Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Crack propagation in brittle material is not only crucial for structural safety evaluation,but also has a wideranging impact on material design,damage assessment,resource extraction,and scientific research.A thorough investigation into the behavior of crack propagation contributes to a better understanding and control of the properties of brittle materials,thereby enhancing the reliability and safety of both materials and structures.As an implicit discrete elementmethod,the Discontinuous Deformation Analysis(DDA)has gained significant attention for its developments and applications in recent years.Among these developments,the particle DDA equipped with the bonded particle model is a powerful tool for predicting the whole process of material from continuity to failure.The primary objective of this research is to develop and utilize the particle DDAtomodel and understand the complex behavior of cracks in brittle materials under both static and dynamic loadings.The particle DDA is applied to several classical crack propagation problems,including the crack branching,compact tensile test,Kalthoff impact experiment,and tensile test of a rectangular plate with a hole.The evolutions of cracks under various stress or geometrical conditions are carefully investigated.The simulated results are compared with the experiments and other numerical results.It is found that the crack propagation patterns,including crack branching and the formation of secondary cracks,can be well reproduced.The results show that the particle DDA is a qualified method for crack propagation problems,providing valuable insights into the fracture mechanism of brittle materials.

Impact Analysis of Microscopic Defect Types on the Macroscopic Crack Propagation in Sintered Silver Nanoparticles

Sintered silver nanoparticles(AgNPs)arewidely used in high-power electronics due to their exceptional properties.However,the material reliability is significantly affected by various microscopic defects.In this work,the three primary micro-defect types at potential stress concentrations in sintered AgNPs are identified,categorized,and quantified.Molecular dynamics(MD)simulations are employed to observe the failure evolution of different microscopic defects.The dominant mechanisms responsible for this evolution are dislocation nucleation and dislocation motion.At the same time,this paper clarifies the quantitative relationship between the tensile strain amount and the failure mechanism transitions of the three defect types by defining key strain points.The impact of defect types on the failure process is also discussed.Furthermore,traction-separation curves extracted from microscopic defect evolutions serve as a bridge to connect the macro-scale model.The validity of the crack propagation model is confirmed through tensile tests.Finally,we thoroughly analyze how micro-defect types influence macro-crack propagation and attempt to find supporting evidence from the MD model.Our findings provide a multi-perspective reference for the reliability analysis of sintered AgNPs.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

Comparison on crack propagation under tension at 150℃ of Mg-2Zn-1.5Mn alloy sheets with and without crack notch

Generally,edge crack of rolled magnesium alloy sheets initiates in the RD(rolling direction)-ND(normal direction)plane and then propagate in the RD-TD(transverse direction)plane.Hence,the Mg-2Zn-1.5Mn(ZM21)alloy sheets with and without crack notch were designed to carry out in-situ tensile experiments under 150℃(the same temperature of rolling),with the aim to understand their crack propagation mechanism.The scanning electron microscopy(SEM)and electron backscattered diffraction(EBSD)techniques were utilized to reveal microstructural evolution in real time at designated displacements.The results show that the prismatic slip,basal slip,and extension twining play synergistic role in coordinating strain during the tensile process in ZM21 alloy sheet at 150℃.In both tensile samples with and without crack notch,localized strain is mainly concentrated at relatively fine grain area and the grain boundaries or triple junctions of the grains with large basal Schmid factor(SF)difference,which eventually leads to severe surface roughening and subsequent crack initiation.Compared with the sample without crack notch,the pre-cracked sample exhibits severer deformation at the crack tip due to strain concentration.Strain gradient distribution is observed at the crack tip region in the pre-cracked sample.The crack propagation path of the sample with pre-crack is identified and the underlying mechanism is also discussed.

Fatigue crack propagation of 7050 aluminum alloy FSW joints after surface peening

The surface composite modification of the 7050 aluminum alloy friction stir-welded joints was performed by shot peening(SP)/multiple rotation rolling(MRR)and MRR/SP,and the fatigue performance of the nugget zone(NZ)was investigated.The results demonstrated that the fatigue life of SP/MRR samples is longer than that of MRR/SP.On the plane 150μm below the surface.The grains with high angle grain boundary account for 71.5%and 34.3%for MRR/SP and SP/MRR samples,respectively.The crack propagation path of the MRR/SP is transgranular and intergranular,and it is intergranular for the MRR/SP.Multitudinous fatigue striations and some voids appeared at the fracture during the stable crack propagation stage.However,fatigue striations for SP/MRR are with smaller spacing,fewer holes,and smaller size under SP/MRR compared with fatigue fracture of MRR/SP.The differences in fatigue properties and fracture characteristics of the NZ are related to the microstructure after the two combined surface modifications.

