=Paper=
{{Paper
|id=Vol-3896/short7
|storemode=property
|title=A mathematical modeling of surface periodic relief after nanosecond laser processing
|pdfUrl=https://ceur-ws.org/Vol-3896/short7.pdf
|volume=Vol-3896
|authors=Vitalii Mocharskyi,Bogdan Kovalyuk,Oksana Sitkar
|dblpUrl=https://dblp.org/rec/conf/ittap/MocharskyiKS24
}}
==A mathematical modeling of surface periodic relief after nanosecond laser processing==
https://ceur-ws.org/Vol-3896/short7.pdf
A mathematical modeling of surface periodic
relief after nanosecond laser processing
Vitalii Mocharskyi, Bogdan Kovalyuk and Oksana Sitkar
Ternopil Ivan Puluj National Technical University, Ruska street, 56, Ternopil, 46001, Ukraine
Abstract
The paper proposes a mathematical model of the material surface periodic relief formation after
nanosecond laser processing. The effect of a transparent condensed medium on the periodic
structures formation on the material surface is shown. Mathematical modeling of temperature fields
in the material during laser processing was carried out. It is shown that the surface layers undergo
rapid melting, evaporation and transition into a plasma state. Modeling of plasma pressure showed
that large pressure values occur on the material surface during irradiation, which are much higher
during processing in a transparent condensed medium than in air. The correlation between the
conducted modeling and the conducted experiments (determination of the recoil impulse of the
ablation products and SEM images of the steel surface) is shown. The main parameters on which
the wavelength of the solidifying material depends are determined.
Keywords ⋆1
Nanosecond laser, mathematical modeling, periodic relief
1. Introduction
There are many different ways to modify the surface of materials. One of the most modern,
technological and precise is laser processing [1-4]. This technology makes possible to obtain a
structure and properties in the near-surface layers of the material that are radically different
from the structure and properties of the base material [5-8]. As a result, the product after laser
processing can have much better characteristics, which increases its reliability, service life,
etc.
It should be noted that in order to increase the processing depth, as well as to obtain
various structures on the surface of materials, in addition to the technological parameters of
the laser installation itself (laser pulse energy, pulse duration, wavelength, etc.) [9-11], the
transparent condensed medium (water, epoxy resin, etc.) in which processing is carried out
also affects [12]. It allows to redistribute the energy that reaches the surface of the processed
material, increase the plasma pressure and, as a result, the action of shock waves in the depth
of the material, in addition, some elements of the transparent condensed medium can
penetrate into the near-surface layers of the processed material.
Therefore, modeling the processes during laser treatment is very important in order to
optimally choose laser irradiation regimes, which is useful for obtaining a predetermined
⋆
ITTAP’2024: 4th International Workshop on Information Technologies: Theoretical and Applied Problems, October 23-
25, 2024, Ternopil, Ukraine, Opole, Poland
1
vitaliimocharskyi@gmail.com (V. Mocharskyi); kovalyukdan@ukr.net (B. Kovalyuk); manjovska@gmail.com
(O. Sitkar)
0000-0003-4153-6832 (V. Mocharskyi); 0000-0002-8085-0165 (B. Kovalyuk); 0000-0001-9352-4660 (O. Sitkar)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
periodic relief of various materials, because field studies are usually much more expensive
than mathematical modeling.
2. Modeling of the temperature field during laser
processing of materials
To modeling the temperature fields in the material, it is necessary to solve the thermal
conductivity equation and one of the solutions is the next equation:
, (1)
where
q – energy flux density;
t – laser pulse duration;
a – coefficient of thermal conductivity of the material;
λ – thermal conductivity;
z – depth of the heated layer;
ierfc (u) – probability integral function.
Figure 1: Temperature distribution in steel during irradiation in a transparent condensed
medium.
Figure 1 shows the modeled distribution of the temperature field along the depth of the
irradiated material. We can see that the temperature in the thin near-surface layer is several
times higher than the melting temperature during processing. As a result, the material
intensively melts, evaporates and turns into plasma.
These data are confirmed by scanning electron microscopy images of steel surfaces after
nanosecond laser treatment in water (Figure 2). It can be seen that the surface underwent
melting, intense boiling, which is evident from the number of pores. The periodic waves is
clearly directed from the center of irradiation to the edges of the laser spot, which also
indicates the plasma pressure and the recoil impulse of the ablation products.
Figure 2: SEM image of steel surface after nanosecond laser processing
3. Modeling of the plasma pressure during laser
processing of materials
The pressure during irradiation of materials in air can be determined by the formula:
Ppl = (аplt)-1/3I3/4, (2)
where
I – intensity of laser radiation;
t – laser pulse duration;
αpl - coefficient characterizing plasma properties.
To modeling the plasma pressure during laser processing in a transparent condensed
medium, it is convenient to use the formula:
(3)
where
γ – adiabatic index,
D1, D2 – propagation speeds of the compression wave front;
ρ1, ρ2 – densities of unexcited mediums 1 and 2.
Figure 3: Dependence of plasma pressure on Figure 4: Dependence of plasma pressure on
the intensity of laser radiation during the intensity of laser radiation during
processing in air processing in transparent condensed medium
Figures 3 and 4 show that high pressures occur on the surface of materials during
nanosecond laser irradiation. Moreover, the plasma pressure during irradiation in a
transparent condensed medium differs from the pressure during irradiation in air by almost 10
times at the same laser pulse intensities.
Conducted experiments to determine the recoil impulse using the pendulum method of
ablation products during irradiation (Figure 5), showed that when irradiated in a transparent
condensed medium the recoil impulse is an order of magnitude higher than the recoil impulse
when processed in air. These data correlate with the calculations that were made above. It is
shown that a transparent condensed medium can change the form and structure of the
obtained periodic relief on the surface of materials after irradiation.
