1.1 Interaction of Lasers and Materials
5
the absorbed laser energy distribution applies to the material surface, and under this
precondition, the temperature field model is built to analyze the heating and cooling
process during the laser processing. The heat transfer phase from the surface material
into the matrix mainly follows the Fourier law of heat conduction. The heat source
model of the laser varies with different materials. For metallic material, the laser
absorption length is very limited. Laser absorption occurs within 1–5 μm of the
material surface. The heat source model can be expressed as follows:
Q V (x,y,z,t) = AI 0 (x, y, t)δ(z)
(1.6)
where: A—Absorptivity of the laser by the material;
I 0 (x, y, t)—Distribution of the laser intensity on the material surface;
δ (z)—Dirac function.
The laser intensity I 0 (x, y, and t) is usually represented as the production of spatial
distribution I 0 (x, y) and dimensionless time waveform B (t). Typical wave forms
B (t) include step wave, rectangular wave, triangular wave, trapezoidal wave, and
Gaussian waveform, etc.
During the laser heating process, the thermal physical parameters of material
(absorption coefficient, specific heat, thermal diffusivity, and thermal conductivity
coefficient) vary with the temperature, however, for most of materials, the change of
heat physical parameters is relatively little as the temperature changes, nearly equal
to a constant, or the temperature in the process may be regarded as average value.
In the following discussion, it’s assumed that the thermal physical parameters of
material are independent of the temperature.
When the laser beam of Gaussian distribution stands still relative to the material
surface, the maximum value distribution of the temperature field on the semi-infinite
material surface is as follows:
T =
AP
kπ 3/2 r
arctan
4ατ
r 2
(1.7)
where: A—Laser absorptivity;
P—Laser power;
r—Equivalent radius of the laser beam;
k—Heat conductivity coefficient of material;
α—Thermal diffusion coefficient of material.
Heating of the material by the laser is correlated to various factors, such as laser
power density, equivalent radius of the laser beam, and material heating time by the
laser. The equivalent radius is generally defined as the distance from the center of
the laser beam to the position when the light intensity drops to 1/e of the central light
strength. For the Gaussian beam, the equivalent radius is ω/
√
2 (ω is the spot size
of the Gaussian beam). If the time characteristic constant τ 0 = r
2 /4α is introduced,
Eq. (1.7) can be rewritten as:
5
the absorbed laser energy distribution applies to the material surface, and under this
precondition, the temperature field model is built to analyze the heating and cooling
process during the laser processing. The heat transfer phase from the surface material
into the matrix mainly follows the Fourier law of heat conduction. The heat source
model of the laser varies with different materials. For metallic material, the laser
absorption length is very limited. Laser absorption occurs within 1–5 μm of the
material surface. The heat source model can be expressed as follows:
Q V (x,y,z,t) = AI 0 (x, y, t)δ(z)
(1.6)
where: A—Absorptivity of the laser by the material;
I 0 (x, y, t)—Distribution of the laser intensity on the material surface;
δ (z)—Dirac function.
The laser intensity I 0 (x, y, and t) is usually represented as the production of spatial
distribution I 0 (x, y) and dimensionless time waveform B (t). Typical wave forms
B (t) include step wave, rectangular wave, triangular wave, trapezoidal wave, and
Gaussian waveform, etc.
During the laser heating process, the thermal physical parameters of material
(absorption coefficient, specific heat, thermal diffusivity, and thermal conductivity
coefficient) vary with the temperature, however, for most of materials, the change of
heat physical parameters is relatively little as the temperature changes, nearly equal
to a constant, or the temperature in the process may be regarded as average value.
In the following discussion, it’s assumed that the thermal physical parameters of
material are independent of the temperature.
When the laser beam of Gaussian distribution stands still relative to the material
surface, the maximum value distribution of the temperature field on the semi-infinite
material surface is as follows:
T =
AP
kπ 3/2 r
arctan
4ατ
r 2
(1.7)
where: A—Laser absorptivity;
P—Laser power;
r—Equivalent radius of the laser beam;
k—Heat conductivity coefficient of material;
α—Thermal diffusion coefficient of material.
Heating of the material by the laser is correlated to various factors, such as laser
power density, equivalent radius of the laser beam, and material heating time by the
laser. The equivalent radius is generally defined as the distance from the center of
the laser beam to the position when the light intensity drops to 1/e of the central light
strength. For the Gaussian beam, the equivalent radius is ω/
√
2 (ω is the spot size
of the Gaussian beam). If the time characteristic constant τ 0 = r
2 /4α is introduced,
Eq. (1.7) can be rewritten as: