Single Crack Research Articles

Effect of Crack Angle and Length on Mechanical and Ultrasonic Properties for the Single Cracked Sandstone Under Triaxial Stress Loading-Unloading

The disturbance due to coal mining causes the surrounding rock to undergo a complex process of stress changes during which the axial pressure and the confining pressure usually change accordingly at the same time. Existing studies generally investigated this process from a static perspective, which was not rigorous. The mechanical characterization of rock is very important to understand the failure of rock mass and the safety of mining during mining disturbance. Based on theoretical analysis, we conducted axial loading and radial unloading tests on the cracked sandstone, which was combined with the ultrasonic testing technology to examine its failure rules and to characterize and analyze its failure process using longitudinal wave velocity. The results demonstrated that crack length and angle had a significant impact on the strength and mechanical properties of sandstone, and the former had a greater impact on the strength of sandstone than the latter. As the crack length increased, the strength, elastic modulus, and deformation modulus of sandstone decreased, and the strength of sandstone increased as the crack angle increased. Elastic and deformation moduli first decreased and then increased. Furthermore, Poisson’s ratio increased slowly, then decreased slowly, and finally increased rapidly as the lateral pressure coefficient diminished, and Poisson’s ratio was more sensitive to changes in the angle. In this study, the change of longitudinal wave velocity reflected the whole process of sandstone failure. When the wave velocity was stable, the rock was at the yield limit point. Moreover, when the wave velocity was unstable, the sandstone was in a progressive failure period, and as a result, the wave velocity decreased and the sandstone cracked.

Crack interaction and fracturing of geomaterials with multiscale cracks

Geomaterials contain numerous cracks whose interaction affects the macroscopic mechanical properties of the materials significantly. We propose a mechanical model of cracks of 3 scale levels to investigate the pattern of crack propagation and possible failure modes produced. For modelling crack interaction between different scale levels, we model the unloading domain of influence of a single crack as the sphere with the diameter being the crack size drawn around the crack center. When the tip of a lower scale crack propagates into the influence domain of a crack of a higher scale level, the propagating crack of a lower scale will be unloaded and never grow from this tip. Propagation and coalescence of cracks of different scale levels for different initial crack concentration result in different patterns of cracks propagation and failure. For relatively lower initial crack concentrations, the interaction of cracks of the first scale level dominates, producing failure due to the coalescence of cracks of the first scale level. With the increase of the initial crack concentration, the coalescence of cracks of the third scale level dominates leading to failure at a higher initial concentration. With the further increase of the initial crack concentration, the failure is produced by the coalescence of cracks of the second scale level. At even higher initial crack concentrations the failure is again produced by the coalescence of cracks of the first scale level. The dynamic strength decreases with the increase in the initial crack concentration. • A model of interaction, growth and coalescence of self-similar cracks of 3 scale levels is proposed. • The unloading effect of higher scale level cracks on the propagation of lower scale level cracks is considered. • Degradation of the effective deformation modulus is considered in solving crack-tip equations of motion. • The discreteness of crack propagation at the accelerating stage of loading is discovered. • At certain intervals of the initial crack concentration cracks of the lowest scale level will coalesce first.

Impact characteristic and crack propagation mechanisms of large-size molybdenum alloy single crystal and polycrystal

The impact characteristic and crack propagation mechanism for large-size Mo3Nb single crystal with a diameter of about 30 mm have been investigated and disclosed comprehensively by Charpy impact test. The fracture analysis shows that the single crystal crack propagates radially, resulting in a multi-step distribution on the fracture surface. The fracture of Mo3Nb polycrystal is composed of cleavage and quasi-cleavage, exhibiting a trans-granular fracture feature. The impact toughness of single crystal shows orientation dependence, which is attributed to the crack propagation path. Compared with the straight path, the waved path can delay the crack propagation and absorb higher impact energy. The impact toughness of Mo3Nb single crystals is lower than that of Mo3Nb polycrystal at room temperature because the single crystal lacks the coordinated deformation of grain boundary. The analysis of dislocation arrangement for Mo3Nb single crystal shows the different crack propagation paths is caused by the mobility of screw segments, which are controlled by the double cross-slip multiplication mechanism. However, the waved fracture morphology of Mo3Nb polycrystal is caused by the effect of grain boundaries instead of the cross-slip of screw dislocation.

