6.1. Calibration results

Due to the uncertainty related to the depth, only the molten pool width is taken into account, while the former issue will be addressed in future work. At the beginning, a trial simulation is carried out to check how the temperature field is sensitive to the parameters change. A directly measured thermal field is not available for this work; hence, the comparison is done with respect to results retrieved from the literature [20]. The enthalpy is indeed modified to keep the thermal field under control. New values for enthalpy are shown in Table 6. Only the last enthalpy value is modified increasing the specific heat for vapor by a factor of 10. This helps to decrease the maximum nodal temperature.

The thermal behavior of molten pool is shown in Figure 20, which gives an idea about how elevated is the temperature of the zone irradiated by the laser.

This is due to the fact that the molten pool width is narrower than the experimental data and the conductivity needs to be increased. The calibration is, in a nutshell, an iterative algorithm that changes the conductivity with a trial factor as long as the numerical data well reproduce the experimental measurement. The algorithm involves MatLab® and ANSYS® as it is shown in the diagram presented in Figure 21.

The correction factor for conductivity is shown in Table 7. Notice that the correction is applied only to those values above the melting temperature.

Results coming from calibration are shown in Figure 22.


Table 6. Calibrated value for enthalpy.


Table 7. Calibrated value for thermal conductivity.

A very narrow temperature peak can be noticed in Figure 23. The highest peak is due to the heat source applied directly onto the probe. The other peaks are related to the reheating of the solidified area as the heat source is applied on the surrounding areas. In this example, the scan element is subject to remelting only once. The melting and cooling process occurs with very high gradients and this is the main source of the thermal residual stresses affecting the as-

Finite Element Thermal Analysis of Metal Parts Additively Manufactured via Selective Laser Melting

http://dx.doi.org/10.5772/intechopen.71876

153

Figure 23. Temperature development of a point at the surface of the powder bed.

A three-dimensional FE model is developed using ANSYS® to study the thermal behavior of the molten pool in building a single layer via SLM process. At the beginning, the scanning strategy adopted by the laser is simulated by a path simulator built using MatLab. Then, the FE analysis framework is extensively explained with special regard to thermal properties applied to the model. Dynamic mesh refinement is used to reduce the computational cost of the simulation. Special care is taken in devising a mapped mesh discretization scheme, ensuring that the traveling subdomain centered on the laser spot changes as less as possible the mesh of the remaining subdomain. Finally, a calibration procedure is applied to fit the numerical results with the experimental measurements. The simulation results agree reasonably well with experimental and literature results and give some insight into the mutual interaction among the process parameters. Useful indications can be gained to optimize the process parameters, to estimate the adhesion between the layers, and to identify the best building strategy. This model can be further developed by incorporating the nodal temperature field into a structural analysis for predicting the resulting stress and

built parts.

strain field.

8. Conclusions

Figure 22. Molten pool behavior with calibrated parameters.

### 7. Results

After parameters calibration, the simulation of a SLM process can be carried out. Because of the high number of laser spots, the simulation must be applied only to a small portion of the powder bed. Only one layer is considered and the adopted laser scanning strategy is the meander path. In order to gather information about the thermal field evolution into the bed powder, the time evolution of the temperature field is sampled on a spot selected as a temperature probe. The corresponding results are shown in Figure 23. The small window shows powder bed and meandering path. The black point along the meandering path represents the probe, which the temperature graph refers to.

Finite Element Thermal Analysis of Metal Parts Additively Manufactured via Selective Laser Melting http://dx.doi.org/10.5772/intechopen.71876 153

Figure 23. Temperature development of a point at the surface of the powder bed.

A very narrow temperature peak can be noticed in Figure 23. The highest peak is due to the heat source applied directly onto the probe. The other peaks are related to the reheating of the solidified area as the heat source is applied on the surrounding areas. In this example, the scan element is subject to remelting only once. The melting and cooling process occurs with very high gradients and this is the main source of the thermal residual stresses affecting the asbuilt parts.

### 8. Conclusions

7. Results

Thermal conductivity (W/mK)

Table 7. Calibrated value for thermal conductivity.

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

probe, which the temperature graph refers to.

Figure 22. Molten pool behavior with calibrated parameters.

After parameters calibration, the simulation of a SLM process can be carried out. Because of the high number of laser spots, the simulation must be applied only to a small portion of the powder bed. Only one layer is considered and the adopted laser scanning strategy is the meander path. In order to gather information about the thermal field evolution into the bed powder, the time evolution of the temperature field is sampled on a spot selected as a temperature probe. The corresponding results are shown in Figure 23. The small window shows powder bed and meandering path. The black point along the meandering path represents the

Temperature (C) Solid Powder 14.9567\*5 14.9567\*5 14.9567\*5 14.9567\*5 7.4784\*5 7.4784\*5 7.4784\*5 7.4784\*5

> A three-dimensional FE model is developed using ANSYS® to study the thermal behavior of the molten pool in building a single layer via SLM process. At the beginning, the scanning strategy adopted by the laser is simulated by a path simulator built using MatLab. Then, the FE analysis framework is extensively explained with special regard to thermal properties applied to the model. Dynamic mesh refinement is used to reduce the computational cost of the simulation. Special care is taken in devising a mapped mesh discretization scheme, ensuring that the traveling subdomain centered on the laser spot changes as less as possible the mesh of the remaining subdomain. Finally, a calibration procedure is applied to fit the numerical results with the experimental measurements. The simulation results agree reasonably well with experimental and literature results and give some insight into the mutual interaction among the process parameters. Useful indications can be gained to optimize the process parameters, to estimate the adhesion between the layers, and to identify the best building strategy. This model can be further developed by incorporating the nodal temperature field into a structural analysis for predicting the resulting stress and strain field.
