Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-19T01:35:47.069Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of Self Damping and Higher-Order Geometrical Nonlinearity on History of Springback Amount for a Rectangular HSLA Steel Plate

Published online by Cambridge University Press:  27 June 2017

H. L. Dai ,
Z. H. Xiao ,
H. J. Jiang ,
A. H. Luo  and
W. L. Xu
H. L. Dai*
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangsha, China State Key Laboratory of Development and Application Technology of Automotive SteelBaosteel GroupShanghai, China Key Laboratory of Advanced Design and Simulation Technology for Special EquipmentsMinistry of EducationChangsha, China
Z. H. Xiao
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangsha, China State Key Laboratory of Development and Application Technology of Automotive SteelBaosteel GroupShanghai, China Key Laboratory of Advanced Design and Simulation Technology for Special EquipmentsMinistry of EducationChangsha, China
H. J. Jiang
Affiliation:
College of Mechanical EngineeringZhejiang University of TechnologyHangzhou, China
A. H. Luo
Affiliation:
State Key Laboratory of Development and Application Technology of Automotive SteelBaosteel GroupShanghai, China
W. L. Xu
Affiliation:
State Key Laboratory of Development and Application Technology of Automotive SteelBaosteel GroupShanghai, China
*
*Corresponding author (hldai520@sina.com)
Get access

Abstract

By introducing the concept of forming springback anti-coupled systems and considering the influence of the self damping effect, meanwhile establishing higher-order geometrical nonlinear equation of a high strength and low alloy (HSLA) steel plate, then a set of nonlinear dynamic springback governing equations of the plate are obtained. The finite difference method, Newmark method and iterative method are applied to solve the whole problem. Numerical results denote that the boundary conditions, thickness-length ratio of the plate and initial impact velocity of the impactor have great influence on the springback amount of the rectangular HSLA steel plate, besides the natural frequency is affected a lot by the boundary conditions and thickness-length ratio. The effect of higher-order geometrical nonlinearity on the springback amount of the plate can be ignored, considering the first-order geometrical nonlinearity is enough accurate for such similar nonlinear dynamic problems.

