Cracks In Brittle Materials Research Articles

3D internal crack propagation in brittle solids under non-uniform temperature field: Experimental and numerical simulation

In the field of engineering, elevated temperatures often induce thermal stress. Especially in brittle materials, the propagation of internal cracks under such thermal stress is frequently the primary cause of failure. We utilize the 3D internal laser-engraved crack technology to create internal cracks at various locations inside the half-Brazilian disk specimens. By precisely controlling the power of the heating device, we achieved temperature non-uniformity of the external heat source, resulting in uneven heating of the material’s surface. Simultaneously, by adjusting the geometry of the material and using semi-Brazilian disk specimens, we generated uneven temperature gradients and thermal capacities along different heat conduction paths. The internal cracks at different locations also affect the distribution of thermal stress in the material, further influencing the formation of the non-uniform temperature fields (NUTF). Through the above methods, we successfully conducted physical experiments on the 3D propagation of internal cracks in brittle materials under NUTF. Additionally, we utilized J-integral and the finite element method for thermal analysis to conduct thermo-mechanical coupled 3D numerical simulations. Furthermore, we employed a polarising microscope to analyze the microscopic morphology of 3D internal cracks. Finally, we revealed the mechanism of 3D internal crack propagation under NUTF. The results show that prefabricated internal cracks in group A produce “n-shaped” crack at a height of 15 mm and “u-shaped” cracks at heights of 25 mm and 35 mm. Meanwhile, in group B, the eccentric prefabricated internal cracks ultimately produce “s-shaped” cracks. Through analysis, it was determined that the differential formation occurred due to relative sliding between the upper and lower surfaces of the crack under longitudinal shear stress induced by NUTF. Group A cracks have smooth surfaces, which are mode I-II cracks. group B generated “lance-like” fractures with obvious “anti-binary tree”, which are mixed mode I-II-III cracks. These findings provide an experimental and theoretical basis for the study of 3D internal crack propagation modes under NUTF and deepen the understanding of fracture mechanics in brittle materials.

Dynamic propagation of moving cracks in brittle materials by field-enriched finite element method

We propose a field-enriched finite element model to simulate the dynamic growth of moving cracks in brittle solids. The paper introduces the dynamic model and verifies its accuracy by analyzing dynamic stress intensity factors during the propagation of a mode-I moving crack. We also simulate crack bifurcation using a specific criterion. Our numerical method successfully reproduces experiments, including the Kalthoff-Winkler experiment, three-point bending test under impact load, and compact compression specimen (CCS) experiment. Finally, we investigate how the location of a circular hole influences the propagation paths of a pre-existing straight crack using a numerical model including both the hole and the crack (COSSCC). Several numerical examples demonstrate the ability of dynamic field-enriched finite element method in simulating dynamic moving cracks.

Analysis of Micro-Evolution Mechanism of 3D Crack Initiation in Brittle Materials with Hole under Uniaxial Compression.

This article investigates the microscopic mechanism of crack initiation and propagation in three-dimensional embedded cracks in brittle materials containing circular holes. First, a method for the development of transparent, brittle materials is proposed. Second, UCS tests were conducted on transparent, brittle materials containing circular holes and internally embedded three-dimensional cracks. Finally, a numerical model was established in PFC3D to analyze the crack initiation and propagation mechanism. The results show that when α = 0° (α refers to the pre-existing crack inclination), the upper tip of the pre-existing crack appears as a tensile wing crack, and the lower tip of the pre-existing crack appears as a tensile-shear mixed crack. When α = 30°, no wing crack appears, and the tensile crack on the fracture surface only appears after the hole cracks. When α = 60 and 90°, a tensile wing crack and an anti-wing tensile-shear mixed crack appear at the upper tip of the pre-existing crack. A tensile wing crack appears at the lower tip of the pre-existing crack and appears "self-limiting". During the propagation of wing cracks to the surface of the specimen, the transition sequence of the crack propagation mechanism is tensile through failure-tension-shear mixed failure-tensile failure. It can be seen that the interaction between the crack and hole has an important influence on the evolution mechanism of the crack and the failure mode of the specimen.

