6. Calibration

It has been proven that the computational performances can be strongly enhanced using a simplified numerical model. Nevertheless, results are greatly affected by the lack of accuracy due to several simplifications applied to the model. A calibration procedure is necessary to reduce this issue: the material properties and the boundary conditions can be modified trying to fit numerical results with experimental data. The comparison is based on the molten pool dimension measured from a solidified seam. Moreover, since only a single seam is needed for the calibration, the geometrical domain can be halved along the symmetry plane, saving computational cost. The main reason for the calibration is that ANSYS® does not consider elements which behave as liquid elements. The only way to simulate melting and cooling is to change the material properties and in particular thermal conduction and enthalpy, even though conduction does not apply for liquids.

As a consequence, the thermal properties are not well-defined for temperatures above the melting point. In this situation, a convective parameter should be used. This consideration permits the change of the parameters as needed, trying to simulate the convective behavior with a fictitious conduction parameter. The calibration procedure aims to adjust the thermal properties (only above the melting point) whereby fitting the molten pool size to the experimental data. The parameters adjusted by the calibration are enthalpy and thermal conductivity: the enthalpy is modified to control the temperature field while the conductivity is mainly responsible for the size of the molten pool. Specifically, metallographic inspections, as shown in Figure 19, are used to estimate width and depth of the molten pool.

Figure 18 shows a single molten seam obtained overlapping multiple layers. The seam was melted using the process parameters listed in Table 1. It has been cut and analyzed in order to gather information about the width and depth of the molten pool. Measured values are:

• Width = 183 38 μm

to ANSYS®. At this point, the temperature field of the previous mesh can be applied to the new

• Uncommon new nodes will have an interpolated temperature from the old ones due to

As a result, the simulation time dropped from 15 minutes/spot to 71 seconds/spot reducing the calculation time by 92%. As already mentioned before, the main parameter, which greatly affects the simulation time, is the number of substeps. The optimal value thereof was found through a convergence analysis based on the plot shown in Figure 17. It can be noted that an increment in the time step size Δt has a much more pronounced effect on the solution time rather than on maximum nodal temperature (a measure of the solution accuracy). A reasonable trade-off between accuracy and simulation time is a time step size of 3 μs, allowing for 1% error in maximum temperature estimation and a computation time reduction of 80%. It is worth noting that the overall time reduction, due to mesh refinement and time step size reduction, is equal to 98.5%.

The uniform mesh model and the one implementing DMR was tested applying a laser beam on a straight line and the results are shown in Figure 21. It can be seen that the temperature scale has only some little negligible variations. The DMR model well represents the physical phe-

It has been proven that the computational performances can be strongly enhanced using a simplified numerical model. Nevertheless, results are greatly affected by the lack of accuracy due to several simplifications applied to the model. A calibration procedure is necessary to reduce this issue: the material properties and the boundary conditions can be modified trying to fit numerical results with experimental data. The comparison is based on the molten pool dimension measured from a solidified seam. Moreover, since only a single seam is needed for the calibration, the geometrical domain can be halved along the symmetry plane, saving computational cost. The main reason for the calibration is that ANSYS® does not consider elements which behave as liquid elements. The only way to simulate melting and cooling is to change the material properties and in particular thermal conduction and enthalpy, even

As a consequence, the thermal properties are not well-defined for temperatures above the melting point. In this situation, a convective parameter should be used. This consideration permits the change of the parameters as needed, trying to simulate the convective behavior with a fictitious conduction parameter. The calibration procedure aims to adjust the thermal properties (only above the melting point) whereby fitting the molten pool size to the experimental data. The parameters adjusted by the calibration are enthalpy and thermal conductivity: the enthalpy is modified to control the temperature field while the conductivity is mainly responsible for the size of the molten pool. Specifically, metallographic inspections, as shown

in Figure 19, are used to estimate width and depth of the molten pool.

• Common new nodes will have the same temperature as the old ones

nomena and is a trade-off between result accuracy and computation time.

mesh as an initial condition in the following way:

150 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

the \*MOPER APDL command.

though conduction does not apply for liquids.

6. Calibration

• Depth = 107 38 μm

The deviation related to measurements is mainly related to the narrow geometry and tiny dimensions of the object. Its width is only 4-5 times larger than the dimensions of the metal powder particles; therefore, the profile is not regular. It represents the minimum thickness that can be obtained with a single scan of the laser beam on the powder bed. Notice from Figure 19 that the molten seam undergoes the re-melting process with the application of successive layers and therefore the depth is not a reliable parameter. Nevertheless, the object is helpful in order to evaluate the real width of the molten pool.
