Novel Methodologies for Preventing Crack Propagation in Steel Gas Pipelines Considering the Temperature Effect

Using the software ANSYS-19.2/Explicit Dynamics,this study performedfinite-element modeling of the large-diameter steel pipeline cross-section for the Beineu-Bozoy-Shymkent gas pipeline with a non-through straight crack,strengthened by steel wire wrapping.The effects of the thread tensile force of the steel winding in the form of single rings at the crack edges and the wires with different winding diameters and pitches were also studied.The results showed that the strengthening was preferably executed at a minimum value of the thread tensile force,which was 6.4%more effective than that at its maximum value.The analysis of the influence of the winding dia-meters showed that the equivalent stresses increased by 32%from the beginning of the crack growth until the wire broke.The increment in winding diameter decelerated the disclosure of the edge crack and reduced its length by 8.2%.The analysis of the influence of the winding pitch showed that decreasing the distance between the winding turns also led to a 33.6%reduction in the length of the straight crack and a 7.9%reduction in the maximum stres-ses on the strengthened pipeline cross-section.The analysis of the temperature effect on the pipeline material,within a range from-40℃ to+50℃,resulted in a crack length change of up to 5.8%.As the temperature dropped,the crack length decreased.Within such a temperature range,the maximum stresses were observed along the cen-tral area of the crack,which were equal to 413 MPa at+50℃ and 440 MPa at-40℃.The results also showed that the presence of the steel winding in the pipeline significantly reduced the length of crack propagation up to 8.4 times,depending on the temperature effect and design parameters of prestressing.This work integrated the existing methods for crack localization along steel gas pipelines.

Mechanism of internal thermal runaway propagation in blade batteries

Blade batteries are extensively used in electric vehicles,but unavoidable thermal runaway is an inherent threat to their safe use.This study experimentally investigated the mechanism underlying thermal runaway propagation within a blade battery by using a nail to trigger thermal runaway and thermocouples to track its propagation inside a cell.The results showed that the internal thermal runaway could propagate for up to 272 s,which is comparable to that of a traditional battery module.The velocity of the thermal runaway propagation fluctuated between 1 and 8 mm s^(-1),depending on both the electrolyte content and high-temperature gas diffusion.In the early stages of thermal runaway,the electrolyte participated in the reaction,which intensified the thermal runaway and accelerated its propagation.As the battery temperature increased,the electrolyte evaporated,which attenuated the acceleration effect.Gas diffusion affected thermal runaway propagation through both heat transfer and mass transfer.The experimental results indicated that gas diffusion accelerated the velocity of thermal runaway propagation by 36.84%.We used a 1D mathematical model and confirmed that convective heat transfer induced by gas diffusion increased the velocity of thermal runaway propagation by 5.46%-17.06%.Finally,the temperature rate curve was analyzed,and a three-stage mechanism for internal thermal runaway propagation was proposed.In Stage I,convective heat transfer from electrolyte evaporation locally increased the temperature to 100℃.In Stage II,solid heat transfer locally increases the temperature to trigger thermal runaway.In StageⅢ,thermal runaway sharply increases the local temperature.The proposed mechanism sheds light on the internal thermal runaway propagation of blade batteries and offers valuable insights into safety considerations for future design.

Advances in ice avalanches on the Tibetan Plateau

As some of the greatest natural disasters in the cryosphere,ice avalanches(IAs)seriously threaten lives and cause catastrophic damage to the resource environment,but a comprehensive overview of the state of knowledge on IAs remains lacking.We summarized 63 IAs on the Tibetan Plateau(TP)since the 20th century,of which,over 20 IAs occurred after the 21st century.The distributions of IAs are mainly concentrated in the southeastern and northwestern TP,and the occurrence time of IAs is mostly concentrated from July to September.We highlight recent advances in mechanical properties and genetic mechanisms of IAs and emphasize that temperature,rainfall,and seismicity are the inducing factors.The failure modes of IAs are summarized into 6 categories by examples:slip pulling type,slip toppling type,slip breaking type,water level collapse type,cave roof collapse type,and wedge failure type.Finally,we deliver recommendations concerning the risk assessment and prediction of IAs.The results provide important scientific value for addressing climate change and resisting glacier-related hazards.

