Single Crack Research Articles

Effect of lamina orientation, crack severity, and fillers on dynamic parameters of hybrid composite cantilever beam with double transverse cracks

AbstractModern‐day research in composite material development primarily focuses on tailoring combinations by proportions of constituent materials and monitoring the changes in their targeted properties. In line with this trend, a new class of glass fiber reinforced polymer hybrid composite beam of size 600 mm×50 mm×6 mm is fabricated by adding graphene (average particle size:10 μm), and flyash (average particle size: 60 μm). The dynamic behavior of the hybrid beam by introducing two transverse cracks at different positions with varying crack depths is studied by employing analytical, finite‐element, and experimental approaches. The dimensionless relative natural frequencies of the cracked/faulty hybrid beam obtained by the proposed methods are compared with the intact hybrid beam. Also, a comparison is made for the hybrid beam with a single crack. An increase in relative crack depth resulted in an increase in values of dimensionless compliances. Further, the effect of fiber orientation and lamina stacking sequence on the dynamic parameters of the hybrid beam are also analyzed. The introduction of the second crack induces higher nonlinearity in bending modes of vibration.

Characterizing the cracking process of various rock types under Brazilian loading based on coupled Acoustic Emission and high-speed imaging techniques

Tensile strength is one of the important mechanical properties of rock and rock-like materials and its accurate estimation and understanding of its failure mechanism are crucial for efficient design of structures on or within the rock masses. Amongst various approaches developed for estimating this property, Brazilian testing has received considerable attention analytically, numerically and experimentally. The test has been deployed for a wide range of materials such as rock, concrete, and ceramic, however its fracturing process at micro and macro scales has not yet been properly characterized. Thus, in this study, for a full understanding of the fracturing process of different rock types under indirect tensile loading, the coupled Acoustic Emission (AE) and high-speed imaging techniques were used to characterize the generated micro and macrocracks under Brazilian loading. The characteristics of AE parameters and the evolution of micro-macro cracks were investigated for three different rocks including sandstone, coal and granite at different sizes and loading configurations. A systematic framework was developed to exhibit the link between micro and macro fracturing processes under Brazilian loading. It was noted that the tensile microcracks are the first to initiate during the Brazilian failure with high intensity compared to shear microcracks. Transition in microcracking mechanism from tension to shear was evident in the samples with high brittleness. The tensile microcracks showed ascending trends with a decrease in geometrical or volumetric sample size for granite and sandstone, while its trend for coal was inconclusive due to its unique intrinsic fracture network or so-called “cleat network”. At macro scale level, single and multiple cracking mechanisms were observed in the tested samples where those with high shear microcracks mostly revealed failure under multiple cracking. Finally, some insights were provided into the transition from single tensile cracking to multiple tensile/shear cracking based on high-speed image data with high resolution.

Nano‐Cracks and Glass Carving from Non‐Symmetrically Converging Shocks

AbstractA method is presented to carve into a glass submerged in water with laser‐induced surface and shock waves. It starts with an elliptic wave source that launches an elliptically converging Rayleigh and shock wave. At the wave focus a single microscopic crack with controlled location and orientation is induced that has a length of a few micrometers and a width of about 100 nm. Through successive surface waves, this crack may be extended along a specific direction which can be controlled by adjusting the distance, shape, and orientation of the laser focus. Here, either point‐like or elliptical laser foci are generated using a spatial light modulator. Furthermore, when the crack is guided along a closed circular path using a point like laser focus, a conchoidal hole may be carved through the glass slide demonstrated with a 160 µm thick cover slip. The shock waves are modeled in the fluid and the elastic waves in the glass in three dimensions with a finite‐volume framework that accounts for fluid‐structure interaction. The resulting pressures and stresses for both the elliptical and point‐like Rayleigh and shock wave sources are reported.

