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.

Study of deep transportation and plugging performance of deformable gel particles in porous media

Deformable gel particles(DGPs) possess the capability of deep profile control and flooding. However, the deep migration behavior and plugging mechanism along their path remain unclear. Breakage, an inevitable phenomenon during particle migration, significantly impacts the deep plugging effect. Due to the complexity of the process, few studies have been conducted on this subject. In this paper, we conducted DGP flow experiments using a physical model of a multi-point sandpack under various injection rates and particle sizes. Particle size and concentration tests were performed at each measurement point to investigate the transportation behavior of particles in the deep part of the reservoir. The residual resistance coefficient and concentration changes along the porous media were combined to analyze the plugging performance of DGPs. Furthermore, the particle breakage along their path was revealed by analyzing the changes in particle size along the way. A mathematical model of breakage and concentration changes along the path was established. The results showed that the passage after breakage is a significant migration behavior of particles in porous media. The particles were reduced to less than half of their initial size at the front of the porous media. Breakage is an essential reason for the continuous decreases in particle concentration, size, and residual resistance coefficient. However, the particles can remain in porous media after breakage and play a significant role in deep plugging. Higher injection rates or larger particle sizes resulted in faster breakage along the injection direction, higher degrees of breakage, and faster decreases in residual resistance coefficient along the path. These conditions also led to a weaker deep plugging ability. Smaller particles were more evenly retained along the path, but more particles flowed out of the porous media, resulting in a poor deep plugging effect. The particle size is a function of particle size before injection, transport distance, and different injection parameters(injection rate or the diameter ratio of DGP to throat). Likewise, the particle concentration is a function of initial concentration, transport distance, and different injection parameters. These models can be utilized to optimize particle injection parameters, thereby achieving the goal of fine-tuning oil displacement.

Analysis of rotor eddy current loss and thermal deformation of magnetic liquid double suspension bearing

Magnetic-liquid double suspension bearing(MLDSB)is a new type of suspension bearing based on electromagnetic suspension and supplemented by hydrostatic supporting.Without affecting the electromagnetic suspension force,the hydrostatic supporting effect is increased,and the real-time coupling of magnetic and liquid supporting can be realized.However,due to the high rotation speed,the rotor part produces eddy current loss,resulting in a large temperature rise and large ther-mal deformation,which makes the oil film thickness deviate from the initial design.The support and bearing characteristics are seriously affected.Therefore,this paper intends to explore the internal effects of eddy current loss of the rotor on the temperature rise and thermal deformation of MLDSB.Firstly,the 2D magnetic flow coupling mathematical model of MLDSB is established,and the eddy current loss distribution characteristics of the rotor are numerically simulated by Maxwell software.Secondly,the internal influence of mapping relationship of structural operating parameters such as input current,coil turns and rotor speed on rotor eddy current loss is revealed,and the changing trend of rotor eddy current loss under different design parameters is explored.Thirdly,the eddy cur-rent loss is loaded into the heat transfer finite element calculation model as a heat source,and the temperature rise of the rotor and its thermal deformation are simulated and analyzed,and the influ-ence of eddy current loss on rotor temperature rise and thermal deformation is revealed.Finally,the pressure-flow curve and the distribution law of the internal flow field are tested by the particle image velocimetry(PIV)system.The results show that eddy current loss increases linearly with the in-crease of coil current,coil turns and rotor speed.The effect of rotational speed on eddy current loss is much higher than that of coil current and coil turns.The maximum temperature rise,minimum temperature rise and maximum thermal deformation of the rotor increase with the increase of eddy current loss.The test results of flow-pressure and internal trace curves are basically consistent with the theoretical simulation,which effectively verifies the correctness of the theoretical simulation.The research results can provide theoretical basis for the design and safe and stable operation of magnetic fluid double suspension bearings.

Stereo particle image velocimetry measurement of 3D soil deformation around laterally loaded pile in sand

A developed stereo particle image velocimetry(stereo-PIV) system was proposed to measure three-dimensional(3D) soil deformation around a laterally loaded pile in sand.The stereo-PIV technique extended 2D measurement to 3D based on a binocular vision model,where two cameras with a well geometrical setting were utilized to image the same object simultaneously.This system utilized two open software packages and some simple programs in MATLAB,which can easily be adjusted to meet user needs at a low cost.The failure planes form an angle with the horizontal line,which are measured at 27°-29°,approximately three-fourths of the frictional angle of soil.The edge of the strain wedge formed in front of the pile is an arc,which is slightly different from the straight line reported in the literature.The active and passive influence zones are about twice and six times of the diameter of the pile,respectively.The test demonstrates the good performance and feasibility of this stereo-PIV system for more advanced geotechnical testing.