Keywords

Springback anti-coupled systemsHigher-order geometrical nonlinearityRectangular HSLA steel plate
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 5 , October 2017 , pp. 673 - 685
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Chen, S. X., The Crooked Springback of Panel and Type Material Controls the Principle and Method, House of National Defense Industry Press, Beijing (1990).Google Scholar
2. Song, L. and Yang, J., “The Board Material Crooked Springback Analysis and Project that Take Shape Control the Survey,” Forging Pressing Technology, 1, pp. 18–22 (1996).Google Scholar
3. Fu, B. L., The New Theory Each Other of Crooked Sheet Metal Work, House of National Defense Industry press, Beijing (2003).Google Scholar
4. Fu, B. L., Chen, Y. J. and Liu, H. M., “Springback Variational Principles of Bending of Straight Beams with Large Deflection,” Journal of Materials Processing Technology, 187, pp. 220–223 (2007).CrossRefGoogle Scholar
5. Carden, W. D., Geng, L. M., Matlock, D. K. and Wagoner, R. H., “Measurement of Springback,” International Journal Mechanical Science, 44, pp. 79–101 (2002).Google Scholar
6. Geng, L. M. and Wagoner, R. H., “Role of Plastic Anisotropy and Its Evolution on Springback,” International Journal of Mechanical Sciences, 44, pp. 123–148 (2002).Google Scholar
7. Zhu, L., Beaudoin, A. J., Macewen, S. R. and Kocks, U. F., “On the Time-Dependent Inelastic Deformation of Metals,” 8th International Conference on Numerical Methods in Industrial Forming Processes, Columbus, Ohio (2004).Google Scholar
8. Wang, J. F., Wagoner, R. H., Carden, W. D., Matlock, D. K. and Barlat, F., “Creep and Anelasticity in the Springback of Aluminum,” International Journal of Plastics, 20, pp. 2209–2232 (2004).CrossRefGoogle Scholar
9. Lim, H., Lee, M. G., Sung, J. H. and Wagoner, R. H., “Time-Dependent Springback,” International Journal Material Forming, 1, pp. 157–160 (2008).CrossRefGoogle Scholar
10. Lim, H., Lee, M. G., Sung, J. H., Kim, J. H. and Wagoner, R. H., “Time-Dependent Springback of Advanced High Strength Steels,” International Journal of Plastics, 29, pp. 42–59 (2012).CrossRefGoogle Scholar
11. Taherizadeh, A., Ghaei, A., Green, D. E. and Altenhof, W. J., “Finite Element Simulation of Springback for a Channel Draw Process with Drawbead Using Different Hardening Models,” International Journal of Mechanical Sciences, 51, pp. 314–325 (2009).CrossRefGoogle Scholar
12. Farsi, M. A. and Arezoo, B., “Experimental Study of High-Strength Low-Alloy Sheet Metal Components with Holes on the Bbending Surfaces,” Proceeding of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 223, pp. 387–394 (2009).Google Scholar
13. E, , D. X., and Liu, Y. F., “Springback and Time-Dependent Springback of 1Cr18Ni9Ti Stainless Steel Tubes under Bending,” Materials & Design, 31, pp. 1256–1261 (2010).Google Scholar
14. Park, T., Chung, K., Ryou, H., Lee, M. G. and Wagoner, R., “Numerical Simulation of Time-Dependent Springback Behavior for Aluminum Alloy 6022-T4 Sheet,” 10th International Conference on Numerical Methods in Industrial Forming Processes, Pohang, South Korea, (2010).Google Scholar
15. Ghaei, A. and Green, D. E., “Numerical Implementation of Yoshida-Uemori Two-Surface Plasticity Model Using a Fully Implicit Integration Scheme,” Computational Materials Science, 48, pp. 195–205 (2010).CrossRefGoogle Scholar
16. Liu, R. D. et al., “The Influence of Forming on Collision Performance of TRIP780 and HSLA340 Steel Parts,” Advanced Materials Research, 337, pp. 171–177 (2011).CrossRefGoogle Scholar
17. Broggiato, G. B., Campana, F., Cortese, L. and Mancini, E., “Comparison between Two Experimental Procedures for Cyclic Plastic Characterization of High Strength Steel Sheets,” Journal of Engineering Materials and Technology, 134, pp. 255–263 (2012).CrossRefGoogle Scholar
18. Achouri, M., Gildemyn, E., Germain, G., Dal Santo, P. and Potiron, A., “Influence of the Edge Rounding Process on the Behaviour of Blanked Parts: Numerical Predictions with Experimental Correlation,” The International Journal of Advanced Manufacturing Technology, 71, pp. 1019–1032 (2014).CrossRefGoogle Scholar
19. Xia, Z. Q. and Łukasiewicz, S., “Nonlinear Damped Vibrations of Simply-Supported Rectangular Sandwich Plates,” Nonlinear Dynamics, 8, pp. 417–433 (1995).CrossRefGoogle Scholar
20. Łukasiewicz, S. and Xia, Z. Q., “Nonlinear Damped Vibrations of Simply-Supported Sandwich Plates in a Rapidly Changing Temperature Field,” Nonlinear Dynamics, 9, pp. 369–389 (1996).CrossRefGoogle Scholar