Improved virtual extensometer measurement method in complex multi-fracture situation

To overcome the limitation of the virtual extensometer method in measuring the crack opening displacement (COD) in the process of complex multi-crack propagation of rock, the measurement error of Digital Image Correlation (DIC) local deformation is theoretically analyzed. An improved virtual extensometer method for measuring the COD is proposed, which considers the temporal and spatial characteristics of crack development in the process of complex crack propagation. The accuracy of the proposed method is verified by the strain localization band numerical simulation test and indoor single crack simulation test. Furthermore, the method is applied to the two-dimensional similarity simulation test of simulating complex multi-fractures in rock stratum. The COD obtained by the traditional and improved methods is compared with the measured COD. The results show that in the case of multiple complex cracks, to obtain the COD accurately, the relative distance between the virtual extensometer measuring point and the crack should be greater than half of the sum of the width of the crack strain localization zone and the subset size. With the development of the crack, the relative distance between the virtual extensometer measuring point and the crack should increase with the increase of the width of the crack strain localization zone. The error of the COD measured by the traditional method increases with fracture development, and the maximum is 21.20%. The maximum relative error between the COD measured by the improved method and the measured crack opening is 3.61%. The research results improve the accuracy of the virtual extensometer in measuring the COD under complex multi-crack conditions.

Effect of Fiber Orientation Angle on Stress Intensity Factor of Composite Plate Using Extended Finite Element Method (XFEM)

This paper presents the effect of fiber orientation angle on the stress intensity factor SIF for carbon epoxy composite plates with single-edge, center, and inclined cracks of varying lengths under tensile load. The stress intensity factor and shape factor were calculated individually for each case, with nine different fiber orientation angles computed using the extended finite element method XFEM concepts. It is found the stress intensity factor increases with increasing crack lengths while the shape factor decreases. In the case of single edge cracks, the SIF increases in the average value reached (173 %) for composite plates with different fiber orientation angles, while in the case of the center crack, the average value of SIF reaches (81 %). It was observed in this study that the increases in stress intensity factor and the decreases in the shape factor with different crack lengths were more stable in the composite plate with a fiber orientation angle of 75°. The higher values of SIF at an angle of 75° are because of the high probability of fiber slippage at 75° due to induced shear stresses in addition to the tensile stresses at the fiber-matrix interface. As a result, the crack tip has a high-stress intensity factor.

Mechanical characteristics of single cracked limestone in compression-shear fracture under hydro-mechanical coupling

This paper creates single cracked specimens by the prefabricated crack in the middle of a standard cylindrical specimen of limestone. The MTS815 rock mechanics test system was used to perform conventional triaxial compression tests on single cracked limestone specimens under different confining pressures and water pressures. The theory of linear elastic fracture mechanics is used, the fracture mode of single-cracked limestone is analyzed and the rock compression-shear fracture criterion under hydro-mechanical coupling is deduced and verified experimentally. The results show that the deviatoric stress–strain curve of single-cracked limestone has a unique double stress peak behavior of high front and low back (crack inclination angle β = 15°) and low front and high back (crack inclination angle β = 45°). The crack initiation stress and peak strength of single crack limestone show a significant decreasing trend with increasing water pressure and increasing with increasing confining pressure. The highest values of crack initiation stress and peak strength for specimens with crack inclination angle β = 75°, secondary for specimens with β = 15° and smallest for specimens with β = 45° under the same confining pressure and water pressure. Based on the fracture mechanics theories, the stress intensity factor of open crack and open crack closed by force increases with the increase of water pressure. The effective stress intensity factor and mixing factor increase with the increase of the crack inclination angle. In addition, the advantage angle βm is detected to be related to the friction coefficient of the crack surface, and the range of values of the advantage angle of the open crack subjected to pressure to closure is obtained to vary between 45° and 67.5°. Additionally, the advantage angle for the open crack is 45°, which indicates that the specimen crack inclination angle with β = 45° is the easiest to initiate cracking, and the conclusion is in concordance with the test results.

Evaluation of self-healing in concrete using linear and nonlinear resonance spectroscopy

In this study, self-healing in concrete incorporating two types of healing agents, i.e., 1) a self-healing capsule and 2) supplementary cementitious materials with crystalline admixtures, is monitored using linear and nonlinear resonance acoustic spectroscopy techniques. Beam-shaped concrete specimens are prepared using the healing agents, and after 28 days, a single vertical crack with a width ranging from 0.25 to 0.35 mm is generated at the center of the specimens. To monitor the self-healing process in concrete, the samples are vibrated via impact-based excitation methods in the flexural and longitudinal directions, whereas the linear resonance frequency and acoustic nonlinearity parameter α are measured for two months. Additionally, the acoustic nonlinearity parameter is analyzed using two different methods: 1) multiple impacts with manually controlled amplitude, and 2) single impact with artificially controlled amplitude by changing the windowing region in a signal. Test results show that the linear resonance frequency increases up to 86%–97% that of the uncracked condition after 63 days of self-healing. The linear trend of the resonance frequency is correlated significantly with the decrease in the external crack area, but the change in α is affected by the presence of partially filled cracks than by the overall crack area.

Novel size-dependent finite element formulation for modal analysis of cracked nanorods

It is a remarkable engineering problem how possible structural damages in nano/micro scaled mechanical elements affect the working performance and mechanical behavior of nano/micro-electro-mechanical system (NEMS/MEMS) organizations. There are various nano/micro-scale mechanical elements that can be modelled as one-dimensional and continuous systems in NEMS/MEMS organizations. With this motivation, the free vibration analysis of nano scaled axial rods with a single crack is examined by employing the nonlocal finite element formulation for the first time in the literature in this study. Firstly, the differential equation of nonlocal vibration of nanorods is presented for a single crack. Next, a nonlocal finite element formulation developed for the case of crack is proposed. The local and nonlocal nondimensional frequency parameters of cracked nanorods are compared with some studies in the literature. Additionally, nondimensional frequencies of nanorods are presented with several tables and graphics according to different parameters such as nonlocal parameter, mode number, crack intensity and crack location. Detailed discussions of the numerical results are given, and the conclusions deduced from these discussions are summarized.

Dynamic interaction between complex defect and crack in functionally graded magnetic-electro-elastic bi-materials

This paper aims to develop an effective theoretical method for analyzing the interaction of interfacial crack and complex defect in functionally graded magnetic-electro-elastic bi-materials with exponential variation under the action of anti-plane incident SH-wave. The boundary value problem of interest is solved by Green’s function method. The mechanical model of the cracks is constructed through interface conjunction and crack deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips of the left crack are expressed. The validity of the present method is verified by comparing with a single crack model in previous work. Through the analyses of numerical cases, it can be concluded that the DSIF is related with 3 factors：the geometry of complex defect and crack, the characteristics of incident wave and the inhomogeneity of materials. Comparing with dual integral equations in dealing with asymmetric defects, the method in this paper is relatively more flexible and applicable, also it comes up with a new way to study fracture problems in functionally graded magnetic-electro-elastic materials with more complex defects.

Experimental and Computational Investigations on Fretting Fatigue Crack Growth in Dovetail Joints

Fretting fatigue is a significant damage mode for turbine engine blade/disk components. In the present work, fretting fatigue crack growth of a nickel-based superalloy was experimentally and computationally investigated. Fretting fatigue experiments of dovetail joints were conducted under loading ratio , and the results revealed that the fretting fatigue cracks nucleated in multiple sites on the contact edge, which was accompanied by oxide wear debris and propagated with a single through-thickness crack. The crack growth rate was determined based on the variation of applied loading ratio in the experiments. With the help of the maximum tensile stress criterion, the friction coefficient of the fretting pair was determined from simulations of the fretting fatigue crack propagation. With the increasing friction coefficient, the kinking angle of the fretting crack approaches a stable value. The stress was verified to have significant effects on the short crack kinking and implemented in the maximum tensile stress criterion. A methodology based on fracture mechanics was proposed to identify the friction coefficient on the fretting surfaces.

Fatigue and static damage in curved woven fabric carbon fiber reinforced polymer laminates

Failure mechanisms of curved cross-ply laminates under static and fatigue loading have been studied extensively, but the examination of fabric laminates which are the most commonly used ply type in curved supports in airplane wing structures is lacking. In this study, unidirectional (UD) and fabric carbon fiber reinforced polymer (CFRP) laminates are examined to elucidate the failure initiation mechanisms of laminated composites under fatigue and static loading. The crucial point of the research is applying the analyses using fabric laminate with a currently used stacking sequence in commercial airplanes. In addition to the fabric laminate, UD laminate is also included in the research to compare the real complex stacking with the simplest stacking. In the experiments, it is observed that both static and fatigue failures initiate roughly at the maximum radial stress location (approximately 35% of the thickness from the inner radius). For UD laminates, there is no visible difference between the failure mechanisms under static and fatigue loadings. However, for fabric laminates, fatigue failure is observed to occur as a single major crack at the maximum radial stress location as in UD laminates, whereas static failure is observed to occur as multiple diffusive cracks at the maximum radial stress location. Additionally, cracks grow mostly as intralaminar cracks connected with regions of occasional interlaminar cracks.

Strength Characteristics and Failure Mechanism of Granite with Cross Cracks at Different Angles Based on DIC Method

The engineering rock mass is generally composed of the rock matrix and structural plane and is an anisotropic inhomogeneous geological body. Accidents such as roof collapse and well caving caused by joint and fissure expansion occur frequently during tunnel excavation and service, resulting in serious casualties and economic losses. It is of great theoretical significance and engineering value to study the fracture mechanism of the jointed rock mass to ensure the stability of the surrounding rock and the safe and efficient utilization of the urban underground space. To investigate the effects of crossed cracks on mechanical properties and failure characteristics of rock, wire cutting equipment is employed to make rock samples with different crossed cracks, and then acoustic emission system and digital image correlation technique are used to study the fracture process of rock samples under uniaxial compression. It has been found that the strength of rock samples with a single crack is generally larger than that of samples with cross cracks, and the strength changed with the angle of the crack in a “V” shape. When the angle of preexisting crack is 60°, the rock strength reaches the lowest. The primary crack has a more obvious influence on rock strength and is the main controlling factor of rock fracture. The initiation stress of rock samples with a single crack changes more significantly with angle. When the angle of the primary crack is 45°, the rock sample is most prone to crack initiation failure, and the crack initiation stress is only 1/4 to 1/2 of the strength. There are two types of cracks: wing and anti-wing, and the tensile cracks are the main ones. It is revealed that the fracture of cracked rock has significant directional characteristics. For the samples with cross cracks, the primary crack is the main control factor of crack initiation, and the secondary crack has a certain guiding effect on the crack.

Study on Crack Propagation and Coalescence in Fractured Limestone Based on 3D-DIC Technology

To deeply understand the influence of crack inclination angle on crack propagation and coalescence in fractured limestone, uniaxial compression tests were carried out on limestone specimens with prefabricated cracks. The strain field evolution diagram of the failure process of the specimens was obtained using 3D digital image correlation technology (3D-DIC technology). This, in combination with the crack propagation diagram, was used to analyze the entire failure process of the limestone specimens. The test results show that the evolution process of the principal strain field agrees well with the process of crack initiation, propagation, and coalescence. The crack development process is the process of the high strain zones consistently propagating and also the process of micro-cracks appearing, developing, and nucleating to form macro-cracks. With the increase in the parallel crack inclination angle, the stress concentration zone of the intermediate crack transfers from both ends of the crack to the middle. Meanwhile, the coalescing crack type between the parallel crack and the intermediate crack changes from a coexisting tensile crack and tensile-shear crack to a single tensile crack. With the increase in the parallel crack inclination angle, the failure of the fractured limestone specimens changes from simple splitting or tensile failure to the coexistence of tensile-shear fracture and splitting. 3D-DIC technology provides an effective method to study crack propagation and coalescence during rock failure.

A Unified Model for Fibers With Divergent Pullout Behaviors in Strain Hardening Cementitious Composites (SHCC)

Strain Hardening Cementitious Composites (SHCC) are materials exhibiting high tensile ductility with the formation of multiple cracks. Since the mechanical properties of SHCC members are governed by the interfacial characteristics between fibers and matrix, understanding the mechanism of single fiber pullout behavior is crucial for SHCC material design. Existing model was set up based on Polyvinyl Alcohol (PVA) fibers, making it inapplicable to other kinds of synthetic fibers those exhibit divergent pullout behaviors. As a result, the simulated curves cannot agree well with the tested results of SHCC made with other fibers or hybrid fibers. In this study, a unified single fiber pullout model was proposed to take divergent kinds of fiber pullout behavior into account. Five parameters were defined to describe the single fiber pullout behavior, where the frictional strength during the pullout stage and the blocking length of fiber under pulley force were for the first time introduced. For verification purpose, fiber-pullout samples with Polyethylene terephthalate (PET) and PVA fibers were tested and the results agree well with the simulated curves from proposed model. The stochasticity of each parameters were then analyzed and described by normal distribution, through which fibers with various random pullout behaviors can be incorporated into a larger scale modelling. Therefore, the fiber-bridging constitutive law for a single crack was calculated and compared with the single crack test results, which confirmed again the validity of the proposed model.

Weight function method and stress intensity factor for two unsymmetric through-thickness and quarter-elliptical corner cracks at circular hole

Two unsymmetric through and quarter-elliptical corner cracks at a circular hole are frequently encountered in aircraft structures. Stress intensity factors for these crack geometries are the prerequisite for aircraft damage tolerance analysis. However, compared to single and symmetric double crack(s) case, the present two unsymmetric through and corner cracks at a hole is much more complicated because more geometric variables are involved. In the present article, the two-dimensional displacement-based weight function method is extended to derive the weight functions of two unsymmetric hole-edge cracks. Accurate and wide-range weight functions and stress intensity factors are obtained. The two-dimensional weight function for the hole-edge cracks is further used in the slice synthesis weight function method to compute stress intensity factors for two unsymmetric quarter-elliptical corner cracks at a circular hole. The solution accuracy is extensively verified through comparisons to stress intensity factors obtained using finite element analysis. Compared to 3D finite element method, the present slice synthesis weight function method is 500 times faster, and therefore can provide accurate and very efficient tool for fatigue and fracture analysis of structures containing through and quarter-elliptical corner hole-edge cracks.

Effects of multi-cracks and thermal-mechanical coupled load on the TSV reliability

Three-dimensional (3D) integrated packaging technology is gradually moving from the laboratory to the market. Through silicon via (TSV) is the most critical structural unit in 3D integrated packaging. However, during the TSV manufacturing process flow and its service process, many micro cracks will be generated in the TSV microstructure. The multi-cracks seriously threaten the reliability of the TSV and affect the device performance and service life. The existing literature often focus on a single crack under thermal load alone, which obviously does not match the actual situation and leads to larger analysis errors. Based on the theory of elastoplastic fracture mechanics and multi-physics coupling analysis, this paper explored the effects of multi-cracks and thermal-mechanical coupled load on the reliability of TSVs using numerical analysis. Using the J integral value as the indicator, the effects of crack numbers, crack locations, crack lengths, crack propagation directions and thermal-mechanical coupled load on the crack propagation of TSV structures were studied. Based on the research results, suggestions were made for TSV structure design and manufacturing process optimization. The main goal of this paper is to explore the influence of cracks and thermal-mechanical coupled loads on TSV microstructure through numerical analysis. Due to the micro-scale of the TSV structure, the above targets are difficult to obtain through experimental tests. The research methods and results of this paper can provide important references for the reliability evaluation and optimization design of TSV microstructures.

Study on instability discriminating condition and permeability variation of triangle articulated structure in highly inclined goaf

The huge, inclined goaf formed by the mining of steeply inclined and extra thick coal seams has the characteristics of occupying a large space and being subject to complex breaking behavior of its overlying rock structure, especially the rock block structure characteristics of the interface area between the goaf and the lower working face which is difficult to be characterized, leading to a hidden danger when mining the lower working face. In response to the aforementioned problems, the following conclusions are drawing as follows: (1) with the aid of the contradiction method, the critical condition governing instability of the triangular articulated structure was obtained to explain the correctness of the assumption of the triangular hinged structure; (2) three-point truss structure was composed of key layer blocks; (3) in the stabilization stage of the triangular hinged structure, the fracture network area was extracted, and the centerline intensive equivalent method of a single fracture segment was adopted to directly measure the equivalent length. Meanwhile, the value of equivalent average width with the equivalent length of a single crack was calculated by integral operation and equivalent figure calculation; (4) the mathematical expressions of permeability which was positively exponential function related to the ratio of equivalent average width to equivalent length were derived. Furthermore, the vectorized solution of seepage rate was carried out respectively for the goaf area and the extracted network area by using COMSOL software. The distribution of the strong seepage area of CBM and the ratio of equivalent average width to equivalent length is found to be consistent to a large extent, which provides theoretical support for subsequent CBM management.

A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

A damage constitutive model of rock-like materials containing a single crack under the action of chemical corrosion and uniaxial compression

A semi-analytical solution to organic contaminants transport through composite liners considering a single crack in CCL

Compacted clay liners (CCLs) are extensively used as engineering barriers for groundwater and soil pollution. The existence of cracks/fractures in CCL caused by thermally induced shrinkage is reported to importantly damage the performance of the CCL. An analytical model is developed to study the effects of the cracks/fractures on the migration of organic contaminants through a composite liner system. Laplace transformation and Laplace inversion using the Stehfest method are adopted to derive the analytical solution, which is validated by the experimental data. The existence of crack shows a significant impact on the breakthrough curve and bottom flux of organic contaminants. Increasing the crack width from 1 to 25 mm results in an enhancement of contaminant bottom concentration by a factor of 280. Increasing the adsorption factor and degradation rate of contaminants can effectively improve the performance of the composite liner with cracks. The effects of degradation of contaminants on the breakthrough curve are found to be more significant for the case with a larger retardation factor. This may be due to the fact that increasing the retardation factor can significantly slow down the transport of contaminants, which may indirectly create a longer period for the degradation of contaminants.

Quantitative evaluation on self-healing capacity of cracked concrete by water permeability test – A review

Crack healing is an effective way to recover the mechanical properties and improve the durability of concrete. This can be achieved either by autogenous healing or adding healing agents into cementitious materials. Although quantitative evaluation on self-healing capacity of cracked concrete is difficult, sealing ratio obtained by water permeability test is a useful indicator for assessing healing efficiency, which is closely related to the characteristics and morphology of crack. In this work, the empirical formulas linking quantified geometry of a single crack (i.e., crack width, tortuosity and surface roughness) and transmissivity are first reviewed and analyzed. Then, the relationship between crack geometry and sealing ratio is established and discussed. At last, some recommendations about the quantitative evaluation on self-healing capacity of cracked concrete are given.