﻿ 船用碳纤维复合材料层合板的水下抗爆性能研究
 舰船科学技术  2023, Vol. 45 Issue (23): 74-77    DOI: 10.3404/j.issn.1672-7649.2023.23.013 PDF

1. 嘉兴南湖学院 机电工程学院，浙江 嘉兴 314000;
2. 嘉兴南湖学院 信息工程学院，浙江 嘉兴 314000

Research on underwater explosion resistance of carbon fiber composite laminated plates for ships
HU Hui1, WANG Wei2
1. Jiaxing Nanhu University, College of Mechanical and Electrical Engineering, Jiaxing 314000, China;
2. Jiaxing Nanhu University, College of Information engineering, Jiaxing 314000, China
Abstract: In this paper, the technology of carbon fiber composite laminate is analyzed, its mathematical model is discussed, the structure of this material is studied, and the characteristic curve of PVC material is given. The process of underwater explosion is analyzed, and the numerical test, empirical formula and pressure error of shock wave under different explosion distance are obtained, and the pressure at 1 500 mm away from the explosion point is analyzed. Finally, the underwater antiknock performance of the ship is studied.
Key words: carbon fiber     composite materials     underwater anti riot
0 引　言

1 碳纤维复合材料层合板技术 1.1 碳纤维复合材料模型

 e_{ft}^2 = {\left( {\frac{{{\varepsilon _{11}}}}{{X_t^\varepsilon }}} \right)^2} - 1\left\{ \begin{aligned} { \geqslant 0}，&{{\mathrm{failed}}}，\\ { \lt 0}，&{{\mathrm{elastic}}} 。\end{aligned} \right. (1)
 $e_{fc}^2 = {\left( {\frac{{{\varepsilon _{11}}}}{{X_c^\varepsilon }}} \right)^2} - 1\left\{ {\begin{array}{*{20}{c}} { \geqslant 0}，&{{\mathrm{failed}}}，\\ { \lt 0}，&{{\mathrm{elastic}}}。\end{array}} \right.$ (2)
 $e_{mt}^2 = {\left( {\frac{{{\varepsilon _{22}}}}{{Y_t^\varepsilon }}} \right)^2} - 1\left\{ {\begin{array}{*{20}{c}} { \geqslant 0}，&{{\mathrm{failed}}} ，\\ { \lt 0}，&{{\mathrm{elastic}}} 。\end{array}} \right.$ (3)
 $e_{mc}^2 = {\left( {\frac{{{\varepsilon _{22}}}}{{Y_c^\varepsilon }}} \right)^2} - 1\left\{ {\begin{array}{*{20}{c}} { \geqslant 0}，&{{\mathrm{failed}}}，\\ { \lt 0}，&{{\mathrm{elastic}}}。\end{array}} \right.$ (4)
 $e_{ld}^2 = {\left( {\frac{{{\varepsilon _{33}}}}{{Z_t^\varepsilon }}} \right)^2} + {\left( {\frac{{{\varepsilon _{13}}}}{{S_{13}^\varepsilon }}} \right)^2} + {\left( {\frac{{{\varepsilon _{12}}}}{{S_{12}^\varepsilon }}} \right)^2} - 1\left\{ {\begin{array}{*{20}{c}} { \geqslant 0，} & {{\mathrm{failed}}}，\\ { \lt 0}，& {{\mathrm{elastic}}} 。\end{array}} \right.$ (5)

 ${H_i} = \left\{ {\begin{array}{*{20}{c}} 0，&{{e_i} \leqslant 0}，\\ {\dfrac{1}{{e_i^n}}}，&{{e_i} \gt 0} ，\end{array}} \right.$ (6)

 $\varepsilon = {C_d}\sigma \text{。}$ (7)

 ${\left( {\frac{{{\sigma _n}}}{{{\sigma _N}}}} \right)^2} + {\left( {\frac{{{\sigma _s}}}{{{\sigma _S}}}} \right)^2} + {\left( {\frac{{{\sigma _t}}}{{{\sigma _T}}}} \right)^2} = 1\text{。}$ (8)

