Crack Propagation Patterns Research Articles

Anisotropic Mechanical Behaviors of Shale Rock and Their Relation to Hydraulic Fracturing in a Shale Reservoir: A Review

Shale gas is an important supplement to the supply of natural gas resources and plays an important role on the world’s energy stage. The efficient implementation of hydraulic fracturing is the key issue in the exploration and exploitation of shale gas. The existence of bedding structure results in a distinct anisotropy of shale rock formation. The anisotropic behaviors of shale rock have important impacts on wellbore stability, hydraulic fracture propagation, and the formation of complex fracture networks. This paper briefly reviews previous work on the anisotropic mechanical properties of shale rock and their relation to hydraulic fracturing in shale reservoirs. In this paper, the research status of work addressing the lithological characteristics of shale rock is summarized first, particularly work considering the mineral constituent, which determines its physical and mechanical behavior in essence. Then the anisotropic physical and mechanical properties of shale specimens, including ultrasonic anisotropy, mechanical behavior under uniaxial and triaxial compression tests, and tensile property under the Brazilian test, are summarized, and the state of the literature on fracture toughness anisotropy is discussed. The concerns of anisotropic mechanical behavior under laboratory tests are emphasized in this paper, particularly the evaluation of shale brittleness based on mechanical characteristics, which is discussed in detail. Finally, further concerns such as the effects of bedding plane on hydraulic fracturing failure strength, crack propagation, and failure pattern are also drawn out. This review study will provide a better understanding of current research findings on the anisotropic mechanical properties of shale rock, which can provide insight into the shale anisotropy related to the fracture propagation of hydraulic fracturing in shale reservoirs.

Dynamic impact experimental and global cohesive element method to shale fracture characterization

The fracture behavior and various of mechanical mechanisms of shale are greatly influenced by the bedding surface. To study the effects of bedding angles on the crack propagation patterns and dynamic fracture properties, the shale notched semi-circular bend (NSCB) specimens were studied by the modified split Hopkinson pressure bar (SHPB) device, three-dimensional digital image correlation (3D-DIC) system with the high-speed (HS) photography and ABAQUS finite element software. The research results showed that at the same impact velocity, the 30°, 45° and 60° beddings played an obvious deflexion effect on the shale crack propagation. However, the 0° and 90° bedding did not deflect the crack propagation. The dynamic fracture toughness of shale NSCB specimens increased with the increase of impact loading rate but the increase magnitude decreased with the higher impact rate. The kinetic energy during specimen fracture was calculated by the extracting displacement data from the 3D-DIC, and it was found that the kinetic energy accounted for less than 6% of the absorbed energy during the dynamic compression of the shale. The crack propagation characteristics of ABAQUS simulation was approximately consistent with the experimental results. It is conducive to the study of shale gas fracturing and the formation of complex seam networks in shale and it is of great research significance for the efficient extraction of shale gas.

Fracture behavior of sandstone with partial filling flaw under mixed-mode loading: Three-point bending tests and discrete element method (DEM) numerical approach

The fracture behavior of natural fracture in the geological reservoir subjected to filling property, affects the crack initiation and propagation under stress perturbation. Partial filling flaws were intermediate between open fractures and filled fractures, the fracture response may be worth exploring. In this work, the effect of the filling property of sandstone with partial filling flaws on the fracture behavior was systematically investigated based on three-point bending tests and the numerical approach of discrete element method (DEM). In the laboratory, semi-circular three-point bending tests were carried out with partial filling flaws of various filling strengths. Based on this, numerical simulations were used to further investigate the effect of the filling ratio and the inclination of the partial filling flaw on the mechanical and fracture responses, and the effect of the partial filling flaw under mixed-mode loading on the fracture mechanism was elucidated coupled with acoustic emission (AE) characteristics. The obtained results showed that the increase in filling strength and filling ratio of partial filling flaw led to an increase in peak strength, with a decreasing trend in peak strength with the inclination of partial filling flaw. In terms of crack propagation pattern, the increasing filling strength of the partial filling flaw induced the transformation of the fracture mechanism toward deflection, with a tortuosity path, while the filling ratio and inclination of partial filling flaw led to fracture mechanism change from deflection to penetration and attraction, accompanied with a larger AE event source in filler. Accordingly, the b-value based on the Gutenberg-Richter equation fluctuated between 5 and 4 at low filling ratio and inclination and remained around 5 at high filling ratio and inclination of partial filling flaw. Related results may provide an application prospective for reservoir stimulation using the natural fracture system.

Determination of the influence of particle spatial distribution and interface heterogeneity on tensile fracture of ordinary refractory ceramics by applying discrete element modelling

The microstructures and local characteristics of ordinary refractory ceramics are heterogeneous. The discrete element (DE) method was used to consider the variation in particle spatial distributions and statistically distributed interface properties (uniform, Weibull) between elements. In addition, three Weibull distributions with different shape parameters were evaluated. A uniaxial tensile test was used to study the effects of particle spatial distributions and interface property distributions on the stress–strain curve, tensile strength, and crack propagation. The results of the test show that the particle spatial distribution significantly influences crack propagation and fracture patterns, and the interface condition plays an important role in mechanical responses, crack propagation, and fracture mechanisms and patterns. The discrete element modelling of uniaxial tensile and compressive tests shows that brittle materials exhibit asymmetric mechanical responses to compression and tension loading including static Young’s modulus.

Fatigue performance of carbon fiber‐reinforced polymer strengthened single‐edge cracked steel plates: Effects of adhesive property and CFRP arrangement

AbstractCarbon fiber‐reinforced polymer (CFRP) is increasingly used to improve the fatigue behavior of damaged steel structures due to its advantages, including high strength and convenient processing. However, several issues, such as the effects of the adhesive property and CFRP arrangement, still need to be studied. In this study, a total of 20 single‐cracked steel specimens were tested under fatigue load, including two unstrengthened specimens, six single‐sided strengthened specimens, and 12 double‐sided strengthened specimens. The failure mode, fatigue life, crack propagation pattern, and interface damage development were obtained from experiments. The results show that epoxy resin structural adhesives (adhesives Araldite 420 and J133C) have the best bonding properties with CFRP. For the conventional epoxy adhesives, Araldite 420 and J133C can considerably improve fatigue life, which increased by more than 44.84 times to unstrengthened specimens. CFRP plate strengthening can significantly improve the fatigue life of single‐edge cracked steel plates. For the double‐sided strengthened specimens, the fatigue life can be improved by 6.93–44.84 times that of unstrengthened specimens. For the single‐sided, the fatigue life can be improved by 2.24–2.77 times. Properties of epoxy adhesive have a more significant effect on fatigue life compared to the thickness of the CFRP plate due to debonding.Highlights Ductile epoxy adhesives are most conducive to improving the fatigue behavior of CFRP strengthened steel plates. The fatigue life of steel plates can be improved by increasing the thickness of CFRP plates and using double‐sided CFRP strengthening. Interface debonding is the main failure mode of CFRP plates strengthening single‐edge cracked steel plates under fatigue.

XFEM-Based Study of Fatigue Crack Propagation in Rocket Deflector Troughs under Coupled High-Temperature and Impact Conditions

This research investigated fatigue crack propagation on the lower surface of rocket deflector troughs in offshore rocket launch platforms. Initially, a numerical model of an offshore rocket launch platform was established using ABAQUS based on the Extended Finite Element Method (XFEM). Subsequently, two variable parameters—the initial crack length and initial tilt angle—were introduced. This research systematically analysed the impact of these parameters on the fatigue crack propagation patterns in both the maximum stress and maximum deformation regions of the deflector channels under the combined conditions of high temperature and impact. Finally, the research indicated that the propagation length of surface cracks in the deflector trough exhibited an initial increase followed by a decrease with the rise in the pre-set inclination angle. Notably, the stable propagation rate of the crack in the region of maximum deformation surpassed that observed in the region of maximum stress. Through meticulous comparative analysis, it was evident that temperature loading significantly exacerbated the initiation and propagation of cracks, particularly in the upper region of the deflector channel’s lower surface.

Integrating Image Processing and Machine Learning for the Non-Destructive Assessment of RC Beams Damage

Non-destructive testing (NDT) is a crucial method for detecting damages in concrete structures. Structural damage can lead to functional changes, necessitating a range of damage detection techniques. Non-destructive methods enable the pinpointing of the location of the damage without causing harm to the structure, thus saving both time and money. Damaged structures exhibit alterations in their static and dynamic properties, primarily stemming from a reduction in stiffness. Monitoring these changes allows for the determination of the failure location and severity, facilitating timely repairs and reinforcement before further deterioration occurs. A systematic approach to damage detection and assessment is pivotal for fortifying structures and preventing structural collapse, which can result in both financial and human losses. In this study, we employ image processing to categorize damaged beams based on their crack growth and propagation patterns. We also utilize support vector machine (SVM) and k-nearest neighbor (KNN) methods to detect the type, location, and extent of failures in reinforced concrete beams. To provide context and relevance for the laboratory specimens, we will compare our findings to the results from controlled experiments in a controlled laboratory setting.

Numerical Simulation of Crack Propagation and Branching Behaviors in Heterogeneous Rock-like Materials

The characterization and understanding of crack evolution in non-uniform geological structures are crucial for predicting the mechanical response of rock-like materials or structures under varying loading conditions. In this study, an improved Peridynamic model with a degree of heterogeneity characterized by random pre-breaking “bonds” coefficients is introduced to capture the intricacies of crack initiation, propagation, and branching behaviors in heterogeneous rock-like materials. MATLAB discrete programs for heterogeneous material models and PD simulation programs based on the FORTRAN language were developed. The effectiveness of the heterogeneous PD model in simulating crack propagation and branching patterns in heterogeneous materials has been verified through dynamic and static (quasi-static) loading cases with pre-notch. The different levels of heterogeneity not only affect the direction of crack propagation but also determine the crack deflection direction and branching patterns. The crack propagation path appears to possess obvious asymmetry in the crack propagation direction. As the load applied continues to increase, the asymmetric multi-crack branching phenomenon will occur. The higher the level of heterogeneity, the more complex the behaviors of crack propagation and branching become. This research provides valuable insights into the interplay of material heterogeneity and crack evolution, offering a foundation for improved numerical simulations and contributing to the broader field of geomechanics.

Phase-field modeling of anisotropic crack propagation based on higher-order nonlocal operator theory

This paper presents a novel higher-order nonlocal operator theory for the phase-field modeling of brittle fracture in anisotropic materials. Incorporating higher order nonlocal operators can enhance the accuracy of the phase-field model by effectively capturing long-range interactions that hold significance in numerous materials. The reproducing kernel particle method is employed to derive a nonlocal differential operator to enhance computational stability and accuracy. Moreover, the proposed method eliminates the need for direct computation of derivatives of the modified kernel function, which avoids the calculation of moment matrix derivatives and improves computational efficiency. The phase-field modeling of polycrystalline materials, considering the anisotropic fracture resistance of each grain, is implemented using this numerical framework. The present method is able to capture different scenarios intergranular and transgranular crack propagation patterns in polycrystalline materials. The proposed method involves a detailed representation of the complex process of crack initiation and propagation in 2D and 3D models of polycrystalline materials.

Fatigue tests of multiplanar concrete-filled steel tubular KK-joints with inner ring stiffeners

Wind turbine structures are subjected to prolonged cyclic loading, with fatigue issues being particularly prominent. This study aims to investigate the fatigue performance of multiplanar concrete-filled steel tubular (CFST) KK-joints with inner ring stiffeners. Fatigue tests were conducted on these joints, and comparison specimens were designed, including one with a circular hollow section (CHS) tubular joint and another with a CFST joint. The results indicated that the incorporation of inner concrete and ring stiffeners led to a significant reduction in the hot spot stress within tubular joints. The maximum hot spot stress concentration factor (hot-spot SCF) of CFST KK-joints with inner ring stiffeners decreased by 39.7% compared to CHS KK-joints and by 8.7% compared to CFST KK-joints. Furthermore, an increase in the brace thickness-to-chord thickness ratio τ from 0.94 to 1.24 for CFST KK-joints with inner ring stiffeners resulted in a corresponding 74.3% increase in hot-spot SCF. Additionally, fatigue tests were conducted to ascertain the failure modes, crack propagation patterns, and fatigue lives of specimens. These measured fatigue lives were compared with the S–N curves given by different codes. Notably, it was observed that the curve proposed by DNV/CCS exhibited the most suitable correlation with the experimental results.

A combined interface phase field (CIPF) model for interfacial crack propagation

The phase field method has been very popular in the past decade because it can handle complex crack propagation problems without ad hoc criteria. In this paper, a combined interface phase field (CIPF) model is proposed to better investigate the fracture behaviours of composite systems with a finite-thickness interface. To build the CIPF model, a new numerical method named the modified crack surface displacement extrapolation (MCSDE) method is proposed to determine the real interfacial fracture toughness. Then, an effective interfacial fracture toughness is given based on the coupling relationship between the length scale parameter and the interface thickness. We investigate crack propagation behaviours in bi-material structures with varied initial notch positions and sandwich specimens using the CIPF model. The results show that the MCSDE method can effectively and accurately determine the interface fracture toughness, and the difference between the calculated results and the results obtained by the sing-leg bending (SLB) experiment is 6%. The CIPF model can not only simulate the propagation of cracks in bulk, but also simulate the propagation of cracks between interfaces. For different positions of the initial notch, the propagation patterns of cracks and the mechanical response of the structure are very different.

Flexural performance of 3D printed concrete structure with lattice infills

Large-scale 3D printed concrete structures with lattice infill will result in lightweight components with high mass-specific strength, and faster fabrication, compared to conventional casting methods. However, the effect of different infill patterns on mechanical performance is still not addressed clearly in many scientific publications. This study investigates the bending performance of 3D-printed concrete beams with four infill patterns such as lattice, triangular, lattice-triangular, and sinusoidal tested in vertical (layer deposition direction) and transverse (layer translation direction) loading directions. The load versus displacement curves and crack propagation patterns are investigated both via Finite Element (FE) simulations and experiments. The FE results corroborated by experiments indicated that the triangular patterns perform better than lattice-shaped infill counterparts particularly under the transverse loading direction exhibiting the highest flexural deformation resistance capacity. The findings of this study would be useful in latticing large-scale concrete structures for diverse applications.

Modeling on the effect of automated fiber placement induced gaps in curved composite laminates

Automated placement technology has been widely used due to its excellent processing adaptability for large composite components with complex geometric structures. Whereas, it still poses challenges to study the effect of manufactured gaps induced by automated placement on curved composite parts. This study proposes a new geometric reconstruction approach based on consolidation and sweeping formation to model manufactured gaps. Additionally, a mechanical model incorporating the reconstructed geometry and the cohesive layer method is established to predict the physical behaviors of curved laminates. The micrograph of automated placement-induced gaps with 90° orientation was used to verify the rationality of the geometric reconstruction approach of gaps forming in the preparation process of composite materials. According to predictions of the proposed mechanical model, the effect of − 45° oriented gap defects on curved laminates was validated via four-point bending tests that confirmed alignment between predictions and experimental results for peak load, crack propagation, and failure patterns. Experimental results show that due to the differences in spatial local geometric features, orientations of gap defects would reduce the bending strength to different degrees and significantly affect the failure pattern of curved laminates. Furthermore, curved laminates with wider gaps experience a more considerable reduction in load-bearing capacity.

Experimental study on crack propagation pattern and fracture process zone evolution based on far-field displacement by using DIC

This study utilizes digital image correlation (DIC) technology to measure the far-field displacements and strains of rock specimens during the entire loading and unloading. Through analyzing the distributions of strain, displacement and their variations per unit length at different stages, the variations of both length and migration velocity of the fracture process zone (FPZ) were studied, and the crack propagation was also investigated. In addition, the entire path of crack propagation was observed by scanning electron microscope (SEM). The results reveal that (1) the fractured ligament can be divided into three zones based on the displacement variation per unit length: intact zone, crack propagation zone, and FPZ. (2) The FPZ length reaches its maximum at the peak load and then decreases, and the minimum length even is only 1/3–1/2 of the maximum length. The FPZ migration velocity is − 48 to 1460 m/s. FPZ’s microscale features are intergranular microcracks, transgranular microcracks, cleavage, and debris on fracture surface and around main crack propagation path. (3) The crack propagation length during peak load to peak-post 90% accounts for more than 1/3–1/4 of the entire post-peak length. Crack propagation is alternating fast and slow, i.e., the velocity of crack propagation varies regularly in the range of 24–700 m/s. The region of crack initial propagation is more severely damaged compared to other propagation regions.

Finite element analysis of bird impact with windshield of a vehicle

The car's windscreen, which birds frequently come into contact when driving, determined to be one of the primary causes of severe bird as well as passengers, injuries. For the design and assessment of vehicle safety performance, finite element-based analysis of object strike to the windshield is commonly employed. The majority of the simpler windshield models utilized in simulations for various object strike research. However, for a reliable prediction of injuries during a car to bird accident, accurate modelling of the windshield and different glass materials considered as mechanical behaviour is required. The goal of this article is to look into potential windshield replacement options that simulate a collision between a bird and a car. Different materials' laminated glass windshields put to the test. The finite element simulation model's stress and crack patterns recorded, and they verified against actual work or common car windshield glass. The three-layer laminated glass finite element models created. For the crack propagation pattern, the element deletion method and share node techniques used. The assessment and simulation findings compared using fine mesh sizes based on the four different glass material qualities and a chosen alternative glass material, as well as existing research on ball drop testing for pedestrian head injuries. The simulated results of the laminated model of annealed glass of three layers and a 5 mm rectangular mesh demonstrate good agreement with the results of the experiments and previous simulations using finite elements. Next, the car's windshield was fitted with this model of annealed glass. In accordance with the EEVC protocol on pedestrian protection, impact testing simulating bird strikes conducted. When results for bird deceleration, fracture pattern, and windshield energy absorption compared to test results for pedestrian head injury, a good agreement shown.

Two-Way Slab Punching Shear Resistance: Experimental Insights into Basalt-FRP Bar as Flexural Reinforcement

This study seeks to experimentally evaluate the punching shear performance of two-way concrete slabs reinforced with conventional steel and basalt fiber-reinforced polymer (basalt-FRP) bars subjected to punching loading condition. Basalt-FRP bars offer high tensile strength and corrosion resistance but are understudied in two-way concrete slabs concerning punching shear. This study aims to fill this gap, with key implications for future structural design considerations. To achieve the objectives of the study, six large-scale square slabs were fabricated and subjected to a concentric load until failure. The parameters of the experiment included are the type of reinforcement used (either basalt-FRP or steel), the percentage of basalt-FRP used (ranging from 0.88% to 1.77%), the size of the basalt-FRP bars used (either 16 or 12 mm), and the concrete’s compressive strength (25, 30, and 35 MPa). The findings from the tests showed that incorporating basalt-FRP bars with one-quarter equivalent axial stiffness (ρ(Ef/Es)) to that of steel significantly enhanced the punching shear resistance of flat slabs, achieving approximately 65% of the capacity observed in steel-reinforced control sample. Moreover, increasing the amount of basalt-FRP bar reinforcement to half of the equivalent axial stiffness of steel had a substantial effect in improving shear strength, reaching approximately 89% of the capacity observed in the steel-reinforced specimen and concurrently reducing deflection during the failure. Additionally, the reinforcement type and concrete compressive strength played a crucial role in determining the ultimate load, failure modes, and crack propagation patterns. The study reveals discrepancies between experimental results and existing models for punching shear in FRP-reinforced slabs. Certain prevalent models prove to be conservative in their estimates, while others offer more accurate predictions, indicating the need for comprehensive model refinement. The investigation found that one model, encompassing the majority of variables affecting punching shear, exhibited the highest level of precision, with a slight adjustment recommended to enhance its accuracy further. This study suggests a sustainable, more durable way to reinforce concrete in bridges and high-rise buildings, potentially improving construction efficiency, enhanced service life, and potential updates to building codes.

Cracking Behavior and Stress Field Evolution in Coal Specimens Containing Bedding under Uniaxial Compression.

During the underground mining process, various coal seams with different bedding structures are often encountered. The presence of bedding structures is one of the primary factors that influence the strength and deformation characteristics of the coal seam and then affect gas extraction and gas disaster prevention. However, there is still a lack of mechanical properties of coal rock with structural anisotropy influenced by bedding structures. In this study, numerical models were established by using the particle flow code method to simulate coal specimens containing bedding with varying inclination angles. The results demonstrate the impact of the bedding inclination angle on the mechanical properties, crack propagation patterns, and the temporal and spatial evolution of the stress field in coal specimens with bedding during the loading process. Furthermore, three crack initiation patterns were investigated for coal specimens with different bedding angles. Additionally, the quantitative relationship between the mechanical properties and the fractal dimension was analyzed. The numerical simulation results were effectively validated through laboratory tests.

Effects of Damage Mode on Crack Propagation Pattern in Additively Manufactured Honeycomb Cellular Panel

Effects of Damage Mode on Crack Propagation Pattern in Additively Manufactured Honeycomb Cellular Panel

Microstructural fatigue fracture behavior of glycated cortical bone.

The current study aims to simulate fatigue microdamage accumulation in glycated cortical bone with increased advanced glycation end-products (AGEs) using a phase field fatigue framework. We link the material degradation in the fracture toughness of cortical bone to the high levels of AGEs in this tissue. We simulate fatigue fracture in 2D models of cortical bone microstructure extracted from human tibias. The results present that the mismatch between the critical energy release rate of microstructural features (e.g., osteons and interstitial tissue) can alter crack initiation and propagation patterns. Moreover, the high AGEs content through the increased mismatch ratio can cause the activation or deactivation of bone toughening mechanisms under cyclic loading. The fatigue fracture simulations also show that the lifetime of diabetic cortical bone samples can be dependent on the geometry of microstructural features and the mismatch ratio between the features. Additionally, the results indicate that the trapped cracks in cement lines in the diabetic cortical microstructure can prevent further crack growth under cyclic loading. The present findings show that alterations in the materials heterogeneity of microstructural features can change the fatigue fracture response, lifetime, and fragility of cortical bone with high AGEs contents. Cortical bone models are created from microscopy images taken from the cortical cross-section of human tibias. Increased glycation contents in the cortical bone sample can change the crack growth trajectories.

Estimation of multiple crack propagation pattern in concrete using Voronoi tessellation method

Estimation of multiple crack propagation pattern in concrete using Voronoi tessellation method