Thermal modelling of Selective Laser Melting: Thermal modes and multi-scale

Selective Laser Melting (SLM) is an Additive Manufacturing (AM) technique that uses a laser to selectively melt metallic powder in a layer-wise manner, in order to produce functional metal components. It offers great freedom in design and facilitates fast iterations, with the potential of speeding up development phases throughout a wide range of industries. Despite these opportunities, its application into industry is limited. One of the problems that is a limiting factor, is the high residual stress and large deformations that are introduced to the components during manufacturing. This is detrimental to the fatigue strength of a part and can even lead to cracks. In order to be able to understand, predict and eventually prevent such phenomena, a wide range of numerical models is already available in literature. Each of these models focus at one of more specific aspects of the SLM process. However an accurate prediction of the residual stresses for a complete component, requires detailed knowledge on the thermal history throughout the component. Due to a moving heat source, this problem is transient by nature and due to the local heat input by the laser, steep temperature gradients arise. This requires a fine discretisation, resulting in a computationally expensive model. The goal of this thesis is to contribute to the development of a computationally efficient process model of SLM, by developing a computationally efficient and reasonably accurate model of the thermal evolution of a part manufactured with the SLM process. In this work, two different modelling approaches are investigated, both use the Finite Difference (FD) method to discretise the problem at hand. The first approach uses thermal modes, which is the application of a modal solution to the heat equation. This method aims to use a truncated number of superposed eigensolutions and thereby reduce the computational load. Numerical eigenvalues and eigenvectors (also called thermal modes), were obtained for a SLM-relevant two dimensional example with insulated boundaries and a stationary instantaneous Gaussian heat source. The results are compared to the analytic solution to this problem, and by means of a convergence study settings are found that provide an accurate yet efficient discretisation. Due to the temporal variation of the loading, a relatively large amount of thermal modes needed to be retained to obtain an accurate solution. Introducing also spatial variation of the loading in a moving heat source example causes the thermal modes approach not have a significant advantage over a standard numerical integration method in terms of computation time. The second approach is the multi-scale approach. This method aims at modelling the different length scales, which are present in an SLM process by nature, with different models. The region close to the laser spot is discretised in a fine manner, the remainder of the domain is discretised coarsely. The FD method that is used, can only work on a uniform grid, i.e. it cannot handle a gradual mesh refinement. Instead an abrupt change between the coarse and the fine grids exists, which poses a challenge in coupling the two. For the coupling from the coarse region towards the fine region, the use of coupling nodes is proposed. The temperature values of these coupling nodes are found using interpolation on the temperature values of neighbouring coarse nodes, and serve as input to the calculations in the fine region. For the coupling from the fine towards the coarse region, the use of heat flux over the interface between the fine region and coarse region is proposed. The outward heat flux is calculated for every fine node on the interface, these values are used to heat up the surrounding coarse nodes. Also for this approach a convergence study was used to find settings that provide an accurate yet efficient discretisation. Despite some concerns on the discretisation of the laser movements, satisfactory results are obtained. A comparison of a multi-scale simulation to a simulation using a fine discretisation throughout the whole domain, showed that the multi-scale approach is an order of magnitude faster. By a comparison of two different scan patterns it has been shown that the multi-scale approach is indeed able to track the local thermal history. Thereby it can be concluded that the multi-scale approach has the potential to reduce the computational load of calculating the thermal evolution of a part produced with the SLM process, whilst still being reasonably accurate. This modelling approach is not fully mature yet, therefore recommendations for further research are given.Mechanical, Maritime and Materials EngineeringPrecision and Microsystems EngineeringEngineering Mechanic