Dynamic Crack Research Articles

Meshfree simulation of dynamic brittle and quasi-brittle fracture using a local damage model based on lattice particle method

In this paper, the particle size-dependent issue of Lattice Particle Method (LPM) for simulating dynamic brittle and quasi-brittle fracture is addressed by coupling LPM with a local damage model based on fracture energy. The proposed model is simple and more robust than the Stress Intensity Factor (SIF)-based approach as it can model mixed-mode fracture with multiple cracks without any application-dependent tuning parameter. Numerical procedures for estimating the dissipative energy and the crack tip velocity for LPM simulation are also proposed. A series of benchmark problems involving dynamic fracture and crack branching are simulated using the proposed model. Good agreements are found against existing experimental observation and solutions from other numerical methods. Although a Cartesian-like (structured) lattice configuration is employed in the current LPM method, physically meaningful and accurate crack patterns can still be captured without any special numerical treatment.

Rate-dependent augmented finite element method for fast arbitrary crack growth

Experimental observations indicate that fast crack growth often exhibits a rate dependency, which is caused by the viscosity of the material and the dissipation of energy resulting from the branching of microcracks. To address this phenomenon in simulation modeling, this study introduces a rate-dependent augmented finite element method designed for analyzing fast arbitrary crack growth. The method utilizes the maximum principal stress criterion to simulate arbitrary crack growth and predict the path of crack growth. The elements where crack growth is expected are divided into subelements, and they are re-assembled by incorporating rate-dependent cohesive elements between them to construct augmented finite elements. The cohesive elements are based on a rate-dependent trapezoid traction–separation relationship, where the critical traction and fracture toughness are modeled as functions of the separation rate and crack growth speed. The augmented finite elements only contain external nodal degrees of freedom (DoFs), while internal nodal DoFs are condensed. They can be utilized as conventional elements. A numerical algorithm based on the proposed method was developed in this article, and it was implemented in ABAQUS via user element subroutine. The effectiveness of this method and algorithm is validated through an example of dynamic crack growth in a double cantilever beam. The results demonstrate agreement with experimental and computational findings reported in the literature. Additionally, the method was applied to other structures, yielding reasonable outcomes. Analysis of these examples confirms the method’s utility in predicting fast arbitrary crack growth under dynamic load conditions.

A stable numerical framework for long-time dynamic crack analysis

This paper introduces a stable numerical framework designed to address dynamic crack problems over long-time intervals. The initial step involves the temporal discretization of the governing dynamic equilibrium equations using the arbitrary order Krylov deferred correction method. To ensure precise boundary condition matching, a novel numerical implementation is incorporated into the Krylov deferred correction technique. Subsequently, the resulting system of spatial partial differential equations at each time node is solved using the meshless generalized finite difference method with 4th-order expansions in regions close to the crack-tips and 2nd-order expansions in areas far from the crack-tips. This combined approach capitalizes on the strengths of both the Krylov deferred correction technique and the generalized finite difference method, enabling stable simulations of dynamic cracks with the large time step and without the need for mesh generation. Notably, we refine the collocation nodes near crack tips to attain accurate numerical results for displacement and stress field. Several numerical experiments involving diverse impact loadings are conducted to validate the developed framework. Furthermore, a comparison is made between the dynamic stress intensity factors obtained using our approach and those from existing methods.

Experimental Study on Dynamic Tensile Mechanical Behavior and Fracture Mechanical Characteristics of Sandstone with a Single Prefabricated Fissure