Simulation of the dynamic cracking of brittle materials using a nonlocal damage model with an effective strain rate effect

In this study, a nonlocal multiscale damage model that considers the effect of a strain rate is presented. Moreover, this model is combined with the scaled boundary finite element method (SBFEM) and quadtree mesh for dynamic crack propagation in quasi-brittle materials. The scaling centre of each SBFEM subdomain was selected as the material point, and the bond connecting two material points was referred to as the material bond. Microscopic damage was quantified based on the stretch rate of the material bond, and macroscale topological damage was calculated by taking the weighted average of the microscopic damage over the bonds within the influence domain. The bell distribution function is utilised as the weight function in the calculation of the nonlocal weight function. To account for the impact of the strain rate during dynamic loading, an effective rate R is introduced to enhance multiscale damage by modifying the damage threshold and bond softening coefficient throughout the analysis process. By analysing the energetic degradation function of the phase field, which establishes a connection between the macroscale topological damage and energy-based damage, a nonlocal multiscale damage model was incorporated into the framework of the SBFEM. Quadtree mesh discretization was employed to achieve rapid and high-quality multilevel mesh generation by effectively utilising the hanging nodes. Three typical dynamic cracking examples were simulated using the proposed model, and the results were compared with the relevant experimental results and references. The results show that the method is suitable for accurate dynamic cracking simulation in quasi-brittle materials. Moreover, the results indicate that the proposed method can spontaneously simulate dynamic crack bifurcation without introducing additional crack bifurcation criteria. For a compact tensile test of concrete under different loading rates, the method proposed in this study can accurately simulate the corresponding failure modes. The results also show that without considering the effect of the strain rate, the damage develops rapidly in an unconstrained state, which is inconsistent with the actual case.

Crack branching at low tip speeds: spilling the T

Using the criterion that a crack will extend along the direction of maximum circumferential stress, this paper demonstrates the influence of the coupling between the crack-parallel T-stress and the tip speed on the directional (in)stability of dynamics cracks in brittle materials, i.e., branching, turning, and limiting velocities. The proposed (in)stability criterion evolves within the theory of dynamic fracture: we build on the work of Ramulu and Kobayashi (1983) by introducing a reference distance ahead of the crack-tip to incorporate the contribution of the higher-order terms in the asymptotic solution of the elastic crack-tip fields. The theoretical aspect is first explored, a methodology to numerically (and experimentally) advocate the instability—as a co-action of T-stress and a fast-running crack—is then proposed and validated on Borden et al. (2012)’s branching benchmark. An experimental setup combining Ultra-High-Speed High-Resolution imaging with advanced Digital Image Correlation algorithms and a novel crack-branching inertial impact test enables for never-seen-before quantification of the rich dynamical behaviour of the fracture. This permits the experimental validation of the developed crack (in)stability criterion.

A phase-field-based multi-physics coupling numerical method and its application in soil–water inrush accident of shield tunnel

The mixed-mode cracking of brittle materials in multi-physics coupling problems has always been a research hotspot. In this study, a phase-field-based multi-physics coupling numerical method is established to simulate the mixed-mode cracking of brittle materials under fluid–structure coupling. The proposed method is available to simulate the mixed-mode cracks of arbitrary topology, and the cracking behavior is governed by a crack evolution equation. To ensure consistency of the crack evolution equation, the crack-driving force is innovatively unified with the critical energy release rate. The phase-field-based multi-physics coupling numerical method is implemented in the finite element framework. Then, the proposed method is applied to simulate the structural discontinuous crack damage (SDCD) induced by soil–water inrush in shield tunnel under complicated geological conditions with confined water. Compared with the field inspection and monitoring, the numerical model performs well in simulating the SDCD and deformation of tunnel lining. It is also found that the soil–water inrush has a significant effect on the distribution of water-earth pressure acting on the tunnel lining, and the internal force of tunnel lining is redistributed during the evolution of SDCD.

