Crack motion in viscoelastic solids: The role of the flash temperature

We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this “low-speed” regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a “hot-crack” propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.     

Self-oscillating regime of crack propagation induced by a local phase transition at its tip

We report an analytical study of propagation of a straight crack with a stress-induced local phase transition at the tip. We obtain its contribution to the dynamic fracture energy in explicit form and demonstrate that it nonmonotonically depends upon the crack tip velocity. We show that its descending part gives rise to the instability of the steady propagation regime. We obtain the dynamic phase diagram and indicate those domains where self-oscillating regimes of the crack motion take place.     

Fracture and friction: Stick-slip motion

We discuss the stick-slip motion of an elastic block sliding along a rigid substrate. We argue that for a given external shear stress this system shows a discontinuous nonequilibrium transition from a uniform stick state to uniform sliding at some critical stress which is nothing but the Griffith threshold for crack propagation. An inhomogeneous mode of sliding occurs when the driving velocity is prescribed instead of the external stress. A transition to homogeneous sliding occurs at a critical velocity, which is related to the critical stress. We solve the elastic problem for a steady-state motion of a periodic stick-slip pattern and derive equations of motion for the tip and resticking end of the slip pulses. In the slip regions we use the linear friction law and do not assume any intrinsic instabilities even at small sliding velocities. We find that, as in many other pattern forming system, the steady-state analysis itself does not select uniquely all the internal parameters of the pattern, especially the primary wavelength. Using some plausible analogy to first-order phase transitions we discuss a soft selection mechanism. This allows to estimate internal parameters such as crack velocities, primary wavelength and relative fraction of the slip phase as functions of the driving velocity. The relevance of our results to recent experiments is discussed.     

Flame spreading over liquid ethanol

Flame spreading over liquid ethanol has been experimentally characterized for ethanol for subflash temperatures, in two different channels. Three different spreading regimes have been observed. A uniform region (with flame velocities close to 10 cm/s) appears for values of the initial surface liquid temperature above a critical value . For values an oscillatory regime occurs. For very low temperatures, , a new uniform regime appears with slow propagation velocities (close to 1 cm/s). The critical point has been described as a Hopf bifurcation, while resembles a homoclinic connection. Received 16 October 1998 and Received in final form 23 June 1999     

Crack growth on the basal plane in single crystal zinc: experiments and computations

Crack propagation on the basal planes in zinc was examined by means of in situ fracture testing of pre-cracked single crystals, with specific attention paid to the fracture mechanism. During quasistatic loading, crack propagation occurred in short bursts of dynamic crack extension followed by periods of arrests, the latter accompanied by plastic deformation and blunting of the crack-tip. In situ observations confirmed nucleation and propagation of microcracks on parallel basal planes and plastic deformation and failure of the linking ligaments. Pre-existing twins in the crack path serve as potent crack arrestors. The crystallographic orientation of the crack growth direction on the basal plane was found to influence both the fracture load as well as the deformation at the crack-tip, producing fracture surfaces of noticeably different appearances. Finite element analysis incorporating crystal plasticity was used to identify dominant slip systems and the stress distribution around the crack-tip in plane stress and plane strain. The computational results are helpful in rationalizing the experimental observations including the mechanism of crack propagation, the orientation dependence of crack-tip plasticity and the fracture surface morphology.     

Supersonic crack propagation in a class of lattice models of mode III brittle fracture

We study a lattice model for mode III crack propagation in brittle materials in a stripe geometry at constant applied stretching. Stiffening of the material at large deformation produces supersonic crack propagation. For large stretching the propagation is guided by well-developed soliton waves. For low stretching, the crack-tip velocity has a universal dependence on stretching that can be obtained using a simple geometrical argument.     

Crack propagation in amorphous polymers and their composites

The fracture energy of a polymer depends strongly on the viscoelastic responses of the material, and therefore is a function of temperature and crack velocity. The toughness of a composite is determined by the way in which the reinforcing filler modifies the energy dissipating mechanisms of the polymeric matrix.

The fracture toughness of a variety of polymeric glasses and their composites with glass beads, glass fibers, and rubber particles was measured. The velocity of rapidly moving cracks and the crack propagation rates under controlled loading conditions were also measured.

It was found that the crack propagation velocities in unfilled and glass bead filled materials were controlled by the longitudinal stress waves in the matrix and that the only effects of the glass beads were to blunt the crack tip and limit the viscous deformation. The effect on fracture toughness was relatively small and either positive or negative, depending on which of the above two factors dominated.

The presence of rubber particles as a second phase lowered terminal crack propagation velocities and greatly increased the fracture toughness, indicating a crack retarding effect of the rubber particles. This is related to the induction of crazes in the matrix by the rubber phase.

