含曲线裂纹结构的三维断裂与疲劳裂纹扩展模拟研究
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摘要
损伤容限设计思想是公认的保障飞机安全性和经济性的科学思想。损伤容限设计以断裂力学为基础,以含裂纹结构的剩余强度评估和疲劳裂纹扩展寿命预测为两大核心任务。当前损伤容限设计所依据的理论是传统的二维断裂力学理论,所依赖的技术平台是商用CAD/CAE软件平台。传统二维理论和现有商用软件的局限性导致当前损伤容限设计面临着两大困难:一是对于非标准裂纹结构的评定缺乏相应的理论依据,因此不得不做最保守的评估;二是含裂纹结构的CAE模型建立流程繁琐,直接导致剩余强度分析工作量巨大和疲劳裂纹扩展模拟预测难以实现。针对这两大问题,本文分别从理论和技术方面展开了系统深入的研究,主要取得了以下进展:
(1)建立了各种典型三维裂纹的CAE子模型数据库,开发了基于几何模型和有限元模型的三维裂纹自动建模技术。在此基础上,建立了参数化后处理模块,从而实现了从建模到后处理的全程序控制,为实现复杂结构的剩余强度评定和疲劳裂纹扩展模拟提供了技术保障。
(2)发展了基于三维约束因子的等效厚度的概念。此概念将曲线裂纹线上的点与某一厚度的穿透直裂纹板中面上的裂纹尖端点建立了一种等价关系,进而可以将基于穿透直裂纹板得到的材料数据合理的应用于曲线裂纹,解决曲线裂纹的剩余强度评估、裂纹张开应力计算和裂纹扩展寿命预测等关键问题。这一概念为损伤容限分析中从实验室标准试件到实际复杂结构之间的鸿沟建立了一座桥梁。
(3)以等效厚度概念和三维断裂理论为基础,建立了非穿透曲线裂纹试件的双参数断裂准则,将非穿透曲线裂纹试件与穿透直裂纹试件的断裂评估统一起来,可以广泛应用于各种非穿透曲线裂纹试件断裂评估,为复杂三维裂纹结构的剩余强度评定奠定了理论基础。
(4)以等效厚度和条带屈服模型为基础,建立了非穿透曲线裂纹闭合模型。此模型能够准确计算非穿透曲线裂纹前沿张开应力和有效应力强度因子幅度,进而可以应用于裂纹扩展寿命以及形状演化模拟预测。
(5)通过对比三种谱载疲劳裂纹扩展塑性区模型(Wheeler模型、Willenborg/Chang模型和等效损伤模型)中迟滞参数在平面应力、平面应变和三维约束状态下的值,发现裂尖三维应力约束状态对塑性区尺寸的影响会进一步影响到模型中对于超载迟滞和反向超载加速的评估和裂纹扩展速率的预测。在应用塑性区模型对谱载疲劳裂纹扩展进行预测时,必须准确计算裂尖三维约束因子,进而得到精确地塑性区尺寸和裂纹扩展速率。
在此基础上,本文将提出的相关方法、技术和模型在具体的工程结构损伤容限分析中做了应用。结果表明,本文的研究结果为当前损伤容限设计面临的核心科学技术问题提供了可行的解决办法。
The conception of damage tolerance design has been widely recognized as the scientific thought to ensure security and economical efficiency of aircrafts. Based on the theory of fracture mechanics, the two core tasks of damage tolerance design are residual strength assessment and prediction of fatigue crack growth for cracked structure. At present, the theoretical basis and technical platform of damage tolerance design are two-dimensional (2D) fracture mechanics and commercial CAE software, which bring two major difficulties: first, it usually has to do the most conservative assessment due to lack of appropriate theoretical basis for non-standard cracked structures in the framework of 2D fracture theory; second, the assessment of residual strength and fatigue crack growth simulation is involved due to the complicated operations for building CAE model of cracked structure. For these two issues, the theories and modelling technics of part-through curve cracks are studied systematically and deeply. The main progresses are as follows:
(1) The CAE sub-models of typical three-dimensional (3D) cracks are established and gathered to a sub-model database. Then the 3D crack auto-building-model technique is developed to insert crack sub-model to geometric or finite element model. On this basis, a parameterized post-processing module is established. Accordingly, the entire process from model building to post-processing can be entirely controlled in the program files, which provides technical support for residual strength assessment and fatigue crack growth simulation of complex 3D cracked structure.
