﻿ 超快激光切割金属材料中快速相变的数值模拟
 上海理工大学学报  2020, Vol. 42 Issue (5): 441-447 PDF

Numerical simulation on the rapid phase transformation of metal under the action of moving light source
ZHANG Qi, LI Ling
School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: The phase change heat transfer of multi-pulse laser irradiated gold thin plates was studied by using a two-dimensional dual temperature model. The position of solid-liquid interface was determined by the equivalent specific heat capacity method and the influence of laser parameters on the heat transfer process was studied. The results show that when the laser illuminates the gold thin plate vertically, the overall temperature of the surface increases continuously, but decreases slightly during the pulse interval, and the temperature peak is slightly delayed compared to that at the center of the laser action. As the laser moves, the temperature at the laser spot will show a peak and then fall back. The lateral change of the heat-affected zone during laser action is larger than the longitudinal one, where the heat transfer from the moving light source to the inside plays a major role. During the pulse interval, the longitudinal change of the heat-affected zone is larger than the lateral one, where the internal heat conduction of the gold thin plate plays a major role. As the laser is irradiating, the melting state extends continuously in the lateral direction, while the depth of melting is also constantly increasing. Increasing the incident pulse laser energy causes the melting time to advance and the melting depth to increase.
Key words: multi-pulse laser     two-dimensional two-temperature model     solid-liquid interface     equivalent specific heat capacity     thermal influence

1 物理模型与数学方法 1.1 物理模型

 图 1 物理模型 激光照射表面 Fig. 1 Physical model. Laser irradiated surface
1.2 数学方法

 $\begin{split} {{{C}}_{\rm{e}}}\frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{t}}}} =& \frac{\partial }{{\partial {{x}}}}\left( {{{{k}}_{\rm{e}}}\frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{x}}}}} \right) + \frac{\partial }{{\partial {{y}}}}\left( {{{{k}}_{\rm{e}}}\frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{y}}}}} \right) -\\ & {{G}}\left( {{{{T}}_{\rm{e}}} - {{{T}}_{\rm{l}}}} \right) + {{S}} \end{split}$ (1)
 $\begin{split} {{{C}}_{\rm{l}}}\frac{{\partial {{{T}}_{\rm{l}}}}}{{\partial {{t}}}} =& \frac{\partial }{{\partial {{x}}}}\left( {{{{k}}_{\rm{l}}}\frac{{\partial {{{T}}_{\rm{l}}}}}{{\partial {{x}}}}} \right) + \frac{\partial }{{\partial {{y}}}}\left( {{{{k}}_{\rm{l}}}\frac{{\partial {{{T}}_{\rm{l}}}}}{{\partial {{y}}}}} \right) +\\ & {{G}}\left( {{{{T}}_{\rm{e}}} - {{{T}}_{\rm{l}}}} \right) + {\rm{\rho }}{{{L}}_{\rm{f}}}\frac{{{\rm{d}}f}}{{{\rm{d}}t}} \end{split}$ (2)

 ${{f}} = \left\{ {\begin{array}{*{20}{l}} 1,&{{{{T}}_{\rm{l}}} > \left( {{{{T}}_{\rm{m}}} + {\rm{\delta }}{{{T}}_{\rm{l}}}} \right)}\\ {\dfrac{{{\rm{}}{{{T}}_{\rm{l}}} - {{{T}}_{\rm{m}}} + {\rm{\delta }}{{{T}}_{\rm{l}}}}}{{2\,{\rm{\delta }}\,{{{T}}_{\rm{l}}}}}},&{{{T}}_{\rm{m}}} - \delta {{{T}}_{\rm{l}}} < {{{T}}_{\rm{l}}} < {{{T}}_{\rm{m}}} + \delta {{{T}}_{\rm{l}}}\\ 0,&{{{{T}}_{\rm{l}}}<{{{T}}_{\rm{m}}} - \delta {{{T}}_{\rm{l}}}}\!\!\!\!\!\! \end{array}} \right.\!\!\!\!\!\!$ (3)

