Title: Incorporating non-linear effects in fast semi-analytical thermal modelling of powder bed fusion

Abstract: The usefulness of semi-analytical thermal models for predicting the connection between process, microstructure and properties in powder bed fusion has been well illustrated in recent years. Such an approach provides the promise of accuracy comparable to tools that are orders of magnitude more computationally expensive. The opportunity to make predictions that span several orders of magnitude in space and time comes at the cost of significant simplifications, limiting fully quantitative predictions without empirical calibration. This approach relies on solving a linear problem meaning that first order non-linear effects induced by e.g. the temperature dependence of material properties and surface boundary conditions, are not incorporated. Here, we revisit these limitations and highlight ways that temperature varying material properties and radiative heat loss from the melt pool can be systematically accounted for. These corrections, made with an eye to minimizing additional computational overhead, bring the technique's predictive capability much closer to that of high fidelity thermal simulations. Quantitative comparisons to experiments are used to illustrate the important impact of including such corrections.