正交复合材料I型裂纹动态响应焦散线实验研究

利用高速摄影技术与光学焦散线技术相结合,对冲击下正交复合材料I型裂纹尖端的动态应力集中问题进行了光测力学实验研究。记录了两种层状碳纤维/环氧树脂复合材料在冲击作用下I型裂纹尖端的动态焦散斑图,提取反映材料局部应力集中问题的力学参数:焦散斑特征尺寸,进而比较两种复合材料的抗冲击性能。这些研究工作对于复合材料冲击性能评估具有工程应用价值和科学研究意义。     

正交复合材料Ⅰ型裂纹动态响应焦散线实验研究

利用高速摄影技术与光学焦散线技术相结合，对冲击下正交复合材料Ⅰ型裂纹尖端的动态应力集中问题进行了光测力学实验研究。记录了两种层状碳纤维／环氧树脂复合材料在冲击作用下Ⅰ型裂纹尖端的动态焦散斑图，提取反映材料局部应力集中问题的力学参数：焦散斑特征尺寸，进而比较两种复合材料的抗冲击性能。这些研究工作对于复合材料冲击性能评估具有工程应用价值和科学研究意义。     

A theory of caustics for mixed-mode fast running cracks

The method of caustics (shadow spot method) has proven to be a powerful optical method to measure stress intensity factors in static and dynamic fracture mechanics problems. In this paper, a theory of caustics was developed for elastodynamically propagating cracks under inplane mixed-mode conditions. Complex potentials for the general solutions of a near-tip field which have been previously derived by the authors were used in this theoretical development. Completely analytical expressions were derived for the caustic curves as well as for the initial curves for fast running cracks under inplane mixed-mode conditions. The effects of crack velocity and mixed-mode condition on the caustic pattern and the initial curve were investigated. New procedures were also proposed for the evaluation of the dynamic stress intensity factors K_I and K_II using the overall dimensions of the caustic pattern. The method of caustics developed here enables one to study quantitatively various mixed-mode dynamic fracture phenomena such as crack branching, crack curving, and crack kinking.     

A STUDY OF RESIDUAL CAUSTICS GENERATED FROM FATIGUE CRACKS

Abstract— The method of caustics was used to determine the stress intensity factor of fatigue cracks in steel compact tension specimens. Under zero load a residual caustic was observed at the tip of a fatigue crack indicating the presence of a residual stress field. Caustics were generated at increasing static loads and the stress intensity factors were compared with those predicted by theory. It was found that the difference between each measured stress intensity factor and its corresponding theoretical value was a constant for the range of loads. This difference was shown statistically to be equal to the stress intensity factor determined from the residual caustic. The proposed mechanism for the formation of this residual caustic was probably due to crack tip plasticity effects and not due to crack closure. It was concluded that residual caustics can be measured to quantify crack tip behaviour in fatigue cracks and have been shown to be a useful tool in the measurement of residual stress fields.     

Analysis of the optical method of caustics for dynamic crack propagation

In the interpretation of experimental data on dynamic crack propagation in solids obtained by means of the optical method of caustics, it has been customary to neglect the effect of material inertia on the stress distribution in the vicinity of the crack tip. In this paper, the elastodynamic crack tip stress field is used to establish the exact equations of the caustic envelope formed by the reflection of light rays from the surface of a planar solid near the tip of a propagating crack. These equations involve the instantaneous crack tip speed, the material parameters and the instantaneous dynamic stress intensity factor, and they can be used to determine the stress intensity factor for given material parameters and crack tip speed. The influence of inertial effects on stress intensity factor measurements for system parameters typical of experiments with PMMA specimens is considered. It is found that the stress intensity factor values inferred through a dynamic analysis may differ by as much as 30–40% from values based on a quasi-static analysis.     

Dynamic initiation and propagation behaviour of sub-interfacial cracks in PMMA/aluminium bi-material system

The paper describes studies on the dynamic initiation and growth of sub‐interfacial cracks in a PMMA/aluminium bi‐material system using high‐speed photography combined with the method of caustics. Dynamic fracture phenomena such as crack propagation trajectories, crack velocity, phase angle and stress intensity factor were determined from recordings of a series of dynamic caustic patterns surrounding the propagating sub‐interfacial crack tip.. There is a considerable influence of the distance between the interface and the crack on fracture characterization.     

Theoretical development of the method of caustics for intersonically propagating interfacial crack

In this paper, a theory of caustics for an intersonically propagating interfacial crack is developed. Using the first invariant of stress singular field in the vicinity of the intersonically propagating tip of an interface crack, mapping equations are derived for the caustic curve on the reference plane as well as the initial curve on the specimen plane. The effect of the crack velocity on the caustic pattern is investigated. Two practically measurable characteristic dimensions are proposed. Using these characteristic dimensions, a simple procedure is also proposed for the evaluation of the stress singularity factor for the intersonically propagating interfacial crack.     

