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1. 北京航空航天大学 航空科学与工程学院, 北京 100191;
2. 中国空间技术研究院, 北京 100094

Post-buckling damage analysis and fatigue life prediction of thin plate
XIAO Hao1, HU Weiping1 , ZHANG Miao2, MENG Qingchun1
1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. China Academy of Space Technology, Beijing 100094, China
Abstract:Post-buckling damage of thin plate under compressive load in plan was studied, and the fatigue life of plate was predicted by taking the coupling effect of buckling and fatigue damage into account. Firstly, the finite element model was established, and the critical buckling load and buckling mode were obtained by linear buckling analysis, then the large deflection theory was adopted, first order buckling mode was applied as the initial displacement perturbation, and the corresponding critical buckling load was determined by nonlinear bucking analysis of thin plate. Secondly, damage evolution equation of thin plate material under monotonic loading was established based on damage mechanics theory and method, and parameters of damage evolution were obtained by the parameter identification based on the material fatigue test results. Post-bucking damage was analyzed base on nonlinear bucking analysis results and damage evolution equations. Finally, the effect of fatigue load was took into consideration, finite element numerical method was used to solve the problem based on damage mechanics theory, considering the coupling effect of the damage caused by load each time and post-bucking stress strain fields analyze, the fatigue life of the structure was achieved by repeating iterative computations. The research provides a new method and a practical means for the analysis of post-buckling damage and fatigue life considering post-buckling damage of engineering structures.
Key words: plate     post-buckling     damage     fatigue life     nonlinear theory

1941年,von Kármán和Tsien[3]根据非线性大挠度理论,提出了板壳后屈曲分析的一般方法以及非线性屈曲理论.Donnell和Wan[4]于1950年将非线性大挠度分析推广到非完善圆柱薄壳.Koiter[5]用摄动法研究了弹性结构的初始后屈曲性态,导出了临界压力与缺陷参数之间的关系,并提出了初始缺陷敏感度的概念.1968年,Stein[6]提出了非线性前屈曲一致理论,解释了经典线性理论与实验之间差异的原因.非线性屈曲分析考虑了结构屈曲前的变形,计算结果更符合实际情况.

 图 1 结构几何模型Fig. 1 Geometry model of the structure

 图 2 屈曲载荷临界点Fig. 2 Critical point of buckling load

 图 3 失稳点离面位移随外载的变化曲线Fig. 3 Variation curve of deflection of instability point with external load
 图 4 失稳点的von Mises应力变化曲线Fig. 4 Variation curve of von Mises stress of instability point
3 板结构的后屈曲损伤分析

3.1节已经建立了材料在疲劳载荷作用下的损伤演化方程,方程中包含有β,mk,εth等材质参数,这些参数需要根据材料标准件的疲劳试验结果来确定.

 参数 泊松比 E/GPa σp0.2/MPa σb/MPa 数值 0.3 68 395 474 注:σp0.2—屈服应力；σb—极限应力.

 应力水平/MPa 196 221 270 中值疲劳寿命/次 326 500 19 900 99 900

 参数 mk σth/MPa β D0,1 数值 1.758 119 0.000 3 0.237

 图 5 KT=1,R=0.1时计算结果与实验点对比曲线Fig. 5 Comparison of experimental points and calculation results when KT=1,R=0.1

1) 利用ANSYS软件计算结构在某一载荷循环下的应力应变场.

2) 根据上一步计算得到的应力应变场,通过APDL语言对ANSYS软件进行二次开发,计算每个单元的损伤力学等效应力.

3) 利用APDL语言,在ANSYS软件中计算每个单元在ΔN次载荷循环之后,损伤度的增量:

4) 由上述计算得到的各个单元的损伤度可知每个单元的等效弹性模量的变化量,在ANSYS软件中重新赋予各个单元弹性模量,在上次计算结果基础上,进行下一个加载循环的应力应变分析.

5) 重复步骤2)~步骤4)的过程,直到某一单元损伤度达到或超过1,此时的ΔN的累积值即为疲劳裂纹萌生寿命.

 图 6 损伤力学有限元法计算流程图Fig. 6 Calculation flow chart of damage mechanics with finite element method
4.2 计算结果

 图 7 不同损伤度下结构失稳点位移变化曲线对比Fig. 7 Comparisons of deflection changing curves of instability points in different damage degrees

 图 8 裂纹萌生寿命随几何缺陷幅值比的变化曲线Fig. 8 Changing curve of crack initiation life with different geometric imperfection amplitude ratios

1) 首先对板进行了线性屈曲分析,得到了屈曲临界载荷以及屈曲位移模态,为后续的非线性屈曲分析提供了位移扰动形式.

2) 以线性屈曲分析得到的一阶屈曲位移模态作为板的初始几何缺陷,对板进行非线性屈曲分析,得到了板的非线性屈曲载荷,其值要低于特征值屈曲分析得到的屈曲临界载荷.

3) 建立了板后屈曲损伤分析模型,并根据板材料的标准件疲劳试验结果确定损伤演化方程中的各材质参数.

4) 建立了考虑后屈曲过程的板的疲劳寿命分析方法,通过损伤力学-有限元数值解法,可以考虑加载循环过程中板的后屈曲与疲劳损伤的耦合作用.

5) 分析初始几何缺陷的大小对板裂纹萌生寿命的影响,结果表明,初始几何缺陷对结构的疲劳寿命有很明显影响,因此,一方面在制造过程中应尽量提高加工精度,减小几何缺陷;另一方面,在预估结构疲劳寿命时应根据实际测量结果正确估计几何缺陷的大小,以便给出更符合实际情况的寿命预估结果.

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#### 文章信息

XIAO Hao, HU Weiping, ZHANG Miao, MENG Qingchun

Post-buckling damage analysis and fatigue life prediction of thin plate

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(3): 523-529.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0174