A Robot-Assisted Microscopy System for Digital Image Correlation in Fatigue Crack Growth Testing

BackgroundDigital image correlation (DIC) with microscopes has become an important experimental tool in fracture mechanics to study local effects such as the plastic zone, crack closure, crack deflection or crack branching. High-resolution light microscopes provide 2D images but the field of view is limited to a small area and very sensitive to its alignment. A flexible positioning system is therefore needed to collect such DIC data during the entire fatigue crack growth process.ObjectiveWe present in our paper a new experimental setup for local high-resolution 2D DIC measurements at any location and at any time during fatigue crack growth experiments with a non-fixed DIC microscopy system.MethodsWe use a robot to move the 2D DIC microscope to any location on the surface of the specimen. Optical and tactile methods automatically adjust the system and ensure highest image quality as well as accurate alignment. In addition, an advanced repositioning method reduces out-of-plane motion effects.ResultsThe robot is able to achieve a repositioning accuracy of less than 0.06 mm in vector space, resulting in very low Von Mises strain scattering of 0.07 to 0.09% in the DIC evaluation. The system minimizes systematic errors caused by translation and rotational deviations. Effects such as crack deflection, crack branching or the plastic zone of a fatigue crack can be investigated with a field of view of 10.2 x 6.4 mm2.ConclusionsThe robot supported DIC system generates up to 8000 high-quality DIC images in an experiment that enables the application of digital evaluation algorithms. Redundant information create confidence in the results as all revealed effects are comprehensible. This increases the information content of a single fatigue crack growth test and accelerates knowledge generation.

The influence of circular cavity on the characteristics of dynamic crack propagation in rocks using a single notch triangle approach

We used a novel single-notch triangle (SNT) sample to conduct dynamic fracture tests and investigate the effect of a circular cavity on the dynamic fracture mechanisms that occur in fractured rock masses subjected to a single crack under dynamic loads. Dynamical loads were applied with a drop hammer weight device. A modified finite difference method code was developed to simulate the dynamic cracking behavior of SNT samples under the action of impact loading. Next, we calculated the maximum principal stress and circumferential stress around the circular cavity and investigated dynamic crack initiation toughness (DCIT) by applying both experimental and numerical approaches. We also investigated the mechanisms that occur in the circular cavity with regards to the initiation of dynamic cracking and the cracking behavior by applying numerical models. Analysis demonstrated that the circular cavity promotes cracking initiation behavior and that the most significant impact was detected at a horizontal offset distance of 15 mm. Furthermore, the crack initiation time and DCIT were used effectively to evaluate the dynamic stability of cracks. However, the DCIT is accurate parameter for investigating how a mass of fractured rock changes according to different dynamic loads. We found that the roughness of the fractured surface around the crack tip was more significant than that of the fractured surface behind the circular cavity; this demonstrated that the circular cavity enhanced the energy consumed during crack propagation.

Experimental and Computational Techniques of Free In-Plane Vibration of a Fixed Support Curved Beam with a Single Crack

Experimental and Computational Techniques of Free In-Plane Vibration of a Fixed Support Curved Beam with a Single Crack

EXPERIMENTAL INVESTIGATION OF THE EFFECT OF STRAIN RATE ON THE CRUSHING STRENGTH OF A CELLULAR CONCRETE

The strain rate dependent compressive strength of an autoclaved aerated concrete (AAC) having a density of 600 kg m-3 was experimentally investigated between quasi-static and high strain rates (2x10-3-~4150 s-1) through quasi-static and dynamic compression, confined compression and indentation tests. High strain rate equilibrium and direct impact non-equilibrium compression tests in conjunction with the high strain rate confined compression and indentation tests were conducted in a compression Split Hopkinson Pressure Bar. The experimental results showed two different regions of the compressive strength-dependency on the strain rate: a low-strain rate-dependent region from quasi-static to ~18 s-1 and a high-strain ratedependent region from ~18 s-1 to ~1000 s-1. The switch of the failure mode from the single axial cracking at quasi-static strain rates to the extensive axial and circumferential cracking at increasing strain rates was ascribed to both the axial and radial inertia. The dynamic increased factor (DIF=dynamic strength/static strength) showed an abrupt increase after ~18 s-1 as similar with the compressive strength. The mean confined and indentation strength values also increased as the velocity increased, while the mean confined compression strength values were shown to be comparable with the dynamic compressive strength values. The inertia and strain rate contributions to the enhancement of DIF until about 1000 s-1 were predicted by taking the quasistatic indentation strength as the full confinement strength.

Influence of the Crack Angle on the Deformation and Failure Characteristics of Sandstone under Stepped Cyclic Uniaxial Compression with a Constant Lower Limit

Engineering rock structures containing joints and fissures are frequently subjected to discontinuous periodic disturbances of varying amplitudes. To attain the quantitative relationship between the crack angle and the mechanical and deformation properties of rock under complex stress paths, uniaxial cyclic loading and unloading tests with increasing stress gradients were conducted on sandstone specimens containing a single crack of different angles. Our results showed that the bearing capacity of the sandstone increased as the crack angle increased. The irreversible strain and elastic moduli of the rock presented a sudden increase when entering the next cycle of the stepped loading. However, the entire loading process can be divided into three stages according to their respective trends. These three stages correspond to the three stages of rock deformation, i.e., the pore crack compaction stage, the elastic deformation to the stable micro-elastic crack development stage, and the unstable crack development stage. In addition, the crack angle of sandstone showed a negative correlation with the irreversible strain, but a positive correlation with the elastic modulus. With the increasing crack angle, the failure mode of the rock changed from the tensile-shear failure to the shear failure, and then to the interlayer dislocation failure.

Dynamic anti-plane response of circular inclusion in bi-material structure with interfacial periodic cracks due to the SH wave

This paper investigates the dynamic anti-plane response of the circular inclusion in the bi-material structure with interfacial periodic cracks due to the SH wave. In our analysis, we use the ‘conjunction’ technology and Green’s function method. The bi-material structure consists of two isotropic elastic right-angle domains consisting of a circular elastic inclusion and a series of periodic cracks at the bi-material interface. The periodic cracks are created to satisfy the free conditions of the stresses by using the interface ‘conjunction’ technology. The Green’s functions are also solved to obtain the displacement solutions of the out-place point source loaded on the vertical boundaries of the right-angle plane. The first Fredholm integral equations with unknown force systems are then established based on the continuity conditions at the bi-material interface. As an example, the distributions of the dynamic stress concentration factor (DSCF) around the circular inclusion are obtained and shown graphically. The numerical results indicate that compared with a single crack having periodic cracks strengthens the situation of the dynamic stress concentration around the inclusion.

Study on the effect of multi-source solid waste on the performance of its backfill slurry

The preparation of slurry from multi-source solid waste for underground backfill adds a way out for solid waste disposal, which is beneficial to reduce environmental impact. In this paper, the effects of gangue, fly ash, gasification coarse slag and desulfurization gypsum on the fluidity, early strength, thermal stability and other properties of the backfill slurry were studied by fluidity test, strength test, Thermo-Gravimetric Analysis (TGA), Scanning Electron Microscope (SEM) and X-ray Diffraction (XRD). The results show that: (1) When G/SW (mass ratio of gangue to solid waste) < 23%, gangue is beneficial to improve the fluidity and early strength of backfill slurry; with the increase of fly ash content, the fluidity of backfill slurry decreases, but its early strength increases; gasification coarse slag has a negative effect on the fluidity of backfill slurry, but it is beneficial to its early strength when GCS/SW (mass ratio of gasification coarse slag to solid waste) < 33%; desulfurization gypsum can improve the fluidity of the backfill slurry, but it is not conducive to the increase of early strength. (2) The compression failure mode of the backfill is mainly divided into the crack-intensive failure, the single main crack penetration splitting failure, and the double main crack conjugate splitting failure. (3) Endothermic dehydration reactions of adsorbed water and crystallization water generally occur at 55–65 °C and 110–130 °C for backfill with different solid waste contents; As the temperature continues to increase, the backfill material undergoes a slow exothermic decomposition reaction; Increasing the content of gangue, fly ash and gasification coarse slag and reducing the content of desulfurized gypsum can make the backfill less weight loss at high temperature and better thermal stability. (4) The main mineral phases in the backfill material are gypsum and quartz, and there are also a small amount of acicular and hexagonal hydration products thaumasite. After high temperature, the thaumasite is dehydrated and decomposed. The research results are helpful to deeply understand the performance of multi-source solid waste for underground backfilling.

Initiation and propagation of a single internal 3D crack in brittle material under dynamic loads

Different defects are widely distributed inside natural rock masses, and the development of these defects poses a potentially severe threat to the entire structural stability and safety. Most studies at present are concentrated on the propagation of two-dimensional (2D) penetrated cracks under static loads. In this paper, a series of tests were carried out on cubic glass specimens containing a closed pre-crack using a split Hopkinson pressure bar (SHPB) system, aiming to investigate the internal three-dimensional (3D) crack growth under dynamic compression. The results indicate that the dynamic compressive strength of the cubic specimen is influenced by the inclination direction of the 3D pre-crack. Theoretical analysis of the circumferential stress field at the pre-crack tip reveals the mechanism behind dominant crack initiation and favorable direction, which are also affected by non-singular T stress along and perpendicular to the pre-crack plane, as well as friction between crack planes. Through the post-mortem examination, the mode III fracture characteristics, crack bifurcation and Wallner lines are observed in fracture morphology. The terminal length of wrapped wing cracks subjected to dynamic loads is sensitive to pre-crack inclination angle, while it is approximately 1–1.5 times the pre-crack radius under static compression.

Modeling the Crack Interference in X80 Oil and Gas Pipeline Weld.

Based on the numerical simulation method of the virtual crack closure technique (VCCT), an interference model was established to investigate the physical problem of two interacting cracks of different sizes in the welding zone of oil and gas pipelines. The obtained results of the current interference problem were compared with those of single crack case. Various crack configurations, such as different crack spacing and different crack sizes, were analyzed. The characteristic quantity fluid pressure load P during the crack propagation process, the peak value of the von Mises stress distribution field of the crack growth path, as well as the difference ∆Bx between the peak value of the magnetic induction intensity component at the crack and the value of the magnetic induction intensity component at its symmetrical position were calculated. The crack interaction scale factors, including γP, γMises, and γΔBx, were compared and analyzed. The numerical modeling results show that when the unequal-length double cracks interfere with each other, the cracks are more likely to propagate toward each other. The tendency of the double-cracks to propagate toward each other gradually weakens as the distance between the crack tips increases and is finally the same as that of single-crack cases. It was also found that the effect of large-sized cracks on small-sized cracks is greater than that of small-sized ones on large-sized ones. The numerical modeling results could be applied for the prediction and analysis of multicrack damage in oil and gas pipeline welds.

Improved XFEM for multiple crack analysis: Accurate and efficient implementations for stress intensity factors

The extended finite element method (XFEM) has achieved unprecedented success in crack analysis. However, challenges still remain for a multiple crack simulation. One issue is the difficulty of level set construction, where cracks are generally represented by combinations of different level set functions. Another issue is the rapidly increasing condition number of the global stiffness matrix, which is even more severe than the single crack case. In order to overcome these issues, we make two improvements as follows. On the one hand, inspired by the discontinuous description via cover cutting in Numerical Manifold Method (and later phantom node method in XFEM), we propose a level set templated cover cutting method, which makes use of level set values to cut a nodal patch and then to add virtual nodes. This method, which combines the advantages of both the level set method and the cover cutting technique, is simple and straightforward to implement. The method also plays a role in templated subdivision of discontinuous elements and hence presents an efficient and robust integration scheme. On the other hand, we extend the Improved XFEM (IXFEM), previously proposed by our research group, to the scenario of multiple crack problems. The method fundamentally eliminates the daunting issues of linear dependence and ill-conditioning of the standard XFEM, because it uses an extra-dof-free singularity enrichment around the crack tip. Numerical studies on multiple crack problems show that the developed approach offers various advantages: (1) Highly accurate SIF evaluation over the standard XFEM; (2) Well-conditioning of the global stiffness matrix independent of the number of cracks — condition number being of the same order as the standard FEM; (3) Efficient and robust linear system solving and geometric computations. Thus the developed approach is well capable of modeling arbitrary multiple crack problems.

