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The Mechanism of Surface Low Defect in Sheet Metal Stamping Hongqing Shen1,2 a, Shuhui Li1,2 b and Guanlong Chen1,c 1Auto Body Manufacturing Technology Center, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China 2State Key Laboratory of Mechanical System and Vibration, Shanghai 200240, PR China ashenhongqing82@tom.com, blishuhui@sjtu.edu.cn, cglchen@sjtu.edu.cn Keywords: surface low; surface deflection; stamping; sheet metal forming; local buckling. Abstract. In this paper, the mechanism of surface low defect in sheet metal stamping is studied. Firstly, we simulate the forming procedure of a stamping component by Finite Element Method (FEM) to observe the growth of surface low defect. And then, we establish an analytical model and deduce the critical stress for local buckling. Finally, we take advantage of the critical stress to detect local buckling areas in the component. The FE simulation result shows that during springback the non-uniform displacement in the thickness direction forms surface low. Moreover, the detected local buckling area agrees with the experimental surface low area. This indicates that the essence of surface low phenomenon is panel’s local buckling under the residual compressive stress during springback. Introduction Surface low defects are small local deflections in large flat panels containing sudden shape changes. They have a great influence on automobiles’ appearance. These defects are strictly detected and controlled in body manufacturing. Liu et al. [1] proposed an optical reflection method to evaluate the surface low defect in pressed automobile panels. Andersson [2] used an optical system, called WMS-system, to detect surface low in a sample stamping panel. In addition he also used stylus measurement in his experiment. Fu et al. [3] used stoning method to detect surface low defects around the corner of an embossment. With the development of finite element method, it becomes possible to predict surface low by numerical analysis. Fukumura et al. [4] simulated surface low defects in an automobile door exterior panel. Park et al. [5] developed a curvature-based algorithm to visualize the surface low defects in simulation. Hu et al. [6] developed a stoning algorithm to visualize the surface low defects in simulation. Andersson [2] adopted a curvature-based visualization algorithm to verify the consistence between experiment result and simulation prediction. Nowadays the mechanism of the surface low defect is of great concern. Based on experiment results, Yang Y.Y. et al. [7] pointed out that the residual compression stress was the mechanics condition of the surface deflection initiation. In Numisheet 2008, Wang Huiping et al. [8] made a study on a surface distortion predictor for sheet metals. They believed that the mechanism of surface distortion was panel’s local buckling. In this paper, the mechanism of surface low defects in sheet metal forming is further studied. FE Simulation In this study, the experiment by Fu et al. [3] is simulated. In Fig. 1 is the section view of the experimental die setup. The radius of the die bottom surface is 170 mm and the draw depth is 40 mm. The embossment at the die bottom is 150×150 ×10 mm3. A sample panel is shown in Fig. 2. The experimental blank is circular. Its radius is 500 mm. Low carbon steel for the automobile exterior panel is adopted. Detailed characteristics of the material are listed in Table 1. Advanced Materials Research Vols. 538-541 (2012) pp 377-381 Online available since 2012/Jun/14 at www.scientific.net ? (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMR.538-541.377 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 128.120.38.17, National Cheng Kung University, Tainan, Taiwan-10/01/14,12:02:33) Fig.1 Section view of the experimental die setup. Fig. 2 A sample panel in the experiment. Table 1 Characteristics of the experiment material Thickness [mm] Young’s Module [GPa] Poisson’s ratio Yield strength [MPa] Ultimate tensile strength [MPa] Total elongation, L Normal anisotropy, r Strain hardening exponent, n 0.7 207 0.333 157 520 0.4 1.75 0.23 Since the sample is symmetric, we establish only one quarter of the sample and define symmetric boundary conditions on the symmetry axes. In Fig. 3 is the FE model. The FE model simulates the drawing and springback of the panel. The drawing procedure is simulated with ABAQUS Explicit and the springback is simulated with ABAQUS Standard. For simplicity, the material is assumed isotropic. The linear, finite-membrane-strain, reduced-integration, quadrilateral shell element (S4R) is adopted. This element has been proved robust and suitable in sheet metal forming. Meshes around the embossment are carefully refined to describe the small deflection. The minimum elements are about 1×1 mm2 Fig. 3 FE model of the stamping test. Fig.4 The analytical model. Analytical Model The surface low problem is simplified as a rectangular plate under plane stress condition, shown in Fig. 4. The length of the plate is a, the wide of the plate is b and its thickness is t. The plate is compressed by a uniformly distributed stress,xσ, in the x direction and tensioned by a uniformly distributed stress, yσ, in the y direction. The boundary conditions of the plate model are assumed to be simply supported at the four sides. The depth of surface defect is close to the thickness of the sheet, so the deformation of the middle surface is considered. The balance differential equation is 3444222 2422422(2)212(1)xyxy EtNNN xxyyxyxy ωωωωωω ν ??????