Research Papers

Distortions and Residual Stresses at Layer-by-Layer Additive Manufacturing by Fusion

[+] Author and Article Information
V. A. Safronov, R. S. Khmyrov, D. V. Kotoban

Moscow State University of
Technology “STANKIN,”
Vadkovsky per. 3a,
Moscow 127055, Russia

A. V. Gusarov

Moscow State University of
Technology “STANKIN,”
Vadkovsky per. 3a,
Moscow 127055, Russia
e-mail: av.goussarov@gmail.com

Manuscript received October 13, 2015; final manuscript received August 17, 2016; published online October 7, 2016. Assoc. Editor: Z. J. Pei.

J. Manuf. Sci. Eng 139(3), 031017 (Oct 07, 2016) (6 pages) Paper No: MANU-15-1513; doi: 10.1115/1.4034714 History: Received October 13, 2015; Revised August 17, 2016

Thermal shrinkage of the added material can distort the manufactured part and generate residual stresses. Experiments are carried out on growing the beams of rectangular cross section. The beams bend with formation of a concave top surface. The distortion is characterized by the curvature radius. The curvature radius significantly increases with the beam height, however, its variation with the layer thickness is within the experimental uncertainty. The proposed mathematical model assumes sequential addition of thermally expanded elastic layers. It explains the experiments and indicates the existence of finite limits for the stress and the deformation fields and the curvature radius at small layer thickness. The proposed model can be applied to predict residual stresses and deformations arising in complicated parts.

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Fig. 2

Measured distortion of the beam after detachment from the substrate: (a) top surface and (b) longitudinal profile of the vertical displacement along five parallel lines (points) and the parabolic fit (curve)

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Fig. 1

Bridge-like sample for studying the residual distortion: (a) as fabricated and (b) detached from the substrate

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Fig. 3

Single layer of length l loaded with force F

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Fig. 4

The first and the second layers at the instant of application of the second layer (a) and after its cooling (b)

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Fig. 5

The first three layers at the instant of application of the third layer (a) and after its cooling (b)

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Fig. 6

Calculated deformation profiles in the vertical direction for the beams with H = 5 mm and h = 200 and 350 μm as fabricated on the substrate and after detachment: model estimates at the middles of the layers (symbols), approximate formulas (solid lines), and the asymptotics at h→ 0 (dashed lines)

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Fig. 7

Curvature radius R of the beam versus beam height H at h = 200 μm (a) and versus layer height h at H = 5 mm (b): mean values (points); mean square deviations (vertical bars); theoretical prediction (solid line); theoretical asymptotics (dashed line)



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