Study on superplastic blow-forming of 8090 Al Li sheets in an ellip-cylindrical closed-die

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1 International Journal of Machine Tools & Manufacture 42 (2002) Study on superplastic blow-forming of 8090 Al Li sheets in an ellip-cylindrical closed-die Y.-M. Hwang a,, H.S. Lay a, J.C. Huang b a Department of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 804, Republic of China b Institute of Material Science and Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan 804, Republic of China Received 25 September 2001; accepted 1 May 2002 Abstract The purpose of this paper is to explore the plastic deformation behavior of the sheet during blow-forming of a superplastic sheet into an ellip-cylindrical closed-die by the finite element method. A finite element commercial code DEFORM is used to carry out the simulations and calculate the pressurization profile and sheet thickness distribution during the blow-forming process. A pressure control algorithm is proposed to keep the maximum strain rate in the deformation zone of the sheet equal to the target value, which corresponds to the highest m value of the material being superplastically formed. The effects of various forming conditions, such as the friction coefficient between the sheet and die and the aspect ratio of the die, on the forming pressure and thickness distribution of the product are discussed. Experiments using 8090 Al Li sheets on superplastic blow-forming in an ellipcylindrical closed-die are also carried out. The theoretical predictions of thickness distribution of the product are compared with experimental results Elsevier Science Ltd. All rights reserved. Keywords: Superplastic blow-forming; Finite element analysis; Ellip-cylindrical closed-die 1. Introduction Superplasticity appearing in some metallic materials such as 8090 Al Li alloys, Ti 6Al 4V alloys, etc. has been widely utilized in various forming processes such as forging, extrusion, blow-forming and so on, which are known as superplastic forming (SPF) [1 3]. A few works concerning SPF processes have focused on metallurgical experimental research [1,2]. However, studies using experimental approaches are often time-consuming and of low efficiency. Among the analytical investigations [4 9] on SPF processes, Ghosh and Hamilton [4] used the plane strain analysis to explore the effects of the thickness of the sheets and the shape of the die on the optimized pressurization profile during blow-forming in a long rectangular box die. Ragab [5] investigated the thickness distribution in a cylindrical or conical die, but the plane strain analysis and the sticking mode for the contact between the sheet and die were adopted in the Corresponding author. Fax: address: ymhwang@mail.nsysu.edu.tw (Y.-M. Hwang). analysis. Holt [7] examined the effects of the forming pressure, geometrical shape and mechanical properties (K, m-valve) of the sheet on the thickness distribution and shape of the products during blow-forming of a circular sheet. Chandra and Chandy [8] developed a computational process model using the membrane element method for superplastic forming in a box with complex cross-sectional shape. Kim et al. [9] used axisymmetric and plane strain line elements to develop an incremental rigid viscoplastic finite element model for simulations on a superplastic forming process with axisymmetric or plane strain deformation. Lee and Huh [10] used a finite element code and the convective coordinate system to simulate a superplastic forming/diffusion bonding process of four sheet sandwich parts. Bonet et al. [11] have proposed a finite element model using incremental flow formulation to simulate superplastic forming of thin sheet [12] and thick sheet components [13]. Bonet et al. also proposed a pressure control algorithm [14] incorporated into their finite element program during the simulation of superplastic forming, in order to obtain the optimum strain rate. The present authors have developed a general math /02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S (02)00055-X

2 1364 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) Nomenclature a long axis of the die b short axis of the die H height of the die K strength coefficient m strain-rate sensitivity P i forming pressure r die root radius R die entry radius t 0 initial sheet thickness T forming time T time increment ē effective strain rate ē max maximum strain rate in the deformation zone of the sheet ē tar target strain rate m friction coefficient between the sheet and die s effective stress ematical model considering uniform thinning [15] and non-uniform thinning [16] in the free bulged region to examine the optimized pressurization profile and thickness distribution of the products in blow-forming into a circular closed-die and even in a conical closed-die [17]. In this study, the finite element method is used to simulate the plastic deformation of 8090 Al Li sheets in an ellip-cylindrical closed-die, in which the deformation of the sheet belongs to the category of three-dimensional analysis. The effects of various forming conditions such as the friction coefficient, the aspect ratio of the die, etc. on the optimized pressurization and thickness distributions of the product will be discussed. Furthermore, experiments using 8090 Al Li sheets on superplastic blow-forming in an ellip-cylindrical closed-die are also carried out to verify the validity of this model. C is a very large positive number, which is called the penalty constant and is interpreted as the bulk modulus. dē and dė v are the variations in strain rate and volumetric strain rate, respectively, derived from an arbitrary variation dv i. t i is the surface traction stress. By the finite element discretization procedure, Eq. (1) can be converted to non-linear algebraic equations. For detailed descriptions of the finite element theory and the modeling formulations, please refer to Ref. [18]. The schematic diagram for blow-forming in an ellip-cylindrical closed-die is illustrated in Fig. 1, where a, b and H are the long axis, short axis and the height of the die, respectively; R is the die entry radius; r is the die root radius; and t 0 is the initial sheet thickness. Because of symmetry, only one-quarter of the objects are shown. If the strain hardening effect is neglected due to hot for- 2. Finite element modeling A commercial finite element code DEFORM is applied to simulate the plastic deformation of the SPFed sheet during blow-forming in an ellip-cylindrical closed-die. The finite element code is based on the flow formulation approach using an updated Lagrange procedure. The basic equation for the finite element formulation from the variational approach is ė v dė v dv t i dv i ds 0, (1) dp v where s dē dv C v s 3 2 (s ijs ij) 1/2, ē 3 2 (ė ijė ij ) 1/2, ė v ė ii. SF Fig. 1. Schematic illustration of the superplastic blow-forming in an ellip-cylindrical closed-die.

