Stress waves due to fracture of glass in bending

An experimental investigation was performed of the stress waves generated by the fracture of glass beams of rectangular cross-section subjected to pure bending. Both longitudinal and bending waves are emitted during the fracture process. The characteristics of these waves indicate that fracture of the cross-section proceeds in three fairly-distinct successive stages: (i) rapid fracture from the surface on the tensile side of the beam to or slightly beyond the neutral axis, (ii) relatively slow advancement of the fracture front due to redistribution of the initial compressive stresses, and (iii) complete fracture due to the return of the emitted longitudinal pulse to the partially fractured cross-section as a tensile wave.     

共晶基陶瓷复合材料的断裂韧性

应用细观力学方法研究了由具有随机尺寸和方位的棒体共晶体构成的共晶基陶瓷复合材料的断裂韧性.首先根据棒状共晶体的细观结构特性,考虑共晶体边界处的微观滑移确定共晶陶瓷复合材料的开裂应力,当外载荷达到开裂应力时,裂纹开始扩展.然后分析裂纹表面处的棒状共晶体桥联力使裂纹产生闭合效应,减小裂纹尖端的应力集中,建立棒状共晶体桥联增韧机制;再依据棒状共晶体拔出过程中摩擦力做功,建立棒状共晶体拔出增韧机制.最后在棒状共晶体的桥联与拔出增韧机制的基础上,得到了共晶基陶瓷复合材料断裂韧性的理论表达式.结果表明共晶基陶瓷复合材料的断裂韧性与棒状共晶体的长径比密切相关.     

Dynamic crack growth under stress wave loading

The crack growth process has been analysed on the basis of a fracture criterion of a dynamic stress intensity factor when a crack in an infinite plate was subjected to a pulse type of stress wave. The crack velocity and the amount of crack extension were related to the constant amplitude and the duration of the stress pulse. The calculated amount of crack extension was well in agreement with the experimental one for the polymer material Acrylite (which is similar to polymethylmethacrylate) found by the authors, thus indicating the validity of the present approach.     

On the effect of pulse loads on dynamic rock fracture

The objective of this research was to develop an analytical model which is capable of predicting the fracture pattern in the rock surrounding a wellbore upon which a dynamic loading pulse is applied. The development of the model followed the principle of elastodynamic fracture mechanics. Specifically, inherent cracks are assumed to exist around the edge of the wellbore. Depending on the pulse shape, these cracks are activated to form various fracture patterns. The criterion for initiation of crack growth is determined by the magnitude of the dynamic stress intensity factor associated with the crack. The finite element code HONDO was used to calculate the dynamic stress intensity factors. Analytical predictions were correlated with field experimental data and good agreements were found.     

Crack propagation in an elastic solid subjected to general loading—III. Stress wave loading

The stress intensity factor of a half-plane crack extending non-uniformly in an isotropic elastic solid subjected to stress wave loading is determined. A plane stress pulse strikes the crack at time t = 0, the wavefront being parallel to the plane of the crack. At some arbitrary later time t = τ, the crack begins to extend at a non-uniform rate. It is found that the stress intensity factor is a universal function of instantaneous crack-tip velocity times the stress intensity factor for an equivalent stationary crack. An energy rate balance fracture criterion is applied to obtain an equation of motion for the crack tip. The delay time between the arrival of the incident pulse and the onset of fracture is also calculated for this fracture criterion.     

Some characteristics of thermal fracture in glass

Techniques for obtaining controlled fractures in sheet glass by means of thermal stress are outlined. The velocity behavior of fracture under different stress configurations is analyzed, and it is seen that the nature of crack is strongly influenced by the ambient stress field. The peak velocity of a typical free-running fracture is observed to be 1450 m/sec and the corresponding crack opening to be 4 microns.     

