复合材料断裂力学参量的实验测定

本文采用三维云纹干涉仪同步测量含裂纹复合材料弯曲板的面内位移场及离面位移场，并对离面位移场云纹图进行计算机自动采集和处理，编制了云纹数字图像处理软件。文中推导了正交异性复合材料弯曲问题的离面位移场表达式，得到了弯曲板裂纹尖端位移w与应力场强度因子K1的关系式。通过实测位移，结合裂尖位移场推导出应力强度因子K1值。     

紧凑拉伸试件应力强度因子的解析-变分解法以及有关系统计算结果

本文推导了在材料断裂性能测试中常见的受钉传载荷含边缘裂纹试件应力与位移的函数项级数表达式。该级数逐项满足弹性力学所有基本方程、裂纹表面边界条件与绕钉孔的合力平衡条件以及位移单值条件。通过以最小势能原理为基础的变分方程满足其余的静力边界条件,从而求解级数中的待定系数并确定应力强度因子。计算结果表明,级数收敛迅速、正确,计算节省机时,简化数据准备工作。本文还通过计算指出了目前通用的有关矩形紧凑拉伸试件应力强度因子计算公式与曲线的不准确性并且给出了正确、系统的计算曲线,同时还提供了圆形紧凑拉伸试件系统的计算结果。     

云纹／光栅测试技术的几点讨论

本文用信号处理的方法系统地阐述了云纹／光栅测试技术。以面内云纹／光栅测试为例，首先说明了光栅是位移和变形信息的空间载体；位移和应变分别是对载体的相位和频率调制；而云纹现象则是试件栅频谱向零频处平移的结果或说云纹是对光栅载体信号解调的过程；进而讨论了云纹技术与光栅技术的本质区别。其次分析了云纹／光栅测试系统的性能，讨论了条纹分析方法及数字图象处理手段对云纹／光栅系统的测试精度、灵敏度、空间分辨率的影响。     

界面剪切实验研究

用云纹干涉法测量了带边裂纹的双材料四点简支梁在剪切作用下界面表面的剪应变分布及界面两侧局部表面的位移场（Ｕ、Ｖ场），试件是由弹性模量相差悬殊的铝合金和环氧塑料两种材料制成。文中给出了试件制备、实验方法和测试结果。     

求解混合型裂纹应力强度因子的围绕积分法

本文用复变函数理论推导出裂纹的辅助场，并用Ｂｅｔｔｉ功互等定理给出求解混合型裂纹应力强度因子的远场围绕积分法，此方法与积分路径的选择无关，用有限元法计算出远离裂纹尖端的位移场和应力场，就可通过计算绕裂端的围线积分，精确地给出混合型裂纹的应力强度因子Ｋ１和Ｋ１的数值解。     

用二维贴片云纹干涉法测定复合型应力强度因子

1.二维贴片云纹干涉法某些较复杂的具一般性的复合型应力强度因子,例如具有单边斜裂纹受三点弯曲的矩形梁(图1),测定一维位移难於确定其复合型应力强度因子,必须采用能提供二维位移的实验技术.本文采用图2所示光路,其中,准直镜5射出的两光束相干涉,形成铅垂y方向的虚光栅;经半透半反光镜6分束的准直光,一部分直接射向试件9,另一部分通过与试件表面垂直的全反镜8再反射到试件9.两者相干形成水平x方向的     

用围线积分法计算压电材料面外剪切问题的应力强度因子

本文把Ｂｅｔｔｉ功互等原理推广到压电材料的面外剪切问题中，并且根据Ｐａｋ的压电材料Ⅲ型裂纹问题复势解，给出了其裂端位移，电势，应力和电位移的渐近解及相应的辅助场具体，然后，把有限元数值作为真实平衡状态，把推导出的辅助场作为辅助平衡状态，利用围线积分法出了压电材料Ⅲ型裂纹问题的应力强度因子ＫⅡ和电强度因子ＫⅣ。算例表明，计算结果与理论解符合得很好。     

用围线积分法计算压电材料面外剪切问题的应力强度因子

本文把Ｂｅｔｉ功互等原理推广到压电材料的面外剪切问题中，并且根据Ｐａｋ的压电材料Ⅲ型裂纹问题复势解，给出了其裂端位移、电势、应力和电位移的渐近解及相应的辅助场具体形式。然后，把有限元数值解作为真实平衡状态，把推导出的辅助场作为辅助平衡状态，利用围线积分法计算出了压电材料Ⅲ型裂纹问题的应力强度因子ＫⅢ和电强度因子ＫⅣ。算例表明，计算结果与理论解符合得很好     