3 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) ming, the plastic flow stress for the superplastic material can be expressed approximately as s Kē m, (2) where K is the strength coefficient of the sheet, ē is the effective strain rate, and m is the strain-rate sensitivity. During blow-forming, the sheet along the peripheral of the die is fixed perfectly. Throughout the analysis, the following assumptions are employed: (1) the material is isotropic; (2) the elastic strain is neglected; (3) the strain hardening effect is ignored; (4) an isothermal process is considered; and (5) a constant friction factor at the interface between the sheet and die is considered. Concerning the pressure control algorithm, a few control schemes have been proposed in order to produce maximum ductility and obtain a most uniform thickness distribution of the product. For example, a linear interpolation of the pressures at the previous iteration step was proposed by Kim et al. [9] to determine the optimum load time relationship in punch forming. Bonet et al. [12] considered that the solutions to the equilibrium equations in the formulation of the finite element model must satisfy additionally the scalar strain rate constraint equation to calculate the optimum pressure control scheme. Afterwards, Bonet et al. [14] modified the previous control scheme. They considered a weighted average of the strain rates in the neighborhood of the Fig. 2. Flow chart for the numerical simulations in the blow-forming process. Fig. 3. Geometrical configuration between the sheet and die: (a) before forming, (b) during forming and (c) after forming.

4 1366 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) simulations, it is assumed that the sheet along the periphery of the die is fixed perfectly; in other words, there is no metal flow from the periphery into the cavity of the die. Two thousand five hundred (2500) six-face brick elements are generated by the software MicroStation, then inputted into the software DEFORM to carry out the simulation of blow-forming. The long axis, short axis Fig. 4. Maximum strain rate variation during the forming process. maximum occurring strain rate, rather than the particular element experiencing the maximum equivalent strain rate. They reported that the pressure cycle using the new algorithm was in better agreement with the experiments. In this paper, a pressure control algorithm for keeping the maximum strain rate, ē max, in the deformation zone of the sheet to be equal to a target strain rate is proposed as P i(t+ T) 1 ln ē max ē i(t), (3) tar P where P i(t) is the forming pressure needed at time T; T is the time increment and ē tar is the target strain rate, which corresponds to the maximum m value of the SPFed material. The feature of this pressure control algorithm is quite simple and is able to prevent oscillations or rapid changes in the forming pressure. The forming pressures obtained according to this control algorithm are called the optimized pressurization profile. The flow chart for predicting the optimized pressurization profile and the thickness distribution of the product is shown in Fig Mesh configurations of the sheet and die Fig. 3(a), (b) and (c) shows the configurations of the sheet and die before forming, during forming and after forming, respectively. Because of symmetry, only onequarter of the objects are shown in these figures. During Fig. 5. Thickness distribution in the long axis direction (a) and short axis direction (b) after forming.