Initiation and propagation of a single internal 3D crack in brittle material under dynamic loads

Different defects are widely distributed inside natural rock masses, and the development of these defects poses a potentially severe threat to the entire structural stability and safety. Most studies at present are concentrated on the propagation of two-dimensional (2D) penetrated cracks under static loads. In this paper, a series of tests were carried out on cubic glass specimens containing a closed pre-crack using a split Hopkinson pressure bar (SHPB) system, aiming to investigate the internal three-dimensional (3D) crack growth under dynamic compression. The results indicate that the dynamic compressive strength of the cubic specimen is influenced by the inclination direction of the 3D pre-crack. Theoretical analysis of the circumferential stress field at the pre-crack tip reveals the mechanism behind dominant crack initiation and favorable direction, which are also affected by non-singular T stress along and perpendicular to the pre-crack plane, as well as friction between crack planes. Through the post-mortem examination, the mode III fracture characteristics, crack bifurcation and Wallner lines are observed in fracture morphology. The terminal length of wrapped wing cracks subjected to dynamic loads is sensitive to pre-crack inclination angle, while it is approximately 1–1.5 times the pre-crack radius under static compression.

Prediction of ring crack initiation in ceramics and glasses using a stress–energy fracture criterion

AbstractCrack initiation in brittle materials upon spherical indentation is associated with the tensile radial stresses during loading. However, location of crack onset often differs (offset) from the site of maximal stress. In addition, experiments reveal a strong dependency of crack initiation forces on geometrical parameters as well as the surface condition of the sample. In this work, a coupled stress–energy fracture criterion is introduced to describe the initiation of ring cracks in brittle materials, which takes into account the geometry of the contact and the inherent strength and fracture toughness of the material. Several experiments reported in literature are evaluated and compared. The criterion can explain the location offset of the ring crack upon loading, as observed in various ceramics and glasses. It also predicts the ring crack initiation force upon contact loading, provided that surface compressive stresses, introduced during grinding or polishing processes, are taken into account. Furthermore, the stress–energy criterion may be employed to estimate the surface residual stress of ceramic parts, based on simple contact damage experiments.

Simulation of heat conduction and thermal cracking of brittle materials using the particle-based discontinuous deformation analysis

This paper proposes a particle heat conduction and expansion model (PHCE) in the context of particle-based discontinuous deformation analysis (PDDA) to simulate the heat conduction and thermal cracking of brittle materials. The thermal-mechanical coupling model consists of three parts. In the first part, a virtual rectangular heat conduction channel is assumed between each active contact pairs. The temperature distribution is solved based on the heat conduction equation and the network of the channels. In the second part, the particle radii are updated according to the thermal expansion. In the third part, the mechanical analysis is carried out with the new particle radii. To correctly reproduce the macroscopic thermal conductivity, a geometrical correction factor is introduced, which is found related to the porosity and coordination number. The proposed coupling model, abbreviated as PHCE-PDDA, is verified by three examples, the steady-state heat conduction, transient heat conduction and the thermal mechanical coupling test. Furthermore, two thermal cracking problems are also modeled. The initiation and propagation of the thermal cracks can be well captured. The final crack patterns agree well with those observed from experiments, indicating that the proposed method is effective for the modelling of heat conduction and thermal cracking in brittle materials.

Reduction of Cracks in Marble Appeared at Hydro-Abrasive Jet Cutting Using Taguchi Method.

The appearance of cracks in brittle materials in general and in marble, in particular, is a problem in the hydro-abrasive jet cutting process. In this paper is presented a method to reduce the appearance of cracks when cutting with a hydro-abrasive jet of marble by using statistical analysis. The Taguchi method was used, establishing the main parameters that influence the process. Research design was based on performing experiments by modifying the parameters that influence the process. In this way, it has been shown that the stochastic effects resulting from the marble structure can be reduced. A careful study was made of the behavior of marble under the action of the hydro-abrasive jet, and of the behavior of the whole process in the processing of brittle materials. Results of experiments confirmed the hypothesis that statistical analysis is a procedure that can lead to a decrease in the number of cracks in processing. The measurement was performed with precise instruments and analyzed with recognized software and according to the results obtained, the reduction of the number of cracks is achieved through use of low pressure, a minimum stand-off distance and a small tube diameter. In this way, the paper presents a new and effective tool for optimizing the cutting with a hydro-abrasive jet of marble.

