A computationally efficient thermal model for selective laser melting

Selective laser melting (SLM) is a widely used additive manufacturing method for building metal parts in a layer-by-layer manner thereby imposing almost no limitations on the geometrical layout of the part. The SLM process has a crucial impact on the microstructure, strength, surface quality and even the shape of the part, all of which depend on the thermal history of material points within the part. In this paper, we present a computationally tractable thermal model for the SLM process which accounts for individual laser scanning vectors. First, a closed form solution of a line heat source is calculated to represent the laser scanning vectors in a semi-infinite space. The thermal boundary conditions are accounted for by a complimentary correction field, which is computed numerically. The total temperature field is obtained by the superposition of the two. The proposed semi-analytical model can be used to simulate manufacturing geometrically complex parts and allows spatial discretisation to be much coarser than the characteristic length scale of the process: laser spot size, except in the vicinity of boundaries. The underlying assumption of linearity of the heat equation in the proposed model is justified by comparisons with a fully non-linear model and experiments. The accuracy of the proposed boundary correction scheme is demonstrated by a dedicated numerical example on a simple cubic part. The influence of the part design and scanning strategy on the temperature transients are subsequently analysed on a geometrically complex part. The results show that overhanging features of a part obstruct the heat flow towards the base-plate thereby creating local overheating which in turn decrease local cooling rate. Finally, a real SLM process for a part with an overhanging feature is modelled for validation of the proposed model. Reasonable agreement between the model predictions and the experimentally measured values can be observed.