Study on Crack Propagation Parameters of Tunnel Lining Structure Based on Peridynamics

The numerical simulation results utilizing the Peridynamics(PD)method reveal that the initial crack and crack propagation of the tunnel concrete lining structure agree with the experimental data compared to the Japanese prototype lining test.The load structure model takes into account the cracking process and distribution of the lining segment under the influence of local bias pressure and lining thickness.In addition,the influence of preset cracks and lining section formon the crack propagation of the concrete lining model is studied.This study evaluates the stability and sustainability of tunnel structure by the Peridynamics method,which provides a reference for the analysis of the causes of lining cracks,and also lays a foundation for the prevention,reinforcement and repair of tunnel lining cracks.

Fatigue crack propagation in fine-grained magnesium under low temperature tension-tension cyclic loading

Fine-grained magnesium was tested under stress-controlled tension-tension cyclic loading at -30 ℃ and the tested sample was observed using scanning electron microscope and electron backscatter diffraction to explore the fatigue behavior and crack propagation. The fatigue data showed that the material experienced cyclic softening followed by cyclic hardening before the final fracture failure. The microscopic observations demonstrated that the cracks were almost perpendicular to the loading direction with some zigzags and the cracks progressed along both small angle grain boundaries and large angle grain boundaries. Although the cracks were mainly propagated along large angle grain boundaries, the value of grain boundary angle was not the primary factor to determine the crack propagation direction. The local residual strain from the rolling process was released due to the crack propagation and there was more strain relaxation at regions closer to the cracks.

Phase-field-crystal simulation of nano-single crystal microcrack propagation under different orientation angles

The propagation mechanism of microcracks in nanocrystalline single crystal systems under uniaxial dynamic and static tension is investigated using the phase-field-crystal method.Both dynamic and static stretching results show that different orientation angles can induce the crack propagation mode,microscopic morphology,the free energy,crack area change,and causing fracture failure.Crack propagation mode depends on the dislocation activity near the crack tip.Brittle propagation of the crack occurs due to dislocation always at crack tip.Dislocation is emitted at the front end of the crack tip and plastic deformation occurs,which belongs to ductile propagation.The orientation angles of 9°and 14°are brittleductile mixed propagation,while the orientation angles of 19°and 30°are brittle propagation and no dislocation is formed under dynamic tension.The vacancy and vacancy connectivity phenomenon would appear when the orientation angle is14°under static tension,and the crack would be ductile propagation.While the orientation angle is 19°and 30°,the crack propagates in a certain direction,which is a kind of brittle propagation.This work has some practical significance in preventing material fracture failure and improving material performance.

A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.

Peridynamic Study on Fracture Mode and Crack Propagation Path of a Plate with Multiple Cracks Subjected to Uniaxial Tension

How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but difficult issue in fracture mechanics.Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation,branch and propagation in materials and structures through a meshfree discrete technique.In this paper,the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions.We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension.The results are consistent with those predicted by classical fracture mechanics.The fracture mode and crack propagation path are also determined.The calculation shows that the brittle fracture process of the plate with multiple cracks can be conveniently and correctly simulated by the peridynamic motion equation with boundary conditions.

A Bidimensional Finite Element Study of Crack Propagation in Austempered Ductile Iron

Austempered ductile iron(ADI)is composed of an ausferritic matrix with graphite nodules and has a wide range of applications because of its high mechanical strength,fatigue resistance,and wear resistance compared to other cast irons.The amount and size of the nodules can be controlled by the chemical composition and austenitizing temperature.As the nodules have lower stiffness than the matrix and can act as stress concentrators,they influence crack propagation.However,the crack propagation mechanism in ADI is not yet fully understood.In this study,we describe a numerical investigation of crack propagation in ADIs subjected to cyclic loading.The numerical model used to calculate the stress intensity factors in the material under the given conditions is built with the aid of Abaqus commercial finite element code.The crack propagation routine,which is based on the Paris law,is implemented in Python.The results of the simulation show that the presence of a nodule generates a shear load on the crack tip.Consequently,even under uniaxial tensile loading,the presence of the nodule yields a non-zero stress intensity factor in mode II,resulting in a deviation in the crack propagation path.This is the primary factor responsible for changing the crack propagation direction towards the nodule.Modifying the parameters,for example,increasing the nodule size or decreasing the distance between the nodule and crack tip,can intensify this effect.In simulations comparing two different ADIs with the same graphite fraction area,the crack in the material with more nodules reaches another nodule in a shorter propagation time(or shorter number of cycles).This suggests that the high fatigue resistance observed in ADIs may be correlated with the number of nodules intercepted by a crack and the additional energy required to nucleate new cracks.In summary,these findings contribute to a better understanding of crack propagation in ADIs,provide insights into the relationship between the presence of nodules and the fatigue resistance of these materials,and support studies that associate the increased fatigue resistance with a higher number of graphite nodules.These results can also help justify the enhanced fatigue resistance of ADIs when compared to other cast irons.

Study on the Law of Hydraulic Fracture Propagation in Low Permeability Thin Interbed Reservoir

The third member of Weixinnanliu in the west of the South China Sea develops thin interbeds, and the vertical extension of fracturing fractures is excessive. Once the fractures extend vertically to the upper and lower aquifers, it is easy to cause water flooding of oil wells, and the effect after fracturing is not obvious. The present work aims to explore the longitudinal extension law of fractures in Low Permeability Thin Interbed Reservoir based on the finite element calculation platform. A three-dimensional expansion model of hydraulic fractures in the target reservoir was established, and the displacement, fracturing fluid viscosity, minimum horizontal principal stress difference, vertical stress, interlayer thickness, perforation point separation were studied. The interlayer distance and other factors affect the crack propagation law. The research results show that the thin interbed fractures have three forms: T-shaped fractures, through-layer fractures, and I-shaped fractures;for the target layer, the overlying stress is relatively large, and the minimum principal stress is along the horizontal direction. Vertical cracks;the farther the perforation point is or the greater the stress difference, the smaller the thickness of the interlayer required to control the fracture height;the stress difference is 3 MPa, and the distance between the perforation points exceeds 10 m, the thickness of the interlayer is required to be ≥4 m;In order to ensure that the width of the fracture in the middle spacer does not affect the placement of the proppant, it is recommended that the displacement be controlled within 3 m3/min and the viscosity of the fracturing fluid is 150 mPa·s;in addition, the thickness of the spacer required to control the fracture height is different due to different geological parameters. Different, different wells need targeted analysis.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Experimental study on the effect of unloading rate on gneiss rockburst

Rockburst are often encountered in tunnel construction due to the complex geological conditions.To study the influence of unloading rate on rockburst,gneiss rockburst experiments were conducted under three groups of unloading rates.A high-speed photography system and acoustic emission(AE)system were used to monitor the entire process of rockburst process in real-time.The results show that the intensity of gneiss rockburst decreases with decrease of unloading rate,which is manifested as the reduction of AE energy and fragments ejection velocity.The mechanisms are proposed to explain this effect:(i)The reduction of unloading rate changes the crack propagation mechanism in the process of rockburst.This makes the rockbursts change from the tensile failure mechanism at high unloading rate to the tension-shear mixed failure mechanism at low unloading rate,and more energy released in the form of shear crack propagation.Then,less strain energy is converted into kinetic energy of fragments ejection.(ii)Less plate cracking degree of gneiss has taken shape due to decrease of unloading rate,resulting in the destruction of rockburst incubation process.The enlightenments of reducing the unloading rate for the project are also described quantitatively.The rockburst magnitude is reduced from the medium magnitude at the unloading rate of 0.1 MPa/s to the slight magnitude at the unloading rate of 0.025 MPa/s,which was judged by the ejection velocity.

Instrumented oscillographic study on impact toughness of an axle steel DZ2 with different tempering temperatures

Compared with the conventional Charpy impact test method,the oscillographic impact test can help in the behavioral analysis of materials during the fracture process.In this study,the trade-off relationship between the strength and toughness of a DZ2 axle steel at various tempering temperatures and the cause of the improvement in impact toughness was evaluated.The tempering process dramatically influenced carbide precipitation behavior,which resulted in different aspect ratios of carbides.Impact toughness improved along with the rise in tempering temperature mainly due to the increase in energy required in impact crack propagation.The characteristics of the impact crack propagation process were studied through a comprehensive analysis of stress distribution,oscilloscopic impact statistics,fracture morphology,and carbide morphology.The poor impact toughness of low-tempering-temperature specimens was attributed to the increased number of stress concentration points caused by carbide morphology in the small plastic zone during the propagation process,which resulted in a mixed distribution of brittle and ductile fractures on the fracture surface.

Dynamic response mechanism and precursor characteristics of gneiss rockburst under different initial burial depths

To investigate the influence mechanism of geostress on rockburst characteristics,three groups of gneiss rockburst experiments were conducted under different initial geostress conditions.A high-speed photography system and acoustic emission(AE)monitoring system were used to monitor the entire rockburst process in real time.The experimental results show that when the initial burial depth increases from 928 m to 1320 m,the proportion of large fracture scale in rockburst increases by 154.54%,and the AE energy increases by 565.63%,reflecting that the degree and severity of rockburst increase with the increase of burial depth.And then,two mechanisms are proposed to explain this effect,including(i)the increase of initial geostress improves the energy storage capacity of gneiss,and then,the excess energy which can be converted into kinetic energy of debris ejection increases,consequently,a more pronounced violent ejection phenomenon is observed at rockburst;(ii)the increase of initial geostress causes more sufficient plate cracks of gneiss after unloading ofσh,which provides a basis for more severe ejection of rockburst.What’s more,a precursor with clear physical meaning for rockburst is proposed under the framework of dynamic response process of crack evolution.Finally,potential value in long term rockburst warning of the precursor obtained in this study is shown via the comparison of conventional precursor.

A modified smoothed particle hydrodynamics method considering residual stress for simulating failure and its application in layered rock mass

Residual strength is an indispensable factor in evaluating rock fracture,yet the current Smoothed Particle Hydrodynamics(SPH)framework rarely considers its influence when simulating fracture.An improved cracking strategy considering residual stress in the base bond SPH method was proposed to simulate failures in layered rocks and slopes and verified by experimental results and other simulation methods(i.e.,the discrete element method).Modified Mohr–Coulomb failure criterion was applied to distinguish the mixed failure of tensile and shear.Bond fracture markψwas introduced to improve the kernel function after tensile damage,and the calculation of residual stress after the damage was derived after shear damage.Numerical simulations were carried out to evaluate its performance under different stress and scale conditions and to verify its effectiveness in realistically reproducing crack initiation and propagation and coalescence,even fracture and separation.The results indicate that the improved cracking strategy precisely captures the fracture and failure pattern in layered rocks and rock slopes.The residual stress of brittle tock is correctly captured by the improved SPH method.The improved SPH method that considers residual strength shows an approximately 13%improvement in accuracy for the safety factor of anti-dip layered slopes compared to the method that does not consider residual strength,as validated against analytical solutions.We infer that the improved SPH method is effective and shows promise for applications to continuous and discontinuous rock masses.

Crack mechanism of ground fissures in loess layer of Fenwei Basin, China

The Fenwei Basin, covered by loess, experiences severe ground fissure disasters. These disasters disrupt the continuity of the loess and pose significant threats to engineering construction safety along transportation routes. Nevertheless, the crack characteristics and the influence zone of ground fissures in the loess layer remain inadequately investigated. To effectively prevent and control ground fissure disasters, physical model tests and the PFC(particle flow code) numerical simulation method are used to investigate the crack mechanism of buried ground fissures in the loess layer. The results show that there are two main cracks in the layer profile, which have a Y-shape morphology. As the dip angle of the preset cracks increased from 60° to 90°, the main deformation zone at the surface gradually shifted towards the footwall. The process of crack propagation from depth to surface is divided into five stages. Additionally, the results confirm the accuracy of the width of the rupture zone d2in the footwall calculated by the cantilever beam theory. These findings can offer theoretical guidance for determining the avoidance distance of ground fissures in loess regions, as well as for implementing disaster prevention and corresponding control measures for various stages of buried ground fissure propagation.

Toughening ultrastrong low-density steel by textured δ-ferrite lamellas

By both the Charpy V-notched impact and the projectile tests, we here investigated the dynamic fracture behavior of a recently developed ultrastrong lightweight steel comprising a hierarchical martensitic matrix, dispersed ultra-fine-retained austenite grains and oriented δ-ferrite lamellas, the latter being due to high Al and Si contents employed for low-density design. This steel shows a superior combination of specific ultimate tensile strength and impact toughness to other ultrastrong steels and has successfully arrested a real steel-cored bullet shot. These are attributed to the densely textured δ-ferrite lamellas that can deflect the propagating cracks until they are trapped and enclosed besides austenite-to-martensite transformation crack closure, leading to more energy consumed before failure. These results suggest a new pathway for toughening ultrastrong lightweight steels.