Crack Velocity Research Articles

Origin of the Static Fatigue Limit in Oxide Glasses

Oxide glasses exhibit slow crack growth under stress intensities below the fracture toughness in the presence of water vapor or liquid water. The log of crack velocity decreases linearly with decreasing stress intensity factor in Region I. For some glasses, at a lower stress intensity, Ko, log v asymptotically diminishes where there is no measurable crack growth. The same glasses exhibit static fatigue, or a decreasing strength for increasing static loading times, as cracks grow and stress intensity eventually reaches the fracture toughness. In this case, some glasses exhibit a low stress below which no fatigue/failure is observed. The absence of slow crack growth under a low stress intensity factor is called the fatigue limit. Currently, no satisfactory explanation exists for the origin of the fatigue limit. We show that the surface stress relaxation mechanism, which is promoted by molecular water diffusion near the glass surface, may be the origin of the fatigue limit. First, we hypothesize that the slowing down of slow crack growth takes place due to surface stress relaxation during slow crack growth near the static fatigue limit. The applied stress intensity becomes diminished by a shielding stress intensity due to relaxation of crack tip stresses, thus resulting in a reduced crack velocity. This diminishing stress intensity factor should result in a crack growth rate near the static fatigue limit that decreases in time. By performing Double Cantilever Beam crack growth measurements of a soda‐lime silicate glass, a decreasing crack growth rate was measured. These experimental observations indicate that surface stress relaxation is causing crack velocities to asymptotically become immeasurably small at the static fatigue limit. Since the surface stress relaxation was shown to take place for various oxide glasses, the mechanism for fatigue limit explained here should be applicable to various oxide glasses.

Crack velocity jumps engendered by a transformational process zone.

We study a concerted propagation of a fast crack with the process zone where a rearrangement of the solid structure takes place. The latter is treated as a second-order local phase transformation. We demonstrate that the propagation of such a zone gives rise to a nonlinear frictionlike force exerted on the crack tip, resisting its propagation. Depending on the temperature, it produces three regimes of crack motion, which differ in the behavior of the crack tip process zone: (i) always existing, (ii) only emerging at a high crack speed, and (iii) flickering. We show that the latter regime exhibits crack velocity jumps.

Hybrid phase field simulation of dynamic crack propagation in functionally graded glass-filled epoxy

Abstract Numerical simulation of dynamic crack propagation in functionally graded glass-filled epoxy (FG) beams using a regularized variational formulation is presented. The Griffith’s theory based hybrid phase field approach for diffusive fracture is taken, which is able to accurately simulate complex behaviors of dynamic crack growth in FGMs. The FG beams under impact loads experimented by Kirugulige and Tippur (Exper. Mech. 2006; 46:269–281) are considered, taking the same configurations, material property, crack location, and other relevant assumptions. The crack paths, crack length, crack velocity, energies, etc., computed through the hybrid phase field model are numerically analyzed, and some of those results are directly compared with the experimental data. Due to lack of necessary information regarding impact loading profiles and boundary conditions in setting the tests, the simulations become difficult as an inappropriate definition of loading and boundary conditions can significantly alter the outputs of numerical solutions. This issue is important and thus is discussed. Two specific loading profiles, the constant and the linear displacement velocities, are taken into account, while free-free FG beams are considered. We show that good agreements of crack paths between the experiment and phase field approaches can be obtained. Numerical results also confirm a significant effect of elastic gradients on final crack paths. Similar to the experimental results, we also found that the crack path kinks significantly when situated on the stiffer side compared to the compliant side of the FG specimen.

Theoretical, experimental and numerical investigations on crack growth in fracture mechanical graded structures

Crack propagation is not only influenced by the loading situation but also by a material gradation within the structure. Therefore, it has to be examined how the crack propagation behavior changes when a crack grows through regions which are characterized by different fracture mechanical material properties. Within the scope of this paper, especially the influence of a fracture mechanical material gradation on the beginning of stable crack propagation, the crack velocity, the crack propagation direction as well as on the occurrence of unstable crack growth for statically and cyclically loaded components is discussed. In this context, a developed concept for the prediction of crack propagation in fracture mechanical graded structures, experimental investigations as well as numerical simulations of crack growth are presented. The experimental considerations clarify the influence of the material gradation and confirm the predictions of the new concept. The numerical simulations of crack growth indicate the influence of the material gradation especially on the lifetime of graded components.

