Simulate Crack Initiation Research Articles

Study on the fracture behavior in clayey geomaterials under moisture diffusion by phase field modeling

Clayey geomaterials are prone to cracking under changing moisture conditions, which substantially compromises their engineering properties. When moisture intrusion and boundary constraints act in tandem on geomaterials, the relevance of multi-physics field processes to complex cracking phenomena remains underexplored. To provide deeper insight into the effect of moisture transport on the cracking behavior of clayey geomaterials, a theoretical model for moisture-induced fracture is proposed. The model combines moisture diffusion, volume deformation dependent on moisture conditions, and phase field fracture, and is solved using the finite element method with a user-defined element subroutine. The developed subroutine is applied to simulate soil desiccation experiments and mudstone water absorption tests. The results reveal that moisture gradients induce non-uniform expansion or shrinkage within the clayey geomaterials. The neighboring geomaterial particles mutually constrain these deformations, resulting in an internal stress field that serves as the primary cause of cracking. Stability and sensitivity analyses validate the reliability of the numerical framework. The proposed model can effectively simulate crack initiation, extension, and convergence during humidification or desiccation processes in both two and three dimensions. This study charts a feasible path for numerical simulation and mechanical mechanism exploration of cracking behaviors in clayey geomaterials during water migration.

A 3D peridynamic model for fracture analysis of transversely isotropic solids

The classical continuum mechanics (CCM) has limitations in simulating crack initiation and propagation, and the peridynamic (PD) theory overcomes these shortcomings. This study proposed a 3D transversely isotropic PD model based on the micro-beam bond model. Firstly, the micromoduli of the micro-beam bond applied to the transversely isotropic 3D solid model are derived based on the elastic matrix relationship between the different coordinate systems. Secondly, the strain energy density expressions of arbitrary material points are expressed in both the PD theory and the CCM theory using strain and elastic matrix under the assumption of homogenization, respectively. Finally, by equating the strain energy density expressions under the two theories based on the conservation of energy, the constitutive model parameters of the 3D transversely isotropic PD model are solved. Numerical examples of crack propagation demonstrate the effectiveness of the proposed model in addressing dynamic 3D fracture problems.

ANALYZING THE PERFORMANCE OF HIP CEMENT SPACERS: INVESTIGATION OF CRACK BEHAVIOR THROUGH A MULTISCALE APPROACH

Close collaboration between surgeons and engineers is paramount in the intricate process of designing and evaluating hip joint prostheses. In revision surgeries, cement spacers play a vital role, but their effectiveness hinges on the reinforcement of the cement, bone, and femur to minimize stress. To assess the fracture behavior of reinforced spacers, we employ a comprehensive three-dimensional approach that analyzes the three primary materials used for full stems: titanium, ceramics, and stainless steel. Our analysis focuses on evaluating the von Mises stress and stress intensity factor along the crack tip using linear elastic analysis. Additionally, we utilize the extended finite element Method (X-FEM) to simulate crack initiation and propagation in non-reinforced cement spacers. By comparing the results obtained from these two methods, we gain valuable insights into the influence of different materials on the performance and durability of reinforced spacers. Our findings unequivocally demonstrate that reinforcing spacers with ceramic and stainless-steel full stems are exceptionally effective techniques for enhancing the strength of hip spacers. Specifically, we observed a significant reduction of stress levels by 30% in various hip prosthesis components, along with a notable 23% decrease in the stress intensity factor for spacers reinforced with ceramic stems. These insights are invaluable for spacer designers and can contribute significantly to improving the durability of hip joint prostheses, ultimately minimizing the need for early hip revisions.

Phase field study on fracture behavior of crushable polymer foam

Polymer foam is a widely used material across various industries for its lightweight and exceptional energy absorption capability. Nevertheless, its porous structure and compaction properties present challenges in simulating crack initiation and propagation. The phase field method has attracted much attention for its advantages in predicting cracks. In this paper, we combine the phase field method with the “crushable foam” model and introduce the modified Drucker-Prager failure criterion to establish the phase field model of polymer foam materials. Material parameters are calibrated using experimental data from uniaxial compression, uniaxial tensile and shear punching experiments. The typical tensile, shear and compression instability fracture processes of polyurethane are then simulated using the proposed model, and the numerical results agree well with the experimental results. This indicates that the coupled phase-field crushable foam model not only exhibits the compaction properties of polymer foam materials but also accurately predicts its crack propagation under complex loading. Studying the fracture behavior of polymer foams under complex loads can enhance their engineering applications.

