Analytical modelling of heat accumulation in laser based additive manufacturing processes of metals

The flexibility of additive manufacturing processes results from the principle of subsequently adding small amounts of material in individual layers or beads on top of each other. The periodic input of energy required to melt the material can lead to an accumulation of heat, which increases the temperature of the part and changes the local temperature distribution in the melt pool. This heat accumulation results in local shape deviations of the part and can lead to inhomogeneous solidification conditions coinciding with inhomogeneous grain structures and potentially inhomogeneous mechanical properties or build failures. To produce high quality parts with homogeneous properties and to reduce unproductive dwell times, a comprehensive knowledge of the heat accumulation phenomena is required. The present work considers an explicit analytical description of the heat accumulation effect, which allows for a mathematical analysis of the influence of all contributing process parameters on the temperature increase of the part. The analytical equations were derived from simplified heat conduction equations and validated by comparison with temperature measurements from literature. The calculated temperature increase shows a good agreement with measurements observed during additive manufacturing of different materials and alloys in case of cladding or building volumes with direct energy deposition (DED) and laser powder bed fusion (LPBF). Finally, the obtained analytical solution is used to derive optimization strategies aiming to reduce heat accumulation while simultaneously increasing productivity.