Glass Fracture in the Region of Its Contact with Steel Balls

Results of experiments on indentation of steel balls of various diameters into glass specimens shaped as rectangular parallelepipeds are reported. The limiting load of formation of an annular crack near the contact area and the radius of this crack are experimentally determined. The field of the contact stress in the fracture region is found by using the Huber solution of the Hertz problem of ball indentation into an elastic half-space. Modeling fracture caused by contact interaction is based on using the local criterion of the maximum stress and several nonlocal criteria: average stress criterion, Nuismer criterion, and gradient criterion. For calculating the parameter that has the length dimension and is included into the nonlocal fracture criteria, the ultimate tensile stress and the critical stress intensity factor of glass are experimentally determined for beams without and with a notch. It is demonstrated that the experimental data on the annular crack radius are most adequately predicted by the gradient criterion among all criteria considered in the study. However, this criterion overpredicts the ultimate tensile stress in the course of beam bending, which is caused by the scale factor.     

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J–A₂ three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J–A₂ approach.     

Plasticity and fracture of martensitic boron steel under plane stress conditions

Two series of multiaxial experiments are performed to characterize the mechanical behavior of a hot formed martensitic 22MnB5 boron steel. In the first series, flat specimens of uniform cross-section are subjected to various combinations of tensile and shear loading to characterize the elasto-plastic response. Butterfly-shaped specimens of non-uniform cross-section are used for the second series to study the onset of fracture in the martensitic steel. It is found from the analysis of the experimental results that the planar isotropic Hill’48 yield function along with an associated flow rule provides good estimates of the stress–strain response over a wide range of loading paths. The fracture experiments demonstrate that the crack initiation depends strongly on the loading state. A simple stress triaxiality dependent phenomenological fracture model is calibrated to describe the onset of fracture. Using the proposed plasticity and fracture model, numerical simulations of the fracture of tensile specimens of different notch radii are performed and compared with experiments.     

Crack propagation in an elastic solid subjected to general loading— IV. Obliquely incident stress pulse

The stress intensity factors of a half-plane crack extending nonuniformly in an isotropic elastic solid subjected to stress wave loading are considered. A plane stress pulse is obliquely incident on the crack, and the wavefront strikes the crack at some initial time. At some arbitrary later time, the crack begins to extend at a nonuniform rate. It is found that the mode I and mode II stress intensity factors each have the form of the product of a universal function of instantaneous cracktip speed with the stress intensity factor for an equivalent stationary crack. An energy-rate balance fracture criterion is applied to obtain an equation of motion for the crack tip and to determine the actual delay time between the arrival of the incident wave and the onset of fracture as a function of angle of incidence of the loading wave.     

脆性材料在双向应力下的断裂实验与理论分析

研究了脆性材料在双向应力下的断裂特性和失效机理，特别是在平行于裂纹的应力对临界断裂参数的影响方面进行了实验上和理论上的研究．采用玻璃、陶瓷等脆性材料进行了平面双向拉伸和单向拉伸试验，并对实验结果进行比较．观测直通裂纹的启裂和扩展过程，证明了双向应力对裂纹驱动力有明显影响，讨论了裂纹扩展的应变准则．     

高韧性合金钢断裂韧性及疲劳裂纹扩展门槛值的联合试验方法

在柴油机曲轴、连杆等关键零部件的可靠性设计和失效评估中,断裂韧性及疲劳裂纹扩展门槛值分别是衡量材料抵抗裂纹失稳扩展和裂纹开始扩展的重要指标．但是,对于高韧性合金材料,难以通过常规试验所推荐的厚度确定平面应变断裂韧性,而门槛值的测定通常不但非常耗时,且难以直接应用于不同循环特性的实际结构．本文针对高韧性合金钢34CrNi3MoA,提出一种将断裂韧性和疲劳裂纹扩展门槛值试验合二为一的试验方法,即用同一个试件可以同时测定门槛值和断裂韧性．利用断裂韧性关于试件厚度的渐近特性,以几种较薄试件的试验,确定平面应变状态下的断裂韧性．试验结果还表明,裂纹扩展门槛值的试件厚度依存性可以忽略,并给出了任意循环特性（应力比）下的门槛值计算公式．     

Drag load modeling for multiple fractures in a borehole

Fracture mechanics modeling of multiple fractures generated by a tailored pressure pulse in a borehole is a complex, coupled gas dynamics/solid mechanics problem. The specific problem addressed in this paper is the determination of crack tip stress intensity factors for arbitrary drag loadings along the crack surfaces. Fracture networks containing an even number of equally spaced radial cracks of alternating lengths are used as models. Finite element calculations and integration schemes similar to those used for arbitrary normal loads along the crack surfaces are performed. Stress intensity factors arising from the drag loadings tend to increase with increasing crack length ratios. Thus, effects of drag loading may be significant in determining crack tip stress intensity factors for a multiple fracture network generated by a controlled gas pulse.     

