Experimental and numerical analysis of vibrating cracked plates at resonant frequencies

Owing to the advantages of noncontact and fullfield measurement, an optical system called the amplitude fluctuation electronic speckle pattern interferometry (AFESPI) method with an out-of-plane setup is employed to investigate the vibration of a cantilever square plate with a crack emanating from one edge. Based on the fact that clear fringe patterns will be shown by the AFESPI method only at resonant frequencies, both the resonant frequencies and the vibration mode shapes can be obtained experimentally at the same time. Three different crack locations will be discussed in detail in this study. One is parallel to the clamped edge, and the other two are perpendicular to the clamped edge. The numerical finite element calculations are compared with the experimental results, and good agreement is obtained for resonant frequencies and mode shapes. The influences of crack locations and lengths on the vibration behavior of the clamped cantilever plate are studied in terms of the dimensionless frequency parameter (λ ²) versus crack length ratio (a/L). The authors find that if the crack face displacements are out of phase, a large value of stress intensity factor may be induced, and the cracked plate will be dangerous from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, causing a zero stress intensity factor, and the cracked plate will be safe.     

基于有限元方法对人工径向裂纹薄圆板振动辐射声场的研究

在有限元模态分析的基础上，提取了含人工径向裂纹的周界固定薄圆板各单元的相关参数，并将瑞利积分离散化后进而计算了裂纹圆板辐射声场的轴向声压分布和r=0．5m球面上声场指向性。结果表明，径向裂纹不仅使模态裂解为关于裂纹的对称模态和反对称模态，而且使声场分布有显著的变化。通过完整圆板辐射声场计算验证了本文提出方法的正确性。可用于求解任意形状穿透裂纹薄圆板辐射声场的计算。     

Grid Method for Microscale Discontinuous Deformation Measurement

The objective of this paper is to explore both grid method and Digital Image Correlation (DIC) technique for microscale and discontinuous displacement measurements, such as those associated with crack tips. First, the principle of the grid method is revisited. The grid method and DIC technique are then applied to computer generated images to calculate the displacement field around crack tips. Finally, the grid method is applied to actual experimental images of fracture tests which are conducted inside a Scanning Electron Microscope (SEM) chamber. A new technique is developed to generate microscale pattern that is suitable for both grid method and DIC technique. The displacement fields calculated from grid method are compared with those from DIC technique to identify the strengths and weaknesses of each technique for the microscale and discontinuous displacement measurements. It has been determined that grid method can obtain data closer to the discontinuity than DIC; however, DIC produces smoother displacement fields at the far field. Using this new pattern generation technique, both grid method and DIC technique can be applied to the fracture test at the microscale to complement with each other to achieve the best experiment results.     

橡胶磨损花纹裂纹角的分形计算法

在考察橡胶磨损花纹裂纹角与橡胶磨损表面分形维数关系的基础上,提出了用分形计算橡胶磨粒磨损的磨损花纹裂纹角的新方法,发现丁苯橡胶和丁腈橡胶磨损花纹的裂纹角在不稳定磨损阶段基本保持不变,而在稳定磨损阶段则随法向载荷的增大而减小．     

A contact force model in the dynamic analysis of contactable cracks

In this paper a finite element method in the time domain is proposed to analyze the dynamic response of contactable cracks. By this method, the contact normal stress caused by impact or contact of the crack faces can be directly obtained and then the motion of the model containing the contactable cracks can be calculated, and the processes of contact, slip and separation of the crack faces can also be correctly determined and simulated. The method proposed can be used to study the scattering problems of an elastic wave caused by the crack and the dynamic extension problems of the crack arising from impact or cyclic loading. Numerical examples indicate that the method is efficient and accurate enough. It is also shown that the effect of dynamic contact of crack faces on the motion of itself and the area near the crack is significant by comparing the results with the contact considered and neglected.     

界面裂纹的路径选择与数值模拟

利用界面断裂能和荷载混合度的概念研究界面裂纹的扩展路径，利用有限元数值方法模拟界面裂纹的扩展过程，再现界面断裂的各种几何构型．研究表明，界面的断裂能和混合度完全控制了裂纹在界面附近的扩展过程．数值预测的裂纹路径与理论结果一致     

THE PROBLEM OF I-II COMBINED PLANE CRACK SOLVED WITH WESTERGAARD STRESS FUNCTION

直接获得I-II复合型平面裂纹问题裂纹尖端区域的应力场是一个比较复杂的问题,在此应用Westergaard应力函数求解I-II复合型平面裂纹问题,导出了裂纹尖端区域应力分量的表达式。该方法推导过程简单,物理概念清晰,其结果与一般断裂力学教材和文献中的结果一致。同时,应用叠加原理将裂纹面上的作用力转化为裂纹外边界的受力,给出了解决裂纹面上有作用力的I-II复合型平面裂纹问题的解题方法。     

直接计算应力强度因子的扩展有限元法

系统地给出了直接计算应力强度因子的扩展有限元法。该方法以常规有限元法为基础,利用单位分解法思想,通过在近似位移表达式中增加能够反映裂纹面的不连续函数及反映裂尖局部特性的裂尖渐进位移场函数,间接体现裂纹面的存在,从而无需使裂纹面与有限元网格一致,无需在裂尖布置高密度网格,也不需要后处理就可以直接计算出应力强度因子,并且大大简化了前后处理工作。最后通过两个简单算例验证了该方法的精度,分析了影响计算结果的因素,并与采用J积分计算的应力强度因子作了对比,得出了两种方法计算精度相当的结论。     

压应力对压剪裂纹扩展的影响研究

本文针对压剪裂纹的启裂及扩展问题,研究了脆性材料中裂纹面压应力变化对其扩展的影响规律.借助双轴加载试验机可自由调节两个轴位移和力的优势,设计了一种单边对称双裂纹压剪试样.试验中,施加裂纹面压应力至不同的预设值后,使剪应力单调增大直至裂纹启裂及扩展,得到不同预设压应力下压剪裂纹启裂及扩展规律. 随着预设压应力增大,启裂角增大,裂纹扩展路径与初始裂纹的偏角也增大.但随着压应力增大,启裂角增大至一定值后趋于稳定,实验发现,依据裂纹是否闭合,压应力对压剪裂纹扩展的作用大致可分为两个阶段:闭合前,压应力对裂纹启裂载荷及启裂角、扩展路径均有影响,预设压应力增大,裂纹启裂载荷增大、启裂角增大,扩展路径愈来愈偏离初始裂纹方向;闭合后,压应力虽然增大,启裂角和临界压剪应力比始终恒定,压应力对临界剪力和扩展路径存在一定影响.研究表明,裂纹启裂角与启裂时的压剪应力比存在一定的对应关系.启裂时的压剪应力比增大,启裂角增大,启裂时的压剪应力比恒定,启裂角不变.      

功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载的响应分析

在忽略界面裂尖端裂纹面相互叠入的条件下,对功能梯度材料与均质材料交界面上Ⅰ-型裂纹对简谐动载响应问题进行了分析。利用傅立叶变换,将问题的求解转换为对以裂纹面上位移差为未知函数的对偶积分方程的求解。为了求解对偶积分方程,将裂纹面上的位移差函数展开为雅可毕多项式的级数形式。最终给出了裂纹长度、入射波频率和材料性质对应力强度的影响。结果表明,当界面材料不连续时,获得了具有普通1/2奇异性的近似解。