Lamé curve approximation for the assessment of the 3D temperature distribution in keyhole mode welding processes

Abstract

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.

On the numerical treatment of heat sources in laser beam welding processes

“…The second model utilized in this study is based on the definition of Lamé curves which define the shape of the weld pool geometry. In order to determine the exact weld pool geometry, a priori steady state thermofluid dynamics simulation is necessary, see [3]. Here, a constant temperature within the defined region of the heat source is assumed.…”

“…In order to be able to describe the process of laser beam welding numerically, the implementation of a heat source, which represents the heat input of the laser beam, is indispensable. In this article, two models will be considered in more detail, Goldak's model, see [1] and [7], and a model which is based on Lamé curves, see [2] and [3]. The identification of the set of process and model parameters is not in the focus of this paper, thus all parameters are assumed to be known.…”

“…It is represented as a heat flux on the system and thus supplies laser beam melting zone liquid weld seam outflowing metal vapor laser induced plasma steam/plasma channel energy into the body following a Gaussian distribution. The second model picks up the idea of an isothermal region that mimics the geometry of the melt pool, see [2] and [3]. In this approach, the melting temperature of the material is specified and thus a complex calibration of the heat source is not required since it arises from an a priori steady state thermofluid dynamics simulation.…”

A volumetric heat source model for the approximation of the melting pool in laser beam welding

“…On one hand, a model based on isotherms, see refs. [1] and [2], and on the other hand, a modified conical model representing a volumetric heat source. Although both models are based on the data from a previous CFD simulation, the heat input is applied in different ways, namely through Dirichlet boundary conditions or body forces.…”

“…In order to achieve such enhancements, two heat source models will be discussed below. The first model is developed by the “Bundesanstalt für Materialforschung und ‐prüfung” that represents an equivalent heat source model, compare [1] and [2]. This means that an isotherm is reconstructed from prior Computational Fluid Dynamics (CFD) simulations using Lamé curves and transferred into the simulation through Dirichlet boundary conditions.…”