Analysis and Prediction of Size Effect on Laser Forming of Sheet Metal

Geometric effects play an important role in laser forming process; however, few investigations have been reported on the geometric size effect other than sheet thickness. In this paper, the influence of size effect, including sheet width and sheet length, on laser induced deformation is experimentally, numerically and analytically investigated. A size matrix is designed to cover a wide range of sheet width and length for experiments and numerical simulation. Distinctive trends in bending angle are observed for varying sheet width, length or both. The results are interpreted in terms of heat sink effect and bending non-uniformity. An analytic model is developed to facilitate size effect prediction. The model is based on the solution to a moving strip heat source over a finite size sheet and on the account for pre-bending effect among consecutive segments on the scanning path. It is compared with an existing analytical model and numerical simulation. INTRODUCTION Laser forming is a flexible forming process that forms sheet metal by means of stresses induced by external heat instead of external force. Understanding various aspects of laser forming has been a challenging problem of considerable theoretical and practical interest. The relationships of bending distortion and process parameters, material properties and workpiece thickness have been developed in analytical models. Additional information, such as influence of strain hardening, strain rate effects and edge effect have also been reported in experimental and numerical investigations. The geometric effects in laser forming, however, have not been fully studied. Most studies focused on the effect of workpiece thickness without considering other geometric attributes. Scully (1987) proposed that plate thickness s0 is one of the primary factors in laser forming and he adopted a quantity ) /( 0 V s P that was used in arc welding to study the effect of plate thickness on bending angle, but he did not give an exact relationship between them. Koloman and Karol (1991) proposed an analytical model in which the bending angle is a function of the reciprocal of the square of thickness. However, the bending angles calculated from this formula are some orders of magnitude too large compared with experiments. Vollertsen (1994a, 1994b) proposed a simple two-layer model based on the