﻿ 双轴非比例低周疲劳载荷下船体裂纹板累积塑性数值分析
 舰船科学技术  2022, Vol. 44 Issue (10): 43-48    DOI: 10.3404/j.issn.1672-7649.2022.10.009 PDF

Numerical analysis of accumulative plasticity of hull cracked plate subjected to biaxial non-proportional low-cycle fatigue loading
DU Bo, QIU Sheng-lin, DENG Jun-lin, DONG Da-wei, LU Rui-tao, HOU Rui-han
School of Mechanical and Marine Engineering, Beibu Gulf University, Qinzhou 535011, China
Abstract: The analysis of hull stress under uniaxial load can not satisfy the existing problems in the current marine engineering. Therefore, the biaxial non-proportional low-cycle fatigue loading considering accumulative plastic failure with hull crack plate under theory analysis in this paper. The effects of different phase difference, stress ratio and biaxial ratio on accumulative plastic damage was explored by numerical analysis. It provides a reasonable basis for accurate assessment the effect of accumulative plastic on the crack growth behavior of hull plates under non-proportional biaxial low-cycle fatigue.
Key words: hull cracked plate     biaxial low-cycle fatigue     non-proportional load     accumulative plasticity     numerical analysis
0 引　言

1 理论分析

 $\Delta {\varepsilon _{ij}} = \frac{{1 + \upsilon }}{E}\Delta {\sigma _{ij}} - \frac{\upsilon }{E}\Delta {\sigma _{kk}}{\delta _{ij}} + \frac{3}{2}\frac{{2f(\Delta {\sigma _{eq}}/2)}}{{\Delta {\sigma _{eq}}}}{S_{ij}}，$ (1)

 $\left\{ {\begin{array}{*{20}{c}} {\Delta {S_{ij}}{\text{ = }}\Delta {\sigma _{ij}} - \dfrac{1}{3}\Delta {\sigma _{kk}}{\delta _{ij}}} ，\\ {\Delta {\sigma _{eq}}{\text{ = }}\sqrt {\dfrac{3}{2}\Delta {S_{ij}}\Delta {S_{ij}}} } 。\end{array}} \right.$ (2)

 $d{\varepsilon _{p,n + 1}} = {\left( {\frac{{{f_1}}}{Z}} \right)^n} = \sqrt {\frac{2}{3}d\varepsilon _{n + 1}^p:d\varepsilon _{n + 1}^p} 。$ (3)

 $\Delta {\varepsilon _{p,n + 1}} = = \sum\limits_{i = 1}^{n + 1} {d{\varepsilon _{p,n + 1}}} = {\sum\limits_i^{n + 1} {\left\langle {\frac{{{f_1}}}{Z}} \right\rangle } ^n} = \sum\limits_i^{n + 1} {\sqrt {\frac{2}{3}d\varepsilon _i^p:d\varepsilon _i^p} }，$ (4)

 $\begin{split}\Delta {\varepsilon _{p,eq}} =& \frac{{\Delta {\varepsilon _{p,x}}}}{{\left( {1 - {\nu ^2}} \right)}}\times\\ &\sqrt {\left[ {1 + {\nu ^2} - \nu } \right]\left[ {1 + {{\left( {\frac{{\Delta {\varepsilon _{p,y}}}}{{\Delta {\varepsilon _p}_{,x}}}} \right)}^2}} \right] - \left[ {1 + {\nu ^2} - 4\nu } \right]\frac{{\Delta {\varepsilon _{p,y}}}}{{\Delta {\varepsilon _{p,x}}}}} \end{split}。$ (5)

2 数值分析 2.1 数值模型

Chaboche本构模型能够较好地表征结构构件在裂纹尖端区域的累积塑性现象，经过一系列有限元计算及修正优化，确定Chaboche模型系数如表1所示。

 图 1 裂纹板数值计算模型 Fig. 1 Numerical calculation model of cracked plate
2.2 数值分析结果与讨论 2.2.1 裂纹尖端应力应变场

2.2.1.1 相位差φ的影响

 图 2 不同相位差下载荷路径 Fig. 2 Load paths under different phase differences

 图 3 不同相位差作用下裂纹板应力应变迟滞回线 Fig. 3 Stress-strain hysteresis loop of cracked plate under different phase differences
2.2.1.2 双轴应力比λ的影响

 图 4 不同双轴应力比作用下的应力应变迟滞回线 Fig. 4 Stress-strain hysteresis loop under different biaxial stress ratios
2.2.1.3 应力比R的影响

 图 5 不同应力比作用下的应力应变迟滞回线 Fig. 5 Stress-strain hysteresis loop under different stress ratios

2.2.2 裂纹尖端应力应变云图

 图 6 不同相位差下裂纹尖端应力应变云图 Fig. 6 Stress-strain contours of crack tip at different phase differences
2.2.3 低周疲劳与累积塑性相互作用

 图 7 不同非比例低周疲劳载荷下累积塑性应变与循环次数关系曲线 Fig. 7 Relationship between accumulative plastic strain and cycle times under different non-proportional low-cycle fatigue loads
2.2.4 双轴累积塑性变形分析

 图 8 不同非比例低周疲劳载荷条件下裂纹板塑性应变累积变化关系曲线 Fig. 8 Accumulative variation curves of plastic strain of cracked plates under different non-proportional low-cycle fatigue loads

 图 9 不同非比例低周疲劳载荷条件下裂纹板塑性应变累积率变化关系曲线 Fig. 9 Variation curves of plastic strain accumulation rates of cracked plates under different non-proportional low-cycle fatigue loads

3 结　语

1）通过数值仿真计算不同相位差φ、双轴应力比λ和应力比R对双轴非比例载荷作用下应力应变迟滞回线的影响。可以发现在不同应力比和相位差下，迟滞回线应变水平随着变量的增加而向单调增大，应力水平则单调减小。对于不同双轴应力比，随着双轴应力比增加，应力应变水平都随变量增大而减小。

2）在双轴非比例载荷下低周疲劳累积塑性数值计算中，十字型模型的累积塑性随着循环周期的增加而增加，其累积塑性应变由初期变化后，稳定至非零值，并且，不同的相位差、双轴应力比和应力比对累积塑性应变都有影响。

3）在双轴应力比及相位差恒定的情况下，随着应力比R的增加，累积塑性应变及累积塑性应变率单调增加；而当双轴应力比不同时，可以发现累积塑性应变先增大后缓慢减小，并且裂纹尖端的累积塑性现象与主应力密切相关。此外，随着相位差的增加对累积塑性应变值也有一定影响。

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