Crack Propagation Trajectory Research Articles

Biologically inspired adaptive crack network reconstruction based on slime mould algorithm.

The dynamic crack propagation trajectories play a crucial role in enhancing our understanding of spatial mechanisms involved in crack expansion. However, visualization of internal cracks under complex crack conditions has always been a challenge. Biological networks have been honed by many cycles of evolutionary selection pressure and are likely to yield reasonable solutions to such combinatorial optimization problems. This study applied the slime mould algorithm to improve the accuracy of internal crack localization in rocks and employed Minimum spanning tree and Gaussian mixture model to construct the crack propagation trajectories. By introducing the concept of bond length, the evolution characteristics of crack levels were effectively characterized. Research results showed that this approach effectively preserves essential crack localization information while mitigating the influence of interfering parameters, providing crack characterization results that exhibit high consistency with actual fracture patterns. The curves of cumulative bond length and relative bond length over time conform to the trend of a Growth/Sigmoidal curve. The strength of the bond was correlated with the temporal process of crack propagation. This result could be helpful for analyzing crack trajectories and predicting rock stability.

Analysis of tooth root three-dimensional fatigue crack initiation, propagation, and fatigue life for spur gear transmission

The gears in aviation gear systems are susceptible to fatigue fracture due to high-speed, heavy-load, and load alternation operating conditions. Therefore, a numerical calculation model with multiple mesh positions loading form has been proposed in this paper to analyze the fatigue crack initiation and propagation behavior, and to estimate the fatigue life of these gears. The fatigue life of the gear is determined by separately calculating the fatigue crack initiation life and the fatigue crack propagation life. The tooth root fatigue stress and the fatigue initiation life are calculated by the multi-axial fatigue life prediction method with the Smith-Watson-Topper criterion and the critical plane method. Afterwards, the tooth root stress–strain field is calculated in Finite element (FE) software and the stress intensity factors of the crack tip are calculated in three-dimensional (3D) crack analysis software. Then, the tooth root fatigue crack propagation trajectory and the fatigue crack propagation life are obtained separately. Finally, the influence mechanism of the loading conditions, the geometry parameters of gears, and the initial crack positions on the tooth root fatigue crack initiation life, propagation life, and fatigue crack propagation trajectory are analyzed, and a tooth fatigue test bench is built for verifying the crack propagation trajectory.

Method of understanding for investigation of crack propagation trajectory and fracture aspects in dental cracks on view of fracture mechanics theories.

Current research introduces understanding of dental-cracks mechanistic with fundamental fracture behavior in natural-teeth and orthodontics including mode I crack under both tension and compression, mode II crack under both clockwise-shear and anticlockwise-shear and mixed-mode cracks under both compression-shear and tension-shear. It depends on experimental models of transparent-Plexiglas including pre-cracks of different orientations angle (b) based on fundamental theoretical fracture analysis with comparison. Problem-concept, cracking aspects of fracture-initiation, propagation-direction, fracture-increment length, critical external-load and fracture path are predicted experimentally and theoretically using directional fracture approach and directional strain-energy density theory. Tests are carried out for (36) samples for compression and tension in LEFM. Friction-resistance between crack-surfaces is considered with derivation of equations and charts. Negative stress-intensity factor (-KI) is developed for solving complicated problems of cracks under occlusal compression loads. The occlusal loads are compression and shear producing lateral tensile mixed mode cracks. The critical propagation angle (qc), critical propagation load (sc) and critical propagation envelope of stress intensity factors (KI-KII) are developed with respect to crack orientation angle (b) with comparisons. They are necessary to predict the fracture propagation early before teeth-failure. It helps for prevention and control of dental-cracks, correct-restoration, prosthodontics, orthodontics, and development of new dental-materials and technologies.

Crack growth in sandwich-structured foam core graphite epoxy laminate composite using a phase-field modelling approach

The laminated sandwich composites have wide structure-making applications in the automotive and aviation fields due to their lightweight and superior flexural rigidity properties. Making grooves or holes to assemble more than one structure induces crack discontinuities near the stress concentration region in these sandwich structures. The present work examines the effect of crack discontinuities on the mechanical performance and failure process of the sandwich structures under different loading conditions. Phase field method (PFM) has been presented and implemented using in-house developed MATLAB code. The effect of holes, multiple cracks, number of cores, and loading conditions are analyzed for the mechanical and fracture behavior of the structure. Load-carrying capacity, threshold displacement value for crack initiation, crack propagation trajectory, and energy absorption capacity are compared for various crack discontinuities under different loading conditions. Approximately 35% increase in load carrying capacity is observed in equivalent multiple core sandwich structures.

Study on the superposition effect of stress waves and crack propagation law between blastholes at different angles

The drilling and blasting method is extensively employed in various industries such as mining and infrastructure construction. In the majority of blasting operations, strip-charges are predominantly utilized, while blastholes often exhibit an angled orientation in practical engineering scenarios. To investigate the stress wave superposition effect and the crack propagation law among blastholes at varying angles, this study employs a high-speed digital image correlation system to conduct blasting model experiments. The results indicate that: the fractal dimension of the crack propagation trajectory decreases progressively as the angle increases. the von Mises strain-time curve of the specimen initially increases and then decreases. As the angle between the blastholes widens, the fractal dimension of the crushing zone and blasting crack among the blast borehole decreases accordingly, suppressed the blasting effect of the blasted medium. On the central axis between the two holes, the stress superposition becomes more obvious in the direction away from the initiation point, and the peak value of strain is the highest at the bottom of the blastholes. When the angle between the blastholes is 30°, the strain in the specimen takes the longest to decline from peak to valley, and the blasting stress wave sustains its influence for an extended duration, thus maximizing the use of blasting energy. Conversely, when the angle between the blastholes is 0°, the specimen experiences the shortest duration of blasting action and the least efficient energy utilization.

Fracture behaviour characterisation of FRP-reinforced concrete based on digital image correlation and acoustic emission technology

In order to identify the dynamic fracture characteristics of fibre-reinforced polymer (FRP)-reinforced concrete, three-point bending fracture tests of FRP-reinforced concrete with five different strain loading rates (10−1/s, 10−2/s, 10−3/s, 10−4/s and 10−5/s) are carried out. The fracture behaviour of FRP-reinforced concrete is analysed using digital image correlation (DIC) and acoustic emission (AE) techniques. Crack propagation in FRP-reinforced concrete beams during the fracture process is observed and a quantitative relationship is established between the AE parameters and the load level before the ultimate load is reached. Test results on the variation of the AE parameters can characterise the internal damage behaviour of the FRP-reinforced concrete beams and monitor the distribution characteristics of any cracks. The crack propagation trajectory of the FRP-reinforced concrete beams can be observed using the DIC technique and quantitative analysis of the crack opening displacement (COD) can be achieved.

Numerical modeling of crack propagation from open and closed flaws in rock

The traditional fracture criterion performs well when calculating crack propagation under tensile conditions, but a zigzag crack propagation path was obtained under compression, which is inconsistent with experimental results. This study indicates that the positive and negative oscillations of the mode-II stress intensity factor (KII) under compressive loading during crack propagation is the reason for the zigzag trajectory of crack propagation. Such oscillation of KII can be effectively eliminated when the non-singular stress (T-stress) at the flaw tips is considered, and thus, the path of crack propagation can also be smoothed. However, due to the complicated calculations of the stress intensity factors and T-stress at each step of crack propagation, it is not suitable for simulation in fast, complex environments and multi-flaws. Also, the lack of a shear fracture criterion in traditional fracture methods leads to difficulty in studying shear crack propagation in rock. Therefore, a strength-based localized maximum stress (SLMS) criterion was proposed in this study to model both tensile and shear crack propagations in rock more efficiently, conveniently, and accurately. Then, the crack propagation processes in both plate and Brazilian disc specimens with a single flaw under uniaxial and biaxial compression were modeled to investigate the effects of the flaw inclination angle, friction coefficient, and loading level on the crack propagation path. The influence of the contact friction between the flaw surfaces on the contact status and the crack propagation path during the crack propagation process was also analyzed. Also, the crack propagation in a plate with a single flaw under biaxial tension was modeled, which shows bifurcation crack propagation when the lateral tension is several times larger than the axial tension. All the modeled results indicated that the proposed SLMS criterion can get better results when modeling crack propagations for open or closed flaws under tension or compression conditions.

Investigation of the compression-shear fracture characteristics of flaw-filled sandstone under confining pressure

In the field of rock engineering, the coupled effects of confining pressure and crack filling material on rock mechanical properties have not received widespread attention. In this study, the central cracked Brazilian disk specimen was used to investigate the fracture properties of sandstone in compression-shear loading mode in a confining pressure and crack-filling environments. Variations in peak load and fracture toughness were quantitatively evaluated for different confining pressures and fillings, accompanied by the establishment of quantitative relationships related to fracture toughness. The trend of linear increase in effective fracture toughness versus confining pressure arises primarily from the contribution of confining pressure. The filling material weakens the fracture toughness of the rock to a certain extent, which is attributed to the accumulation of energy during the failure of the sandstone and the reduction of the stress concentration at the crack tip. The crack propagation trajectory mainly exhibits the characteristics of a stretched wing crack, but shows a transition trend towards a shear crack to a certain extent.

Crack propagation analysis and fatigue life assessment of high-strength bolts based on fracture mechanics

To investigate the effect of initial cracks on the fatigue performance of high-strength bolts for high-speed train brake discs, the fatigue crack propagation behavior of high-strength bolts under the coupling action of preload and dynamic fatigue load was investigated experimentally and numerically based on the theory of linear elastic fracture mechanics. Firstly, fatigue tests of high-strength bolts with initial crack defects were carried out, and then a three-dimensional accurate numerical model with the hexahedral mesh for a bolt-nut was established by MATLAB, and the fatigue crack propagation behaviors were investigated using ABAQUS-FRANC3D interactive technology. In this paper, the effects of the initial crack state, the bolt preload, the axial excitation load, and the friction coefficient of the screw pair on crack propagation life were emphatically studied, and the simulated crack propagation trajectory and crack propagation life agreed well with the experimental results. The findings indicated that 0°-oriented cracks beginning at the maximum principal stress were predicted to have the shortest fatigue life. The crack propagation life was sensitive to the initial crack size, the coefficient of initial crack geometry, and the bolt preload, but not to the friction coefficient of the screw pair. Furthermore, when evaluating the effect of fatigue load on crack propagation, the load ratio, the mean load, and the load range should all be considered.

Investigation on the multimodal failure characteristics of cement mortar under uniaxial compression loading

The physical condition and durability of cement-based structures can easily decrease after years of operation due to exposure to severe scenarios associated with internal defects, aggressive usage, and continuous load changes. Therefore, accurately assessing such infrastructures is essential for ensuring safety and serviceability and preventing hazards. In this study, an experimental investigation of the multimodal failure characteristics of cement mortar with various sand contents at different uniaxial compressive loading rates was conducted. Specifically, the multimodal failure characteristics include three main categories: mechanical properties (e.g., compressive strength), one-dimensional signals (e.g., micro-vibration and electromagnetic radiation), and two-dimensional videos/images (e.g., crack propagation trajectory). A geophysical acquisition and a high frame rate camera were employed to simultaneously record the micro-vibration, electromagnetic radiation and crack propagation videos of the cement specimens in a uniaxial compression test. Based on the computer vision technique and the feature pyramid network (FPN), an automatic pixel-level crack segmentation method was proposed to extract cracks of each critical moment in the fracture video. Then, the fractal dimension and crack area were calculated to quantitatively depict the crack propagation trajectory. Finally, the stress drop, micro-vibration, electromagnetic radiation, and crack propagation trajectory characteristics were analysed and discussed. The experimental results indicate the following. (1) The FPN offers a practical way to identify cracks in structures of cement-based materials at the pixel-level. (2) The micro-vibration, electromagnetic radiation, and crack propagation trajectory exhibit good consistency. In particular, the area and fractal dimension of cracks positively correlate with the stress drop of cement under compression loading. (3) The peak and cumulative energy values of micro-vibration and electromagnetic radiation tend to increase as the sand content increases when subjected to the same loading rate.

Phase field study of the thermo-electro-mechanical fracture behavior of flexoelectric solids

Piezoelectrics working in a temperature varying environment are prone to thermo-electro-mechanical fracture due to their brittle nature. In the meantime, flexoelectricity can greatly influence the fracture behavior of piezoelectrics since large strain gradients exist near the crack tip. In this paper, a novel phase field model is developed to investigate the thermo-electro-mechanical fracture behavior of piezoelectrics with consideration of the flexoelectric effect. In the proposed phase field model, the crack surfaces are assumed to be thermally adiabatic and electrically impermeable. The damage driving force is derived from the Clausius-Duhem inequality where the mechanical part is regarded as the driving force for the crack evolution. The mechanical driving force is decomposed to properly characterize the mixed mode crack propagation behavior. The governing equations of the four-field-problem are derived from the variational principle and solved numerically with the mixed finite element method. The fracture behavior of the flexoelectric solid under combined thermal, electrical and mechanical loads is then investigated by phase field modelling. The numerical results indicate that the proposed phase field model can well characterize the multi-physical effects and predict complex crack propagation trajectories in flexoelectric solids. Besides the mechanical and electrical loads, the thermal effect, the flexoelectric effect and the temperature dependence of the flexoelectric coefficients can all have significant influences on the thermo-electro-mechanical fracture behavior of flexoelectric solids. The present phase field model can thus act as a promising numerical tool to predict the reliability of flexoelectric components working in a temperature varying environment.

Acoustic Emission Characteristics and Damage Evolution Analysis of Sandstone under Three-Point Bending Test

In order to study the prevention of roadway roof bending, sinking, and breaking and the prevention of dynamic disasters such as the appearance of rock bursts, three-point bending experiments of sandstone under different spans were carried out. By using stress loading system and acoustic emission technology, the acoustic emission characteristic parameters of the sandstone fracture process were analyzed, the precursory information of rock bending fracture was explored, and the evolution law of sandstone damage based on acoustic emission characteristics was obtained. The results showed that according to the variation of acoustic emission ringing count, the load-time curve was divided into four typical stages: the first stage showed an overall increasing trend; the second stage showed an obvious increasing trend; the third stage showed obvious accelerated growth and the acoustic emission ringing count reached the maximum at the moment of rupture. In the fourth stage, the amplitude and frequency of the ringing count are large and high. With the increase in span, the cumulative ringing counts of AE decreased, and the rate of change gradually decreased. The fracture process of three-point bending sandstone can reflect the precursor information of rock fracture from time domain, frequency domain, and R value (ratio of cumulative acoustic emission ringing count to cumulative energy count). In time domain, the evolution characteristics of AE cumulative ringing count stage II can be used to predict the three-point bending fracture of sandstone. The peak frequency shows a linear increase after a spike and then an accelerated increase to a rupture, and the boundary point between the spike and the linear and nonlinear can be obtained. The decrease in R value can indicate that the main crack is growing in the specimen. According to the damage rate, the characteristics of the damage variables can be divided into five stages: stationary and low, gradually increasing, gradually decreasing, main crack coalescence, and complete fracture. With the increase in span, the fracture damage shows a decreasing trend. The residual damage fluctuates between 0.38 and 0.40 due to the difference in crack propagation trajectory. It has theoretical research value for revealing the internal mechanism of rock bending and fracture and has engineering guiding significance for mine pressure and rock strata control and dynamic disaster prevention.

Cosserat ordinary state-based peridynamic model and numerical simulation of rock fracture

The propagation and coalescence of rock cracks is the direct cause of instability in many geotechnical engineering structures. To predict the rock crack propagation trajectory and coalescence mode, an ordinary state-based peridynamic (OS-PD) based on the Cosserat continuum is proposed. Compared with classical OS-PD model considering only pairwise force, the effects of the pairwise moment between two material points is also considered in the proposed Cosserat ordinary state-based peridynamic (COS-PD) model. The rotational stiffness and rotation angle are introduced to characterize the microdeformation and microstructure of rock, and the expression of rotational stiffness coefficient is derived. Three numerical cases are presented to compare the performance of OS-PD model and COS-PD model. The effect of the rotational stiffness on crack growth is investigated. The results show that the rock failure process is accelerated by the introduction of pairwise moment, the crack propagation type and coalescence mode are more inclined to shear failure with the increase of rotation stiffness coefficient. Compared with experimental results, it is found that COS-PD model could extend classical OS-PD model and better capture the evolution process of the rock crack.

Experimental Study of Dynamic Fracture in Structurally Heterogeneous Materials on the Example of Rocks

The development of micro- and macrocracks in rocks under dynamic influence is considered. The important role of structural features of rocks on this process is noted. Based on ultrasound studies, it is shown that rock samples, as a rule, are heterogeneous and differ in the distribution of longitudinal wave velocity values in certain local regions. The initial heterogeneity determines the spatial development of the microcrack development area under external influence. Using optical microscopy and computer X-ray microtomography, the parameters of microcracks were determined on the example of granite after exposure. Experimental studies using optical, electron and scanning confocal laser microscopy were performed to evaluate the parameters of microcracks in granite. Structural features of rocks affect the nature of the development, trajectory and speed of crack propagation.

Numerical solutions for crack problems during elastomer forming

Generically, thermoset elastomers are often referred to as rubber. It is characterized by the chemical bonding between polymer chains. One of the important problems that plague elastomer manufacturing and rubber parts under service is cracks. Predicting the main factors affecting crack propagation trajectories during forming and after curing time is an important challenge. For this purpose, numerical analysis was implemented by using the commercial ABAQUS/CAE software package. A three-dimensional model was established to predict the important factors that affect this process. During the analysis, the effect of forming velocity and the amount of kinetic energy on the distortion of rubber material and crack propagation is explored in detail by using different forming punch velocities. The drop velocity of the upper insert (punch) on the rubber pad was taken as 10 m/s, 7 m/s, and 5 m/s, respectively. Consequently, while each forming velocity will generate different kinetic energy between the interaction surfaces, the change in crack behavior and the normal stress can be monitored in different positions. As a result, among these velocities, it was found that the low forming velocity of the upper insert (punch) is better than the others in forming rubber where cracks and distortions were at minimum values. Also, the amount of kinetic energy is low enough in the case of low speeds and can affect the results significantly. In addition, it was found that the generated stresses have a significant impact on the crack development in a specific area, especially near the fillets and sharp edges. It was concluded that calculating the parameters affecting the crack growth and predicting the crack propagation trajectories using the finite element method is a significant method for predicting and solving crack problems before tool fabrication

A Computational Framework for 2D Crack Growth Based on the Adaptive Finite Element Method

As a part of a damage tolerance assessment, the goal of this research is to estimate the two-dimensional crack propagation trajectory and its accompanying stress intensity factors (SIFs) using the adaptive finite element method. The adaptive finite element code was developed using the Visual Fortran language. The advancing-front method is used to construct an adaptive mesh structure, whereas the singularity is represented through construction of quarter-point single elements around the crack tip. To generate an optimal mesh, an adaptive mesh refinement procedure based on the posteriori norm stress error estimator is used. The splitting node strategy is used to model the fracture, and the trajectory follows the successive linear extensions for every crack increment. The stress intensity factors (SIFs) for each crack extension increment are calculated using the displacement extrapolation technique. The direction of crack propagation is determined using the theory of maximum circumferential stress. The present study is carried out for two geometries, namely a rectangular structure with two holes and one central crack, and a cracked plate with four holes. The results demonstrate that, depending on the position of the hole, the crack propagates in the direction of the hole due to the unequal stresses at the crack tip, which are caused by the hole’s influence. The results are consistent with other numerical investigations for predicting crack propagation trajectories and SIFs.

Study of the interaction mechanism of oppositely propagating cracks by dynamic photoelasticity and numerical simulation

The interaction mechanism of oppositely propagating cracks is an important basis for the study of rock fracture under dynamic loading. In this article, the stress field superposition and crack tip stress evolution are deeply investigated during the interaction of oppositely propagating cracks by using dynamic photoelastic experiment method and numerical simulation analysis. Obtained results indicate that the cracks interaction process is accompanied by the deflection of the crack, and the deflection of the cracks is mainly affected by the shear stress field at the crack tip. According to the difference of the crack deflection characteristics, the interaction process of the oppositely propagating cracks can be divided into two stages. The Stage I: the non-interlaced stage and Stage II: the interaction stage after the mutual staggered. It includes the period of Stage I that the oppositely propagating cracks are not interlaced with each other; the Stage II is the interaction period after the oppositely propagating cracks are interlaced with each other. The effects of stress intensity factor K I, stress intensity factor K II and far-field T stress on crack propagation process should be comprehensively considered when predicting the crack growth trajectory. The interaction of the stress field between cracks is the main factor determining the crack propagation trajectory. In addition, the vertical spacing between cracks also has a significant effect on the fracture behavior of oppositely propagating cracks. When the vertical distance between the two cracks is large, the local stress fields at the crack tip cannot overlap and interfere with each other, and the oppositely propagating cracks will expand independently of each other.

Adaptive Finite Element Modeling of Linear Elastic Fatigue Crack Growth.

This paper proposed an efficient two-dimensional fatigue crack growth simulation program for linear elastic materials using an incremental crack growth procedure. The Visual Fortran programming language was used to develop the finite element code. The adaptive finite element mesh was generated using the advancing front method. Stress analysis for each increment was carried out using the adaptive mesh finite element technique. The equivalent stress intensity factor is the most essential parameter that should be accurately estimated for the mixed-mode loading condition which was used as the onset criterion for the crack growth. The node splitting and relaxation method advances the crack once the failure mechanism and crack direction have been determined. The displacement extrapolation technique (DET) was used to calculate stress intensity factors (SIFs) at each crack extension increment. Then, these SIFs were analyzed using the maximum circumferential stress theory (MCST) to predict the crack propagation trajectory and the fatigue life cycles using the Paris' law model. Finally, the performance and capability of the developed program are shown in the application examples.

Stress-controlled fatigue of HfNbTaTiZr high-entropy alloy and associated deformation and fracture mechanisms

The stress-controlled fatigue tests are carried out at a stress ratio of 0.1 and a frequency of 10 Hz, and span both low-cycle and high-cycle regimes by varying the applied stress amplitudes. The high-cycle fatigue regime gives a fatigue strength of 497 MPa and a fatigue ratio of 0.44. At equivalent conditions, the alloy's fatigue strength is greater than all other high-entropy alloys (HEAs) with reported high-cycle fatigue data, dilute body-centered cubic alloys, and many structural alloys such as steels, titanium alloys, and aluminum alloys. Through in-depth analyses of crack-propagation trajectories, fracture-surface morphologies and deformation plasticity by means of various microstructural analysis techniques and theoretical frameworks, the alloy's remarkable fatigue resistance is attributed to delayed crack initiation in the high-cycle regime, which is achieved by retarding the formation of localized persistent slip bands, and its good resistance to crack propagation in the low-cycle regime, which is accomplished by intrinsic toughening backed up by extrinsic toughening. Moreover, the stochastic nature of the fatigue data is neatly captured with a 2-parameter Weibull model.

3D modelling of fatigue crack growth and life predictions using ANSYS

This study uses ANSYS mechanical APDL 19.2 to predict crack propagation trajectories and fatigue crack growth at constant amplitude loading. Mixed-mode fatigue life assessment is implemented by the Paris law model for different configuration of modified compact tension specimen (MCTS) in linear elastic fracture mechanics (LEFM). The methodology includes: evaluating stress intensity factors (SIFs), a direction of crack propagation and estimating fatigue life via incremental crack growth process. Predicted crack growth path in the present analysis revealed a change in orientation of the hole proportionately affected fatigue crack life cycles. The propagation of fatigue crack is mostly attracted to the hole and the crack could either curve its path and grow towards it, or bypass the hole and propagate. The mixed-mode fatigue crack path and fatigue crack growth from this study were validated by several crack growth experimental and numerical results in literature.