Direct laser deposition metal 3D printing at different temperatures of the printer’s chamber: computer simulation

Metal 3D printing technology is a promising manufacturing method. The quality of the printed product can pass for mechanical application, if the anisotropy of the microstructure, imperfections, deformation, and residual stress of the printed sample could be lower than the appropriate level or if they are fully illuminated. Thermal stress is one of the significant reasons for deformation in the 3D printed samples. Thermal stresses are the direct consequence of the local temperature gradient. In this research, the effect of the temperature printer’s chamber (from room temperature to 900 C) was studied on thermal stress and subsequent total deformation in the printed sample. The printed sample is a six-layers-printed walk, which could be considered as a building block of other complex shapes and give us inside about deformation. The computational results show a meaningful reduction in thermal stress and deformation at the higher temperature of the printer’s chamber . The lower final deformation of the printed sample is an important subject, especially for samples with complex shapes.

results could be used for the optimization of the manufacturing process. There are some researches that coupled macroscale thermal simulation coupled with mesoscale microstructural evaluation [18][19][20][21]. There are several published kinds of research on mesoscale microstructural simulations for powder bedbased additive manufacturing in the first layer of the print [22][23][24][25][26][27]. In addition, there are researches on addressing the grain structure of the additively manufactured materials, especially for powder bed fusion [27][28][29][30]. There are some experimental and computational investigations and papers discussed on thermal stress and deformation in additively manufactured metallic alloys [1,[31][32][33]. Thermal stress and deformation of additively manufactured are about several hundred MPa [34,35] and several micrometers for small samples [36][37][38][39], respectively. This level of deformation is high enough, especially for complex shapes to reject the printed sample for application. So, we need to investigate some methods to optimize and reduce the level of thermal stress and deformation.
Although parameters like scan speed, laser power, and metal powder feeding rate in the DLD method could vary the level of thermal stress and subsequent deformation, the temperature of the printer's chamber may have a considerable effect on thermal stress, which investigated in this research. This research computationally presented the effect of different temperatures of the printer's chamber on thermal stress and local deformation of the printed sample by the direct laser deposition (DLD) method.

-Computational method
In this research, AM Comp Tech computational package for process modeling metal 3D printing was used (http://manufacture.technology/). The computational outputs of this code are 3D thermal and mechanical (von Mises stress/deformation) history during metal 3D printing by the DLD printing method. The software is solving conservative equations (conservation of energy and momentum) by finite difference numerical methods.  o Thermal analysis Equation 1 was used for thermal analysis in which is density, is the specific heat, is temperature, is time, is the thermal conductivity, and is the source of heat. ℎ represents both the thermal convection and radiation coefficients. The value of was considered to be 0.9, as recommended for hot-rolled steels [40].
The energy balance in the equation (2) was applied as a thermal boundary condition. This equation has the physical meaning of thermal convection and radiation. In this simulation, the thermal conductivity and specific heat capacity are considered temperature-dependent (Fig 2). o Mechanical analysis The equations 3 to 7 were used to calculate the displacement of each position as a result of temperature (thermomechanical simulation). Then, the results were used to calculate stress and strain. The used equations are as follows which is the strain, is stress, is the module of elasticity, is thermal expansion coefficient, is the Poisson ratio, are Lame coefficients, , are displacement in , are directions, respectively:   o Powder feeding In metal 3D printing and DLD method, metal powders are blown to the laser to be melted by laser and thus, adding a new layer during metal 3D printing. A method was used to consider this subject in the simulation. New nodes (for newly melted powders which are added from the nozzle) will be added to the defined position (exactly under the nozzle) on the previously printed part of the model during each time step. This is the used method to update the model to consider newly melted metal powders through the nozzle (fig 4). In this research, we considered a constant temperature for melted powders as the initial condition rather than using laser energy and conventional Gaussian surface heat source, top-hat distribution, or Goldak's double ellipsoid heat source [41] as a boundary condition. The higher temperature of melted powders means higher laser power. -

Results and discussions
In this research, a wall is printed to check the thermomechanical responses if the sample prints at different temperatures of the printer's chamber. This wall could be considered as a building block for any other complex shapes. The printed wall has 2.5 mm width, 20 mm length, and 6 mm height. The beam (travel) speed and powder feeding rate are set to 2 mm.s -1 , 100 mg.s -1 , respectively. Each printed pass has a 1 mm height with these travel speed and powder feeding rates. So, this wall must be printed with six passes.  Thermal stress and deformation are the direct consequence of the thermal history of the printed sample, and they would have a lower value if the local temperature gradient is lower. The local temperature gradient is lower in the samples, which are printed at the higher chamber's temperature.
Hence, it could be expected to lower thermal stress if the sample is printed at a higher temperature. This subject is shown in fig 7, and the von Mises stress shows a considerable reduction in stress level by 3D printing at a higher temperature of the printer's chamber. Although the lower thermal stress may cause lower deformation, the modulus of elasticity has a much lower value at high temperatures. It means that the printed sample is softer at a higher temperature. So, the total deformation must be checked to see if it would be reduced by increasing the temperature of the printer's chamber or not.
Simulation results show a meaningful reduction in the total deformation if the sample is printed at a higher temperature. This subject has been shown in fig 8. The total deformation is the vector sum of all directional displacements of the systems. The computational results show that the total deformation is in the range of micrometers.   So far, the thermal stress and total deformation have been checked at some key points of the printed sample to see how the values changes by the time.
The thermal stress and deformation levels in the printed sample could be shown for some cross-sections. This subject was checked at three cross-sections exactly at the end of the printing. The temperature, thermal stress, and total deformation profiles at the end of the printing were shown in fig 9, fig 10, and fig  11, respectively. The simulation results confirm a lower level of thermal stress and total deformation if the sample is printed at a higher temperature.
As it is obvious in fig 9, the temperature gradient through the printed sample is lower at a higher temperature. A higher temperature gradient means higher thermal stress and deformation if the modulus of elasticity remains constant. So, the combination of the value of elastic modulus and local temperature gradient shapes the level of thermal stress and the total deformation. For example, if the sample prints at 27 C (chamber's temperature), the temperature gradient is lower for the cross-sections closer to the substrate . Fig 9 b shows that the temperature gradient is lower for at 1.5 mm cross-section in comparison with 3.5 mm and then 5.5 mm, which 5.5 mm has a higher temperature gradient, which shows an increase in the thermal stress in fig 10. If it is technically possible to print at a higher temperature, the total deformation level is considerably lower versus printing at room temperature. If the sample experiences higher temperatures especially higher than austenitization temperature of steel alloys, the final microstructure would be almost uniform and possibly no columnar grain structure. -

Conclusions
Metal 3D printing is an exciting manufacturing method but needs more optimizations of the printing process to have a reliable product directly for structural applications. This research tried to address the effect of the temperature of the printer's chamber on the evolution of the thermal stress and total deformation in the 3D printed sample by the DLD method. The simulation was done at constant print speed, laser power, and rate of metal powders injection but the different temperature of the printer's chamber. Simulation results show that the temperature of the printer's chamber influences the thermomechanical response. The thermal stress in the 3D printed sample by the DLD method is reducing by increasing the temperature of the printer's chamber. The total deformation in the 3D printed sample by the DLD method is reducing by increasing the temperature of the printer's chamber.
If it is technically possible to print at a higher temperature, the total deformation level is considerably lower versus printing at room temperature.