Physics-informed neural network frameworks for crack simulation based on minimized peridynamic potential energy

Physics-informed neural networks (PINNs), which are promising tools for solving nonlinear equations in the absence of labeled data, have been successfully applied for continuum field approximation in fluid mechanics, solid mechanics, thermodynamics, and other scientific and engineering problems. However, it is equally necessary to solve discontinuous problems such as cracking behaviors in structures and materials, which are challenging to describe using partial differential equations in traditional solid mechanics frameworks. In this work, PINNs are established with the constraint of integral–differential equations in bond-based peridynamic to simulate crack initiation and propagation behaviors in quasi-brittle plates. To solve the cracking behaviors, the initial displacements of the plate are determined by minimizing the total potential energy through the optimization of global network parameters. The subsequent displacements during crack initiation or propagation are characterized by transfer learning to accelerate convergence. The simulated crack paths for four cases with or without precracks are consistent with those obtained in existing studies based on experiments or numerical simulations. Moreover, the effects of network regularization and neuron scales on the nonlinear displacement characterization performance are investigated.

Finite Element Modelling and Experimental Validation of the Graphite Cutting Process

Graphite is extensively used in the engineering field due to its unique properties, and the study of its cutting mechanism has become particularly important. However, the brittle fracture mechanism of graphite makes it rather easy for cracks with a unique pattern of initiation and growth to develop when processing. Herein, the ABAQUS was selected to establish a finite element model (FEM) of the graphite cutting process. The internal crystal structure of graphite was modelled by a Voronoi structure, and a cohesion unit was globally embedded into the solid unit to simulate crack initiation and growth. In addition, the complete process of chip formation and removal was demonstrated. The analysis of the simulation results showed that the graphite material underwent three periodic cycles of material removal during the cutting process, i.e., large, tiny, and small removal stages. Meanwhile, the simulation results indicated that when ac was large enough, the crack gradually grew inside the graphite and then turned to the upper surface of the graphite. However, when ac was tiny enough, the cracks hardly expanded towards the inside of the graphite but grew upwards for a short period. Then, orthogonal cutting experiments of graphite were conducted, and the FEM was verified based on the experimental chip morphology, machined surface morphology, and current geometric model of the graphite cutting process. The simulation and experimental results were consistent. The hereby-presented FEM was a complement to simulations of the processing of brittle materials.

An enhanced adaptive coupling strategy of peridynamics and finite element method via variable horizon approach for simulating quasi-static fracture problems

An enhanced adaptive coupling method of peridynamic (PD) theory and the finite element method (FEM) is performed that combines the advantages of both approaches and can be used to simulate quasi-static fracture problems. In the proposed model, PD is used to simulate crack initiation and propagation, whereas the FEM is used to simulate domains without damage to improve efficiency. The influence of ghost forces is reduced by introducing a transition subregion with a variable horizon, thereby significantly improving the accuracy of the model, which is verified by application to a plane stress problem. The conventional coupling model requires pre-partitioning of the solution domain, which is difficult to achieve when modeling certain problems, such as the initiation of cracks at unknown locations. Hence, the adaptive conversion criterion is introduced to ensure that subregions automatically evolve as cracks grow, thereby obviating the need for prior knowledge of crack propagation paths. The proposed model is applied to three standard laboratory tests of quasi-static fracture and its performance is validated by the good agreement of its results with reference solutions or experimental observations. The model accurately simulates complex fracture problems involving crack initiation, irregular crack propagation, and crack coalescence.

A phase field model to simulate crack initiation from pitting site in isotropic and anisotropic elastoplastic material

A multiphysics phase field framework for coupled electrochemical and elastoplastic behaviors is presented, where the evolution of complex solid-electrolyte is described by the variation of the phase field variable with time. The solid-electrolyte interface kinetics nonlinearly depends on the thermodynamic driving force and can be accelerated by mechanical straining according to the film rupture-dissolution mechanism. A number of examples in two- and three- dimensions are demonstrated based on the finite element-based MOOSE framework. The model successfully captures the pit-to-crack transition under simultaneous electrochemical and mechanical effects. The crack initiation and growth has been demonstrated to depend on a variety of materials properties. The coupled corrosion and crystal plasticity framework also predict the crack initiation away from the perpendicular to the loading direction.