A new 3D continuous-discontinuous heat conduction model and coupled thermomechanical model for simulating the thermal cracking of brittle materials

This paper proposes a new 3D continuous-discontinuous heat conduction model to consider the thermal resistance effect of cracks and dynamic crack propagation during heat transfer. Combining this heat conduction model and the finite-discrete element method (FDEM), we construct a coupled thermomechanical model for solving thermal cracking problems in brittle materials. The mechanical fracture calculation utilizes virtual joint elements between adjacent solid elements for fracture simulation. On the other hand, virtual joint elements are not included in the heat conduction model to improve numerical efficiency. When new cracks are generated, the node sharing relationship is dynamically updated in the heat conduction calculation to consider the thermal resistance effect of cracks. In this study, the proposed models are verified by simulating heat transfer, coupled thermomechanical, and thermal cracking problems in brittle materials. The numerical simulations are consistent with analytical solutions, and a complex thermal crack process can be realistically captured. These numerical examples verify the correctness of the proposed models, which can be powerful tools for solving heat transfer, coupled thermomechanical, and thermal cracking problems in brittle materials.

Discussion of hardening effects on phase field models for fracture

Phase field models have been successfully applied in recent years to a variety of fracture mechanics problems, such as quasi-brittle materials, dynamic fracture mechanics, fatigue cracks in brittle materials, as well as ductile materials. The basic idea of the method is to introduce an additional term in the energy functional describing the state of material bodies. A new state variable is included in this term, the so-called phase field, and enables to determine the surface energy of the crack. This approach allows to model phenomena such as crack initiation, crack branching and buckling of cracks, as well as the modelling of the crack front in three-dimensional geometries, without further assumptions. There is yet no systematic investigation of the influence of strain hardening on crack development within the phase field method. Thus, the aim of the paper is to provide an analysis of the effect of kinematic and isotropic hardening on the evolution of the phase field variable.

Spatial and Temporal Discreetness as a Crucial Property of the Dynamic Fracture Process

The paper discusses the dynamic propagation of cracks in brittle materials under various loads. The crack propagation is studied under both quasi-static and the shock-pulse loading conditions. Particular attention is paid to the dependences characterizing the crack propagation and having a non-stationary character. Thus, for the case of crack propagation under quasi-static loading, the crack velocity oscillations phenomenon is investigated. The problem related to the scatter of the stress intensity factor values which is observed in a number of experiments in course of the crack propagation under high-rate loading conditions is studied. The studies have been carried out using the finite element method with the structure–time fracture which is introduced into the computational scheme and which fundamentally determines the discrete mechanism of the fracture processes at a given scale level. Both quantitative and qualitative comparison of the calculation results with the available experimental data has been carried out. It is shown that taking into account the spatial and temporal discretization of the process makes it possible to explain a number of experimentally observed effects that do not fit into the traditional theoretical concepts of the dynamic fracture theory.

An Experimental and Numerical Study on the Influence of Filling Materials on Double-Crack Propagation

Filling materials such as clay or sand widely exist in natural rock joints and work as weak bonds between the joint surfaces. The fillings affect rock deformation and failure behavior, and show different influences in terms of single crack or multiple cracks. While most of the literature have focused on unfilled cracks in brittle materials, this study aims to investigate various filling materials on the crack behavior, e.g., initiation, secondary cracks and peak strength. In this paper, the crack propagation in rock-like specimens with double-filled and unfilled cracks are investigated experimentally and numerically. Uniaxial compression tests were conducted and the experimental observations indicate that the peak stress and first crack initiation stress of the specimens vary with different geometries and different filling materials, while the crack initiation location and the pattern of crack coalescence show similar behavior between filled and unfilled cracks. In parallel to the experimental tests, numerical simulations were carried out using a modified phase field model (PFM) to complement the experiments and provide a new perspective. The PFM is found to produce consistent stress–strain curve, strength, and crack patterns with those observed in the experimental tests for both unfilled and filled cracks.

