfaces. These effects are taken into account when geometric nonlinearity option is activated in the nonlinear solution procedure of ANSYS. The frictions at blank interfaces, i.e. flexible medium-blank and blank-form block, were assumed to follow Coulomb’s model. The friction coefficients at the former and latter interfaces were considered as 0.2 and 0.1 for lubricated conditions, respectively [8]. Interface elements were used to model the areas of potential contact. In this study, all potential contact surfaces were modelled as deformable and ANSYS handles these tasks by providing a contact wizard based on a contact–target surface scheme with an adjustable impenetrability constraint that assures contact compatibility. Based on the above considerations, the FFP model has been generated as shown in Fig. 2. The rubber has been modelled by using four-node HYPER158 10-node tetrahedral hyperelastic solid elements. The number of nodes and elements are 1052 and 554, respectively. HYPER158 is applicable to nearly incompressible rubber-like materials with arbitrarily large displacements and strains. The blank and the form block are modelled with SOLID92 3D 10-node tetrahedral structural solid elements that have plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities. 2290 and 3473 elements, and 4932 and 6137 nodes are, respectively, employed for the former and the latter models.
where W=
n k+m=1
1 Ckm (I1 − 3)k + (I2 − 3)m + κ(I3 − 1)2 2
I1 , I2 and I3 are the strain invariants, which are expressed in terms of the principal stretch ratios λ1 , λ2 and λ3 . κ is the bulk modulus and I3 = 1 for incompressible material behaviour. The hyperelastic constants, Ckm , determine the material response. The hyperelastic description in this study is based on the two-parameter Mooney–Rivlin model (n = 1 in Eq. (1)) [7]. The Mooney–Rivlin constants, namely C01 and C10 , for any given hyperelastic material are determined from experiments. C01 and C10 , respectively, correspond to
377
Fig. 2. The finite element model.
378
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
True Stress (MPa)
600 500 400 300 200
0 0,00 Fig. 3. The contact–target elements at the interfaces.
Contact elements, namely CONTA174 and TARGE170, have been created at the interfaces as presented in Fig. 3. CONTA174 is used to represent contact and sliding between 3D “target” surfaces modelled with TARGE170 and a deformable surface, defined by this element. The element is applicable to 3D structural contact analysis. It has the same geometric characteristics as the solid element face with which it is connected. Contact occurs when the element surface penetrates one of the target segment elements (TARGE170) on a specified target surface. Here Coulomb friction is allowed [6]. 2780 elements and an impenetrability constraint of 0.1 have been used for this task. The forming loads were applied on the blank in terms of displacements on the top surface of the rubber pad. Hundred loadsteps and a substep value of 100 with limits varying from 10 to 200 have been employed during solution. The selection of these step numbers is critical since these affect the accuracy of the integrations carried out at successive numerical operations.
3. The experimental input data The necessary blank material mechanical properties for FFP simulations were obtained from tension tests. Flat tension specimens from 1 mm thick commercial aluminium and steel sheets along their rolling directions were prepared and tested in laboratory according to TS138/EN10002-1 standard. These experiments were carried out on Instron 8516+ universal testing machine [9]. The true stress–true strain diagrams from these tests are shown in Fig. 4. The elasticity moduli (E) and Poisson’s ratios (ν) are 71 and 200 GPa, and 0.334 and 0.3 for aluminium and steel specimens, respectively. The form block material is assumed to be steel with a modulus of elasticity of 200 GPa and a Poisson’s ratio of 0.3.
Steel specimen Aluminium specimen
100 0,05
0,10
0,15
0,20
0,25
0,30
True Strain (mm/mm) Fig. 4. True stress–true strain diagrams for aluminium and steel blank materials.
Natural rubber was originally used in FFP applications. Later, with the development of plastics, several elastomers were considered. Of these elastomers, polyurethane turned out to be the most suitable for FFP [10]. One of the strongest points of polyurethane is its ability to be moulded in a wide range of harnesses. Polyurethane also has the ability to withstand temperatures of up to 150 ◦ C and loading of up to 50,000 cycles before replacement. Waltz [11] has obtained experimental Mooney–Rivlin constants for polyurethane rubber with Shore A hardnesses ranging from 35 to 70◦ . From these data, two types with 55 and 70◦ hardness values (see Table 1) have been used as flexible medium in the simulations.
4. Results and discussion This study concentrates on the significant parameters associated with FFP process. The analyses are carried out by varying the process parameters during simulations. One of the parameters is the advancement of the polyurethane chamber. Since, polyurethane is assumed incompressible, its advance is directly proportional to the amount of free volume between the form block, which is accounted for springback, and the blank material. The simulations show the effect of excessive rubber advance by nonconvergence and necking behaviour in the blank. In this study, a 5 mm advancement has been calculated and applied for the polyurethane pad. Another parameter is the hardness of the pad. In order to determine the effect of hardness, the values listed in Table 1 have been incorporated in the simulations. The results are given Fig. 5a and b for the soft and hard polyurethane pads, respectively. The simulations revealed that as the Shore A
Table 1 Mechanical properties of rubber pad materials used in the simulations Polyurethane rubber
Hardness Shore A (◦ )
Mooney–Rivlin constant C10 (MPa)
Mooney–Rivlin constant C01 (MPa)
G (MPa)
E (MPa)
Poisson’s ratio (ν)
Type 1 Type 2
55 70
0.382 0.736
0.096 0.184
0.956 1.839
2.868 5.517
0.49997 0.49997
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
379
Fig. 6. von Mises stresses for steel blank materials using hard polyurethane pad.
