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.
There are many different ways to modify the surface of materials. One of the most modern,
technological and precise is laser processing [
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.) [
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 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 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. 3. Modeling the plasma pressure during laser processing of materials The pressure during irradiation of materials in air can be determined by the formula: To modeling the plasma pressure during laser processing in a transparent condensed medium, it is convenient to use the formula:
Ppl = (аplt)-1/3I3/4, where I – intensity of laser radiation; t – laser pulse duration; αpl - coefficient characterizing plasma properties. where γ – adiabatic index, D1, D2 – propagation speeds of the compression wave front; ρ1, ρ2 – densities of unexcited mediums 1 and 2. (2) (3)
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.
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:
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).
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.
And now is possible to find the wavelength of the solidifying material: (5) (6)