One-Dimensional Thermomechanical Model for Additive Manufacturing Using Laser-Based Powder Bed Fusion

Abstract

We investigate the thermomechanical behavior of 3D printing of metals in the laser-based powder bed fusion (L-PBF) process, also known as selective laser melting (SLM). Heat transport away from the printed object is a limiting factor. We construct a one-dimensional thermoviscoelastic continuum model for the case where a thin fin is being printed at a constant velocity. We use a coordinate frame that moves with the printing laser, and apply an Eulerian perspective to the moving solid. We consider a steady state similar to those used in the analysis of production processes in the process industry, in the field of research known as axially moving materials. By a dimensional analysis, we obtain the nondimensional parameters that govern the fundamental physics of the modeled process. We then obtain a parametric analytical solution, and as an example, illustrate it using material parameters for 316L steel. The nondimensional parameterization has applications in real-time control of the L-PBF process. The novelty of the model is in the use of an approach based on the theory of axially moving materials, which yields a new perspective on modeling of the 3D printing process. Furthermore, the analytical solution is easy to implement, and allows fast exploration of the parameter space.

Keywords

• additive manufacturing
• laser-based powder bed fusion (L-PBF)
• selective laser melting (SLM)
• mathematical modeling
• coupled problem
• multiphysics