Dynamic fracture analysis of crack–defect interaction for mode I running crack using digital dynamic caustics method

The crack–defect interaction mechanism was studied both experimentally and numerically. Experimental results found that the presence of empty hole before crack results in both the velocity and stress intensity factor of crack decrease. More energy accumulated at crack–hole tip before second initiation. Dynamic stress intensity factor is qualitatively in accord with Crack velocity, but it oscillates strongly with hole size increasing. Numerical study shows that the stress concentration would be reduced significantly when the modulus radio between the inclusion and the matrix is more than 0.5. Results may shed lights on the interaction behavior between running crack and inclusion.

The roles of cohesive strength and toughness for crack growth in visco-elastic and creeping materials

A cohesive-zone analysis for crack propagation in a linear visco-elastic/creeping material is presented. The concept of a viscous fracture length is defined; this serves an analogous role to the elastic fracture length in determining the conditions under which fracture is controlled by the continuum crack-tip stress field. It is shown that there are two regimes for viscous crack growth. The first regime occurs in the limit of small viscous fracture lengths, when the crack-tip stress field has a region exhibiting the inverse square-root dependence expected from classical linear fracture mechanics. In this regime, the crack velocity is proportional to the fourth power of the stress-intensity factor. This is consistent with an existing analytical model developed for crack growth in linear polymers. The second regime occurs for large viscous fracture lengths, where classical fracture mechanics is not appropriate. In this regime, the crack velocity has a weaker dependence on the applied load, and can be modeled accurately by the solution to the problem of a viscous beam on an elastic foundation. At higher crack velocities, when the viscous fracture length exceeds the elastic fracture length, the expected transition to elastic fracture occurs.

Development of the fracture-based flexibility index for asphalt concrete cracking potential using modified semi-circle bending test parameters

Asphalt concrete (AC) pavement sustainability can be achieved by enhancing mixture durability, improving construction practices, optimizing pavement design, and maximizing the use of recycled resources to reduce life-cycle investments. Recycled materials are commonly used to improve sustainability of AC pavement as they replace natural resources and reduce initial construction costs and greenhouse gases during the material production phase. However, net savings, in terms of environmental and economic impact, can only be realized if the performance targeted by the initial design is achieved. The use of RAP and RAS may result in a significant reduction in the demand for virgin, quarried aggregates and, more importantly, asphalt binder. However, replacing virgin materials in AC mixtures with aged, stiffer binders poses numerous technical challenges in terms of mixture volumetrics and thermal (low temperature) and flexural fatigue cracking resistance. This paper introduces a practical fracture test method to screen AC mixtures’ cracking resistance using the semi-circular bending test geometry. The selection procedure of the test method is presented along with the development of a flexibility index (FI) derived from the load-displacement curves. A discussion about the effect of viscoelasticity on fracture process is provided. The results indicate positive correlation between SCB test results and other independent fatigue tests. The proposed FI reflects positive correlation with the crack velocity, indicating brittleness of the materials, obtained from the same SCB experiments. The paper also provides a validation of the proposed IL-SCB test method results, including fracture energy and flexibility index (FI), using the number of cycles to fatigue cracking failure obtained from an accelerated pavement test sections.

Numerical simulation of dynamic brittle fracture of pipeline steel subjected to DWTT using XFEM-based cohesive segment technique

In the past several numerical studies have addressed the ductile mode of fracture propagation. However, the brittle mode of pipeline failure has not received as much attention yet. The main objective of this study is to predict brittle fracture behaviour of API X70 pipeline steel by means of a numerical approach. To this end, the eXtended Finite Element Method (XFEM)-based cohesive segment technique is used to model Drop Weight Tear Test (DWTT) of X70 pipeline steel at -100°C. In this model the dynamic stress intensity factor and crack velocity are calculated at the crack tip at each step of crack propagation.

