疲劳裂纹扩展研究及在装载机横梁寿命估算中的应用
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摘要
结构和机械的疲劳是一个十分复杂的问题,疲劳研究是一个存在大量经验性规律和相互矛盾观点的研究领域。因为影响材料疲劳强度和寿命的因素很多,而且绝大多数影响因素目前还无法很好地从物理模型及数学模型上给予合理的定量描述,加之试验条件与实际应用条件之间存在较大差异,因此尽管研究已积累了大量理论成果与试验数据,仍然无法对疲劳强度和寿命问题做出比较通用而且比较准确的预测和分析。一方面,实际工程应用在疲劳研究指导下采取相关措施确实能有效防止疲劳破坏,但另一方面,使用的指导方针对不同应用甚至同样应用却仍然无法阻止疲劳破坏案例的发生。这说明疲劳问题不论从理论上还是在实践中都没有完全解决。随着现代社会发展多样性和节奏加快的需求,疲劳问题越来越成为国内外学术界和产业界关注的重点。
本文研究了工程机械构件的疲劳问题。工程机械是人类社会应用广泛的重要工具之一,随着现代科学技术的发展,对工程机械结构提出了越来越高的要求,不仅要求有较高的承载力,减少原材料的使用,还要求结构有较高的疲劳寿命。因此,世界上发达国家都极为重视并开展工程机械强度评定、疲劳寿命估算和疲劳强度设计等方面的研究。利用现有理论进行构件疲劳强度分析、破坏预防和计算剩余寿命,常常与构件的具体形貌以及所处工况环境密切相关,计算分析的思路及使用的具体方法也相差很大,因而非常有必要对实际工程构件的疲劳问题进行研究。
本文以实际工程机械构件疲劳破坏为背景开展构件疲劳寿命研究,主要以疲劳裂纹扩展理论为基础,研究疲劳裂纹扩展的宏观机理,提出疲劳裂纹扩展的改进公式,从有利于实际操作出发对公式中重要物理量进行研究,并提出了相应的计算公式；本论文结合实际工程构件的工作循环进行有限元模拟,对构件各种工况下的力学场量进行分析,得出疲劳寿命研究所需的应力分布载荷谱；本文提出规范化的疲劳分析技术路线,在分析中分别采用目前比较流行的理论公式以及本文建立的公式对具体工程构件进行疲劳寿命分析,并对结果进行对比比较。本文还针对影响疲劳裂纹扩展因素多样复杂的特点,对构件疲劳寿命进行优化设计,建立计算机神经网络对疲劳寿命进行评估分析。具体说来,本文工作结果表现为以下几个方面：
总结分析了疲劳理论,断裂力学理论和损伤力学理论等各种历史研究及当代研究中,适用于工程机械构件应用的研究成果,包括关于疲劳裂纹产生、扩展的理论模型、机理、各种判据。将影响疲劳裂纹扩展的各种因素进行分类筛选,找出与本文研究密切相关的因素,为后面的研究奠定力学理论基础。
重点研究了疲劳裂纹扩展的机理及其扩展公式。对承受动荷载的结构构件,在荷载大小远低于材料屈服强度甚至是疲劳极限的条件下仍能发生屈服乃至破坏,以往的研究对此类现象的机理没有作出直观易懂的解释。签于此,本文提出疲劳裂纹扩展的宏观扩展机理,即将动荷载的惯性效应产生的应力强度因子附加到构件的受载上去,也就是说,虽然发生疲劳破坏的构件承受的动荷载在瞬时力的大小上远远小于构件材料的屈服强度,但由于动荷载的惯性作用,构件上实际承受的荷载大小很可能超过其疲劳相关的承载能力而发生屈服并产生裂纹扩展。
疲劳裂纹扩展的改进公式是根据所提出的疲劳机理以及目前疲劳裂纹扩展理论应用最广泛的判据提出的。裂纹扩展有两个重要的关节点,分别是裂纹扩展门槛值与材料断裂韧度。本文的判据分别是裂纹扩展实际驱动力大于裂纹门槛值时,裂纹就开始扩展。裂纹扩展实际驱动力大于材料的断裂韧度时,材料或构件就断裂,在此点之后就不存在裂纹的扩展问题,而在此值之前裂纹一直是按某一大小稳定扩展。本文在这两个判据的基础上,提出改进的疲劳裂纹扩展公式。改进公式完全由裂纹驱动力、裂纹扩展阻力和裂纹形态特征表示的,突出了简单易懂的物理意义和应用方便的特点,而且该公式所表示的曲线涵盖了整个裂纹扩展全过程,包含了影响裂纹扩展的所有重要因素。
本文对改进公式中的裂纹扩展门槛值和材料的断裂韧度分别进行了研究。对于裂纹扩展门槛值,根据断裂力学中裂纹扩展裂尖中应力分布和裂尖处的塑性区的大小以及疲劳扩展的疲劳极限图,提出了用常规材料实验性能参数,如屈服强度、泊松比、弹性模量和加载参数应力比表示的裂纹扩展门槛值估算公式。而对材料的断裂韧度,则根据其标准试验的曲线,经简化提出了用材料性能参数和几何尺寸表示的估算公式。对两个公式分别进行了实例计算验证,其误差在工程允许的范围之内。