Modelling of debris-flow susceptibility and propagation: a case study from Northwest Himalaya

The geological and geographical position of the Northwest Himalayas makes it a vulnerable area for mass movements particularly landslides and debris flows. Mass movements have had a substantial impact on the study area which is extending along Karakorum Highway(KKH) from Besham to Chilas. Intense seismicity, deep gorges, steep terrain and extreme climatic events trigger multiple mountain hazards along the KKH, among which debris flow is recognized as the most destructive geohazard. This study aims to prepare a field-based debris flow inventory map at a regional scale along a 200 km stretch from Besham to Chilas. A total of 117 debris flows were identified in the field, and subsequently, a point-based debris-flow inventory and catchment delineation were performed through Arc GIS analysis. Regional scale debris flow susceptibility and propagation maps were prepared using Weighted Overlay Method(WOM) and Flow-R technique sequentially. Predisposing factors include slope, slope aspect, elevation, Topographic Roughness Index(TRI), Topographic Wetness Index(TWI), stream buffer, distance to faults, lithology rainfall, curvature, and collapsed material layer. The dataset was randomly divided into training data(75%) and validation data(25%). Results were validated through the Receiver Operator Characteristics(ROC) curve. Results show that Area Under the Curve(AUC) using WOM model is 79.2%. Flow-R propagation of debris flow shows that the 13.15%, 22.94%, and 63.91% areas are very high, high, and low susceptible to debris flow respectively. The propagation predicated by Flow-R validates the naturally occurring debris flow propagation as observed in the field surveys. The output of this research will provide valuable input to the decision makers for the site selection, designing of the prevention system, and for the protection of current infrastructure.

Numerical modeling of fracture propagation of supercritical CO_(2)compound fracturing

The exploitation of shale gas is promising due to depletion of the conventional energy and intensification of the greenhouse effect.In this paper,we proposed a heat-fluid-solid coupling damage model of supercritical CO_(2)(SC-CO_(2))compound fracturing which is expected to be an efficient and environmentally friendly way to develop shale gas.The coupling model is solved by the finite element method,and the results are in good agreement with the analytical solutions and fracturing experiments.Based on this model,the fracture propagation characteristics at the two stages of compound fracturing are studied and the influence of pressurization rate,in situ stress,bedding angle,and other factors are considered.The results show that at the SC-CO_(2)fracturing stage,a lower pressurization rate is conducive to formation of the branches around main fractures,while a higher pressurization rate inhibits formation of the branches around main fractures and promotes formation of the main fractures.Both bedding and in situ stress play a dominant role in the fracture propagation.When the in situ stress ratio(δ_(x)/δ_(y))is 1,the presence of bedding can reduce the initiation pressure and failure pressure.Nevertheless,it will cause the fracture to propagate along the bedding direction,reducing the fracture complexity.In rocks without bedding,hydraulic fracturing has the lengthening and widening effects for SC-CO_(2)induced fracture.In shale,fractures induced at the hydraulic fracturing stage are more likely to be dominated by in situ stresses and have a shorter reorientation radius.Therefore,fracture branches propagating along the maximum principal stress direction may be generated around the main fractures induced by SC-CO_(2)at the hydraulic fracturing stage.When the branches converge with the main fractures,fracture zones are easily formed,and thus the fracture complexity and damage area can be significantly increased.The results are instructive for the design and application of SC-CO_(2)compound fracturing.

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.

Heat transfer enhanced inorganic phase change material compositing carbon nanotubes for battery thermal management and thermal runaway propagation mitigation

Developing technologies that can be applied simultaneously in battery thermal management(BTM)and thermal runaway(TR)mitigation is significant to improving the safety of lithium-ion battery systems.Inorganic phase change material(PCM)with nonflammability has the potential to achieve this dual function.This study proposed an encapsulated inorganic phase change material(EPCM)with a heat transfer enhancement for battery systems,where Na_(2)HPO_(4)·12H_(2)O was used as the core PCM encapsulated by silica and the additive of carbon nanotube(CNT)was applied to enhance the thermal conductivity.The microstructure and thermal properties of the EPCM/CNT were analyzed by a series of characterization tests.Two different incorporating methods of CNT were compared and the proper CNT adding amount was also studied.After preparation,the battery thermal management performance and TR propagation mitigation effects of EPCM/CNT were further investigated on the battery modules.The experimental results of thermal management tests showed that EPCM/CNT not only slowed down the temperature rising of the module but also improved the temperature uniformity during normal operation.The peak battery temperature decreased from 76℃to 61.2℃at 2 C discharge rate and the temperature difference was controlled below 3℃.Moreover,the results of TR propagation tests demonstrated that nonflammable EPCM/CNT with good heat absorption could work as a TR barrier,which exhibited effective mitigation on TR and TR propagation.The trigger time of three cells was successfully delayed by 129,474 and 551 s,respectively and the propagation intervals were greatly extended as well.