Influence of confining prestress on the transition from interface defeat to penetration in ceramic targets

Abstract Replica scaled impact experiments with unconfined ceramic targets have shown that the transition velocity, i.e., the impact velocity at which interface defeat ceases and ceramic penetration occurs, decreased as the length scale increased. A possible explanation of how this scale effect is related to the formation of a cone crack in the ceramic has been presented by the authors in an earlier paper. Here, the influence of confinement and prestress on cone cracking and transition velocity is investigated. The hypothesis is that prestress will suppress the formation and growth of the cone crack by lowering the driving stress. A set of impact experiments has been performed in which the transition velocity for four different levels of prestress has been determined. The transition velocities as a function of the level of confining prestress is compared to an analytical model for the influence of prestress on the formation and extension of the cone crack in the ceramic material. Both experiments and model indicate that prestress has a strong influence on the transition from interface defeat to penetration, although the model underestimates the influence of prestress.

The effect of fluid composition, salinity, and acidity on subcritical crack growth in calcite crystals

AbstractChemically activated processes of subcritical cracking in calcite control the time‐dependent strength of this mineral, which is a major constituent of the Earth's brittle upper crust. Here experimental data on subcritical crack growth are acquired with a double torsion apparatus to characterize the influence of fluid pH (range 5–7.5) and ionic strength and species (Na2SO4, NaCl, MgSO4, and MgCl2) on the propagation of microcracks in calcite single crystals. The effect of different ions on crack healing has also been investigated by decreasing the load on the crack for durations up to 30 min and allowing it to relax and close. All solutions were saturated with CaCO3. The crack velocities reached during the experiments are in the range 10−9–10−2 m/s and cover the range of subcritical to close to dynamic rupture propagation velocities. Results show that for calcite saturated solutions, the energy necessary to fracture calcite is independent of pH. As a consequence, the effects of fluid salinity, measured through its ionic strength, or the variation of water activity have stronger effects on subcritical crack propagation in calcite than pH. Consequently, when considering the geological sequestration of CO2 into carbonate reservoirs, the decrease of pH within the range of 5–7.5 due to CO2 dissolution into water should not significantly alter the rate of fracturing of calcite. Increase in salinity caused by drying may lead to further reduction in cracking and consequently a decrease in brittle creep. The healing of cracks is found to vary with the specific ions present.

A configurational force approach to model the branching phenomenon in dynamic brittle fracture

This publication discusses a material or configurational force approach based crack propagation scheme for dynamic fracture, in which the formulation of the material forces is derived from a Lagrangian density where inertia effects are taken into account. In dynamics, the crack driving force can generally be much larger than in the static case. In order to study the capability of the method, an algorithm based on the principle of local symmetry (PLS) is introduced into an implicit solution scheme which requires an additional iterative algorithm to seek for energy minimization. By other explicit approaches, it is not possible to study the crack bifurcation phenomenon, which is well known in dynamic fracturing.It is observed that many micro branches evolve from the main crack in case of fast crack propagation. Thus, the energy flow into the main crack tip is divided between the main crack and the micro-branches. To introduce the micro-cracking effect to the fracture toughness, a fracture criterion as a function of the crack velocity is used in the model, in order to represent realistically the resistance of the cracked structure. In conclusion, it is shown that the proposed method based on the implicit description of energy minimization, is capable of explaining the physics behind the branching phenomenon and it offers a mesh objective solution for a structure even with a coarse mesh.

Observation of the Kibble-Zurek Mechanism in Microscopic Acoustic Crackling Noises.

Characterizing the fast evolution of microstructural defects is key to understanding “crackling” phenomena during the deformation of solid materials. For example, it has been proposed using atomistic simulations of crack propagation in elastic materials that the formation of a nonlinear hyperelastic or plastic zone around moving crack tips controls crack velocity. To date, progress in understanding the physics of this critical zone has been limited due to the lack of data describing the complex physical processes that operate near microscopic crack tips. We show, by analyzing many acoustic emission events during rock deformation experiments, that the signature of this nonlinear zone maps directly to crackling noises. In particular, we characterize a weakening zone that forms near the moving crack tips using functional networks, and we determine the scaling law between the formation of damages (defects) and the traversal rate across the critical point of transition. Moreover, we show that the correlation length near the transition remains effectively frozen. This is the main underlying hypothesis behind the Kibble-Zurek mechanism (KZM) and the obtained power-law scaling verifies the main prediction of KZM.