为了验证所提出的公式以及其公式用于寿命计算的效果,本文以实际工程机械构件破坏为背景,进行了构件的寿命计算分析。在这项研究中,首先对机械构件在其工作循环周期内的承载工况进行分析,在此基础上,采用有限元进行数值模拟,得出构件的应力应变分布场量,建立了进行疲劳寿命研究所需的应力分布载荷谱。然后对构件进行疲劳寿命分析。由于疲劳寿命分析只是强度分析中的一个类别,在实际应用中如何区分判定并最终导入执行,必须遵循明确清晰的步骤,本文建立了如下技术路径。
首先应判定是否属于疲劳问题,不是则归入其他强度问题,如果是则应选择疲劳寿命计算的方法,方法确定后再对构件进行疲劳强度校核。针对本文构件,通过分析表明发生的是疲劳累计损伤破坏,因而分别利用线性累积损伤理论、非线性损伤理论和有限元疲劳寿命模拟进行寿命计算,将三种方法的计算结果进行比较后发现,本构件完全可以满足工程设计的寿命要求。但现实构件却在使用期限非常短时就发生断裂。针对该情况,利用断裂力学的逆向分析思维,假设初始裂纹大小,采用最常使用的有裂纹估算公式和本文提出的裂纹扩展公式,分别估算可能隐含初始裂纹构件的寿命。通过与实际断裂情况比较表明,本文提出公式的结果与现有公式的结果相差不大,但本文提出的公式能更好地反映裂纹扩展的实际特点,是一个非常缓慢发展的过程。
本文对影响裂纹扩展的各个因素进行了优化研究,并对各因素的重要程度进行了排序。结果表明,裂纹起裂角、初始裂纹大小和应力比是最重要的影响因素,而板厚等几何形状影响并不是特别重要。而且裂纹起裂角对疲劳裂纹扩展寿命的影响大于初始裂纹,这与以往研究中的认识是明显不同的。结果还表明,若对裂纹扩展曲线两个判据点的重要程度进行比较,门槛值的影响要远远大于材料断裂韧度,这也是以往研究中没有提到的。另外,本文还建立了神经网络模型对疲劳寿命进行人工智能预测。通过实施该项技术模拟,可以不用考虑计算公式,而直接输入影响裂纹扩展的各个具体因素数值,而得到构件的寿命估算。这些新的研究结果或认识虽然尚有待更多的试验与实例验证,同时打开了疲劳研究的新思路。
Fatigue is a very complicated problem for the structure and machinery. And fatigue researches contain a quantity of empirical laws and contradictory views. There are many influencing factors on fatigue strength and fatigue life. At present, most influencing factors can't quantitatively describe fatigue phenomenon with physical models or mathematical models. And there are big differences between test conditions and practical applications. Although a lot of theory results and test data have been obtained, accurate prediction and analysis for the fatigue strength and fatigue life can't realized better. One hand, fatigue destroy can be prevented efficiently with fatigue research results and taking related measures in actual engineering application. On the other hand, though the same principles guide the same applications, fatigue destroy accidents still can't be prevented. All facts show that fatigue problem still can't be solved completely on theories and practice. With the more requirements of rapid development diversity in society, fatigue more and more has been an important problem on academic circles and industry circles in home and abroad.
The dissertation mainly studies the fatigue problem of the engineering machinery members. The engineering machinery is one of important tools in the human society application. With the development of modern science technology, more and more high demands are put forward for the engineering machinery. Not only high bearing capacity is demanded in order to decrease the material use, but also long fatigue life is requested for structure. The researches of machinery strength valuation, design and fatigue life estimation are paid more attention and developed. When the researches are done with the existing theories, the shape characteristics and case environments of machinery members become important influencing factors. Besides, calculation steps and use methods are also very different.
Fatigue life researches were developed based on the destroy of actual machinery member in the dissertation. On the basis of fatigue crack propagation theory, macroscopic mechanism and new improved formula of fatigue crack propagation was proposed. Simultaneously, the important physical parameters of the formula were studied due to the actual application. Also, the FEM simulation of machinery member was done according to the working process of machinery. And the stress load spectrums were drawn in combination with the mechanical analysis of all working cases. All these results could provide theory basis for the later fatigue analysis. Moreover, the normalized fatigue analysis steps were presented. The popular theory formula and the improved formula were adopted to analyzed the fatigue life of actual machinery member, respectively. And the results were compared. At last, with the neural network intelligent technology, the optimization analysis of fatigue life was carried out because of many complex influencing factors in fatigue researches. In summary, the research results of this dissertation are as followed.
Firstly, many existing theories were summarized in the dissertation, such as Fatigue theory, Fracture Mechanics theory, Damage Mechanics theory, fatigue crack propagation theory results, models and criterion. The related important factors of influencing crack propagation were found out by means of analysis of all factors, which provide preparation for the following research.
The dissertation mainly focus on the researches of mechanism and formula for the fatigue crack propagation. Though the interior stress is far less than the yield strength or fatigue limit, the structure member bearing dynamic load still may yield or destroy. The existing theories don't explain this problem with reasonable methods. So, the macroscopic mechanism of fatigue crack propagation was proposed in the dissertation. Inertial effect of dynamic load was added to the member. That is, though stress magnitude acting on machinery member is far less than the yield strength of material, the actual stress magnitude may exceed the bearing capacity of member and induce further crack propagation.
At present, there are two most wide used fatigue crack propagation criterions. They are crack propagation threshold and material fracture toughness. For the threshold, the criterion is that the crack will grow if the driving force is more than the threshold. And for the fracture toughness, the crack will grow steady if the driving force is less than the fracture toughness. Else, the member will destroy. On the basis of these two criterions, the improved fatigue crack propagation formula was presented. Physical meaning of the improved formula is simple and it is easy to be applied. The improved completed formula was induced by two crack propagation curve and it is suitable for the whole crack propagation process. Furthermore, the crack propagation curve contains all important factors affecting crack propagation.
The two important parameters, crack propagation threshold and fracture toughness, in the improved formula, were also studied. For the crack propagation threshold, according to the stress distribution, plastic zone size around crack tip and fatigue limited curve of crack propagation, the new formula was put forward with routine test parameters of material capacity and loading parameters, such as, yield strength, Poisson ratio, elastic modulus and stress ratio. For the fracture toughness of material, based on the simplified curve, the formula is described with material capacity parameters and geometry size. The two formula were checked by test data, respectively. Allowable error is in the permission scope of the project.
In order to check the effect of the improved formula, Fatigue life researches were developed based on the destroy of actual machinery member in the dissertation. Based on the analysis of bearing load case of the actual members in engineering machinery, the dissertation makes use of the FEM numerical simulation and obtains the stress-strain distribution of the members and builds the stress distribution load spectrum that is needed in the analysis of practical members fatigue life. Fatigue life analysis is only a sort of strength analysis, it must follow clear steps in practical application. This dissertation offers such a method.
For the study object in this dissertation, firstly, it should justify whether it belongs to fatigue problem, if so, fatigue life calculation method is in need. Then, fatigue strength correction is needed. It shows that the members in this dissertation suffer the fatigue accumulative damage. Thus, linear accumulative damage theory and nonlinear damage theory are used to calculate life separately. Then, making use of Finite Element method, fatigue life was also obtained. Comparing the three calculation results, it can be found that the results satisfy the requirement of the engineering design without the fatigue damage within the scope of the bearing load in project. But practical members broke up within a short use time. For this problem, using the reverse analysis and supposing the size of initial crack and applying the crack estimation formula that is most acceptable and the improved formula in the dissertation, the life was estimated for the crack member. In compared with actual cases, the results of the improved formula are more suitable for the crack propagation process.