A smeared-crack-based field-enriched finite element method for simulating cracking in quasi-brittle materials

When the node search strategy is used to determine the crack damage domain in field-enriched finite element method, some nodes may be repeatedly calculated or missed. To overcome the drawback, the smeared-crack-based field-enriched finite element method is proposed to simulate crack initiation and propagation. The exponential function with two parameters is employed to accurately define the damage domain and to represent cracks. The reasonable values of parameters of exponential function are defined by the convergence study. Finally, the proposed method is applied to investigate crack initiation, propagation and coalescence in quasi-brittle materials, and the results show that the proposed method can solve the crack propagation problem effectively.

A 2D/3D implicit gradient-enhanced nonlocal meso-scale damage model for deformation and fracturing of brittle materials

An implicit gradient-enhanced nonlocal meso‑scale damage model is developed to investigate deformation and fracturing of brittle materials. In the model, an implicit gradient integration scheme is adopted to deal with mesh dependency and strain localization. The mechanical parameters are assigned randomly using a Weibull statistical distribution to reflect the material heterogeneity at the meso‑scale. A linear elastic damage constitutive law with residual strength is used to describe the stress-strain relationship at the mesoscale and the Mohr-Coulomb criterion as well as the tensile stress criterion are used to evaluate the damage of the elements in tension or shear. The local equivalent strain is replaced by a nonlocal description employing the non-local implicit gradient model. Benchmark tests are conducted to document the potential of the model in simulating crack initiation and propagation processes in brittle materials. The benchmark tests also demonstrate that the proposed non-local damage model can effectively achieve strain localization and eliminate mesh dependency to some extent.

COUPLED CRYSTAL PLASTICITY PHASE-FIELD MODEL FOR DUCTILE FRACTURE IN POLYCRYSTALLINE MICROSTRUCTURES

A wavelet-enriched adaptive hierarchical, coupled crystal plasticity, phase-field finite element model is developed in this work to simulate crack initiation and propagation in complex polycrystalline microstructures. The model accommodates initial material anisotropy and crack tension-compression asymmetry through orthogonal decomposition of stored elastic strain energy into tensile and compressive counterparts. The crack evolution is driven by stored elastic and defect energies, resulting from slip and hardening of crystallographic slips systems. A finite element model is used to simulate the fracture process in a statistically equivalent representative volume element reconstructed from electron back-scattered diffraction scans of experimental microstructures. Multiple numerical simulations with the model exhibits microstructurally sensitive crack propagation characteristics.

New nonlocal multiscale damage model for modelling damage and cracking in quasi-brittle materials

A new method for the simulation of crack initiation and propagation in quasi-brittle materials is proposed that combines the scaled boundary finite element method and a nonlocal multiscale damage model. The scaling centre of the scaled boundary finite element subdomain is taken as the material point. Microscopic damage is defined in terms of the stretch rate of bonds of material points, and macroscale topologic damage is evaluated as the weighted average of microscale damage over bonds in the influence domain. Through the energetic degradation function of phase field analysis, which connects energy-based damage and macroscale topologic damage, the nonlocal multiscale damage model is inserted into the framework of the scaled boundary finite element method. The quadtree discrete mesh technique is used to rapidly obtain a high-quality multilevel mesh by taking full advantage of the hanging nodes that it allows. A detailed arc length method for solving nonlinear equations is also presented in this paper. Four typical examples, one Mode I and three mixed-mode cracking simulations, show that the proposed method can be used to simulate crack initiation and propagation in quasi-brittle materials and correctly describe crack propagation paths and load-deformation curves. Compared with other methods, the nonlocal multiscale damage model presented in this paper can provide a more accurate description of local cracking damage zones, and the results are more reasonable, with higher calculation accuracy and efficiency. The numerical examples also indicate that there is no mesh sensitivity problem when the mesh size of the damage process region is less than 1/5 of the radius of the influence domain.

