Use of a multivariate optimization algorithm to develop a self-consistent numerical heat transfer model for laser spot welding

Laser spot welding as a joining method offers many outstanding advantages, such as localized heating and melting, high weld-strength-to-weld-size ratio, and minimal heat affected zone. These provide the benefits of low heat distortion, repeatability, ability to automate and high throughout that are always in demand in industry. An accurate knowledge of the temperature-time history of the weld pool is a prerequisite for reliable prediction of the weld dimensions, final microstructure and mechanical properties of the weld joint. Measurement of the weld thermal cycle in the laser weld pool is nearly impossible due to high peak temperature, rapid melting and solidification, and the complex flow of liquid metal within a small weld pool. Mathematical modeling of the laser spot welding process has emerged as a useful tool for the prediction of the temperature-time history and weld pool dimensions. However, the reliability of the predicted values of temperature history and weld dimensions significantly depends on the accuracy of the input parameters provided in such models. For example, the value of the absorption coefficient is a significant input parameter for modeling the laser spot welding process. However, the same is rarely available with adequate reliability and is also difficult to assign from scientific principles alone. This work presents a novel mathematical framework where the values of a set of uncertain input parameters for mathematical modeling are identified inherently by integrating a finite element based heat transfer simulation using adaptive volumetric heat source and a multivariate optimization algorithm.