In the dissertation, the fatigue life was also be predicted with neural network intelligent technology. By this technology, the importance of each influencing factor on crack propagation was ranked. It shows that the initial angle, initial crack size and stress ratio are all the most important influencing factors. But that of the plate thickness is secondary. Moreover, the initial angle is more important than the initial crack size, which is very different from the past researches. It also shows that the importance of crack threshold is far more than that of fracture toughness, which isn't mentioned in the previous researches. All researches in the dissertation will be tested by more tests and data in future. And all works also present new aims of the fatigue researches.
本文研究了工程机械构件的疲劳问题。工程机械是人类社会应用广泛的重要工具之一,随着现代科学技术的发展,对工程机械结构提出了越来越高的要求,不仅要求有较高的承载力,减少原材料的使用,还要求结构有较高的疲劳寿命。因此,世界上发达国家都极为重视并开展工程机械强度评定、疲劳寿命估算和疲劳强度设计等方面的研究。利用现有理论进行构件疲劳强度分析、破坏预防和计算剩余寿命,常常与构件的具体形貌以及所处工况环境密切相关,计算分析的思路及使用的具体方法也相差很大,因而非常有必要对实际工程构件的疲劳问题进行研究。
本文以实际工程机械构件疲劳破坏为背景开展构件疲劳寿命研究,主要以疲劳裂纹扩展理论为基础,研究疲劳裂纹扩展的宏观机理,提出疲劳裂纹扩展的改进公式,从有利于实际操作出发对公式中重要物理量进行研究,并提出了相应的计算公式；本论文结合实际工程构件的工作循环进行有限元模拟,对构件各种工况下的力学场量进行分析,得出疲劳寿命研究所需的应力分布载荷谱；本文提出规范化的疲劳分析技术路线,在分析中分别采用目前比较流行的理论公式以及本文建立的公式对具体工程构件进行疲劳寿命分析,并对结果进行对比比较。本文还针对影响疲劳裂纹扩展因素多样复杂的特点,对构件疲劳寿命进行优化设计,建立计算机神经网络对疲劳寿命进行评估分析。具体说来,本文工作结果表现为以下几个方面：
总结分析了疲劳理论,断裂力学理论和损伤力学理论等各种历史研究及当代研究中,适用于工程机械构件应用的研究成果,包括关于疲劳裂纹产生、扩展的理论模型、机理、各种判据。将影响疲劳裂纹扩展的各种因素进行分类筛选,找出与本文研究密切相关的因素,为后面的研究奠定力学理论基础。
重点研究了疲劳裂纹扩展的机理及其扩展公式。对承受动荷载的结构构件,在荷载大小远低于材料屈服强度甚至是疲劳极限的条件下仍能发生屈服乃至破坏,以往的研究对此类现象的机理没有作出直观易懂的解释。签于此,本文提出疲劳裂纹扩展的宏观扩展机理,即将动荷载的惯性效应产生的应力强度因子附加到构件的受载上去,也就是说,虽然发生疲劳破坏的构件承受的动荷载在瞬时力的大小上远远小于构件材料的屈服强度,但由于动荷载的惯性作用,构件上实际承受的荷载大小很可能超过其疲劳相关的承载能力而发生屈服并产生裂纹扩展。
疲劳裂纹扩展的改进公式是根据所提出的疲劳机理以及目前疲劳裂纹扩展理论应用最广泛的判据提出的。裂纹扩展有两个重要的关节点,分别是裂纹扩展门槛值与材料断裂韧度。本文的判据分别是裂纹扩展实际驱动力大于裂纹门槛值时,裂纹就开始扩展。裂纹扩展实际驱动力大于材料的断裂韧度时,材料或构件就断裂,在此点之后就不存在裂纹的扩展问题,而在此值之前裂纹一直是按某一大小稳定扩展。本文在这两个判据的基础上,提出改进的疲劳裂纹扩展公式。改进公式完全由裂纹驱动力、裂纹扩展阻力和裂纹形态特征表示的,突出了简单易懂的物理意义和应用方便的特点,而且该公式所表示的曲线涵盖了整个裂纹扩展全过程,包含了影响裂纹扩展的所有重要因素。
本文对改进公式中的裂纹扩展门槛值和材料的断裂韧度分别进行了研究。对于裂纹扩展门槛值,根据断裂力学中裂纹扩展裂尖中应力分布和裂尖处的塑性区的大小以及疲劳扩展的疲劳极限图,提出了用常规材料实验性能参数,如屈服强度、泊松比、弹性模量和加载参数应力比表示的裂纹扩展门槛值估算公式。而对材料的断裂韧度,则根据其标准试验的曲线,经简化提出了用材料性能参数和几何尺寸表示的估算公式。对两个公式分别进行了实例计算验证,其误差在工程允许的范围之内。
为了验证所提出的公式以及其公式用于寿命计算的效果,本文以实际工程机械构件破坏为背景,进行了构件的寿命计算分析。在这项研究中,首先对机械构件在其工作循环周期内的承载工况进行分析,在此基础上,采用有限元进行数值模拟,得出构件的应力应变分布场量,建立了进行疲劳寿命研究所需的应力分布载荷谱。然后对构件进行疲劳寿命分析。由于疲劳寿命分析只是强度分析中的一个类别,在实际应用中如何区分判定并最终导入执行,必须遵循明确清晰的步骤,本文建立了如下技术路径。