5 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) and the height of the die are a 60 mm, b 30 mm and H 20 mm, respectively. The die entry radius is R 8 mm. The flow stress of the sheet is s 268ē 0.48 MPa. The friction coefficient between the sheet and die is m 0.3. The iteration methods adopted for solving the nonlinear equations in DEFORM are Newton Raphson and the direct iteration method. The direct iteration method is used to generate a good initial guess for the Newton Raphson method, whereas the Newton Raphon itself method is used for speedy final convergence. The convergence criteria for the iteration are the velocity error norm v / v and the force error norm F / F 0.01, where v is defined as (v T v) 1/2. From these figures, it is known that this finite element model can simulate superplastic blow-forming in an ellip-cylindrical closed-die effectively. 4. Simulation results and discussion Fig. 4 shows the maximum strain rates vs. time diagram between the present control algorithm and the constant pressure control approach. The forming conditions are shown in the figure and the target strain rate is set to be ē tar s 1. From Fig. 4, it is known that the maximum strain rates ē max are always kept near the target strain rate ē tar using the present control algorithm. On the other hand, using the constant pressure control approach (P i 0.8 MPa), ē max is larger than ē tar at the early stage and decreases monotonically at the late stage. Fig. 5(a) and (b) shows the thickness distributions after forming in the long and short axis directions, respectively, between the present control algorithm and the constant pressure control approach. From Fig. 5(a) and (b), it is known that the thickness distributions predicted by this control algorithm are more uniform than those predicted by the constant pressure control approach. That is because, using this control algorithm, the maximum strain rates in the deformation zone are always kept at about s 1, at which strain rate the material has a larger m value, and accordingly a more uniform thickness distribution can be obtained. The numerical simulations are based on the material constants of K 268 MPa, T 520 C, m 0.48 and ē tar s 1 chosen from 8090 Al Li alloys [14]. Fig. 6. Effects of friction coefficient on the optimized pressurization profile. The forming conditions used to simulate the forming pressures and the thickness distributions are summarized in Table 1. Fig. 6 shows the effects of the friction coefficient between the die and sheet on the forming pressure with the die entry radius R 8 mm. From Fig. 6, it is known that the forming pressure decreases with increasing friction coefficient. Because the sheet volume flowing into the free bulged region is reduced by friction force, the thickness in the free bulged region and hence the forming pressure decrease accordingly. The forming time needed to complete the blow-forming process, however, increases with increasing friction coefficient. Fig. 7(a) and (b) displays the effects of the friction coefficient between the die and sheet on the thickness distributions of products in the long and short axis directions, respectively. From Fig. 7(a) and (b), it is clear Table 1 The forming conditions employed in the simulations of the blow-forming process No. a (mm) b (mm) H (mm) R (mm) m , 5, , 0.3, , 20, , 30, K 268 MPa, m 0.48, r 1.5 mm, ē tar s 1

6 1368 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) Fig. 8. Effects of die height on the optimized pressurization profile. Fig. 7. Effects of friction coefficient on the thickness distribution in the long axis direction (a) and short axis direction (b) after forming. that the thickness distributions of products become less uniform as the friction coefficient increases. Generally speaking, the minimum thickness is found to be located at the die root for all friction coefficients in the long axial thickness distribution, whereas, in the short axial thickness distribution, the position for the minimum thickness is shifted from the die root to the die center Fig. 9. Effects of aspect ratio on the optimized pressurization profile.

7 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) as the friction coefficient decreases, because it is easier for the sheet to flow into the die root corner as m decreases. Fig. 8 shows the effects of the die height on the forming pressure. In the case of H 15 mm, which means the die is shallower, the forming time for the die root corner radius of the free bulged region reaching r 1.5 mm is shorter and the corresponding pressure is larger compared with those in the other deeper cases. For a deeper die, such as H 28 mm, there is enough time for the pressure to reach its maximum value. Also, because the average thickness becomes thinner, the for- Fig. 11. Schematic illustration of the instrument for superplastic blow-forming. Fig. 10. Effects of aspect ratio on the thickness distribution in the long axis direction (a) and short axis direction (b) after forming. Fig. 12. Optimized pressurization profiles predicted by this model and actually inputted in the experiments.

