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.

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.

Experimental study on 3D internal penny-shaped crack propagation in brittle materials under uniaxial compression

Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

Improved Staggered Algorithm for Phase-Field Brittle Fracture with the Local Arc-Length Method

The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.

Discrete element modeling on the crack evolution behavior of brittle sandstone containing three fissures under uniaxial compression

Based on experimental restilts of brittle, intact sandstone under uniaxial compression, the micro-parameters were firstly confirmed by adopting particle flow code （PFC2D）. Then, the validation of the simulated models were cross checked with the experimental results of brittle sandstone containing three parallel fissures under uniaxial compression. The simulated results agreed very well with the experimental results, including the peak strength, peak axial strain, and ultimate failure mode. Using the same micro- parameters, the numerical models containing a new geometry of three fissures are constructed to investigate the fissure angle on the fracture mechanical behavior of brittle sandstone under uniaxial compression. The strength and deformation parameters of brittle sandstone containing new three fissures are dependent to the fissure angle. With the increase of the fis- sure angle, the elastic modulus, the crack damage threshold, and the peak strength of brittle sandstone containing three fissures firstly increase and secondly decrease. But the peak axial strain is nonlinearly related to the fissure angle. In the entire process of deformation, the crack initiation and propagation behavior of brittle sandstone containing three fissures under uniaxial compression are investigated with respect to the fissure angle. Six different crack coalescence modes are identified for brittle sandstone containing three fissures under uniaxial compression. The influence of the fissure angle on the length of crack propagation and crack coalescence stress is evaluated. These investigated conclusions are very important for ensuring the stability and safety of rock engineering with intermittent structures.

PROBABILISTIC MODELING OF BRITTLE FRACTURE WITH PRIOR DUCTILE CRACK EXTENSION

A computation framework for brittle fracture which incorporates weakest link statistics and a microme- chanics model reflecting reflecting local damage of the material is described.The Weibull stress W emerges as a probabilistic fracture parameter to define the condition leading material failure. Unstable crack propa- gation occurs at a critical value of W which may be attained paior to or following some amount of duc- tile crack extension. A realistic model of ductile crack growth using the computation cell methodology is used to define the evolution of near tip stress fields during crack extension. An application of proposed framework to predict the measured geometry and ductile tearing effects on the statistical distributio of fracture toughness for the pipe line steel welded joint is described.

Effect of nanosized NbC precipitates on hydrogen-induced cracking of high-strength low-alloy steel

We investigated the effect of nanosized NbC precipitates on hydrogen-induced cracking(HIC)of high-strength low-alloy steel by conducting slow-strain-rate tensile tests(SSRT)and performing continuous hydrogen charging and fracture analysis.The results reveal that the HIC resistance of Nb-bearing steel is obviously superior to that of Nb-free steel,with the fractured Nb-bearing steel in the SSRT exhibiting a smaller ratio of elongation reduction(Iδ).However,as the hydrogen traps induced by NbC precipitates approach hydrogen saturation,the effect of the precipitates on the HIC resistance attenuate.We speculate that the highly dispersed nanosized NbC precipitates act as irreversible hydrogen traps that hinder the accumulation of hydrogen at potential crack nucleation sites.In addition,much like Nb-free steel,the Nb-bearing steel exhibits both H-solution strengthening and the resistance to HIC.

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(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 twodimensional(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.

Hydrogen-induced cracking behaviors of Incoloy alloy 825

The effect of hydrogen on the fractttre behaviors of Incoloy alloy 825 was investigated by means of slow strain rate testing （SSRT） Hydrogen was introduced into the sample by electrochemical charging. The results show that surface microcracks form gradually during ag- ing at room temperature when desorption of hydrogen takes place after hydrogen charging at a current density of 5 mA/cm^2 for 24 h. SSRT shows that the increase of ductility loss is significantly obvious as the hydrogen charging current density increases. Scanning electron microscopy （SEM） images reveal ductile fracture in the pre-charged sample with low current densities, while the fracture includes small quasi-cleavage regions and tends to be brittle fracture as the hydrogen charging current density increases to 5 mA/cm^2.

