A mathematical model of the chevron-like wave pattern on a weld piece

Abstract

In welding processes in general the surface of a metallic weld displays a chevron-like pattern. Such a pattern is also clearly seen to be present if welding is carried out using a laser beam. In the welding process a laser beam is directed normally on the metal undergoing translation and usually penetrates it to form a keyhole. The keyhole is surrounded by a molten region, the weld pool. Even if a CO2 laser is used, there are numerous fluctuations and instabilities that occur, so that the keyhole imposes forcing frequencies on the molten weld pool, additional to vibrations attendant on the process of translation. The weld pool in turn responds by supporting a spectrum of waves of different frequencies involving the natural frequency of the weld pool as well as various forcing frequencies. These waves are surface tension-type capillary waves and previous publications have attempted to model their behaviour mathematically, although not all aspects of the problem have always been included. The wave pattern that is manifested in the chevron-like pattern seen on the weld piece is, however, not necessarily identical to the wave pattern present in the weld pool. This is because the chevron-like wave pattern forms as a result of several complicating effects that arise as the weld specimen cools on its surface immediately after the weld has been formed. This process involves the waves on the surface of the weld pool freezing to form the chevron-like wave pattern. A feature that is often ignored is the fact that the waves on the weld pool can only be regarded as irrotational if the translation speed is sufficiently low. This paper describes mathematically the formation of the chevron-like wave pattern based on suitable simplifying assumptions to model the process. The purpose of welding is to join metals together and the ultimate success of this process depends on the effectiveness with which this is achieved. This final weld state is likely to depend eventually not only on the elastic properties of the weld once it is achieve, but also on the manner in which this weld state is realised. The mathematical description of the way in which this chevron-like pattern forms is a step toward a more comprehensive understanding of this process.