Thermal modelling of Selective Laser Melting: A semi-analytical approach

Selective Laser Melting (SLM) is a 3D-printing method to produce metal parts. In SLM a part is manufactured layer-by-layer by selectively melting a metal powder with a laser. Although SLM is a promising process for the production of high-quality parts, the implementation in high-tech industry is held back by a few barriers. One of the main barriers in the adoption of the process as a new production method are the high residual stresses and large deformations that arise in a part during manufacturing. The residual stresses may limit the load resistance and contribute to the formation of thermal cracks. Furthermore, it is difficult to ensure a constant quality during the build-process, resulting in e.g. varying porosity throughout the part. To obtain a better understanding of the process and predict processing and structural part characteristics prior to production, various modelling techniques have been proposed in literature. The majority of these models attempt to capture the movement of the laser by means of the finite element method (FEM). However, the fine discretization required to capture the steep thermal gradients in the vicinity of the moving laser spot, renders these types of models computationally too expensive to perform a full build-analysis of a component. Moreover, the transient nature of the heat transfer problem also increases the computational requirements. The aim of this research is to develop an efficient and simple, yet reasonably accurate thermal model of the SLM process, that is able to describe the influence of the process parameters on the level of residual stresses and the amount of porosity. To reach this objective, a semi-analytical modelling approach is proposed. The moving laser is represented with a set of point sources for which the closed form analytical solution is known. This solution efficiently captures the transient nature of the heat transfer problem and the steep thermal gradients in the vicinity of the moving laser. Since analytical solutions for a point source are limited to simple problems with specific types of boundary and initial conditions, a complementary correction field is superposed to the analytical solution to prescribe boundary conditions of interest. Predictions of the analytical part of the semi-analytical model are compared to experimental data, and it is found that, for the majority of the data, the predictions are within 10\% of the experimental values. Furthermore, results of the semi-analytical model are compared to an infinite series solution for a simple problem and show good correspondence, indicating that the implementation of the model is correct. A sensitivity analysis of the analytical part of the model to changes in the material properties, process parameters and scanning strategy is performed. It reveals that these factors significantly influence the melt pool dimensions and the maximum spatial thermal gradients that occur over time. It is suspected that the maximum spatial thermal gradient over time is a measure for the residual stresses in the end-product and that the stability of the melt pool influences the amount of porosity. Consequently, it is expected that by controlling the process parameters and scanning strategy, the porosity and residual stresses can be controlled. Single and multi-layer predictions are presented using the semi-analytical model. The simulations demonstrate that the scanning of overlying layers has a significant impact on the thermal history in the layers below, resulting in additional cycles of rapid heating and cooling. Furthermore, it is found that the time between the scanning of subsequent layers is sufficient for the material to cool down to the build-chamber temperature. This means that subsequent layers can be modelled separately. In an initial speed comparison with respect to a FEM-model the semi-analytical model is shown to have the potential to be much faster (up to three orders of magnitude) than a standard FEM-model. Consequently, it is a promising method to investigate e.g. the porosity and the residual stresses throughout several layers, and may potentially be used for the process optimization of small problems. However, in the current implementation the coarse numerical discretization limits the resolution at which the temperature profile can be evaluated. This limits the accuracy with which the melt pool dimensions and the maximum thermal gradient can be predicted. Concluding, the semi-analytical model provides a reasonably accurate thermal description of the SLM process. It is a promising method to investigate the amount of porosity and the level of residual stresses as introduced during the SLM process in a computationally efficient manner. Some recommendations for future research are given.Engineering MechanicsPrecision and Microsystems EngineeringMechanical, Maritime and Materials Engineerin