(2) A conception of equivalent thickness is proposed based on the three-dimensional constraint factor. This conception establishes an equivalent relationship between a point on curve crack front line and straight-through crack tip in the mid plane of plate. Based on the equivalence, the material fracture parameters or data obtained from straight-through cracked plates can be reasonably used to assess residual strength, crack opening stress, crack propagation life and other key issues. This conception bridges the gap between standard specimens in laboratory to practical complex structures.
(3) Based on the equivalent thickness conception and 3D fracture theory, a two-parameter fracture criterion of non-through curve cracked specimen is proposed which unifies the fracture assessment of non-through curve cracked specimens and standard straight-through cracked plates. This criterion can be widely used in fracture assessments for various part-through curve cracked structures, and build a theoretical foundation of residual strength assessment for complex 3D cracked structures.
(4) Based on the equivalent thickness conception and the strip yield model, a crack closure model of part-through curve cracked specimen is proposed. This model can be used to calculate the opening stresses and effective stress intensity factor ranges along non-through curve crack front line. Therefore, the crack growth life and crack shape evolution can be predicted.
(5) The values of retardation factors in three typical spectrum loading fatigue crack growth models (Wheeler model, Willenborg/Chang model and equivalent damage model) in plane stress, plane strain and 3D stress constraint state are systematically studied and compared. It is found that the influence of 3D stress state on plastic zone size in front of crack tip will further significantly affect the overload retardation or reverse acceleration. When the plastic zone models are used to predict spectrum loading fatigue crack growth, it is necessary to accurately calculate the 3D constraint factor in front of crack tip, and then the accurate plastic zone size and crack propagation rate can be obtained.
Based on the above studies, the proposed methods, techniques and models are used to damage tolerance analyses of specific engineering structures. It is shown that the current research results provide a viable solution for the major scientific and technological problems in damage tolerance design.
(1)建立了各种典型三维裂纹的CAE子模型数据库,开发了基于几何模型和有限元模型的三维裂纹自动建模技术。在此基础上,建立了参数化后处理模块,从而实现了从建模到后处理的全程序控制,为实现复杂结构的剩余强度评定和疲劳裂纹扩展模拟提供了技术保障。
(2)发展了基于三维约束因子的等效厚度的概念。此概念将曲线裂纹线上的点与某一厚度的穿透直裂纹板中面上的裂纹尖端点建立了一种等价关系,进而可以将基于穿透直裂纹板得到的材料数据合理的应用于曲线裂纹,解决曲线裂纹的剩余强度评估、裂纹张开应力计算和裂纹扩展寿命预测等关键问题。这一概念为损伤容限分析中从实验室标准试件到实际复杂结构之间的鸿沟建立了一座桥梁。
(3)以等效厚度概念和三维断裂理论为基础,建立了非穿透曲线裂纹试件的双参数断裂准则,将非穿透曲线裂纹试件与穿透直裂纹试件的断裂评估统一起来,可以广泛应用于各种非穿透曲线裂纹试件断裂评估,为复杂三维裂纹结构的剩余强度评定奠定了理论基础。
(4)以等效厚度和条带屈服模型为基础,建立了非穿透曲线裂纹闭合模型。此模型能够准确计算非穿透曲线裂纹前沿张开应力和有效应力强度因子幅度,进而可以应用于裂纹扩展寿命以及形状演化模拟预测。
(5)通过对比三种谱载疲劳裂纹扩展塑性区模型(Wheeler模型、Willenborg/Chang模型和等效损伤模型)中迟滞参数在平面应力、平面应变和三维约束状态下的值,发现裂尖三维应力约束状态对塑性区尺寸的影响会进一步影响到模型中对于超载迟滞和反向超载加速的评估和裂纹扩展速率的预测。在应用塑性区模型对谱载疲劳裂纹扩展进行预测时,必须准确计算裂尖三维约束因子,进而得到精确地塑性区尺寸和裂纹扩展速率。
在此基础上,本文将提出的相关方法、技术和模型在具体的工程结构损伤容限分析中做了应用。结果表明,本文的研究结果为当前损伤容限设计面临的核心科学技术问题提供了可行的解决办法。