Investigation on hydrogen-induced cracking susceptibility of HG980D steel with yield strength 900 MPa

In this paper, the microstructure and hardness of HG980D heat-affected zone （HAZ） at different cooling rate t8/3 were studied, the implant critical fracture stress under three diffusible hydrogen conditions were measured, and the hydrogeninduced cracking （H1C） fructograph of steel HG980D were analyzed, The experimental results show that martensite exists in HAZ of HG980D till ts/3 ≥ 150 s, the harden quenching tendency of HG980D is greater; The implant critical fracture stress is related to difJhsible hydrogen content significantly, at low hydrogen level, high restraint stress is needed to nucleate HIC, the fraetograph is mainly mierovoid coalescence, bat at high hydrogen level, only small restraint stress can cause H1C occurrence, the fractograph is mainly quasicleavage. It is very important to choose ultra-low hydrogen welding consumable to weld steel HG980D to prevent hydrogen-induced cracking.

ANTIPLANE SHEAR FIELDS NEAR A CRACK-TIP IN A BRITTLE DAMAGED MATERIAL

In this paper,a simplified brittle damage model is proposed according to the Mazars-Lemaitre damage model for concrete.A closed-form solution for a mode Ⅲ crack is obtained based on the simplified model under small scale damage conditions,which allows for discontinuities of displacement-gradient and tangential stress on the damage boundary.It is pointed out that the discontinuities of field variables near the tip region exist for the brittle damaged material induced by the softening effect of the material.

Identifying crack initiation stress threshold in brittle rocks using axial strain stiffness characteristics

As an estimate for the in-situ spalling strength around massive underground excavations to moderately jointed brittle rocks, crack initiation stress marks the initiation of rock micro fracturing. It is crucial to accurately identify crack initiation stress level by proper method. In this study, confined compression tests of sandstone samples are used to examine the validity/applicability of proposed axial strain stiffness method. The results show that by highlighting the minuscule changes in stress-strain curve, the axial strain stiffness curve provided further insight into rock failure process and revealed five stages:(a) irregular fluctuation,(b) nearly horizontal regular fluctuation,(c) irregular fluctuation gradually decreasing to zero,(d) extreme fluctuation, and(e) near zero, which mainly correspond to five stages of stress–strain curve. The ratio of crack-initiation stress to peak strength determined using this approach is 0.44–0.51, similar to the ranges previously reported by other researchers. In this method, the key is to accurately detect the end point of the stage(b), "nearly horizontal regular fluctuation" characterized by a sudden change in axial strain stiffness curve, and the sudden change signifies crack initiation in rock sample. Finally, the research indicates that the axial strain stiffness curve can provide a mean to identify the crack-initiation stress thresholds in brittle rocks.

CRACK TIP STRUCTURE AND DUCTILE-BRITTLE TRANSITION IN BULK SINGLE CRYSTALS

Based on the crack tip structure a new model of ductile -brittle transition was proposed. Using this new model we calculated the dependence of the transition temperature-strain rate over a wide range of strain rate. Finally the significance of this new model is discussed in detail.

CRITICAL NOTCH(CRACK)SIZE AS A CHARACTERISTIC PARAMETER EVALUATING CRYOGENIC BRITTLENESS IN LOW CARBON STEEL

The effect of notch depth on the cryogenic fracture behavior has been studied using a low car- bon steel.An analysis was made for the fracture features at T_c~*(cryogenic brittleness-char- acteristic temperature)at which the facture load reaehes a valley value.Furthermore,accord- ing to the experimental results and engineering design practice,a concept of critical notch (crack)'size for cryogenic brittleness,a_c,as well as its limit value a_c~*,was put forward and recommended to be a basic characteristic parameter for controlling the brittleness. Mathematical derivation was carried out to give the expression of a_c and a_c~*,the reliability of which was verified by the modeling tests under both static and cyclic loading conditions.

Threshold Stress Intensity of Hydrogen-Induced Cracking and Stress Corrosion Cracking of High Strength Steel

The threshold stress intensity of stress corrosion cracking(SCC) for 40 CrMo steel in 3.5%NaCl solution decreased exponentially with the increase of yield strength.The threshold stress intensity of hydrogen-induced cracking during dynamical charging for 40 CrMo steel decreased linearly with the logarithm of the concentration of diffusible hydrogen.This equation was also applicable to SCC of high strength steel in aqueous solution.The critical hydrogen enrichment concentration necessary for SCC of high strength steel in water decreased exponentially with the increase of yield strength.Based on the results,the relationship between K_(ISCC) and σ_(ys) could be deduced.

