基于混沌分形理论的金属疲劳损伤过程的特征分析

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摘要为了有效地分析金属疲劳损伤过程中裂纹扩展与演化的特征，提出利用混沌分形理论对蕴含疲劳裂纹扩展规律的超声非线性输出信号进行分析，用Lyapunov指数、K熵、关联维数等特征量对金属疲劳损伤过程的特性进行表征和评价。采用RITEC公司的RAM-5000系统获得具有不同疲劳损伤程度试件的超声非线性输出信号，计算疲劳过程中的Lyapunov指数、K熵、关联维数。分析结果表明金属疲劳损伤过程中超声非线性输出信号具有混沌特性；Lyapunov指数、关联维数、K熵等特征值随疲劳循环次数单调递增，当宏观裂纹出现后趋于饱和，说明疲劳损伤过程中试件内部的复杂程度和混沌特征逐渐增强；由疲劳过程中微裂纹的演化规律可知，混沌分形特征值可以有效地表征试件在疲劳过程中裂纹的变化规律和群体性行为。因此混沌分形理论可以有效地分析金属疲劳损伤过程中裂纹扩展与演化的特征，根据混沌分形特征值—疲劳循环次数的关系，为试件的疲劳寿命预测提供了一种新的分析方法。

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关键词 ：非线性超声, 疲劳损伤, Lyapunov指数, 关联维数, K熵

Abstract：To effectively extract the characteristics of crack extension and evolution in the process of fatigue damage, the chaos and fractal theory were presented to analyze the output signal of receiver in nonlinear ultrasonic system, the Lyapunov exponent, correlation dimension and K entropy evaluated the nonlinear characteristics of fatigue damage. The ultrasonic nonlinear output signals were gathered by the RAM-5000 system, chaos and fractal theory were used to analyze them and the Lyapunov exponent, correlation dimension and K entropy were calculated. The study showed that the ultrasonic nonlinear output signal of metal fatigue damage had chaotic characters; The Lyapunov exponent, correlation dimension and K entropy monotonously increased with fatigue damage, and reached stable when the macro cracks appeared. Chaotic characteristic values could effectively characterize the evolution of crack and fully reveal the nonlinearity of metal fatigue. Therefore the chaos and fractal theory could effectively extract the characteristics of crack extension and evolution in the process of fatigue damage, this provided a new analysis method for the fatigue life analysis based on the relationship between chaotic characteristic values and fatigue life.

Key words： nonlinear ultrasonic fatigue damage lyapunov exponent correlation dimension k entropy

收稿日期: 2016-05-17 出版日期: 2017-10-28

引用本文:

张玉华1,李欣欣2,黄振峰2,毛汉领2. 基于混沌分形理论的金属疲劳损伤过程的特征分析[J]. 振动与冲击, 2017, 36(21): 72-76.
ZHANG Yuhua1 LI Xinxin2 HUANG Zhenfeng2 MAO Hanling2. Feature analysis of metal fatigue damage process based on chaos and fractal theory. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(21): 72-76.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2017/V36/I21/72

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