The structural stability of engineering rock mass under dynamic disturbance is directly associated with the fracture mechanics properties in engineering practice. Fully understanding the rock’s fracture mechanical behavior and crack evolution caused by stress concentration at the crack tip in engineering rock mass under dynamic load can offer useful insight into the rock’s dynamic fracture mechanism. A dynamic test using split-Hopkinson pressure bar (SHPB) test system was performed on a single prefabricated fissure sandstone centrally cracked Brazilian disk (CCBD) specimens. Based on the theory of fracture mechanics and one-dimensional stress wave theory, the dynamic crack initiation criterion of CCBD specimen is proposed, and the regression model of sandstone’s dynamic fracture toughness under the coupling effect of fissure angle and strain rate is established by using response surface methodology (RSM). The influence of strain rate and fissure angle on stress wave characteristics, dynamic tensile mechanical behavior, and fracture mechanics characteristic was investigated in this study. The findings demonstrate that: (1) The fissure angle plays a pivotal role in determining the failure mode of sandstone. As the fissure angle increases, three distinct failure modes emerge in the sandstone specimens, while variations in strain rate have minimal impact on the fracture mode of these specimens. (2) Alterations in the fissure angle result in changes to the waveform of transmitted waves. When the fissure angle is below 30°, the transmitted wave exhibits “double peak” characteristics; when it exceeds 30°, a “single peak” waveform is observed. This phenomenon can be attributed to diffraction principles governing incident waves. (3) When the impact pressure is 0.2 MPa, the peak load initially exhibits an increase followed by a decrease, with the peak load reaching its maximum at a fracture angle of 60°; when the impact pressures are 0.3 and 0.5 MPa, there exists a negative correlation between the peak load and the fissure angle. (4) The influence of strain rate on sandstone’s fracture resistance is predominant, with alterations in fissure angle exerting an auxiliary effect on this property. The research results can provide a theoretical and experimental basis for dynamic disaster prevention in urban underground space.

A Fractal-Based Quantitative Method for the Study of Fracture Evolution of Coal under Different Confining Pressures

To study the dynamic crack evolution process of loaded coal from the perspective of fractals, we carried out in situ industrial CT scanning tests of loaded coal under different confining pressures, visualizing loaded coal fracturing. Combined with fractal theory, the temporal and spatial evolution law of coal cracks is described quantitatively. The results provide two findings: (1) from the perspective of two-dimensional images and three-dimensional space, the evolution characteristics of cracks in coal under different confining pressures were basically the same in each loading stage. During the loading stages, the cracks exhibited a change rule of a slow reduction, initiation/development, rapid increase, expansion, and penetration. (2) The fractal dimension of coal was calculated by introducing fractal theory, and its change law was in good agreement with the dynamic changes of the cracks, which can explain the influence of the confining pressure on the loaded coal. The fractal dimension showed three stages: a slight decrease, a stable increase, and then a significant increase. The larger the confining pressure, the more obvious the limiting effect. Thus, our approach provides a more accurate method for evaluating the spatial and temporal evolution of cracks in loaded coal. This study can be used to predict the instability failure of loaded coal samples.

Numerical study on dynamic cracking characteristic and mechanism of quasi-brittle materials under impulsive loading

This study focuses on investigating the dynamic cracking behaviors of quasi-brittle materials under impulsive loading using the extended non-ordinary state-based peridynamic (NOSB-PD) model. This extended model incorporates two stress-based failure criteria: Mohr-Coulomb and maximum tensile stress criteria, to represent shear and tensile fractures of quasi-brittle materials, respectively. By analyzing the evolution characteristics of the maximum principal stress obtained from the NOSB-PD model, the fracture mechanisms of quasi-brittle materials subjected to impulsive loading are explored. The research reveals that tensile failure predominantly governs the initiation and propagation processes of quasi-brittle materials under impulsive loading. The stress concentration effect, transfer effect, and dissipation effect observed in the maximum principal stress fields provide insights into the cracking mechanism during the failure processes of such materials. To validate the findings, the crack initiation modes and crack propagation paths obtained from the NOSB-PD model are compared with those obtained from the existing experimental and numerical approaches. The results demonstrate that the extended NOSB-PD model is effective in addressing fracture problems associated with quasi-brittle materials under impulsive loading conditions.

Improved XCT image automatic segmentation for quantitative characterization of the meso-morphological features in the damaged braided composite fabric

Accurately identifying various meso-morphological features and sub-phases within the damaged braided composite fabric is crucial for assessing the mechanical properties of composites under complex loading conditions and different processing parameters. However, obtaining 3D reconstructions that can be quantitatively analyzed is still a challenge, primarily due to the low contrast of the meso-morphological features (yarn tow and matrix crack networks). In this work, a new data enhancement algorithm is proposed to generate a realistic-looking artificial training dataset for enriching the information of the meso-morphological features. Then, the effect of various training networks and training parameters (the size of real and hybrid training dataset, number of epochs) on segmentation performance were examined. Finally, the meso-morphological features were statistically analyzed to accurately evaluate the mechanical properties of the composite material. The work presented here provides an effective tool that enables the quantitative analysis of the dynamic crack evolution process under the axial load of the composite materials.

Dual Horizon Peridynamic Approach for Studying the Effect of Porous Media on the Dynamic Crack Growth in Brittle Materials

Dual Horizon Peridynamic Approach for Studying the Effect of Porous Media on the Dynamic Crack Growth in Brittle Materials

An explicit improved meshless numerical manifold method for dynamic crack propagation

Accurately simulating the dynamic propagation of cracks is critical to investigating the mechanisms of rock fracture under dynamic loading. The meshless numerical manifold method, characterized by its node-based interpolation approximation akin to the meshless method and the dual-cover of numerical manifold method, is particularly suitable for crack analysis and has been successfully applied to quasi-static crack propagation. This paper aims to extend its application to the simulation of dynamic crack propagation. Initially, the meshless numerical manifold method's nodal arrangement and numerical integration scheme are enhanced to address dynamic problems more effectively, referred to as the Improved Meshless Numerical Manifold Method (iMNMM). Subsequently, we introduce a novel mass lumping method grounded in rigorous mathematical principles, an energy-conserving extended degrees of freedom inheritance strategy and a crack propagation criterion based on dynamic stress intensity factors. Additionally, the viscous artificial boundaries and the “large mass” acceleration method are incorporated to impose the acceleration and zero-displacement boundary conditions. Further, the improved explicit meshless numerical manifold method based on the central difference method is established for dynamic crack propagation. Finally, for verification, iMNMM is tested on several numerical examples. Numerical results manifest that iMNMM can enable the simulation of dynamic crack propagation with larger, constant time steps.

Fracture analysis of orthotropic functionally graded materials using element-based peridynamics

A fracture model of orthotropic functionally graded materials (FGMs) based on element-based peridynamics (EBPD) is proposed. Two-dimensional (2D) orthotropic FGMs use three-node triangular elements to describe the force density of EBPD. Due to the gradient difference of material properties inside the element, the Gauss integral formula is used to average the node performances to the integral point of the element. The equations of motion for EBPD is established, which is also applied to orthotropic FGMs by the Gauss integral formula. The micromodulus coefficient of the EBPD is derived for orthotropic FGMs. The critical strain energy density criterion is used as the failure criterion to simulate the quasi-static and dynamic fracture problems. A series of numerical examples, including displacement analysis, stress analysis, dynamic crack propagation of FGM beam, and crack growth of orthotropic FGMs under four-point bending load, are used to validate the accuracy of the fracture model of orthotropic FGMs. The proposed model can be helpful to the material gradient design for FGMs satisfying certain requirements.

Modeling dynamic cracks initiation and propagation with the local to global approach

AbstractThe recently proposed local to global (L2G) method shows an excellent ability of modeling complex arbitrary cracking problem with high efficiency and robustness. Here, we extend the L2G to model dynamic cracks initiation and propagation, in which additional nodes are dynamically introduced to capture displacement discontinuities induced by cracks' propagation, but displacements/accelerations of additional nodes are obtained by solving local nonlinear problems of cracked elements associated with a crack. This unique operation removes the divergence risks caused by adding nodes, and improves the numerical efficiency by decreasing iteration times of the global problem. Crack branching problem is also taken into consideration in current work. Numerical examples for dynamic cracks propagation are provided to demonstrate the effectiveness and robustness of the proposed method.

