Figure 1.
Thermo-fluid flow model.
Figure 1.
Thermo-fluid flow model.
Figure 2.
Grain structure evolution model: (a) a regular network of cellular automata model, where is the cell size, (b) a cross-section view of the network, and (c) the information carried by each cell during the simulation.
Figure 2.
Grain structure evolution model: (a) a regular network of cellular automata model, where is the cell size, (b) a cross-section view of the network, and (c) the information carried by each cell during the simulation.
Figure 3.
Regular octahedral envelope.
Figure 3.
Regular octahedral envelope.
Figure 4.
Schematic illustration of the one-way coupling method, taking a 2D case as an example, where the temperature of the finer CA cell is interpolated from the coarser FVM cell.
Figure 4.
Schematic illustration of the one-way coupling method, taking a 2D case as an example, where the temperature of the finer CA cell is interpolated from the coarser FVM cell.
Figure 5.
Microstructure development in AM 316L stainless steel A using bi-directional scan without rotation: (
a) The continuous growth of grains in a slender domain (highlighted by a black row) along the centreline across melt pools, (
b) cells in the region labeled (3) epitaxially grew from ones in the region (2) which did grow from existing cells in the region (1), (
c) the corresponding inverse pole figure of grains in (
b) indicating that the cells in regions labeled (1), (2), and (3) belong to the same grain due to epitaxial growth, but have 90° changes in the growth direction, (
d) melt pools on the top layer of a 316L build with measured dimensions are 90 ± 20
m in depth and 145 ± 30
m in width. The dashed lines in (
b,
c) denote the melt pool boundary. (This figure is reproduced from [
6]).
Figure 5.
Microstructure development in AM 316L stainless steel A using bi-directional scan without rotation: (
a) The continuous growth of grains in a slender domain (highlighted by a black row) along the centreline across melt pools, (
b) cells in the region labeled (3) epitaxially grew from ones in the region (2) which did grow from existing cells in the region (1), (
c) the corresponding inverse pole figure of grains in (
b) indicating that the cells in regions labeled (1), (2), and (3) belong to the same grain due to epitaxial growth, but have 90° changes in the growth direction, (
d) melt pools on the top layer of a 316L build with measured dimensions are 90 ± 20
m in depth and 145 ± 30
m in width. The dashed lines in (
b,
c) denote the melt pool boundary. (This figure is reproduced from [
6]).
Figure 6.
Longitudinal cross-section ( plane) view of a single track simulation result, where the white curves represent the solidus and liquidus isotherms, and the arrows represent the flow field within the melt pool.
Figure 6.
Longitudinal cross-section ( plane) view of a single track simulation result, where the white curves represent the solidus and liquidus isotherms, and the arrows represent the flow field within the melt pool.
Figure 7.
Transverse cross-section ( plane) view of the single laser track. The left part is from simulation result and the right part from experiment data.
Figure 7.
Transverse cross-section ( plane) view of the single laser track. The left part is from simulation result and the right part from experiment data.
Figure 8.
Microstructure simulation results for Case P180V63: (a) 3D view, (b) pole figures (PF) of the solidification grain structure within the fusion zone.
Figure 8.
Microstructure simulation results for Case P180V63: (a) 3D view, (b) pole figures (PF) of the solidification grain structure within the fusion zone.
Figure 9.
Several 2D views of the single-track simulation results: (a) top view of CA result, (b) transverse cross-section map of CA, and (c) longitudinal cross-section map of CA result, where white dotted lines represent the boundary of the melting zone and black dotted lines represent the locations of the cross-section.
Figure 9.
Several 2D views of the single-track simulation results: (a) top view of CA result, (b) transverse cross-section map of CA, and (c) longitudinal cross-section map of CA result, where white dotted lines represent the boundary of the melting zone and black dotted lines represent the locations of the cross-section.
Figure 10.
Solidification parameters of the longitudinal section of the melt pool center: (a) temperature gradient magnitude G, (b) solidification rate R, (c) morphology factor , and (d) cooling rate , for cases with laser power varied within the range [140 W, 200 W], and constant laser scan speed of 0.63 m/s. The abscissa represents the distance from the top surface of the melt pool.
Figure 10.
Solidification parameters of the longitudinal section of the melt pool center: (a) temperature gradient magnitude G, (b) solidification rate R, (c) morphology factor , and (d) cooling rate , for cases with laser power varied within the range [140 W, 200 W], and constant laser scan speed of 0.63 m/s. The abscissa represents the distance from the top surface of the melt pool.
Figure 11.
The grain structure cross sections: (a–d) transverse cross-section map, (e–h) longitudinal cross-section map of the results for cases with laser power varied within the range of [140 W, 200 W], and the constant laser scan speed of 0.63 m/s.
Figure 11.
The grain structure cross sections: (a–d) transverse cross-section map, (e–h) longitudinal cross-section map of the results for cases with laser power varied within the range of [140 W, 200 W], and the constant laser scan speed of 0.63 m/s.
Figure 12.
