摘要
带孔的零部件,如螺栓连接件等,在工程结构中有着广泛地应用。由于应力集中、零件之间接触作用,在孔边常常出现裂纹。应力强度因子是计算裂纹扩展率、剩余强度和疲劳寿命的重要参数。因此,为了确保安全,充分地利用材料,准确确定这种含裂结构的应力强度因子具有很大的实际意义。含接触的孔边裂纹问题可分为两种情况:(1)裂纹面接触问题,例如动载荷作用下的孔边裂纹问题。(2)含裂纹的部件与其它部件接触问题,如含裂螺栓连接件。考虑接触作用的孔边裂纹问题是十分复杂的。一般来说,很难获得分析解。为此,本文采用有限元法研究了四种孔边裂纹问题的应力强度因子:第一个问题是在远场拉伸载荷作用下机械连接件中螺栓孔四分之一椭圆角裂纹应力强度因子数值研究。第二个问题是在平行于裂纹的冲击压缩载荷作用下裂纹面接触对有限板中心孔单边水平裂纹动态应力强度因子的影响。第三个问题是在冲击压缩载荷作用下有限板中圆孔单边斜裂纹动态应力强度因子数值研究。第四个问题是在离心载荷作用下汽轮机叶轮T型叶根槽表面裂纹应力强度因子数值研究。
上述问题的分析模型采用通用有限元软件ANSYS产生,裂纹尖端的平方根应力奇异性通过四分之一节点奇异单元来模拟。从经典的线弹性断裂理论出发,利用位移外插方法,给出了二维裂纹和椭圆型裂纹问题应力强度因子计算公式,这些公式为确定上述问题的应力强度因子提供了方便。
在第一个问题的研究中,考虑了螺栓孔与螺栓(销)的接触作用,研究了孔与销之间的间隙对接触压力和应力强度因子的影响。发现接触压力和接触区域随着间隙的变化而改变。在有间隙的情况下,通过在孔边施加均匀或余弦分布载荷代替孔销之间的接触作用是不恰当的。应力强度因子的数值结果表明:随着孔与螺栓之间间隙的增加,螺栓孔角裂纹沿裂纹前缘各点的I型应力强度因子也增加。这些结果表明间隙量对I型应力强度因子有很大的影响,在对这种含裂纹机械连接件进行裂纹扩展、剩余强度和疲劳寿命评估时需要恰当考虑间隙。同时也发现,螺栓孔角裂纹的I型应力强度因子在最深点达到最大值。在第二问题的研究中,考虑了裂纹面的接触作用,研究了裂纹面接触对动态应力强度因子的影响,计算了在裂纹面有无接触情况下的动态应力强度因子。数值结果表明:考虑裂纹面的接触作用,可以消除负I型和裂纹面相互穿透或重叠现象;裂纹面接触作用对I型动态应力强度因子有很大的影响。因此,在动载荷作用下,准确的裂纹分析应包括裂纹面的接触作用,否则计算的I型动态应力强度因子与真实值有很大的差别。第三个问题讨论了裂纹面摩擦对动态应力强度因子的影响。数值结果表明:随着摩擦系数的增加,裂纹面切向相对位移减小,相应的II型动态应力强度因子也减小;裂纹面接触摩擦对II型动态应力强度因子有很大的影响。如果忽略裂纹面摩擦,II型动态应力强度因子会被高估。此外,还可以看到,摩擦对裂纹面上法向相对位移、裂纹面上的接触压力及I型动态应力强度因子影响不大。在第四个问题的研究中,使用了周期对称有限元模型,考虑了叶根与叶根槽的接触作用。数值结果表明:汽轮机叶轮T型叶根槽半椭圆表面裂纹的I型、II型和III型应力强度因子都在表面点达到最大值;即使只施加离心载荷,汽轮机叶轮T型叶根槽表面裂纹也不能被认为是纯I型裂纹。此外,还研究了沿T型叶根角裂纹前缘各点的I型应力强度因子,主要结果是I型应力强度因子在角裂纹的最深点达到最大值。这些结果对这种含裂叶片和叶轮的强度评估和剩余寿命的预测具有很大的实用价值。
总之,在工程结构中有很多问题牵涉到裂纹和接触,本文的研究可以作为解决工程实际中这类问题的参考。
Components containing holes, such as bolted joints, are widely used in engineering structures. Cracks often exist at hole-edge because of stress concentration, contact interaction between components. Stress intensity factors are the important parameters in evaluating the crack growth, residual strength, and fatigue life of the cracked structures. Therefore, in order to ensure safety and make full use of the materials, accurate determination of stress intensity factors for cracked structures have great practical significance. The hole-edge crack problems involving contact interaction can be divided into two cases: (1) crack face contact problems, such as hole-edge crack problem under dynamic loading; and (2) problems of cracked components loaded through contact with another component, such as bolted joints with cracks. The problem of the hole-edge crack involving contact interaction is quite complicated. Usually, it is very difficult to obtain the analytical solution for the cracked problems. In this dissertation, the stress intensity factors of four hole-edge crack problems are investigated by using finite element method. The first problem is the numerical investigation of the stress intensity factors for the quarter-elliptical corner cracks at the bolt-hole of mechanical joints subjected to remote tension. The second one is the effect of contact between the crack surfaces on the dynamic stress intensity factors for a single edge horizontal crack at the center hole of a finite plate under compressive impact loading parallel to the crack. The third is the numerical investigation of the dynamic stress intensity factor for a single edge slant crack emanating from a circular hole in a finite plate subjected to compressive impact loading. The fourth is the numerical investigation of the stress intensity factors for a semi-elliptical surface crack at the T-root groove of a turbine disc under centrifugal loading.