Time effect and prediction of broken rock bulking coefficient on the base of particle discrete element method

Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.

Quasi-static tensile deformation and fracture behavior of a highly particle-filled composite using digital image correlation method

Polymer bonded explosives (PBXs) are highly particle-filled composite materials.This paper experimentally studies the tensile deformation and fracture behavior of a PBX simulation by using the semi-circular bending (SCB) test.The deformation and fracture process of a pre-notched SCB sample with a random speckle pattern is recorded by a charge coupled device camera.The displacement and strain fields on the observed surface during the loading process are obtained by using the digital image correlation method.The crack opening displacement is calculated from the displacement fields,the initiation and propagation of the crack are analyzed.In addition,the damage evolution and fracture mechanisms of the SCB sample are analyzed according to the strain fields and the correlation coefficient fields at different loading steps.

Understanding the mechanisms of friction stir welding based on computer simulation using particles

Friction stir welding(FSW) is a novel technique for joining different materials without melting. In FSW the welded components are joined by stirring the plasticized material of the welded edges with a special rotating pin plunged into the material and moving along the joint line. From the scientific point of view,the key role of the FSW processes belongs to formation of the special plasticized conditions and activation of physical mechanisms of mixing the materials in such conditions to produce the strong homogeneous weld. But it is still a lack of complete understanding of what are these conditions and mechanisms.This paper is devoted to understanding the mechanisms of material mixing in conditions of FSW based on a computer simulation using particles. The movable cellular automaton method(MCA), which is a representative of the particle methods in mechanics of materials, was used to perform all computations.Usually, material flow including material stirring in FSW is simulated using computational fluid mechanics or smoothed particle hydrodynamics, which assume that the material is a continuum and does not take into account the material structure. MCA considers a material as an ensemble of bonded particles. Breaking of inter-particle bonds and formation of new bonds enables simulation of crack nucleation and healing, as well as mass mixing and micro-welding.The paper consists of two main parts. In the first part, the simulations in 2 D statements are performed to study the dynamics of friction stir welding of duralumin plates and influence of different welding regimes on the features of the material stirring and temperature distribution in the forming welded joints. It is shown that the ratio of the rotational speed to the advancing velocity of the tool has a dramatic effect on the joint quality. A suitable choice of these parameters combined with additional ultrasonic impact could considerably reduce the number of pores and microcracks in the weld without significant overheating of the welded materials.The second part of the paper considers simulation in the 3 D statement. These simulations showed that using tool pins of different shape like a cylinder, cone, or pyramid without a shoulder results in negligible motion of the plasticized material in the direction of workpiece thickness. However, the optimal ratio of the advancing velocity to the rotational speed allows transporting of the stirred material around the tool pin several times and hence producing the joint of good quality.

Compressive response and microstructural evolution of in-situ TiB_(2)particle-reinforced 7075 aluminum matrix composite

The hot forming behavior,failure mechanism,and microstructure evolution of in-situ TiB_(2)particle-reinforced 7075 aluminum matrix composite were investigated by isothermal compression test under different deformation conditions of deformation temperatures of 300−450℃ and strain rates of 0.001^(−1)s^(−1).The results demonstrate that the failure behavior of the composite exhibits both particle fracture and interface debonding at low temperature and high strain rate,and dimple rupture of the matrix at high temperature and low strain rate.Full dynamic recrystallization,which improves the composite formability,occurs under conditions of high temperature(450℃)and low strain rate(0.001 s^(−1));the grain size of the matrix after hot compression was significantly smaller than that of traditional 7075Al and ex-situ particle reinforced 7075Al matrix composite.Based on the flow stress curves,a constitutive model describing the relationship of the flow stress,true strain,strain rate and temperature was proposed.Furthermore,the processing maps based on both the dynamic material modeling(DMM)and modified DMM(MDMM)were established to analyze flow instability domain of the composite and optimize hot forming processing parameters.The optimum processing domain was determined at temperatures of 425−450℃ and strain rates of 0.001−0.01 s^(−1),in which the fine grain microstructure can be gained and particle crack and interface debonding can be avoided.