Numerical simulation for the initial state of avalanche in polydisperse particle systems

Numerical simulation is employed to investigate the initial state of avalanche in polydisperse particle systems.Nucleation and propagation processes are illustrated for pentadisperse and triadisperse particle systems,respectively.In these processes,particles involved in the avalanche grow slowly in the early stage and explosively in the later stage,which is clearly different from the continuous and steady growth trend in the monodisperse system.By examining the avalanche propagation,the number growth of particles involved in the avalanche and the slope of the number growth,the initial state can be divided into three stages:T1(nucleation stage),T2(propagation stage),T3(overall avalanche stage).We focus on the characteristics of the avalanche in the T2 stage,and find that propagation distances increase almost linearly in both axial and radial directions in polydisperse systems.We also consider the distribution characteristics of the average coordination number and average velocity for the moving particles.The results support that the polydisperse particle systems are more stable in the T2 stage.

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.

Dynamic Characteristics of the Long Runout Rock-ice Avalanche at High Altitude——A Case from the Zelongnong Basin,Eastern Himalayan Syntaxis,China

Rock-ice avalanches have frequently occurred in the Eastern Himalayan Syntaxis region due to climate change and active tectonic movements.These events commonly trigger catastrophic geohazard chains,including debris flows,river blockages,and floods.This study focuses on the Zelongnong Basin,analyzing the geomorphic and dynamic characteristics of high-altitude disasters.The basin exhibits typical vertical zonation,with disaster sources initiating at elevations exceeding 4000 m and runout distances reaching up to 10 km.The disaster chain movement involves complex dynamic effects,including impact disintegration,soil-rock mixture arching,dynamic erosion,and debris deposition,enhancing understanding of the flow behavior and dynamic characteristics of rock-ice avalanches.The presence of ice significantly increases mobility due to lubrication and frictional melting.In the disaster event of September 10,2020,the maximum flow velocity and thickness reached 40 m/s and 43 m,respectively.Furthermore,continuous deformation of the Zelongnong glacier moraine was observed,with maximum cumulative deformations of 44.68 m in the distance direction and 25.96 m in the azimuth direction from March 25,2022,to August 25,2022.In the future,the risk of rock-ice avalanches in the Eastern Himalayan Syntaxis region will remain extremely high,necessitating a focus on early warning and risk mitigation strategies for such basin disasters.

Evidence of ancient rock-ice avalanches along the China-Bhutan Chomolhari Range,and their implications for demise of the summit

Large-scale rock-ice avalanches resulting from the interaction of tectonics and climate are characterized with high mobility,huge volumes of sediment,and rapid denudation,being a major agent of landscape evolution in high altitude mountainous regions.Specifically,the extreme glaciated slope failures often transform into extraordinarily large and mobile debris flows,resulting in disastrous consequences such as sedimentation and desertification.Due to a dearth of on-site observation data and experimental data collection,our comprehension of the geomorphic and kinematic characteristics of rock-ice avalanches remains poor.Here we report a cluster of ancient rock-ice avalanches spreading along the Chomolhari range of the China-Bhutan Himalayas.By integrating remote sensing image interpretation with detailed field investigations,we demonstrate the geomorphic and sedimentary characteristics of four events among the avalanches.The estimated volumes of the four are 23.73 Mm³,39.69 Mm³,38.43 Mm³,and 38.25 Mm³,respectively.The presence of pre-existing moraines or alluvial fans constrained their movement,resulting in deposition features such as marginal digitated lobes at higher elevations and large depressed areas in the interior.Applying the Savage-Hutter theory,we calculate the basal friction angle and travel angle of these ancient rock-ice avalanches that are both less than 10°,affirming the similarity of these avalanches in the study area to those occurring in other regions.Our study significantly contributes to understanding the geomorphic and kinematic characteristics of rock-ice avalanches in high-altitude mountainous regions,providing valuable insights into their response to the disproportionate growth of Himalayan peaks.

