Optical Penetration Depth of Laser beams in Powder Bed

During powder bed fusion processes, the laser power intensity decreases as the beam penetrates through the powder bed. The depth at which the absorbed intensity decreases to 1/e (~37%) of the initial absorbed intensity [4] is defined as the Optical Penetration Depth (OPD. Estimating the correct powder absorption and OPD values is critical to model powder bed fusion processes and predict the properties of the finished components.

In dense metals, OPD is less than 100 nm [1,2]. At the surface of a powder bed, however, multiple reflection and absorption effects occur at a macroscopic level. In other words, when a Gaussian laser beam (typically used in laser powder bed fusion machines) impacts the powder bed, it experiences multiple reflections through the powder layers. Such phenomenon causes drastic deviation from the Gaussian distribution of energy beneath the top surface. As a result, the actual optical penetration depth is larger than that in dense materials [3].

light scattering in powder layers [1]

A ray tracing model [2] is conventionally used to model OPD in powders. This type of modelling takes into account the multiple reflections and the absorption of light by particles organised randomly in a layer. As the laser interacts with powder particles, four main phenomena occur:

• transmission,
• forward scattering,
• backward scattering,
• and entirely absorption of the laser beam [6].

These phenomena depends on granulometric properties such as powder size, powder bed density, and material properties [3-6]. Generally, the ray tracing model shows a good coincidence when comparing the results with the experimental data.

Measurements of spherical Ni powder layers with particles size of -20um shows OPD~20um [3], while OPD~200um for powder size of 50-75um [3]. In addition, the absorption of Ni and Fe is in a same range [5]. For spherical powder particles of 316L of size of -45um, the OPD can be estimated using ray tracing to about 170um [1].

References
[1] A finite element model of thermal evolution in laser micro Sintering, Jie Yin · Haihong Zhu, Linda Ke, Panpan Hu, Chongwen He, Hu Zhang, Xiaoyan Zeng, Int J Adv Manuf Technol DOI 10.1007/s00170-015-7609-x
[2] Wang XC, Laoui T, Bonse J, Kruth JP, Lauwers B, Froyen L (2002) Direct selective laser sintering of hard metal powders: experimental study and simulation. Int J Adv Manuf Technol 19(5):351–357. doi:10.1007/s001700200024
[3] Fischer P, Romano V, Weber HP, Karapatis NP, Boillat E, Glardon R (2003) Sintering of commercially pure titanium powder with a Nd:YAG laser source. Acta Mater 51(6):1651–1662. doi:10.1016/s1359-6454(02)00567-0
[4] P.Fischer, Romano V, Weber HP. Modeling of near infrared pulsed laser sintering of metallic powders 2003;5147:292–8.
[5] Tolochko NK, Khlopkov Y V., Mozzharov SE, Ignatiev MB, Laoui T, Titov VI. Absorptance of powder materials suitable for laser sintering. Rapid Prototyp J 2000;6:155–61. doi:10.1108/13552540010337029.
[6] Streek a., Regenfuss P, Exner H. Fundamentals of energy conversion and dissipation in powder layers during laser micro sintering. Phys Procedia 2013;41:858–69. doi:10.1016/j.phpro.2013.03.159