Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 81 (2014 ) 981 986 11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014, Nagoya Congress Center, Nagoya, Japan Springback of extruded 2196-T8511 and 2099-T83 Al-Li alloys in stretch bending Tianjiao Liu a, Yongjun Wang a,*, Jianjun Wu a, Xiaojiao Xia a, Wei Wang b, Shunhong Wang b a School of Mechanical Engineering, Northwestern Polytechnical University, Xi an 710072, China b AVIC Xi an Aircraft Industry (group) Company Ltd, Xi an 710089, China Abstract Al-Li alloys extrusions improve the performance of advanced aircraft due to their low density and high stiffness. In order to determine whether 2196-T8511 and 2099-T83 Al-Li alloys extrusions with high ultimate tensile strength/young s modulus ratios, also exhibit significant elastic recovery, the springback behaviors of the two Al-Li alloys extrusions under displacement controlled cold stretch bending are addressed, using the simple plasticity deformation theory, the explicit/implicit FEM and the physical experiments. The results show that applied post-stretch strain affects springback of extrusions. The two Al-Li alloys extrusions show time-dependent springback at room temperature. The analytical solution and finite element simulation are effective means to assess the impact of material and process parameters on springback in stretch bending. 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of Nagoya University and Toyohashi University of Technology. Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University Keywords: Springback; Stretch bending; Al-Li alloys; Extrusions 1. Introduction Compared with the other aluminum alloys, higher elastic modulus, lower density, higher specific strength and more favorable damage tolerance properties can be attained in Al-Li alloys. Among various extrusion bending *Corresponding author. Tel.: +86-29-88493717. E-mail address: wyongjun@nwpu.edu.cn (Wang Yongjun) 1877-7058 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University doi:10.1016/j.proeng.2014.10.128
982 Tianjiao Liu et al. / Procedia Engineering 81 ( 2014 ) 981 986 methods such as the press bending, the stretch bending is a feasible one for achieving stable bending of the Al-Li alloys extrusions. However, the springback is inevitable due to the high ratio of the yield strength to Young s modulus of the Al-Li alloys. Up to now, great efforts have been conducted on the springback of stretch bending for extrusion. Ueno et al. (1981) introduced an approximate calculation for springback in the stretch-bending of channels. The results showed that the springback can be greatly reduced by applying an additional tension which is greater than the initial tension. El-Domiaty and Elsharkawy (1998) and Elsharkawy and El-Domiaty (2001) introduced models for stretch-bending of U-section and T-section beams. Corona (2004) presents a formulation that can be used to make predictions of springback of extrusions with thin-walled cross-section subjected to bend-stretch forming. Clausen et al. (1999) experimentally obtained the effects of tensile sequence, geometry on stretch bending of aluminum extrusions. Hopperstad et al. (1999) illustrated the valuable use of re-liability-based numerical analysis for predicting the final geometry of the workpiece in a stretch-bending operation for aluminium extrusions. The numerical study (Clausen et al. 2001) shows that springback is primarily controlled by the pre-stretching level and strain hardening properties. Clausen et al. (2000) experimentally and numerically proposed method of springback of stretch bending of two generic aluminium bumper sections. Paulsen and Welo (1996, 2002) introduced model of springback of stretch bending of rectangular hollow sections. Liu et al. (2010) introduced a model for stretch-bending of complex section profile. In this study, the complex cross-section was meshed using pixel points, and then the parameters of crosssection are calculated. Yu and Li (2011) introduced a model of springback in rotary stretch bending process of L- section extrusion. Zhao et al. (2013) introduced a model on stretch bending springback of profile with arbitrary cross-section in the loading method of pretension and moment based on the bilinear kinematic hardening material model hypothesis. In this paper, the springback under different process variables was investigated at room temperature on stretch bending of 2099-T83 and 2196-T8511 Al-Li alloys extrusions with Z-section and T-section. At first, displacement controlled stretch bending model is developed; Secondly, the experimental and numerical procedure used to measure springback in 2099-T83 and 2196-T8511 Al-Li alloys extrusions are detailed. Lastly, the springback under different process variables are presented and discussed, compared with the experimental data. 2. Stretch bending model One of the extrusion stretch bending methods is displacement controlled stretch bending. It is usually conducted in three steps. First the extrusion is stretched by pulling it with the jaws at its end. Second the jaws move, resulting in an increasing contact between the punch and the extrusion until bending is complete. Third an additional increase of the post-stretch displacement may be applied. 2.1. Basic assumptions The analytical model is developed for the bending and unloading processes, respectively. The assumptions are as follows: Plane sections remain planar throughout deformation and springback; The stress state is uniaxial with only a circumferential stress; Neutral axis is zero-extension fiber; Strain is proportional to z as shown in Fig.1(a); Isotropic, homogeneous material behavior is adopted; Springback occurs purely elastically; No distinction between engineering and true strain; The shear stress can be neglected since it is very small; The Young modulus is considered constant to the increase of plastic strain; No change in extrusion height for pure bending.
Tianjiao Liu et al. / Procedia Engineering 81 ( 2014 ) 981 986 983 (a) (b) loaded Extrusion T M h contact zn w(z) z x y T M die Ri T M Fig.1. (a) Extrusion cross-sectional geometry and coordinates. (b) Stretch bending of an extrusion over a rigid die. 2.2. Distribution of strain and stress 1) Pre-stretch The strain component (hereafter denoted by for simplicity) is described as pre 1 1 u pre / L, where u 0 pre is the pre-stretch displacement, and L 0 is the original length of extrusion. The stress component pre is described elastoplastically as E K n if, 0 if, 0 (1) where E is Young s modulus, 0 is the yield stress, K and n are strain hardening constants. 2) Bending The strain component bend (hereafter denoted by for simplicity) is given by z z 2 R n n (2) where z is the through-height coordinate, taking values between 0 and h, h represents height, The parameters R n (the radius of the neutral axis as shown in Fig. 1(b)) is kinematic boundary conditions, that is they are geometric quantities chosen independently to represent the one bending state of the model. For the displacement controlled stretch bending, in general, the strain neutral layer is located mould surface feature position layer (R i is the radius of the die), that is R, z n 0. n R i (3) Coulomb friction is assumed: where, and p are shear stress, friction coefficient and pressure between the die and the extrusion. The sign is determined by the direction of relative motion between the tool and the workpiece. The normal force due to friction T can be obtained by integrating along the contact length: T T0 e, (4) where is the half contact angle.
984 Tianjiao Liu et al. / Procedia Engineering 81 ( 2014 ) 981 986 3) Post-stretch The strain component post (hereafter denoted by for simplicity) is given by. The stress 3 2 post (hereafter denoted by 3 for simplicity) can be evaluated using Eq. (1). The moment (M) at the end of the poststretch stage for an extrusion can be evaluated by h M 3( z) ( z zc) w( z) dz, 0 (5) where w is the width of the extrusion where the coordinate is z, and h is the section height. 2.3. Prediction of radius springback Springback occurs after the moment and tension force are removed. It is defined by radius springbackr/r, where R denotes the radius of an arbitrary reference axis that joins the same geometric points on the cross sections of the extrusion, is given by R r R, R R 1 R 1 r M EI, (6) where I is the moment of inertia of the cross section and is the change of curvature. 3. Experimental and numerical methodologies 3.1. Stretch bending springback test Each material was cut to obtain extrusion specimen, 3000 mm. The die (R=1604) was set as lubrication (MoS 2 grease) to minimize the friction between the die and the specimen. At the end of the test, the bent extrusions were compared with the sample immediately and the gap of the residual radius was measured onto the paper within approximately 2 hours of the completion of the measure operation. The springback measure was done 48 days later again. The displacement controlled stretch bending test machine, A-7B of L&F Industries, as shown in Fig. 2. 3.2. Finite element simulation Fig.2. Stretch bending test: (a) stretch bending test equipment and (b) unloaded samples after testing. A finite element model of the stretch bending test was constructed for 2196 and 2099 using a commercial finite element program, ABAQUS/Explicit (forming) and ABAQUS/Standard (springback). A mesh with 4200 shell elements (element designation S4R), 300 14 elements along the length and cross section directions, was used with
Tianjiao Liu et al. / Procedia Engineering 81 ( 2014 ) 981 986 985 99 integration points through the thickness sufficient to avoid significant integration error. For simplicity, the Von Mises yield function and isotropic hardening model were used. A friction coefficient =0.2 was obtained by comparing measured and simulated pre-stretch and post-stretch forces throughout the stretch bending tests. 4. Results and discussion 4.1. Experimental results Uniaxial tension tests were conducted for two Al-Li alloys in extrusion direction at a nominal strain rate of ~6.7 10-4 s -1. The results are shown in Fig. 3(a). As shown in Fig. 4, post-stretch strain affects springback of extrusions. Typically, post-stretch strain dominates the springback radius with higher forces reducing springback. In agreement with previous work (Lim et al., 2012), 2196-T8511 and 2099-T83 Al-Li alloys show time-dependent behavior 48 days after forming as shown in Fig. 3(b). In general, 2196 with higher strength shows larger timedependent springback. The experimental data of axial force T (shown in Fig. 1(b)) in three steps is shown in Fig. 3(c). The axial force is increasing with the increasing contact between the die and the extrusion. Fig. 3. (a) Engineering stress-strain curve of Al-Li alloys, (b) time-dependent springback of Al-Li alloys and (c) force data in the three steps. 4.2. Result comparisons and error analysis Based on above mathematical and FE model, the springback corresponding to material and process variables are calculated and compared with the experimental results with different process variables. As shown in Fig. 4(a), the analytical prediction provides the consistent tendency of the elastic recovery with the increase of the post-stretch strains. As shown in Fig. 4(b), it is found that the numerical predictions for radius springback agree with the experimental results with the relative error less than nearly 13%. For the analytical prediction, the discrepancy is mainly originated from the mentioned assumptions in Section 2.1 and uniform stress/strain distributions calculated in the analytical model; for the numerical ones, the discrepancy is mainly caused by the idealized contact conditions used in FE models such as unchanged friction conditions and stable tooling movements. Fig.4. (a) Comparison of the measured and analytical springback and (b) comparison of the measured and simulated springback.