Finite element analysis models of the problems mentioned above are created by ANSYS. The square-root stress singularity around the crack front is simulated by quarter point singular elements. From classical theory of linear elastic fracture mechanics, the formulas for stress intensity factors for two-dimensional crack and elliptical crack are derived by using the displacement extrapolation method. These formulas provide a convenient method for the determination of stress intensity factors for those problems mentioned above.
In the analysis of the first problem, contact interaction between the bolt-hole and the bolt (or pin) is considered, and the effects of the amount of clearance between the hole and the pin on the contact pressures and stress intensity factors are investigated. It is found that the contact pressure and contact region are variable in clearance. In the case of clearance being present, it is not appropriate that the contact interaction between the hole and the pin is replaced by applying uniform or cosine pressure distribution on bolt-hole boundary. Numerical results of the stress intensity factors show that the mode I stress intensity factors along the bolt-hole corner crack front increase with an increase in clearance between the hole and the bolt. These results indicate that the amount of clearance has a significant influence on the stress intensity factors for mode I, and its proper consideration is required to evaluate the crack growth, residual strength, and fatigue life of the cracked mechanical joints. At the same time, it is also discovered that the mode I stress intensity factor for bolt-hole corner crack reaches its maximum value at the deepest point. In the investigation of the second one, contact interaction between the crack surfaces is considered, and the effects of crack face contact on the dynamic stress intensity factors are investigated. The dynamic stress intensity factors with and without contact elements along crack surfaces are evaluated. Numerical results show that the negative mode I and a interpenetration or overlap between the crack surfaces may be prevented by taking account of the contact interaction of the crack edges, and crack face contact has a significant influence on mode I dynamic stress intensity factors. A more accurate analysis for a cracked problem under dynamic loading should include the contact interaction of the crack faces, otherwise the calculated dynamic stress intensity factors for mode I are significantly different from the true values. The third problem discusses the effect of the friction between the crack surfaces on the dynamic stress intensity factors. Results indicate that, with increasing friction, the tangential relative displacements at the crack edges and dynamic stress intensity factors for mode II decrease, and the frictional contact between the crack surfaces has a great influence on mode II dynamic stress intensity factors. If the friction between the crack surfaces is ignored, the mode II dynamic stress intensity factors may be overestimated. Additionally, it can be discovered that the friction at the crack edges has little influence on dynamic stress intensity factors for mode I, normal relative displacements, and contact pressures of the crack surfaces. In the fourth problem, finite element model with cyclic symmetry boundary conditions is used, and the contact interaction between the blade root and its groove is considered. Numerical results indicate that the mode I, II, and III stress intensity factors for semi-elliptical surface crack at the T-root groove of a turbine disc reach the maximum values of their individual modes at surface point, and the surface cracks can not be considered as pure mode I even if only centrifugal loadings are applied. Additionally, the mode I stress intensity factor along the corner crack front at T-root are investigated. Main result is the stress intensity factor for mode I reaches the maximum value at the deepest point of the corner crack. These results have a great practical valve for strength evaluation and fatigue life prediction of the cracked blade and disc.
In conclusion, there are many problems involving crack and contact in engineering structures. The study of the paper may be regarded as a reference for solutions of the problems encountered in engineering practices.
引文
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