Theoretical development of the method of caustics for intersonically propagating interfacial crack

In this paper, a theory of caustics for an intersonically propagating interfacial crack is developed. Using the first invariant of stress singular field in the vicinity of the intersonically propagating tip of an interface crack, mapping equations are derived for the caustic curve on the reference plane as well as the initial curve on the specimen plane. The effect of the crack velocity on the caustic pattern is investigated. Two practically measurable characteristic dimensions are proposed. Using these characteristic dimensions, a simple procedure is also proposed for the evaluation of the stress singularity factor for the intersonically propagating interfacial crack.     

Theoretical simulations of a propagating crack subjected to in-plane stress wave loading by caustic method

The optical method of caustics for measuring the dynamic stress intensity factor in a transient process is investigated in this study. The transient full-field solutions of a propagating crack contained in an infinite medium subjected to step-stress wave and ramp-stress wave loadings are used to establish the exact equations of the initial and caustic curves. The results of the stress intensity factor obtained from the caustic method are compared with theoretical predictions and some experiments. The results demonstrate that a significant deviation can occur in the determination of the dynamic stress intensity factor from shadow spot measurements. The factors, such as screen distance, magnitude of loading, crack speed and rising time which can influence the accuracy of the experimental measurements are discussed in detail. In addition, the valid region of the dynamic stress singular field for the propagating crack is discussed in detail and it gives a better understanding of the appropriate region of measurements for investigators. This revised version was published online in July 2006 with corrections to the Cover Date.     

基体裂纹-异型夹杂相互作用焦散线实验研究

该文通过透射式静态焦散线方法利用三点弯曲梁断裂实验对异型夹杂与基体裂纹的相互作用进行研究。首先得到不同夹杂情况下I型裂纹尖端的焦散斑图,引入焦散斑纵横轴长之比β反映焦散斑在夹杂作用下的畸变特性;其次,提取相应的焦散斑特征尺寸,并得到I型裂纹的应力强度因子K_I;最后,基于不同夹杂情况下裂尖焦散斑、裂尖应力强度因子与裂尖和夹杂之间距离的关系,揭示不同夹杂对裂纹尖端应力场奇异性影响规律。实验研究结果为含异型夹杂结构的强度设计和断裂性能评估提供实验依据。     

Three-dimensional effects in the determination of stress intensity factors by the method of caustics

A thorough investigation of the dependence of the stress-optical constants on the degree of triaxiality in the stress field is undertaken. This study is essential for the evaluation of stress intensity factors in crack problems by the method of caustics, since the state of stress around the crack tip, generally, is three-dimensional. Results showing the variation of the stress-optical constants around the crack tip are displayed. Based on these results a new methodology for the experimental evaluation of stress intensity factors by caustics is proposed. According to this methodology stress intensity factors can be determined even for the case when the initial curve of the caustic lies in the region where the state of stress is three-dimensional and cannot be approximated as plane stress or plane strain.Presented at Fourth Greek National Congress on Mechanics, 26–29 June 1995, held at Xanthi, Greece.     

Singularities and perturbations for far-field caustics in the neighborhood of a crack tip

Summary Adapting the principle of least time by Fermat, the farfield caustics around a crack tip were studied as a variational problem. The singular reflected rays were probed and classified using singularity theory; furthermore the singular directions were also defined.In addition, applying perturbation theory the stress intensity factor at a crack tip is evaluated, considering higher-order terms of the Muskhelishvili complex potential.It was shown that higher approximations can be achieved with this method from caustics engendered from initial curves of a larger than usual radius convenient for problems of plasticity and elastic anisotropy.With 6 Figures     

含周期性裂纹正交各向异性板平面问题的应力场分析

通过引入适当的Westergaard应力函数,采用复变函数方法和待定系数法对含周期性裂纹正交各向异性纤维增强复合材料板的Ⅰ 型、Ⅱ型问题中裂纹尖端附近的应力场进行了力学分析。在远处对称载荷与斜对称载荷作用下,先给出Ⅰ型、Ⅱ型问题在裂纹尖端处的应力强度因子,然后导出用应力强度因子表示的Ⅰ型、Ⅱ型裂纹问题应力场的解析表达式。此外,应力场大小与材料常数有关,这是正交各向异性材料不同于各向同性材料的特征。由于裂纹的周期分布,应力强度因子的大小取决于形状因子。结果表明,形状因子随着裂纹长度的增加而增大,随着裂纹间距的增大而逐渐下降,当裂纹间距趋于无穷大时,退化为含单个中心裂纹正交各向异性纤维增强复合材料板的结果。      

Interferometry for the evaluation of the dynamical optical and mechanical properties of transparent materials

A theory is developed which leads to an interferometric method for determining the dynamic ratio, Poisson's ratio to the modulus of elasticity, and the dynamic stress-optical coefficients of transparent plates, both during the same set of tests and without attaching mechanical or electrical sensors on the surface of the specimen.

The method requires a monochromatic light source, that is, a parallel beam is directed perpendicularly to the vicinity of a crack tip which exists in the plate specimen under investigation. The rays impinging on the crack tip are transmitted through the plate and reflected by the two parallel surfaces of the plate. At the same time, because of the variation of the optical path (index of refraction and thickness of the plate) in the said area, the rays are refracted in such a way as to form two caustic surfaces, one by the transmitted and one by the reflected rays. These two caustic surfaces, when intercepted with two opaque screens, provide two strongly illuminated curves of a general epicycloid shape called caustics.

