Anisotropic Fracture Research Articles

Research on the approximate equation inversion method for the physical properties parameters of OA media with decoupling of stress and fracture effects

Pre-stack seismic inversion is an effective method for predicting reservoir physical parameters. At the same time, azimuth seismic data is a reliable source of information for predicting underground reservoir elastic parameters, fracture parameters, and interface parameters and has rich underground information. However, it is difficult to determine whether the anisotropy of the reservoir is caused by stress or the original fractures. Therefore, distinguishing the influence of fractures and initial stress in the reservoir from azimuth seismic data is the key to predicting reservoir parameters. Because of the problem of insufficient consideration of the influence of stress and fracture weakness in OA media, based on Born's first-order scattering theory and Bayesian inversion framework, an approximate equation for the reflection coefficient decoupling fracture anisotropy and stress-induced anisotropy was constructed, and a linear inversion method based on the approximate equation was developed, realizing the exploration of methods for predicting fracture weakness and stress action parameters. Model testing and actual work area application have verified the feasibility and practicability of predicting underground medium parameters from seismic response characteristics.

Phase field fracture in elastoplastic solids: a stress-state, strain-rate, and orientation dependent model in explicit dynamics and its applications to additively manufactured metals

Phase field models have gained growing popularity in analysing fracture behaviour of materials. However, few have been explored to simulate dynamic ductile fracture to date. This study aims to develop a phase field framework considering strain rate, stress state, and orientation dependent ductile fracture under dynamic loading. Firstly, governing equations of displacement and phase fields are formulated in an explicit finite element framework. Secondly, constitutive relations are established with a hypoelastic-plasticity framework, encompassing the influence of material orientation and strain rate on both plasticity and fracture initiation. Stress states dependent fracture initiation is also considered. Thirdly, finite element implementation and corotational formulation for constitutive equations are derived. To validate the proposed model, finally, additively manufactured samples, involving material-level and crack propagation specimens are tested under dynamic loading conditions. Overall, the proposed phase field model can properly reproduce the experimental force-displacement curves and crack paths. Uniaxial tension tests reveal that a higher strain rate can lead to a higher hardening curve and lower ductility. Other material specimens further demonstrate the capability to predict stress state and orientation dependent dynamic fracture. To simulate dynamic crack paths accurately, it is necessary to consider anisotropic fracture initiation. Lastly, the phase field model was applied for the first time to predict the dynamic response of triply periodic minimal surface (TPMS) structures. Dynamic crack patterns were effectively captured, and the fracture mechanisms were thoroughly analysed. This study provides an explicit phase field framework for dynamic ductile fracture, with applications to additively manufactured materials and structures.

Numerical investigation on bending characteristic and ductile fracture of AA7075 thin-walled beam using advanced orthotropic plasticity and fracture models

Thin-walled structures manufactured from the 7075 aluminum alloy are gaining tremendous attention in the automotive industry for their potential to reduce vehicle weight. However, the bending characteristics and rupture behavior of the AA7075 thin-walled beams under unexpected collision events have not been extensively studied. This study aims to fill that gap through a detailed numerical investigation of the bending deformation and failure mechanism of AA7075 thin-walled beams under quasi-static three-point bending at room temperature. Full-size, three-dimensional numerical simulations of laboratory-scale AA7075-T6 hat-shaped beam were conducted using the ABAQUS/Explicit solver. The material elastic–plastic response is described by a rate-independent constitutive description, incorporating advanced non-quadratic orthotropic plasticity and anisotropic ductile fracture criteria via VUMAT subroutines. Results indicate that the simulations accurately reproduced experimental observations, including the loading-displacement curves and deformation patterns. The bending behavior of the AA7075-T6 thin-walled beams aligns with typical bending collapse mechanisms, consistent with Kecman’s theory. The rupture process exhibits ductile fracture characteristics, with heterogeneous stress distribution across the material thickness affecting crack initiation rates between the upper and lower surfaces. Notably, the stress state at the fracture’s half-thickness section approximates an equi-biaxial tension condition. These findings provide essential insights into the bending deformation and failure mechanisms of AA7075 thin-walled structures under unexpected impact loading.

Anisotropic Fracture Evolution and Size Effect of the Fracture Process Zone in Laminated Shales Derived from Digital Image Correlation

Anisotropic Fracture Evolution and Size Effect of the Fracture Process Zone in Laminated Shales Derived from Digital Image Correlation

Influence of Temperature and Bedding Planes on the Mode I Fracture Toughness and Fracture Energy of Oil Shale Under Real-Time High-Temperature Conditions

The anisotropic fracture characteristics of oil shale are crucial in determining reservoir modification parameters and pyrolysis efficiency during in situ oil shale pyrolysis. Therefore, understanding the mechanisms through which temperature and bedding planes influence the fracture behavior of oil shale is vital for advancing the industrialization of in situ pyrolysis technology. In this study, scanning electron microscopy (SEM), CT scanning, and a real-time high-temperature rock fracture toughness testing system were utilized to investigate the spatiotemporal evolution of pores and fractures in oil shale across a temperature range of 20–600 °C, as well as the corresponding evolution of fracture behavior. The results revealed the following: (1) At ambient temperature, oil shale primarily contains inorganic pores and fractures, with sizes ranging from 50 to 140 nm. In the low-temperature range (20–200 °C), heating primarily causes the inward closure of inorganic pores and the expansion of inorganic fractures along bedding planes. In the medium-temperature range (200–400 °C), organic pores and fractures begin to form at around 300 °C, and after 400 °C, the number of organic fractures increases significantly, predominantly along bedding planes. In the high-temperature range (400–600 °C), the number, size, and connectivity of matrix pores and fractures increase markedly with rising temperature, and clay minerals exhibit adhesion, forming vesicle-like structures. (2) At room temperature, fracture toughness is highest in the Arrester direction (KIC-Arr), followed by the Divider direction (KIC-Div), and lowest in the Short-Transverse direction (KIC-Shor). As the temperature increases from 20 °C to 600 °C, both KIC-Arr and KIC-Div initially decrease before increasing, reaching their minimum values at 400 °C and 500 °C, respectively, while KIC-Shor decreases continuously as the temperature increases. (3) The energy required for prefabricated cracks to propagate to failure in all three directions reaches a minimum at 100 °C. Beyond 100 °C, the absorbed energy for crack propagation along the Divider and Short-Transverse directions continues to increase, whereas for cracks propagating in the Arrester direction, the absorbed energy exhibits a ‘W-shaped’ pattern, with troughs at 100 °C and 400 °C. These findings provide essential data for reservoir modification during in situ oil shale pyrolysis.

An anisotropic eigenfracture approach accounting for mixed fracture modes in wooden structures by the Representative Crack Element framework

Finite Element analysis of anisotropic fracture phenomena in wood is a challenging task, particularly when dealing with intricate loading scenarios and mode-specific behavior. The appeal of energetically motivated approaches, such as the eigenfracture method, is that they enable simulation of fracture without prior knowledge of the crack path. The promising eigenfracture method has shown good numerical performance for isotropic materials, and this contribution showcases its application to anisotropic materials. Wood is one such anisotropic material and in this manuscript, the directional dependence of both elasticity and fracture evolution are incorporated into the eigenfracture approach. Further, the eigenfracture approach is used in conjunction with Representative Crack Elements (RCE), which permit accurate modeling of physical crack deformations. The governing equations are systematically derived and implemented into the Finite Element framework. By representative numerical examples, some advantages over the alternative phase-field method are demonstrated. Another highlight of this work is that it is possible to provide a realistic ratio of the energy release rates parallel to and perpendicular to the fiber direction in order to achieve physically accurate crack patterns. Additionally, the calculation effort is reduced, because the unknowns required to determine the crack kinematics can be solved analytically at the material level, a feature that also enables parallelization.

Cracking Mechanism and Inhibition Strategies of Polycrystalline NCM Electrode Particles.

Developing a high-energy-density cathode material (LiNi1-x-yCoxMnyO2, NCM) for lithium-ion batteries is crucial to the electric vehicle and energy storage industries. However, the continuous insertion/extraction of Li+ generates diffusion-induced stress, causing NCM particles to crack or even pulverize, leading to battery capacity loss and limiting its wider commercial application. Current experimental studies are primarily postmortem examinations, and it is difficult to capture the particle cracking evolution. Simulation studies frequently ignore or simplify anisotropic volume contraction, demonstrating an insufficient understanding of the cracking mechanism of NCM polycrystalline particles, and cracking prevention strategies still need improvement. Therefore, we develop an anisotropic polycrystalline fracture phase-field model (AP-FPFM) that focuses on the anisotropic volume contraction of primary particles and precisely generates grain boundary distribution, coupling with Li+ diffusion, mechanical stress, and particle cracking. We employ AP-FPFM to demonstrate the behavior and mechanism of NCM polycrystalline particle cracking and illustrate the necessity and importance of anisotropic volume contraction to understand particle cracking. Furthermore, we explore the effects of average primary particle size, secondary particle size, and core-shell structure modulation on crack initiation and propagation and propose strategies to inhibit or migrate NCM polycrystalline particle cracking. This work provides theoretical support for revealing the cracking mechanism of anisotropic polycrystalline NCM particles and supplying optimization strategies to suppress particle cracking and improve the mechanical stability.

Aperture Field Anisotropy Control on Immiscible Displacement Patterns in Rough Fractures

AbstractTwo‐phase flow displacement in rock fractures is crucial for various subsurface mass transfer processes and engineering applications. In fractures, the displacement of a less viscous fluid by a more viscous one (i.e., viscosity ratio M > 1) involves viscous forces help stabilizing the displacement front in presence of capillary pressure fluctuations. Although previous studies have reported displacement patterns in isotropic fractures, the impact of anisotropic fractures on displacement patterns has not been systematically examined. In this study, we conducted flow‐rate‐controlled drainage experiments to examine how anisotropic aperture fields affect displacement patterns. We observed the transition of displacement patterns from capillary fingering (CF) to crossover zone (CZ) to compact displacement pattern (CD) based on variations in transverse pore‐filling event (TPFE) frequency, which characterizes the competition between capillary and viscous forces. Increasing aperture correlation length in the transverse direction leads to increased TPFE frequency at a low flow rate, destabilizing displacement front. While the increasing aperture correlation length in longitudinal direction suppressed TPFE frequency, stabilizing displacement front. Therefore, the critical capillary number (CaCF‐CZ), which indicates the onset of the CF‐CZ transition, decreases as the aperture field varies from transversely to longitudinally correlated. At high flow rates, TPFEs almost disappeared, indicating that anisotropy did not affect CZ‐CD transition (CaCZ‐CD). Furthermore, we modified theoretical models of CaCF‐CZ and CaCZ‐CD by incorporating the aperture anisotropy factor, achieving a good fit with the experimental data. This study demonstrates the critical role of aperture field anisotropy in controlling two‐phase displacement patterns and provides a theoretical framework for predicting multiphase flow behavior in natural fractures.

Crack-tip cleavage/dislocation emission competition behaviors/mechanisms in magnesium: ALEFM prediction and atomic simulation

Structural properties and reliability of materials can be improved by increasing fracture toughness. At the atomic scale, the fracture is a material separation process, and the fracture toughness of materials is associated with the atomic-scale crack-tip behaviors/mechanisms. The crack-tip behaviors are relevant to the energy state of atoms in the system. Atomic thermal oscillation increases with increasing temperature, which may affect/alter the crack tip behaviors. This work is the first to investigate the temperature-dependent crack-tip cleavage/dislocation emitting competition in magnesium (Mg) using anisotropic linear elastic fracture mechanics theory, Density Functional Theory (DFT), and atomic simulation. Crack-tip behaviors are examined using a specially designed ‘K-field’ loads model. DFT calculations show that a single crystal system with lower entropy and higher Gibbs free energy implies stronger interatomic bonding that favors a higher KIc. Changes in the stress distribution initiate a brittle-ductile transition in crack-tip behavior. The ductile crack tip can be blunted by continuous crack-tip dislocations nucleation/slip, and the evolution of the ductile crack-tip geometry from sharp to semicircular structure significantly decreases the stress concentration at the crack tip. A new criterion of the crack-tip force vector is established, which reasonably explains the geometrical evolution of ductile crack tip where the angle θ between the crack plane and the slip plane is 0∘<θ<90∘ and θ=90∘. This work expands the atomic-scale brittle/ductile crack-tip behaviors/mechanisms of Mg, which provides a reference for crack-tip behavior analysis in engineering research.

