## Influence of Order on Curved Surface Shape in Laser Forming with Multiple Parallel Heating

Tetsuya Akiyama 1, Takanori Kitamura 1, Kengo Higashi 2, Hiroaki Kuramoto 3 and Daisuke Kishi 3

1 Department of Materials Science and Engineering, Faculty of Engineering, Kyushu Institute of Technology
2 Department of Materials Science and Engineering, Undergraduate School of Engineering, Kyushu Institute of Technology
3 Department of Materials Science, Graduate School of Engineering, Kyushu Institute of Technology

#### Abstract:

Laser forming is a technique for forming a target curved surface by locally bending or shrinking by heating like linear heating process in shipbuilding. In the shipbuilding site, it is empirically known that the final curved surface shape changes due to the influence of thermal history, if the heating order is changed. However, the main cause has not been clarified yet. The authors studied mathematically the relation between the in-plane strain and the curved surface shape in the twisted curved surface forming. Then, it was shown that the difference of in-plane strain distributions caused by the difference in heating order suppressed or promoted twisted deformation. Therefore, if different in-plane strain distributions are formed by changing the heating order with parallel heating lines, bowl-shaped curved surfaces and saddle-shaped curved surfaces can be formed separately. In this paper, we carried out theoretical calculations using a macroscopic dynamic model, simulation by finite element method and experiments of laser forming. And we examined the relationship between heating order and in-plane strain and the possibility of forming bowl and saddle shaped curved surfaces separately. As a result, it was shown by FEM analysis that the peak value of the inherent strain generated by the late heating order is larger than that by early heating order. And we could explain the reason with a macroscopic dynamic model. In addition, by changing the heating order with parallel heating lines, it was possible to form bowl and saddle shaped curved surfaces separately. Finally, we could explain the cause of bowl or saddle shaped curved surface forming using thermal history by changing longitudinal shrinkage distribution.