单向静压下柱状炮孔端部爆生裂纹的扩展规律

高地应力对岩层地下工程爆破动态断裂过程有重要影响。采用数字激光动态焦散线测试系统,研究了不同单向静压下柱状炮孔端部爆生裂纹动态断裂行为,明确了柱状炮孔端部爆生裂纹的扩展规律。结果表明:单向静压越大,端部裂纹平均扩展长度越短,但单向静压下端部裂纹尖端积聚能量的快速释放会导致裂纹初始扩展速度提升;裂纹尖端应力强度因子基本随单向静压增加而递减,单向静压越大,应力强度因子随时间下降越剧烈,裂纹的止裂韧度越高,止裂时间越早;单向静压作用下的爆生裂纹在整个扩展阶段基本表现为I型裂纹,无静压作用下爆生裂纹在扩展初期表现为I型裂纹,中后期表现为复合型裂纹。研究结果对认识静压作用下的柱状炮孔端部破坏机理具有一定意义。     

定向断裂双孔爆破含缺陷介质裂纹扩展的动焦散试验

利用爆炸加载数字激光动态焦散线试验系统,进行双孔爆破爆炸应力波作用下缺陷介质裂纹扩展试验。研究了含水平预制裂纹和竖直预制裂纹的介质裂纹扩展路径、速度、加速度和裂尖动态应力强度因子变化规律。试验结果表明:在爆炸应力波作用下,预制裂纹尖端起裂,并扩展。炸药爆炸后,主裂纹的扩展速度迅速达到峰值,之后开始振荡减小,其加速度呈现波浪起伏式的振荡变化。次裂纹起裂后速度增大至峰值,然后开始减小。主裂纹尖端的动态应力强度因子K_Ⅰ从峰值振荡减小,又振荡增加至第二个峰值,之后振荡减小。次裂纹尖端的动态应力强度因子K_Ⅰ达到最大时,次裂纹起裂,之后K_Ⅰ振荡减小。裂纹扩展的过程中K_Ⅱ基本都小于K_Ⅰ。     

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.     

Multilayered piezomagnetic/piezoelectric composite with periodic interfacial Yoffe-type cracks under magnetic or electric field

The problem of periodic mode-III Yoffe-type cracks propagating subsonically along the interfaces in a multilayered piezomagnetic/piezoelectric composite under in-plane magnetic or electric field is studied. By means of periodic conditions, the analysis of the multilayered problem is simplified to a bilayer model with an interfacial Yoffe-type crack, which can be reduced to the Cauchy singular integration equation of the first kind, by utilizing the Fourier transform. The normalized dynamic stress intensity factor (NDSIF) can be obtained numerically. Results show that the NDSIF generally depends on the layer thickness ratio, crack moving speed, electric or magnetic loading as well as material properties. In regard to the curve monotony of the NDSIF versus the passive layer thickness, there generally exist three different cases distinguished by a parameter, θ, which depends on the crack moving speed as well as material mismatch parameters. Similar behavior has been reported for the periodic static cracks where the different monotonies are judged by the material mismatch parameter G (Wan et al. in Eng. Fract. Mech. 84:132–145, 2012). The present results reduce to those of periodic static cracks when considering the vanishing crack speed. As far as the curve monotony and the judging parameter are concerned, no matter what the crack moving speed is, the Yoffe-type crack problem is identical to the static crack problem when the piezomagnetic and piezoelectric layers share the same shear wave velocity. In addition, detailed analyses are also provided for NDSIF versus crack moving speed for different layer thickness ratio and material mismatch parameters. This study can be considered as an extension of the previous analysis of periodic static cracks problem and is expected together to provide some guidelines for the optimal design of a multilayered PM/PE composite.     

An analytical and numerical study of a dynamically accelerating semi-infinite crack in a linear viscoelastic material

In a previous paper, a general method was presented for constructing the solution to the problem of a semi-infinite, mode III crack propagating dynamically through an infinite, general linear viscoelastic body. The only restrictions placed upon the crack tip speed were that it have constant sign and in magnitude not exceed the glassy shear wave speed. In the present contribution, those previous analytical results are applied to a study of dynamic unsteady crack growth in a linear viscoelastic body. In particular, a numerical algorithm for computing the stress intensity factor is given along with example simulations of running cracks using the Achenbach-Chao viscoelastic model and a stress intensity factor (SIF) fracture criterion. We also compare the transient SIF with the dynamic steady state SIF, and examine the transition to constant crack speed for a dynamically accelerating crack in a viscoelastic material.     

基于分形理论不同装药量的爆破动焦散线实验研究

为研究装药量对爆生裂纹扩展行为的影响。采用透射式数字激光动态焦散线实验系统,分析了不同装药量的爆生裂纹扩展规律,并基于计盒维数的计算原理,编写MATLAB程序计算爆生裂纹的分形维数。结果表明:①起爆后裂纹扩展分2阶段,Ⅰ阶段(0～114.3μs)为爆炸应力波与爆生气体对裂纹尖端的作用,在裂纹的起裂时刻扩展速度达到峰值,随即迅速降低;Ⅱ阶段(114.3μs～裂纹止裂)在反射应力波对裂纹尖端的作用下,裂纹扩展速度继续提升;②裂纹扩展速度峰值、动态应力强度因子峰值、粉碎区面积、爆生裂纹分形维数与装药量正相关;③采用回归分析与线性拟合的方法,得到了裂纹扩展速度与裂纹扩展轨迹分形维数的线性关系,同一裂纹扩展速度的变化符合分形规律。     

Dynamic analysis for two-dimensional multiple crack division

Based on the concept of linear-elastic fracture mechanics, two dynamic adjustments are made upon the static form of the crack-extension force ζ for the problem of evenly spaced radial cracks spreading out from a point and terminating on a circular locus. The first adjustment is concerned with the magnitude of the local dynamic stress tending to open the crack. This dynamic stress can be approximated by the circumferential stress near a circular locus of stress relief expanding at a constant speed provided that the arc length between adjacent crack ends is sufficiently small in comparison with the circle radius. The second adjustment is concerned with the influence of crack speed on the crack-opening displacement and on the rate of release of stress field energy, ζ. This can be determined by application of the crack closure method for a traveling crack. These two dynamic adjustments are found to be opposite in direction. The degree of compensation depends on the speed of crack propagation and the Poisson's ratio of the material.     

用圆孔内单边裂纹平台巴西圆盘和实验-数值-解析法确定砂岩的动态起裂和扩展韧度

在I型(张开型)动态断裂实验中,利用大直径(?100 mm)分离式霍普金森压杆径向冲击圆孔内单边裂纹平台巴西圆盘试样。考虑了材料惯性效应和裂纹扩展速度对动态应力强度因子的影响,用实验-数值-解析法确定了高加载率和高裂纹扩展速度情况下,砂岩的动态起裂韧度和动态扩展韧度。由动态实验获取试样的动荷载历程,采用裂纹扩展计(Crack Propagation Gauge,CPG)测定试样断裂时刻和裂纹扩展速度,获得裂纹扩展速度对应的普适函数值。然后将动荷载历程带入到有限元软件中进行动态数值模拟,求出静止裂纹的动态应力强度因子历程,再用普适函数值对其进行近似修正。最后根据试样的起裂时刻和穿过CPG中点的时刻,由相应的动态应力强度因子历程分别确定砂岩的动态起裂和动态扩展韧度,它们分别随动态加载率和裂纹扩展速度的提高而增加。     

Mikrofraktographische Analyse des Delaminationswachstums in zyklisch belasteten Kohlenstoffaser/Duroplastharz-Verbundwerkstoffen

Microfractographic Analysis of Delamination Growth in Fatique Loaded – Carbon Fibre/Thermosetting Matrix Composites Carbon-fibre-reinforced plastics (CFRP) are known to be considerably less sensitive to fatigue loading than aluminium (Al) alloys, for instance. However, even in the presence of small delaminations, the damage tolerance of structural components may be considerably reduced. The scope of the present contribution is to investigate fatigue phenomena in CFRP materials (with thermosetting matrix) by means of microfractography. The microgfractographic features of the fracture surfaces mirror the processes of deformation and fracture at the delamination front. The fatigue fracture behaviour of a CFRP laminate subjected to cyclic mixed-mode loading is determined by matrix-controlled failure mechanisms. Under pure mode-II loading conditions, rollers in addition to fatigue striations appear in the fibre imprints whose formation mechanism was explained by means of high-resolution field-emission scanning electron microscopy (FE-SEM). The ratio between the local tensile and shear stress components influences the propagation direction of secondary cracks originating at the fibres. The local fracture propagations in these secondary cracks can be recognised through the fatigue striations appearing on the surface of the matrix. A comparison with static mixed-mode loading reveals that in both cases the crack propagation follows the path of the local maximum main stress. Applying mathematical relationships derived from the theory of elasticity permitted developing a mixed-mode loading model which makes it possible to predict the crack processes and hence to explain the formation of typical fracture-morphological features.     

