Computationally efficient thermal-mechanical modelling of selective laser melting

The Selective laser melting (SLM) is a powder based additive manufacturing (AM) method to produce high density metal parts with complex topology. However, part distortions and accompanying residual stresses deteriorates the mechanical reliability of SLM products. Modelling of the SLM process is anticipated to be instrumental for understanding and predicting the development of residual stress field during the build process. However, SLM process modelling requires determination of the heat transients within the part being built which is coupled to a mechanical boundary value problem to calculate displacement and residual stress fields. Thermal models associated with SLM are typically complex and computationally demanding. In this paper, we present a simple semi-analytical thermal-mechanical model, developed for SLM that represents the effect of laser scanning vectors with line heat sources. The temperature field within the part being build is attained by superposition of temperature field associated with line heat sources in a semi-infinite medium and a complimentary temperature field which accounts for the actual boundary conditions. An analytical solution of a line heat source in a semi-infinite medium is first described followed by the numerical procedure used for finding the complimentary temperature field. This analytical description of the line heat sources is able to capture the steep temperature gradients in the vicinity of the laser spot which is typically tens of micrometers. In turn, semi-analytical thermal model allows for having a relatively coarse discretisation of the complimentary temperature field. The temperature history determined is used to calculate the thermal strain induced on the SLM part. Finally, a mechanical model governed by elastic-plastic constitutive rule having isotropic hardening is used to predict the residual stresses.