Extended Voronoi cell finite element method for multiple crack propagation in brittle materials

This paper introduces a new extended Voronoi cell finite-element method (X-VCFEM) for modelling the propagation of multiple cracks in brittle materials. The direction of the crack propagation is adaptively determined in terms of the maximum energy release rate near the crack tip, and we apply a remeshing strategy that a node at a last incremental crack tip in the crack advance process is replaced by a node pairs to realize the gradual crack propagation. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the assumed stress hybrid formulation which also includes the polynomial terms and the reciprocal terms. Then several numerical examples are used to demonstrate the effectiveness and accuracy of X-VCFEM enriched by some singular stress terms of Williams expansion by comparing X-VCFEM results with those computed by the commercial finite element package ABAQUS or established results in the literature. At last, two numerical examples are given to simulate multiple crack propagation in brittle media. The effects of morphological distributions such as length, orientation and dispersion on the crack propagation are studied. It is obvious that the X-VCFEM has great advantage of analyzing large regions of the microstructure with multiple growing and interacting cracks.

The characteristics of high speed crack propagation at ultra high loading rate

It is important to understand the characteristics of high speed crack in brittle materials under ultra high loading rate forming through impact loading condition, which is important for understanding the impact damage evolution of ceramics and solid explosives. In this paper, a lattice spring model, which can accurately show the mechanical properties of brittle materials, is used to study the evolution law and mechanism of crack path and crack velocity in brittle materials under ultra high loading rate. This model uses the quantitative parameter mapping method proposed by Gusev to solve the spring stiffness coefficient of the model accurately, and the fracture criterion of the model based on the energy balance principle of Griffith is set up. Simulations show that the path of high speed crack behave the evolution process of a single crack and then micro-branching crack and bifurcation crack finally under the influence of ultra high loading rate. The crack propagation distance between the beginning and the bifurcation decreases with the increase of the loading rate; the crack bifurcation is not immediately after the crack initiation, but as the crack propagation speed reaches the critical value, the expansion path produces more secondary cracks, and then the crack is bifurcated. With the increase of loading rate, the average velocity of cracks gradually increases in three stages, but it shows a different variation after reaching the stable value. In the single crack stage, the steady average velocity is 0.584 times the Rayleigh wave velocity (CR), and there exists only a very small velocity oscillation; the steady value of the average crack velocity corresponding to the differential fork phase is 0.5 times the Rayleigh wave velocity, accompanied by a certain oscillation; The average speed of the stable crack corresponding to the bifurcation stage is much higher than the value of the first two stages, and it can reach 0.638 times the Rayleigh wave speed. It is also accompanied by obvious speed oscillation. The study of the propagation of cracks under different loading rates can predict the internal crack growth rate, propagation direction, and extension distance of brittle materials such as ceramics and rocks.

Study on the arresting mechanism of two arrest-holes on moving crack in brittle material under impacts

To develop the technique of arresting running cracks is essential because it can be used to protect cracked structures being further damaged. In this paper, a specimen of large semicircular edge crack with two arrest-holes (LSECTH) was proposed. The specimens were made of cement, river sand, fly ash and water. Impact experiments were carried out in the LSECTH specimens with different two-hole spacing (35 mm, 40 mm, 45 mm, 50 mm, 55 mm, 60 mm and 70 mm) under drop-weight impacts. Crack propagation gauges (CPGs) were used to monitor the fracturing time and crack speed. The interaction characteristic between the crack and two arrest-holes was investigated numerically by the AUTODYN code. In the numerical models, the failure criterion of maximum tensile stress and shear stress were employed for the brittle material. The crack propagation path, the circumferential stress of crack tip and the stress state between the two arrest-holes were analyzed. The calculation results indicate that compressive stresses between the two arrest-holes induced by the shape change from circle to ellipse play a key role in confining the vertical crack propagation. Both experimental and numerical results indicate that the two arrest-holes have suppressing action on moving crack; as the two arrest-hole spacing decreases, the suppressing action intensifies.