求解界面裂纹应力强度因子的围线积分法

本文基于Ｂｅｔｔｉ功互等定理和双材料界面裂纹辅助场，提出了一种求解界面裂纹应力强度因子的方法，即远场围线积分法。此方法与积分径的选择无关，用有元元法计算出远离裂纹尖端的位移场和应力场，应可通过计算绕裂尖围线的积分，精确地给出界面裂纹应力强度因子ＫＩ和ＫⅡ。     

40Cr材料动态起裂韧性KId（）的实验测试

描述了利用Ｈｏｐｋｉｎｓｏｎ压杆技术加载三点弯曲试样测试４０Ｃｒ，材料动态起裂韧性ＫＩｄ（）的试验方法。试样上的动态载荷历程由Ｈｏｐｋｉｎｓｏｎ杆直接测得，并分别代入动态有限元程序及近似公式求得动态应力强度因子历史；由贴在试样裂尖附近的应变片确定起裂时间，最终确定起裂时的动态应力强度因子值，即动态起裂韧性ＫＩｄ（）。试验结果表明:利用Ｈｏｐｋｉｎｓｏｎ压杆技术加载三点弯曲试样测试材料动态起裂韧性的方法是可行的，起裂时，动态有限元的位移法、应力法及近似公式法求得的动态应力强度因子值比较吻合；在本文的载荷速率下，４０Ｃｒ材料动态起裂韧性ＫＩｄ（）与准静态裂韧性ＫＩｄ（）相比，降低了约２８％。     

Dynamic fracture toughness determined from load-point displacement

The paper presents a method to determine dynamic fracture toughness using a notched three-point bend specimen. With dynamic loading of a specimen there is a complex relation between the stress-intensity factor and the force applied to the specimen. This is due to effects of inertia, which have to be accounted for to evaluate a correct value of the stress-intensity factor. However, the stress-intensity factor is proportional to the load-point displacement if the fundamental mode of vibration is predominant in the specimen. The proportionality constant depends only on the geometry and stiffness of the specimen. In the present method we have measured the applied force and load-point displacement by a modified Hopkinson pressure bar, where two-point strain measurement has been used to evaluate force and displacement for times greater than the transit time for elastic waves in the Hopkinson bar. We have compared the method with the stress-intensity factor derived from strain measurement near the notch tip and good agreement was obtained. The method is well suited for high-temperature testing and results from fracture toughness tests of brittle materials at ambient and elevated temperatures are presented.     

Three-dimensional speckle interferometric investigation of the stress-intensity factor along a crack front

The variation in Mode I stress-intensity factor throughout the thickness of an ASTM standard compact tension specimen was determined using scattered-light speckle interferometry. Two very thin sheets of coincident coherent light traveling in opposite directions were passed through a Plexiglas specimen normal to the crack faces. A double-exposed photograph of the scattered-light speckle pattern was taken while the specimen was subjected to a small load increment. From this double-exposed photograph, the change in the crack-opening displacement could be determined. From the information about the crack-opening displacement in the region of the crack tip, the stress-intensity factor was calculated for various interior planes and on the surface of the specimen. For the compact tension specimen tested, the stress-intensity factor did not vary throughout the specimen's thickness. The method of scattered-light speckle interferometry proved to be very powerful in solving this complex three-dimensional problem.     

An analytical and experimental stress analysis of a practical mode II fracture test specimen

A boundary-collocation method has been employed to determine the Mode II stress-intensity factors for a pair of through-the-thickness edge cracks in a finite isotropic plate. An elastostatic analysis has been carried out in terms of the complete Williams stress function employing both even and old components. The results of the numerical analysis were verified by a two-step procedure whereby the symmetric (Mode I) and antisymmetric (Mode II) portions of the solution were independently compared with existing solutions. Since no previous analytical solutions existed for the asymmetric loading of an edge-cracked plate, the complete solution was verified by comparison with a photoelastic analysis. A compact shear (CS) specimen of Hysol epoxy resin was loaded in a photoelastic experiment designed to study the isochromatic-fringe patterns resulting from the Mode II crack-tip stress distribution. The experiment verified that a pure mode II stress distribution existed in the neighborhood of the crack tips, and confirmed the accuracy of the boundary-collocation solution for the Mode II stress-intensity factors. Specimen center-line stress-distribution data were obtained photoelastically and employed to refine the boundary-collocation analysis. Agreement between the analytically and experimentally determined Mode II stress-intensity factors was excellent.     