Experimental Study on the Identification and Diagnosis of Dynamic Crack Propagation in the Piston Rods of Process Gas Compressors in Underground Gas Storage

Ensuring the reliability of process gas compressors is critical for underground gas storage, as piston rod fractures can lead to serious accidents, such as natural gas leaks or explosions. On-time monitoring and early detection play a vital role in preventing catastrophic consequences, minimising costs, and reducing production losses due to unplanned downtime. This study presents a novel accelerated life-testing method designed to replicate the fracture events of reciprocating compressor piston rods. By accelerating the induced crack initiation and propagation to the final fracture, comprehensive analyses of the fracture results are performed to reveal the piston rod fracture mechanism and the resulting secondary damage to the unit. The research further presents an innovative approach for identifying piston rod crack propagation by means of acoustic emission. Through kinetic analysis and time–frequency domain analysis, the study elucidates two mechanisms responsible for triggering crack signals during the compressor operation: the contact impact between the crosshead pin and the bearing due to the piston rod load reversal, and crack propagation occurring before the maximum tensile load is reached. In addition, the study identifies the piston rod crack expansion signal frequency band and achieves a high-sensitivity identification of crack dynamic growth by extracting signal sub-band features associated with crack propagation. Then, a prediction model of the fatigue crack growth rate was established based on the AE energy release rate, which provides a quantitative assessment of dynamic crack propagation during compression. This method aims to provide a maintenance strategy for piston rod fractures, thereby increasing the operational safety of critical dynamic equipment in underground gas storage.

Singular integral method based closed form solution for moving EMPS model in semipermeable two‐equal‐collinear cracked MEE material

AbstractThis paper presents the analytical closed‐form solutions of moving two equal collinear semipermeable cracks in magneto‐electro‐elastic material considering the strip electric‐magnetic polarization saturation (EMPS) model. To simulate the dynamic/moving cracks problem, two equal collinear Yoffe type cracks moving with a constant subsonic velocity along the plane of the cracks is considered. The problem is solved by considering semipermeable crack face conditions and under the in‐plane electro‐magnetic‐mechanical loading. Applying distributed dislocation technique and symmetry of the collinear cracks, the problem is reduced into simultaneous singular integral equations which have been solved in closed form expressions using finite Hilbert approach. The explicit expressions for dynamic distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), and local stress intensity factors (LSIFs) are evaluated for both the cases of the EMPS model (magnetic zone is smaller or greater than electric zone). For evaluation of inner and outer electric and magnetic zone lengths (MZLs), an iterative approach is applied to solve the developed two non‐linear equations. Also, to implement the semipermeable crack‐face conditions, a bisection iterative method has been applied. Based on the developed closed form solutions, numerical studies are presented for standard fracture parameters with respect to crack propagation velocity, electrical loading and inter‐crack space distance. This study shows that electric displacement and magnetic induction defined over the crack‐surface for semipermeable conditions decrease whereas the numerical values of saturated zone lengths, COD, COP, COI, and LSIFs increase with increasing crack propagation velocity. Moreover, for both static and dynamic cracks problems, the significant crack‐interaction effects have been observed on all the studied fracture parameters except the crack‐face conditions.

Effects of Driving Parameters on TBM Dynamic Response and Cracking of the Disc Cutter Ring: A Case Study

Effects of Driving Parameters on TBM Dynamic Response and Cracking of the Disc Cutter Ring: A Case Study

Experimental and computational investigation of heat transfer during quenching of semi-solid aluminum plates under hot cracking condition