The conception of damage tolerance design has been widely recognized as the scientific thought to ensure security and economical efficiency of aircrafts. Based on the theory of fracture mechanics, the two core tasks of damage tolerance design are residual strength assessment and prediction of fatigue crack growth for cracked structure. At present, the theoretical basis and technical platform of damage tolerance design are two-dimensional (2D) fracture mechanics and commercial CAE software, which bring two major difficulties: first, it usually has to do the most conservative assessment due to lack of appropriate theoretical basis for non-standard cracked structures in the framework of 2D fracture theory; second, the assessment of residual strength and fatigue crack growth simulation is involved due to the complicated operations for building CAE model of cracked structure. For these two issues, the theories and modelling technics of part-through curve cracks are studied systematically and deeply. The main progresses are as follows:
(1) The CAE sub-models of typical three-dimensional (3D) cracks are established and gathered to a sub-model database. Then the 3D crack auto-building-model technique is developed to insert crack sub-model to geometric or finite element model. On this basis, a parameterized post-processing module is established. Accordingly, the entire process from model building to post-processing can be entirely controlled in the program files, which provides technical support for residual strength assessment and fatigue crack growth simulation of complex 3D cracked structure.
(2) A conception of equivalent thickness is proposed based on the three-dimensional constraint factor. This conception establishes an equivalent relationship between a point on curve crack front line and straight-through crack tip in the mid plane of plate. Based on the equivalence, the material fracture parameters or data obtained from straight-through cracked plates can be reasonably used to assess residual strength, crack opening stress, crack propagation life and other key issues. This conception bridges the gap between standard specimens in laboratory to practical complex structures.
(3) Based on the equivalent thickness conception and 3D fracture theory, a two-parameter fracture criterion of non-through curve cracked specimen is proposed which unifies the fracture assessment of non-through curve cracked specimens and standard straight-through cracked plates. This criterion can be widely used in fracture assessments for various part-through curve cracked structures, and build a theoretical foundation of residual strength assessment for complex 3D cracked structures.
(4) Based on the equivalent thickness conception and the strip yield model, a crack closure model of part-through curve cracked specimen is proposed. This model can be used to calculate the opening stresses and effective stress intensity factor ranges along non-through curve crack front line. Therefore, the crack growth life and crack shape evolution can be predicted.
(5) The values of retardation factors in three typical spectrum loading fatigue crack growth models (Wheeler model, Willenborg/Chang model and equivalent damage model) in plane stress, plane strain and 3D stress constraint state are systematically studied and compared. It is found that the influence of 3D stress state on plastic zone size in front of crack tip will further significantly affect the overload retardation or reverse acceleration. When the plastic zone models are used to predict spectrum loading fatigue crack growth, it is necessary to accurately calculate the 3D constraint factor in front of crack tip, and then the accurate plastic zone size and crack propagation rate can be obtained.
Based on the above studies, the proposed methods, techniques and models are used to damage tolerance analyses of specific engineering structures. It is shown that the current research results provide a viable solution for the major scientific and technological problems in damage tolerance design.
引文
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