The principle and application of sticking film moiré internnferometry

This paper presents a new method for obtaining a high-resolution one-dimensional or two-dimensional moiré pattern on a specimen. The technique uses a holographic film that adheres to the specimen. The film is twice exposed by a virtual holographic grating, then it is removed from the specimen, devellped, fixed, bleached, and illuminated. This process produces clearly visible moiré patterns. The method is used to measure elastic modulus values of some materials, deflection and longitudinal displacement of a beam, stress-intensity factors (SIF), crack-opening displacement (COD,J integral, and a dynamic deformation. This paper explains the principles of the method, derives two displacement equations of two-dimensional moiré interferometry, and discusses the reliability, range of application, and measuring precission of the new method.     

Long wavelength impact of izod fracture specimens: An experimental/numerical investigation

Elastic wave propagation fields for a stationary crack in an Izod fracture specimen have been investigated. Moiré interferometry was used to obtain the asymptotic cracktip displacement fields under Hopkinson bar loading at sampling rates on the order of 100 kHz. Mixed-mode stress-intensity factors as a function of time were extracted from the displacement data using local asymptotic extrapolation. Two-dimensional continuum finite elements were employed and agreement was found between actual experiment and two-dimensional computation.     

Solution of a flat elliptical crack in an electrostrictive solid

Based on the assumption that the elastic strain of electrostrictive materials is a higher-order small quantity, this paper studies the 3D problem of an infinite electrostrictive solid with a flat elliptical crack which is electrically permeable. According to existing solutions of similar problems in pure elastic materials, with the displacement function method, we first derived explicit expression for displacement potential function and obtained stress field near the crack and open displacement of crack surface. Then, the general solution for the stress intensity factor was derived, and the corresponding solutions were also presented for a penny-shaped crack and a permeable line-crack as two special cases of the present problem. Finally, numerical results were given to discuss the effect of environment at infinity and electric field inside the crack on the stress-intensity factors.     

Mixed-mode crack-tip deformations studied using a modified flexural specimen and coherent gradient sensing

An optical mapping of deformation fields and evaluation of fracture parameters near mixed-mode cracks in homogeneous specimens under elastostatic conditions is undertaken. A modified edge notched flexural geometry is used in the study and its ability in providing a relatively wide range of mode mixities is demonstrated. A full-field, optical shearing interferometry called ‘coherent gradient sensing’ (CGS) is used in the study. Crack-tip parameters such as stress-intensity factors, mode mixity and energy-release rate are measured from the interference patterns. The patterns are analyzed using Williams' mixed-mode, asymptotic expansion field. An expression for energy-release rate for the specimen is also derived using beam theory. The theoretical stress-intensity factors are then obtained using a mode-partitioning method based on moment decomposition. Experimental measurements and theoretical predictions are found to be in good agreement. Limitations of the mode-partitioning method used in the investigation are also pointed out.     

A new fracture-toughness test method for thick-walled cylinder material

A new method for measuring the plane-strain fracture toughness of the material from a thick-walled cylinder is presented. This method utilizes a notched, “C”-shaped test specimen, pin loaded in tension. This specimen has the advantage of most efficiently utilizing the available material to obtain the maximum possible triaxial constraint at the crack tip. Stress-intensity-factor calibrations for this specimen were obtained by two independent experiments. These are a compliance test, as originally proposed by Irwin, and a fatigue-crack-growth test, as suggested by James and Anderson. Very good agreement was obtained between the results of these two experiments. A stress-intensity calibration for a similar geometry was also obtained using a finite-element analysis and a method developed by Kobayashi to determine stress-intensity factors from finite-element results. The results of this method appear to be low by about 10 percent. Comparative fracture-toughness tests of material from a 2-in.-thick plate of special aircraft quality, 4340 steel, were conducted using the proposed new test method and the ASTM standard bend specimen. These results agreed within 2 percent.     

求解混合型裂纹应力强度因子的围线积分法

本文用复变函数理论推导出裂纹的辅助场，并用Betti功互等定理给出求解混合型裂纹应力强度因子的远场围绕积分法．此方法与积分路径的选择无关，用有限元法计算出远离裂纹尖端的位移场和应力场，就可通过计算绕裂端的围线积分，精确地给出混合型裂纹的应力强度因子KⅠ和KⅡ的数值解．     

Determination of fracture parameters using embedded fiber-optic sensors

The applicability of embedded fiber-optic sensors for the determination of fracture parameters is demonstrated. A Mach-Zehnder interferometric setup is used and mode-1 stress-intensity factors are obtained by embedding single-mode fibers in single-edge-notched specimens fabricated from Plexiglas. Optical fibers are embedded in-plane to measure axial strains at various depths and also in the transverse direction to measure the transverse strains, from which stress-intensity factors are determined. In both cases the experimental results compare well with the theoretical predictions.