Nonlinear Heat Transfer Analysis of The Laser Deposition Process
ADINA is widely used for simulating different heat transfer problems in solids and structures. A variety of analysis options such as conduction, convection, radiation, phase change, temperature-dependent and time-dependent thermal properties and element birth/death are available. In addition to the heat transfer problems, many field problems (e.g., seepage, electric conduction, electrostatic field analysis) can also be modeled through the analogies between their governing differential equations and the heat transfer equation .
In this News, we present an example of heat transfer analysis where ADINA is used for modeling the spatial and temporal temperature distribution resulting from the laser deposition of tungsten carbide-cobalt (WC-Co) alloy. This process is an example of the Laser Engineered Net Shaping (LENS®) technique .
The LENS® process is used to fabricate metal and composite parts directly from CAD solid models using a powder injected into a molten pool created by a focused, high-powered laser beam. As the laser beam moves along the work piece consecutive layers are sequentially deposited, thereby producing a three-dimensional component (Figure 1). During the deposition, tungsten carbide (WC) does not melt while cobalt (Co) experiences phase change. This, under certain processing conditions, can result in an inhomogeneous microstructure, which is believed to be responsible for the unique mechanical properties of this alloy .
Figure 1 Schematic of the Laser Engineered Net Shaping (LENS®) process
The aim of the 3D finite element analysis of the laser deposition process is to obtain the temperature history of the entire sample, hence providing a better insight into the mechanism involved in the formation of these microstructures.
In the transient thermal analysis of the deposition process, both thermal conductivity and specific heat of the WC-Co are
The movie above shows the temperature distribution in the sample during the deposition process. Two laser passes form a new layer of WC-Co, which is laid upon the previous layer and the process is repeated. After the completion of each laser pass, there is a time delay before starting the new pass.
Figure 2 Temperature-dependent thermal properties of the WC-Co alloy
(SS304 is a stainless steel, shown here for comparison) 
While experimental methods such as in situ thermal imaging can also provide the temperature history during the laser deposition process, they can only give the temperature variation in the vicinity of the molten pool. In contrast, the 3D finite element analysis can provide the global picture for the entire sample.
Figure 3 depicts the spatial variation of temperature obtained using thermal imaging and finite element analysis for the third deposition layer at one point in time. As can be seen, the model predicts the temperature profile within the molten pool fairly well, but for the region farther away from the molten pool, the model predicts a more rapid decrease in temperature with distance compared to the experimental observation, which may be due to the simplifying assumptions mentioned earlier and the limited accuracy of the experimental results.
Figure 3 Comparison between experimental and finite element results for the temperature profiles in the opposite traverse direction in layer 3 
Figure 4 compares the temperature at the center of the molten pool and the half-length of the molten pool between the experiment and FEM. Results compare reasonably well.
Figure 4 Comparison between experimental and finite element results for half-length of the molten pool and temperature of the molten pool center 
This finite element study shows that, when one layer is being deposited, remelting occurs in the top portion of the previous layer, resulting in the coarsening of the WC particles while the bottom portion of the previous layer is only reheated, which has less effect on the grain growth. This results in microstructure with alternating sub-layers in the WC-Co alloy.
The advanced heat transfer capabilities of ADINA can be used for solving many industrial problems where moving heat sources, phase changes, time-dependent and/or temperature-dependent thermal properties are needed in the model. Of course, the stresses caused by thermal processes as required in many analyses (including laser welding, laser cladding, surface hardening, and many more) can also be calculated, and the analyses can also include fluid flows.
- ADINA Thermal Theory and Modeling Guide: ARD 09-8, May 2009
- Two articles on LENS®: Wikipedia; Sandia National Laboratories
- Y. Xiong, W.H. Hofmeister, Z. Cheng, J.E. Smugeresky, E.J. Lavernia, J.M. Schoenung, "In situ thermal imaging and three-dimensional finite element modeling of tungsten carbide-cobalt during laser deposition", Acta Materialia, Vol. 57, pp. 5419-5429, 2009
Laser deposition, temperature-dependent material property, element birth/death, moving heat source, phase change, Laser Engineered Net Shaping (LENS®), rapid prototyping, alloy
Courtesy of Y. Xiong, E.J. Lavernia, J.M. Schoenung (Univ. of California, Davis); W.H. Hofmeister (Univ. of Tennessee Space Institute); Z. Cheng (Earth Mechanics Inc.); and J.E. Smugeresky (Sandia National Laboratories)