损伤力学方法预估构件的疲劳裂纹形成寿命
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摘要
构件疲劳失效已经成为工程领域中的重要课题,构件疲劳失效过程可分为裂纹形成与裂纹扩展两个阶段。对于裂纹扩展阶段,目前基本上都是采用断裂力学方法进行分析。就裂纹形成阶段而言,一般采用的分析方法有两种。一种是完全的试验方法,直接通过与实际情况相同或相似的试验来获取所需要的疲劳数据。这种方法虽然可靠但昂贵且费时,故可行性不高。另一种方法是试验与统计经验相结合的方法。这种方法着眼于利用已有的标准试验结果,依照经验性的当量原则或修正办法,对实际情况的疲劳指标进行估算。然而,如果要对千差万别的实际情况进行完备的修正,势必要进行大量的统计试验,这往往是不现实的。疲劳裂纹形成寿命问题的研究,具有较大的理论和实际意义。
本文致力于应用损伤力学方法研究大范围损伤下工程构件的疲劳裂纹形成寿命的预估。重点讨论建立大范围损伤下工程构件疲劳裂纹形成寿命预估的耦联变分原理及其应用,得到了较为完整的求解该问题的新体系。
推导了直杆拉压时的疲劳裂纹形成寿命预估的封闭解,给出了直梁纯弯曲时的疲劳裂纹形成寿命预估的封闭解。应用最小二乘法给出了确定损伤演化方程中材料常数的方法。损伤演化方程中材料常数的确定,是损伤力学中最基本和很重要的工作。
采用直接方法推导了圆轴扭转、矩形截面梁纯弯曲、直梁横力弯曲等的疲劳裂纹形成寿命的封闭解。应用虚功原理推导了平面应力板状构件疲劳裂纹形成寿命的封闭解。给出了上述各种构件疲劳裂纹形成寿命的预估方法和指定疲劳裂纹形成寿命下工作应力的计算方法。
对大范围损伤条件下平面应力板状构件的疲劳裂纹形成寿命预估问题,采用变分原理进行了分析。定义了该问题的耦联系统,建立了该耦联系统的零差功原理、耦联势能原理和耦联余能原理。应用耦联势能原理导出了平面应力板状构件在大范围损伤条件下的疲劳裂纹形成寿命预估的封闭解。
定义了大范围损伤条件下疲劳裂纹形成问题三维构件损伤力学求解的耦联系统,建立了该耦联系统的零差功原理、耦联势能原理和耦联余能原理。应用耦联势能原理得到了三维构件在大范围损伤条件下的疲劳裂纹形成寿命预估的封闭解。进一步得到了横力弯曲直梁、纯弯曲直梁、扭转圆轴、拉压直杆的疲劳裂纹形成寿命的封闭解。
作为本文方法的应用,对冷轧机支承辊疲劳裂纹形成寿命进行了研究,给出了预估其疲劳裂纹形成寿命的方法,并计算了算例。为预估冷轧机支承辊的疲劳裂纹形成寿命提供了新思路和新方法。
Fatigue failure is an important consideration in the design of most of the engineering compenents, a fatigue failure consists of two steps: crack initiation and crack propagation. in general terms, there are two methods in analyzing crack initiation. The methods based on test obtain key fatigue data by carrying out some tests which conditions are the same as practical conditions, or similar to practical conditions. Although the data are creditable derived from the tests, costs are more expensive and hinder its implementation. Based on some empirical equivalent principles and modified methods, another method combines tests with statistics analysis, which evaluates fatigue index of practical conditions by use of existing test data. Unforturnately, numerous statistical tests must be completed in order to gain perfect modifications for various practical conditions. Obviously, the study on crack initiation lives is much important in theoretical exploration and practical application. This dissertation is mainly devoted to evaluate fatigue crack initiation lives of engineering compenents with large range damage by use of damage mechanics. Focal points focus on establishing the variational principles of coupled systems and its applications for evaluating fatigue crack initiation lives of engineering compenents with large range damage, a set of new system is developed for this problem.
The closed form solutions are derived to evaluate fatigue crack initiation lives for a pole subjected to a stretch or compression loading, and a beam subjected to a pure bending load. Applying least squares technique, the method to determine material constants in damage evolution equations is established. This part of work is fundamental and much important in damage mechanics analysis.
Applying direct method, the closed form solutions are obtained for evaluating crack initiation lives of a circular shaft subjected to twist loading, a rectangular section beam subjected to pure bending load, and a beam subjected to transverse bending load. Applying virtual work principle, the closed form solution is obtained for evaluating crack initiation lives of a plane compenent under plane stress. The methods of evaluating fatigue crack initiation lives and determining working stress under assigned fatigue crack initiation lives are given for those compenents mentioned above.
Applying variational principles, fatigue crack initiation lives is evaluated for a plane compenents with large range damage. Coupled system is defined firstly, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of a plane compenent under plane stress.
For three dimensional compenents with large range damage, coupled system is defined for solving the problem of fatigue crack initiation, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of three dimensional compenents with large range damage. The closed form solutions are obtained for evaluating crack initiation lives of a circular shaft subjected to a twist loading, a beam subjected to a pure bending load or a transverse bending load, and a pole subjected to a stretch or compression loading.
