Crack Velocity Research Articles

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

AbstractIn this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.

Understanding Mechanism of Crack Velocity Transition by Numerical Simulation

Understanding Mechanism of Crack Velocity Transition by Numerical Simulation

Crack branching in polymers

One of the little-studied problems of modern mechanics and the physics of fracture is the crack branching in materials of a different nature. For its research, an analysis of the criteria and mechanisms for crack branching. The investigations of crack branching in polymers and metals, fractographic investigation of the fracture surface, criteria for crack branching as a dynamic stress intensity factor, crack speed are considered. Experimental studies of crack branching in a brittle polymer, measuring of crack velocity by breaking the conductive strips with rectilinear propagation and branching of the crack have been carried out. A measurement installation was created on the basis of a precision signal converter of resistance thermometers and thermocouples “Tercon” connected to a computer. It is established that the crack at branching in brittle polymers reaches the limiting propagation speed 500–800 m/s. A hypothesis is proposed for the physical mechanism of crack branching.

An assessment of the effectiveness of the analytical methods to fracture propagation control using accurate mathematical modelling

Simple analytical methods are usually used to fracture propagation control in pipeline systems transmitting the natural gas and carbon dioxide mixtures. The minimum of fracture arrest toughness is determined employing analytical approaches such as the Battelle Two-Curve Method (BTCM), for example. The decompression wave speed in the gases and the crack propagation velocity in the pipe wall material are calculated independently from each other and compared thereafter. The crack is arrested if those two curves plotted at the same figure are not intersected. The accuracy and universality such kind of approaches is in great doubt because the effect of gas decompression on the crack velocity is not considered. An assessment of the accuracy and effectiveness of engineering analytical approaches to fracture propagation control is considered in the paper using accurate mathematical modelling. A coupled transient mathematical model of dynamic crack propagation in the shock tube is developed to determine the minimum of fracture arrest toughness/wall thickness. Here in the study, the model of crack propagation in the pipe wall is integrated into one-dimensional model of compressible thermal multi-component natural gas mixture flow in a shock tube. The dynamic pressure at the crack tip is determined numerically from gas decompression model. Both models work together consistently at each time step one after another. The set of mass, momentum and enthalpy conservation equations is solved for the natural gas. Thermo-physical properties of multi-component natural gas mixture are calculated by solving the Equation of State in the form of the Soave-Redlich-Kwong (SRK-EOS) model. Gas decompression model is validated against the experiments. The proposed accurate numerical tool simulates a continuous development of crack propagation together with rapid decompression of the natural gas mixture, and its arrest (or not) after some time successfully. The proposed coupled model shows that the crack is not arrested in the case where the analytical approach (BTCM) points to the crack arrest because two curves are not intersected in the figure. This makes it possible to base on the conclusion that the engineering analytical method (i.e. Two-Curve Method) does not work in some cases and cannot give 100% of confidence in assessing. The error in the assessment using the analytical method can reach up to 10%.

Crack propagation in porous polymer sheets with different pore sizes

Physical understanding of crack propagation is a fundamental issue in the industry. In the literature, crack velocities of polymer materials are strongly dependent on their visco-elastic properties and energy release rates. Recently, numerical and theoretical studies have proposed that structural sizes in polymers also influence on crack propagation. Here, using polymer sheets with similar visco-elastic properties but with different pore sizes, we vary explicitly the representative structural size and examine the effect of the size on crack propagation. Findings in this work help us to understand crack propagation in polymer materials and bio-inspired materials which have porous structures.

Loading rate effect on crack velocity in ultra-high-performance fiber-reinforced concrete

Loading rate effect on crack propagation in ultra-high-performance fiber-reinforced concrete (UHPFRCs) was investigated using a pre-notched three-point bending specimen in an improved-strain energy frame impact machine (I-SEFIM) and image processing techniques. The crack velocity of up to 984 m/s and the crack initiation strain rate of up to 271 s−1 were observed. Crack velocity in UHPFRCs increased as the applied strain rate increased. Fiber reinforcements significantly affected on the crack velocity in the UHPFRC at static rates, but slightly did at high strain rates. There is a strong correlation between the strain-rate sensitivity and the dynamic crack growth characteristics of UHPFRCs.

