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

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Abstract

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.

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Abbreviations

α:

Thermal diffusivity

αb :

Final bending angle

αth :

Coefficient of thermal expansion

ρ:

Material density

A :

Absorption coefficient

B :

Sheet width (orthogonal to scanning direction)

E :

Young modulus

K :

Curvature

L :

Sheet length (along scanning direction)

P :

Laser power

T :

Temperature

T 0 :

Room temperature

T up :

Temperature of irradiated surface

c p :

Heat capacity

d :

Laser beam length (along scanning direction)

k :

Coefficient of thermal conductivity

l :

Laser beam width (orthogonal to scanning direction)

q :

Absorbed power

s :

Sheet thickness

s 1 :

Thickness of heated volume

t :

Interaction time

v :

Laser scanning velocity

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Authors and Affiliations

  1. Department of Mechanical Energy and Management Engineering, University of L’Aquila, Monteluco di Roio, 67040, l’Aquila, AQ, Italy

    Francesco Lambiase

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  1. Francesco Lambiase
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Correspondence to Francesco Lambiase.

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Lambiase, F. An Analytical Model for Evaluation of Bending Angle in Laser Forming of Metal Sheets. J. of Materi Eng and Perform 21, 2044–2052 (2012). https://doi.org/10.1007/s11665-012-0163-x

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  • DOI: https://doi.org/10.1007/s11665-012-0163-x

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