Analytical modeling of axis geometry effect in laser peen forming

Laser peen forming (LPF) is a novel flexible process by utilizing pulse laser to induce mechanical deformation on the specimen surface. It is of great importance to quantitatively evaluate the geometry effect on deforming behavior in LPF for both shape forming and distortion correction. This is very helpful for process planning to improve the shaping efficiency and accuracy. In this study, analytical modeling and numerical simulation are carried out to investigate the geometry effect of axis with a simplified shape. Considering that plate deformation by uniformed LPF can be assumed as beam bending with an arc shape, an analytical model is proposed to analyze its geometry effect by utilizing equivalent bending moment. The model is validated by the numerical model of LPF developed based on the eigenstrain. The result shows the developed analytical model can provide a consistent prediction of axis geometry effect, but the accuracy is depending on the initial radius of axis arc. By using the analytical modeling of LPF, the bending characteristic of LPF on the double curvature plate is studied. The prediction is more accurate when the radius of axis arc is large. When the radius of axis arc is less than 5000 mm, the axis has some effect on the bending of LPF, with the increase of the axis radius, the geometry effect of axis is gradually decreased.