The influence of impacting orientations on the failure modes of cracked tunnel

Underground tunnels are often subjected to dynamic loadings, and the dynamic loadings may come from various directions. To study the influence of loading orientations on the failure modes of cracked tunnels, laboratory impact experiments were conducted by a drop weight testing apparatus with synchronized measuring system. Green sandstone was selected as the experimental material to fabricate the tunnel samples, a pre-crack emanating from tunnel roof was designed to simulate the natural crack around a tunnel. In the process of dynamic loading tests, strain gauges were employed to determine crack time-to-fracture and crack velocity. Numerical simulation was carried out by the finite element software ABAQUS and the finite difference software AUTODYN. Crack initiation fracture toughness (IFT) was evaluated by experimental-numerical technique and the failure behavior of tunnel model under different orientation impacts was presented in this paper. The studying results show that as impacts come from tunnel roof, tunnel failure mainly occurs near the crack tip and the tunnel bottom (or the tunnel foot); as impact come from tunnel sidewall, the tunnel failure only occurs at the two sides of arch shoulder. The dynamic initiation fracture toughness of the pre-crack in the tunnel models is greatly related to the impact loading orientations.

On terminal crack velocities in glasses

AbstractA review of the literature shows that terminal crack velocity, vct, should be correlated with the longitudinal elastic wave velocity, and the structure and density of glasses. Theoretical predictions of vct by the Mott‐Roberts‐Wells model match experimental measurements for some key glasses, including fused silica and low‐density borosilicates. It is suggested that the slower vct results obtained for many other glasses are due to structural variations that cause crack front perturbations. The conclusions of this paper are most likely applicable to ceramics as well.

Validated simulations of dynamic crack propagation in single crystals using EFEM and XFEM

Brittle and quasibrittle materials such as ceramics and geomaterials fail through dynamic crack propagation during impact events. Simulations of such events are important in a number of applications. This paper compares the effectiveness of the embedded finite element method (EFEM) and the extended finite element method (XFEM) in modeling dynamic crack propagation by validating each approach against an impact experiment performed on single crystal quartz together with in-situ imaging of the dynamic fracture using X-ray phase contrast imaging (XPCI). The experiment is conducted in a Kolsky bar (generating a strain rate on the order of $$10^3\,\text {s}^{-1}$$ ) that is operated at the synchrotron facilities at the advanced photon source (APS). The in situ XPCI technique can record the dynamic crack propagation with micron-scale spatial resolution and sub-microsecond temporal resolution, and the corresponding images are used to extract the time-resolved crack propagation path and velocity. A unified framework is first presented for the dynamic discretization formulations of EFEM and XFEM. This framework clarifies the differences between the two methods in enrichment techniques and numerical solution schemes. In both cases, a cohesive law is used to describe the fracture process after crack initiation. The simulations of the dynamic fracture experiment using the two simulation approaches are compared with the in situ experimental observations and measurements. The performance of each method is discussed with respect to capturing the early crack propagation process.

Slow crack growth in silica aerogels: A review

The sub-critical crack growth in hydrophobic (as prepared) and hydrophilic (oxidized) silica aerogel was studied using the Dynamic fatigue experiment and the Double-Cleavage-Drilled-Compression test (DCDC). The effect of oxidation treatment is clearly evidenced. The temperature and water vapor content dependence on the crack growth rate is measured between 22 °C and 110 °C with relative air moisture ranging from 5 to 80% RH. Like dense silica, crack growth velocities were found to decrease when increasing the temperature at a constant water vapor concentration. Surprisingly, the crack velocity also decreases when increasing water vapor content at constant temperature. Such a behavior is contrary to expected results usually encountered in glasses. We assume that a capillary condensation phenomenon of water vapor inside the aerogel porosity takes place, inducing internal compressive stresses.

