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 哈尔滨工程大学学报  2019, Vol. 40 Issue (8): 1406-1413  DOI: 10.11990/jheu.201807107 0

### 引用本文

ZHAO Shilun, CHEN Chaohe, JIANG Yong, et al. Fatigue crack growth assessment of semisubmersibles based on plate thickness diminution[J]. Journal of Harbin Engineering University, 2019, 40(8), 1406-1413. DOI: 10.11990/jheu.201807107.

### 文章历史

Fatigue crack growth assessment of semisubmersibles based on plate thickness diminution
ZHAO Shilun , CHEN Chaohe , JIANG Yong , SHEN Yijun
Naval Architecture and Ocean Engineering R & D Center of Guangdong Province, South China University of Technology, Guangzhou 510000, China
Abstract: This work focuses on the calculation and prediction of fatigue crack growth life. In this work, the fatigue assessment of existing cracks in the connection between the columns and braces of semisubmersibles is performed by considering plate thickness diminution. The appropriate coefficient of plate thickness diminution is selected in accordance with the code. Then, the exponential rate model is applied to calculate the remaining plate thickness after 20 years. The size of the remaining plate thickness is input to analyze the overall and local responses of the structure. The wave dispersion data and transfer function are used to obtain the discretized random fatigue load. Crack growth is calculated by applying a single curve model of crack growth rate. The failure assessment diagram (FAD) is added to the propagation cycle for safety evaluation. The calculated critical size and life of the crack are smaller than those of a plate with complete thickness, and the crack propagation life of a load with a single constant amplitude is smaller than that of a discrete random load. Results show that the rationality of the evaluation and calculation can be improved by accounting for plate thickness diminution in the analysis of the structural response of semisubmersibles and by using the discretized mode to address random fatigue load and FAD to evaluate crack growth.
Keywords: semisubmersible    crack growth    thickness diminution    fatigue analysis    failure assessment diagram (FAD)    fatigue crack propagation    growth rate    flaw assessment

1 疲劳扩展分析方法

1.1 疲劳载荷离散化处理

1) 针对不同工况，选取一系列浪向、波高与周期的组合，进行海洋工程结构物的整体有限元应力响应分析，计算其在单位波高下同一周期下不同相位的应力响应；

2) 提取同一周期下的最大应力σmx及最小应力σmn，计算传递函数的疲劳应力幅:

 $\Delta \sigma_{\text { unit }}=\operatorname{SCF}\left(\sigma_{m x}-\sigma_{m n}\right)$ (1)

3) 某工况下的疲劳扩展应力幅Δσi的大小可以利用波高Hi乘以传递函数的单位波高疲劳应力幅Δσunit:

 $\Delta \sigma_{i}=H_{i} \cdot \Delta \sigma_{\mathrm{unit}}$ (2)

 $n_{y i}=365 \times 24 \times 3600 \times p_{i} p_{j} / T_{z i}$ (3)

1.2 疲劳裂纹扩展率模型

 $\mathrm{d} a / \mathrm{d} N=A\left[\left(\Delta K_{R 0}\right)^{m}-\left(\Delta K_{R t h 0}\right)^{m}\right]$ (4)

 $\Delta K_{R 0}=M_{R} \Delta K$ (5)

1.3 疲劳扩展评估流程

1) 由于波浪载荷对于海洋工程结构物的作用是近似平衡随机的，因此进行疲劳载荷离化时忽略载荷加载次序的影响。

2) 疲劳扩展常数Am按照BS 7910的建议，可以选取单一裂纹扩展模型的参数，20 ℃海洋环境下，A=2.3×10-12m=3[9]

3) 应力强度因子通过式(6)计算为：

 $\Delta K=Y(a) \cdot \Delta \sigma \sqrt{\pi a}$ (6)

4) 由于材料应力-应变数据的缺乏，因此本文将选用Option 1评估曲线进行裂纹扩展的安全计算。

Option 1评估曲线表达式为：

 $\left\{ \begin{array}{l} f\left( {{L_r}} \right) = {\left( {1 + 0.5L_r^2} \right)^{ - 0.5}} \cdot \left[ {0.3 + 0.7\exp \left( { - \mu L_r^6} \right)} \right],\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{L_r} \le 1\\ f\left( {{L_r}} \right) = f(1) \cdot L_r^{(N - 1)/(2N)},1 < {L_r} \le {L_{r,\max }}\\ f\left( {{L_r}} \right) = 0,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{L_r} > {L_{r,\max }} \end{array} \right.$ (7)

5) 生产厂商提供的结构物材料的断裂韧性数据为裂纹尖端张开位移δC，可通过式(8)获得断裂韧性KC

 $\delta_{C}=K_{C}^{2} /\left(X \sigma_{y} E^{\prime}\right)$ (8)

2 结构板厚削减的分析方法

2.1 板厚削减程度与发生区域

 $t_{c}=(1-k) t_{\mathrm{gross}}$ (9)

2.2 板厚腐蚀速率模型

 ${d_p}\left( t \right) = \left\{ \begin{array}{l} 0,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;t \le {\tau _c}\\ {d_{p\infty }}\left( {1 - {{\rm{e}}^{ - \left( {t - {\tau _c}} \right)/{\tau _t}}}} \right),\;\;\;\;\;t > {\tau _c} \end{array} \right.$ (10)

 ${\tau _t} = {d_{p\infty }}/\tan \alpha$ (11)

 Download: 图 2 板厚腐蚀随时间变化指数曲线 Fig. 2 Curve of plate corrosive thickness versus time
3 半潜式平台疲劳裂纹扩展评估 3.1 平台结构建模与裂纹基本信息

3.2 板厚腐蚀余量计算

3.3 结构节点应力响应分析

 Download: 图 6 2种板厚下节点应力响应对比 Fig. 6 Comparison on stresses under two plate thicknesses

3.4 疲劳裂纹扩展评估

 ${\sigma _{hs}} = 0.5 \times \left( {3{\sigma _{0.5t}} - {\sigma _{1.5t}}} \right)$

3.5 结果分析与讨论

4 结论