【作者】 刘媛；

【导师】 吕运冰；

【作者基本信息】 武汉理工大学 ， 工程力学， 2004， 硕士

【摘要】 对于那些长期经受交变载荷作用的机械零件和工程构件，疲劳破坏是一种主要的破坏模式。疲劳学无论从工程上还是从理论意义上都是一门重要学科。而结构的疲劳又是一个受到大量不确定因素影响的极其复杂的现象。作为断裂力学的一个新的分支，概率断裂力学从概率和统计的角度对结构进行疲劳可靠性分析，充分考虑了疲劳破坏过程中出现的不确定因素，将影响疲劳裂纹扩展速率的各参数看作是服从某一种概率分布的随机变量。这是应用于结构疲劳安全性评估中的一种科学合理的新方法。 本文主要通过对亚临界裂纹扩展阶段各种随机因素的统计分析，找到了可以推广应用的，体现两材料系数之间具有强负相关性的统计相关式，并验证了在一定条件下，材料系数是影响裂纹扩展速率的主要因素。论文的架构主要依据了下列几个基础理论：数理统计、概率论、疲劳学以及断裂力学等。论文包括以下几个部分的内容： 论文首先阐述了疲劳断裂可靠性一般理论以及应用于疲劳可靠性分析中的概率统计基础理论。介绍了概率断裂力学的理论基础，及疲劳破坏过程中裂纹扩展的一般规律，以及影响疲劳裂纹扩展的因素。 其次，论述了疲劳裂纹扩展公式中各随机参数对疲劳扩展速率的影响。将以往文献中通常看作是确定性的材料系数随机化，通过对大量数据进行数理统计的分析，将疲劳裂纹扩展速率Paris公式中材料系数c和n视为随机变量，采用最小二乘法对c和n进行数值拟合，从而得到二者的统计相关性表达式。 然后，采用Pearson x~2分布拟合检验的方法，对n进行非参数假设检验分析，判定其概率分布形式，并根据c和n之间的统计相关式，推得c的概率分布形式。进一步分析了二者对疲劳亚临界裂纹扩展寿命的影响。 最后，应用概率断裂力学方法(PFMA)，对含初始裂纹体的直升机金属材料(铝合金)构件的疲劳裂纹扩展寿命进行可靠性分析。通过算例，将疲劳裂纹扩展速率公式中的各个参量全部随机化，并预测构件在给定可靠度下的疲劳裂纹扩展寿命。更多还原

【Abstract】 Fatigue failure is the main failure mode for the machinery parts and engineering structures under alternate loading over a long period of time. Fatigue is an important subject whether in theory or in engineering. It is the main work to predict fatigue life in fatigue damage Analysis. Usually the fracture theory are used in the fatigue crack propagation life estimation. After the Industrial Revolution in the early 19th century, the phenomenon of fatigue was taken into account and studied. A lot of research has been developed during the whole world, however, there are still many problems to be solved for researchers. Usually the fatigue life can be estimated by the determination method. However, the fatigue of structure is such a complicated phenomenon affected by many uncertainties that it is necessary to analyze the structural fatigue from the point of probability and statistics. Probabilistic Fracture Mechanics is a branch of fracture mechanics, so the various parameters affecting the fatigue propagationg are considered as randomized. It is an effective and new method to evaluate the structural fatigue reliability by Probabilistic Fracture Mechanics Approach (PFMA).In this paper, through the statistical analysis of the random factors in the stage of sub-critical propagation of cracks, the statistical correlation equations between the two material coefficients are obtained and can be generalized. Furthermore, it can be concluded that cracks propagation rate is influenced greatly by material coefficients in the condition considered in this study. The paper is based on the following foundational theories: statistics, probability analysis, fatigue and fracture mechanics. The work includes several parts as the following:Firstly, fatigue and fracture reliability theory is introduced, along with the statistics theory and its application in fatigue reliability analysis. The theory of probabilistic fracture mechanics is presented. Then the general rule and influential factors of cracks propagation occurred in fatigue failure are discussed.Secondly, the influences of the random parameters on fatigue propagation are discussed in the fatigue propagation Paris formula. In the existing literature, thematerial coefficients are simply considered as constants. Yet the material coefficients C and n in Paris formula are randomized in this study. Using the least square method, the statistical correlation between C and n is obtained through the numerical value collocation.Then, using Pearson x2 testing method, one of the coefficients n following the rule of distribution in statistics is tested. Furthermore, according to the the statistical correlation between C and n , the influence of both C and n on propagation life of fatigue cracks is discussed.Finally, applying Probabilistic Fracture Mechanics Approach (PFMA), the reliability analysis is carried out for helicopter metal material (aluminum alloy) structure having initial cracks. By an example, each parameters are randomized in the Paris formula, and the propagation life of fatigue of the structure is prognosticated on the presented reliability.更多还原