0
Research Papers: Heat Transfer in Manufacturing

# Model of Radiation and Heat Transfer in Laser-Powder Interaction Zone at Selective Laser Melting

[+] Author and Article Information
A. V. Gusarov, I. Yadroitsev, Ph. Bertrand, I. Smurov

DIPI Laboratory, Ecole Nationale d’Ingénieurs de Saint-Etienne (ENISE), 58 rue Jean Parot, Saint-Etienne 42023, France

J. Heat Transfer 131(7), 072101 (May 01, 2009) (10 pages) doi:10.1115/1.3109245 History: Received April 15, 2008; Revised January 28, 2009; Published May 01, 2009

## Abstract

A model for coupled radiation transfer and thermal diffusion is proposed, which provides a local temperature field. Single-line scanning of a laser beam over a thin layer of metallic powder placed on a dense substrate of the same material is studied. Both the laser beam diameter and the layer thickness are about $50 μm$. The typical scanning velocity is in the range of 10–20 cm/s. An effective volumetric heat source is estimated from laser radiation scattering and absorption in a powder layer. A strong difference in thermal conductivity between the powder bed and dense material is taken into account. The above conditions correspond to the technology of selective laser melting that is applied to build objects of complicated shape from metallic powder. Complete remelting of the powder in the scanned zone and its good adhesion to the substrate ensure fabrication of functional parts with mechanical properties close to the ones of the wrought material. Experiments with single-line melting indicate that an interval of scanning velocities exists, where the remelted tracks are uniform. The tracks become “broken” if the scanning velocity is outside this interval. This is extremely undesirable and referred to as the “balling” effect. The size and the shape of the melt pool and the surface of the metallurgical contact of the remelted material to the substrate are analyzed in relation to the scanning velocity. The modeling results are compared with experimental observation of laser tracks. The experimentally found balling effect at scanning velocities above $∼20 cm/s$ can be explained by the Plateau–Rayleigh capillary instability of the melt pool. Two factors destabilize the process with increasing the scanning velocity: increasing the length-to-width ratio of the melt pool and decreasing the width of its contact with the substrate.

<>

## Figures

Figure 1

Selective laser melting. (a) Fabricated parts. (b) Scheme of the process: (I) deposition of a powder layer, (II) scanning of the first layer, and (III) layer-by-layer fabrication. and (c) Detailed view of the laser-powder interaction zone: (1) fabrication plate, (2) roller, (3) powder delivery piston, (4) fabrication piston, and (5) laser beam.

Figure 2

Laser radiation transfer in a powder layer on a substrate: (Q0) incident power density, (z) depth, (L) layer thickness, (θ) radiation propagation angle, and (I(z,θ)) radiation intensity

Figure 3

(a) Dimensionless radiative flux q=Q/Q0 and (b) volumetric heat source u=U/(βQ0) in the powder layer versus dimensionless depth ξ for various values of optical depth λ at the reflectivity of dense material ρ=0.7

Figure 4

Total absorptivity of the system powder-substrate A and fractions of the incident laser radiation absorbed by the surface of the substrate As and in the powder A−As versus optical depth of the powder layer λ at the reflectivity of dense material ρ=0.7

Figure 5

Radial profiles of power density in the incident laser beam employed for the calculations. The total beam power and the FWHM are specified for each curve.

Figure 6

Cross-sections of laser tracks on the stainless steel substrate without powder: calculated phase diagrams (upper row) and experimental micrographs (lower row)

Figure 7

Laser beam scanning of a 50 μm powder layer with optical thickness λ=2 at the incident laser power of 30 W, the laser beam FWHM of 60 μm, and the scanning velocity of 20 cm/s. Distributions at the symmetry plane y=0: (a) normal component of net laser radiation flux density Q, (b) volumetric heat source due to absorption of laser radiation U, (c) temperature T, (d) temperature T at the top powder surface z=0, and (e) melt pool shape.

Figure 8

Comparison between experiments ((a) and (b)) and calculations ((c) and (d)) at various scanning velocities (marked on the top of each column): (a) top view of remelted tracks; (b) cross section micrographs; (c) calculated phase distribution in cross-section with the substrate on the bottom, the powder on the sides, and the remelted zone in the center; and (d) surface temperature distribution. The broken-line circles on diagrams (d) are projections of the laser beam.

Figure 9

Qualitative evolution of phase distribution in the cross-section of a track with the substrate on the bottom, the powder on the sides, and the melt in the center: (a) just melted and (b) after minimizing the melt surface

Figure 10

Widths of the powder-consumed band and the contact of the remelted material with the substrate versus the scanning velocity: experiments (points) and calculations (lines) at two values of the optical thickness, λ=2 and λ=3

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections