Mode Crack Research Articles

Numerical prediction and experiments for 3D crack propagation in brittle materials based on 3D-generalized maximum tangential strain criterion

Accurately predicting and tracing the three-dimensional (3D) propagation and fracture trajectory of a crack inside brittle materials is challenging. One difficulty is that the 3D crack propagation exhibits complex I/II/III mixed-mode expansion, and there is a lack of accurate crack initiation criteria and effective simulation methods. In our previous studies, the 3D-generalized maximum tangential strain (3D-GMTSN) criterion was proposed to determine the direction and onset of 3D fracture initiation. In this study, a Python program based on the 3D-GMTSN criterion is developed and integrated into FRANC3D to predict the 3D propagation trajectory of an arbitrary crack inside brittle solids. To verify the reliability of the new method, three different types of 3D crack modes, namely Internal Inclined Cracks Cuboid (IICC), Edge Notched Disc Bend (ENDB), and Three-Point Bending (TPB), are used for fracture experiments. The 3D crack propagation morphology is identified using high-resolution CT imaging techniques. The IICC, ENDB, and TPB models are simulated using the new method and the conventional numerical method based on the maximum shear stress (MSS), maximumtensile stress (MTS), and maximum energy release rate (MERR) criteria. Comparisons indicate that the proposed method based on the 3D-GMTSN criterion can predict the 3D crack propagation trajectory more accurately than the conventional methods.

Fracture mode classification of UHPC based on deep learning and wavelet time–frequency spectrum derived from acoustic emission waveform

Fracture mode categorization is essential in identifying the failure stage, evaluating the damage characteristics, and providing references for structural maintenance. Acoustic emission (AE), as a passive nondestructive technique, presents great potential in damage characterization of cementitious materials and structures. In this study, a convolutional neural network (CNN) and gated recurrent unit (GRU) integrated model for tensile, shear, and mixed cracking mode classification of ultra-high-performance concrete (UHPC) was proposed and verified based on AE waveform features. First, four-point bending and direct shear tests for UHPC specimens were carried out, respectively, to generate AE waveform signals corresponding to different cracking modes (tensile, shear, and mixed ones). Subsequently, the collected one-dimensional AE signals were converted into two-dimensional time–frequency spectrum by continuous wavelet transform. And an AE dataset was constructed after manual labeling based on the corresponding relationships between cracking modes and wavelet time–frequency spectra. Then, an automatic CNN-GRU automatic classification model was established using wavelet time–frequency spectrum images as input variables, where the CNN extracts spatial image features, and the GRU screens time dependencies and realizes final classification. The proposed CNN-GRU model achieves an accuracy of 96.17% for cracking mode classification of UHPC, which is superior both in computational accuracy and efficiency to lightweight CNN and AlexNet. Classification outcomes for UHPC specimen under four-point bending and direct shear tests revealed the proportion of tensile cracks progressively decreased with the increase of damage, while shear cracks exhibited the opposite trend. The percentage of mixed mode cracks maintained relatively stable throughout the failure stages. The model proposed in this study presents favorable performance to reveal the underlying damage evolution mechanism during UHPC fracture, which can also provide references for the cracking mode classification of other cementitious materials and structures.

Acoustic emission monitoring of a large-scale 50-year-old prestressed concrete bridge girder during an eccentric three-point bending test

Deterioration of reinforced and prestressed concrete structures is one of the main challenges in structural engineering. As the majority of our infrastructure is built around 1960-1980, most structures have reached or will soon reach their design lifetime, giving rise to more structural problems and costs in the coming decades. It is therefore important to develop efficient assessment schemes allowing to assure the safety and reliability of these existing structures and to estimate their residual lifetime. Within the framework of the Bridge|50 research project, a 50-year-old prestressed concrete bridge showing signs of corrosion damage was decommissioned. The bridge girders were recovered and have been subjected to large-scale load tests with varying loading patterns. This paper presents the results acquired during acoustic emission (AE) monitoring of one of the I-shaped girders during a monotonic three-point bending test with an eccentric point load. The results show that the failure mode and location could be detected based on AE activity and zonal AE localization. The onset of concrete cracking was observed by a decrease in peak frequency of the AE signals. Average frequency (AF) and rise angle (RA) value analysis was used to characterize the crack mode, which shifted from tensile to shear mode during bending.