Anisotropic mechanical behavior and failure of foldcore structures of fibre-reinforced composites under impact loading

The foldcore sandwich structure presents a novel approach to impact resistance, making it a compelling subject for research into its mechanical and damage behaviors. This work investigates the damage fracture state and its anisotropic damage behaviour of foldcores subjected to impacts by both experimental and simulation methods. To explore the damage mechanisms of foldcore structures and assess how different foldcore types influence their fracture behaviour, we employed the hot-press method to fabricate V-shaped and S-shaped foldcore structures. Subsequently, impact tests were conducted on these structures to uncover their underlying mechanisms, and Hashin’s failure criterion was utilized in the in-face folding direction and out-face folding direction to simulate the damage process and investigate its anisotropy. This study revealed that foldcore structures exhibit anisotropic damage and fracture under impact loading. Damage is predominantly observed along the in-plane folding direction of the foldcore structure, with the damage primarily manifesting as tensile damage to the fibers. The damage incurred by foldcore structures mainly affects the bending region of the structure, where the V-shaped and S-shaped foldcore structures exhibit different damage geometries.

Fracture of Ti3C2-TiO2 atomically thin films

MXene exhibits outstanding electrical conductivity, but its susceptibility to oxidation can impede its conductivity potential. While there is extensive research on the electrical, mechanical properties, and fracture behavior of pure MXene, the exploration of the oxidized MXene is rare, especially for the commonly observed Ti3C2-TiO2 mixtures. In this study, we conducted molecular dynamics (MD) and Density Functional Theory (DFT) approaches and, for the first time, discovered three stable crystal structures of pure MXene with attached TiO2 layers: Loose, Comb, and Tight. For each of these structures, we investigated the anisotropic mechanical and fracture behaviors based on two loading scenarios: ribbon and pre-cracked single layers. The results indicate that the anisotropic behavior is predominantly manifested in Loose and Tight structures. The structural asymmetry of Comb results in a larger and evolving cohesive zone. The direction of the TiO2 layer-MXene interface bonds influences the material's strength, with the Tight structure exhibiting the highest resistance to fracture.

Effect of monovacancy defects on anisotropic mechanical behavior of monolayer graphene: A molecular dynamics study

The mechanical properties of monolayer graphene were studied using molecular dynamics (MD) simulation. The simulation results show that the tensile stress in the [010] crystal direction is greater than that in the [110] and [100] directions under uniaxial tensile. This confirms that graphene exhibits anisotropic behavior when subjected to external loading, resulting in changes in the Young's modulus in different directions. The calculated Young's modulus were 764.68 GPa, 532.50 GPa and 697.83 GPa for the [010], [110] and [100] directions, respectively. On this basis, the effect of defects on the mechanical properties was also considered. When there are vacancy defects, the stress concentration is linearly distributed along the Zigzag direction on both sides of the atomic vacancy defects. The effect of crack defects on the mechanical properties of graphene [010] crystal direction is the most significant. With the increase of crack size, the difference in fracture strength and fracture toughness calculated by MD simulation and the Griffith model decreases gradually. The potential energy of the non-defect model was found to be the highest, with the potential energy decreasing as the defect size increases. In addition, it was found that the strain rate also affects the stress-strain behavior of the monolayer graphene. However, when the crack size is large, the difference in the effect of strain rate on the anisotropic tensile fracture stress can be ignored.

An extended gradient damage model for anisotropic fracture

This paper combines energy decomposition and an extended gradient damage (EGD) model to develop an anisotropic fracture framework with decoupling of tensile and shear cohesive laws. By introducing the shear-normal decomposition in the energy form, the driving force of the damage variable is established within the framework of the EGD model, which is then capable of capturing the traction-separation of potential crack surfaces in both shear and normal directions. The intrinsic correspondence between the cohesive law and the damage evolution enables the accurate prediction of anisotropic fracture behavior in the mixed form of Mode I and Mode II. Furthermore, the proposed model also addresses the damage unloading issue, which still remains a challenge in classic phase field theory or non-local damage theory. A number of numerical examples are presented as validation. Some cutting-edge benchmarks, such as complex mixed-mode fracture and perfect shear fracture, are well reproduced.

A Study on Yield Criteria Influence on Anisotropic Behavior and Fracture Prediction in Deep Drawing SECC Steel Cylindrical Cups.

The deep drawing process, a pivotal technique in sheet metal forming, frequently encounters challenges such as anisotropy-induced defects. This study comprehensively investigates the influence of various yield criteria on the anisotropic behavior and fracture prediction in SECC steel cylindrical cups. It integrates Hill'48R, Hill'48S, and von Mises yield criteria in conjunction with Swift's hardening law to evaluate material behavior under complex stress states. Experimental and numerical simulations assess the anisotropy effects across multiple orientations (0°, 45°, and 90°), revealing intricate relationships between stress criteria and material response. The findings indicate significant discrepancies between isotropic and anisotropic models in predicting fracture heights, emphasizing the importance of selecting appropriate yield criteria. Notably, the von Mises criterion results in lower fracture heights, suggesting higher susceptibility to fractures, while the Hill'48R model aligns closely with experimental data, validated through variations in punch corner radius and blank holder force parameters, with a maximum deviation of 3.23%. Hill'48S displays moderate plastic deformation characteristics.

Anisotropic Mechanical Properties and Fracture Mechanism of Transversely Isotropic Rocks under Uniaxial Cyclic Loading

Transversely isotropic rocks, which are special anisotropic materials, are widely encountered in civil, mining, petroleum, geothermal, and radioactive waste-disposal engineering. Rock is frequently subject to cyclic loads resulting from natural and human-caused events. However, to date, the fracture mechanism of transversely isotropic rocks under cyclic loading remains poorly understood. To address this gap, uniaxial monotonic-loading and cyclic-loading tests were performed on slate specimens by the MTS815 system, during which acoustic emission (AE) signals inside the rock were monitored, and finally the fracture surfaces of the tested rock were scanned by scanning electron microscopy (SEM). Through these tests, the anisotropic mechanical properties, damage evolution, AE characteristics and fracture pattern of slate as a transversely isotropic rock were studied. The results show that the peak strength of specimens varies with the loading–foliation angle under monotonic and cyclic loading, following a U-shaped trend. The deformation modulus during unloading is more capable of characterizing the damage inside the specimen than that during loading. By defining the damage degree based on dissipation energy, it is found that the damage variable is influenced by the loading–foliation angle and the cyclic stress step. The AE characteristics of specimens exhibit significant anisotropy, closely correlated to the loading condition and loading–foliation angle. Regardless of cyclic stress step, the AE counts of specimens with a loading–foliation angle of 0° are mainly distributed near the peak region, whereas those of specimens with other loading–foliation angles occur primarily in the early stage of each cyclic loading. Finally, it is revealed that the fracture mechanism of slate specimens is determined by the loading–foliation angle, loading condition, and cyclic stress step.

The finding of anisotropic compatibility of grain boundaries in a directionally solidified superalloy

The anisotropic compatibility of grain boundaries (GBs) is found in a directionally solidified superalloy, when loading is aligned with (L sample) or transverse (T sample) to the grain growth direction. The greater compatibility of GBs is shown in the L sample by calculating the parameter m′ of the GBs using two developed models. The first model considers the theoretical scenario that grains grow along the perfect [001] orientation, and the compatibility between the neighbouring grains with all kinds of orientation difference is calculated. The second model, termed as Schmid-factor-tolerance model, considers the effects of asymmetrical slip systems caused by the deviation of grain growth direction from the [001] orientation in a real microstructure. Validation of the model is achieved through fatigue tests, demonstrating its capability to interpret and predict the crack initiation behaviours at grain boundaries. Combined with the fatigue tests to illustrate the anisotropic fracture behaviours of the L and T specimens, it shows that the intergranular cracks are more likely to occur in the T specimen with poor compatibility, which proves the capability of predicting the intergranular cracks for the Schmid-factor-tolerance model.