21. Wang, L. X. and Melnik, R. V. N., “Numerical Model for Vibration Damping Resulting from the First-Order Phase Transformations,” Applied Mathematical Modelling, 31, pp. 2008–2018 (2007).CrossRefGoogle Scholar
22. Khante, S. N., Rode, V. and Kant, T., “Nonlinear Transient Dynamic Response of Damped Plates Using a Higher Order Shear Deformation Theory,” Nonlinear Dynamics, 47, pp. 389–403 (2007).Google Scholar
23. Salajeghe, S., Khadem, S. E. and Rasekh, M., “Nonlinear Analysis of Thermoelastic Damping in Axisymmetric Vibration of Micro Circular Thin-Plate Resonators,” Applied Mathematical Modelling, 36, pp. 5991–6000 (2012).CrossRefGoogle Scholar
24. Zaitsev, S., Shtempluck, O., Buks, E. and Gottlieb, O., “Nonlinear Damping in a Micromechanical Oscillator,” Nonlinear Dynamics, 67, pp. 859–883 (2012).CrossRefGoogle Scholar
25. Yan, S., Dowell, E. H. and Lin, B., “Effects of Nonlinear Damping Suspension on Nonperiodic Motions of a Flexible Rotor in Journal Bearings,” Nonlinear Dynamics, 78, pp. 1435–1450 (2014).CrossRefGoogle Scholar
26. Barry, O., Oguamanam, D. and Zu, J., “Nonlinear Vibration of an Axially Loaded Beam Carrying Multiple Mass-Spring-Damper Systems,” Nonlinear Dynamics, 77, pp. 1597–1608 (2014).CrossRefGoogle Scholar
27. Moosapour, M., Hajabasi, M. A. and Ehteshami, H., “Thermoelastic Damping Effect Analysis in Micro Flexural Resonator of Atomic Force Microscopy,” Applied Mathematical Modelling, 38, pp. 2716–2733 (2014).CrossRefGoogle Scholar
28. Dai, H. L., Qi, L. L. and Zheng, H. Y., “Buckling Analysis for a Ring-Stiffened FGM Cylindrical Shell under Hydrostatic Pressure and Thermal Loads,” Journal of Mechanics, 30, pp. 403–410 (2014).CrossRefGoogle Scholar
29. Dai, H. L., Dai, T. and Cheng, S. K., “Transient Response Analysis for a Circular Sandwich Plate with an FGM Central Disk,” Journal of Mechanics, 31, pp. 417–426 (2015).CrossRefGoogle Scholar
30. Wang, Y. Q. and Zu, , Jean, W., “Nonlinear Steady-State Responses of Longitudinally Traveling Functionally Graded Material Plates in Contact with Liquid,” Composite Structures, 164, pp. 130–144 (2017).CrossRefGoogle Scholar
31. Wang, Y. Q., Huang, X. B. and Li, J., “Hydroelastic Dynamic Analysis of Axially Moving Plates in Continuous Hot-Dip Galvanizing Process,” International Journal of Mechanical Sciences, 110, pp. 201–216 (2016).CrossRefGoogle Scholar
32. Wang, Y. Q., Liang, L. and Guo, X. H., “Internal Resonance of Axially Moving Laminated Circular Cylindrical Shells,” Journal of Sound and Vibration, 332, pp. 6434–6450 (2013).CrossRefGoogle Scholar
33. Wang, Y. Q., “Nonlinear Vibration of a Rotating Laminated Composite Circular Cylindrical Shell: Traveling Wave Vibration,” Nonlinear Dynamics, 77, pp. 1693–1707 (2014).CrossRefGoogle Scholar
34. Chia, C. Y., Nonlinear Analysis of Plates, McGraw-Hill, New York (1980).Google Scholar
35. Onkar, A. K. and Yadav, D., “Non-Linear Response Statistics of Composite Laminates with Random Material Properties under Random Loading,” Composite Structures, 60, pp. 375–383 (2003).CrossRefGoogle Scholar
36. Xu, Z. L., Elasticity Mechanics, 3rd Edition, Higher Education Press, Beijing (2006).Google Scholar
37. Yang, G. T., Introduction to Elasticity and Plasticity, Tsinghua University Press, Beijing (2004).Google Scholar
38. Choi, I. H. and Lim, C. H., “Low-Velocity Impact Analysis of Composite Laminates Using Linearized Contact Law,” Composite Structures, 66, pp. 125–132 (2004).CrossRefGoogle Scholar
39. Sun, C. and Chattopadhyay, S., “Dynamic Response of Anisotropic Laminated Plates under Initial Stress to Impact of a Mass,” Journal of Applied Mechanics, 42, pp. 693–698 (1975).CrossRefGoogle Scholar
40. Deng, L. and Ye, T., “Nonlinear Dynamic Response of the Circular Plates under Impact of a Mass,” Acta Mechanical Sinica, 22, pp. 420–428 (1990).Google Scholar
41. Fu, Y. M. and Lu, Y. H., “Analysis of the Nonlinear Dynamic Response of Viscoelastic Symmetric Cross-Ply Laminated Plates with Transverse Matrix Crack,” Composite Structures, 72, pp. 469–476 (2006).CrossRefGoogle Scholar
42. Dai, H. L. and Zheng, H. Y., “Creep Buckling and Post-Buckling Analyses of a Viscoelastic FGM Cylindrical Shell with Initial Deflection Subjected to a Uniform In-Plane Load,” Journal of Mechanics, 28, pp. 391–399 (2012).CrossRefGoogle Scholar
43. Dai, H. L., Yan, X. and Yang, L., “Nonlinear Dynamic Analysis for FGM Circular Plates,” Journal of Mechanics, 29, pp. 287–295 (2013).CrossRefGoogle Scholar
44. Chen, Y., “Springback Finite-Element Analysis for Large Deflection of Bending Thin Plate,” Journal of Plastics Engineering, 12, pp. 59–62 (2005).Google Scholar