Experimental and computational models for three-dimensional crack-fiber interactions

This study sheds light on the small-scale interaction of a three-dimensional matrix crack with a fiber. The experiments with a model brittle-matrix/brittle-fiber system record the three-dimensional growth history of an initially penny-shaped fracture which quasi-statically propagates toward and around a cylindrical inclusion. Crack growth histories are obtained by hydraulically fracturing a cement matrix with embedded glass rods. These experimentally determined crack patterns support micromechanical computational simulations which were conducted using a three-dimensional surface integral method. The implications for tailoring interfacial friction to increase the crack resistance of brittle materials (e.g., ceramic matrix/ceramic fiber composites) are discussed.     

Analytical solution for a Mode III crack in a 3D beam lattice

The brittle fracture behavior of an open cell foam is considered. The foam is modeled by an infinite lattice composed of elastic straight-line beam elements (struts) having uniform cross-sections and rigidly connected at the nodal points. The beams are parallel to the three mutually orthogonal lattice vectors thus forming a microstructure with rectangular parallelepiped cells.A semi-infinite Mode III crack is embedded in the lattice and, for the considered antiplane deformation, each node has three degrees of freedom, namely, the displacement parallel to the crack front and two rotations about the axes perpendicular to this direction. The analysis method hinges on the discrete Fourier transform, which allows to formulate the crack problem by means of the Wiener–Hopf equation. Its solution yields closed-form analytical expressions for the forces and the displacements at any cross-section, and, in particular, at the crack plane. An eigensolution for the traction-free crack faces and K-field remote loading is derived from the solution for the loaded crack using a limiting procedure. An analytical expression for the fracture toughness is derived from the eigensolution by comparing the remote stress field and the stresses in the near-tip struts. The obtained expression is found to be consistent with the known analytical and experimental results for Mode I deformation. It appears, that the dependence of the fracture toughness upon shape anisotropy ratio of the lattice material is non-monotonic. The optimal value of this parameter, which provides the maximum crack arresting ability is determined.     

Application of bimaterial interface corner failure mechanics to silicon/glass anodic bonds

Motivated by the existence of a universal singular stress field at bimaterial interface corners, a fair amount of work has been performed to support the use of the corresponding critical stress intensities to correlate fracture initiation. The approach is in the spirit of interface fracture mechanics but applicable to a different class of problems, specifically, when a crack does not previously exist (or cannot be detected, at least economically), and when subsequent crack propagation does not necessarily occur along the interface. Here we further progress toward the development, understanding, and application of the approach, both experimentally and theoretically, for a series of silicon/glass anodically bonded structures. To this end we designed and fabricated two series of silicon/glass anodically bonded bimaterial specimens with different interface corner geometries that commonly arise from different silicon etching technologies. Offset three-point flexure tests were performed that resulted in brittle fracture that initiated at the interface corner. From a rigorous stress analysis at the interface corner, we determined the order of the stress singularities and the angular variation of the stress fields. We computed the corresponding stress intensities via full-field finite element analyses of the silicon/glass specimens loaded in offset three-point flexure. Measured fracture data show that although the failure stress varies significantly with bond size, the corresponding critical stress intensity of the dominant mode is constant, thus providing support for its use as a fracture initiation criterion. In the light of both the stress analysis and the measured fracture data, we discuss the effect of mode mixity (loosely shearing versus opening) and show that it has little influence on the results for the specimens and loading considered in this study. Via an idealized model of a small crack, either interfacial or extending into one of the adherends, we study the effects of geometrical perturbations at the interface corner on the stress state, and discuss implications for fracture analysis and interpretation of fracture data. We also explore the prediction of the crack initiation angle and achieve reasonable success with a simple criterion based on the maximum circumferential stress near the uncracked interface corner.     

