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To ensure the long-term integrity of a rock mass, understanding the time-dependent fracturing is essential. For this reason, the study of subcritical crack growth in rock has been conducted by various researchers. It has been clarified that the influence of water is significant for the increase of the crack velocity in rock. Even though the surrounding environment is alkali, the crack velocity in rock decreased if the concentration of calcium ion in water is high. This phenomenon is basically microscopic. Even though subcritical crack growth happens in a rock mass, it is impossible to detect this phenomenon, because the aperture of the crack is on the order of micrometer. Since the study of subcritical crack growth is fundamental, it is often considered that its application to rock engineering project is difficult. However, industry-academia collaboration related to radioactive waste disposal has been started after obtaining the result with high reproducibility and clarifying the influence of surrounding environment on the change of the crack velocity in various rock materials. In addition, some international collaboration has been started to research the influence of subcritical crack growth on the weathering in rock and time-dependent deformation in a rock mass under excavation. It is suggested that the future development is possible even though we conduct some fundamental studies which may be useless apparently for rock engineering projects and natural phenomena.

To ensure the long-term integrity of a rock mass, understanding the time-dependent fracturing is essential. For this reason, the study of subcritical crack growth in rock has been conducted by various researchers. It has been clarified that the influence of water is significant for the increase of the crack velocity in rock. Even though the surrounding environment is alkali, the crack velocity in rock decreased if the concentration of calcium ion in water is high. This phenomenon is basically microscopic. Even though subcritical crack growth happens in a rock mass, it is impossible to detect this phenomenon, because the aperture of the crack is on the order of micrometer. Since the study of subcritical crack growth is fundamental, it is often considered that its application to rock engineering project is difficult. However, industry-academia collaboration related to radioactive waste disposal has been started after obtaining the result with high reproducibility and clarifying the influence of surrounding environment on the change of the crack velocity in various rock materials. In addition, some international collaboration has been started to research the influence of subcritical crack growth on the weathering in rock and time-dependent deformation in a rock mass under excavation. It is suggested that the future development is possible even though we conduct some fundamental studies which may be useless apparently for rock engineering projects and natural phenomena. [ABSTRACT FROM AUTHOR]

• The effects of temperature on fracture toughness and subcritical crack growth parameters were studied under mode II loading. • Fracture toughness testing under mode II loading was conducted using the SC4PB sample. • The subcritical crack growth parameters were determined using the constant stress rate test. • The influence of different inert strengths on the subcritical growth parameters was investigated. • The crack velocity was evaluated under various temperature conditions. Studying subcritical crack growth is crucial to investigating the long-term behavior of rocks under applied loads and evaluating the long-term stability of underground and surface structures in rock masses. While considerable research has been done to determine subcritical crack growth parameters in mode I, Studies on subcritical crack growth under mode II loading are limited despite its important applications in rock engineering problems. The purpose of the study is to understand the thermal effect on the fracture behavior of hornfels rock, which were heated at 25 °C (without thermal treatment), 250 °C, 500 °C, and 750 °C, respectively. The subcritical crack growth parameters were determined using the constant stress rate test and one of the available fracture mechanics tests for mode II loading, namely, the four-point bending test. Experiments were conducted at three fixed displacement rates of 0.06 mm/min, 0.6 mm/min, and 6 mm/min, and three experiments were performed in each case to ensure repeatability. The results showed that the fracture toughness of hornfels samples increased with increasing temperature up to 250 °C and then decreased with increasing heat treatment temperature. The fracture toughness decreased drastically due to the thermal breakdown of the quartz crystal structure and the creation of wider intergranular fractures. The study indicated that for the hornfels samples, the subcritical parameter A decreased and beyond this temperature, parameter A began to increase while parameter n remained relatively constant as the temperature rose to 750 °C. The subcritical crack growth rate was calculated using the subcritical crack growth parameters and the stress intensity factor under mode II loading. For a certain value of the stress intensity factor K II , the highest subcritical crack velocity occurred at the temperature of 750 °C (5.76×10−7–2.47×10−1 m/s), and the lowest velocity of the subcritical crack occurred at the temperature of 250 °C (3.30×10−11–6.84×10−5 m/s). The impact of inert strength, calculated at the highest loading rate, on subcritical parameters across various temperatures was examined. The findings indicate that the subcritical crack growth parameter A is reliant on inert strength. [ABSTRACT FROM AUTHOR]

• DIC setup with high-speed camera can capture crack propagation in brittle ceramics. • Accurate method to determine R-curves for ceramics is experimentally from DIC images. • Reaction-bonded SiC–B 4 C has higher crack resistance compared to monolithic SiC. • Increase thickness of β-SiC rim around α-SiC grains offers higher crack resistance. • Decrease Si amount between main α-SiC grains to nm level increases SiC–B 4 C toughness. The current research uses the Digital Image Correlation (DIC) approach to study the fracture behaviour of Reaction-Bonded Silicon Carbide-Boron Carbide (SiC–B 4 C) ceramic (RBSBC). A Photron camera with 137,500 fps was used to capture the crack propagation at an interframe time frame of 2.6 ms before final fracture. The purpose was to capture the rapid brittle behaviour of the ceramic during the onset of crack propagation. The RBSBC failed in a transgranular manner like most monolithic SiC-based materials as Hexoloy-SA. The presence of randomly dispersed coarse B 4 C grains helps in deflecting the crack path which increases the overall crack length. The material's resistance to crack propagation (R-curve) was measured using the crack tip opening displacement, the stress intensity at the crack tip K I , and the J -integral against crack extension. Two methods were used to determine the K I : experimentally based on the displacement values at the crack tip as obtained from the DIC images, and quasistatic based on the fracture load and the geometrical dimension of the crack. The experimentally-determined K I and J resulted in higher values compared to the quasistatic ones. However, they reflect the actual conditions at the crack tip, while the quasistatic conditions underestimate the resistance-plot. The RBSBC has higher R-curve compared to commercially available SiC-only materials as Hexoloy-SA and ABC-SiC. To improve the crack-resistance of RBSBC, the Si amount should decrease to a nm level, while the percentage of B 4 C grains should increase and be evenly dispersed across the material. [ABSTRACT FROM AUTHOR]

Three‐point bending tests on notched plain concrete beams and lightly reinforced concrete beams were carried out with a drop‐hammer impact instrument. The shape of the specimen followed the RILEM recommendation, that is, 150 mm × 150 mm in cross section, 800 mm in length, and span was kept constant 600 mm. And only one conventional steel bar was placed in the lightly reinforced concrete beam. The high‐speed camera and digital image correlation (DIC) technology were applied to catch the fracture process under dynamic loads. And the reaction force, mid‐span deflection, crack velocity, the horizontal strain of concrete at the notch root, and the strain of steel bar midpoint were measured over three impact velocities (i.e., 9.89 × 102, 1.71 × 103, and 2.21 × 103 mm/s). The test results showed that the dynamic fracture energy for plain concrete and reinforced concrete increased with the increase of the impact velocity. When the impact velocity reached 2.21 × 103 mm/s, the steel bar reached yielding, which resulted in the influence from reinforcement on fracture energy weakened. Both of the dynamic fracture toughness for plain concrete and lightly reinforced concrete increased linearly as the growth of impact velocity. Furthermore, the crack extended with a decreasing speed for plain concrete and reinforced concrete. And the first‐stage crack velocity in concrete was inhibited effectively by steel bar, but the inhibitory effect declined as the increase of impact velocities. [ABSTRACT FROM AUTHOR]

The fracture toughness and fracture energy of ultra‐high‐performance fiber‐reinforced concrete (UHPFRC) at both static and impact rates (43–92 s−1) were investigated using double‐edge‐notched tensile specimens. Two types of steel fiber, smooth and twisted fiber, were used in producing UHPFRC with different volume ratios of 0.5%, 1.0%, 1.5%, and 2%. The results indicated that UHPFRCs produced very high fracture resistance at impact rates, with first stress intensity factor (KIC) up to 3.995 MPa√m, critical stress intensity factor (KIC*) up to 7.778 MPa√m, and fracture energy (GF) up to 86.867 KJ/m2, which were 2.5, 5.0, and 16.9 times higher than those of ultra‐high‐performance concrete, respectively. The KIC* was clearly sensitive to the applied loading rate, whereas the KIC and GF were not. Smooth fiber specimens exhibited not only higher KIC* and GF at impact rates but also higher dynamic increase factor than twisted fiber specimens. A minimum fiber volume content of 1% should be used in UHPFRC to provide a significant enhancement in crack resistance. The maximum value of UHPFRC crack velocity at impact rates was found to be 527 m/s by using a dynamic fracture mechanic model. [ABSTRACT FROM AUTHOR]

This study is aimed at evaluating continuum scale predictions of dynamic crack propagation and branching in brittle materials using local damage modeling. Classical experimental results on crack branching in PMMA and the corresponding nonlocal modeling results by Wolff et al. (Int J Numer Meth Eng 101(12):933, 2015) are used as a benchmark. An isotropic damage model based on a frame-invariant effective strain is adapted. Mesh objectivity is achieved by calibrating the damage model for a suitable element size and subsequently retaining that mesh size in all subsequent analyses. Crack propagation and branching are predicted by simulating accurately the test conditions. It is found that a local, rate-independent damage model considerably overpredicts the dynamic crack velocity and the extent of crack branching. Subsequently, the effect of various strain rate-dependent phenomena, viz. material viscoelasticity, rate-dependent strength, fracture energy, and failure strain is evaluated. Incorporating the material strain rate effects is found to improve the predictions and match the test data. In this regard, radially scaling the damage law is found to work the best. Despite an overprediction of micro-branching, the macro-crack branching is found to occur in agreement with the Yoffe instability criterion. Overall, various experimentally observed aspects of dynamic cracks are reproduced, including acceleration of cracks to a steady state velocity, increased micro-branching and macro-branching with increased strain rates, and crack velocity dependence of energy dissipation and fracture surface area. [ABSTRACT FROM AUTHOR]

The paper discusses the dynamic propagation of cracks in brittle materials under various loads. The crack propagation is studied under both quasi-static and the shock-pulse loading conditions. Particular attention is paid to the dependences characterizing the crack propagation and having a non-stationary character. Thus, for the case of crack propagation under quasi-static loading, the crack velocity oscillations phenomenon is investigated. The problem related to the scatter of the stress intensity factor values which is observed in a number of experiments in course of the crack propagation under high-rate loading conditions is studied. The studies have been carried out using the finite element method with the structure–time fracture which is introduced into the computational scheme and which fundamentally determines the discrete mechanism of the fracture processes at a given scale level. Both quantitative and qualitative comparison of the calculation results with the available experimental data has been carried out. It is shown that taking into account the spatial and temporal discretization of the process makes it possible to explain a number of experimentally observed effects that do not fit into the traditional theoretical concepts of the dynamic fracture theory. [ABSTRACT FROM AUTHOR]

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The dynamic fracture behavior of notched semi-circular bending(NSCB) subjected to hammer impact loading was studied by using caustics experimental method.The results show that the shear stress at the crack tip increased with the offset distance increased, and correspondingly, the crack changed from mode I to mixed mode I-II, the time from impact force loaded to crack initiation also increased, moreover, the crack deflecting angle became more fluctuating with crack propagation;the crack velocity increased rapidly under dynamic load until it reached a certain value with continual fluctuation, with the ratio of crack vertical displacement to the total vertical lengthλ> 0.8, the crack velocity sharply decreased because of the effect of the local compressive stress around the hammer;as the offset distance increased, the initial fracture toughness KIC decreased, whereas KIIC increased;while the dynamic propagation toughness increased gradually with crack propagation.

The goals of our study were to calculate the subcritical crack growth (SCG) parameters of two veneering ceramics stored in water or Streptococcus mutans (S. mutans) biofilm and remineralizing medium, with indentation flaws. Feldspar (VM7) and leucite‐reinforced (VM13) glass ceramic disks (Vita Zahnfabrik, Bad Säckingen, Germany) were made according to ISO 6872. Some specimens were indented with a Vickers diamond and the crack dimensions were measured. The specimens were fractured for a calculation of inert strength or further stored in water or submitted to pH variation, under preloading tension. Finally, the SCG parameters were calculated after the specimens were fractured under four stressing rates (MPa/s). Weibull analysis was conducted on non‐indented specimens. XPS was performed as qualitative analysis. The subcritical crack of leucite ceramic did not vary with the media storage, but the glass‐ceramic experienced a retarded growth after pH variation. The materials presented low Weibull modulus. Qualitative elemental analyses showed chemical modification on both ceramics. Therefore, the crack growth of leucite‐reinforced ceramic was less affected by the environment pH than glass‐ceramic. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Highlights • The crack initiation and velocity at high speed were successfully tested by using the modified I-SEFIM. • The crack velocity increased as the applied strain rate increased. • The fiber reinforcement significantly affected on the crack velocity in the UHPFRCs at static rates, but it slightly did at high strain rates. • The strain-rate sensitivity of UHPFRC is strongly correlated with the dynamic crack growth mechanism. Abstract 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. [ABSTRACT FROM AUTHOR]