Effect of particle characteristics on deformation of particle reinforced metal matrix composites

The particle characteristics of 15%SiC particles reinforced metal matrix composites(MMC)made by powder metallurgy route were studied by using a statistical method.In the analysis,the approach for estimation of the characteristics of particles was presented.The study was carried out by using the mathematic software MATLAB to calculate the area and perimeter of each particle, in which the image processing technique was employed.Based on the calculations,the sizes and shape factors of each particle were investigated respectively.Additionally,the finite element model(FEM)was established on the basis of the actual microstructure.The contour plots of von Mises effective stress and strain in matrix and particles were presented in calculations for considering the influence of microstructure on the deformation behavior of MMC.Moreover,the contour maps of the maximum stress of particles and the maximum plastic strain of matrix in the vicinity of particles were introduced respectively.

Reusing oxide-based pulverised fly ash and medical waste particles to develop electroless nickel composite coatings(Ni–P/fly ash and Ni–P/SiO2–Al2O3)

Recycling and reusing materials from waste have become a nexus in the development of sustainable materials,leading to more balanced technologies.In this study,we developed a composite coating by co-depositing recycled ceramic particles,pulverised fly ash(PFA)and medical ceramics(MC),into a nickel–phosphorus matrix using a typical electroless plating process.Scanning electron microscopy(SEM)images indicated well-dispersed particles in the Ni–P matrix.However,compared with the MC particles,the PFA particles were distributed scantily with a lower content in the matrix,which could be due to the less impingement effect during the co-deposition.A modified microstructure with refined grains was obtained for the PFA-incorporated composite coating,as seen in the SEM micrograph.The X-ray diffraction result of the MC-incorporated composite coating showed the formation of Nix Siy phases in addition to the typical Ni3 P phases for the heattreated electroless Ni–P coatings.Upon heat treatment,the PFA-reinforced composite coating,due to a modified microstructure,exhibited a higher microhardness up to HK0.05818,which is comparable to that of the traditional SiC particle-embedded composite coating(HK0.05825).The findings can potentially open up a new strategy to further advance the green approach for industrial surface engineering.

Numerical simulation of the blocking process of gelled particles in porous media with remaining polymers

Gelled particles can be transferred deeply inside oil reservoirs to block water channels due to their physicochemical characteristics, including swelling, deformation, and synergetic effect （reacting with polymers）, and then the injection profiles are significantly modified. At present, research on gelled particles is mainly focused on laboratory studies of drive mechanisms, and rarely on mathematical models describing the blocking process of gelled particles. In this paper, the blocking process of gelled particles is divided into two sub-processes： deposition and desorption due to particle deformation. A mathematical model based on filtration theory is proposed considering the effect of characteristics of gelled particles on the blocking process. Blocking laws were simulated and researched using the mathematical model. Results of the simulation of the blocking of gelled particles are quite consistent with the experimental results, which confirms the reliability of the mathematical model developed.

Large deformation simulations of geomaterials using moving particle semi-implicit method

Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.

Numerical simulation of the effects of the impact velocity on the particle deposition characteristics in cold gas dynamic spraying

In this study, the effects of the impact velocity on the particle deposition characteristics in cold gas dynamic spraying （CGDS） of 304 stainless steel （SS） on an interstitial free （IF） steel substrate are numerical simulated by means of a finite element analysis （FEA）. The results have illustrated that when the particle impact velocity exceeds a critical value at which adiabatic shear instability of the particle starts to occur. Meanwhile, the fatten ratio and impact crater depth （or the effective contacting area ） increase rapidly. The particle-substrate bonding and deposition mechanism can be attributed to such an adiabatic shear deformation induced by both the compressive force and the slide friction force of particle. The critical velocity can be predicted by numerical simulation, which is useful to optimize the CGDS processing parameters for various materials.

Application of Reproducing Kernel Particle Method in an Analysis of Elasto-plastic Deformation Under Taylor Impact

The Reproducing Kernel Particle Method (RKPM) is one of several new meshless numerical methods de- veloped internationally in recent years. The ideal elasto-plastic constitutive model of material under a Taylor impact is characterized by the Jaumann stress- and strain-rates. An updated Lagrangian format is used for the calculation in a nu- merical analysis. With the RKPM, this paper deals with the calculation model for the Taylor impact and deduces the control equation for the impact process. A program was developed to simulate numerically the Taylor impact of projec- tiles composed of several kinds of material. The simulation result is in good accordance with both the test results and the Taylor analysis outcome. Since the meshless method is not limited by meshes, it is believed to be widely applicable to such complicated processes as the Taylor impact, including large deformation and strain and to the study of the dy- namic qualities of materials.

