Analytical Thermal Modeling of Metal Additive Manufacturing by Heat Sink Solution

Abstract

Metal additive manufacturing can produce geometrically complex parts with effective cost. The high thermal gradients due to the repeatedly rapid heat and solidification cause defects in the produced parts, such as cracks, porosity, undesired residual stress, and part distortion. Different techniques were employed for temperature investigation. Experimental measurement and finite element method-based numerical models are limited by the restricted accessibility and expensive computational cost, respectively. The available physics-based analytical model has promising short computational efficiency without resorting to finite element method or any iteration-based simulations. However, the heat transfer boundary condition cannot be considered without the involvement of finite element method or iteration-based simulations, which significantly reduces the computational efficiency, and thus the usefulness of the developed model. This work presents an explicit and closed-form solution, namely heat sink solution, to consider the heat transfer boundary condition. The heat sink solution was developed from the moving point heat source solution based on heat transfer of convection and radiation. The part boundary is mathematically discretized into many heats sinks due to the non-uniform temperature distribution, which causes non-uniform heat loss. The temperature profiles, thermal gradients, and temperature-affected material properties are calculated and presented. Good agreements were observed upon validation against experimental molten pool measurements.

Computer Simulation of Hydrodynamic and Thermal Processes in DLD Technology

“…Therefore, the availability of a physically adequate and fast mathematical model that allows the performance of numerical modeling will facilitate the development and optimization of technological parameters for the direct laser deposition process. A large number of papers describe the use of various numerical schemes of finite element analysis [ 9 , 10 , 11 ], analytical models [ 12 ], and even statistical models [ 13 ] for modeling thermal and hydrodynamic processes. However, in most of them, the case of cladding the bead on a thick and wide substrate is considered.…”

Additive manufacturing of CuCr1Zr by development of a gas atomization and laser powder bed fusion routine

“…Furthermore, an understanding of the melt pool induced by the micro-welding processes and the melt pool dynamics (see [17,18]) allows the adjustment of the LPBF-built microstructures [19]. For the consideration of the melt pool and temperature fields during the LPBF process, analytical and numerical approaches are available (see for example [14,20,21]).…”

Effect of Process Parameters on Distortions Based on the Quantitative Model in the SLM Process

“…As the column gap increases, which decreases the stiffness of the support structures, the residual stress in each layer decreases. According to Equation (12), reducing the stiffness of the support structures is equivalent to reducing the value of E s A s , which increases the absolute value of the displacement. Then, the residual stress will be reduced correspondingly (refer to Equation ( 13)).…”

“…Kruth et al [9] first proposed the temperature gradient mechanism (TGM) to explore the residual stress mechanism in the powder bed fusion. The method is then widely used to qualitatively analyze transient distortions during the process [10][11][12]. However, it focuses on microtemperature distribution, which determines local residual stresses and distortions and cannot explain the distortion after the process or even after cut from the substrate.…”