The size of the caustics is directly related to the applied load, the material properties and the distance specimen-screen. Their ratio, however, as it is taken at equally distant screens, depends only on the optical and mechanical properties of the material in question.

In addition, an interferogram consisting of fringes, as formed from rays reflected by the two surfaces of the plate, is obtained. The fringe number depends on the wavelength of the light source and the optical path. When the plate specimen is loaded, the optical path changes. This results in a change of the fringe number and consequently to a displacement of fringes with respect to a reference point as they are observed on an opaque screen.

The ratio of the two caustics, taken during a static test, and the number of displaced fringes per applied load, taken during a dynamic test, provide enough information for the determination of the aformentioned mechanical and optical parameters.

Experiments conducted according to the method developed on acrylic plates and for a tensile impulse of total time duration of 600 μsec produced a reduced by 23.5% ratio of Poisson's ratio to modulus of elasticity from the static value and a reduced by 21% stress-optical coefficient from the static value.     

含倾斜裂纹三点弯动态断裂试验研究

为研究冲击荷载下巷道围岩不同角度径向裂纹的破坏机制,采用落锤冲击加载平台和数字激光动态焦散线实验系统,以有机玻璃为试验材料,设计冲击荷载下半圆孔上不同角度裂纹的三点弯动态断裂试验,记录预制裂纹的角度α的改变对裂纹动态力学行为的影响,通过分析动态应力强度因子和裂纹扩展轨迹的分形维数对实验现象进行归纳总结。研究发现:①预制裂纹角度对裂纹尖端应变能的积累和释放的快慢有较大影响,随着角度的增大,起裂时间变短,起裂更容易,裂纹尖端应变能积累的更快;②裂纹尖端应变能释放的快慢在α=45°两侧表现出不同的规律;③不同角度裂纹的Ⅰ型动态应力强度因子随时间的变化规律具有相似性,但最大值却具有差异性;④不同角度裂纹的扩展轨迹满足一定的分形规律。     

The method of caustics in environmental cracking

A simple and powerful crack growth criterion under combined environmental conditions and applied loads is formulated for mixed-mode situations based on the method of caustics. It is established that the axis of symmetry of the caustic represents the crack growth direction, while the crack growth condition is expressed in terms of the diameter of the caustic. Caustics can easily be obtained by illuminating the specimen in the vicinity of the crack tip by a laser light beam and recording the optical pattern on a viewing screen at some distance from the specimen. An elegant procedure for the experimental study of environmental cracking is thus developed.     

爆炸载荷下边界锐V型切口尖端裂纹扩展行为

为了研究爆炸应力波作用下板条边界锐V型切口端部的动态扩展行为,采用动态焦散线实验方法,进行了爆炸载荷下板条边界锐V型切口端部裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界锐V型切口端部的扩展过程中,裂纹扩展速度、加速度和切口端部动态应力强度因子随时间是波动变化的.扩展速度最大值达到210m/s,裂...     

爆炸载荷下边界锐V型切口尖端裂纹扩展行为

为了研究爆炸应力波作用下板条边界锐V型切口端部的动态扩展行为,采用动态焦散线实验方法,进行了爆炸载荷下板条边界锐V型切口端部裂纹扩展规律的实验研究。研究结果表明,爆炸应力波作用下,板条试件边界锐V型切口端部的扩展过程中,裂纹扩展速度、加速度和切口端部动态应力强度因子随时间是波动变化的。扩展速度最大值达到210m/s,裂纹扩展加速度最大值为9.47Mm/s2,切口端部动态应力强度因子KdⅠ最大值为0.6MN/m3/2。     

动焦散线在爆炸裂纹扩展试验研究中的应用

爆炸裂纹的动态扩展问题是爆炸力学研究的热点。本文建立了爆炸加载的动焦散线测试系统,解决了试验中的有效光学图片获取、精确同步控制等问题,为进一步定量分析爆炸裂纹扩展规律提供了一种新的有效实验方法。采用爆炸加载的透射式动焦散实验系统,初步研究了爆炸载荷下的裂纹起裂、发展和止裂的动态扩展行为,分析其破坏模式和动态应力强度因子、裂纹扩展速度的变化,并研究了爆炸裂纹穿过有机玻璃板的人工层理的规律。     

动焦散线在爆炸裂纹扩展试验研究中的应用

爆炸裂纹的动态扩展问题是爆炸力学研究的热点。本文建立了爆炸加载的动焦散线测试系统,解决了试验中的有效光学图片获取、精确同步控制等问题,为进一步定量分析爆炸裂纹扩展规律提供了一种新的有效实验方法。采用爆炸加载的透射式动焦散实验系统,初步研究了爆炸载荷下的裂纹起裂、发展和止裂的动态扩展行为,分析其破坏模式和动态应力强度因子、裂纹扩展速度的变化,并研究了爆炸裂纹穿过有机玻璃板的人工层理的规律。