Crack Front Interaction with Self-Emitted Acoustic Waves.

The interaction of a propagating crack in implanted silicon with self-emitted acoustic waves results in periodic patterns on fractured surfaces. Direct measurement of the acoustic emission ahead of the fracture front shows the emergence of dominant acoustic frequency related to the crack velocity. It is shown that the surface modifications are made of roughness modulations due to periodic deviations of the crack front. A physical mechanism explaining the pattern formation is proposed, well in agreement with the observed pattern wavelengths.

Crack tip opening angle during unstable ductile crack propagation of a high-pressure gas pipeline

A full gas burst test was conducted to clarify the CTOA history during ductile crack propagation in a high-pressure pipeline. The measurement results obtained by high-speed camera observation and image processing showed that the CTOA value remains constant during crack propagation despite the large changes in the crack velocity. The numerical results of a series of finite element analyses supported the intrinsic implications of the experimental results. Consequently, the validity of the constant CTOA criterion, which has the potential to improve the accuracy and efficiency of numerical simulations of unstable ductile crack propagation in a high-pressure pipeline, was verified.

VISCOELASTIC RESPONSE DURING CRACK PROPAGATION OF UNFILLED AND FILLED SBR

ABSTRACT The crack propagation behavior of unfilled and filled styrene–butadiene rubber (SBR) in steady and dynamic tearing was investigated using tensile tests on trousers samples and tear fatigue measurements on single edge notched tension (SENT) samples, respectively. For the unfilled sample, both types of measurements indicated that the tearing energy is dominated by the viscoelastic response of the polymer. This was demonstrated by the creation of crack growth master curves using the horizontal shift factors obtained from mastering the complex modulus. The tearing energy increased with increasing crack velocity and decreasing temperature as required by the time-temperature superposition principle. The crack growth master curves followed a power law with the same exponent for steady and dynamic tearing. This exponent agrees fairly well with the exponent predicted by linear viscoelastic crack propagation theory. For steady tearing at high crack propagation rates, systematic deviations from the master curves appeared, which were attributed to flash temperature effects. For the filled SBR, which contained 50 phr carbon black, only dynamic tearing was found to be dominated by the viscoelastic response of the polymer. For steady tearing, filler networking seemed to alter crack propagation rates significantly, so that the viscoelastic fingerprint was no longer visible. For the filled sample, additional measurements with a high preload were conducted. It was demonstrated that a single master curve can be constructed, only if the (static) preload contribution is neglected and the dynamic contribution of the energy density is used for the evaluation of the tearing energy. This master curve showed two distinct slopes at high and low crack velocities. It is argued that the higher slope at low crack speeds is relevant for lifetime predictions based on the integration of the Paris–Erdogan power law. Under conditions in which the viscoelastic crack propagation holds, very slow crack growth rates can be explored at reasonable testing times by measurements at elevated temperatures.

Crack plane deflection and shear wave effects in the dynamic fracture of silicon single crystal

Fracture paths in crystalline solid can be significantly altered upon encountering stress perturbations. Here, we investigate the dynamic cleavage deflection in (001) silicon single crystal wafers under three-line bending load. It is found that the crack propagates preferentially along the (110) cleavage plane. However, when the crack front interacts with shear waves induced by the line-contact, it tends to deflect onto the (111) cleavage plane and forms secondary Wallner lines. Yet, the crack deflection is not permanent and a recovery process to the (110) plane is observed, suggesting that the (110) cleavage plane remains energetically prevailing during the high-speed crack propagation. We show that the ratio between the dynamic fracture energy of the (111) plane and that of the (110) plane at the deflection position is invariably larger than the one when the local crack velocity is lower than 40% of the Rayleigh wave speed. This confirms that the crack deflection is triggered by shear waves. Therefore the theory of crystallographic direction dependence of dynamic fracture toughness evolutions proposed in earlier literature needs to be further assessed before generalization.

How Supertough Gels Break.

