Efficient Thermal Modelling and Topology Optimization for Additive Manufacturing

With the advent of Additive Manufacturing (AM) techniques, the design principle of `form follows function' no longer remains a utopian proposition. The unprecedented design freedom offered by AM is making it possible to conceptualize highly performant designs by efficiently leveraging geometrical complexity. The increase in design freedom requires novel design tools which are tailored to capitalize on the form freedom offered by AM. Topology optimization (TO) is such a computational design tool which can find the optimal geometric layout of a part to achieve a pre-defined objective, while satisfying certain constraints. However, AM processes have inherent manufacturing constraints which should be considered at the design stage to ensure manufacturability. The suitability of TO as an ideal design tool is already widely recognized and there have been significant research efforts to integrate AM constraints within TO. In this regard, most AM-oriented TO methods utilize geometry-based constraint where a geometric AM design guideline is integrated within TO. The maturity of research in this direction is evident by the fact that most commercial CAD packages are already equipped with TO plugins including these geometry-based AM constraints. Although beneficial, such geometry-based TO constraint do not guarantee defect-free fabrication since manufacturability is not only a function of geometry, but depends on a range of complex physical interactions during the process. Therefore, a TO method that accounts for more of the physics of the AM process would enhance the likelihood of achieving better quality parts with reduced defects.
This thesis is focused on laser based powder bed fusion (L-PBF) since it is the most widely utilized AM technique for metal parts. However, L-PBF suffers from certain constraints which critically compromise the part quality and inhibit its adoption as a mainstream manufacturing method. Among the constraints, the issue of local overheating remains a critical barrier as it leads to poor surface quality, inferior mechanical properties and/or build failures. Moreover, uneven heating/cooling thermal cycles due to overheating could lead to development of undesirable residual stresses and distortions. Typically, overheating is associated with downfacing surfaces called overhangs which led to development of geometry-based design guidelines, for example, avoidance of geometric features with overhangs more acute than a certain threshold. This guideline has been the most common AM constraint to integrate within TO. However, it is evident by a number of numerical and experimental studies in the literature, that the avoidance of overhangs does not guarantee overheating free designs. Therefore, the two aims of this thesis are (1) to thoroughly investigate local overheating during L-PBF process using computational models and (2) to develop a novel TO for generating overheating free AM ready designs. In this regard, the extremely high computational cost of L-PBF models was identified as the biggest challenge for both the objectives i.e. quick assessment of overheating-prone features in AM parts and integration of a L-PBF thermal model with TO.
The first half of this thesis deals with a systematic investigation of the simplifications commonly used in the thermal modelling of the heat transfer phenomena during the L-PBF process. The simplifications have been classified based on the spatio-temporal resolution they assume for modelling the process. With help of numerical experiments, the findings reveal the relationship between spatio-temporal simplifications and their ability to capture certain process attributes. For example, it is found that if peak process temperatures are to be predicted, then short laser exposure times should be specified in the computational domain. On the contrary, if temperatures far away from the topmost layer are analyzed, a simplified model assuming a longer exposure time can capture it. These findings serve as guidelines in making informed choices while setting up an L-PBF thermal model. In addition to this, numerical discretization requirements associated with different simplifications are also provided. Next, a deeper investigation of relevant simplifications for detecting local overheating is presented. Three novel simplifications based on the analytical solution of the heat equation are presented which drastically reduce the computational expense while retaining the ability to identify overheating prone features. The most simplified model in this regard utilizes a localized steady-state analysis which provides maximum computational gain of approximately 600 fold as compared to a high fidelity transient simulation.
The second half of the thesis presents the integration of the aforementioned steady-state L-PBF thermal model with the density- based TO method. This is achieved by formulating a novel constraint which limits the peak temperature predicted by the simplified L-PBF model. This novel physics-based TO method is validated using in-situ optical tomography (OT) measurements. Comparing OT based overheating data across geometry-based and physics-based TO designs, it is revealed that the latter have a lower tendency of overheating. Finally, the usability of the new TO method is demonstrated on an industrial injection mould. Another application of the novel TO is demonstrated by designing support structures for optimal heat evacuation.
Based on the findings presented in thesis, it can be concluded that a physics-based TO method offers significant advantages over a purely geometry-based approach. In particular, it is shown that overheating avoidance cannot be assured just by avoiding acute overhangs. While for overheating detection even a simplification to steady-state analysis was possible, it is expected that for other aspects the full thermal history must be evaluated, which presents a challenge for future work. Apart from development of the novel TO approach, the second major contribution of this thesis are the insights developed regarding modelling simplifications which assist in drastically reducing the computational expenses associated with L-PBF modelling. It is expected that outcomes from this thesis will positively contribute towards development of efficient modelling techniques which will also inherently benefit further advancement of physics-based TO methods.