A Probabilistic Approach to the Fatigue Crack Propagation under Non-stationary Random Loading

疲劳裂纹扩展有时会导致结构的灾难性破坏。为了对结构进行安全性评估，必须对服役载荷下的疲劳裂纹扩展进行估算。在大多数情况下，实际使用载荷是随机的，必须建立随机载荷下疲劳裂纹扩展的估计方法，从实际应用角度来看，最好利用简单、常规的等幅加载试验获得的数据来预测随机载荷下真实的结构的疲劳行为。近年来，基于Elber提出的“裂纹闭合”概念，人们对随机载荷和常幅载荷下的疲劳行为之间的关系进行了大量的研究。在这些研究中，由于纯随机载荷的复杂性，没有采用纯随机载荷，而且两者之间的关系也没有得到明确，因此，本研究进行了随机载荷下的疲劳裂纹扩展试验，并与常幅载荷试验进行了比较。在微机辅助下，自动记录了试样在长周期疲劳循环过程中的裂纹闭合现象。结果表明，考虑裂纹闭合是研究疲劳裂纹扩展的必要条件，随机载荷下的疲劳行为可以由等幅试验来预测。在此基础上，对多个试件进行了等应力幅下的疲劳试验。利用基于马尔可夫链概念的Bogdanoff概率模型（B模型）对结果进行了分析。结果表明，B模型有可能成为研究疲劳裂纹扩展统计特性的有用工具。

Crack extention by fatigue may sometimes cause a catastrophic failure of structure. For the safety assessment of structure, it is indispensable to estimate fatigue crack growth under service loading. In most cases actual service load are random, and the estimating methor for fatigue crack growth under random loading must be setablished.For practical use, it is very preferable that the prediction of fatigue behavior in real structures under random loading could be made using the data obtained by constant amplitude loading test which is simple and routine test. Many investigations have been carried out in order to clarify the releationship between fatigue behaviors under random loading and constant amplitude loading, recently based on the concept of "crack closure" proposed by Elber. In these investigations, however, pure random load has not been applied because of its complexity, and the relationship nas not been clarified yet.In this study, fatigue crack propagation tests under random loading are carried out as well as constant amplitude loading tests for comparison. Crack closure phenomna of the specimens are automatically recorded over a long period of fatigue cycles aided by micro-computer system. It is shown that consideration of crack closure is essential for examination of fatigue crack growth and fatigue behavior under random loading may be predicted from constant amplitude test. Furthermore, fatigue tests are carried out under the condition of the same constant stress amplitude on many specimens. The results are analyzed using Bogdanoff's probabilistic model (B model) based on Markov chain concept. It is shown that the B model has the possibility for proveding a useful tool for examining the statistical properties of fatigus crack growth.