Mantle avalanches in a Venus-like stagnant lid planet

Stagnant lid planets are characterized by a globe-encircling,conducting lid that is thick and strong,which leads to reduced global surface heat flows.Consequently,the mantles of such planets can have warmer interiors than Earth,and interestingly,a pyrolitic mantle composition under warmer conditions is predicted to have a distinctly different mantle transition zone compared to the present-day Earth(Hirose,2002;Stixrude and Lithgow-Bertelloni,2011;Ichikawa et al.,2014;Dannberg et al,2022).Instead of olivine primarily transforming into its higher-pressure polymorphs such as wadsleyite and then ringwoodite,at pressures corresponding to 410 km and 520 km depth in Earth,respectively,it instead transforms into a mineral assemblage of wadsleyite,majorite,and ferropericlase(WMF),and then to majorite+ferropericlase(MF),before finally transforming into bridgmanite at pressures corresponding to 660 km depth in Earth(Stixrude and Lithgow-Bertelloni,2011;Ichikawa et al.,2014).Convective motions in stagnant lid planets are dominated by small-scale instabilities(cold drips)forming within the mobile rheological sublayer under the rigid lid.Using ASPECT and a thermodynamic model of a pyrolitic mantle composition generated by HeFESTo,we show that under certain conditions,the small drips can pond atop the WMF-MF mineral phase transition.The barrier to convective flow arises from the WMF mineral phase assemblage having an effective negative thermal expansivity(Stixrude and Lithgow-Bertelloni,2022).Although large-scale downwellings that typically occur within mobile lid planets are able to pass through the WMF zone without difficulty(Dannberg et al.,2022;Li RP et al.,2024),the smaller and less negatively buoyant nature of downwelling drips in stagnant lid planets are more susceptible to these effects,which leads to an ephemeral layering of the mantle.Our numerical models show that in stagnant lid planets with mantle potential temperatures that exceed 1900 K,the smaller,cold drips from the lid continue to pile up until enough of them have coalesced that they collectively avalanche as a larger instability into the deeper interior.

Robust autofocusing propagation in turbulence

Turbulence in complex environments such as the atmosphere and biological media has always been a great challenge to the application of beam propagation in optical communication, optical trapping and manipulation. To overcome this challenge, this study comprehensively investigates the robust propagation of traditional Gaussian and autofocusing beams in turbulent environments. In order to select stable beams that exhibit high intensity and high field gradient at the focal position in complex environments, Kolmogorov turbulence theory is used to simulate the propagation of beams in atmospheric turbulence based on the multi-phase screen method. We systematically analyze the intensity fluctuations, the variation of the coherence factor and the change in the scintillation index with propagation distance. The analysis reveals that the intensity fluctuations of autofocusing beams are significantly smaller than those of Gaussian beams, and the coherence of autofocusing beams is better than that of Gaussian beams under turbulence. Moreover, autofocusing beams exhibit less oscillation than Gaussian beams, indicating that autofocusing beams propagate in complex environments with less distortion and intensity fluctuation. Overall, this work clearly demonstrates that autofocusing beams exhibit higher stability in propagation compared with Gaussian beams, showing great promise for applications such as optical trapping and manipulation in complex environments.

Theoretical model of current propagation in a helical coil with varying geometry and screen tube

An analytical model of current propagation in a helical coil with varying geometry is developed.It can be used for post-acceleration and post-focusing of ions produced via laser-driven target normal sheath acceleration and generation of electromagnetic pulses.We calculate the current that propagates in a helical coil and suggest a method for improving its dispersion properties using a screening tube and with pitch and radius variation.The electromagnetic fields calculated with the analytical model are in agreement with particle-in-cell simulations.The model provides insights into the physics of current propagation in helical coils with varying geometries and enables a numerical implementation for rapid proton spectrum computations,which facilitate the design of such coils for future experiments.

Research on the correlation between the dual diffusion behavior of zinc in InGaAs/InP single-photon avalanche photodiodes and device performance

