Pulsed Laser Ablation: 2D Model for Crater Formation on Fe
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rl.gamaliell
Abstract
The most important part to understand in pulsed laser material removal systems is the physical
phenomena happening on the laser ablation process. In laser ablation process a portion of mass
from a sample is removed by using a laser beam. It’s generally a basic method for a solid material.
The intense laser energy is applied over the material surface generating a series of emitted and
monitored photons. A two-dimensional model is developed to show and analyze the crater
formation on Fe by applying a nanosecond laser beam. The numerical solution of the heat equation
is used to investigate the influence of process parameter during laser machining of metal
microstructures. Forward Finite-Difference method is applied. The laser pulse is considered to have
Gaussian temporal and spatial profiles. The relation between temperature and energy density and
the material change of state was considered while the heat diffusion in the gas phase is ignored due
to the assumption that the liquid-gas transition removes material.
Introduction
Ablation is the principal means of material removals when using pulsed lasers. According to the
Oxford dictionary, Ablation is defined as “1. The loss of solid material by melting, evaporation, or
erosion. 2.- The surgical removal of body tissue.” The word ablation was taken from the Latin word
“Ablation”, which is used for “to remove”. After a small research onto the roots, it can be clearly
seen that it’s a blanket term used to describe different instances. Originally, Laser Ablation was
planned as an alternative manufacturing technique for conventional photolithography.
The ablation mechanism is directly dependent upon the material with which photons are
interacting. Ablation is a result of short wavelength light radiation. When a laser beam couples with
a material, photons combat atomic bonds; the size of a photon is dictated by its energy.
Laser milling of metals have infinity of industrial applications; however, it’s considered as a complex
method to carry out. Generally, milling systems use long pulses, microsecond duration. Long pulse
durations generate high ablation rates but the extensive thermal penetration depth, laser melting
and recast dominate the process sending a result with a poor quality. During last researches,
progress in laser milling of metals has been achieved using shorter laser pulse at higher repetition
rates. Long pulses for laser milling are generally applied to high surface roughness, which prevents
the broader us of this technology, especially for micro-tools manufacturing.
Th process works by focusing a laser onto a substrate to a remove material that is on its surface. The
amount of material removed depends on the intensity, pulse length, and wavelength of the laser,
as well as the material itself. The area absorbs the laser that is being directed on it, thereby breaking
down the chemical bonds within the area.
Ablation process has many different uses, particularly as the whole process is undergone with
minimal excess heat being transferred to the surrounding area of the material being used. This
means that the process will have little to no effect on the parts of the material that you don’t want
it to, and so is great for a wide range of materials, including plastic, metal, ceramic, and even
biological tissue.
The success and efficiency of the process depend on a number of factors. These factors are:
• Wavelength: The wavelength needs to be selected carefully with a minimum absorption
depth. This is so that there is a high energy deposition within a small volume, resulting in a
quick and efficient ablation outcome.
• Pulse Duration: Using shorter pulse durations is better to perform the maximum peak
power and to minimize the thermal damage that is inflicted on the surrounding area.
• Pulse Repetition Rate: It needs to be high enough so that the heat caused by the ablation
is maintained and is not left any time to cool. It will result in a more successful ablation as
energy waste will be reduced.
• Beam Quality: It needs to be of sufficient quality to perform the process successfully. The
quality will be determined by its brightness, its focus, and its homogeneity. The beam size
will also need to be controlled so that you don’t laser ablate too large an area.
Theorical Model of laser-material Interaction
This work is on modelling the interactions between a nanosecond (ns) laser source and metals. The
incident laser radiation in the form of a pulse train is absorbed in the material near the surface of
the workpiece and creates a localized thermal load.
The laser interaction is considered as a volume heat source and is calculated using the following
formula:
A(x,z,t) = a * Io * p(t,x) * e^(a*z)
Where:
A is the absorption coefficient [m-1] for the sample material.
P(t,x) refers to the temporal and spatial profiles of the laser pulse
Io is the peak on-line laser intensity [Wm^-2]
Io Formula
Where f is the laser pulse frequency (kHZ), T the pulse duration (s), Ep the pulse energy (J) and Ro
the radius of the laser beam spot at the focus.
Numerical Solution
A two-dimensional numerical model was developed by using Finite Difference Method (FDM) to
determine the temperature distribution across a thin metallic plate and thus to predict the material
removal rate and the negative side effects as well.
FDM can be used to approximate the solution of partial differential equations. Explicit method is
used in this project. It requires less computational time than the implicit, while also being easier to
implement. In FDM, first order partial derivatives are replaced with the Forward Difference.
(7)
Central Difference is used to approximate the second order derivatives.
(8)
(9)
Terms , , and represent the truncation error of the approximation and are
neglected for the purpose of this simulation.
Equation (1) is substituted with appropriate terms obtained from equations (7), (8), (9), and
rearranged to give equation (10):
(10)
For simplicity, constants can be group together to give a single parameter .
(11)
Equation (10) is rearranged to give the final formula (12) used to calculate the temperature of the
node at the following time increment in the simulation.
(12)
In the developed simulation, the volume heat source term is calculated separately for each node
at each time increment, using equation (13), and saved in a 3-dimensional array .
(13)
Initial and Boundary conditions
Dx = 2um
Dz = 0.4um
Initial Temperature = 20
T(t,x->+-infty,z)=20
T(t,x->+-infty,z)=20
Dt <<
%dt<<(0.5*rho*Cp*dx^2*dz^2) / (k *(dx^2 + dz^2)); %dt =
(0.5 * rho * Cp * dx^2 * dz^2) /k (dz^2 + dz^2); 3.3
nanoseconds
1
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