﻿ 细观尺度下船舶轴系三维编织复合材料剩余强度预测
 舰船科学技术  2023, Vol. 45 Issue (23): 62-66    DOI: 10.3404/j.issn.1672-7649.2023.23.011 PDF

1. 中国船舶集团有限公司第七一一研究所，上海 201108;
2. 江苏科技大学 能动学院，江苏 镇江 212003

Prediction of residual strength of 3D braided composites for marine shafting at mesoscale
MA Bing-jie1, ZHU He2, XING Xue1, CHEN Bo2
1. Shanghai Marine Diesel Engine Research Institute, Shanghai 201108, China;
2. School of Energy and Power, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: In order to reveal the evolution law of residual strength of 3D braided composites ship shafting after fatigue loading, the fatigue failure and static tensile failure conditions of each component of 3D braided composite were introduced based on the progressive damage method at the meso-scale, and the changes of fiber bundle structure of 3D braided composite during fatigue loading were considered. A prediction model of residual strength of 3D braided composites after fatigue loading was established. The tensile test of 3D braided composite was carried out after tensile fatigue, and the residual strength test data with cycles of 25%, 50% and 75% were obtained. The calculation results of the prediction model show that the error between the predicted value and the test value of the residual strength is less than 10%, and the error between the actual measured size and the calculated size of the test part is less than 5% under the corresponding number of cycles. The prediction results have a high precision, which shows the validity of the prediction model.
Key words: ship shafting     3D braided     micromechanics     fatigue damage     residual strength
0 引　言

1 编织角-循环数模型及其参数确认

 $\frac{{\gamma \left( n \right)}}{{\gamma \left( 0 \right)}} = {\left[ {a\left( {1 - {e^{ - n}}} \right) + 1} \right]^b}。$ (1)

2 单胞模型 2.1 几何模型

 图 1 内部单胞几何模型 Fig. 1 Geometric model of inner cell
2.2 周期性边界条件设置

 $u_i^{j + } - u_i^{j - } = \bar {{\varepsilon _{ik}}} \left( {x_k^{j + } - x_k^{j - }} \right) = \bar {{\varepsilon _{ik}}} \Delta x_k^j。$ (2)

 $\left\{ \begin{array}{l} {U_{{F_b}}} - {U_{{E_b}}} = 0，\\ {V_{{F_b}}} - {V_{{E_b}}} = 0 ，\\ {W_{{F_b}}} - {W_{{E_b}}} = \bar \varepsilon \left( A \right) \times h，\\ {U_{{B_b}}}-{U_{{A_b}}}=\bar \varepsilon \left( A \right) \times 8{b_1}，\\ {V_{{B_b}}} - {V_{{A_b}}} = 0 ，\\ {W_{{B_b}}} - {W_{{A_b}}} = 0 ，\\ {U_{{C_b}}} - {U_{{D_b}}} = 0 ，\\ {V_{{C_b}}}-{V_{{D_b}}}=\bar \varepsilon \left( A \right) \times 8{b_1}，\\ {W_{{C_b}}} - {W_{{D_b}}} = 0 ，\\ {U_A} = {V_A} = {W_A} = 0 ，\\ {V_B} = {W_B} = {U_E} = {V_E} = {U_D} = {W_D} = 0 。\end{array} \right.$ (3)

2.3 纤维束/基体脱黏的模拟

2.4 疲劳分析中的失效判定 2.4.1 疲劳过程中的纤维束失效判定

 ${\left[ {\frac{{{\sigma _{11}}}}{{{X_{11}}}}} \right]^2} + \alpha \left[ {\frac{{{\sigma _{12}}}}{{{S_{12}}}}} \right] + \alpha \left[ {\frac{{{\sigma _{13}}}}{{{S_{13}}}}} \right] \geqslant 1 ，$ (4)

 ${\left[ {\frac{{{\sigma _{22}} + {\sigma _{33}}}}{{{Y_{22}}}}} \right]^2} + \frac{{\left( {\sigma _{23}^2 - {\sigma _2}{\sigma _3}} \right)}}{{{S_{23}}^2}} + {\left[ {\frac{{{\sigma _{12}}}}{{{S_{12}}}}} \right]^2} + {\left[ {\frac{{{\sigma _{13}}}}{{{S_{13}}}}} \right]^2} \geqslant 1。$ (5)

2.5 疲劳载荷下试验件最终破坏判定准则

1）单胞内纤维束沿纵向破坏的有限单元比例超过50%；

2）断裂损伤贯穿整个单胞截面；

3）单胞内应力随应变的增加开始下降。

2.6 三维编织复合材料疲劳预测流程

 图 2 三维编织复合材料进行疲劳后剩余强度预测计算流程图 Fig. 2 Flow diagram for predicting residual strength of 3D braided composites after fatigue

1）通过输入几何和工艺参数得到三维编织复合材料几何模型，进行网格划分、组分材料的定义及周期性边界条件的加载，完成周期性单胞的建模工作；

2）通过二分法调整载荷，使单胞平均应力达到疲劳最大应力水平，然后在次应力下进行应力分析，采用应力水平、循环数的三维Hashin疲劳失效准则对单元进行失效判定，检查单元是否发生破坏，若所有单元均无破坏，则判定是否达到最大循环数，若达到循环数，则停止计算，若没有达到循环数，则增加循环数增量，进行材料的退化，并进行单胞几何修正，重新进行单元划分、材料定义、载荷施加、应力分析；若单元发生失效，则对单元进行相应刚度退化，如此循环计算，直至到达材料最终失效。

3 模型验证 3.1 编织角-循环数数学模型验证

 $\frac{{\gamma \left( {{n \mathord{\left/ {\vphantom {n N}} \right. } N}} \right)}}{{\gamma \left( 0 \right)}} = {\left[ { - 0.452\left( {1 - {e^{ - \frac{n}{N}}}} \right) + 1} \right]^{0.183}}。$ (6)

 图 3 编织角随循环数的变化 Fig. 3 The change of braided angle with the number of cycles

3.2 三维编织复合材料疲劳剩余强度模型验证

 图 4 循环数1001后纤维的失效状态 Fig. 4 Failure status of the fiber after cycle number 1001

 图 5 循环数为2001失效状态 Fig. 5 Failure status of the fiber after cycle number 2001

 图 6 循环数为1001失效状态 Fig. 6 Failure status of the matrix after cycle number 1001

 图 7 循环数为2001失效状态 Fig. 7 Failure status of the matrix after cycle number 2001

4 结　语

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