Crack propagation in glass coatings under expanding spherical contact

The growth of transverse cracks under expanding spherical contact in a model system consisted of soda-lime glass bonded to a polycarbonate substrate is observed in situ from below or from the polished edge of the bilayer. Abrasion or chemical etching is employed on the coating surfaces to control the initial fracture. In the limit case of monoliths, the crack mouth becomes fully engulfed by the expanding contact, which results in a much steeper crack angle compared to the classical Hertzian cone case. As the coating thickness is reduced, flexure stresses are set in the coating which drive the cone crack to well away from the contact circle and initiate semi-elliptical-like radial cracks at the subsurface, right under the contact. Common to all three fracture modes is an initial unstable propagation phase following by a stable growth, with detrimental failure associated with severe damage to the top surface and/or delamination at the coating/substrate interface taking place at loads several times the fracture initiation loads.LEFM in conjunction with a large-strain FEM contact code is used to study the post-initiation fracture, with the crack path controlled by the principal stress trajectory or zero-mode II S.I.F. The analysis exposes the leading geometric and material parameters in each fracture mode, which may be useful in the design of bilayer structures for optimal mechanical performance. The well-known Auerbach law governing the initial fracture of monoliths is found to apply also to the bilayer crack systems within a certain range of the problem parameters. The numerical prediction for the crack profiles and the fracture envelopes generally collaborate well with the tests.     

含埋藏椭圆形裂纹金属构件电磁热止裂时热应力场分析

对带有椭圆埋藏裂纹金属构件在脉冲放电瞬间的热应力场进行了理论分析。在热应力场的求解中,利用了热传导和非定常热应力理论,由求解的热应力场公式发现：在脉冲放电瞬间,电磁热在裂纹尖端形成热压应力场,热压力场可有效地抑制裂纹的扩展。以Cr12MoV模具钢中埋藏椭圆裂纹止裂为例,具体计算了脉冲放电瞬间的热应力场分布情况,为空间裂纹电磁热止裂技术的实际应用提供了理论基础。     

Simulation of glass cutting with an impinging hot air jet

Thermal cutting of glass sheet due to an impinging hot air jet is simulated and analyzed. Induced thermal stresses due to the moving heat source can be used to stably initiate and attract a crack toward the jet axis. Relative motion between the jet and glass sheet then can be used to cut the glass sheet. This paper presents a theoretical study of this process for straight cuts. Process simulation is accomplished by analyzing the coupled temperature and stress fields together with the fracture mechanics criteria for the crack growth.A finite element remeshing technique is employed for the analysis and singular elements are used around the crack tip for a more precise computing of the stress intensity factor. It is shown that a certain minimum air jet temperature for a given nozzle velocity and a certain maximum air jet velocity for a given temperature are required for continuous cutting. The results of the simulation show a good agreement with the published results in the literature. However a variating nature is detected for the distance between the crack tip and the air jet nozzle from a starting value to the steady-state one.     

Plasticity aspects of interfacial fracture for polymer/glass specimens

Experimental results suggest that the interfacial fracture resistance is minimal for approximate near tip Mode I accompanied by positive and negative near tip Mode II. Finite-strain FE analysis is made for an elastic–plastic medium bonded to an ideally elastic medium with an interface crack. Small-scale plasticity conditions are invoked and examined in relation to the elastic–plastic stress distribution along the bond line. Plasticity engenders a tendency to turn near tip biaxiality towards pure Mode I regardless of the mixed-mode loading. High levels of hydrostatic stress are attained. For different mode mixities of the applied load, the dependence of the elastic–plastic normal bond stress on load level is examined. It is found that under positive Mode II loading, the normal bond stress σ_yy tends to saturate as the load level rises. This does not occur for Mode I and negative Mode II loading. In addition, deformation patterns inside the plastic zone are examined for mixed-mode situations. A displacement criterion based on the normal bond crack opening suggests a dependence of the critical load level on the extent of mixed mode. Under positive mode II fracture, traces of the ductile material are found at the top of the elastic substrate. Some of these conclusions appear to be consistent with the fracture patterns observed for LD-polyethylene/glass interfacial mixed-mode fracture.