986 Tianjiao Liu et al. / Procedia Engineering 81 ( 2014 ) 981 986 5. Summary and conclusions Combining with the experimental and analytical methods, the FEM numerical analysis is conducted to characterize the springback behaviors of the 2196-T8511 and 2099-T83 Al-Li alloys extrusions under displacement controlled stretch bending. The main results are as follows: (1) Applied post-stretch strain affect springback of extrusions. Typically, post-stretch strain dominates the springback radius with higher forces reducing springback. (2) The two Al-Li alloys, show time-dependent springback after forming, and 2196-T8511 with higher strength showed larger time-dependent springback. (3) The analytical solution and finite element simulation are effective means to assess the impact of material and process parameters on springback in stretch bending. Acknowledgements The work has been performed under the joint project between NPU and XAC. The authors greatly appreciate the support of XAC. This work was supported by the National Natural Science Foundation of China (Grantno.51275420). References Clausen, A., Hopperstad, O., Langseth, M., 1999. Stretch bending of aluminum extrusions: effect of geometry and alloy. Journal of Engineering Mechanics 125(4), 392 400. Clausen, A., Hopperstad, O., Langseth, M., 1999. Stretch bending of aluminum extrusions: effect of tensile sequence. Journal of Engineering Mechanics125(5), 521 529. Clausen A., Hopperstad O., Langseth M., 2001. Sensitivity of model parameters in stretch bending of aluminium extrusions International Journal of Mechanical Sciences 43(2), 427-453 Clausen, A., Hopperstad, O., Langseth, M., 2000. Stretch bending of aluminium extrusions for car bumpers, Journal of Materials Processing Technology 102, 241-248. Corona, E., 2004 A simple analysis for bend-stretch forming of aluminum extrusions International Journal of Mechanical Sciences 46(3), 433-448. El-Domiaty, A., Elsharkawy, A., 1998. Stretch-bending analysis of U-section beams, International Journal of Machine Tools and Manufacture 38 (1 2), 75-95. Elsharkawy, A., El-Domiaty, A., 2001. Determination of stretch-bendability limits and springback for T-section beams Journal of Materials Processing Technology 110(3), 265-276. Hopperstad, O.S., Leira, B.J., Remseth, S., Trømborg, E., 1999. Reliability-based analysis of a stretch-bending process for aluminium extrusions, Computers & Structures 71(1), 63-75. Liu, L., Wang, Y.J., Liu, R., Kang, Q.Z., Qiu, Z.X., 2010. Springback analysis of stretch-bending forming of complex section profile, Steel Research International 81(9), 761-764. Paulsen, F., Welo, T., 1996. Application of numerical simulation in the bending of aluminium-alloy profiles, Journal of Materials Processing Technology 58, 274-285. Paulsen, F., Welo, T., 2002. A design method for prediction of dimensions of rectangular hollow sections formed in stretch bending, Journal of Materials Processing Technology 128(1 3), 48-66. Rioja, R.J., Liu, J., 2012. The evolution of Al-Li base products for aerospace and space applications, Metallurgical and Materials Transactions A 43(9), 3325 3337. Ueda, M., Ueno, K., Kobayashi, M., 1981. A study of springback in the stretch bending of channels, Journal of Mechanical Working Technology 5 (3-4), 163-179. Wagoner, R.H., Wang, J.F., Li, M., 2006. Springback, Chapter in ASM Handbook, Volume 14B: Metalworking: Sheet Forming. ASM, Materials Park, OH, pp.733 755. H. Lim, M.G. Lee, J.H. Sung, J.H. Kim, R.H. Wagoner, 2012. Time-dependent springback of advanced high strength steels, International Journal of Plasticity 29, 42 59. Yu, C.L., Li, X.Q., 2011. Theoretical analysis on springback of L-section extrusion in rotary stretch bending process, Transactions of Nonferrous Metals Society of China 21(12), 2705-2710. Zhao, J., Zhai, R.X., Qian, Z.P., Ma, R., 2013. A study on springback of profile plane stretch bending in the loading method of pretension and moment, International Journal of Mechanical Sciences 75, 45-54.