Glass fibers had a tendency to bridge the tip of a propagating crack, thereby greatly increasing the fracture toughness. In this case the work of fracture comes from a combination of the elastic strain energy stored in the fibers, the energy dissipated in debonding the fibers from the matrix, and the fracture energy of the matrix itself.     

晶体相场法研究应力状态及晶体取向对微裂纹尖端扩展行为的影响

采用晶体相场模拟研究了单向拉伸作用下初始应力状态、晶体取向角度对单晶材料内部微裂纹尖端扩展行为的影响, 以(111)晶面上的预制中心裂纹为研究对象探讨了微裂纹尖端扩展行为的纳观机理, 结果表明: 微裂纹的扩展行为主要发生在<011>(111)滑移系上, 扩展行为与扩展方向与材料所处的初始应力状态及晶体取向紧密相关. 预拉伸应力状态将首先诱发微裂纹尖端生成滑移位错, 进而导致晶面解理而实现微裂纹尖端沿[011]晶向扩展, 扩展到一定程度后由于位错塞积, 应力集中, 使裂纹扩展方向沿另一滑移方向[101], 并形成锯齿形边缘; 预剪切应力状态下, 微裂纹尖端首先在[101]晶向解理扩展, 并诱发位错产生, 形成空洞聚集型长大的二次裂纹, 形成了明显的剪切带; 预偏变形状态下微裂纹尖端则直接以晶面解理形式[101]在上进行扩展, 直至断裂失效; 微裂纹尖端扩展行为随晶体取向不同而不同, 较小的取向角度会在裂纹尖端形成滑移位错, 诱发空位而形成二次裂纹, 而较大的取向角下的裂纹尖端则以直接解理扩展为主, 扩展方向与拉伸方向几近垂直.     

Application of stereo vision to the study of mixed-mode crack-tip deformations

A stereo vision is applied to evaluate crack-tip parameters for fracture specimens subjected to a mixed-mode loading (tension and shear). By using a special loading device, the applied remote loading is oriented at an angle with respect to the axis of the crack. At each loading angle, the calibrated vision system was rotated so that the axis of the crack is parallel to the horizontal or vertical axis of the image frame. At a load close to the crack initiation, the displacement field around the crack-tip region of the fracture specimen was measured relative to a specimen coordinate system located at the crack tip of the fracture specimen. During the experiment, the fracture specimen was subjected to rigid body translation and rotation. Hence, the displacement fields are affected by the rigid body translation and rotation. Using the experimentally determined displacements and the analytically determined displacements with several higher order terms being included, the stress intensity factors and the amount of rigid body translation and rotation were calculated through a least-squares fit. The effect of the rigid body motion on the measured displacements was then eliminated using the computed rigid body translation and rotation. Experimental results indicate that a K_I and K_II dominant region is observed in the corrected displacement fields.     

Local waiting time fluctuations along a randomly pinned crack front

The propagation of an interfacial crack along a heterogeneous weak plane of a transparent Plexiglas block is followed using a high resolution fast camera. We show that the fracture front dynamics is governed by local and irregular avalanches with very large size and velocity fluctuations. We characterize the intermittent dynamics observed, i.e., the local pinnings and depinnings of the crack front by measuring the local waiting time fluctuations along the crack front during its propagation. The deduced local front line velocity distribution exhibits a power law behavior, P(v) alpha v-eta with eta=2.55+/-0.15, for velocities v larger than the average front speed . The burst size distribution is also a power law, P(S) alpha S-gamma with gamma=1.7+/-0.1. Above a characteristic length scale of disorder Ld approximately 15 microm, the avalanche clusters become anisotropic providing an estimate of the roughness exponent of the crack front line, H=0.66.     

Dynamic caustics and its applications

For the study of elastodynamic problems of propagating cracks it is necessary to evaluate the dynamic stress intensity factor K^d_I which depends on the form of expressions for the stress components existing at the running crack tip at any instant of the propagation of the crack and the corresponding dynamic mechanical and optical properties of the material of the specimen under identical loading conditions. In this paper the distortion of the form of the corresponding reflected caustic from the lateral faces of a dynamically loaded transparent and optically inert specimen containing a transverse crack running under constant velocity was studied on the basis of complex potential elasticity theory and the influence of this form on the value of the dynamic stress intensity factor was given. The method was applied to the study of a propagating Mode I crack in a PMMA specimen under various propagation velocities and the corresponding dynamic stress intensity factor K^d_I evaluated. Also, crack propagation behaviour of notched composites in dynamic loading modes are reviewed and evaluated. A relatively large data base using metal-epoxy particulates, rubber-toughened poly(methyl methacrylate), and Sandwich plates are given. In all cases, a combination of high-speed photography and the optical method of dynamic caustics has been used. Results on the dynamic crack propagation mode, fracture toughness and crack propagation velocities of several rubber-modified composite models are presented. The composite models studied include specimens with one and/or two ‘complex’ two-stage inclusions, i.e. PMMA round inclusions surrounded by concentric rubber rings, one and/or press-fifting inclusions without rubber interface, all under dynamic loading. In all cases both qualitative and quantitative results were obtained. Also, results on crack propagation mode, crack propagation velocity, stress intensity factors and on the influence of the sandwich phases on crack propagation mode are presented.     

