Crack Propagation Research Articles

A simplified method for predicting overflow-induced crack propagation in gravity dams using genetic algorithm and material-based model

Cracks are always a serious concern in the stability analysis of gravity dams. One of the main reasons for the initiation of cracks is overflows. In evaluating dam safety under flood conditions, it is crucial to consider the balance between the strength of the dam body and the propagation of cracks. In this context, simplified equations serve as valuable tools in dam design as they offer a quick and efficient way to estimate the behavior of the dam structure. In this study, firstly using a polygonal material-based model (P-MBM), which is improved in considering the softening behavior of joints, the micro-crack propagation in masonry material is investigated. Then, based on performing 81 numerical simulations in a parametric study on the geometrical and geotechnical properties of the dam subjected to overflow, a great database of the behavior of different dams is investigated. Then, using the genetic algorithm, a set of equations is proposed, and their accuracy is validated through UDEC simulations and some theoretical methods from existing literature. For all models, the crack tends to be horizontal at the initial phase. Then, due to increasing the compressive stresses on the downstream side, the fractures tend to the dam toe. The results also indicate that the proposed equations can reasonably determine the behavior of gravity dams and the development of cracks in the dam body. The outcomes highlighted the considerable effects of geometry and geotechnical properties on dictating the trajectory of crack growth.

Study on the mesoscopic mechanical behavior and damage constitutive model of micro-steel fiber reinforced recycled aggregate concrete

This study employs in-situ 4D CT experimental techniques to investigate the mesostructured changes and mechanical behavior of micro steel fiber-reinforced recycled aggregate concrete (MSF-RAC) under uniaxial compression and cyclic loading conditions. The research aims to address the scientific problem of limited understanding of how micro steel fibers affect the mesoscopic mechanical behavior and structural damage characteristics of recycled aggregate concrete. High-resolution CT scanning technology was utilized for real-time observation of crack initiation and propagation, revealing the micro-mechanisms by which micro steel fibers enhance RAC. The study found that incorporating micro-steel fibers significantly improves the density of the interfacial transition zone (ITZ), inhibits crack development, and enhances the mechanical properties of the concrete. Based on these observations, an improved stiffness degradation damage constitutive model was proposed, which comprehensively considers the distribution orientation of micro steel fibers and ITZ characteristics. The model effectively predicts the stress-strain relationship of MSF-RAC under various conditions, demonstrating high accuracy and practicality. These findings provide important theoretical support and experimental evidence for the optimal design of RAC, showcasing significant engineering application value by promoting the sustainable use of recycled materials in construction.

Linear fractal evolution characteristics of rock crack distributions during loading process

To investigate the fractal characteristics of rock crack distributions during the loading process, discrete element method was used to make rock samples with joints and record the crack propagation. The Box-counting method was used to quantitatively analyze the fractal dimension of the crack distribution at each moment, and the relationship between the crack fractal dimension and strain ratio was established based on fractal theory. The results indicated that the relationship between the fractal dimension of the crack distribution and strain ratio showed a strong linear characteristic. By transforming this linear relationship into a linear function, the slope of the function was found to be linked to the failure patterns of the sample, and a refinement coefficient (damage-fracture reduction factor) was identified from the slope as an effective basis for determining the degree of sample damage and fracture. The damage-fracture reduction factor can be categorized: 0.25–0.5 (spilt and fracture), 0.5–0.9 (synergy between fracture and damage), 0.9–1 (microcrack asymptotic damage). Owing to the linear fractal characteristics, an expression for the damage variables influenced by failure patterns can be established from the geometric aspect. In addition, the linear fractal characteristics of the cracks were verified in other acoustic emission and crack extension experiments.

Research on mechanical properties of steel-polypropylene fiber concrete and application of beam structure

Concrete faces the difficulties of low tensile strength and poor crack resistance in building structures. In order to remedy this deficiency. In this paper, steel-polypropylene hybrid fiber reinforced concrete (SPFRC) was prepared by adding steel fiber (SF) and three kinds of polypropylene fiber (PF) to C50-grade concrete. The mechanical properties and microstructure of SPFRC were studied with different fiber combinations and content, obtaining the best hybrid combination. Based on this, the bending resistance and cracking of SPFRC beam members were investigated. The results demonstrate that the addition of fiber improves the compressive strength of ordinary concrete by 0.16% ∼ 17.69%, the splitting tensile strength by 15.18% ∼ 47.45%, and the bending strength by 3.54% ∼ 26.77%. Compared with single-fiber concrete, the hybrid fiber can achieve better internal microstructure, which further enhances the mechanical properties of the material. Hybrid fibers overlap within concrete beams, effectively redistributing stress and inhibiting the formation and propagation of cracks. For the three types of SPFRC beams, the cracking load is increased by 14.29% ∼ 28.57% compared with PC beam, the ultimate bearing capacity is increased by 9.68% ∼ 19.35%. The optimal dosage is determined as 1.0% SF, 0.6% Embossed polypropylene fiber (PBF). It provides reference for the application of SPFRC in flexural members.

Enhancing thixotropic properties of epoxy resin and mechanical properties of epoxy resin thermosets by polyethyleneimine functionalized carbon nanotubes

Epoxy resin (ER) thermosets are widely applied in various fields due to their high mechanical strength, thermal stability and chemical corrosion resistance. However, the brittleness of ER thermosets and low thixotropic property of ER matrix largely limits their further development. Here, this article develops branched polyethyleneimine (PEI) functionalized carbon nanotube (PEI@CNT) as high-performance nanofiller for simultaneously strengthening and toughening ER thermosets. Benefiting from good dispersity and rich amine groups of PEI@CNT, effective interfacial bonding between PEI@CNT and ER is achieved. The ER thermoset with 0.5 wt% PEI@CNT shows increase in tensile strength by 24.8 % and fracture elongation by 30.0 % compared with pristine ER thermoset. The enhanced mechanical properties of PEI@CNT modified ER thermosets can be ascribed to the chemical interaction between PEI@CNT and ER matrix as well as the formed crack propagation, which can dissipate a lot of fracture energy, further improving the strength and toughness of the ER composites. More importantly, the thixotropic property of ER matrix is largely improved after adding the PEI@CNT filler. This work reports a high-performance nanofiller for enhancing mechanical properties of ER thermosets and processability of ER matrix.

Analysis of Fracturing Expansion Law of Shale Reservoir by Supercritical CO2 Fracturing and Mechanism Revealing

The rapid expansion of reservoir fractures and the enlargement of the area affected by working fluids can be accomplished solely through fracturing operations of oilfield working fluids in geological reservoirs. Supercritical CO2 is regarded as an ideal medium for shale reservoir fracturing owing to the inherent advantages of environmental friendliness, excellent capacity, and high stability. However, CO2 gas channeling and complex propagation of fractures in shale reservoirs hindered the commercialization of Supercritical CO2 fracturing technology. Herein, a simulation method for Supercritical CO2 fracturing based on cohesive force units is proposed to investigate the crack propagation behavior of CO2 fracturing technology under different construction parameters. Furthermore, the shale fracture propagation mechanism of Supercritical CO2 fracturing fluid is elucidated. The results indicated that the propagation ability of reservoir fractures and Mises stress are influenced by the fracturing fluid viscosity, fracturing azimuth angle, and reservoir conditions (temperature and pressure). An azimuth angle of 30° can achieve a maximum Mises stress of 3.213 × 107 Pa and a crack width of 1.669 × 10−2 m. However, an apparent viscosity of 14 × 10−6 Pa·s results in a crack width of only 2.227 × 10−2 m and a maximum Mises stress of 4.459 × 107 Pa. Additionally, a weaker fracture propagation ability and reduced Mises stress are exhibited at the fracturing fluid injection rate. As a straightforward model to synergistically investigate the fracture propagation behavior of shale reservoirs, this work provides new insights and strategies for the efficient extraction of shale reservoirs.

A computational approach for phase-field model of quasi-brittle fracture under dynamic loading

AbstractA computational model is formulated for studying dynamic crack propagation in quasi-brittle materials exposed to time-dependent loading conditions. Under such conditions, inertial effects of structural components play an important role in modelling crack propagation problems. The computational model is proposed within the theory of regularised cracks which uses a damage-like internal variable. Here, fracture considers phase-field damage which gives rise to a material degradation in a narrow material strip defining the regularised crack. Based on the energy formulation using the Lagrangian of the system, the proposed computational approach introduces a staggered scheme adopted to solve the coupled system and providing it in a variational form within the time stepping procedure. The numerical data are obtained by quadratic programming algorithms implemented together with a finite element code.

Application of time-temperature superposition principle for cracking characterization of asphalt mixtures using semi-circular bend test

In recent decades, numerous laboratory tests have been developed to characterize the cracking performance of asphalt mixtures. Among these, the semi-circular bend (SCB)-based Illinois flexibility index test (I-FIT) (AASHTO T 393) has emerged as a favored method due to its straightforward specimen preparation and better sensitivity to mixture variables. However, the cracking susceptibility of asphalt mixtures is significantly influenced by temperature and loading rate, leading to a discrepancy in performance between standard test conditions and real-world scenarios. To address this challenge, this study explores the applicability of the time-temperature superposition principle (TTSP) for the SCB test. The study evaluates four mixtures incorporating reclaimed asphalt pavement (RAP) and/or reclaimed asphalt shingles (RAS) across various loading rates and temperature combinations. Findings suggest that TTSP can be applied to the SCB test without significantly impacting cracking performance indices such as flexibility index and post-peak slope. Furthermore, the study also demonstrates that TTSP can be applied in the crack propagation phase during the post-peak domain of the mixtures. The findings of the study will allow laboratories to develop more flexible testing plans without compromising the accuracy and reliability of performance parameters by adjusting the loading rate corresponding to the test temperature and vice versa. Consequently, this approach can potentially make a balanced mix design (BMD) practice more implementable.

Restoration of Strength in Polyamide Woven Glass Fiber Organosheets by Hot Pressing: Case Study of Impact and Compression after Impact

Thermoplastic composite organosheets (OSs) are increasingly recognized as a viable solution for automotive and aerospace structures, offering a range of benefits including cost-effectiveness through high-rate production, lightweight design, impact resistance, formability, and recyclability. This study examines the impact response, post-impact strength evaluation, and hot-pressing repair effectiveness of woven glass fiber nylon composite OSs across varying impact energy levels. Experimental investigations involved subjecting composite specimens to impact at varying energy levels using a drop-tower test rig, followed by compression-after-impact (CAI) tests. The results underscore the exceptional damage tolerance and improved residual compressive strength of the OSs compared to traditional thermoset composites. This enhancement was primarily attributed to the matrix’s ductility, which mitigated transverse crack propagation and significantly increased the amount of absorbed energy. To mitigate impact-induced damage, a localized hot-pressing repair approach was developed. This allowed to restore the post-impact strength of the OSs to pristine levels for impact energies below 40 J and by 83.6% for higher impact energies, when OS perforation was observed. The measured levels of post-repair strength demonstrate a successful restoration of OS strength over a wide range of impact energies, and despite limitations in achieving complete strength recovery above 40 J, hot-pressing repair emerges as a promising strategy for ensuring the longevity of thermoplastic composites through repairability.

Monitoring damage evolution of SiCf/PyC/SiC mini-composites using electrical resistivity: Crack opening distance and interphase retention rate based electromechanical modeling

Electrical resistance is closely related to the damage of ceramic matrix composites (CMC) such as matrix crack, crack opening distance (COD), and interphase retention rate, giving it the potential to become a new non-destructive testing (NDT) technique. An electro-mechanical experiment method was designed for the tensile test of ceramic matrix mini-composites (CMMC). An optical in-situ tensile test was performed to obtain the pattern of matrix crack propagation. The result confirms that matrix crack saturation may not occur before the material fractures. An electromechanical model considering the COD was established to identify the damage situations. A new method for preparing ceramic matrix micro-composites composed of a single fiber and a single-layer pyrolytic carbon (PyC) interphase was realized. The accurate in-situ resistivity of the PyC was measured based on the micro-composites.

Entropy‐based method considering nonlinear hardening effect to predict the crack propagation life of superalloy GH4169 at elevated temperature

AbstractThis paper aims to determine the relationship between thermodynamic entropy generation and fatigue crack propagation life of superalloy GH4169 at 300–650°C. The entire specimen was considered as the thermodynamic system. The plastic energy dissipation in the crack tip was obtained by finite element simulation utilizing the Chaboche nonlinear hardening model. Then the cyclic entropy generation rate (CEGR) and the accumulated entropy generation are calculated by combining simulation and experimental methods. Results show that the CEGR is a power function of the stress intensity factor range, and it is almost a constant at fatigue failure. The fatigue fracture entropy (FFE) increases as fatigue cycles at failure increase at constant temperature, but it first decreases and then increases when temperature increases from 300 to 650°C. A fatigue life prediction model based on the thermodynamic damage parameter is established and verified by comparison with experimental results and available data in the literature.

Study of Prefabricated Crack Propagation on Monocrystalline Silicon Surfaces for Grinding Damage Analysis

Crack generation and propagation are critical aspects of grinding processes for hard and brittle materials. Despite extensive research, the impact of residual cracks from coarse grinding on the cracks generated during fine grinding remains unexplored. This study aims to bridge this gap by examining the propagation law of existing cracks under indentation using the extended finite element method. The results reveal that prefabricated cracks with depths less than the crack depth produced on an undamaged surface tend to extend further without surpassing the latter. Conversely, deeper prefabricated cracks do not exhibit significant expansion. A novel method combining indentation and prefabricated cracks with fracture strength tests is proposed to determine crack propagation. Silicon wafers with varying damaged surfaces are analyzed, and changes in fracture strength, measured by the ball-on-ring method, are utilized to determine crack propagation. The experimental results confirm the proposed crack evolution law, validated by damage assessments across different grinding processes, which is suitable for crack damage. The findings demonstrate that residual cracks from coarse grinding are negligible in predicting the maximum crack depth during fine grinding. This research provides a crucial foundation for optimizing the wafer thinning process in 3D stacked chip manufacturing, establishing that changes in fracture strength are a reliable indicator of crack propagation feasibility.

A length-free phase field model for epoxy adhesive materials based on modified Drucker–Prager criterion

Characterizing the cracking behavior of epoxy adhesive material is of great importance for composite structures. Recently, the phase field model has emerged as the preferred method for predicting the crack propagation. This paper presents a length-free phase field model considering the characteristics of epoxy adhesive materials. The proposed model is formulated within a framework that decomposes the phase field fracture driving force, ensuring that it adequately considers the tension/compression asymmetry of the epoxy adhesive materials. The effects of hydrostatic pressure, deviational stress, and friction are incorporated into the model by employing a modified Drucker-Prager failure criterion. The failure criterion is included in the phase field model using the effective stress invariants. Furthermore, the internal length scale, previously considered to lack real physical meaning, is reformulated based on material strength. This model addresses the challenge of measuring the internal length of epoxy materials. It serves as a valuable reference for applying phase field models to epoxy materials. The accuracy of the model is validated through an L-shaped plate simulation, and an attempt using the model to predict the crack development in thick epoxy adhesive joints is undertaken. Several representative samples are simulated, including three double cantilever beams with different configurations. The numerical results demonstrate a good correlation with experimental data, highlighting the potential of the model in simulating the crack propagation in epoxy adhesive joints.

Influence of confining pressure on rock fracture propagation under particle impact

Revealing the influence of confining pressure on the propagation and formation mechanism of rock cracks under particle impact is significant to deep rock excavation. In this study, the three-dimensional fracture reconstruction of the rock after particle impact was carried out by CT scanning, and the stress and crack field evolution of the rock under particle impact were analyzed by PFC2D discrete element numerical simulation. The results demonstrate that after particles impact, a fracture zone and intergranular main crack propagation zone are formed in the rock. The shear stress and tensile stress caused by compressive stress are the main reasons for the formation of the fracture zone, while the formation of the intergranular main crack propagation zone is mainly due to tangential derived tensile stress. The confining pressure induces prestress between rock particles such that the derived tensile stress needs to overcome the initial compressive stress between the particles to form tensile fractures. And the increase in the confining pressure leads to increases in the proportion of shear cracks and friction effects between rock particles, resulting in an increase in energy consumption for the same number of cracks. From a macroscopic perspective, the confining pressure can effectively inhibit the generation of cracks.

X-IGA Used for Orthotropic Material Crack Growth

In this paper, we propose a new approach for numerically simulating the growth of cracks in unidirectional composite materials, termed extended isogeometric analysis, evaluating the maximum stress intensity factor and T-stress. To validate our approach, we used a small anisotropic plate with two edge cracks, beginning with formulating the governing equations based on the energy integral method, Stroh’s Formula, and the Elastic Law describing the behaviour of anisotropic materials, while considering boundary conditions and initial states. A MATLAB code was developed to solve these equations numerically and to post-process the tensile stress and the stress intensity factor (SIF) in the first mode. The results for the SIF closely match those obtained using the extended finite element method (X-FEM), with a discrepancy of only 0.0021 Pa·m0.5. This finding underscores the credibility of our approach. The extended finite element method has demonstrated robustness in predicting crack propagation in composite materials in recent years, leading to its adoption by several widely used software packages in various industries.

On the anisotropic fracture behaviour of AA2050-T84 thick plate

Anisotropy in the fracture behaviour of AA2050-T84 was investigated using 2D digital image correlation (DIC)-assisted 3-point bending fracture toughness test on specimens with crack propagation direction oriented along the normal direction (ND) and rolling direction (RD). The tensile properties along the RD indicated slightly higher yield strength (482 ± 8 MPa) than ND sample (469 ± 9 MPa), while the fracture toughness in terms of energy release rate was higher when the notch was oriented along the ND (35.3 ± 1 kJ/m2) compared to the RD (18.5 ± 0.9 kJ/m2). Fractography of the fractured surfaces and detailed electron backscatter diffraction (EBSD) analysis of the microstructure along crack paths unveiled higher crack tortuosity with extensive secondary cracking in the TD-ND specimen than in the TD-RD. DIC measurements clearly showed a larger deformation zone for the TD-ND specimen also as which corroborated the plastic zone size determined using linear elastic fracture mechanics (LEFM). Additionally, the crystallographic model of tilt and twist angle differences between the neighbouring grains was employed to explain the increase in crack path tortuosity and higher dissipation of plastic work contributing to superior fracture toughness for the TD-ND sample.

The correlation between material deformed microstructure and rolling contact fatigue crack propagation of U71Mn rail when matching with CL60 wheel

Deformed microstructure and rolling contact fatigue (RCF) cracks are the two predominant damage characteristics of the field wheel and rail materials from the cross-sectional view. The proportion of two damage characteristics varied under different operating conditions. Thus, this study aims to investigate the correlation between material deformed microstructure and RCF crack propagation of U71Mn rail when matching with CL60 wheel using a twin-disc testing machine. An initial deformed microstructure layer on U71Mn rail material was first obtained by testing under dry condition, and then the RCF crack propagation tests were conducted under water condition. Results indicated that when the crack depth was smaller than the initial deformed microstructure layer depth, the deformed orientation dominated the crack propagation direction; when the depth of crack propagation towards the matrix exceeded the depth of newly formed deformed microstructure region, crack propagation direction dominated the microstructure deformed orientation. The increase in the initial deformed microstructure layer depth would intensify both the crack length and depth, and also would result in thicker newly formed deformed microstructure region. The Pearson correlation coefficient between initial deformed microstructure layer depth and crack depth was 0.998. The influence of initial deformed microstructure layer depth on wear rate was slightly greater than crack depth.

Study on crack propagation characteristics of rocks with different lateral pressure based on joint monitoring of DIC and AE

During the process of rock failure, the characteristics of crack propagation affect the fracture characteristics and macroscopic mechanical behavior of rocks, indirectly affecting the safety and stability of rock engineering. In order to study the evolution characteristics of cracks during rock failure under different lateral pressure, based on an improved digital image correlation (DIC) and acoustic emission (AE) signal recognition method, a visual biaxial servo loading device was developed to conduct biaxial compression tests on mudstone with prefabricated cracks of the same inclination angle. The research results indicate that the stages of crack propagation include microcracks propagation, crack tip formation, stable macroscopic cracks propagation, and unstable macroscopic cracks propagation. As the lateral pressure increased, the initiation frequency of cracks decreased, the quantity of propagation decreased, and the propagation path shortened, indirectly increasing the bearing strength of rocks. The initiation stress, peak stress, and elastic modulus of pre-cracked rocks with lateral pressure ≤ 2 MPa were lower than those of pre-cracked rocks with lateral pressure > 3 MPa, with the minimum reduction amplitude of 14.1%, 21.2%, and 12.6%, respectively. As the lateral pressure decreased, the dispersion of the AE main frequency distribution increased and accelerated its downward expansion. The surface temperature curves of rocks were prone to fluctuations and rapid upward evolution characteristics corresponding to crack tip formation and crack propagation, respectively. The research results provide theoretical and engineering references for the mining of weak coal seams.

Experimental and meshless numerical simulation on the crack propagation processes of marble SCB specimens

In order to correctly understand the rock multi-fissure interactions and crack propagation laws, three-point bending fracture tests of the marble semi-circular bend samples (SCB samples) are carried out, and the crack propagation processes are simulated by the Smoothed Particle Hydrodynamics (SPH) method. Results show that: Cracks initiate from the guide fissure tip and propagate vertically in the SCB sample with no obstacle fissures; The overlap positions of crack1 and the obstacle fissure are biased towards the lower left end of the obstacle fissure with the increase of the inclination angle α; With the increase of the eccentric distance d, the overlap positions of crack1 and the obstacle fissure are biased towards the upper right end of the obstacle fissure; The peak load of the samples decreases with the increase of inclination angle α, while increases with the increase of eccentric distance d. The “failure coefficient” η is introduced into the conventional SPH momentum equations, which can simulate the multi-fissure propagations of the SCB samples. The simulation results are consistent with the experimental results, and the mechanisms of the crack propagation morphologies between the guide fissure and the obstacle fissure are discussed. The research results can provide some references for correctly understanding the crack propagation mechanisms of multi-fissure rock masses and the applications of the SPH method into simulating rock multi-fissure interactions.

Effects of aggregate's type and orientation on stress concentration and crack propagation of modeled concrete applied a shear force

This study focused on planarizing natural modeled aggregate concrete (NMC), recycled modeled aggregate concrete (RMC), and brick modeled aggregate concrete (BMC) for analyzing the influences of aggregates on shearing failure mechanism. A designed apparatus was used to load a shear force for the specimens and analyzed the global and local strain fields near the interface transition zone (ITZ) using digital image correlation (DIC) analysis. Additionally, we employed COMSOL software simulation to understand the crack initiation process and damage evolution mechanism of related concrete. Our findings revealed that the brick aggregate leaded to the lowest modulus of elasticity and compressive strength, resulting in poor shear resistance. However, the recycled aggregate model exhibited the highest shear resistance, primarily due to the old mortar acting as a buffer layer in the ITZ. During loading, the stress in the NMC model concentrated in the load transfer zone and gradually moved to the left and right sides of the built-in aggregate model until fracture, as observed through DIC analysis. The stress distribution of the RMC was similar with those of the NMC, but the BMC showed a distinct stress distribution pattern. Furthermore, the corner of the built-in modeled aggregate significantly influenced the crack propagating path and stress distribution. Therefore, the modeled aggregate corner plays a crucial role in the shear behavior of concrete, affecting both crack propagation and overall mechanical performance. The practical implications of our study can inform the design and application of recycled concrete.