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A technique for calculating the main solidification parameters for a two-dimensional columnar crystal growth during complete penetration laser beam welding of thin steel sheets was developed. Given that the weld pool interface is described by Lamé curves (superellipses) within the horizontal plane of growth, general analytical solutions were derived for the geometry of the crystal axis and the corresponding growth rate and cross-sectional area of the crystal. A dimensionless analysis was performed to provide insights on the dependence of the solidification parameters on the shape and dimensions of the rear part of the weld pool boundary. The derived solutions were applied for the case of complete penetration laser beam keyhole welding of 2 mm thick 316L austenitic chromium-nickel steel sheets. It was shown that the reconstruction of the weld pool boundary with Lamé curves provides higher accuracy and flexibility compared to results obtained with elliptical functions. The validity of the proposed technique and the derived analytical solutions was backed up by a comparison of the obtained solutions to known analytical solutions and experimentally determined shapes and sizes of the crystals on the top surface of the sheet. The dimensions of the calculated crystal axis correlated well with the experimentally obtained results.
A novel approach for the reconstruction of an equivalent volumetric heat source from a known weld pool shape is proposed. It is based on previously obtained weld pool geometries from a steady-state thermo-fluid dynamics simulation. Hereby, the weld pool dimensions are obtained under consideration of the most crucial physical phenomena, such as phase transformations, thermo-capillary convection, natural convection, and temperature-dependent material properties. The algorithm provides a time and calibration efficient way for the reproduction of the weld pool shape by local Lamé curves. By adjusting their parameters, the identification of the finite elements located within the weld pool is enabled. The heat input due to the equivalent heat source is assured by replacing the detected nodes’ temperature by the melting temperature. The model offers variable parameters making it flexible and adaptable for a wide range of workpiece thicknesses and materials and allows for the investigation of transient thermal effects, e.g., the cooling stage of the workpiece. The calculation times remain acceptably short especially when compared to a fully coupled process simulation. The computational results are in good agreement with performed complete-penetration laser beam welding experiments.
The geometrical characteristics of the weld end crater are commonly used as a means of validating numerical results in welding simulations.
In this paper, an analytical model is developed for calculating the cooling stage of the welding process after the moving energy source is turned off. Solutions for various combinations of heat sources and heated bodies are found. It is shown that after turning off the Energy source, additional melting of the base material in the longitudinal direction may occur due to the overheated liquid metal. The developed technique is applied to complete-penetration keyhole laser beam welding of 2 mm thick austenitic stainless-steel plate 316L at a Welding speed of 20 mm/s and a laser power of 2.3 kW. The results show a theoretical increase in the weld end crater length of up to 19% compared to the length of the steady-state weld pool. It is found that at the moment of switch off, the weld end crater center, where solidification of the liquid metal ends, is shifted from the heat source axis toward the weld pool tail. The solidification rate and the direction of crystallization of the molten material during the welding process and those in the weld end crater differ significantly. A good agreement between the computational results and the welding experiments is achieved.
A numerical framework for simulation of the steady-state thermal behaviour in keyhole mode welding has been developed. It is based on the equivalent heat source concept and consists of two parts: computational thermo-fluid dynamics and heat conduction. The solution of the thermo-fluid dynamics problem by the finite element method for a bounded domain results in a weld pool interface geometry being the input data for a subsequent heat conduction problem solved for a workpiece by a proposed boundary element method. The main physical phenomena, such as keyhole shape, thermo-capillary and natural convection and temperature-dependent material properties are taken into consideration. The developed technique is applied to complete-penetration keyhole laser beam welding of a 15 mm thick low-alloyed steel plate at a welding speed of 33 mm/s and a laser power of 18 kW. The fluid flow of the molten metal has a strong influence on the weld pool geometry. The thermo-capillary convection is responsible for an increase of the weld pool size near the plate surfaces and a bulge formation near the plate middle plane. The numerical and experimental molten pools, cross-sectional weld dimensions and thermal cycles of the heat affected zone are in close agreement.