Decompression wave speed and crack velocity measurements during S4 test in water pressurized plastic pipes: Part 1. Experimental methods

In a Small Scale Steady State (S4) test apparatus of ISO 13477, instrumentations were designed and successfully adapted to determine decompression wave speed and crack velocity during rapid crack propagation event in water-filled plastic pipes. The basic design for decompression wave speed measurement involved the use of high-frequency dynamic pressure transmitters, located external to the water-filled pipe and connected to pressure measurement positions inside the pipe, by means of stainless steel tubes. For the crack velocity measurements, timing wire system with the required circuitry capable of giving the precise temporal indication of the propagating crack was designed and employed. In this paper, detailed design of instrumentations adapted to the S4 test apparatus and the assessment techniques used to obtain decompression wave speed and crack velocity are described. It was also demonstrated that the methods developed were viable for these measurements which are known to affect the rapid crack propagation behavior in water-filled plastic pipes.

The loading rate effect on Mode II fracture toughness of composites interleaved with CNT

The loading rate effect on Mode II interlaminar fracture toughness (ILFT) is examined in this study with interleaved epoxy/carbon fabric laminates tested under dynamic conditions. Specifically, an SP1 protein-treated carbon nanotube-reinforced epoxy leaf is inserted at the midplane of the laminates, and the fracture properties are measured by the crack lap shear method at two different loading rates. Whereas our preliminary study performed under quasi-static conditions showed that this specific interleaving generated an ~85% improvement in the Mode II ILFT, the current work shows that the occurrence and magnitude of the improvement depend on the loading rate and crack velocity, with different effects on the initiation and the instable/stable propagation stages. Improvements in Mode II ILFT for both the crack initiation and propagation phases can reach up to ~145% for certain dynamic loading conditions.

Dynamic crack propagation: quasistatic and impact loading

Simulation of dynamic crack growth under quasistatic loading was performed using finite element method with embedded incubation time fracture criterion. The uniqueness of the stress intensity factor – crack velocity relationship (K-v) is discussed. It is shown that the use of the structural–time approach and the fracture incubation time criterion enables us to predict successfully the results of experiments both on quasistatic and on impact loading of samples with cracks. Comparison of calculated K-v relationships with experimental data for various loading conditions leads to the conclusion that the dependence of the crack velocity on the stress intensity factor cannot be considered as a unique material law because the properties of this dependence are strongly determined by the sample configuration, the history, and the loading method.

Influence Yield Stress on Arrest Pressure in Pipe Predicted by CTOA

In this paper, the resistance to ductile crack extension is discussed in terms CTOA. Selection of CTOA is based on the reduced number of parameters and the low sensitivity to pipe geometry. Numerical simulations of crack propagation and arrest based on CTOA use the node release technique, which is described. Results on a pipe made in steel API L ,X52, X65 and X 100 are presented. The influence material parameters on crack arrest and velocity using this technique are presented. For the same decompression wave pressure, the crack propagation velocity is inversely proportional to the resistance to crack extension of the material, which is the dominant parameter. The crack velocity versus decompression is expressed by a CTOAc function of resistance to crack extension

大理石におけるサブクリティカルき裂進展の周辺環境依存性

It is important to investigate time-dependent deformation and fracturing in rock for the purpose of ensuring the long-term stability of structures in a rock mass. Subcritical crack growth is one of the main causes of time-dependent fracturing in rock. It is known that subcritical crack growth is influenced by not only stress but also surrounding environment. Studies of subcritical crack growth have been widely conducted for silicate rocks such as igneous rocks and sandstones. On the other hand, information of subcritical crack growth in carbonate rocks is not enough. Especially, influence of surrounding environmental conditions on subcritical crack growth in carbonate rocks has not been clarified yet. In this study, we investigated subcritical crack growth in carbonate rocks. Specifically, we investigated the influence of temperature and relative humidity on subcritical crack growth in air and in water. Macedonian marble was used as a rock sample. To measure subcritical crack growth, we used the load relaxation method of the double-torsion test. It was shown that the crack velocity increased when the temperature was higher at a constant relative humidity in air and in water. In addition, the crack velocity increased with increasing the relative humidity at a constant temperature. It is concluded that the temperature and relative humidity influence subcritical crack growth in carbonate rock in air and in water. From the results obtained in this study, it can be suggested that the condition with low temperature and low humidity is desirable for the long-term integrity of a carbonate rock.