Fracture of highly stretched materials challenges our view of how things break. We directly visualize rupture of tough double-network gels at >50% strain. During fracture, crack tip shapes obey a x∼y^{1.6} power law, in contrast to the parabolic profile observed in low-strain cracks. A new length scale ℓ emerges from the power law; we show that ℓ scales directly with the stored elastic energy and diverges when the crack velocity approaches the shear wave speed. Our results show that double-network gels undergo brittle fracture and provide a testing ground for large-strain fracture mechanics.

Slow crack growth resistance of electrically conductive zirconia-based composites with non-oxide reinforcements

Slow crack growth (SCG) behavior of four zirconia-based composites reinforced with 40 vol% WC, TiC, NbC or TiCN were studied by means of double-torsion testing. Compared to monolithic zirconia, the composites had a higher resistance to fast fracture, i.e., higher fracture toughness. The extent of toughening depended on the reinforcement type, shifting the V-KI (crack velocity versus stress intensity factor) curve parallel to higher KI values. More importantly, these composites were less sensitive to SCG. Identical V-KI/KIC curves with steeper slopes compared to monolithic zirconia were observed for the investigated composites, independent on the reinforcement type. No rising R-curve was measured, at least in the crack-size domain investigated by SCG. Therefore, the higher SCG resistance of the composites was due to the intrinsic stress-assisted corrosion resistance of the covalent non-oxide secondary phase.

A Numerical Study on Extent of Crushed Zone Around Blasthole in Basalt Rock

Proper understanding of the rock breakage mechanism is important in tunnelling and mining activities. The excavation design uses complex energy distribution pattern when explosion and rock-blast occurs. This paper investigates the effect of a controlled-blast in rock mass using a numerical technique. The rock material properties were determined and fitted in an advance material damage model using the finite element code LS-DYNA. This material model had three governing surfaces, each of which was dependent upon the plastic strain accumulation. The damage zones around the blast hole were categorised into crushed, seismic and elastic zones. In all the cases, the material within the close vicinity of the explosion, failed in compression, whilst the material at distance away from the explosion, failed in tension. The influence of loading rate and its impact on the fracture pattern was also studied. It was shown that the higher loading rate led to the formation of short cracks and areas with large crack densities whereas longer and definite cracks occurred when the loading rate was slow. In both the cases, the rise time was found to be more significant than the decay time. This lead to the development of a relation between the critical rise time corresponding to the maximum damage. Crack velocities were higher for quick loading rates and achieved one-half the magnitude of P-wave velocity observed on basalt rock. The results of this model were validated using the case study of a tunnel excavation in Western Ghats of Peninsular India The numerically obtained ground vibrations in the old tunnel were observed to be under the permissible limits. Likewise, the vibrations deduced in the new tunnels indicated the initiation of cracks. Notwithstanding the above, a reasonably good comparison was obtained between the measured and predicted peak particle velocities.

A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals

• Moving crack in 1D hexagonal piezoelectric quasicrystals is studied. • Full electroelastic field induced by a running crack is obtained. • Field intensity factor is independent of the crack speed. • Energy release rate is dependent on the crack speed. • Crack bifurcation is judged by the maximum energy release rate. A Yoffe-type moving crack in one-dimensional hexagonal piezoelectric quasicrystals is considered. The Fourier transform technique is used to solve a moving crack problem under the action of antiplane shear and inplane electric field. Full elastic stresses of phonon and phason fields and electric fields are derived for a crack running with constant speed in the periodic plane. Obtained results show that the coupled elastic fields inside piezoelectric quasicrystals depend on the speed of crack propagation , and exhibit the usual square-root singularity at the moving crack tip . Electric field and phason stresses do not have singularity and electric displacement and phonon stresses have the inverse square-root singularity at the crack tip for a permeable crack. The field intensity factors and energy release rates are obtained in closed form. The crack velocity does not affect the field intensity factors, but alters the dynamic energy release rate. Bifurcation angle of a moving crack in a 1D hexagonal piezoelectric quasicrystal is evaluated from the viewpoint of energy balance. Obtained results are helpful to better understanding crack advance in piezoelectric quasicrystals.