Grain size distributions for cases with laser power varied within the range of [140 W, 200 W] and the constant laser scan speed of 0.63 m/s.
Figure 12.
Grain size distributions for cases with laser power varied within the range of [140 W, 200 W] and the constant laser scan speed of 0.63 m/s.
Figure 13.
Solidification parameters of the longitudinal section of the melt pool center: (a) temperature gradient magnitude G, (b) solidification rate R, (c) morphology factor , and (d) cooling rate , for cases with laser scan speed vary within the range of [0.53 m/s, 0.83 m/s], and the constant laser power of 180 W. The abscissa represents the distance from the top surface of the melt pool.
Figure 13.
Solidification parameters of the longitudinal section of the melt pool center: (a) temperature gradient magnitude G, (b) solidification rate R, (c) morphology factor , and (d) cooling rate , for cases with laser scan speed vary within the range of [0.53 m/s, 0.83 m/s], and the constant laser power of 180 W. The abscissa represents the distance from the top surface of the melt pool.
Figure 14.
The grain structure cross sections: (a–d) transverse cross-section map, (e–h) longitudinal cross-section map of the results for cases with laser power varied within the range [0.53 m/s, 0.83 m/s], and the constant laser power of 180 W.
Figure 14.
The grain structure cross sections: (a–d) transverse cross-section map, (e–h) longitudinal cross-section map of the results for cases with laser power varied within the range [0.53 m/s, 0.83 m/s], and the constant laser power of 180 W.
Figure 15.
Grain size distributions for the cases with laser scan speed vary within the range of [0.53 m/s, 0.83 m/s] and the constant laser power of 180 W.
Figure 15.
Grain size distributions for the cases with laser scan speed vary within the range of [0.53 m/s, 0.83 m/s] and the constant laser power of 180 W.
Figure 16.
Schematics of layer-wise scan strategy for (a) Strategy I: unidirectional scanning without layer-wise rotation, (b) Strategy II: unidirectional scanning with layer-wise rotation of 180°, and (c) Strategy III: unidirectional scanning with layer-wise rotation of 90°.
Figure 16.
Schematics of layer-wise scan strategy for (a) Strategy I: unidirectional scanning without layer-wise rotation, (b) Strategy II: unidirectional scanning with layer-wise rotation of 180°, and (c) Strategy III: unidirectional scanning with layer-wise rotation of 90°.
Figure 17.
Microstructure simulation results for three-layer and three-track case: (a) 3D view of the result, (b) top view, (c) transverse cross-section map, and (d) longitudinal cross-section map, where white dotted lines represent the boundary of the fusion zone, and black dotted lines represent the locations of the cross-section.
Figure 17.
Microstructure simulation results for three-layer and three-track case: (a) 3D view of the result, (b) top view, (c) transverse cross-section map, and (d) longitudinal cross-section map, where white dotted lines represent the boundary of the fusion zone, and black dotted lines represent the locations of the cross-section.
Figure 18.
Pole figures (PF) of solidification grain structure within the fusion zone of the simulation results of first-layer, first two layers, and three-layer microstructure.
Figure 18.
Pole figures (PF) of solidification grain structure within the fusion zone of the simulation results of first-layer, first two layers, and three-layer microstructure.
Figure 19.
The grain size distribution of the simulation results in the first layer, the first two layers, and the three-layer microstructure.
Figure 19.
The grain size distribution of the simulation results in the first layer, the first two layers, and the three-layer microstructure.
Figure 20.
Cross section of simulation results of microstructure evolution under different scanning strategies, where white dotted lines represent the boundary of the fusion zone.
Figure 20.
Cross section of simulation results of microstructure evolution under different scanning strategies, where white dotted lines represent the boundary of the fusion zone.
Figure 21.
Grain size distribution of the simulation results in the first layer, first two layers, and three-layer microstructure.
Figure 21.
Grain size distribution of the simulation results in the first layer, first two layers, and three-layer microstructure.
Figure 22.
Pole figures (PF) of solidification grain structure within the fusion zone of Strategy I, Strategy II, and Strategy III simulation results.
Figure 22.
Pole figures (PF) of solidification grain structure within the fusion zone of Strategy I, Strategy II, and Strategy III simulation results.
Figure 23.
Keyhole-mode melting simulation results: (a) deep and narrow melt pool, (b) fusion zone with pore defects, where the black dashed line outlines the region for CA simulation, (c) 3D view of the microstructure simulation result, (d) pole figures of solidification grain structure within the fusion zone.
Figure 23.
Keyhole-mode melting simulation results: (a) deep and narrow melt pool, (b) fusion zone with pore defects, where the black dashed line outlines the region for CA simulation, (c) 3D view of the microstructure simulation result, (d) pole figures of solidification grain structure within the fusion zone.
Figure 24.
Two-dimensional views of simulation results under the keyhole mode melting: (a) top view, (b) transverse cross-section map, and (c) longitudinal cross-section map, where white dotted lines represent the boundary of the melting zone and black dotted lines represent the location of the cross-section.