Study on the time delay failure characteristics of sandstone unloading under dynamic disturbance

The rockburst caused by underground engineering excavation exhibits a significant lag effect.Studies have shown that the occurrence of lag-type rockburst is closely related to the delayed failure of rocks.This paper focuses on the delayed failure characteristics of unloading-damaged sandstone under the combined action of static load and dynamic disturbance.Numerical simulations are utilized to analyze the delayed failure evolution characteristics and failure mechanisms of sandstone.The results indicate that in triaxial unloading delay failure tests,the duration of loading decreases exponentially with the increase of initial unloading damage.Compared to static load conditions,the duration of loading under dynamic disturbance decreases by more than 43%,and the average strain rate significantly increases.The number of cracks at the endpoint of triaxial unloading delay failure increases as initial unloading damage decreases,with a substantial increase in the number of cracks under dynamic disturbance.These findings provide a valuable reference for the timeliness and delayed rockburst analysis and interpretation of rock damage and failure under high-stress levels.

Elevated temperature compressive deformation behavior of 2024Al matrix composite reinforced by sub-micro Al_2O_3 particles

The compressive behavior of sub-micro Al2O 3P （40%, volume fraction）/2024Al composite was investigated within the temperature range from 270℃ to 620℃ under various strain rates from 0.00042s -1 to 0.14s -1. Results show that the critical compression reduction of the composite presents a saddle law under the combined influence of temperature and strain rate. That means the composites exhibit better deformation ability at higher temperature with higher strain rate （445℃, 0.14s -1） or at lower temperature with lower strain rate （320℃, 0.0042s -1）.

Structure and properties of forming adsorbents prepared from different particle sizes of coal fly ash

In this paper, different particle sizes of coal fly ash FA-R(D50= 15.75 μm), FA-A(D50= 3.61 μm) and FA-B(D50= 1.73 μm) were treated with Na OH solution to prepare the forming adsorbents FFA-R, FFA-A and FFA-B.The structure and adsorption properties of the forming adsorbents for methylene blue(MB) from aqueous solution were examined. The results showed that the specific surface areas and adsorption capacities of the forming adsorbent for MB increased with decreasing particle size of raw coal fly ashes. The adsorption kinetic data of MB on FFA-R, FFA-A and FFA-B fitted the second-order kinetic model very well with the rate constants(k2) of3.15 × 10-2, 3.84 × 10-2and 6.27 × 10-2g·mg-1·min-1, respectively. The adsorption process was not only controlled by intra-particle diffusion. The isotherms of MB on FFA-R, FFA-A and FFA-B can be described by the Langmuir isotherm and the Freundlich isotherm, and the adsorption processes were spontaneous and exothermic.

Influence of Deformation on Light Particles as a Probe of Nuclear Dissipation for a Neutron-Deficient ^178Pb System

Using a diffusion model we investigate deformation effects on the sensitivity of different light particles to nuclear dissipation for a rather neutron-deficlent ^178Pb system. Galculations show that deformation significantly increases the sensitivity of neutron emission to dissipation strength, and that this effect becomes stronger with increasing deformation.

A dynamic large-deformation particle finite element method for geotechnical applications based on Abaqus

In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.

TRACKING DEFORMABLE AND OCCLUDED OBJECTS USING PARTICLE FILTERING AND GVF-SNAKE

An adaptive object tracking algorithm based on particle filtering and a modified Gradient Vector Flow (GVF) Snake is proposed for tracking moving and deforming objects. The original contours of objects are obtained by using the background differencing method,and the true contours of objects can be converged by means of the powerful searching ability of a modified GVF-Snake. Finally,an Energetic Particle Filtering (EPF) algorithm is obtained by combining particle filtering and a modified GVF-Snake,and by using K-means and the EPF algorithm,multiple objects can be tracked. The proposed tracking tactic for partially occluded objects can effectively improve its anti-occlusion ability. Experiments show that this algorithm can obtain better tracking effect even though the tracked object is occluded.