Numerical Simulation Study on Dynamic Interaction between Two Adjacent Wells during Hydraulic Fracturing

The heterogeneity in fracture formation significantly influences the hydraulic fracture propagation among adjacent wells, underscoring the urgency to comprehend the underlying fracture mechanisms. Specifically, in shale gas or oil extraction fracturing operations, stress interactions among neighboring fracturing clusters, or mutual interference during the propagation of parallel fractures, are commonplace. At present, there is relatively little research on the sensitivity parameters of adjacent borehole fracture propagation morphology. Consequently, we employed ABAQUS software 2022 to construct a numerical model simulating the fracturing of adjacent boreholes in opposing directions. Upon validating the model’s fidelity, we systematically explored the influence of various engineering and geological factors on fracture morphology and propagation length. Our findings revealed a three-phase evolution: independent fracture propagation, subsequent mutual repulsion, and, ultimately, mutual attraction. It is worth noting that increasing the elastic modulus from 10 GPa to 80 GPa, and increasing the crack length by 16.30%, is beneficial for crack propagation, while the horizontal stress difference profoundly shapes the crack mode, but has a relatively small impact on the overall crack length. When HSD increases from 0 MPa to 15 MPa, the total crack length only changes by 1.24%. In addition, the filtration coefficient of the reservoir is a key determining factor that has a significant impact on the morphology and length of cracks generated by adjacent boreholes. Increasing the filtration coefficient from 1 × 10−14 m3/s/Pa to 5 × 10−12 m3/s/Pa reduces the total length of cracks by 60.77%. Notably, an optimal injection rate exists, optimizing fracturing outcomes. Conversely, the viscosity of the fracturing fluid exerts a limited influence on fracture morphology and length within the confines of this simulation, allowing for the selection of a suitable viscosity to ensure smooth proppant transport during actual fracturing operations. In designing fracturing parameters, it is imperative to aim for sufficient fracture propagation length while harnessing “stress interference” to foster the development of intricate fracture networks. Ultimately, our research findings serve as a solid foundation for engineering practices involving hydraulic fracture propagation in adjacent boreholes undergoing opposing fracturing operations.

Analysis of failure properties of red sandstone with structural plane subjected to true triaxial stress paths

In order to study the mechanical behavior and failure characteristics of rock mass with the structural plane in complex deep stress environment, the QKX-YB200 true triaxial rockburst test system, acoustic emission, and digital video recorder were adopted to conduct true triaxial loading and unloading indoor tests on the red sandstone cube specimens. The results show that: (1) Under true triaxial loading conditions, all specimens propagate in the form of anti-wing crack, and the dip angle of the structural plane is linearly related to the average value of the anti-wing crack propagation angle; under true triaxial unloading conditions, the specimens with structural plane dip angles of 30°, 45°, and 60° propagate in the form of wing crack, while those with a 90° angle propagate anti-wing cracks, and the closure of structural plane is related to the the crack type at the tips of structural plane. (2) The unstable failure stages in the stress–strain curve under true triaxial unloading are longer and exhibit more pronounced fluctuations; the peak strength of the specimens under the conditions of true triaxial loading and unloading decrease first and then increase with the increase of the dip angle, reaching the lowest at 45°. (3) During the true triaxial unloading tests, the rockburst degree of the intact rock specimens is more violent than that of the specimens with a structural plane. Additionally, the dip angle of the structural plane influences the severity of rockbursts under the same stress path. (4) The crack propagation mechanism and the closure degree of structural planes under different true triaxial stress paths and dip angles are discussed. It is observed that the crack initiation mode around the structural plane tips and the crack mode near free surface are closely related to the stress environment in different areas of the specimens. (5) Based on the indoor test results and previous experimental data, the differences in peak strength characteristics between open structural planes and closed structural planes are preliminarily analyzed and compared.

The role of hydrogen on lead-induced localized corrosion of Alloy 690TT

The vital role of hydrogen on lead-induced localized corrosion of Alloy 690TT in the simulated secondary crevice chemistries of pressurized water reactor at 25 °C is investigated by using surface analysis techniques and calculations. Density functional theory (DFT) calculation reveals that there is a coupling effect between lead and hydrogen on inhibiting the kinetic diffusion of oxygen vacancies. Experimental results show that hydrogen causes the change of most easily-corroded location from the grain/carbide interface to the TiN/nucleus interface in the lead-induced corrosion process, which provides a new interpreting sight as for lead-induced stress corrosion cracking mode of nickel-based Alloys.

Phase field modeling for composite material failure

AbstractA computational framework of anisotropic phase field model is used to investigate the effects of effective critical energy release rate, interface property, and hole shape on the failure of composite material in this paper. This model is implemented in ABAQUS using a user‐defined element (UEL). First of all, the model is validated through a benchmark model. Second, the effective critical energy release rate is introduced, which can improve the accuracy of the simulation result. Then, the influence of strong and weak interfaces on the failure of composite material is studied. It can be found that the interface properties can change the evolution mode of crack and the final load–displacement response. Finally, the effect of hole shapes on the failure of the composite material is also explored, which shows that the bearing capacity of model can be improved by changing the shape of the hole.

Low cycle fatigue behavior of MAR-M247 nickel-based superalloy from 500 to 900 °C: Analysis of cyclic response, microstructure evolution and failure mechanism

Low cycle fatigue behaviors of MAR-M 247 superalloy were investigated at 500 °C, 700 °C and 900 °C. The detailed deformation mechanisms were characterized by scanning electron microscopy (SEM), electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) and the critical resolved stress to active different deformation mechanisms were calculated. The results show that crack propagates along favorable {111} plane at 500 °C, and anti-phase boundary (APB) shearing is the main deformation mechanism. At intermediate temperatures, the cracking mode is similar to 500 °C. The dislocation pinning at L-C lock leads to premature failure. It is difficult for {111} 〈110〉 slip system to shear hard oriented grain with low Schmid factor at 900 °C. Dislocation movement is achieved by Orowan by pass process and thermal activated dislocation climb at high temperature. In addition, the improved life prediction model based on energy method has been constituted and discussed at different temperatures.

Tensile properties of steel fiber reinforced recycled concrete under bending and uniaxial tensile tests

It is important to study the tensile behavior of steel fiber reinforced recycled concrete (SFRRC) for the reliability of structural design. This paper investigates the effects of different mixture systems, including full-NA, full-RCA, full-RFA, full-RA, and full-RA+10%RP, on the tensile behavior of recycled concrete through uniaxial tensile and three-point bending tests. In addition, the effects of the volume content of steel fiber on tensile behavior are investigated. The uniaxial tensile strength and stress-strain curves of SFRRC were tested and the load-deflection, P-CMOD, double K fracture parameter and fracture energy under flexural tensile load were measured. The results show that the incorporation of recycled materials may negatively affect the tensile strength of recycled concrete. Compared with natural concrete, the uniaxial tensile strength decreased by 28.4%–50.2 % and the flexural tensile strength decreased by 17%–42.52 %. In addition, tensile properties, such as initial crack stress, peak strain, double K fracture toughness, and fracture energy, will also decline. The effect of the volume content of steel fibers on the tensile properties of recycled concrete with different mixed systems is analyzed. The steel fiber changes the tensile cracking mode of recycled concrete. When the content of steel fiber exceeds 1 %, the SFRRC of different mixed systems has the phenomenon of deflection hardening. When the fiber content is 2 %, the uniaxial tensile strength is increased by 13.83%–69.07 %. Contrasting with the control group, the recycled concrete group containing 2 % steel fiber showed enhanced fracture energy, which was increased by 15–23 times with different mixture systems. Uniaxial tensile constitutive models of SFRRC have been established under different mixture systems. The tensile stress-strain response of SFRRC was obtained indirectly by inverse analysis. It has been found that flexural tensile tests overestimate the post-crack properties of materials, and this phenomenon is more obvious in recycled concrete. This research is of great significance for the structural design of SFRRC.

Phase-field anisotropic damage with bond-slip model for reinforced concrete beam under the service load

Concrete, as a quasi-brittle material, undergoes a latent damage accumulation preceding macroscopic crack formation, which is further complicated by the intricate interaction between steel reinforcements and concrete in reinforced concrete (RC) structures. Traditional approaches inadequately capture these nuances, especially when it comes to the seamless transition from numerous micro cracks to a visible macro cracks. Phase-field damage theory stands out as a sophisticated tool, integrating sharp cracks into a continuous damage field representation and detailing the entire process of micro-to-macroscopic cracking evolution. In this work, a phase-field damage model that accounts for bond-slip behavior is proposed, grounded in the principle of stress space decomposition to address the inherent tension–compression anisotropy. Newton’s method with a viscosity coefficient of 0.001 enhances simulation accuracy and robustness through optimal convergence. The comparison between rigid bond and bond slip mechanisms indicates a significant difference in their impact on crack modes, revealing the necessity of considering bond slip. As the steel reinforcement ratio increases, the RC beam’s load-bearing capacity increases incrementally, concurrently exhibiting a reduction in macroscopic cracks, steel reinforcement stress, and overall damage severity. However, the comparative advantage of rigid bond in improving RC beam’s resistance against cracking begins to wane as the reinforcement proportion rises. This study thus sheds light on the nuanced interplay between bond characteristics and the cracking behavior of RC beams, providing a comprehensive and advanced perspective.

Investigating the modal behaviors of a deep beam with a transverse open crack

This paper investigates the modal behaviors of a deep beam with a transverse open crack. Unlike cracked shallow beams with aspect ratio (L/h) > 10, cracked deep beams with aspect ratio < 5 simultaneously exhibit near the crack both axial-bending coupling mode caused by mode I crack and shear (or sliding) mode caused by mode II crack, referred to as axial-bending-shear modal coupling. Therefore, for accurate modal behaviors prediction, appropriate compatibility equations accounting for both modes I and II crack should be employed for deriving a frequency equation. Because the derived frequency equation is nonlinear with respect to modal frequency, the modal frequencies are calculated through the Newton–Raphson method. The corresponding mode shapes are determined by substituting the calculated modal frequencies into the spectral solutions for either side of the crack. The validity of the proposed method was demonstrated through comparison to the finite element analysis and experimental results.

A new accelerated thermal fatigue experiment method of pistons and its application

This study proposed a new test method to take the piston instead of the internal combustion engine as the experimental object and use electromagnetic induction heating and auxiliary cooling to simulate the actual operating conditions of the piston during engine start-stop, to achieve accurate control of the temperature of the heating and cooling cycles. The experimental process can be accelerated by worsening the service conditions. In order to prove the feasibility of this scheme, the temperature field distribution, fatigue life, and failure mode of the piston are compared and analyzed using finite element simulation, theoretical calculation, and surface topography observation. The results show that the error between the simulated temperature value of the key point of the piston and the experimental value of the actual operating condition is less than 5%, the position and value of the maximum temperature of the piston under the thermal fatigue test condition are consistent with the actual engine operating condition, the error between the fatigue life test results and the theoretical calculation results is less than 10%, and the location and cracking mode of the main crack is consistent with the actual working condition. It is proved that the test method is reasonable and feasible, which can provide an important guarantee for the fast and efficient design of high-performance pistons.

Peridynamic fracture analysis of film–substrate systems

When subjected to mechanical, thermal, or other loads, film–substrate systems may undergo complex cracking behaviors, which encompass film and substrate cracking, interfacial debonding, and their combinations, exhibiting rich fracture patterns, such as three-dimensional helical cracks. Identifying the mechanisms underlying these fracture phenomena may lead to more advanced strategies for technologically significant applications. In this paper, we develop an interfacial cohesive peridynamic method for fracture analysis of multiple-phase materials. Particularly, we focus on the modeling of coupled film cracking and interfacial debonding in film–substrate systems. By introducing cohesive interfacial bonds to describe the mechanical properties of the interfaces and adopting a displacement-based cohesive failure criterion, the model is able to predict the critical condition and path of interfacial crack propagation. The robustness of the interfacial cohesive peridynamic method is validated through a series of representative examples. We also demonstrate its efficacy in simulating three-dimensional cracks and identify the essential role of the interfacial energy release rate in controlling the cracking mode transition from a restricted pattern to a helical pattern. The numerical predictions of cracking paths and stress distributions agree well with the previous experimental results. This study provides a valuable tool for analyzing different cracking patterns in film–substrate systems and composite materials.

Retrofitting intact and heat-damaged shear-deficient concrete beams using CFRP ropes and dowels

The potential for recovering the shear capacity of heat-damaged beams using carbon-fibre-reinforced polymer (CFRP) ropes was investigated using 12 concrete beams (150 × 250 × 1450 mm3) with shear reinforcement deficiency. Six beams were heated for 2 h at a temperature of 400°C; the others were not heated. All the beams were retrofitted with near-surface mounted CFRP ropes as external U-shaped stirrups, inserted in vertical holes (embedded through reinforcement) or implemented as a hybrid system of both. Lateral dowels were implanted in concrete along with schemes involving U-shaped stirrups to improve resistance against cover separation and shear failure, respectively. The mechanical behaviour of the beams was evaluated under three-point loading, with data collected and analysed to characterise the load–deflection relationships. Cracking and failure modes were analysed. For the heat-damaged beams, the adopted schemes restored load capacity and improved toughness and ductility, but not flexural stiffness. Moreover, implementing ropes as U-shaped external stirrups, terminating 20 mm below the top surface of the beams, helped avert side-cover separation, yet resulted in horizontal shear failure at the level of the upper concrete cover of the damaged beams. The residual strain induced in the U-shaped external stirrups was 14–40%, which is compatible with those reported in other works adopting similar repair methodologies.

A study on three coalescence modes of non-collinear parallel elliptical double cracks

Based on the Gurson-Tvergaard-Needleman (GTN) damage model, this study focused on the coalescence modes of non-collinear parallel elliptical double cracks in a homogeneous plate, and the coalescence modes of elliptical double cracks under different horizontal distances and vertical distances were investigated. The ratio of horizontal distance s to crack length a was taken as the horizontal axis, the ratio of vertical distance h to crack length a was taken as the vertical axis to plot the graph, then the coalescence modes were summarized and compared with the coalescence modes of linear double cracks. It was found that the non-collinear parallel elliptical double cracks exhibited three coalescence modes: crack tip to crack tip coalescing, crack interval to crack interval coalescing, and crack tip to crack interval coalescing. Each coalescence mode had its own characteristics. The three coalescence modes were distributed regularly in three regions in the graph with s/a and h/a as coordinates. When the horizontal distance s and the vertical distance h between the double cracks were equal respectively, there were significant differences in the crack propagation process and coalescence modes between elliptical double cracks and linear double cracks.

In-situ observation of solidification behaviors of Fe-Mn-Cr-Ni-Si alloy during TIG melt-run welding using synchrotron radiation X-ray

The solidification behaviors, including the solidification cracking and solidification mode of the Fe-Mn-Cr-Ni-Si alloys at the weld bead during tungsten inert gas (TIG) melt-run welding, were examined by time-resolved in-situ observations using synchrotron radiation X-ray imaging and X-ray diffraction. The dynamics of initiation and propagation of solidification cracking at the weld bead could be observed at the dendrite scale. For the specimen solidified in the austenite mode at a welding speed of 10 mm/s, solidification cracking with a zigzag interface developed via the coalescence of many small pores at the centerline, where the columnar dendrite tips impinged. Quantitative image analysis indicated that the local tensile strain was highly localized at the centerline, and the critical local tensile strain for the initiation of solidification cracking was approximately 0.04. For the specimen solidifying in the ferrite-austenite mode at the welding speed of 10 mm/s, the centerline solidification cracking was suppressed by the formation of many equiaxed γ-Fe dendrites ahead of the growing columnar δ-Fe dendrites. Grain refinement at the centerline can be achieved at a welding speed of more than 7 mm/s without requiring inoculants.

Strain-rate effect on mechanical properties of rock-like specimens with narrow crack under uniaxial compression

Uniaxial compression tests were carried out on rock-like specimens containing prefabricated narrow crack under various strain rates. Experimental observations and numerical results show that narrow crack will close or partially close or expand under low compressive stress. Due to the unidirectional loading of loading device, the deformation degree of crack tip near the loading end was different with that of crack tip near the bearing end. With the increase of strain rate, the cracking modes can be divided into 3 categories, near vertical splitting failure affected by horizontal crack (α = 0°), anti-N-wing crack (15°≤α ≤ 60°) and wing crack (60°<α ≤ 90°). Both of the initiation angle θ1 of crack tip near the loading end and θ2 of crack tip near the bearing end decreased with the increase of α and strain rate. Specially, when α = 90°, both θ1 and θ2 rose with the increase of strain rate. Moreover, the value of θ2 was greater than that of θ1 under the same α value because of the different deformation characteristics at two tips. Besides, the mechanical properties of fissured rock including peak compressive stress, residual compressive stress, strain at peak stress, elastic modulus and post-peak softening modulus were significantly influenced by the strain rate and inclination angles.

Quantitative study on the influence of strain amplitude on deformation mechanisms and cracking modes during cyclic torsion of AZ31 magnesium alloy

AbstractThe influence of strain amplitude on deformation mechanisms and cracking modes during cyclic torsion of the AZ31 magnesium (Mg) alloy was quantitatively investigated via EBSD‐SEM characterization. At 0.42% strain amplitude, basal slip was the dominated deformation mechanism throughout the entire fatigue life. At 1.732% strain amplitude, the activation of deformation mechanisms was featured by the periodic transition: tension twinning + basal slip (during counterclockwise torsion) then detwinning + tension twinning + basal slip (during reverse torsion). Moreover, cracking along slip traces (ST) and tension twins (TTW) were the primary cracking modes at 0.42% and 1.732% strain amplitude, respectively. ST cracking and TTW cracking preferentially appeared in soft‐oriented grains for basal slip and tension twinning, respectively. The underlying mechanisms governing the activation of various deformation mechanisms, cracking modes, and cyclic stress–strain responses were systematically discussed.

Simulation of coupled elasticity problem with pressure equation: hydroelastic equation

PurposeThe main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.Design/methodology/approach First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.FindingsNumerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.Originality/valueThis is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

Analysis of reflective cracking in asphalt overlaid jointed concrete airfield pavements using a 3D generalized finite element approach

ABSTRACT Asphalt Concrete (AC) overlays are a common strategy for maintaining PCC airfield pavements. However, the movement of joints in the underlying pavement may lead to reflective cracks propagating to the overlay. The problem is highly three-dimensional resulting in mixed mode of cracks due to the aircraft gear loading configurations and underlying concrete pavement joint spacing and design. The development of a 3D model of airfield pavements to predict reflective cracking using Finite Element Method (FEM) and Generalized Finite Element Method (GFEM), is presented in this study. GFEM enrichment strategy and global-local approach are used to achieve efficient framework for developing the models from both computational and user time perspective. Viscoelastic fracture analysis was performed using elastic-viscoelastic correspondence principle. Sensitivity of the domain size, order of approximation and boundary conditions are investigated in the numerical simulations. It is shown that the crack initiation and propagation is a combination of Mode-I (tensile) and Mode-II (shearing) crack opening. The presented models contributes to the mechanistic empirical reflective cracking design algorithm for the FAA pavement design program.