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.

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.

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.

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.

Dynamic tensile behaviour and crack propagation of coal under coupled static-dynamic loading

The fracture behaviour and crack propagation features of coal under coupled static-dynamic loading conditions are important when evaluating the dynamic failure of coal.In this study,coupled static-dynamic loading tests are conducted on Brazilian disc(BD)coal specimens using a modified split Hopkinson pressure bar(SHPB).The effects of the static axial pre-stress and loading rate on the dynamic tensile strength and crack propagation characteristics of BD coal specimens are studied.The average dynamic indirect tensile strength of coal specimens increases first and then decreases with the static axial pre-stress increasing.When no static axial pre-stress is applied,or the static axial pre-stress is 30%of the static tensile strength,the dynamic indirect tensile strength of coal specimens shows an increase trend as the loading rate increases.When the static axial pre-stress is 60%of the static tensile strength,the dynamic indirect tensile strength shows a fluctuant trend as the loading rate increases.According to the crack propagation process of coal specimens recorded by high-speed camera,the impact velocity influences the mode of crack propagation,while the static axial pre-stress influences the direction of crack propagation.The failure of coal specimens is a coupled tensile-shear failure under high impact velocity.When there is no static axial pre-stress,tensile cracks occur in the vertical loading direction.When the static axial pre-stress is applied,the number of cracks perpendicular to the loading direction decreases,and more cracks occur in the parallel loading direction.

The Role of Particles in Fatigue Crack Propagation of Aluminum Matrix Composites and Casting Aluminum Alloys

Fatigue crack propagation （FCP） behaviors were studied to understand the role of SiC particles in 10 wt pct SiCp/A2024 composites and Si particles in casting aluminum alloy A356. The results show that a few particles appeared on the fracture surfaces in SiCp/Al composites even at high △K region, which indicates that cracks propagated predominantly within the matrix avoiding SiC particles due to the high strength of the particles and the strong particle/matrix interface. In casting aluminum alloy, Si particle debonding was more prominent.Compared with SiCp/Al composite, the casting aluminum alloy exhibited lower FCP rates, but had a slight steeper slope in the Paris region. Crack deflection and branching were found to be more remarkable in the casting aluminum alloy than that in the SiCp/Al composites, which may be contributed to higher FCP resistance in casting aluminum alloy.

Effects of water intrusion and loading rate on mechanical properties of and crack propagation in coal–rock combinations

Tackling the problems of underground water storage in collieries in arid regions requires knowledge of the effect of water intrusion and loading rate on the mechanical properties of and crack development in coal–rock combinations. Fifty-four coal–rock combinations were prepared and split equally into groups containing different moisture contents(dry, natural moisture and saturated) to conduct acoustic emission testing under uniaxial compression with loading rates ranging from 0.1 mm/min to 0.6 mm/min. The results show that the peak stress and strength-softening modulus, elastic modulus, strain-softening modulus, and post-peak modulus partly decrease with increasing moisture content and loading rate. In contrast, peak strain increases with increasing moisture content and fluctuates with rising loading rate. More significantly, the relationship between stiffness and stress, combined with accumulated counts of acoustic emission, can be used to precisely predict all phases of crack propagation. This is helpful in studying the impact of moisture content and loading rate on crack propagation and accurately calculating mechanical properties. We also determined that the stress thresholds of crack closure, crack initiation, and crack damage do not vary with changes of moisture content and loading rate, constituting 15.22%, 32.20%, and 80.98% of peak stress, respectively. These outcomes assist in developing approaches to water storage in coal mines, determining the necessary width of waterproof coal–rock pillars, and methods of supporting water-enriched roadways, while also advances understanding the mechanical properties of coal–rock combinations and laws of crack propagation.

Influences of microstructure and texture on crack propagation path of X70 acicular ferrite pipeline steel

The aspects of two pipeline steels with different technologies were investigated by using transmission electron microscopy （TEM） and electron back-scattered diffraction （EBSD）. The microstructure presents a typical acicular ferrite characteristic with fine particles of martensite/austenite （M/A） constituent, which distributes in grains and at grain boundaries. The bulk textures of the pipeline steel plate are {112}〈110〉 and 〈111〉 fibers, respectively, and the {112}〈110〉 component is the favorable texture benefiting for drop weight tear test. Moreover, low angle boundaries and low coincidence site lattice boundaries are inactive and more resistant to fracture than high energy random boundaries.