 $\left( {\frac{{{G_n}}}{{{G_N}}}} \right) + \left( {\frac{{{G_s}}}{{{G_N}}}} \right) + \left( {\frac{{{G_t}}}{{{G_T}}}} \right) = 1\text{。}$ (9)
1.2 碳纤维复合材料层合板的构造

 图 1 PVC材料的应力应变曲线 Fig. 1 Stress-strain curve of PVC material

 $F = \sqrt {{q^2} + {\alpha ^2}{{\left( {p - {p_0}} \right)}^2}} - B\text{。}$ (10)

 $B = \alpha A = \alpha \frac{{{p_c} + {p_t}}}{2}\text{，}$ (11)
 $\alpha = \frac{B}{A}\text{。}$ (12)

p轴上的屈服椭圆中心的计算方法为：

 ${p_0} = \frac{{{p_c} + {p_t}}}{2}\text{。}$ (13)
2 水下爆炸过程分析

 ${p_T} = A{\left( {1 - \frac{{\omega \eta }}{{{R_1}}}} \right)^{{e^{ - \frac{{{R_1}}}{\eta }}}}} + B{\left( {1 - \frac{{\omega \eta }}{{{R_2}}}} \right)^{ - \frac{{{R_2}}}{\eta }}}\text{，}$ (14)

 ${p_w} = \frac{{{\rho _0}{C^2}\mu \left[ {1 + \left( {1 - \frac{{{\gamma _0}}}{2}} \right)\mu - \frac{\alpha }{2}{\mu ^2}} \right]}}{{\left[ {1 - \left( {{S_l} - 1} \right)\mu - {S_2}\frac{{{\mu ^2}}}{{\mu + 1}} - {S_3}\frac{{{\mu ^3}}}{{{{\left( {\mu + 1} \right)}^2}}}} \right]}}\text{。}$ (15)

 ${p_L} = {c_0} + {c_1}\mu + {c_2}{\mu ^2} + {c_3}{\mu ^3}\text{。}$ (16)

 ${p_m} = \left( {\begin{array}{*{20}{l}} {\dfrac{{1.4}}{Z} + \dfrac{{0.56}}{{{Z^2}}} - \dfrac{{0.036}}{{{Z^3}}} + \dfrac{{0.000\;6}}{{{Z^4}}}}，&{0.05 \leqslant Z \leqslant 0.3}，\\ {\dfrac{{0.62}}{Z} - \dfrac{{0.032}}{{{Z^2}}} + \dfrac{{0.21}}{{{Z^3}}}}，&{0.3 \leqslant Z \leqslant 1}，\\ {\dfrac{{0.067}}{Z} + \dfrac{{0.405}}{{{Z^2}}} + \dfrac{{0.329}}{{{Z^3}}}}，&{1 \leqslant Z \leqslant 10} 。\end{array}} \right.$ (17)

 $Z = \frac{R}{{{W^{\frac{1}{3}}}}}\text{。}$ (18)

 图 2 1 500 mm处的压力随时间变化曲线 Fig. 2 Pressure versus time curve at 1 500 mm

 图 3 不同药量下1 500 mm处的压力最大值的变化情况 Fig. 3 Change of maximum pressure at 1 500 mm under different dosage
3 舰船水下抗爆性能分析

 $E = me\text{。}$ (19)

 ${E_k} = \int {\frac{1}{2}\rho {v^2}{\mathrm{d}}V} \text{，}$ (20)
 ${E_l} = {E_S} + {E_p}\text{。}$ (21)

 $E_S=\int_0^l\left(\int_V^{ }\sigma^c\cdot\varepsilon^{el}\mathrm{d}V\right)\mathrm{d}\tau\text{，}$ (22)
 $E_P=\int_0^l\left(\int_V^{ }\sigma^c\cdot\varepsilon^{pl}\mathrm{d}V\right)\mathrm{d}\pi\text{。}$ (23)

 图 4 层合板能量变化曲线 Fig. 4 Energy variation curve of laminated plates

 图 5 碳纤维复合材料层合板中心形变曲线 Fig. 5 Center deformation curve of carbon fiber composite laminates

 图 6 碳纤维复合材料层合板中心速度变化曲线 Fig. 6 Center velocity variation curve of carbon fiber composite laminates

 图 7 层合板剖面形变曲线 Fig. 7 Deformation curve of laminated plate profile
4 结　语

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