Shape Evolution of Unstable, Flexural Cracks in Brittle Materials

In this manuscript, the crack-shape evolution of unstable, flexural cracks was modeled using a continuum mechanics approach applied to dynamic, brittle, and elliptical cracks. The crack-shape evolution was first computed analytically for both flat and fractal cracks and subsequently compared to experimental values inferred from fractographic features present on silicate glass, gallium arsenide, and silicon single crystals fractured in bending. The trends predicted by the analytical model were consistent with the fractographic observations prior to the onset of crack-tip instabilities. It was determined that the effect of the surface roughness was to slow down the crack and to decrease the local crack-front radius of curvature which, in flexural cracks, led to crack shapes elongated along the free surface direction. This work represents the first attempt to predict the crack-shape evolution in rough, brittle samples fractured in bending and to understand the role played by the surface roughness during fast, unstable propagation.

Crack propagation simulation in brittle elastic materials by a phase field method

To overcome the difficulties of re-meshing and tracking the crack-tip in other computational methods for crack propagation simulations, the phase field method based on the minimum energy principle is introduced by defining a continuous phase field variable φ (x) ∈ [0,1] to characterize discontinuous cracks in brittle materials. This method can well describe the crack initiation and propagation without assuming the shape, size and orientation of the initial crack in advance. In this paper, a phase field method based on Miehe's approach [Miehe et al., Comp. Meth. App. Mech. Eng. (2010)] is applied to simulate different crack propagation problems in two-dimensional (2D), isotropic and linear elastic materials. The numerical implementation of the phase field method is realized within the framework of the finite element method (FEM). The validity, accuracy and efficiency of the present method are verified by comparing the numerical results with other reference results in literature. Several numerical examples are presented to show the effects of the loading type (tension and shear), boundary conditions, and initial crack location and orientation on the crack propagation path and force-displacement curve. Furthermore, for a single edge-cracked bi-material specimen, the influences of the loading type and the crack location on the crack propagation trajectory and force-displacement curve are also investigated and discussed. It is demonstrated that the phase field method is an efficient tool for the numerical simulation of the crack propagation problems in brittle elastic materials, and the corresponding results may have an important relevance for predicting and preventing possible crack propagations in engineering applications.

The effect of a pre‐existing crack on a running crack in brittle material under dynamic loads

AbstractBrittle material usually contains plenty of cracks or micro‐cracks, which raises a question that how a pre‐existing crack affects a running crack as they are approaching. In order to investigate such issue, impact experiments were conducted by using double crack semi‐circle (DCSC) specimens. Polymethyl methacrylate (PMMA) was selected to make the DCSC specimens, and a modified SHPB system was used to perform the impact tests. The finite difference code AUTODYN was employed to simulate the crack propagation behavior and propagation path, and the simulated crack paths agree well with the impact test results. Meanwhile the stresses around the crack tips were analyzed and the crack propagation direction was investigated. To calculate the crack dynamic stress intensity factors (DSIFs), finite element code ABAQUS was employed. The results show that the spacing D between the vertical crack tip and the inclined crack center affects the stress distribution and fracture behavior of the vertical crack largely. As the vertical crack approaches the inclined crack, the crack speed is slow down, and tensile stress appears at the inclined crack tip. As the spacing D is small than 50 mm, the vertical crack connects with the middle area of the inclined crack. As the spacing D is 50 mm, the vertical crack connects with either the middle area or the upper tip of the inclined crack. As the spacing D is larger than 50 mm, the vertical crack coalesces with the upper crack tip.