【作者】 王坤茜；

【导师】 徐人平；

【作者基本信息】 昆明理工大学 ， 机械设计及理论， 2012， 博士

【摘要】 疲劳裂纹扩展是疲劳断裂研究中的重要内容,疲劳裂纹扩展速率da/dN一ΔK是工程构件损伤容限分析的重要依据,也是金属材料的主要力学性能之一。疲劳裂纹扩展速率da/dN表达式的研究受到重视,国内外提出了许多da/dN表达式,目前在工程中应用最为广泛的方法是1963年由Paris和Erdogan在试验基础上提出的疲劳裂纹扩展公式——Paris公式,它建立了应力强度因子范围△K和裂纹扩展速率da/dN之间的关系,是当今工程应用中预测疲劳裂纹扩展寿命理论的基础。利用Paris公式分析、预测剩余寿命,有着极为重要的现实意义。在试验研究和解决工程实际问题当中,Paris公式已经有了很大的发展,许多学者对该公式的具体形式做了大量修正工作,但未对其参数c和n的物理本质进行深入研究和探讨。本论文以Paris公式为出发点,研究应力比R对裂纹扩展的影响规律,旨在揭示Paris公式的本质,建立更有效的数学模型,全面系统地研究不同应力下疲劳断裂可靠性问题,以期补充、完善现有的可靠性理论,并用于解决实际问题。本论文在查阅国内外相关文献资料和试验的基础上,以Paris公式为切入点,围绕应力比R对裂纹扩展的的影响展开以下研究工作：首先研究了不同应力比下疲劳断裂的基本规律。通过ADB610钢和30CrMnSiNi2A钢在不同应力比R工况下的疲劳裂纹扩展试验发现应力比R对疲劳寿命和裂纹扩展速率da/dN有着重要影响。虽然从Paris公式的表达式中未直接看到与应力比R有关的参数,但通过研究表明Paris公式的参数C和n与应力比R具有相关性,从应力比R角度指出了参数C和n与应力比R的隐性关系,得出了Paris公式参数C和n随应力比R变化的规律：C(1gC)随着应力比R的增加而减小,n随着应力比R的增加而增大。其次研究了应力比影响下的疲劳断裂可靠性的数学模型。考虑到应力比R对疲劳裂纹扩展的影响规律以及疲劳裂纹扩展的分散性,在Paris公式基础上,建立了一种描述随机疲劳裂纹扩展的R-p-da/dN一ΔK概率模型,该概率模型能定量地表明疲劳裂纹扩展速率da/dN与各主要参数(△K,应力比R)的关系,将应力比R对Paris公式中参数C和n的影响显性化。根据线性回归理论,提出了将非线性关系的数据转化成线性关系进行数据处理的方案,推导出基于Paris公式形式的应力比影响下的疲劳断裂可靠性数学模型。为在类似条件下的材料的疲劳寿命评估提供理论依据,满足工程实际中的应用需求。然后分析研究了不同应力比下的疲劳断裂可靠性的几何图形。两元变量(ΔK,应力比R)的R-p-da/dN-ΔK概率模型,其图形表达不再是简单的二维线形问题,而是三维曲面问题。R-p-da/dN-ΔK概率模型从函数图形角度来看是一系列的曲面族。通过R-p-da/dN-ΔK曲面族可直观分析、研究可靠度p、应力比R和裂纹扩展速率da/dN三者之间的关系。R-p-da/dN-ΔK曲面族在一定的条件下,可退化为概率裂纹扩展p-da/dN-ΔK曲线,为工程概率损伤容限设计和安全可靠性评估作参考。然后还研究了应力比影响下的疲劳断裂可靠性的可信度。考虑数据分散性规律和试样数量对概率评价的影响,将可靠度p和置信度γ相融合,提出R-p-γ-da/dN-△K概率置信度模型,并运用非线性函数线性化原理给出概率置信度模型参数的求解方法。该模型表征研究工作的可信程度。最后研究了疲劳断裂可靠性的计算方法。a-N数据拟合的计算方法是获得高精度p-da/dN-ΔK曲线的重要前提。本论文采用考虑整套数据的随机特性的a-N数据拟合方法,提出统一a-N递增多项式拟合法,为研究不同应力比R下的疲劳断裂可靠性提供科学的依据。并给出两种获得p-da/dN数据的处理方法,指出：基于da/dN数据的统计分析法在理论上较合理；基于p-a-N的求导计算法在应用上较方便；这两种方法相当于把裂纹扩展过程视为同一分布而参数变化的离散型随机过程,二者的计算结果从统计的角度分析无显著性差异。本论文最大的创新点在于：指出了Paris公式具有完整表征疲劳裂纹扩展中应力比的影响的功能,并且在Paris公式的基础上,全面系统地研究了不同应力比R下疲劳断裂的基本规律,裂纹扩展可靠性的数学模型、几何图形以及置信度问题,丰富和完善了Paris公式的内涵,拓展了Paris公式的应用。具体的创新点包括：(1)不同应力比下疲劳断裂的基本规律方面：指出了Paris公式具有完整表征疲劳裂纹扩展中应力比R影响的功能,得出Paris公式的两个重要参数C和n在裂纹扩展中随应力比R变化而变化的规律：C随应力比R的增加而减小,n随应力比R的增加而增大。(2)不同应力比下疲劳断裂可靠性的数学模型方面：根据非线性问题线性化原理,提出将非线性关系的数据转化成线性关系的数据处理方案,推导出基于Paris公式形式的考虑应力比影响的疲劳裂纹扩展可靠性数学模型。(3)不同应力比下疲劳断裂可靠性的几何图形方面：给出了应力比R影响下的R-p-da/dN一ΔK曲面族,进一步讨论了R-p-da/dN一ΔK曲面族的工程应用,并分析了该曲面族的适用范围。(4)不同应力比下疲劳断裂可靠性的可信度方面：为了确保整个研究工作的可信程度,提出了应讨论不同应力比下疲劳断裂可靠性研究的置信度问题,建立了考虑置信度γ的R-p-γ-da/dN一ΔK概率模型,给出了其参数确定的方法。(5)在疲劳断裂可靠性的计算方法方面：提出统一a-N递增多项式拟合法以获得高精度的a-N拟合数据,并给出两种获得p-da/dN数据的处理方法,指出：基于da/dN数据的统计分析法在理论上较合理；基于p-a-N的求导计算法在应用上较方便；这两种方法相当于把裂纹扩展过程视为同一分布而参数变化的离散型随机过程,二者的计算结果从统计的角度分析无显著性差异。更多还原

【Abstract】 The fatigue crack propagation is an important part of fatigue fracture. The fatigue crack growth rate da/dN-ΔK curve is the important basis of fatigue damage tolerate design and safety assessment for structures, it is one of the fundamental material property for metal structures. The research of the expression of fatigue crack growth rate da/dN is taken seriously, a lot of mechanics models are put forward by experts. The most widely used method in engineering is Paris formula, which is the basis for the theory of crack growth life. Paris formula has very important practical significance for analysis, forecast remaining life. Among the experimental study, Paris formula has been greatly developed, many scholars have done a lot of correction for the formula’s specific form. But its parameters C and n have not been study and exploration deeply in physical nature.In this thesis, take the Paris formula as