The present work attempts to study the cooling characteristics of 7050 aluminium alloy under semi-solid conditions during the jet impingement quenching. An aluminium plate heated to 485℃ (10% liquid fraction) is prone to hot cracks, causing large fluctuations in the temperature data. The 2-D direct heat transfer problem is formulated with the finite element technique, and moving boundary conditions are applied to simulate the quenching process. The heat flux is estimated from the boiling curve parameters (Qmax, TDNB, TLeid) by matching the simulated and experimental temperature data. The cracks are incorporated as the interface elements in the finite element domain along with the phase change model to simulatethe heat transfer phenomena. The influence of phase change and hot cracks on heat transfer is studied in detail with static and dynamic cracking conditions. The parity plot reveals that experimental and simulation results are in good agreement for uncracked plates, with an error range of ± 3% and R2 = 0.9987. Phase change incorporation improves the simulation results for cracked plates, reducing the error range from ± 10% (without phase change) to ± 5% (with phase change) along with R2 values of 0.9929 and 0.9863, respectively. The Boiling curve parameters for the cracked plate are found to be Qmax: 7.2 MW/m2, TDNB: 190℃, and TLeid: 450℃. Further, the findings show that the crack originates in the impingement zone of the quenched side of the plate.

The fully coupled thermo-mechanical dual-horizon peridynamic correspondence damage model for homogeneous and heterogeneous materials

To accurately address the thermally induced dynamic and steady-state crack propagation problems for homogeneous and heterogeneous materials involving crack branching, interfacial de-bonding and crack kinking, we propose the fully coupled thermo-mechanical dual-horizon peridynamic correspondence damage model (TM-DHPD). To this end, the integral coupled equations for TM-DHPD are firstly derived within the framework of thermodynamics. And then, the alternative dual-horizon peridynamic correspondence principle is used to derive the constitutive bond force state, heat flow state and their general linearizations. Moreover, the unified criterion for bond damage is proposed to characterize the internal bond damage in a single material and the interface bond damage in dissimilar materials. To ensure convergence and accuracy, the coupled equations are solved using the standard implicit method without the use of artificial damping. In both homogeneous and heterogeneous materials, some representative and challenging numerical cases are examined, such as dynamic crack branching in a centrally heated disk and multiple interface failure of thermal barrier coating. The numerical results are in good agreement with the available experimental results or the previous predictions, which shows the great potential of the proposed TM-DHPD in addressing the physics of numerous thermally induced fractures in the real-world engineering problems.

Development of Micro-mechanical Constitutive Model for Alumina at High Strain Rates Using Unified Mechanics Theory

Ceramic materials used in mechanical applications show variations in their properties due to the presence of cracks. Micro-cracks within the material (size, orientation and density) affect the ceramic material’s strength and other mechanical properties. This study developed a micro-mechanics-based model that accounts for the original orientation of micro-cracks and their propagation as wing cracks. Unlike other micromechanics-based models, the current model defines failure based on entropy associated with crack propagation within the material. Entropy is calculated from energy dissipation from crack propagation from the pre-existing flaws in the ceramic. The Unified Mechanics Theory (UMT) is used to define entropy-based damage in the ceramic material, in which a parameter called thermodynamic state index (TSI) is employed to describe the state of the material. A representative volume element (RVE) with a pre-existing flaw is used to calculate the energy dissipated during the wing crack propagation. The effect of various crack lengths and orientations is incorporated with a probability density function. The strain rate effects are implemented using dynamic crack growth law. The stress-strain curve at strain rate from quasi-static to high strain rate (10-3-106) is plotted for Alumina under dynamic compression.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Dynamic Crack Propagation of Ceramic Materials under High Temperature Thermal Shock

Dynamic Crack Propagation of Ceramic Materials under High Temperature Thermal Shock

Phase field modeling of dynamic fracture in elastoplastic composites with interfacial debonding

In this work, we extend a phase field formulation for dynamic ductile fracture to consider interfacial debonding in elastoplastic composites. The interfacial weak zone is created through a regularization of the sharp interfaces, and the singular strain part along the interfaces is approximated by using a Taylor expansion. Then, a strain density depending on the displacement jump related to matrix/inclusions decohesion is added to the total energy to take into account interfacial debonding. The coupling problems (displacement, plasticity and damage problems) are derived within the variational framework and a staggered iterative algorithmic procedure is described to solve the coupling problems. Numerical examples demonstrate that this method can handle the initiation, propagation, and interaction between bulk dynamic fracture and interface cracks, as well as the anisotropic behavior in the complex microstructure of elastic–plastic composite materials. It also indicates that this model is convergent in terms of mesh refinement.