Journal of Materials Engineering and Performance

, Volume 21, Issue 10, pp 2044–2052 | Cite as

An Analytical Model for Evaluation of Bending Angle in Laser Forming of Metal Sheets

  • Francesco LambiaseEmail author


In this study, an analytical model is developed to evaluate the bending angle in laser forming of metal sheets. The model is based on the assumption of elastic-bending theory without taking into account plastic deformation during heating and cooling phases. A thermal field is first established, then the thermal component of deformation is calculated and it is used in the strain balance to evaluate the bending angle. The basic idea is that it is possible to use a two-layer model whereas the heated layer thickness depends on the effective temperature distribution along the sheet thickness. A comprehensive experimental study is carried out and the main process parameters, i.e., laser power, scanning speed, sheet thickness, were varied among several levels to evaluate the accuracy of the developed model. Model predictions were confirmed by experimental measurements especially on materials with low conductivity. The established analytical model has demonstrated to provide a great insight into the process parameters effects onto the deformation mechanism within pure temperature gradient mechanism and bucking to temperature gradient transition conditions.


analytical model bending mechanism laser forming 



Thermal diffusivity


Final bending angle


Coefficient of thermal expansion


Material density


Absorption coefficient


Sheet width (orthogonal to scanning direction)


Young modulus




Sheet length (along scanning direction)


Laser power




Room temperature


Temperature of irradiated surface


Heat capacity


Laser beam length (along scanning direction)


Coefficient of thermal conductivity


Laser beam width (orthogonal to scanning direction)


Absorbed power


Sheet thickness


Thickness of heated volume


Interaction time


Laser scanning velocity


  1. 1.
    H. Shen and F. Vollertsen, Modelling of Laser Forming—An Review, Comput. Mater. Sci., 2009, 46(4), p 834–840. doi: 10.1016/j.commatsci.2009.04.022 CrossRefGoogle Scholar
  2. 2.
    P. Cheng, Y. Fan, J. Zhang, Y.L. Yao, D.P. Mika, W. Zhang, M. Graham, J. Marte, and M. Jones, Laser Forming of Varying Thickness Plate-Part I: Process Analysis, J. Manuf. Sci. Eng., 2006, 128(3), p 634. doi: 10.1115/1.2172280 CrossRefGoogle Scholar
  3. 3.
    W. Li and L. Yao, Numerical and Experimental Study of Strain Rate Effects in Laser Forming, J. Manuf. Sci. Eng., 2000, 122(3), p 445–451. doi: 10.1115/1.1286731 CrossRefGoogle Scholar
  4. 4.
    P. Cheng, Y. Fan, J. Zhang, Y.L. Yao, D.P. Mika, W. Zhang, M. Graham, J. Marte, and M. Jones, Laser Forming of Varying Thickness Plate-Part II: Process Synthesis, J. Manuf. Sci. Eng., 2006, 128(3), p 642. doi: 10.1115/1.2162912 CrossRefGoogle Scholar
  5. 5.
    F. Vollertsen, An Analytical Model for Laser Bending, Lasers Eng., 1994, 2, p 261–276Google Scholar
  6. 6.
    M. Hoseinpour Gollo, S.M. Mahdavian, and H. Moslemi Naeini, Statistical Analysis of Parameter Effects on Bending Angle in Laser Forming Process by Pulsed Nd:YAG Laser, Opt. Laser Technol., 2011, 43(3), p 475–482. doi: 10.1016/j.optlastec.2010.07.004 CrossRefGoogle Scholar
  7. 7.
    P.J. Cheng and S.C. Lin, An Analytical Model for the Temperature Field in the Laser Forming of Sheet Metal, J. Mater. Process. Technol., 2000, 101, p 260–267CrossRefGoogle Scholar
  8. 8.
    H. Shen, Y. Shi, Z. Yao, and J. Hu, An Analytical Model for Estimating Deformation in Laser Forming, Comput. Mater. Sci., 2006, 37(4), p 593–598. doi: 10.1016/j.commatsci.2005.12.030 CrossRefGoogle Scholar
  9. 9.
    Yau CL, Chan KC, and Lee WB, A New Analytical Model for Laser Bending, LANE, 1997. p 357–366Google Scholar
  10. 10.
    H. Shen, Z. Yao, Y. Shi, and J. Hu, An Analytical Formula for Estimating the Bending Angle by Laser Forming, J. Mech. Eng. Sci., 2006, 220(2), p 243–247Google Scholar
  11. 11.
    L. Zhang, Finite Element Modeling Discretization Requirements for the Laser Forming Process, Int. J. Mech. Sci., 2004, 46(4), p 623–637. doi: 10.1016/j.ijmecsci.2004.04.001 CrossRefGoogle Scholar
  12. 12.
    P. Zhang, B. Guo, D. Shan, and Z. Ji, FE Simulation of Laser Curve Bending of Sheet Metals, J. Mater. Process. Technol., 2007, 184(1–3), p 157–162. doi: 10.1016/j.jmatprotec.2006.11.017 CrossRefGoogle Scholar
  13. 13.
    F. Liu, K. Chan, and C. Tang, Numerical Simulation of Laser Forming of Aluminum Matrix Composites with Different Volume Fractions of Reinforcement, Mater. Sci. Eng. A, 2007, 458(1–2), p 48–57. doi: 10.1016/j.msea.2006.12.110 Google Scholar
  14. 14.
    Z. Ji and S. Wu, FEM Simulation of the Temperature Field During the Laser Forming of Sheet Metal, J. Mater. Process. Technol., 1998, 74, p 89–95CrossRefGoogle Scholar
  15. 15.
    A.K. Kyrsanidi, T.B. Kermanidis, and S.G. Pantelakis, An Analytical Model for the Prediction of Distortions Caused by the Laser Forming Process, J. Mater. Process. Technol., 2000, 104, p 94–102CrossRefGoogle Scholar

Copyright information

© ASM International 2012

Authors and Affiliations

  1. 1.Department of Mechanical Energy and Management EngineeringUniversity of L’Aquilal’AquilaItaly

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