a starting point to study the law of the influence of stress ratio on the crack propagation. The study purpose is to reveal the essence of the Paris formula, create a more effective mathematical model, study systematically the probability problems of fatigue fracture under the stress ratio, in order to supplement and improve the probability theory to solve practical problems.Based on relevant literature information and test data,take the Paris formula as the starting point, around the influence of stress ratio on crack propagation, then expand the following work.Firstly the basic law of the effect of stress ratio on fatigue fracture is studied. By the fatigue crack propagation tests of ADB610steel and30CrMnSiNi2A steel under different stress ratio, the fatigue life and crack growth rate have significantly difference with the change of stress ratio in the same conditions. Stress ratio is not seen directly from the Paris formula expression, but studies have shown that the Paris formula parameters C and n correlate with stress ratio. It reveals the parameter C and n have the recessive relationship with stress ratio and proof the law of the Paris formula parameters C and n with the change of stress ratio:C will decrease with the increase of stress ratio, n will increase with the increase of stress ratio.Secondly, the mathematical model of probability of the fatigue fracture under different stress ratio is studied. In consideration of the evident effects of stress ratio on fatigue crack growth rate and the scatter of fatigue crack growth. Based on Paris formula, a probabilistic model is established to describe the random fatigue crack propagation, the probability model can quantitatively show that the relationship between the fatigue crack growth rate and the main parameters (ΔK and stress ratio). It can externalize the effect of the stress ratio on Paris formula parameters C and n. Using linear regression theory,the data processing method of turning non-linear test data into linear data is put forward, and ultimately deduced the mathematical mode based on Paris formula.Provide a theoretical basis for the assessment of the fatigue life of the material under similar conditions, to meet the application requirements in engineering practice.Thirdly, geometry of the fatigue fracture probability under different stress ratio is analyzed. Based on Paris formula, the graphical representation of R-p-da/dN-ΔA: probabilistic model is no longer a simple two-dimensional curve, but it is a three-dimensional surface. From the graphics point of view R-p-da/dN-ΔK probability model is a series of surface family. By R-p-da/dN-ΔK surface family, under different probability requirements,the law of the influence of continuous stress ratio on the crack growth rate can obtain. R-p-da/dN-ΔK surface family under certain conditions can degenerate into p-da/dN-AK curves for engineering probability damage tolerance design and safety assessment.Then the credibility of the fatigue fracture probability is studied under different stress ratio. Considering the laws of influence of the data dispersion and the number of samples probability evaluation, integration of the probability and confidence, the R-p-γ-da/dN-ΔK probability-confidence model is put forward. The parameters of R-p-γ-da/dN-ΔK probability-confidence model are estimated by using the linear principle