Crack Propagation Speed Research Articles

Deformation rates effects in softwoods: Crack dynamics with lattice fracture modelling

Present study contributes towards understanding crack toughness against the intrinsic deformation rate sensitivity. A methodology for characterizing fracture dependence in softwoods through experimental and numerical analysis has been developed. Time-dependence was found to be the characterising parameter. Image analysis of fracture data acquired with high-speed camera showed that the crack speed histories are stochastic and erratic. In the higher rate range, crack dynamics is characterized as episodic and locally heterogeneous, with irregular jumps and arrests. Critical crack propagation speed at the highest rate tested of 200 mm/min was found to be between 0.7 m/s and 4 m/s (14.3 km/h). Fracture toughness decreased at both slow static and high loading rates, with the mean maximum at 1 mm/min, which is a static deformation rate specific to short-term standard tests. At 200 mm/min deformation rate, inertial effects suggested dynamic fracture response. Explanations of loading rates effects relate to the micro-processes in the fracture process zone (FPZ) and fracture mechanisms, which are simulated with discrete lattice fracture model (LFM). The model included viscous bi-linear stress relaxation into the softening relation and random stochastic finite element properties. Novel characterisation of softwoods is crucial for sensible numerical modeling in seismic structural situations.

Study of a propagating finite crack in functionally graded piezoelectric materials considering dielectric medium effect

This paper provides a study of the problem of a propagating finite crack under in-plane loading in functionally graded piezoelectric materials (FGPMs). The analytical formulations are developed by Fourier transforms and the resulting singular integral equations are solved by using Chebyshev polynomials. By using a dielectric crack model with deformation-dependent electric boundary condition, numerical simulations are made to show the effects of the dielectric medium, the gradient of material properties and the speed of crack propagation on the fracture parameters, such as the stress, electric displacement and crack opening displacement intensity factors. A critical state for the electromechanical loading applied to the FGPMs is observed, which determines whether the traditionally impermeable (or permeable) crack model serves as the upper or lower bound for the dielectric model. The validity of this dielectric crack model is also examined by comparing the results of different existing crack models.

Investigation of dynamic fracture behavior in functionally graded materials

The fast running crack in functionally graded materials (FGMs) is investigated through numerical simulations under impact loading. Some fracture characterizations such as crack propagation and arrest are evaluated by the criterion of the crack tip opening angle. Based on the experimental results, the whole propagation process of the fast running crack is simulated by the finite element program. Thus, the dynamic fracture parameters can be obtained during the crack growing process. In this paper, the crack direction is assumed to be the graded direction of the materials, and the property gradation in FGMs is considered by varying the elastic modulus exponentially along the graded direction and keeping the mass density and Poisson's ratio constant. The influences of the non-homogeneity, the loading ratio and the crack propagation speed on the dynamic fracture response of FGMs are analyzed through the test and numerical analysis. Considering the potential application of FGMs in natural-gas transmission engineering, a functionally graded pipeline is designed to arrest the fast running crack for a short period in high pressure large diameter natural-gas pipelines.

Atomistic simulation of the effect of Ga on crack tip opening in Al bicrystals

Liquid metal embrittlement (LME) in the Al–Ga system is studied using molecular dynamics simulations. Crack tip opening loads are exerted on symmetric tilt Al bicrystals in the presence of liquid Ga. In general, the speed of crack propagation increases in the presence of Ga. However, there is significant variation in the dynamic behavior of the different boundaries studied here. We observe the formation of a sub-grain by grain boundary dissociation (grain boundary phase transformation) in [1 1 0] Σ9 and [1 1 0] Σ11 grain boundaries; this results in crack blunting even in the presence of Ga. In the Σ3 twin, the absence of alternating compressive and tensile stresses present in other boundaries results in fast Ga penetration after the crack path is formed. The structure of grain boundaries apart from thermodynamic considerations significantly affects LME.

Peculiarity of Accelerated Propagation of Fatigue Crack for Medium Carbon Steel under Variable Amplitude Loading

Low cyclic fatigue testing of 45 medium carbon steel with the annular V-notch indicates that the propagation of crack under variable amplitude increase by degrees overloading is faster than that under constant amplitude overloading. Some problems which include the effect of constant amplitude overloading to propagation speed of crack, the suitable loading process of accelerating propagation of fatigue crack, and the fracture figure in suitable loading, should be discussed. Based on the experimental results and the analysis of the fracture surfaces of the specimens, the mechanism of propagation of fatigue crack under the overloading is explored. It is proposed that at the moment of the application of the overloading, the obvious instantaneous increase of crack growth rates is due to crack blunting. Then an adequate way of loading to make propagation of crack quickly is found that provide a basis for the engineering application of extra-low cycle fatigue fracture.

浸炭材の低サイクル衝撃疲労特性に及ぼす表層炭素濃度と硫黄含有量の影響

Effect of surface carbon and sulfur on the low cycle impact fatigue properties in carburized steels were studied by using gear impact testing machine and strain gauge. The results obtained are summarized as follows: The low cycle impact fatigue strength was especially improved by decreasing content of the surface carbon and content of sulfur. It was found that increasing the crack initiation life by decreasing content of the surface carbon, and the initial crack length shorten. Furthermore, It was explained that the crack propagation speed decreased with decreasing sulfide. The method for estimating the crack initiation life from tensile properties of carburized layer is proposed by modifying Manson's Universal Slope Method.

Out‐of‐plane displacement measurement near the crack tip during a crack propagation: Validation of a 3D formulation for a specimen in PMMA loaded in mode I.

AbstractThe fundamental aim of this study is the determination zone of the 3D effects and the transient one at the vicinity of the crack tip during a crack propagation in brittle materials (PMMA) using an optical method (Michelson interferometer). With the obtained interferograms, we can extract the phase (thus the relief) by using a new numerical approach based on the principle of images correlation between real fringes and virtual fringes. Different dynamic tests are realized by a plate loaded in mode I under a constant loading. We compare the obtained data with the two‐dimensional theory of Westergaard (plane stress hypothesis) [1]. With the divergence is established, we propose a new 3D formulation, based on a formulation employed for static crack, which takes into account 3D and transient effects. For the static cracks, the 3D effects relate to a presence of the state of three‐dimensional stresses. However in dynamics, the transient effects appear and are related to the crack propagation velocity. The 3D effects and transient effects lead to results equivalent to experimental ones in terms of displacement but are completely different to results given by the two‐dimensional theory near the crack tip. It is possible to quantify the zone when the plane stress hypothesis is not valid according to the crack propagation speed V. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 103 s−1. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.

Approaches to dynamic fracture modelling at finite deformations

The focus of the present paper is on the finite element modelling of dynamic fracture based on the concept of locally enriched element shape functions in the vicinity of the crack, in line with the eXtended Finite Element Method (X-FEM). For this purpose, the proper governing equations for the case of a propagating crack within a hyperelastic material is established, including the definition of the concept of material motion which kinematically describes the progression of the crack. Furthermore, two different approaches to describe the material degradation and separation are proposed. The first approach, denoted the material crack driving force model, is based on the concept of material (or configurational) forces associated with the material motion. The basic motivation is that, in this context, a driving force is identified at the crack tip, which points in the direction of maximum energy release upon crack propagation. An additional interesting feature of this force is that the projection in the crack propagation direction corresponds to the energy released for such a propagation, whereby an intuitive criterion for crack propagation based on the direction and magnitude of this force is proposed. The second approach is based on the classical cohesive zone concept, extended to include rate effects to capture experimentally observed phenomena such as growing process zones during propagation as well as limited crack propagation speeds well below the theoretical limit. Both models are investigated and compared in a couple of numerical examples in the latter part of the paper, showing both the predictive capabilities as well as some limitations of the two approaches. It has also been shown that, for a specific set of parameters, the two models can reproduce (almost) the same response.

Mechanodestruction of minerals at the crack tip (Overview): 1. Experiment

The kinetics of the amount of volatiles emitted from synthetic and natural calcite single crystals while cleaving and grinding are determined using time-of-flight mass spectrometry. It is revealed that the CO2 emission is a product of mechano destruction rather than the release of impurities trapped in the crystal. Irradiation of calcite increases the CO2 emission. A diffusion–desorption model is suggested to explain the kinetics of volatile emission from cleaved surfaces and experimental results on the emission of volatile products during the mechano destruction of various single crystals are summarized. The effects of several sources of systematic errors are discussed. The yield of volatiles is correlated with the speed of the brittle crack propagation and the physicochemical properties of minerals.

Effects of Notch Shape and Specimen Thickness on Drop-Weight Tear Test Properties of API X70 and X80 Line-Pipe Steels

In the present study, effects of notch shape and specimen thickness on drop-weight tear test (DWTT) properties of API X70 and X80 line-pipe steels fabricated by varying hot-rolling conditions were investigated. The DWTT was conducted on the rolled steels, and the results were discussed in comparison with the Charpy V-notch (CVN) impact test and crack-tip opening angle (CTOA) test data. The DWTT results indicated that the steels rolled in the single-phase region had the higher upper shelf energy (USE) than the steel rolled in the two-phase region, because their microstructures were composed of acicular ferrite (AF). The DWTT energy transition temperature (ETT) of the steel rolled in the two-phase region was the lowest, because it had a finer effective grain size and the lowest volume fraction of hard secondary phases. Chevron notch (CN) DWTT energy density did not increase much with increasing specimen thickness, whereas pressed notch (PN) DWTT energy density increased by 1 to 3 J/mm2, because the total energy of the CN DWTT increased less than that of the PN DWTT due to the larger stress concentration at the CN. The ETT increased with increasing specimen thickness due to the increase in constraint state, and the ETT of the CN DWTT was slightly lower than that of PN DWTT. The measured CTOA showed better correlation with the DWTT propagation energy than with the CVN or DWTT total energy because it was related to the crack propagation speed. The value of sin (2CTOA) reliably showed a linearly proportional relation with the DWTT propagation energy density.

Study of Crack Propagation in PMMA Using Ultrasonic Technique

Attenuation of ultrasonic waves was measured in different notched specimens of Poly(methylmethacrylate) (PMMA) at different points of crack propagation path. Crack propagation takes place when specimens, with initial single edge notch produced using sharp milling cutter, are subjected to different crosshead speeds of a tensile testing machine. These measurements were performed on specimens having different thicknesses by using pulse echo technique at different frequencies. Attenuation measurements results were confirmed by microscopic images. The present study showed that attenuation increases when crack propagation speed increases as a result of an increment of crosshead speed of the applied load. Such relation is not affected by the specimens' thickness. The resulting attenuation curves elucidated the neck zone of the crack.

Experimental Study on the Dynamic Splitting Tensile Behaviour of Concrete

Many structures and buildings such as nuclear power station and chemical plant are often subjected to impact and explosive loadings. The understanding of material response to highamplitude, short-duration, impulse loads is very important, dynamic behavior of concrete under high strain rate has been paid much attention to. In the present paper, experimental study on the dynamic tension behavior of concrete is carried out. Based on the former theoretical introduction, dynamic splitting tensile tests at different strain rates are conducted on 74mm diameter concrete specimens in a Split Hopkinson Pressure Bar to study the effect of strain rate on the dynamic tension behavior of concrete. The mechanism and speed of crack propagation of concrete cylinder planar surface in dynamic splitting tensile test are discussed briefly.

Mode-3 spontaneous crack propagation in symmetric functionally graded materials

The effects of spatially varying the material properties on the mode-3 planar crack propagation characteristics are numerically investigated. The spectral scheme that is available for homogeneous materials is modified to account for the symmetrically varying material properties. Crack propagation in hardening, softening and unsymmetric type of functionally graded have been simulated. A parametric study was performed by systematically varying the material inhomogeneity length scale. Our study indicated that softening and unsymmetric graded materials reduce the resistance to fracture, while a hardening material offers higher fracture resistance with increase in inhomogeneity. Only the transient phase of crack propagation speed was affected by the material property variation, irrespective of whether the material was hardening, softening or an unsymmetric type. The crack always reached a quasi-steady-state velocity, which remained unaffected by the material property inhomogeneity.