Hydrodynamic Pressure and Velocity Distributions in the Interlayer Crack of Ballastless Track under High-Speed Train Load: A Theoretical Analysis

In the abundant rain or poor drainage areas, there will be serious water damage existing in the interlayer of ballastless track. The essence of water damage of ballastless track is a dynamic development process of damage shape under the combined action of train load, hydrodynamic pressure, and flow velocity. In view of the distribution characteristics of hydrodynamic pressure and flow velocity in the interlayer crack of ballastless track under the high-speed train load, the simplified mechanics model for water and composite slab with interfacial crack is proposed in accordance with the water damage characteristics of ballastless track. Based on the conservation of mass and momentum theorem, the analytical expressions of water pressure and velocity in the saturated water crack were deduced. Similarly, the analytical expressions of water pressure and velocity in the unsaturated water crack were deduced by adding the state equation of ideal air. Considering that the water does not flow back timely, the analytical expressions of water pressure and velocity in another kind of unsaturated water crack were deduced. The results show that the hydrodynamic pressure and flow velocity in the interlayer crack are synthetically determined by multiple influencing factors such as fluid viscosity, load characteristic, crack shape, absolute pressure at the crack mouth, and initial volume of the air in the crack, and there is an intersecting phenomenon between influencing factors. When there is a small amount of air at the crack tip, the pressure and velocity distribution in the crack can be divided into three parts in terms of air-water interface and stagnation point. When the crack is filled with water, the hydrodynamic pressure tends to decrease along the direction of the crack mouth, and the distribution along the whole crack approximates to a cubic polynomial curve. Similarly, the flow velocity increases along the direction of crack mouth, and the distribution along the whole crack approximates to a quadratic polynomial curve.

Morphological Approach to Quantifying Soil Cracks: Application to Dynamic Crack Patterns during Wetting‐Drying Cycles

Core Ideas We propose a methodology for soil crack recognition and quantification. Crack skeleton, outline and nodes are produced using morphological algorithms. A novel method for separating cracks is proposed based on SKIZ, distance transform, and watershed segmentation. The approach is assessed on dynamic crack patterns derived from three wetting‐drying cycles. Crack degree, velocity, similarity and network topology within wet‐dry cycles are analyzed. Water flow and solute transport through shrink‐swell soils with desiccation cracks are dominated by the crack distribution and variable hydraulic properties. The quantification of cracks is therefore inevitable for predicting moisture movement in cracked soils. This study presents a morphological approach to crack recognition and quantification based on digital image processing and morphological algorithms. The methodology comprises three sections: image segmentation, morphological processing and parameter calculation. A crack image is first segmented and then subjected to morphological operations including skeletonization, node identification and crack outline extraction. Based on the resulting binary crack image, skeleton and nodes of crack network, we propose a novel approach to crack separation by employing the concept of skeleton by zones of influence (SKIZ) and algorithms including distance transform and watershed segmentation. Calculations of crack parameters are presented and we apply this methodology to quantify the characteristics of dynamic crack patterns derived from wetting‐drying (W‐D) cycles. Crack degree, propagation velocity of cracks, similarity between crack patterns and network topology are exemplified to delineate the dynamic crack patterns. We find that the cracking degree present hysteresis between W‐D processes, similarly to soil shrink‐swell characteristics and water retention curves. The crack skeleton simultaneously, non‐hierarchically and rapidly propagated in successive drying cycles compared to the initial drying process. The similarity between two crack patterns with similar moisture contents derived from W‐D cycles is positively correlated with the drying intensity, and the evolution of the similarity gradually decelerates with decreasing water content. The crack patterns at full desiccation across W‐D cycles exhibit a marked similarity, with a maximum similarity measure of approximately 0.8. Overall, this approach could achieve efficient recognition and quantification of crack patterns and has great potential in the 3‐D quantification of cracks or related structures.