the aluminium. With all parameters remaining the same and using the hard polyurethane, the von Mises stresses except those at the flanges of the steel and aluminium blanks (see Fig. 2) are seen to remain in the elastic region. The effect of friction at the pad-blank and blank-form block interfaces was studied by varying the friction coefficients. For example, raising the friction coefficient from 0.2 and 0.1 to 0.3 and employing the aluminium blank and the hard polyurethane reduced the von Mises stress from 220 to 215 MPa as shown in Figs. 5b and 7, respectively. Finally, the form block was observed to be highly stressed about the flange region during simulations. Such a situation is shown in Fig. 8a where the maximum von Mises stress at the flange of the form block reaches 181 MPa during forming
Fig. 5. The effect of rubber hardness on von Mises stresses in the aluminium blank: (a) soft rubber (Shore A 55◦ ); (b) hard rubber (Shore A 70◦ ).
hardness is increased from 55 to 70◦ , the maximum von Mises stress in the blank material is increased from 210 to 220 MPa. These values are observed to be at the flange, and comparing the two cases, the stresses are only slightly different in the remaining regions. The flange region has undergone plastic deformation, while the bottom is not deformed as can be seen from the figures. Blank material type will obviously affect the outcome of FFP operations due to different mechanical behaviour. Aluminium and steel blanks are considered in the simulations and the results are presented in Figs. 5b and 6, respectively. The maximum von Mises stress in the steel blank was calculated as 314 MPa, while it was found to be 220 MPa for
Fig. 7. von Mises stresses for a friction coefficient of 0.3.
380
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381
Fig. 8. (a) von Mises stresses in the form block. (b) Strains in the polyurethane pad.
of the aluminium specimen with the soft polyurethane. The strain values predicted in the soft rubber pad are given in Fig. 8b. Therefore, considering the pressure applied by the pad material, it should be designed such that its dimensional stability could be preserved during operations.
5. Conclusions The use of finite-element simulation in the better understanding of forming operations is becoming more important as it provides a cheap and efficient way to determine important process parameters. This paper presents, a 3D finite element simulation study concerning the flexible forming process. Conclusions in relation to certain process parameters can be given as follows. One of the outcomes of this study is that a polyurethane pad with a hardness range varying from 55 to 70◦ Shore A can be considered appropriate for flexible forming applications. The advancement of the pad, in other words, the volume swept by the pad, is another important parameter that needs adjustment. The simulation results showed that a variation in pad hardness would not impart a big change on forming stresses in the blank.
The stress distribution trends for different blank materials (such as steel and aluminium in this study) show a resemblance, i.e. reaching their maximum at the flange region. Springback due to blank material type will affect the design of the form block, even if the FFP operation is carried out in one stroke. Changing the lubrication conditions at the contact surfaces shows itself as resulting in slightly lower stresses in the deformed blank. However, the surface finish is known to be affected by these conditions. Finally, the prevention of the form block from being deformed plastically becomes an important issue due to extremely high pressures endured during flexible forming operations.
References [1] S. Kalpakjian, Manufacturing Processes for Engineering Materials, 2nd ed., Addison-Wesley, Wokingham, UK, 1991. [2] E. Battikha, D.J. Browne, Experimental rubber-pad forming of aluminium sheet, in: Proceedings of the Ninth Conference Irish Manufacturing Committee, University College, Dublin, September 1992, pp. 479–487.
M.H. Dirikolu, E. Akdemir / Journal of Materials Processing Technology 148 (2004) 376–381 [3] D.J. Browne, E. Battikha, Optimisation of aluminium sheet forming using a flexible die, J. Mater. Process. Technol. 55 (1995) 218–223. [4] H.C. Kwon, Y.T. Im, D.C. Ji, M.H. Rhee, The bending of an aluminium structural frame with a rubber pad, J. Mater. Process. Technol. 113 (2001) 786–791. [5] G. Sala, A numerical and experimental approach to optimise sheet stamping technologies. Part II. Aluminium alloys rubber-forming, Mater. Design 22 (2001) 299–315. [6] ANSYS Theory Manual for Release 5.6, 11th Edition, ANSYS Inc., November 1999.
381
[7] M. Mooney, A theory for large elastic deformation, J. Appl. Phys. 11 (1940) 582–597. [8] E.M. Mielnik, Metalworking Science and Engineering, McGraw-Hill, New York, 1991. [9] E. Akdemir, Computer aided modelling of rubber pad forming process, MSc Thesis, Kirikkale University, 2002. [10] S. Thiruvarudchelvan, The potential role of flexible tools in metal forming, J. Mater. Process. Technol. 122 (2002) 293– 300. [11] M. Waltz, Private communication. [email protected].