Rock brittleness indices and their applications to different fields of rock engineering:A review

Brittleness is an important parameter controlling the mechanical behavior and failure characteristics of rocks under loading and unloading conditions,such as fracability,cutability,drillability and rockburst proneness.As such,it is of high practical value to correctly evaluate rock brittleness.However,the definition and measurement method of rock brittleness have been very diverse and not yet been standardized.In this paper,the definitions of rock brittleness are firstly reviewed,and several representative definitions of rock brittleness are identified and briefly discussed.The development and role of rock brittleness in different fields of rock engineering are also studied.Eighty brittleness indices publicly available in rock mechanics literature are compiled,and the measurement method,applicability and limitations of some indices are discussed.The results show that(1)the large number of brittleness indices and brittleness definitions is attributed to the different foci on the rock behavior when it breaks;(2)indices developed in one field usually are not directly applicable to other fields;and(3)the term“brittleness”is sometimes misused,and many empirically-obtained brittleness indices,which lack theoretical basis,fail to truly reflect rock brittleness.On the basis of this review,three measurement methods are identified,i.e.(1)elastic deformation before fracture,(2)shape of post-peak stressestrain curves,and(3)methods based on fracture mechanics theory,which have the potential to be further refined and unified to become the standard measurement methods of rock brittleness.It is highly beneficial for the rock mechanics community to develop a robust definition of rock brittleness.This study will undoubtedly provide a comprehensive timely reference for selecting an appropriate brittleness index for their applications,and will also pave the way for the development of a standard definition and measurement method of rock brittleness in the long term.

Mechanical behavior and failure analysis of brittle sandstone specimens containing combined flaws under uniaxial compression

Based on the axial stress-axial strain curves,the effect of fissure angle on the strength and deformation behavior of sandstone specimens containing combined flaws is analyzed.The mechanical parameters of sandstone specimens containing combined flaws are all lower than that of intact specimen,but the reduction extent is distinctly related to the fissure angle.The results of sandstone specimens containing combined flaws are obtained by the acoustic emission,which can be used to monitor the crack initiation and propagation.The ultimate failure mode and crack coalescence behavior are evaluated for brittle sandstone specimens containing combined flaws.Nine different crack types are identified on the basis of their geometry and crack coalescence mechanism(tensile crack,hole collapse,far-field crack and surface spalling)for combined flaws.The photographic monitoring was also adopted for uniaxial compression test in order to confirm the sequence of crack coalescence in brittle sandstone specimens containing combined flaws,which recorded the real-time crack coalescence process during entire deformation.According to the monitored results,the effect of crack coalescence process on the strength and deformation behavior is investigated based on a detailed analysis for brittle sandstone specimens containing combined flaws by using digital photogrammetry.

Femtosecond laser shockwave peening ablation in liquids for hierarchical micro/nanostructuring of brittle silicon and its biological application

This paper presents a new technique,termed femtosecond laser shock peening ablation in liquids(fs-LSPAL),which can realize simultaneous crack micro/nanomanufacturing and hierarchical micro/nanolaser ablation,giving rise to the formation of diverse multiscale hierarchical structures,such as macroporous ratcheted structures and enéchelon microfringes decorated with parabolic nanoripples.Through analysis of surface morphologies,many phenomena have been confirmed to take place during fs-LSPAL,including enéchelon cracks,nanostriation,ripple densification,crack branching,and selective formation of high spatial frequency laser-induced periodic surface structures of 100–200 nm in period.At a high laser power of 700 mW,fs-LSPAL at scanning speeds of 0.2 mm s^-1 and 1 mm s^-1 enables the generation of height-fluctuated and height-homogeneous hierarchical structures,respectively.The height-fluctuated structures can be used to induce‘colony’aggregates of embryonic EB3 stem cells.At 200 mW,fs-LSPAL at 1 mm s^-1 is capable of producing homogeneous tilt macroporous structures with cracked structures interleaved among them,which are the synergistic effects of bubble-induced light refraction/reflection ablation and cracks.As shown in this paper,the conventional laser ablation technique integrated with its self-driven unconventional cracking under extreme conditions expands the horizons of extreme manufacturing and offers more opportunities for complex surface structuring,which can potentially be used for biological applications.

Fracturing damage process in dynamic split experiments of a brittle glass

In this study, the 3-dimensional discrete element method is firstly introduced to explain the fracturing damage process of the dynamic split experiment of a special brittle glass ZnS. The corresponding dynamic split experiment is also performed by using the split Hopkinson pressure bar. Then the numerical results correspond closely to those obtained by experiments, and the fracturing damage mode shows that the sample under high strain rate loading would crack along vertical diameter in the band region between two loading edges, which differs from the static damage mode. Furthermore, by comparing a group of contrast numerical tests, the numerical results prove that loading area upon the top side of samples would influence the fracture mode of dynamic split experiments, which indicates that the narrow loading plane is better.

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.