Figure 5: Recoil impulse pendulum method investigation scheme.
4. Some features of the periodic relief formation on the
material surface after laser processing
One of the possible reasons for the appearance of periodic relief on the surface of the
material after laser treatment is the formation of instabilities due to the occurrence of
thermocapillary processes, which are associated with the dependence of the surface tension
index of the heated material on temperature and the subsequent inhomogeneous melting. This
process is also influenced by the plasma pressure and recoil impulse.
The pressure pulse causes a harmonic wave on the molten surface and a periodic relief is
formed in the horizontal direction, and the oscillations decay exponentially in depth. Then we
can obtain the dispersion equation, where the angular frequency ω is related to the wave
vector κ:
(4)
where
ρ – melt density,
σ – is the surface tension coefficient of the liquid metal layer melted by a laser pulse.
From this formula, the group velocity is determined as the derivative of the angular
frequency along the wave vector:
(5)
And now is possible to find the wavelength of the solidifying material:
(6)
The wavelength of the periodic relief varies depending on the material, its density, the
value of the surface tension coefficient of the melt, the speed of sound in it, laser flux density
and the conditions of irradiation. These data are confirmed by SEM images of steel surfaces
after irradiation in a transparent condensed medium. (Figure 2).
5. Conclusions
The work carried out mathematical modeling of the main factors that affect the formed
periodic relief on the surface of materials after nanosecond laser processing: temperature
fields in the material, plasma pressure and the recoil impulse of the ablation products, and also
showed the influence of thermophysical properties and the surface tension coefficient on the
final wave length of frozen periodic relief. Modeling was implemented in the MATLAB system
using physics and mathematical methods. Also, the modeling results were compared with real
experiments and SEM images.
6. References
[1] Erju Liu, Xi Chen, Yang Jin, Yanbin Chen, Jie Xu, Debin Shan, Bin Guo. Surface
morphology evolution and tribological behavior in nanosecond pulsed laser polishing of
S136 mold steel. Journal of Materials Research and Technology, Volume 22, 2023, Pages
3230-3244.
[2] Yan Wang, Mingyue Zhang, Yinghuai Dong, Jingnan Zhao, Xusheng Zhu, Yuehua Li,
LingFeng Fan, Hepeng Leng. Morphology modelling and validation in nanosecond pulsed
laser ablation of metallic materials. Precision Engineering, Volume 79, 2023, Pages 34-42.
[3] The Method of Materials Surface Defects Analysis Created by Laser Processing.
Mocharskyi, V. , Kovalyuk, B. , Sitkar, O. , Hutsaylyuk, V. , Wachowski, M. CEUR
Workshop Proceedings, 2023, 3628, pp. 151–155
[4] M. Khaleeq-ur-Rahman, M.Z. Butt, Ishrat Mubeen, M.S. Rafique. Investigation of silver
plasma and surface morphology from a nanosecond laser ablation. Materials Chemistry
and Physics, Volume 114, Issues 2–3, 2009, Pages 978-982.
[5] D. Klinger, E. łusakowska, S. Kret, B. Kozankiewicz, D. Żymierska. Surface morphology
created by nanosecond laser annealing of amorphised Si layer—Investigations by
complementary methods. Radiation Physics and Chemistry, Volume 80, Issue 10, 2011,
Pages 1031-1035.
[6] Boustie M, Berthe L, De Resseguier T, Arrigoni M. Laser Shock Waves: Fundamentals and
Applica-tions. Proceedings of the 1st International Symposium on Laser Ultrasonics:
Science, Technology andApplications. 2008. pp. 1–6.
[7] Laurent Berthe, Arnaud Sollier, Patrice Peyre, Remy Fabbro. Study of plasma induced by
laser in water confinement regime: Application to laser shock processing with and
without thermal protective coating. Proceedings of the ICALEO 2003: 22nd International
Congress on Laser Materials Processing and Laser Microfabrication, Jacksonville, Florida,
USA. (pp. 1502).
[8] Lei Chen, Zelin Liu, Chuan Guo, Tongcheng Yu, Minsun Chen, Zhongjie Xu, Hao Liu,
Guomin Zhao, Kai Han. Nanosecond laser-induced controllable periodical surface
structures on silicon, Chin. Opt. Lett. 20, 013802 (2022)
[9] Phuong Thi Nguyen, Jina Jang, Seok-Min Kim, Taeseung Hwang, Junyeob Yeo, Costas P.
Grigoropoulos, Jung Bin In. Nanosecond laser-induced reshaping of periodic silicon
nanostructures. Current Applied Physics, Volume 22, 2021, Pages 43-49.
[10] Zhaoxuan Yan, Xuesong Mei, Wenjun Wang, Aifei Pan, Qingyan Lin, Chenchen Huang.
Numerical simulation on nanosecond laser ablation of titanium considering plasma shield
and evaporation-affected surface thermocapillary convection. Optics Communications,
Volume 453, 2019, 124384.
[11] Yao Lu, YanChao Guan, Yuan Li, LiJun Yang, MaoLu Wang, Yang Wang. Nanosecond
laser fabrication of superhydrophobic surface on 316L stainless steel and corrosion
protection application. Colloids and Surfaces A: Physicochemical and Engineering
Aspects, Volume 604, 2020, 125259.
[12] Vitalii Mocharskyi, Bogdan Kovalyuk, Oksana Sitkar, Laser Shock Wave Surface
Processing Possibilities of Structural Materials, Challenges to national defence in
contemporary geopolitical situation 2022(2022), no. 1, 297-301.