An improved form of smoothed particle hydrodynamics method for crack propagation simulation applied in rock mechanics

The simulation of crack propagation processes in rock engineering has been not only a research hot spot among scholars but also a challenge.Based on this background,a new numerical method named improved kernel of smoothed particle hydrodynamics(IKSPH)has been put forward.By improving the kernel function in the traditional smoothed particle hydrodynamics(SPH)method,the brittle fracture characteristics of the base particles are realized.The particle domain searching method(PDSM)has also been put forward to generate the arbitrary complex fissure networks.Three numerical examples are analyzed to validate the efficiency of IKSPH and PDSM,which can correctly reveal the morphology of wing crack and the laws of crack coalescence compared with previous experimental and numerical studies.Finally,a rock slope model with complex joints is numerically simulated and the progressive failure processes are exhibited,which indicates that the IKSPH method can be well applied to rock mechanics engineering.The research results showed that IKSPH method reduces the programming difficulties and avoids the traditional grid distortion,which can provide some references for the application of IKSPH to rock mechanics engineering and the understanding of rock fracture mechanisms.

Numerical analysis of confinement effect on crack propagation mechanism from a flaw in a pre-cracked rock under compression

In many situations rocks are subjected to biaxial loading and the failure process is controlled by the lateral confinement stresses. The importance of confinement stresses has been recognized in the literature by many researchers, in particular, its influence on strength and on the angle of fracture, but still there is not a clear description for the influence of confining stress on the crack propagation mechanism of rocks. This paper presents a numerical pro- cedure for the analysis of crack propagation in rock-like ma- terials under compressive biaxial loads. Several numerical simulations of biaxial tests on the rock specimen have been carried out by a bonded particle model （BPM） and the influ- ence of confinement on the mechanism of crack propagation from a single flaw in rock specimens is studied. For this purpose, several biaxial compressive tests on rectangular spec- imens under different confinement stresses were modeled in （2 dimensional particle flow code） PFC2D. The results show that wing cracks initiate perpendicular to the flaw and trend toward the direction of major stress, however, when the lat- eral stresses increase, this initiation angle gets wider. Also it is concluded that in addition to the material type, the initiation direction of the secondary cracks depends on confine- ment stresses, too. Besides, it is understood that secondary cracks may be produced from both tensile and shear mechanisms.

CRACK PROPAGATION IN STRUCTURES SUBJECTED TO PERIODIC EXCITATION

In the present paper, asimple mechanical modelis developed to predict thedynamic response of a cracked structure subjected to periodic excitation, which has been used to identify the physical mechanisms in leading the growth or arrest of cracking. The structure under consideration consists of a beam with a crack along the axis, and thus, the crack may open in Mode I and in the axial direction propagate when the beam vibrates. In this paper, the system is modeled as a cantilever beam lying on a partial elastic foundation, where the portion of the beam on the foundation represents the intact portion of the beam. Modal analysis is employed to obtain a closed form solution for the structural response. Crack propagation is studied by allowing the elastic foundation to shorten （mimicking crack growth） if a displacement criterion, based on the material toughness, is met. As the crack propagates, the structural model is updated using the new foundation length and the response continues. From this work, two mechanisms for crack arrest are identified. It is also shown that the crack propagation is strongly influenced by the transient response of the structure.

ANALYSIS OF ELECTRIC BOUNDARY CONDITION EFFECTS ON CRACK PROPAGATION IN PIEZOELECTRIC CERAMICS

There are three types of cracks: impermeable crack, permeable crack and conducting crack, with different electric boundary conditions on faces of cracks in piezoelectric ceramics, which poses difficulties in the analysis of piezoelectric fracture problems. In this paper, in contrast to our previous FEM formulation, the numerical analysis is based on the use of exact electric boundary conditions at the crack faces, thus the common assumption of electric impermeability in the FEM analysis is avoided. The crack behavior and elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and coupled mechanical- electrical loads with different electric boundary conditions on crack faces are investigated. It is found that the dielectric medium between the crack faces will reduce the singularity of stress and electric displacement. Furthermore, when the permittivity of the dielectric medium in the crack gap is of the same order as that of the piezoelectric ceramic, the crack becomes a conducting crack, the applied electric field has no effect on the crack propagation.