An integrated mathematical model for laser welding of thin metal sheets under a variety of laser material processing conditions has been developed and tested against the results of experiments. Full account is taken in the model of the interaction of the laser-generated keyhole with the weld pool. Results calculated from the model are found to agree well with experiment for appropriate values of the keyhole radius. The analysis yields values for power absorption in the metal. In a complementary calculation the total absorption of the laser energy is determined from detailed consideration of the inverse Bremsstrahlung absorption in the plasma and Fresnel absorption at the keyhole walls. To test these results, experiments were performed on 1 mm mild steel using a high-speed video camera, which measured the surface dimensions of the melt pool. Processing parameters were varied to study the effect on the melt pool; parameters considered included traverse speed, laser power and shroud gas species. The general shape of the weld pool was found to depend on whether penetration was full, partial or blind; only the results for full penetration were compared with the theory, which is for complete penetration only.
We propose a simple model to study the Gouy phase effect in the triple-slit experiment in which we consider a non-classical path. The Gouy phase differs for classical or non-classical paths as it depends on the propagation time. In this case the Gouy phase difference changes the Sorkin parameter κ used to estimate non-classical path contribution in a nontrivial way shedding some light in the implementation of experiments to detect non-classical path contributions.
Recently Gouy rotation was observed with focused non-relativistic electron vortex beams. If the electrons in vortex beams are very fast we have to take into account relativistic effects to completely describe the Gouy phase on them. Exact Hermite-Gaussian solutions to the Klein-Gordon equation for particle beams are obtained here that make explicit the 4-position of the focal point of the beam. These are Bateman-Hillion solutions with modified phase factors to take into account the rest mass of the particles. They enable a relativistic expression for the Gouy phase to be determined. It is in fact shown all the solutions are form invariant under Lorentz transformations. It is further shown for the exact solutions to correspond to those of the Schrödinger equation the relative time between the focal point and any point in the beam must be constrained to be a specific function of the relative spatial coordinates.
A thermal model has been developed for laser welding which describes the heat input in terms of point and line sources. The model was used to generate weld profiles which closely matched those found by experiment. Outputs of the model (the thermal gradient GL and the growth rate R) were used to describe the macroscopic grain structure found along the weld centreline. Columnar structures were predicted at low welding speeds (high GL/R ratio) and equiaxed structures at high welding speeds (low GL/R ratio). Using the thermal model, cooling rates of ∼1500 K s–1 were estimated for the lowest welding speed, which increased by an order of magnitude for the highest welding speed considered. There was excellent agreement between the dendrite secondary arm spacings measured by experiment and those predicted using the thermal model.
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