In situ measurement of plasticity accompanying hydrogen induced cracking in a polycrystalline AlZnMg alloy

Hydrogen induced single crack propagation is studied in an embrittled aluminum alloy. Hydrogen is introduced into the system by electrochemical reactions in an acidic aqueous medium. After hydrogen charging, tensile tests are performed in air, on notched samples, with a microtensile machine under an optical microscope. A high magnification of × 2000 is used to follow the single crack initiation and propagation. Digital Image Correlation gives the displacement field on the surface with a spatial resolution of approximately 1 μm. It enables the determination of the position of the crack tip and the local velocity at a sub-grain scale. The von Mises strain is calculated and provides a precise measure of the local plastic field that accompanies crack propagation. In addition to the primary plasticity which is emitted from the crack tip or its immediate neighborhood in the form of two intense slip bands, a secondary plastic zone that spreads over several microns ahead of the tip is sytematically found. The characteristics of the plastic zone are measured, together with the velocity and the applied stress intensity factor. In addition, different fracture mechanisms are found on the fracture surface. In particular there are transitions in the fracture mode from intergranular smooth to transgranular parallel to the grain boundary plane. The local fracture mechanisms, in the vicinity of the surface, are linked to the local velocities and plastic deformations. Surprisingly no strong velocity/plasticity correlations are found while the velocities are scattered over a wide range, which is interpreted as a strong polycrystalline effect.

Study on the effect of hydro‐chemical dissolution on shear properties of rock fractures using the improved discontinuous deformation analysis

AbstractHydro‐chemical erosion has critical effects on the short‐ and long‐term stability of fractured rock masses in subsurface engineering. Attempts have been made to study this water‐rock interaction process using numerical approaches. However, the majority of the existing approaches quantify the degradation based on the homogeneity hypothesis, which leads to unrealistic results in the case of rock mass with discontinuities. In this study, the hydro‐chemical degradation is represented through geometrical variation of a single crack and reflected in the modified bilinear constitutive model by introducing the hydro‐chemical damage factor. Then, discontinuous deformation analysis (DDA) method embedded in such improvements is chosen to implement the direct shearing process of the rock fracture after hydro‐chemical erosion. The results reveal that the peak shear strength decrease with the increase in the acidity solutions, and a logarithmic relation is found between the decreasing percentage of shear properties and soaking time, which are consistent with the laboratory results. Besides, based on the proposed method, the change in peak shear strength presents synchronism with the variation in the mineral ion and concentration, shown to be in good agreement with the basic understanding of the dissolution process. In addition, the failure patterns of the sheared samples under different normal stress are studied. This research provides an effective tool to quantify the hydro‐chemical damage from the microscale and will be a significant complement to the coupled numerical analysis of the water‐rock interaction process.

Seismic Performance of Reinforced Concrete Beams Susceptible to Single-Crack Plastic Hinge Behavior

Following the 2010/2011 Canterbury and 2016 Kaikoura earthquakes, a number of reinforced concrete (RC) beams in high-rise structures developed a single primary crack at the beam-column interface without the formation of distributed secondary cracks along the beam length. Detailed assessments showed that these beams have conforming longitudinal steel ratios and the single-crack mechanism may be due to design and/or construction practices for beam-column joints in the 1980s. In order to investigate the seismic behavior of reinforced concrete beams with detailing that inhibited the spread of flexural yielding, an experimental program was carried out on RC beam specimens, having similar reinforcement detailing to that of beams that developed a single crack at their ends during the Kaikoura earthquake to understand their seismic behavior, postearthquake repairability, and residual low-cycle fatigue life. Experimental results showed that the beams were able to undergo significant inelastic drift demands without loss of lateral resistance and have sufficient residual drift capacity following moderate and large earthquake demands. The response of the beam specimens was dominated by hinge rotation via the bond-slip mechanism. Comparisons showed that the measured drift capacities of the beams exceeded the predicted drift capacities computed using state-of-the-practice procedures.

Effective separation of vehicle, road and bridge information from drive-by acceleration data via the power spectral density resulting from crossings at various speeds

This paper proposes a novel PSD-based algorithm to overcome limitations found in drive-by bridge health monitoring through the application of a transfer function to extract the contact point response from axle accelerations, the removal of the road irregularities by subtracting responses at different speeds in the spatial domain, and the estimation of damage by comparison of the PSD to a reference database. A strength of the algorithm lies in the use of a moving constant force to create the database, greatly simplifying computational and modelling requirements. Theoretical testing is conducted driving a quarter-car over a 15 m simply supported bridge in 1800 damage scenarios defined by a single crack randomly located across the span. The accuracy in locating and quantifying the crack remains unaffected overall when adding 5% Gaussian noise to the accelerations. The highly accurate quantification demonstrates the success in removing vehicular and road components from the axle accelerations.

Engineered cementitious composites - a review

Engineered Cementitious Composites (ECC) is also known as bendable concrete, characterized by tight crack width control. As we know the concrete is brittle in nature, expected to fail catastrophically. To minimize the damages caused by the concrete failure in seismic region we go for special detailing to enhance the ductility nature of concrete members, which leads to a complicated design. To overcome this problem a new type of composites are designed called Engineered Cementitious Composites based on a combination of structural engineering and micromechanics. This paper deals with the literature survey on micromechanics design to achieve the pseudo strain hardening behaviour, i.e. to achieve two criteria’s namely i) Strength Criteria ii) Energy criteria. Both Reinforced Concrete and Fiber Reinforced Concrete shows strain softening behaviour after the appearance of the first crack whereas the ECC shows strain hardening behaviour after the appearance of first crack because of the presence of randomly oriented discontinuous fibers. Regarding Strength criteria, Fiber bridging stress plays a major role and for energy criteria, Matrix toughness plays a major part. By tailoring these two parameters, strain hardening behaviour of the composite can be achieved. Apart from these two parameters mixing of fresh ECC is also an important factor to be considered, since uniform dispersion of fibers leads to bridging of the cracks which makes the composite to have a multiple fine cracks before failure instead of having a big single crack.

Spall fracture forms of high rock samples under uniaxial compression

Prof. L.I. Baron identified five forms of destruction during uniaxial compression of samples of regular geometry of rocks including truncated wedge, wedge, diagonal, longitudinal, and explosive forms. All of them are commonly characterized by the destruction of samples in their central parts showing two or more cracks, while the trajectories of crack development align with the corner points of the samples. Recently, was unexpectedly discovered a spall fracture in the form of a single crack emerged from the side wall of the specimen and propagating into it under uniaxial compression. Based on the discovery, the method for creating stress-strain diagrams for high rock samples was developed using four rock properties such as rock shear resistance limit, contact friction ratio, internal friction ratio, and modulus of elasticity. The stress-strain diagram of the spall fracture of high samples is described by a descending curve, which is typical for the diagrams of fracture created by two adjacent cracks of regular geometry samples. The maximum stresses required for the destruction of high rock samples are lower than those for the destruction of regular geometry samples of rocks with similar physical and mechanical properties.

Simulation of Surface Crack Interaction of Marine Solid Shaft

In the marine industry, an engine transmits power through a marine shaft, also called a propeller shaft, to a propeller drive. Almost all naval architects construct this shaft as a solid cylinder. When a crack shows up in the hub of a shaft, it is essential to take preventative measures. When solid cylinders are exposed to various mechanical stresses, cracking or fracturing is a typical failure, and most of the crack exists in single and multiple cracks. Owing to the possible interactions between fractures, they are likely to play a significant role in how the structure collapses. Consequently, this study is being conducted to address issues emerging from the interaction of multiple cracks during particular loading conditions. This paper will highlight the research conducted on various cracks interacting with parallel configurations on the cylinder's surface. Finite Element Software, AnsysTM has been employed through modelling and simulation to calculate the stress intensity factor (SIF) for various crack geometry features and separation distances under various types of loading. The dimension for length and diameter of the cylinder has been set as 200 mm and 50 mm, respectively. The values of crack depth ratio used is ranged from 0.1 to 0.4 with the increment of 0.1, while for crack aspect ratio is 0.6. The results from the SIFs are normalized for generalization to determine the interaction factor and the relationship between two cracks and a single crack.