The development of InGaAs/InP single-photon avalanche photodiodes(SPADs)necessitates the utiliza-tion of a two-element diffusion technique to achieve accurate manipulation of the multiplication width and the dis-tribution of its electric field.Regarding the issue of accurately predicting the depth of diffusion in InGaAs/InP SPAD,simulation analysis and device development were carried out,focusing on the dual diffusion behavior of zinc atoms.A formula of X_(j)=k√t-t_(0)+c to quantitatively predict the diffusion depth is obtained by fitting the simulated twice-diffusion depths based on a two-dimensional(2D)model.The 2D impurity morphologies and the one-dimensional impurity profiles for the dual-diffused region are characterized by using scanning electron micros-copy and secondary ion mass spectrometry as a function of the diffusion depth,respectively.InGaAs/InP SPAD devices with different dual-diffusion conditions are also fabricated,which show breakdown behaviors well consis-tent with the simulated results under the same junction geometries.The dark count rate(DCR)of the device de-creased as the multiplication width increased,as indicated by the results.DCRs of 2×10^(6),1×10^(5),4×10^(4),and 2×10^(4) were achieved at temperatures of 300 K,273 K,263 K,and 253 K,respectively,with a bias voltage of 3 V,when the multiplication width was 1.5µm.These results demonstrate an effective prediction route for accu-rately controlling the dual-diffused zinc junction geometry in InP-based planar device processing.

Improved Belief Propagation Decoder for LDPC-CRC-Polar Codes with Bit-Freezing

Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.

Topographic seismic effects and avalanche hazard:A case study of Mount Siella(L’Aquila,Central Italy)

In mountainous areas,snow avalanches could be triggered by the shaking produced by earthquakes.The forces induced by the earthquake can cause an irregular increase of shear strength load down the slope,for the presence of complex surface and buried morphologies.Topographic irregularities generate maximum effects of waves amplification linked to wavelengths comparable to the horizontal dimension of the topographic feature.For this reason,the selected time-histories represent an appropriate input for the two-dimensional numerical response analyses when a dynamic phenomenon produce the resonant motion of a whole mountain.This represents an important earthquake-induced hazard in snow-covered mountain areas with high probability of seismic events.Some valleys are located in regions with scare ground motion data and investments on infrastructures are not always accompanied by adequate protection against earthquake-induced avalanches.The paper points out a simple deterministic approach for selecting a set of real accelerograms applied to a real case of Siella Mountain(Central Italy)where a large avalanche destroying a tourist facility of Rigopiano resort on 18 January 2017.The selected time histories were used as input for the two-dimensional numerical model of the subsoil to evaluate the topographic seismic amplification in ridge and compare it with the results of other authors.These methods suggest that morphology-related inertial effects should be considered as an overload action on snow layers when controlling multi-hazard studies and spatial planning.

Protective effect of retaining wall on rock avalanche:A case study of Nayong rock avalanche in China

Rock avalanches are generally difficult to prevent and control due to their high velocities and the extensive destruction they cause.However,barrier structures constructed along the path of a rock avalanche can partially mitigate the magnitudes and consequences of such catastrophic events.We selected a rock avalanche in Nayong County,Guizhou Province,China as a case to study the effect of the location and height of a retaining wall on the dynamic characteristics of rock avalanche by using both actual terrain-based laboratory-model tests and coupled PFC3D-FLAC3D numerical simulations.Our findings demonstrate that a retaining wall can largely block a rock avalanche and its protective efficacy is significantly influenced by the integrity of the retaining wall.Coupled numerical simulation can serve as a powerful tool for analyzing the interaction between a rock avalanche and a retaining wall,facilitating precise observations of its deformation and destruction.The impact-curve characteristics of the retaining wall depend upon whether or not the rock avalanche-induced destruction is taken into account.The location of the retaining wall exerts a greater influence on the outcome compared to the height and materials of the retaining wall,while implementing a stepped retaining-wall pattern in accordance with the terrain demonstrates optimal efficacy in controlling rock avalanche.

Non-dimensional analysis on blast wave propagation in foam concrete:Minimum thickness to avoid stress enhancement

Foam concrete is a prospective material in defense engineering to protect structures due to its high energy absorption capability resulted from the long plateau stage.However,stress enhancement rather than stress mitigation may happen when foam concrete is used as sacrificial claddings placed in the path of an incoming blast load.To investigate this interesting phenomenon,a one-dimensional difference model for blast wave propagation in foam concrete is firstly proposed and numerically solved by improving the second-order Godunov method.The difference model and numerical algorithm are validated against experimental results including both the stress mitigation and the stress enhancement.The difference model is then used to numerically analyze the blast wave propagation and deformation of material in which the effects of blast loads,stress-strain relation and length of foam concrete are considered.In particular,the concept of minimum thickness of foam concrete to avoid stress enhancement is proposed.Finally,non-dimensional analysis on the minimum thickness is conducted and an empirical formula is proposed by curve-fitting the numerical data,which can provide a reference for the application of foam concrete in defense engineering.

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.