Numerical simulation of rock erosion performance of a high-speed water jet using an immersed-body method

Water jet drilling (WJD) is an effective technique for drilling micro-holes in the subsurface for reservoir stimulation . This study aims to investigate numerically the failure mechanism of rock during WJD and to assess the WJD performance before drilling. A 3D fluid-solid coupling model is developed for simulating WJD by coupling a mechanical solver based on the combined finite-discrete element method (FDEM) with a fluid solver using an immersed-body method. The new numerical model is capable of simulating crack initiation and propagation and fragment removal under the impact load of a high-speed water jet. The poroelastic effect is implemented via Biot's theory of poroelasticity . The numerical results show that: (1) rock failure is only observed in the Gildehaus sandstone with the lowest strengths among the three types of rock tested, (2) most of the cracks are tensile failures and pure shear cracks are rare, mixed mode cracks account for 15%∼40% of the total crack number depending on the mechanical boundary conditions , (3) increased water back pressure significantly suppresses jet erosion. The poroelastic effect on the rock failure is insignificant in the mesoscale simulations and will be further investigated using a microscale model in future.

Micromechanics-based phase field fracture modelling of CNT composites

We present a novel micromechanics-based phase field approach to model crack initiation and propagation in carbon nanotube (CNT) based composites. The constitutive mechanical and fracture properties of the nanocomposites are first estimated by a mean-field homogenisation approach. Inhomogeneous dispersion of CNTs is accounted for by means of equivalent inclusions representing agglomerated CNTs. Detailed parametric analyses are presented to assess the effect of the main micromechanical properties upon the fracture behaviour of CNT-based composites. The second step of the proposed approach incorporates the previously estimated constitutive properties into a phase field fracture model to simulate crack initiation and growth in CNT-based composites. The modelling capabilities of the framework presented is demonstrated through three paradigmatic case studies involving mode I and mixed mode fracture conditions.

Study of wave propagation in discontinuous and heterogeneous media with the dynamic lattice method

The development of a new dynamic lattice element method (dynamicLEM) as well as its application in the simulation of the propagation of body waves in discontinuous and heterogeneous media is the focus of this research paper. The conventional static lattice models are efficient numerical methods to simulate crack initiation and propagation in cemented geomaterials. The advantages of the LEM and the developed dynamic solution, such as simulation of arbitrary crack initiation and propagation, illustration and simulation of existing inherent material heterogeneity as well as stress redistribution upon crack opening, opens a new engineering field and tool for material analysis. To realize the time dependency of the dynamic LEM, the equation of motion of forced vibration is solved while using the Newmark-beta method and implementing the non-linear Newton–Raphson Jacobian method. The method validation is done according to the results of a boundary element method (BEM) in the plane P-SV-wave propagation within a plane strain domain. Further tests comparing the generated wave types, simulation and study of crack discontinuities as well as inherent heterogeneities in the geomaterials are conducted to illustrate the accurate applicability of the new dynamic lattice method. The results indicate that with increasing heterogeneity within the material, the wave field becomes significantly scattered and further analysis of wave fields according to the wavelength/heterogeneity ratio become indispensable. Therefore, in a heterogeneous medium, the application of continuum methods in relation to structural health monitoring should be precisely investigated and improved. The developed dynamic lattice element method is an ideal simulation tool to consider particle scale irregularities, crack distributions and inherent material heterogeneities and can be easily implemented in various engineering applications.

Peridynamic Simulation of Cracking Behavior in Thermal Barrier Coatings

Abstract Cracking-induced fracture in thermal barrier coatings (TBCs) is one of the most severe failure mechanisms among TBCs failure cases. Current numerical simulation of cracking behavior in TBCs are mostly developed by FEM-based methods, which have their own disadvantages. The concept of peridynamic (PD) is proposed and developed these years to deal with discontinuous problems, providing new ideas to simulate crack initiation and propagation in TBCs. In this paper, a PD-based numerical model of TBCs is built to discuss cracking behavior in the top coat (TC) layer. Simulation results validate the effectiveness and accuracy of PD in TBCs cracking analysis, compared with SEM observations. And effects of pre-existed cracks in TC, which could obviously interfere original crack propagation path, are also proved and discussed. It could be concluded that PD would be a powerful tool in TBCs crack propagation predictions if provided with more supportive experiment data.