Tm是熔点温度的情况下，δ是一个小数，以防止除以零。

 图 2 激光能量强度在时间和空间上的分布示意图 Fig. 2 Schematic diagram of laser intensity distribution in time and space
 $\begin{split} {{q}} = {{A}}\frac{{2{{E}}}} {{{{\text{π} }}{{{R}}^2}{{{t}}_{\rm{p}}}}}&{\rm{exp}}\left( { - 2\frac{{{{{r}}^2}}}{{{{{R}}^2}}}} \right) \left\{ \exp \left[ - 2.77\frac{\left( {{t}} - 2{{{t}}_{\rm{p}}} \right)^2}{{{t}}_{\rm{p}}^2} \right] \right. + \cdots\\ & \left. \exp \left[ - 2.77\frac{\left( {{t}} - {{n}}{{t}}_{\rm{p}} \right)^2}{{t_{\rm{p}}^2}} \right] \right\} \\[-15pt] \end{split}$ (4)
 ${{r}} = \sqrt {{{\left( {{{x}} - {{{x}}_0}} \right)}^2} + {{\left( {{{y}} - {{{y}}_0}} \right)}^2}} x = vt$

t=0开始计算，初始条件：

 ${{{T}}_{\rm{e}}}\left( {{{x}},\ {{y}},\ 0} \right) = {{{T}}_{\rm{l}}}\left( {{{x}},\ {{y}},\ 0} \right) = 300\;{\rm{K}}$ (5)
 $\frac{{\partial {T_{\rm e}}}}{{\partial t}} = \frac{{\partial {T_{\rm l}}}}{{\partial t}} = 0$ (6)

 ${{y}} = {{H}},\qquad {{q}} = - {{k}}\frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{y}}}}$ (7)
 ${{x}} = 0,\quad{{x}} = {{L}},\quad\frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{x}}}} = \frac{{\partial {{{T}}_{\rm{l}}}}}{{\partial {{x}}}} = \frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{y}}}} = \frac{{\partial {{{T}}_{\rm{l}}}}}{{\partial {{y}}}} = 0$ (8)
 ${{y}} = 0,\qquad{\rm{}}\frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{x}}}} = \frac{{\partial {{{T}}_{\rm{l}}}}}{{\partial {{x}}}} = \frac{{\partial {{{T}}_{\rm{e}}}}}{{\partial {{y}}}} = \frac{{\partial {{{T}}_{\rm{l}}}}}{{\partial {{y}}}} = 0$ (9)
2 结果与讨论 2.1 模型验证

 图 3 损伤阈值的模型和实验数据比较 Fig. 3 Model and experimental data comparison of the damage threshold
2.2 激光移动作用下金薄板的熔化过程

E=0.3 μJ，tp=10 ps，R=10 μm，脉宽间隔dt=40 ps的移动激光照射金薄板的过程进行了模拟研究。金薄板L=25 μm，H=0.5 μm，采用自适应网格技术生成网格，初始网格数为100×100，初始温度为300 K。图4给出了不同时刻其温度场的变化情况。从图4中可以看出，在激光移动过程中，表面温度T整体在不断地上升，而在2个脉冲间隔内即t=40～80 ps以及t=120～160 ps时，表面的最高温度有所降低，这是因为热量不断地向低温区传递。由图4中也可以发现，在脉冲间隔内，热影响区纵向的变化要比横向的变化大，而在激光照射期间，热影响区横向的变化要比纵向的变化大。这是因为脉冲间隔内没有能量的进入，金薄板内部导热占主要作用，而激光照射时则移动光源向内部的热传递占主要作用。

 图 4 不同时刻金薄板晶格的温度分布 Fig. 4 Lattice temperature at different time

 图 5 不同时刻金薄板熔化情况 Fig. 5 Melting at different time

 图 6 表面不同位置的温度 Fig. 6 Surface temperature at different position
2.3 激光能量对照射过程中金薄板快速相变的影响

 图 7 不同入射能量的温度 Fig. 7 Temperature with different incident energy

 图 8 不同入射能量的熔化体积 Fig. 8 Melting volume with different incident energy
3 结　论

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