6
1 Laser Welding Basics
T =
AP
kπ 3/2 r
arctan
τ
τ 0
(1.8)
If the laser-material action time τ is far less than the time characteristic constant
τ 0 ; that is to say, the laser irradiation time is very short, then
arctan
τ
τ 0
≈
τ
τ 0
Equation (1.8) can be simplified to be:
T =
AP
kπ 3/2 r
τ
τ 0
(1.9)
If the laser-material action time τ is far more than the time characteristic constant
τ 0 , the laser irradiation time is relatively long and the temperature field approaches
steady state, thus,
arctan
τ
τ 0
≈
π
2
Equation (1.8) can be simplified to be:
T =
AP
2kπ 1/2 r
(1.10)
If the laser-material action time τ is close to the time characteristic constant τ 0
(generally 0.1 τ 0 ≤ τ ≤ 3τ 0 ), then
arctan
τ
τ 0
≈
τ
4
τ
τ 0
3/8
Equation (1.8) can be simplified to be:
T =
AP
4kπ 1/2 r
τ
τ 0
3/8
(1.11)
Heating of the material by the laser is mainly applied in the laser heat treatment
technique. Usually, under the heat treatment condition, the laser beam applies to the
material surface in the form of scanning, and the laser beam in this case is regarded
as the moving heat source. The temperature field generating the moving heat source
is the quasi-steady state, equivalent to the static temperature field dragging in the
material at the laser scanning speed v, in which case, it’s necessary to define an
equivalent laser action time τ
∗
= Cr/v. To approximately describe the temperature