Phase-field fracture modelling of piezoelectric quasicrystals

In this paper, an electro-elastic phase field model is developed for brittle fracture in piezoelectric quasicrystals. The elastic field of quasicrystals is composite of a phonon field and a phason field. The phonon field, phason field and electric field are coupled with each other, and the phonon and electric loadings trigger the variation of both the phonon and phason elastic energies, which then together contribute to crack evolution. The cracks initiation and propagation in piezoelectric quasicrystals under quasi-static mechanical loading and electric loading can be well predicted. Several numerical examples are performed to evaluate the effects of electric field and anisotropic fracture toughness. Simulation results show that the electric field influences the initial force, peak force, fracture displacement and crack path. For the single-edge notched tensile test, the effects of electric field force on the initial force, peak force and fracture displacement are obvious. For the single-edge notched shear test, the electric field force has no effect on the initial force, but it affects the peak force, fracture displacement and crack path. For the porous plate tensile test, a high-intensity electric field can deflect crack substantially resulting in passing through different holes. Further simulation indicates that the anisotropic fracture toughness has a significant effect on peak force, fracture displacement, and crack path. The present model can be used to simulate various fracture problems of piezoelectric quasicrystals.

Exploring fracture anisotropy in tantalum carbide compounds: A density functional theory approach

AbstractIn this paper, we examine the cleavage fracture anisotropy in tantalum carbides, namely, TaC, α‐Ta2C, and ζ‐Ta4C3 − x, using density functional theory (DFT) calculations. Our investigation identifies the presence of multiple low‐energy cleavage planes indicating multiple potential pathways for crack propagation in these ceramics, even the low symmetry compounds. The anisotropy characteristics of cleavage fractures exhibited by α‐Ta2C and ζ‐Ta4C3 − x closely align with the intrinsic fracture anisotropy observed in TaC. Notably, there exist at least three pyramidal planes in ζ‐Ta4C3 − x whose cleavage energies are less than those of the carbon‐depleted basal planes, previously reported to have the lowest cleavage energy. The observed preference in experiments for cleavage along carbon‐depleted basal planes, exclusive of other identified low‐energy planes, points to factors beyond cleavage energy influencing cleavage plane preference.

Anisotropic fracture behavior of the 3rd generation advanced high-strength – Quenching and Partitioning steels: Experiments and simulation

Advanced high-strength steels (AHSS) have revolutionized the automotive industry by reducing weight without compromising crashworthiness. The new third-generation steels, such as quenching and partitioning (QP) steels, offer exceptional strength and ductility. However, despite the extensive strength-ductility studies, there is a wide knowledge gap in the literature on the fracture behavior of QP steels under a large range of stress states and loading conditions for material forming operations. This study aims to systematically investigate the fracture behavior of QP1000 sheet metal through a combination of experimental and numerical approaches. In addition to the classic fracture dependency on stress states, we particularly focus on the anisotropic behavior in terms of both plasticity and fracture. Mechanical tests with digital image correlation are performed along three loading directions covering stress states from simple shear to plane-strain tension. The evolving non-associated Hill48 (enHill48) model is employed to describe anisotropic plasticity, while the fracture behavior is represented by a partially coupled anisotropic fracture model and a fully anisotropic fracture model. It is concluded that the investigated QP steel shows moderate anisotropic plasticity behavior yet strong fracture anisotropy, which intensifies with the increase of stress triaxiality. The partially coupled anisotropic fracture model, which has shown success for materials with minor anisotropic plasticity, fails to describe the anisotropic fracture and a fully anisotropic model provides significantly improved predictive capability.

Anisotropic characteristics and creep model for thin-layered rock under true triaxial compression

The failure phenomenon of thin-layered rock tunnels not only exhibits asymmetric spatial characteristics, but also significant time-dependent characteristics under high in-situ stress, which is attributed to the time-dependent fracture of thin-layered rocks. This paper conducted a series of true triaxial creep compression tests on typical thin-layered rock siliceous slate with acoustic emission technique to reveal its anisotropic time-dependent fracture characteristics. The anisotropic long-term strength, creep fracturing process, and fracture orientation characteristics of thin-layered rocks under different loading angles (β, ω) and intermediate principal stress were summarized. A three-dimensional (3D) non-linear visco-plastic creep model for thin-layered rock was developed to simulate its anisotropic creep behavior. The time-dependent fracturing of rocks during true triaxial creep loading is reflected through the change of equivalent strain based on an improved Euler iteration method. By constructing the plastic potential function and overstress index related to loading angles and stress state, the anisotropic time-dependent fracturing process and propagation of thin-layered rocks under different loading angles and intermediate principal stress are expounded. The model was validated experimentally to show it can reflect the long-term strength and creep deformation characteristics of thin-layered rocks under true triaxial compression.