Laser Powder Bed Fusion (LPBF) is a metal additive manufacturing process in which a three-dimensional object is obtained by selectively melting and fusing a metallic powder with a heat source, such as a laser beam, in successive thin layers. This process allows to create lightweight parts with complex geometry. However, parts created by LPBF processes may present poor surface quality and can be prone to high residual stresses and deformations that arise during manufacturing. To be able to understand the process and investigate the relation between the thermal history of the part and the deformations that arise, researchers have proposed different thermal models in literature. Most of these models are purely numerical methods in which the temperature history is predicted by implementing finite element and finite difference schemes. However, a finer discretization is required to capture the steep temperature gradients that arise at the vicinity of the laser spot, which results in computational expensive models.
In the Precision and Microsystems Engineering (PME) Department at TU Delft, a semi-analytical approach was proposed to study the thermal history of LPBF processes. This method combines an analytical solution that captures the high spatial gradients of the laser beam and a numerical solution that corrects the analytical solution and enforces the boundary conditions. When the laser beam is near the boundary, the analytical solution is corrected first with the method of images, which dramatically reduces the computational cost when obtaining the solution. However, this approach is only valid for convex polyhedrons. If the domain is non-convex, the method of images cannot be applied. Therefore, the high spatial gradients have to be dealt with finer discretization, and the numerical correction's computational cost becomes prohibitive.
In this thesis, a thermal model is developed for LPBF processes using the semi-analytical approach with a modification in the method of images for concave polyhedrons. In this case, a correction to the method of images, denoted as anisotropic mirror sources, is introduced. This method allows to apply image sources to concave geometries. With this modification, the numerical correction in the semi-analytical method can be implemented with a coarse discretization with high computational efficiency.
Predictions of the proposed thermal model are compared to the predictions of a semi-analytical method without using the method of images. This comparison allows us to validate the proposed thermal model's computational efficiency as it can obtain the thermal history of concave polyhedrons in a computationally inexpensive manner. More importantly, the thermal model proposed demonstrates the possibility of using the method of images in concave polyhedrons.