++=++ ????????? (1) where ω is the deflection, Nx, Ny and Nxy are membrane stress resultants. In this model, Nx, Ny are assumed uniformly distributed along thickness direction and Nxy equals to zero. So Nx, Ny and Nxy can be expressed as 378Materials Processing Technology II 0 xx yy xy Nt Nt N σ σ ?=? ? =? ?= ? (2) According to the boundary condition of the model, the deflection surface of the buckled plate can be represented as 11 sinsinmn mn mxnyA ab ππω∞∞ == =∑∑ (3) where mnA represents the amplitude of deflection. Combining equations (1), (2), (3), we can obtain 22222 11 1sinsin0 mnxy mn mnmnmxnyAtt abDabab ππππππσσ∞∞ == ???????????????? +??=?????????????? ???????????????????? ∑∑ (4) where D is the bending stiffness, 3 212(1) EtD ν = ? . When mnA = 0, the equation has a unique solution, ω≡0. This indicates that the plate keeps flat. When mnA ≠ 0 and 22222 1 0xy mnmn tt abDab ππππ σσ ???????????? +??=???????????? ???????????????? (5) the solution of the equation is not unique. This means the plate buckles. From Eq. (5) we can deduce the buckling compressive stress, 2222222 2222112(1)Buckley Etnana avmbmb π σσ ?????? =++?????? ????????? . (6) Each pair of n and m represents a buckling mode of the model. The critical compressive stress is the minimum value of all the buckling stresses for all the buckling modes. Since 22 2 0 0 y na mb σ>? ? ??? >??? ??? , (7) we can deduce from Eq. (6) that 2222222 2222112(1)Buckley Etnana avmbmb π σσ ?????? =++?????? ????????? 22222 222112(1) Etna avmb π???? >+???? ??????? 22 22.12(1) Et av π > ? (8) So the critical compressive stress can be expressed as: 22 2212(1)cr Et av π σ= ? (9) Results and Discussion In order to observe the growth of the surface low defect, we measure the displacement in the Z direction (drawing direction) at two representative points. The location of the two measure points are shown in Fig. 5. Point A is around the corner of the embossment, where surface low occurs according Advanced Materials Research Vols. 538-541379 to the experimental work by Fu et al. [3]. Point B is near Point A, but surface low does not occur at this point. The difference of the displacement in the Z direction, △Z=ZA-ZB, represents the surface deflection of the local area. Fig. 5 The selected measure points. Fig. 6 The history of surface deflection In Fig. 6 is the history of surface deflection during the entire forming process. During the drawing procedure, the surface deflection fluctuates about the zero value within ±0.1mm. At the end of drawing, the surface deflection is only 0.01 mm. During springback, the absolute value of surface deflection increases dramatically. At the end of springback, the absolute value of surface deflection increases from 0.01 to 0.1 mm (negative value means concave and positive value means convex), 10 times the original value. This indicates that the panel trembles during drawing, but surface low does not grow in this stage. It is during springback that the non-uniform displacement in thickness direction forms surface low. local buckling surface low (stoning) Fig. 7 Minor stress distribution. Fig. 8 The surface low areas and the local buckling areas. In Fig. 7 is the minor stress distribution around the embossment corner. Different from other areas, the minor stress in the surface low area is negative. This indicates that the surface low area is under a plane stress status of compression and tension. According to the analytical model in Fig. 4, buckling may happen if the local compressive stress is larger than the critical value. Table 2 Calculation of the critical stress Sub-domain Compressive stress σx (MPa) The compressive length, a (mm) The critical stress, σcr (MPa) Buckle or not 1 234 12 645 No 2 210 15 412 No 3 190 18 286 No 4 170 22 191 No 5 150 26 137 Yes 6 100 27 127 No 7 50 34 80 No 380Materials Processing Technology II According to the stress distribution in Fig. 7 and Eq. (9), we can calculate the critical stress for the sub-domains divided by the compressive stress level (shown in Table 2). According the results, buckling occurs in the sub-domain 5 whose boundary compressive stress is 150 MPa. Fig. 8 shows the predicted local buckling area and compares it with the experiment results by Fu et al. [3]. It is obvious that the local buckling area agrees with the detected surface low area. This indicates that the essence of surface low phenomenon is panel’s local buckling under the compressive residual stress during springback. Conclusion Our work in this paper focuses on the mechanism of surface low defect in sheet metal stamping. Based on the finite element simulation results, theoretical analysis and the referred experiment result, the following conclusions apply: The stamping panel trembles during drawing, but surface low does not grow in this stage. It is during springback that the non-uniform displacement in thickness direction forms surface low. The panel local buckling under the compressive residual stress during springback is one of the major reasons for surface low in sheet metal stamping. Acknowledgements The authors acknowledge the support from Research Project of State Key Laboratory of Mechanical System and Vibration MSVMS201101, Doctoral Fund of Ministry of Education of China 20100073110034 and ‘Shu Guang’ project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation 10SG13. 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[8] Wang Huiping, Xu Siguang, Cao Jian, Chen Wayne, Cheng Hang S., Wang Chuan-Tao. Prelimilary study on a surface distortion predictor for sheet metals: validation in Yoshida buckling problems.Numisheet 2008, Sep. 1-5, 2008-Interlaken, Switzerland. Advanced Materials Research Vols. 538-541381 Materials Processing Technology II 10.4028/www.scientific.net/AMR.538-541 The Mechanism of Surface Low Defect in Sheet Metal Stamping 10.4028/www.scientific.net/AMR.538-541.377