Multiple Reflections and Fresnel Absorption of Gaussian Laser Beam in an Actual 3D Keyhole during Deep-Penetration Laser Welding

In deep penetration laser welding, a keyhole is formed in the material. Based on an experimentally obtained bending keyhole from low- and medium-speed laser penetration welding of glass, the keyhole profiles in both the symmetric plane are determined by polynomial fitting. Then, a 3D bending keyhole is reconstructed under the assumption of circular cross-section of the keyhole at each keyhole depth. In this paper, the behavior of focused Gaussian laser beam in the keyhole is analyzed by tracing a ray of light using Gaussian optics theory, the Fresnel absorption and multiple reflections in the keyhole are systematically studied, and the laser intensities absorbed on the keyhole walls are calculated. Finally, the formation mechanism of the keyhole is deduced. 1. Introduction When laser beam with high laser intensity irradiates work piece, the material is vaporized, recoil pressure is produced, and a keyhole is formed in the material. Then, laser beam can directly enter the keyhole and propagate in the keyhole by means of multiple reflections on the keyhole wall, and the laser energy is absorbed through the Fresnel absorption. The formation of keyhole enhances the energy-coupling efficiency between laser beam and material. Concerning the Fresnel absorption and multiple reflections in the keyhole, a lot of work has been done. In 1989, Dowden et al. [1] considered the Fresnel absorption, but the way they used is too simple with a uniform laser line source. In 1990, Beck et al. [2] traced rays in a symmetric keyhole at low speed and established a numerical model of the Fresnel absorption. In 1992 and in 1996, Kern [3] and Mueller [4], simulated the Fresnel absorption and multiple reflections in a predetermined 3D keyhole, respectively. In 1994, Kaplan [5] developed a model to calculate the asymmetric keyhole profile and considered the Fresnel absorption and multiple reflections in the keyhole in a simple way. In 1997, Solana and Negro [6] used an axisymmetrical model to analyze keyhole profiles and laser intensity distributions with keyhole depth for the cases of a Gaussian and a uniform top-hat distribution laser beam and studied the effect of multiple reflections inside the keyhole with a free boundary. In 2000, Fabbro and Chouf [7] studied multiple reflections inside the keyhole by tracing a ray. But in all of the above work, the real keyhole shapes were dealt with some simple ways. For example, the keyhole was assumed to be rotationally symmetric. But it is different from reality. In practical deep penetration laser welding, especially in high-speed