Cohesive element simulations capture size and confining stress dependence of rock fracture toughness obtained from burst experiments

Numerical analysis of growth of cracks from a notched borehole under confinement demonstrates the impact of size and confining stress on initiation and propagation behavior of rock fracture at lab scale. A Finite Element framework employing plane strain cohesive elements is applied to simulate crack initiation and propagation behavior. The model is validated by comparing predictions to results of laboratory tests known as “burst experiments”, which have been used for several decades to characterize rock fracture toughness under confined conditions. The simulations capture the crack initiation behavior with three parameter traction-separation law that is the same for all tests. This contrasts with approaches that apply linear elastic fracture mechanics wherein ad hoc stress and size dependence must be introduced to the fracture toughness. Furthermore, the simulations also confirm the limitation of the typical burst experiment configuration owing to ambiguity in identifying the moment of crack initiation, thereby pointing to a straightforward modification of the experiment that will remove this ambiguity, while also indicating that pairing Acoustic Emission monitoring with the typical setup in order to independently detect crack initiation can enable complete characterization of the traction-separation law.

A Fragile Points Method, with an interface debonding model, to simulate damage and fracture of U‐notched structures

AbstractNotched components are commonly used in engineering structures, where stress concentration may easily lead to crack initiation and development. The main goal of this work is to develop a simple numerical method to predict the strength and crack‐growth‐path of U‐notched specimens made of brittle materials. For this purpose, the Fragile Points Method (FPM), as previously proposed by the authors, has been augmented by an interface debonding model at the interfaces of the FPM domains, to simulate crack initiation and development. The formulations of FPM are based on a discontinuous Galerkin weak form where point‐based piece‐wise‐continuous polynomial test and trial functions are used instead of element‐based basis functions. In this work, the numerical fluxes introduced across interior interfaces between subdomains are postulated as the tractions acting on the interface derived from an interface debonding model. The interface damage is triggered when the numerical flux reaches the interface strength, and the process of crack‐surface separation is governed by the fracture energy. In this way, arbitrary crack initiation and propagation can be naturally simulated without the need for knowing the fracture‐patch before‐hand. Additionally, a small penalty parameter is sufficient to enforce the weak‐form continuity condition before damage initiation, without causing problems such as artificial compliance and numerical ill‐conditioning. As validations, the proposed FPM method with the interface debonding model is used to predict fracture strength and crack‐growth trajectories of U‐notched structures made of brittle materials, which is useful but challenging in engineering structural design practices.

Phase-Field Modeling Fracture in Anisotropic Materials

The phase-field method is a widely used technique to simulate crack initiation, propagation, and coalescence without the need to trace the fracture surface. In the phase-field theory, the energy to create a fracture surface per unit area is equal to the critical energy release rate. Therefore, the precise definition of the crack-driving part is the key to simulate crack propagation. In this work, we propose a modified phase-field model to capture the complex crack propagation, in which the elastic strain energy is decomposed into volumetric-deviatoric energy parts. Because of the volumetric-deviatoric energy split, we introduce a novel form of the crack-driving energy to simulate mixed-mode fracture. Furthermore, a new degradation function is proposed to simulate crack processes in brittle materials with different degradation rates. The proposed model is implemented by a staggered algorithm and to validate the performance of the phase-field modelling, and several numerical examples are constructed under plane strain condition. All the presented examples demonstrate the capability of the proposed approach in solving problems of brittle fracture propagation.

A novel physical continuum damage model for the finite element simulation of crack growth mechanism in quasi-brittle geomaterials

This paper addresses a physical damage model and continuum damage-based fracture simulation procedure for simulating crack initiation, growth and cracks coalescence of quasi-brittle geomaterials. The model is proposed by using the principle of minimum dissipative energy combining with Drucker-Prager criterion, in which every parameter of the damage model has clear physical meaning. The procedure coupled with the damage model can be used to simulate competitive fracture process based on finite element method, which is implemented by using the secondary developing tool of ANSYS software. Two benchmark tests of the two pre-cracked rock-like disk specimens were carried. The predicted crack growth paths matched well with the corresponding experimental results. Thus the fracture simulation of dog-bone specimens with different sizes were carried to consider the scale effect, which support the effectiveness and ability of the developed procedure and damage model.