Figure 24.
Two-dimensional views of simulation results under the keyhole mode melting: (a) top view, (b) transverse cross-section map, and (c) longitudinal cross-section map, where white dotted lines represent the boundary of the melting zone and black dotted lines represent the location of the cross-section.
Figure 25.
Microstructure near the pores: (a) coarse grains above pores a, (b) longitudinal cross-section map of the grain structure, where the black dotted lines indicate the location of the transverse cross-section maps for (c) with the presence of Pore a (d) without the presence of Pore and (e) with the presence of Pore b, where white dotted lines represent the boundary of the melting zone and yellow arrow marks several grains blocked by Pore b.
Figure 25.
Microstructure near the pores: (a) coarse grains above pores a, (b) longitudinal cross-section map of the grain structure, where the black dotted lines indicate the location of the transverse cross-section maps for (c) with the presence of Pore a (d) without the presence of Pore and (e) with the presence of Pore b, where white dotted lines represent the boundary of the melting zone and yellow arrow marks several grains blocked by Pore b.
Figure 26.
The cooling rate (with the order of ) near the mushy zone around pore a: (a) results at t = 9.3 × 10 s, (b) results at t = 9.5 × 10 s (c) results at t = 9.7 × 10 s, where the two white curves represent the solidus temperature and liquidus temperature isotherms. The cooling rate of the cells above the pore outlined by the blue curves is smaller than that of the neighboring cells in the mushy zone.
Figure 26.
The cooling rate (with the order of ) near the mushy zone around pore a: (a) results at t = 9.3 × 10 s, (b) results at t = 9.5 × 10 s (c) results at t = 9.7 × 10 s, where the two white curves represent the solidus temperature and liquidus temperature isotherms. The cooling rate of the cells above the pore outlined by the blue curves is smaller than that of the neighboring cells in the mushy zone.
Table 1.
Physical properties of 316L stainless steel [
6,
42,
43,
44].
Table 1.
Physical properties of 316L stainless steel [
6,
42,
43,
44].
Material Properties | Value |
---|
Density, | 7650 kg/m |
Solidus temperature, | 1598 K |
Liquidus temperature, | 1715 K |
Evaporation temperature, | 3090 K |
Latent heat of fusion, | 2.7 × 10 J/kg |
Latent heat of vaporization, | 7.45 × 10 J/kg |
Specific heat, | 770.2 J/(kg·K) |
Viscosity, | 0.00345 Pa·s |
Surface tension coefficient, | 1.6 N/m |
Temperature coefficient of surface tension, | −0.00026 N/(m·K) |
Molecular mass, m | 9.3 × 10 kg |
Boltzmann constant, | 1.3806505 × 10 J/K |
Convective heat transfer coefficient, | 5.7 W/(m K) |
Stefan–Boltzmann constant, | 5.67 × 10 W/(m K) |
Emissivity, | 0.26 |
Laser absorption coefficient, | 0.4 |
Table 2.
Parameters for thermo-fluid flow model.
Table 2.
Parameters for thermo-fluid flow model.
Parameter | Value |
---|
Atmospheric pressure, | 1.013 × 10 Pa |
Ambient temperature, | 293 K |
Laser beam radius, r | 35 m [6] |
Cell size | 4 m |
Table 3.
Nucleation parameters for the CA model [
45].
Table 3.
Nucleation parameters for the CA model [
45].
Parameter | Value |
---|
Site density, | 1 × 10 mm |
Mean undercooling, | 2 K |
Standard deviation of undercooling | 0.5 K |
Cell size | 1 m |
Growth kinetics parameter, | 2.49 × 10 m/(s·K) |
Growth kinetics parameter, | 6.2 × 10 m/(s·K) |
Table 4.
Particle size distribution of 316L stainless steel powder [
6].
Table 4.
Particle size distribution of 316L stainless steel powder [
6].
Diameter (m) | 15 | 18 | 21 | 24 | 27 | 30 | 33 |
Proportion (%) | 15 | 15 | 20 | 18 | 15 | 11 | 6 |
Table 5.
Process parameters of the single-track cases (Note).
Table 5.
Process parameters of the single-track cases (Note).
Case | Laser Power (W) | Scan Speed (m/s) | Layer Thickness (m) |
---|
P140V63 | 140 | 0.63 | 50 |
P160V63 | 160 | 0.63 | 50 |
P180V63 | 180 | 0.63 | 50 |
P200V63 | 200 | 0.63 | 50 |
P180V53 | 180 | 0.53 | 50 |
P180V73 | 180 | 0.73 | 50 |
P180V83 | 180 | 0.83 | 50 |
Table 6.
Comparison of melt pool width and depth between experiment data and simulation results for Case P180V63.
Table 6.
Comparison of melt pool width and depth between experiment data and simulation results for Case P180V63.
| Width | Depth |
---|
Experiment data | 90 m | 145 m |
Simulation result | 87 m | 148 m |
Relative error | 3.3% | 2.1% |