Dynamics of Surfactant-Driven Fracture of Particle Rafts

We investigate the dynamic fracture of a close-packed monolayer of particles, or particle raft, floating at a liquid-gas interface induced by the localized addition of surfactant. Unusually for a two-dimensional solid, our experiments show that the speed of crack propagation here is not affected by the elastic properties of the raft. Instead it is controlled by the rate at which surfactant is advected to the crack tip by means of the induced Marangoni flows. Further, the velocity of propagation is not constant in time and the length of the crack scales as t(3/4). More broadly, this surfactant-induced rupture of interfacial rafts suggests ways to manipulate them for applications.

Propagation of a mode-III interfacial conductive crack along a conductive interface between two piezoelectric materials

An analysis is presented for transient response of a mode-III interfacial crack propagating between two dissimilar piezoelectric half spaces. The dynamic fracture toughness of a piezoelectric interface is examined, which is a central issue related to the interface strength of multi-layered sensors and ferroelectric thin film devices. For the mode-III crack propagation in piezoelectric materials, an electro-acoustic surface wave, the Bleustein–Gulyaev wave, controls the crack propagation speed. It is shown that the propagation of an interfacial crack in piezoelectric media may excite an interfacial electro-acoustic surface wave, the Maerfeld–Tournois wave, which is fundamentally different from the mode-III interfacial crack propagation in purely elastic media. Moreover, it has been discovered that the existence of the Maerfeld–Tournois wave may play a significant role in determining the dynamic fracture toughness for piezoelectric composites.

Temperature-related Cauchy–Born rule for multiscale modeling of crystalline solids

In this study, we develop a temperature-related Cauchy–Born (TCB) rule for multiscale modeling of crystalline solids based on the assumptions that deformation is locally homogeneous and atoms have the same local vibration mode. When employing the TCB rule in the nanoscale continuum approximation, the first Piola–Kirchhoff stress can be explicitly computed as the first derivative of the Helmholtz free energy density to the deformation gradient. Since the Helmholtz free energy is temperature-dependent, multiscale methods consisting of the TCB rule embedded continuum model can be used to elucidate temperature-related physical phenomena at the nanoscale. Stress analyses of canonical ensembles verify the continuum approximation with the TCB rule by comparing the calculated Cauchy stresses with the outcomes of molecular dynamics simulations. As an application of the TCB rule in multiscale modeling, the nanoscale meshfree particle method with the TCB rule demonstrates the same crack propagation phenomenon in a nanoplate as molecular dynamics. This example shows that the temperature effects are significant on the crack propagation speed when the temperature is in a particular range.

Detachment of glass balls from smooth rubber under gravity

In numerous previous experiments for 30 years, we have studied, as much other scientists, especially the group of the English School, the kinetics of adherence of various rigid transparent punches in contact with the plane and smooth surface of a rubber–like material, by measuring the evolution of the radius of contact area when a tensile force is imposed to separate the two bodies. Here, we propose a simple method to predict the kinetics of detachment of several balls submitted to their own weights, i.e. the duration necessary to observe the rupture of contact, when it is impossible to measure the area of contact because the bodies are not transparent, for instance. This method only assumes the knowledge of the dissipation function versus the crack propagation speed at the interface between the rubber sample and the rigid body in contact.

On the simulation of the flaking paint due to internal stresses: A simple model

We present a simple theoretical and experimental model to explain the flaking off of paints, from a pre-existing defect, due to the influence of internal stresses provoked by the variation of ambient temperature and a long or strong illumination. The experimental model is made of two superimposed rubber strips, one of them being submitted to an instantaneous elongation or to a constant speed of strain. The detachment of the other strip, that represents the peeling and the flaking off of the paint layer, is measured and analyzed using concepts of the fracture mechanics, such as the strain energy release rate, in order to determine the conditions of stability and propagation of a crack at the interface, and to draw a master curve representing the dissipation function as a function of the crack propagation speed.

Approximate estimates of fracture speeds for dry slab avalanches

Dry slab avalanches release by propagating shear fractures. It has been suggested that slab wave or fracture speed on horizontal terrain is consistent with the propagation of a flexural wave in the slab. In this note, an alternate proposal is made. Namely, it is proposed that the fracture speed is consistent with dynamic crack propagation speeds from other materials. The theory is compared with an in situ measurement of speed associated with shear fracture propagation in a weak snow pack layer sensed by geophones placed on the surface of a horizontal snow pack. The theory is shown to be consistent with the mechanical properties of alpine snow and known characteristics of slab avalanche release.