﻿ 弯曲塑性变形下含表面裂纹船体板CTOD研究
 舰船科学技术  2018, Vol. 40 Issue (6): 35-39 PDF

Research on CTOD of hull plate with surface crack subjected to large plastic bending
DU Bo, DENG Jun-lin, XIE Ji-gang, WU Guan-hua
Department of Naval Architecture and Engineering, Qinzhou University, Qinzhou 535011, China
Abstract: Based on ship under the situation of hogging and sagging, hull plate subjected to large plastic bending, three-dimensional surface crack depth direction crack tip CTOD of hull plate and the relationship between the equivalent plastic strain of the outermost fibers of the hull plate is studied.And using the method of finite element analysis discussed different influence factors on the crack tip of CTOD, such as shape factor of crack, crack depth and thickness under pure bending, and based on the data of finite element simulation, puts forward the strain-based CTOD estimate formula of hull plate surface crack subjected to large plastic bending.
Key words: hull plate     large plastic bending     surface crack     CTOD
0 引　言

 $J = 2{F^2}\pi a{\sigma _{unc}}{\varepsilon _{unc}}\text{。}$ (1)

 $\frac{J}{{{\sigma _y}t}} = {f_1}{\varepsilon _{unc}} + {f_2}\text{，}$ (2)

Shih[9]推导出CTOD与J积分的单一的对应关系，并对海洋工程中的管道的断裂评估提出了基于测量CTOD的方法。所以本文基于J积分与CTOD的对应关系：

 $J \sim CTOD\text{，}$ (3)

 $CTOD \sim {\varepsilon _{unc}}\text{。}$ (4)

1 有限元分析 1.1 材料模型

 $\sigma = \left\{ {\begin{array}{*{20}{c}}{E\varepsilon \;\;\;\;\;\;\;\;\;\;\varepsilon \leqslant {\varepsilon _Y}}\text{，}\\{{\sigma _y}{{\left( {\displaystyle\frac{\varepsilon }{{{\varepsilon _Y}}}} \right)}^n}\;\;\;\;\varepsilon > {\varepsilon _Y}}\text{。}\end{array}} \right.$ (5)

1.2 几何模型有限元模型建立

 图 1 含半椭圆表面裂纹钢板示意图 Fig. 1 A steel plate with semi elliptical surface crack

 图 2 有限元模型 Fig. 2 The mesh model
1.3 弯曲的施加

Nourpanah N[8]提出当最外层表面的应变达到3%时，构件不含裂纹的塑性应变 ${\varepsilon _{uncp}}$ 处于非常大和危险的水平，又由于表面裂纹属于三维问题，故本文所取应变为等效应变，如下式：

 ${\varepsilon _{uncp}} = \sqrt {\frac{2}{3}({\varepsilon ^2}_{pL} + {\varepsilon ^2}_{pW} + {\varepsilon ^2}_{pt})}\text{。}$ (6)

 图 3 两种弯曲施加方式的对比图 Fig. 3 The comparison of two kinds of bending methods

 图 4 运动约束与施加弯矩转角方向 Fig. 4 The motion constraint and the direction of bending moment

 图 5 CTOD的示意图 Fig. 5 The schematic diagram of CTOD

 ${R_x} = \frac{{2{\varepsilon _{unc}}L}}{t}\text{。}$ (7)
2 结果及讨论

 图 6 裂纹形状因子c/a对CTOD的影响 Fig. 6 The effect of crack shape factor c/a on CTOD

 图 7 裂纹深度对CTOD的影响 Fig. 7 The effect of crack depth on CTOD
2.1 裂纹形状因子c/a的影响

n=10，当裂纹深度给定为a=5 mm，板厚为t=20 mm时，图6中可以看出CTOD随着表面裂纹形状因子的c/a的增大而随之增大，并在同一塑性应变时，CTOD随裂纹形状因子的增长幅度逐渐降低。随着形状因子c/a和塑性应变水平的不断增长，裂纹的CTOD处于非常危险的水平。

2.2 裂纹深度a的影响

2.3 裂纹板厚度t的影响

 图 8 板厚对CTOD的影响 Fig. 8 The effect of plate thickness on CTOD

 图 9 硬化指数对CTOD的影响 Fig. 9 The effect of hardening exponent on CTOD
2.4 硬化指数n的影响

3 塑性弯曲下表面裂纹板的CTOD评估方程

 $\begin{split}\frac{{CTOD}}{a} =& {\eta _0} + {\eta _1}\frac{a}{t} + {\eta _2}\frac{a}{c} + {\eta _3}{\varepsilon _{unc}} + {\eta _4}\frac{a}{t} \cdot \frac{a}{c}+ \\& {\eta _5}\frac{a}{t} \cdot {\varepsilon _{unc}}+ {\eta _6}\frac{a}{c} \cdot {\varepsilon _{unc}} + {\eta _7}{\left( {\frac{a}{t}} \right)^2} +\\& {\eta _8}{\left( {\frac{a}{c}} \right)^2} + {\eta _9}\varepsilon _{unc}^2\text{，}\end{split}$ (8)

 图 10 有限元计算与公式预测对比值 Fig. 10 Comparison between the FE calculation and the formula prediction

 $CTOD \leqslant {\delta _{critical}}\text{。}$

4 结　语

1）在各种影响因素的作用下，三维表面裂纹裂尖处CTOD的值随着应变的增加逐渐增加，但是增长趋势并趋于稳定。其中随着裂纹形状因子c/a的增大，CTOD在同一应变水平时逐步增大，且增长速率减小。随着裂纹深度a的增加，裂尖处CTOD在同一应变水平下也逐步增大，并且增长速率逐渐增大。

2）随着板厚的增加，对裂尖处CTOD的影响在某一应变水平可以忽略，并且在小于该应变大小时，板厚增加对CTOD呈现正作用，在大于该值时，则反之。此外硬化指数对CTOD的影响不可忽略，在n=25的硬化指数下，CTOD的值均大于n=10的情况。

3）在综合各种材料和半椭圆表面裂纹自身的形状因素的影响，本文给出了一个基于有限元模拟的CTOD评估公式。这为评估含表面裂纹板的断裂评估提供了一种新的思路。

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