首先应判定是否属于疲劳问题,不是则归入其他强度问题,如果是则应选择疲劳寿命计算的方法,方法确定后再对构件进行疲劳强度校核。针对本文构件,通过分析表明发生的是疲劳累计损伤破坏,因而分别利用线性累积损伤理论、非线性损伤理论和有限元疲劳寿命模拟进行寿命计算,将三种方法的计算结果进行比较后发现,本构件完全可以满足工程设计的寿命要求。但现实构件却在使用期限非常短时就发生断裂。针对该情况,利用断裂力学的逆向分析思维,假设初始裂纹大小,采用最常使用的有裂纹估算公式和本文提出的裂纹扩展公式,分别估算可能隐含初始裂纹构件的寿命。通过与实际断裂情况比较表明,本文提出公式的结果与现有公式的结果相差不大,但本文提出的公式能更好地反映裂纹扩展的实际特点,是一个非常缓慢发展的过程。
本文对影响裂纹扩展的各个因素进行了优化研究,并对各因素的重要程度进行了排序。结果表明,裂纹起裂角、初始裂纹大小和应力比是最重要的影响因素,而板厚等几何形状影响并不是特别重要。而且裂纹起裂角对疲劳裂纹扩展寿命的影响大于初始裂纹,这与以往研究中的认识是明显不同的。结果还表明,若对裂纹扩展曲线两个判据点的重要程度进行比较,门槛值的影响要远远大于材料断裂韧度,这也是以往研究中没有提到的。另外,本文还建立了神经网络模型对疲劳寿命进行人工智能预测。通过实施该项技术模拟,可以不用考虑计算公式,而直接输入影响裂纹扩展的各个具体因素数值,而得到构件的寿命估算。这些新的研究结果或认识虽然尚有待更多的试验与实例验证,同时打开了疲劳研究的新思路。
Fatigue is a very complicated problem for the structure and machinery. And fatigue researches contain a quantity of empirical laws and contradictory views. There are many influencing factors on fatigue strength and fatigue life. At present, most influencing factors can't quantitatively describe fatigue phenomenon with physical models or mathematical models. And there are big differences between test conditions and practical applications. Although a lot of theory results and test data have been obtained, accurate prediction and analysis for the fatigue strength and fatigue life can't realized better. One hand, fatigue destroy can be prevented efficiently with fatigue research results and taking related measures in actual engineering application. On the other hand, though the same principles guide the same applications, fatigue destroy accidents still can't be prevented. All facts show that fatigue problem still can't be solved completely on theories and practice. With the more requirements of rapid development diversity in society, fatigue more and more has been an important problem on academic circles and industry circles in home and abroad.
The dissertation mainly studies the fatigue problem of the engineering machinery members. The engineering machinery is one of important tools in the human society application. With the development of modern science technology, more and more high demands are put forward for the engineering machinery. Not only high bearing capacity is demanded in order to decrease the material use, but also long fatigue life is requested for structure. The researches of machinery strength valuation, design and fatigue life estimation are paid more attention and developed. When the researches are done with the existing theories, the shape characteristics and case environments of machinery members become important influencing factors. Besides, calculation steps and use methods are also very different.