Quasi-static and dynamic fracture of graphite/epoxy composites: An optical study of loading-rate effects

Strain-rate effects on fracture behavior of unidirectional composite materials are studied. Single-edge notched multi-layered unidirectional graphite composites (T800/3900-2) are investigated to examine fracture responses under static and dynamic loading conditions using a digital speckle correlation method. The fracture parameters for growing cracks are extracted as a function of fiber orientation. A 2D digital image correlation (DIC) method is used to obtain time-resolved full-field in-plane surface displacements when specimens are subjected to quasi-static and impact loading. Stress intensity factor and crack extension histories for pure mode-I and mixed mode cases are extracted from the full-field displacements. When compared to the dynamic stress intensity factors at crack initiation, the static values are found to be consistently lower. The stress intensity factor histories exhibit a monotonic reduction under dynamic loading conditions whereas an increasing trend is seen after crack initiation under quasi-static loading cases. This is potentially due to dominant crack face fiber bridging effects in the latter cases.     

含单侧预制裂纹梁的冲击动态断裂过程试验研究

利用动焦散线试验方法研究了冲击下预制裂纹梁的动态断裂行为,对比分析了冲击荷载作用下单裂纹与双裂纹试件的应力强度因子、扩展轨迹以及速度、加速度等参数的变化规律。试验结果表明:冲击荷载作用下,含双裂纹且主裂纹在冲击点正下方的试件起裂时间最早,裂纹扩展后期朝向次裂纹方向发生较小的偏移;含Ⅰ型单裂纹的试件起裂时间次之,裂纹扩展路径呈直线;含双裂纹且两条裂纹均偏置于冲击点的试件起裂时间最晚,扩展过程中发生明显的曲裂现象。同时,裂纹扩展过程中曲裂现象越严重,裂纹扩展的最大速度就越小。在落锤冲击试件到试件断裂的整个阶段,应力强度因子一直表现出振荡变化。含双裂纹的试件,在主裂纹扩展中期,次裂纹上的应力强度因子有一个快速下降的过程。     

CYCLIC FATIGUE OF ZIRCONIA

Two partially-stabilized zirconia materials, Mg-PSZ and Y-PSZ, were investigated in static and cyclic fatigue tests. The crack growth rates were determined as a function of the stress intensity factor (static tests) and the stress intensity factor range (cyclic tests). For all R-ratios investigated the crack-growth relations are sufficiently described by power laws. An influence of frequency is obvious. Finally, the crack growth behaviour of natural flaws is compared with that of macroscopic cracks     

Initiation and propagation of a penny-shaped crack in a finitely deformed incompressible elastic medium

The effects that the initial lateral stress has on the initiation and the propagation of a penny-shaped crack are investigated on the basis of the theory of small deformations superposed on finite deformation for an incompressible elastic material. Using the methods of the Laplace and Hankel transforms, the crack shape function and the stress distribution with singularities in the crack plane are obtained in closed forms for the crack propagating at a constant speed in the Mooney material. The dynamic stress-intensity factor is obtained as a function of the initial lateral stretch and the ratio of the crack speed to the shear wave speed. For the same crack speed, the value of the dynamic stress-intensity factor increases with increasing lateral stretch, but decreases if the lateral compression increases.The dynamic solutions reduce to the associated static solutions at zero crack speed. For the stationary crack, the stress-intensity factor is shown to be independent of the initial stress. However, the initial lateral stretch increases, but the lateral compression decreases the value of the critical stress required for the initiation of crack growth on the basis of the Griffith theory. The central crack opening displacement is shown to decrease if the lateral stretch increases or the lateral compression decreases.     

Vibrations of elastic infinite and semi-infinite media containing cracks

The problems of stress distribution in an infinite medium and in an elastic half-plane containing line cracks, when the pressure which opens the crack is periodic in time, are considered. These are (1) a cruciform crack in an elastic infinite medium, (2) an edge crack perpendicular to the surface of an elastic half-plane, and (3) their corresponding “exterior” problems. The integral equations corresponding to these problems are obtained. Expressions for the stress intensity factor and the crack energy are derived and numerical results are presented. The equivalence of the stress intensity factor and the crack energy for “exterior” and “interior” problems as established by Stallybrass for the static case is obtained from the dynamic results by letting the frequency tend to zero.     