Self-healing slip pulses along a gel/glass interface

We present experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity: steady sliding at high velocity (>V(c) approximately 100--125 microm/s), characterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a "healing instability" occurring when the local sliding velocity reaches the macroscopic transition velocity V(c). At driving velocities close below V(c), the system exhibits complex spatiotemporal behavior.     

Dynamic optical visualization on the interaction between propagating crack and stationary crack

Dynamic interactions between the propagating crack and the static crack in PMMA material are studied by combining high-speed Schardin camera with optical caustic method. A series of dynamic optical bifocal patterns (the specimen-focused image and the off-focused image) around the propagating crack tip and the static crack tip are recorded for PMMA thin strip which contains two collinear-edge-cracks subjected to tensile loading, the variations of the caustic diameter and the distortion of the caustic shape are revealed due to the influence of local stress singularity at the crack tip. Interactions between the moving crack and the static crack are analyzed by means of the evolution of dynamic fracture parameters. The influence of crack interaction on fracture parameters is discussed based on both a K-dominance assumption and a higher order transient crack-tip expansion. These results will be useful to the evaluation of dynamic properties and the design of structures in the cracked polymer material.     

On the mechanism of hotspot initiation of detonation

A mechanism of the initiation of hotspots in heterogeneous solid high explosives was considered. It was demonstrated that the growth of hotspots may be associated with the propagation of a thermal wave in the deflagration regime only at an early stage of the process. The growth at later stages occurs in the reactive shock regime, a finding that renders the assumption about a very high deflagration wave velocity redundant.     

Low cycle fatigue cracking of Al 20wt% Zn multicrystals

Low cycle fatigue data are reported for multicrystalline specimens (i.e. polycrystals with a few large grains in the gauge section) of age-hardened AlZn alloy with elliptical G. P. zones. Experiments were carried out at constant strain amplitude, room temperature and frequency 2 Hz. The discussion focused on the role and relative importance of grain boundaries, extrusions and coarse slip bands for crack nucleation and propagation. Precipitation free zones bordering the grain boundaries are the most favoured sites of crack nucleation and early crack growth. The prevailing mechanism of the initial stage of transcrystalline cracking is alternating slip or shear. The large cracks with an extended plastic zone tend to follow the extrusions which are formed at the crack tip after sufficients number of cycles.The authors wish to thank Dr. P. Luká of Institute of Physical Metallurgy, Brno, for valuable comments on this work and to Mr. T. Páv, Nuclear Research Institute, e, for conducting the fatigue tests.     

Direct observation and image-based simulation of three-dimensional tortuous crack evolution inside opaque materials

We present a combined novel methodology to study the three-dimensional complex geometry of a tortuous crack and identify the essential features of the crack and its propagation inside a heterogeneous material. We find that some severe damage events occur unexpectedly below a local mode-I crack within the sample; we realize that the severe plastic zone of the local mode-I crack is shifted down by another unseen crack segment hidden behind, which is responsible for the unusual damage phenomenon observed. We also find that the crack grows fast at some locations but slowly at some other locations along the crack front; we recognize that the crack-tip fields are reduced by neighboring hidden crack segments, which accounts for the retarded propagation of some part of the crack front. The feasibility and power of the proposed methodology highlights the potential of a new way to study fracture mechanisms in real materials.     

Shape of a cracking whip

The crack of a whip is produced by a shock wave created by the supersonic motion of the tip of the whip in the air. A simple dynamical model for the propagation and acceleration of waves in the motion of whips is presented. The respective contributions of tension, tapering, and boundary conditions in the acceleration of an initial impulse are studied theoretically and numerically.     

Mean stress effect in fatigue crack propagation

Crack propagation rates in three different grades of mild steel and two types of age hardening aluminium alloys have been measured for different stress ratios. The results show a pronounced stress ratio effect for all these materials. A model of fatigue crack propagation is formulated in terms of the size of the cyclic plastic instability zone at the crack tip rather than the zone of plastic yielding. The micro-plastic instability zone is measured by a parameter involving the ratio of the maximum stress intensity and the stress level at which macro-plastic instability occurs in the $\text{S}\text{N}$ curve of plain fatigue test pieces. Such a parameter provides a means of normalizing crack propagation results obtained for various stress ratios.