Fatigue life researches were developed based on the destroy of actual machinery member in the dissertation. On the basis of fatigue crack propagation theory, macroscopic mechanism and new improved formula of fatigue crack propagation was proposed. Simultaneously, the important physical parameters of the formula were studied due to the actual application. Also, the FEM simulation of machinery member was done according to the working process of machinery. And the stress load spectrums were drawn in combination with the mechanical analysis of all working cases. All these results could provide theory basis for the later fatigue analysis. Moreover, the normalized fatigue analysis steps were presented. The popular theory formula and the improved formula were adopted to analyzed the fatigue life of actual machinery member, respectively. And the results were compared. At last, with the neural network intelligent technology, the optimization analysis of fatigue life was carried out because of many complex influencing factors in fatigue researches. In summary, the research results of this dissertation are as followed.
Firstly, many existing theories were summarized in the dissertation, such as Fatigue theory, Fracture Mechanics theory, Damage Mechanics theory, fatigue crack propagation theory results, models and criterion. The related important factors of influencing crack propagation were found out by means of analysis of all factors, which provide preparation for the following research.
The dissertation mainly focus on the researches of mechanism and formula for the fatigue crack propagation. Though the interior stress is far less than the yield strength or fatigue limit, the structure member bearing dynamic load still may yield or destroy. The existing theories don't explain this problem with reasonable methods. So, the macroscopic mechanism of fatigue crack propagation was proposed in the dissertation. Inertial effect of dynamic load was added to the member. That is, though stress magnitude acting on machinery member is far less than the yield strength of material, the actual stress magnitude may exceed the bearing capacity of member and induce further crack propagation.
At present, there are two most wide used fatigue crack propagation criterions. They are crack propagation threshold and material fracture toughness. For the threshold, the criterion is that the crack will grow if the driving force is more than the threshold. And for the fracture toughness, the crack will grow steady if the driving force is less than the fracture toughness. Else, the member will destroy. On the basis of these two criterions, the improved fatigue crack propagation formula was presented. Physical meaning of the improved formula is simple and it is easy to be applied. The improved completed formula was induced by two crack propagation curve and it is suitable for the whole crack propagation process. Furthermore, the crack propagation curve contains all important factors affecting crack propagation.
The two important parameters, crack propagation threshold and fracture toughness, in the improved formula, were also studied. For the crack propagation threshold, according to the stress distribution, plastic zone size around crack tip and fatigue limited curve of crack propagation, the new formula was put forward with routine test parameters of material capacity and loading parameters, such as, yield strength, Poisson ratio, elastic modulus and stress ratio. For the fracture toughness of material, based on the simplified curve, the formula is described with material capacity parameters and geometry size. The two formula were checked by test data, respectively. Allowable error is in the permission scope of the project.
In order to check the effect of the improved formula, Fatigue life researches were developed based on the destroy of actual machinery member in the dissertation. Based on the analysis of bearing load case of the actual members in engineering machinery, the dissertation makes use of the FEM numerical simulation and obtains the stress-strain distribution of the members and builds the stress distribution load spectrum that is needed in the analysis of practical members fatigue life. Fatigue life analysis is only a sort of strength analysis, it must follow clear steps in practical application. This dissertation offers such a method.
For the study object in this dissertation, firstly, it should justify whether it belongs to fatigue problem, if so, fatigue life calculation method is in need. Then, fatigue strength correction is needed. It shows that the members in this dissertation suffer the fatigue accumulative damage. Thus, linear accumulative damage theory and nonlinear damage theory are used to calculate life separately. Then, making use of Finite Element method, fatigue life was also obtained. Comparing the three calculation results, it can be found that the results satisfy the requirement of the engineering design without the fatigue damage within the scope of the bearing load in project. But practical members broke up within a short use time. For this problem, using the reverse analysis and supposing the size of initial crack and applying the crack estimation formula that is most acceptable and the improved formula in the dissertation, the life was estimated for the crack member. In compared with actual cases, the results of the improved formula are more suitable for the crack propagation process.
In the dissertation, the fatigue life was also be predicted with neural network intelligent technology. By this technology, the importance of each influencing factor on crack propagation was ranked. It shows that the initial angle, initial crack size and stress ratio are all the most important influencing factors. But that of the plate thickness is secondary. Moreover, the initial angle is more important than the initial crack size, which is very different from the past researches. It also shows that the importance of crack threshold is far more than that of fracture toughness, which isn't mentioned in the previous researches. All researches in the dissertation will be tested by more tests and data in future. And all works also present new aims of the fatigue researches.
引文
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