含水裂纹在爆破扰动下的断裂机制

为探究地应力影响下含水裂纹在爆破扰动下的断裂机制,运用断裂力学原理建立了爆破扰动下深部岩体含水裂纹扩展的力学模型,通过定义等效爆破扰动荷载推导出了岩体动静耦合强度因子的计算表达式;同时,通过对拉剪型和压剪型裂纹断裂的分析,了解到爆破扰动、水压力、地应力、裂纹倾角等因素对裂纹断裂的影响方式,获得了裂纹断裂的广义断裂准则,并进行实例运算,结果表明:在拉剪型断裂中,地应力对其相同方向裂纹的断裂起促进作用;在压剪型断裂中,不同侧应力系数下裂纹最易发生断裂的角度与岩体的内摩擦系数有关;爆破扰动荷载相当于增大了裂纹水的压力。     

裂尖具线性分布约束应力的运动裂纹模型及其解析解

以恒定速度运动的Griffith裂纹解析解为著名的Yoffe解。静止裂纹的条状屈服模型即Dugdale模型,将其推广到运动裂纹模型时发现,当裂纹运动速度跨越Rayliegh波速时,裂纹张开位移COD趋于(∞,且表现为间断。通过在裂尖引入一个约束应力区及两个速度效应函数,假设约束应力为线性分布,采用复变函数方法,求得动态应力强度因子SIF与裂纹张开位移COD的解析解。新的结果,在Rayleigh波速下裂纹张开位移连续且为有限值。给出裂纹张开位移的一些数值结果,获得了一些有意义的结论。     

Dynamic fracture mechanics analysis of failure mode transitions along weakened interfaces in elastic solids

Dynamic fracture mechanics theory was employed to analyze the crack deflection behavior of dynamic mode-I cracks propagating towards inclined weak planes/interfaces in otherwise homogenous elastic solids. When the incident mode-I crack reached the weak interface, it kinked out of its original plane and continued to propagate along the weak interface. The dynamic stress intensity factors and the non-singular T-stresses of the incident cracks were fitted, and then dynamic fracture mechanics concepts were used to obtain the stress intensity factors of the kinked cracks as functions of kinking angles and crack tip speeds. The T-stress of the incident crack has a small positive value but the crack path was quite stable. In order to validate fracture mechanics predictions, the theoretical photoelasticity fringe patterns of the kinked cracks were compared with the recorded experimental fringes. Moreover, the mode mixity of the kinked crack was found to depend on the kinking angle and the crack tip speed. A weak interface will lead to a high mode-II component and a fast crack tip speed of the kinked mixed-mode crack.     

Influence of repetitive stiffness variation on crack growth behaviour in wood

Softwoods have a repetitive variation in stiffness over their growth rings, which is due to the difference in cellular structure between the latewood and earlywood. In this paper, the influence of the repetitive stiffness variation on radially growing cracks is studied by detailed finite element analyses, in which the wood material is represented by a layered orthotropic continuum. The distribution of stress around the crack is found to be very different from crack tip stress fields in homogenous isotropic materials. The latewood layer ahead of the crack experiences a significant tensile stress, which indicates that formation of new secondary cracks ahead of the primary crack front is a likely mechanism for crack propagation. This mechanism is also favoured by the fact that the primary crack is subjected to a significant shielding from the stiff latewood, which tends to arrest the primary crack in the soft earlywood layer. Analyses are performed for materials with various growth ring widths, and the calculated results are compared with reported experimental observations.     

An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching

This is the third in a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated. In the first paper crack initiation resulting from stress wave loading to the crack tip as well as crack arrest were reported. It was found that for increasing rates of loading in the microsecond range the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.In the second paper we analyze the occurrence of micro cracks at the front of the running main crack which control the rate of crack growth. The micro cracks are recorded by real time photography. By the same means it is shown that these micro cracks grow and turn away smoothly from the direction of the main crack in the process of branching.In the present paper we report results on crack propagation and branching. It is found that crack propagation occurs at a constant velocity although the stress intensity factor changes markedly. Furthermore, the velocity is determined by the stress wave induced intensity factor at initiation. The terminal velocity in Homalite-100 was found to be about half the Rayleigh wave speed (0.45 C _r ). These observations are analyzed in terms of a microcrack model alluded to in the second paper of this series. A mechanism for crack branching is proposed which considers branching to be a natural evolution from a cloud of microcracks that accompany and lead the main crack. These results are believed to apply to quasi-brittle materials other than Homalite-100 and the reasons for this belief are discussed briefly in the first paper of this series.In the final paper of the series the effect of stress waves impinging on the tip of a rapidly moving crack is examined. Waves affect the velocity and the direction of propagation as well as the process of crack branching.     

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.