A series of internal-pressure failure tests of steel thin-walled cylindrical shells (vessels) is carried out to measure the crack growth rate in the course of breaking current-conducting strips. The experiments use a specially designed measuring setup based on a precision converter of the signals from resistance thermometers and Terkon thermocouples interfaced with a computer. The crack velocity is measured during straight-line crack propagation and crack branching. [ABSTRACT FROM AUTHOR]

Abstract: A thermally activated crack‐velocity formulation that includes a threshold at thermodynamic equilibrium is used in the prediction of long‐term time‐to‐failure for brittle materials. A new closed‐form time‐to‐failure solution is derived for straight cracks propagating under the influence of constant stress. Explicit connections are made between the macroscopic crack‐velocity parameters and the underlying bond‐rupture parameters. A feature of the solution is the divergence of time‐to‐failure for applied loading approaching the thermodynamic threshold. A new reliability framework is developed and long‐term reliability and hazard predictions made using the time‐to‐failure solution. A bathtub hazard curve is shown to be generated by a single crack‐velocity failure mechanism. [ABSTRACT FROM AUTHOR]

Abstract: A method is demonstrated for prediction of ceramic reliability limited by fracture in reactive environments. The simplicity of the method relies on the ceramic displaying ideal indentation‐strength behavior and on the applied loading leading to short‐term power‐law crack velocity behavior. Reactive failure strength measurements, treating flaw size as a variable and failure time as a constraint in a “pass‐fail” test, enable reliability, including both intrinsic and contact flaws, to be predicted. Little to no computation is required. [ABSTRACT FROM AUTHOR]

The stress singularities of a dynamic crack tip in orthotropic composites were studied through caustics. The parametric equations of the caustic and its initial curve surrounding the dynamic crack tip were derived through the elastic dynamic crack solutions of orthotropic composites and the basic principle of reflective caustics. Theoretical caustics and initial curves for three kinds of orthotropic composites were simulated, and the effects of crack velocity on the caustics and initial curves were analyzed. In comparison with numerical results, the dynamic caustic experiment was performed for dynamic cracks along the material axes in unidirectional, fiber-reinforced composites under drop-hammer, three-point-bend loading. [ABSTRACT FROM AUTHOR]

Techniques to measure the relationship between crack velocity and energy-release rate for channeling cracks in thin films and coatings are presented in this paper. The approach uses linear-elastic fracture mechanics to relate the crack spacing, material properties and geometry to the energy-release rate of a channeling crack, by means of detailed finite-element calculations. The velocities of individual cracks are monitored and related to their distance to nearest neighbors as part of these calculations. Other parameters that were identified as being important in determining the energy-release rate were the depth below the surface to which the crack penetrated, and the residual strain in the cracked layer. A technique to determine the crack depth was developed which involved focused-ion beam milling of the specimen, followed by electron microscopy. The residual strain in the crack layer was determined by measuring the crack-mouth opening using atomic-force microscopy, and comparing this to numerical analyses. These approaches were used to analyze a multi-layer system consisting of a polymeric, colloidal-silica nano-composite layer and a primer layer coating a polycarbonate substrate. The crack growth showed a threshold value of energy-release rate corresponding to about 6.6 J/m 2 , with a minimum detectable crack velocity of about 3 nm/s. When the energy-release rate was increased to about 25 J/m 2 , the resultant crack velocity was 10 -2 m/s. The channeling cracks in this system exhibited the characteristics of a thermally-activated rupture process, but showed no evidence of fatigue or stress-corrosion cracking under the conditions studied. [ABSTRACT FROM AUTHOR]

This paper presents the results of experimental studies of the crack propagation velocity and the dynamic fracture toughness of St. 45 steel and D16T Duralumin using a modified Kolsky method with a split Hopkinson bar. The results of microfractographic analysis of samples are given, and the fractal dimension is determined. The critical stress intensity factors are calculated using the obtained fractal dimension values [ABSTRACT FROM AUTHOR]