PSI - Issue 8

416 P. Conti et al. / Procedia Structural Integrity 8 (2018) 410–421 Author name / Structural Integrity Procedia 00 (2017) 000–000 The boundary conditions simulate the laser heating without any mechanical load. The room temperature is set at 353 °K and the bottom face of the baseplate has all the nodes with the same constant temperature (353 °K). At each step, a subroutine defines the position of the laser beam (depending on the scan speed) and calculates the heat flux to be assigned to the element nodes belonging to the beam area in accordance with Eq. (2). Each step consists in an incremental analysis divided in sub steps of nearly 0.001 sec. At each sub step the thermomechanical characteristics are updated according to the new temperature. When the melting temperature is reached the thermal characteristics switch from “powder” to “bulk”. When the temperature lowers again below the melting point, the Young’s modulus switches from “liquid” to “solid”. Tab. I Physical characteristics of the FE model

Value

Units

Geometrical characteristic

Scanned island size Layer thickness Entire model size Baseplate thickness

1 × 1

[mm] [μm] [mm] [mm] [µm] [μm]

20

5 × 5

10

Laser beam diameter (R o ) 50

Element side

25 × 25

Porosity of the powder Absorbance of the layer

0.2 0.3

N° of elements per scanned island side

40

3. Numerical testing program Two sets of FE analysis were performed. The first one to investigate the robustness of the SLM model with respect to small changes in the material characteristics because many of them are evaluated with simplified extrapolation from literature data. The second one to compare different sets of three technological parameters (laser power, overlap and beam speed) in order to evaluate if a FE approach can help in optimizing the SLM process. Both the investigation rely on a DOE approach. 3.1. Robustness evaluation The parameter to investigate are thermal conductivity, specific heat capacity and Young’s modulus. The diagram of fig.2, 4 and 5 were modified and the values were first magnified by a factor 1.1 and then reduced by a factor 0.9 corresponding to a high level and a low level of the characteristics. A set of 8 FE analyses was carried on according to the plan reported in the left side of Tab. II The results of a specific test (test no. 1) with ܵ ݒ = 0.25, ܸ = 25 mm/sec and ܳ = 100 W is displayed in fig.9 and 10. The figures represent the temperature pattern (fig. 9-a) and the residual stresses at the end of the last iteration (fig.9-b). As one can see in fig.9-a, the red spot at the top right of the scanning island is at very high temperature and the material is melted. Moving away from the beam center the material is cooling down. The temperature pattern is not symmetrical because the laser beam was moving from left to right. Fig.9-b display the stress field. Again, the top right corner is free of stress because the material is still liquid. Away from the melted pool, the residual stresses are high because the baseplate prevents the solidified layer from shrinking. We must point out that the stress values are not really significant as the model did not consider the plasticization of the material; the residual deformation should be more significant; the stress values can be used only for comparison purpose between different analyses. Fig.10 displays a detail of fig.9. In this figure, it appears that some cell at the border of the island are not melted and some other, outside, are melted. One must however keep in mind that the islands grow one next to another and these defects will disappear when the surrounding cells will melt at their turn.