Analysis of Dynamic Fracture Parameters in Functionally Graded Material Plates with Cracks by Graded Finite Element Method and Virtual Crack Closure Technique

Based on the finite element software ABAQUS and graded element method, we developed a dummy node fracture element, wrote the user subroutines UMAT and UEL, and solved the energy release rate component of functionally graded material (FGM) plates with cracks. An interface element tailored for the virtual crack closure technique (VCCT) was applied. Fixed cracks and moving cracks under dynamic loads were simulated. The results were compared to other VCCT-based analyses. With the implementation of a crack speed function within the element, it can be easily expanded to the cases of varying crack velocities, without convergence difficulty for all cases. Neither singular element nor collapsed element was required. Therefore, due to its simplicity, the VCCT interface element is a potential tool for engineers to conduct dynamic fracture analysis in conjunction with commercial finite element analysis codes.

Dynamic fracture in rubber toughened polymers: the influence of the fracture surface roughness

Dynamic fracture tests have been performed with rubber toughened polymethylmethacrylate (RT-PMMA) samples. For these kinds of materials the macroscopic crack tip velocity å ≈ 0.6cr is observed to not change during propagation whatever the available dynamic energy release rate. Therefore dynamic fracture energy values GIdc, according to the crack velocity in a classical formalism, are not unique at the branching velocity (approximately 0.6cr). Otherwise the classical formalism considers the amount of created surface during propagation as a flat rectangle (the sample thickness multiplied by the crack length). Nevertheless the RT-PMMA fracture surface roughness are observed to fluctuate as a function of the dynamic energy release rate. The more (respectively less) the dynamic critical energy release rate the rough (respectively smooth) the fracture surface. The real 3D topography of the created surface has to be included in the energy balance to quantify an intrinsic material fracture energy. If not, fracture energy can be significantly underestimated. Using different types of profilometer, the precise amounts of created surfaces for different locations along the fracture were measured both before and after branching at different scales. Since the fracture surface roughness depends on the analysis scale some precautions are requested in the fracture surface analysis. A self-affine geometrical model is introduced using two parameters: the Hurst exponent and the topothesy. The multi-scale description of the fracture surface roughness by a self-affine model is shown to provide a significantly better approximation of the created surface. A new and original geometrical method is introduced to estimate self-affine parameters: the 3D surface scaling method. It is based on the estimate of the amount of created fracture surface using a routine which makes a surface triangulation. Hurst exponents are shown to be unique, χ = 0.6 ± 0.1 for the different fracture zones and measurement scales. It is shown that topothesy ratios indicate a significant difference of fracture surface roughness amplitude depending on the observation resolution when the detrending technique is not correctly introduced. Indeed, the lower the topothesy, the smoother the fracture surface.

Measurement of local brittle fracture stress for dynamic crack propagation in steel

The authors measured the local fracture stress of brittle crack propagation in steel plates. Many studies on brittle crack propagation in steel plates have been implemented based on energy balance, but they have not been able to provide full theoretical explanation to brittle crack propagation and arrest behavior in steel plates. On the other hand, although the local fracture stress concept has been emerging as a factor governing the behavior recently, the local fracture stress has not been evaluated sufficiently because the crack front shape and forming of shear lip have prevent us from implementing accurate FEM analysis of brittle crack propagation. So, we implemented brittle crack propagation tests using specimen with side groove which is designed to increase stress near the plate surface and make the crack front straight. Inputting crack velocities obtained from experiments, FEM analyses were implemented. Our analyses showed the local fracture stress is higher in low temperature than in high temperature. This trend can be explained from the aspect of forming of tear ridge, which is main mechanism to absorb energy during brittle crack propagation in steel plates.