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The paper presents bounded volume heat sources and the corresponding functional-analytical expressions for the temperature field. The power density distributions considered here are normal, exponential and parabolic. The sources model real heat sources like the welding arc, laser beam, electron beam, etc., the convection in the weld pool as well as the latent heat due to fusion and solidification. The parameters of the heat source models are unknown a priori and have to be evaluated by solving an inverse heat conduction problem. The functional-analytical technique for calculating 3D temperature fields in butt welding is developed. The proposed technique makes it possible to reduce considerably the total time for data input and solution. It is demonstrated with an example of laser beam welding of steel plates.

This paper presents volume heat sources and the corresponding functional analytical Solutions for the transient temperature field. The considered energy distributions are normal, exponential and parabolic. The method follows the common approach in Computational Welding Mechanics (CWM) to account for the physics of the welding process and the resulting temperature field by phenomenological models for heat conduction. Therefore, the used heat source models are apparent heat sources that incorporate the real heat input as well as the fluid flow in the weld pool and the latent heat connected with phase transformations. The heat source models provide welding characteristics like thermal cycle and Fusion line in the cross section within short computational time. Consequently, inverse techniques on basis of optimisation algorithms enable the adaptation of the models to the experimental data efficiently. Furthermore, the direct evaluation of the energy distribution for the experimental fusion line in the cross section is demonstrated which enhances the numerical optimisation by reducing the number of unknown model Parameters and providing a reasonable initial guess within the model parameter space. The proposed temperature field models are validated with real laser beam welding experiments.

This paper presents an approach to reconstruct the three-dimensional transient temperature field for fusion welding processes as input data for computational weld mechanics. The methodology to solve this inverse heat conduction problem fast and automatically focuses on analytical temperature field models for volumetric heat sources and application of global optimisation. The important issue addressed here is the question which experimental data is needed to guarantee a unique reconstruction of the experimental temperature field. Different computational-experimental test cases are executed to determine the influence of various sets of discrete experimental data on the solvability of the optimisation problem. The application of energy distributions utilised for laser beam welding allows reconstructing the temperature field efficiently. Furthermore, the heat input into the workpiece determined by the simulation contributes to the evaluation of the thermal efficiency of the welding process.

A numerical model 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-hydrodynamics and heat conduction. The solution of the thermo-hydrodynamics 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 evaluated and experimental molten pool, cross-sectional weld dimensions and thermal cycles of the heat affected zone are in close agreement.