Prediction of Residual Deformation and Stress of Laser Powder Bed Fusion Manufactured Ti-6Al-4V Lattice Structures Based on Inherent Strain Method

Gan, Mingju; Wu, Qi; Long, Lianchun

doi:10.1590/1980-5373-MR-2022-0516

Mingju Gan

Beijing University of Technology, Faculty of Materials and Manufacturing, 100124, Beijing, China.

Qi Wu ^**e-mail: qiwu@bjut.edu.cn

Beijing University of Technology, Faculty of Materials and Manufacturing, 100124, Beijing, China.

https://orcid.org/0000-0002-1167-6247

Lianchun Long

Beijing University of Technology, Faculty of Materials and Manufacturing, 100124, Beijing, China.

*e-mail: qiwu@bjut.edu.cn

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Figure 1
Schematic diagram of the simulation process.

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Figure 2
Thermal physical parameters of Ti-6Al-4V³¹31 Yin J, Peng G, Chen C, Yang J, Zhu H, Ke L et al. Thermal behavior and grain growth orientation during selective laser melting of Ti-6Al-4V alloy. J Mater Process Technol. 2018;260:57-65.^,³²32 Mills KC. Recommended values of thermophysical properties for selected commercial alloys. Cambridge: Woodhead Publishing; 2002. Ti: Ti-6 Al-4 V (IMI 318); p. 211-7..

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Figure 3
Calibration model of melt pool size.

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Figure 4
Thermo-mechanical Coupling Model of LPBF Double Layer Deposition (a) scanning method (b) meshing finite element model.

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Figure 5
(a) Schematic diagram of the dimensions of a lattice cell (b) Schematic diagram of the dimensions of multilayer BCC lattice structure.

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Figure 2
Thermal physical parameters of Ti-6Al-4V³¹31 Yin J, Peng G, Chen C, Yang J, Zhu H, Ke L et al. Thermal behavior and grain growth orientation during selective laser melting of Ti-6Al-4V alloy. J Mater Process Technol. 2018;260:57-65.^,³²32 Mills KC. Recommended values of thermophysical properties for selected commercial alloys. Cambridge: Woodhead Publishing; 2002. Ti: Ti-6 Al-4 V (IMI 318); p. 211-7..

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Figure 3
Calibration model of melt pool size.

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Figure 4
Thermo-mechanical Coupling Model of LPBF Double Layer Deposition (a) scanning method (b) meshing finite element model.

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Figure 5
(a) Schematic diagram of the dimensions of a lattice cell (b) Schematic diagram of the dimensions of multilayer BCC lattice structure.

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Figure 6
Comparison of simulated and experimental melt pools²⁶26 Liang X, Dong W, Hinnebusch S, Chen Q, Tran HT, Lemon J et al. Inherent strain homogenization for fast residual deformation simulation of thin-walled lattice support structures built by laser powder bed fusion additive manufacturing. Addit Manuf. 2020;32:101091..

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Figure 7
(a) Comparison of center line node deformation (b) Comparison of edge line node deformation.

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Figure 8
(a) Residual stress of LPBF double-layer deposition model under two methods (b) Residual stress at different heights along the Z direction.

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Figure 9
Residual deformation and stress results of LPBF manufacturing lattice structures (a) Residual deformation of multilayer BCC lattice structure (b) Residual deformation of BCC lattice cell (c) Residual stress of multilayer BCC lattice structure (d) Residual stress of BCC lattice cell.

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Figure 10
(a) Variation of maximum residual deformation with rod inclination (b) Variation of maximum residual deformation with rod diameter (c) Variation of maximum residual deformation with rod length (d) Variation of maximum residual stress with rod inclination (e)Variation of maximum residual stress with rod diameter (f) Variation of maximum residual stress with rod length.

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Table 1
Parameters of the LPBF process.

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Table 2
Mechanical properties of Ti-6Al-4V³³33 Rangaswamy P, Prime MB, Daymond M, Bourke MAM, Clausen B, Choo H et al. Comparison of residual strains measured by X-ray and neutron diffraction in a titanium (Ti-6Al-4V) matrix composite. Mater Sci Eng A. 1999;259:209-19.^,³⁴34 Vanderhasten M, Rabet L, Verlinden B. Ti-6Al-4V: deformation map and modelisation of tensile behaviour. Mater Des. 2008;29:1090-8..

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Table 3
Size constraints of lattice cell.

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Table 4
Anisotropic thermal conductivity enhancement factor.

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Table 5
Simulation parameter settings.

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Laser power(W)	Scan speed(mm/s)	Scan spacing(mm)	The thickness of powder spread(mm)	Laser beam diameter(mm)	Initial temperature(K)
200	800	0.12	0.04	0.15	298.15

Parameters	Value
Temperature (K)	300	500	700	900	1100	1300
Elastic modulus (GPa)	122.7	110.5	97.4	60.8	24.3	0.2
Plastic tangent modulus (GPa)	2.7	2.6	2.0	0.4	0.02	0.01
Thermal expansion coefficient (10^-6/K)	8.9	9.9	10.8	11.4	11.6	11.9
Yield strength (MPa)	995.5	713.6	538.6	348.1	32.5	6.2
Poisson ratio	0.33	0.35	0.36	0.37	0.39	0.44

Molding angle θ/°	Without support angle θ/°	Rod diameter d/mm	Rod length l/mm	Aspect Ratio l/d
≥20	≥43	≥0.3	≤5	4.39~22.9

Model No.	*w_x*	*w_y*	*w_z*	Melt pool width/μm	Melt pool depth/μm	Width error/%	Depth error/%	Average error/%
1	1	1	1	179.24	49.98	34.3	18.8	26.6
2	1	1	2	163.22	61.68	22.3	0.14	11.2
3	1	1	3	152.42	65.69	14.2	6.6	10.4
4	2	2	6	143.11	68.02	7.3	10.4	8.9
5	3	3	9	132.98	63.36	0.3	2.9	1.6

No.	Rod inclination θ/°	Rod diameter d/mm	Rod length l/mm
1	15~75(Δθ=5)	0.5	4
2	45°	0.2~1.1(Δd=0.1)	4
3	45°	0.5	2~11(Δl=1)

[1] *e-mail: qiwu@bjut.edu.cn

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Prediction of Residual Deformation and Stress of Laser Powder Bed Fusion Manufactured Ti-6Al-4V Lattice Structures Based on Inherent Strain Method

Abstract