As an application, fatigue crack initiation lives of the backup roll of cool rolling mill is evaluated, the method is given for evaluating its fatigue crack initiation lives. An example is presented to demonstrate the application of new method developed by this dissertation in evaluating fatigue crack initiation lives of back-up roll.
本文致力于应用损伤力学方法研究大范围损伤下工程构件的疲劳裂纹形成寿命的预估。重点讨论建立大范围损伤下工程构件疲劳裂纹形成寿命预估的耦联变分原理及其应用,得到了较为完整的求解该问题的新体系。
推导了直杆拉压时的疲劳裂纹形成寿命预估的封闭解,给出了直梁纯弯曲时的疲劳裂纹形成寿命预估的封闭解。应用最小二乘法给出了确定损伤演化方程中材料常数的方法。损伤演化方程中材料常数的确定,是损伤力学中最基本和很重要的工作。
采用直接方法推导了圆轴扭转、矩形截面梁纯弯曲、直梁横力弯曲等的疲劳裂纹形成寿命的封闭解。应用虚功原理推导了平面应力板状构件疲劳裂纹形成寿命的封闭解。给出了上述各种构件疲劳裂纹形成寿命的预估方法和指定疲劳裂纹形成寿命下工作应力的计算方法。
对大范围损伤条件下平面应力板状构件的疲劳裂纹形成寿命预估问题,采用变分原理进行了分析。定义了该问题的耦联系统,建立了该耦联系统的零差功原理、耦联势能原理和耦联余能原理。应用耦联势能原理导出了平面应力板状构件在大范围损伤条件下的疲劳裂纹形成寿命预估的封闭解。
定义了大范围损伤条件下疲劳裂纹形成问题三维构件损伤力学求解的耦联系统,建立了该耦联系统的零差功原理、耦联势能原理和耦联余能原理。应用耦联势能原理得到了三维构件在大范围损伤条件下的疲劳裂纹形成寿命预估的封闭解。进一步得到了横力弯曲直梁、纯弯曲直梁、扭转圆轴、拉压直杆的疲劳裂纹形成寿命的封闭解。
作为本文方法的应用,对冷轧机支承辊疲劳裂纹形成寿命进行了研究,给出了预估其疲劳裂纹形成寿命的方法,并计算了算例。为预估冷轧机支承辊的疲劳裂纹形成寿命提供了新思路和新方法。
Fatigue failure is an important consideration in the design of most of the engineering compenents, a fatigue failure consists of two steps: crack initiation and crack propagation. in general terms, there are two methods in analyzing crack initiation. The methods based on test obtain key fatigue data by carrying out some tests which conditions are the same as practical conditions, or similar to practical conditions. Although the data are creditable derived from the tests, costs are more expensive and hinder its implementation. Based on some empirical equivalent principles and modified methods, another method combines tests with statistics analysis, which evaluates fatigue index of practical conditions by use of existing test data. Unforturnately, numerous statistical tests must be completed in order to gain perfect modifications for various practical conditions. Obviously, the study on crack initiation lives is much important in theoretical exploration and practical application. This dissertation is mainly devoted to evaluate fatigue crack initiation lives of engineering compenents with large range damage by use of damage mechanics. Focal points focus on establishing the variational principles of coupled systems and its applications for evaluating fatigue crack initiation lives of engineering compenents with large range damage, a set of new system is developed for this problem.
The closed form solutions are derived to evaluate fatigue crack initiation lives for a pole subjected to a stretch or compression loading, and a beam subjected to a pure bending load. Applying least squares technique, the method to determine material constants in damage evolution equations is established. This part of work is fundamental and much important in damage mechanics analysis.
Applying direct method, the closed form solutions are obtained for evaluating crack initiation lives of a circular shaft subjected to twist loading, a rectangular section beam subjected to pure bending load, and a beam subjected to transverse bending load. Applying virtual work principle, the closed form solution is obtained for evaluating crack initiation lives of a plane compenent under plane stress. The methods of evaluating fatigue crack initiation lives and determining working stress under assigned fatigue crack initiation lives are given for those compenents mentioned above.
Applying variational principles, fatigue crack initiation lives is evaluated for a plane compenents with large range damage. Coupled system is defined firstly, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of a plane compenent under plane stress.
For three dimensional compenents with large range damage, coupled system is defined for solving the problem of fatigue crack initiation, then zero different work principle, coupled potential energy principle and coupled complementary energy principle are established. Applying coupled potential energy principle, the closed form solution is obtained for evaluating crack initiation lives of three dimensional compenents with large range damage. The closed form solutions are obtained for evaluating crack initiation lives of a circular shaft subjected to a twist loading, a beam subjected to a pure bending load or a transverse bending load, and a pole subjected to a stretch or compression loading.
As an application, fatigue crack initiation lives of the backup roll of cool rolling mill is evaluated, the method is given for evaluating its fatigue crack initiation lives. An example is presented to demonstrate the application of new method developed by this dissertation in evaluating fatigue crack initiation lives of back-up roll.
引文
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