of no-linear function. The probability-confidence model characterize the credibility of the research work.Finally, the calculation method of fatigue fracture probability is studied. The a-N fitting calculation method is an important prerequisite to obtain high-precision p-da/dN-ΔK fitting curve. In this thesis, considering the random nature of the whole set of data, unified a-N incremental polynomial fitting method is proposed under the same test conditions to provide a scientific basis for the study of the influence of different stress ratio on the fatigue crack propagation. And two p-da/dN data processing methods are given. The statistical analysis of the data processing based on da/dN is more reasonable in theory; derivation calculations based on p-a-N is more convenient for application. The calculation results of the two calculation methods have no significant difference from a statistical point of analysis.The innovation of this thesis is followed:It reveals Paris formula to reflect the effects of stress ratio on fatigue crack propagation. And based on Paris formula, the basic law and mathematical model and geometry, confidence of the effects of stress ratio on fatigue fracture probability have been studied comprehensively and systematically. The research enrich and improve the content of the Paris formula and expand the Paris formula.The specific innovations include:(1) In the role of the basic law of the fatigue fracture under different stress ratio: Revealing the Paris formula can reflect the influence of stress ratio on fatigue crack growth, and find the changing laws of two important parameters of the Paris formula with the change of stress ratio. C will decrease with stress ratio increasing; n will increase with stress ratio increasing.(2) In the role of the mathematical model of the fatigue fracture probability under different stress ratio:Using linearization theory,the data processing method of turning non-linear test data into linear data is put forward, and ultimately deduced a probability mathematical mode based on Paris formula.(3) In the role of the geometry of the fatigue fracture probability under different stress ratio:Pointed out the probability mathematical model is a surface family under different stress ratio. Further discussed the application of R-p-da/dN-ΔK surface family, and analyzed the scope of the surface family.(4) In the role of the confidence of the fatigue fracture probability under different stress ratio:In order to ensure the credibility of that the entire work, propose that should discuss the degree of confidence of the fatigue fracture probability. Considering confidence, the R-p-γ-da/dN-ΔK probability-confidence model is established. The method of parameters is given.(5) In the role of calculation method of the fatigue fracture probability: Unified a-N incremental polynomial fitting is proposed under the same test conditions to provide a scientific basis for the study of the influence of different stress ratio on the fatigue crack propagation. And two p-da/dN data processing methods are given. The statistical analysis of the data processing based on da/dN is more reasonable in theory; derivation calculations based on p-a-N is more convenient for application. The calculation results of the two calculation methods have no significant difference from a statistical point of analysis.更多还原