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实验中所用的CFRP是由碳纤维和环氧树脂铺层固化成形,由于树脂基体与碳纤维的热物性差异较大,导致了材料复杂的温度分布并产生热应力,因此将碳纤维和基体两者分层建模。激光在空间中为高斯分布,为了监测轴向、径向热应力的演化特征,采用2维轴对称为激光辐照复合材料的几何模型。
图 1所示为高功率激光损伤复合材料物理模型。激光垂直辐照靶材中心,材料半径a=25mm,环氧树脂单层厚度d=0.1mm(共3层),碳纤维单层厚度h=0.35mm(共2层)。
Figure 1. Geometric model of carbon fiber reinforced epoxy composite irradiated by continuous wave (CW) laser
采用的材料和激光参量如表 1和表 2所示。使用COMSOL Multiphysics有限元分析软件对高功率激光损伤复合材料进行温度场和应力场仿真研究。
Table 1. Laser parameters
radius r/mm wavelength λ/nm radiation time t/s power density E/(W·cm-2) 1 1064 1 293~3453 Table 2. Carbon fiber reinforced epoxy composite parameters
parameter epoxy resin carbon fiber thickness/mm 0.3 0.7 absorptivity 0.8 0.8 material density/(kg·m-3) 1200 1500 coefficient of thermal expansion/ K-1 -4.1×10-6 5.5×10-6 Young’s modulus/GPa 8.4 230 Poisson ratio 0.38 0.32 -
连续激光辐照CFRP进行能量交换的过程中,由于辐照时间较长,激光与复合材料相互作用的主要过程是热传导过程,忽略复合材料与外界的对流和辐射效应,复合材料所吸收的能量全部转化为热能。为了分析连续激光辐照复合材料的温度场及应力场分布,作者在柱坐标系下的热传导过程开始讨论激光作用CFRP的热应力模型。
$ \begin{array}{l} \frac{{\partial {T_i}(r, z, t)}}{{\partial t}} = \frac{{{\kappa _i}}}{{{\rho _i}{c_i}}}\left[ {\frac{{{\partial ^2}{T_i}(r, z, t)}}{{\partial {r^2}}} + \frac{1}{r}\frac{{\partial {T_i}(r, z, t)}}{{\partial r}} + } \right.\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. {\frac{{{\partial ^2}{T_i}(r, z, t)}}{{\partial {z^2}}} + \frac{{{q_i}(r, z, t)}}{{{\kappa _i}}}} \right] \end{array} $
(1) 式中,Ti(r, z, t)表示在t时刻的温度分布;r,z分别是轴对称坐标系中径向和轴向位置; ρi,ci和κi分别表示材料的密度、比热容和导热系数,i分别代表碳纤维或环氧树脂。上述热传导方程的热源可表示为:
$ {q_i}(r, z, t) = {\alpha _i}\left( {1 - {R_i}} \right){I_0}f(r)m(z)g(t) $
(2) $ f(r) = \exp \left( { - \frac{{2{r^2}}}{{r_0^2}}} \right) $
(3) $ m(z) = \exp \left( { - {\alpha _i}z} \right) $
(4) $ g(t) = 1, (0 \le t \le \tau ) $
(5) 式中,αi代表碳纤维或环氧树脂的吸收系数;Ri是碳纤维和环氧树脂的反射率;I0是激光辐照中心功率密度;r0是激光的光斑半径;f(r)和g(t)分别是连续激光的空间分布和时间分布;τ为连续激光辐照时间。
在连续激光辐照CFRP过程中,材料内部产生不均匀分布的温度场,复合材料的连续性限制各部分不能自由膨胀,从而产生热应力。在轴对称坐标系下,与热传导方程相耦合的平衡微分方程可以表示为[17-18]:
$ {\nabla ^2}{u_{ri}} - \frac{{{u_{ri}}}}{{{r^2}}} + \frac{1}{{1 - 2{\mu _i}}}\frac{{\partial {\varepsilon _i}}}{{\partial r}} - \frac{{2\left( {1 + {\mu _i}} \right)}}{{1 - 2{\mu _i}}}{\beta _i}\frac{{\partial {T_i}}}{{\partial r}} = 0 $
(6) $ {\nabla ^2}{u_{zi}} + \frac{1}{{1 - 2{\mu _i}}}\frac{{\partial {\varepsilon _i}}}{{\partial z}} - \frac{{2\left( {1 + {\mu _i}} \right)}}{{1 - 2{\mu _i}}}{\beta _i}\frac{{\partial {T_i}}}{{\partial z}} = 0 $
(7) 式中,▽为梯度微分算子; ur,uz分别表示位移在r,z方向上的分量; εi,μi,βi分别表示体应变、泊松比和材料的热应力系数。设置位移为0、速度为0的初始条件,设置底面边界z方向位移为0,其它边界为自由边界条件。
高功率激光辐照CFRP的温度场和应力场的数值分析
Study on numerical analysis of temperature field and stress field of carbon fiber reinforced polymers irradiated by high power laser
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摘要: 为了研究高功率激光致碳纤维/环氧树脂复合材料的热损伤规律,采用COMSOL软件对多层结构的碳纤维/环氧树脂复合材料的热应力进行模拟计算,取得了不同功率密度激光辐照复合材料的瞬态温度场与应力场的时空分布及变化规律。测量得到不同功率密度的激光作用碳纤维/环氧树脂后的损伤面积和损伤形貌,与数值模拟结果的趋势吻合。结果表明,靶材表面辐照中心点温度在872K时出现温度平台,即相变潜热期与逆相变潜热期,并随着激光功率密度变化;激光辐照靶材对上表面碳纤维产生了极大的轴向压应力,功率密度为293W/cm2时,压应力差值约为1.87MPa;功率密度为3453W/cm2时, 压应力差值约为1.42MPa。这一结果对高功率激光致碳纤维/环氧树脂复合材料的热损伤研究提供了理论基础。Abstract: In order to study the thermal damage law of carbon fiber reinforced epoxy composite induced by high power laser, the thermal stress of carbon fiber reinforced epoxy composite with multilayer structure was simulated by COMSOL software. Theoretical analysis and experimental verification were carried out. The temporal and spatial distribution and change of the transient temperature field and stress field of composite materials irradiated by laser with different power densities were obtained. The damage area and morphology of carbon fiber/epoxy resin treated with different laser power density were measured, which was consistent with the trend of numerical simulation results. The results show that, when the temperature of the irradiation center of the target surface is 872K, a temperature plateau appears, that is, the latent heat period of phase change and the latent heat period of reverse phase change, and changes with the laser power density. The laser irradiation target material produced a great axial compressive stress on the upper surface of the carbon fiber. When power density is 293W/cm2, the compressive stress difference is about 1.87MPa; when power density is 3453W/cm2, the compressive stress difference is about 1.42MPa. This result provides a theoretical basis for the research on the thermal damage of carbon fiber/epoxy resin composites caused by highpower lasers.
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Key words:
- laser technique /
- thermal stress /
- numerical simulation /
- composite material /
- damage characteristics
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Table 1. Laser parameters
radius r/mm wavelength λ/nm radiation time t/s power density E/(W·cm-2) 1 1064 1 293~3453 Table 2. Carbon fiber reinforced epoxy composite parameters
parameter epoxy resin carbon fiber thickness/mm 0.3 0.7 absorptivity 0.8 0.8 material density/(kg·m-3) 1200 1500 coefficient of thermal expansion/ K-1 -4.1×10-6 5.5×10-6 Young’s modulus/GPa 8.4 230 Poisson ratio 0.38 0.32 -
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