8 1370 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) ming pressure needed becomes lower as shown in the figure. Fig. 9 shows the effects of the die aspect ratio (a/b) on the forming pressure. The long axis of the die, a, is fixed at 60 mm. In the case of a b, which means that the die has a circular cross-section and has a larger crosssectional area, the sheet is more easily blow-formed. Thus, at the early stage, the forming pressures are smaller compared with those in the other cases. When b decreases, which means the die becomes deeper due to H/b increasing, there is enough time for the pressure to reach its maximum value. Also when b is smaller, there is smaller cross-sectional area and thus a larger forming pressure is required. Fig. 10(a) and (b)illustrates the effects of the die aspect ratio (a/b) on the thickness distributions of products in the long and short axis directions, respectively. From Fig. 10(a), it is known that as a/b decreases or b increases, which means that the sheet becomes more like a circular shape and has a larger area, the thickness distribution of the products becomes thicker and more uniform. The tendency for the thickness distribution in the short axis direction shown in Fig. 10(b) is different from that in the long axis direction. The location for the minimum thickness is shifted from the die root to the die center as a/b increases, because it is harder for the sheet to flow into the die cavity for a long and slender ellipcylindrical closed-die. 5. Experiments on superplastic blow-forming The experiments on superplastic blow-forming have been performed using a self-designed equipment [19], as shown in Fig. 11. The set-up includes upper and lower parts; both have separately controlled temperature and pressure. Specimens for forming tests were clamped between the upper and lower sections. The die was made of 4340 steel and had an entry radius of 8 mm, long axis a 60 mm, short axis b 30 mm and height of 20 mm. The forming temperature was 525 ± 3 C. Argon gas was used for pressurization in the SPF. The forming pressure was inputted according to the predicted optimized pressurization profile obtained by this model as shown in Fig. 12, where the solid line and dashed line are the optimized pressurization profile predicted by this model and the actually inputted pressure, respectively. From this figure, it is known that the inputted pressure profile truthfully followed that expected. Boron nitride lubricant in the form of liquid solution was used in this study. The lubricant was painted on both sides of the specimen with a brush. The layer of lubricant on the specimen was kept as uniform as possible. The material used for superplastic forming was 1.65 mm thick 8090 SPF sheets, purchased from the Superform Company. The specimens were machined to a circular shape with a diameter of 95 mm. Tension tests were conducted at a constant strain-rate condition in an Instron testing machine attached with a three-zone furnace. Strain rates in the range of 10 5 to 10 3 s 1 were used. To determine the m values, tests of changing strain rate were conducted. The maximum strain-rate sensitivity obtained is 0.48 and the corresponding strain rate is approximately s 1. The stress strain rate relationship can be obtained approximately as s 268ē 0.48 MPa [19]. After blow-forming, the deformed sheets were cut into two parts in the long or short axis direction so that the thickness could be measured easily with a micrometer. The external appearance of an SPFed product is shown in Fig Experimental results and discussion Fig. 14(a) and (b) shows the comparisons between the finite element simulations and experimental data for the thickness distributions of products in the long and short axis directions, respectively. From Fig. 14(a) and (b), it is apparent that the thicknesses predicted by this model at the die entry region are smaller than the experimental Fig. 13. Appearance of the SPF-ed product.

9 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) Fig. 14. Comparison of the thickness distributions of products in the long axis direction (a) and short axis direction (b) between theoretical predictions and experimental measurements. data, whereas those at the bottom of the die are larger than the experimental values. The adopted friction coefficient of m 0.3 along all the surface of the die is a mean value [20]. However, according to experiments [21], sticking can occur over most of the die entry even when the friction coefficient is low. Thus, the friction coefficient at the die entry is larger than 0.3, whereas that at the bottom is possibly smaller than 0.3. If a larger friction coefficient is adopted at the die entry region, it will become more difficult for the sheet to slide into the die cavity and accordingly its thickness will become thicker. On the other hand, a smaller friction coefficient at the die bottom will make it easier for the sheet to slide along the die bottom surface. Thus, the thickness at the

10 1372 Y.-M. Hwang et al. / International Journal of Machine Tools & Manufacture 42 (2002) die bottom will become thinner and closer to the experimental data. Actually, the flow stress of the superplastic sheet is a function of strain rate, strain and the strainrate sensitivity. The approximate equation (2) used in the finite element program is possibly another source of the discrepancy between the analytical and experimental results. 7. Conclusions A simple pressure control algorithm has been proposed and a series of finite element simulations on the plastic deformation behavior of the sheet during superplastic blow-forming in an ellip-cylindrical closed-die have been conducted. The effects of various forming conditions such as friction coefficient, the aspect ratio of the closed-die, etc. on the optimized pressurization profile and thickness distribution of the product were discussed. From the numerical simulations, it can be concluded that: (1) the forming pressure increases with increasing die entry radius and die aspect ratio, whereas it decreases with increasing friction coefficient and height of the die; (2) the uniformity of the thickness distribution of the products increases with increasing die entry radius, whereas it decreases with increasing die height, die aspect ratio and friction coefficient. The validity of this model was verified through comparisons of the analytical and experimental results. Acknowledgements The authors would like to extend their thanks to the National Science Council of the Republic of China under grant no. NSC E The advice and financial support of NSC are gratefully acknowledged. References [1] D.S. Fields Jr., T.J. Stewart, Strain effects in the superplastic deformation of 78Zn 22Al, International Journal of Mechanical Sciences 13 (1971) 63. [2] T.Y.M. Al-Naib, J.L. 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