Numerical simulation of particle breakage of angular particles using combined DEM and FEM

One of the effective parameters of the behavior of rockfill materials is particle breakage. As a result of particle breakage, both the stress–strain and deformability of materials change significantly. In this article, a novel approach for the two-dimensional numerical simulation of the phenomenon in rockfill (sharp-edge particles) has been developed using combined DEM and FEM. All particles are simulated by the discrete element method (DEM) as an assembly and after each step of DEM analysis, each particle is separately modeled by FEM to determine its possible breakage. If the particle fulfilled the proposed breakage criteria, the breakage path is assumed to be a straight line and is determined by a full finite element stress–strain analysis within that particle and two new particles are generated, replacing the original particle. These procedures are carried out on all particles in each time step of the DEM analysis. Novel approach for the numeric of breakage appears to produce reassuring physically consistent results that improve earlier made unnecessary simplistic assumptions about breakage. To evaluate the effect of particle breakage on rockfill's behavior, two test series with and without breakable particles have been simulated under a biaxial test with different confining pressures. Results indicate that particle breakage reduces the internal friction but increases the deformability of rockfill. Review of the v–p variation of the simulated samples shows that the specific volume has initially been reduced with the increase of mean pressures and then followed by an increase. Also, the increase of stress level reduces the growing length of the v–p path and it means that the dilation is reduced. Generally, any increase of confining stress decreases the internal friction angle of the assembly and the sample fail at higher values of axial stresses and promotes an increase in the deformability. The comparison between the simulations and the reported experimental data shows that the numerical simulation and experimental results are qualitatively in agreement. Overall the presented results show that the proposed model is capable with more accuracy to simulate the particle breakage in rockfill.     

Numerical simulation of breakage of two-dimensional polygon-shaped particles using discrete element method

Using DEM (Discrete Element Method), a model is presented to simulate the breakage of two-dimensional polygon-shaped particles. In this model each uniform (uncracked) particle is replaced with smaller inter-connected sub-particles which are bonded with each other. If the bond between these sub-particles breaks, breakage will happen. With the help of this model, it is possible to study the influence of particle breakage on macro and micro mechanical parameters. In this simulation, the evolution of microstructure in granular assemblies can be seen by tracing of coordination number during the shear process. Also variation of contact normal, normal force and tangential force anisotropy can be tracked. To do so, two series of biaxial test simulations (breakage is enabled and disabled) are conducted on assemblies of two-dimensional polygon-shaped particles and the results are compared. The results are presented in terms of macro and micro mechanical behavior for different confining pressures.     

Analysis of catalyst particle strength by impact testing: The effect of manufacturing process parameters on the particle strength

The mechanical strength of porous alumina catalyst carrier beads, used in the reforming units with continuous catalytic regeneration, was measured by impact testing. With this testing method particle strength can be measured at higher strain rates than the traditional crushing test method, hence providing a better simulation of pneumatic conveying and chute flow conditions, and also a large number of particles can be tested quickly. This is important for particles with a brittle failure mode such as the alumina particles used in this work as a wide distribution of mechanical strength usually prevails. Extensive impact testing was carried out first with an industrial sample, in order to understand the failure mechanism of this type of particles and to develop a methodology for analysing the extent of breakage by impact. Then the method was used to analyse the effect of a number of process parameters, such as filler, macroporosity and drying procedure on the particle strength with the aim of optimising the manufacturing process. The impact test results were then used to test the model of breakage behaviour of particulate solids proposed by Vogel and Peukert [Vogel and Peukert, Breakage behaviour of different materials—construction of a mastercurve for the breakage probability. Powder Technol., 129 (2003) pp. 101-110].     

Numerical simulation of particle breakage in dry impact pulverizer

A novel method to simultaneously simulate particle motion and its breakage in a dry impact pulverizer was developed. The motion of particles in the pulverizer was calculated using a discrete phase model (DPM)‐computational fluid dynamics (CFD) coupling model. When the particle impacts against a vessel wall, impact stress acting on the particle is calculated from Hertz's theory as a function of the impact velocity. At the same time, the particle strength as a function of the particle size is calculated from Griffith's theory. If the impact stress is larger than the particle strength, the particle is broken and replaced with smaller fragments. The size distribution of the fragments is obtained from a breakage function proposed. The motion of the fragments is calculated again by using the DPM‐CFD coupling model. By repeating the above calculations over the whole particles, the grinding phenomenon can be simulated. The calculated results showed good agreement with the experimental one, and validity of the proposed method was confirmed. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3601–3611, 2013     

The influence of gravity on dynamic properties in sheared granular flows

The influences of gravity on the granular flow behavior and dynamic properties were experimentally studied in a vertical shear cell device where the shear dilation direction of granular materials was perpendicular to the gravity direction. The particle motions were recorded by a high-speed camera from three different observational views. By using image processing technology and the particle tracking method, the average velocities and granular temperatures in the streamwise and the transverse directions were successfully measured and analyzed. The results show that the anisotropic motions exist in sheared granular flows. The dynamic properties in the streamwise direction are larger than those in the transverse direction. Due to the gravity effect and bulk flow of granular materials, the local packing structure is not homogenous in the vertical shear cell. By comparing the three different observational views in the vertical shear cell, we find that the spatial average velocity and self-diffusion coefficient are the greatest but the shear rate and granular temperature are the smallest when the particles are co-flowing with gravity causing the most dilute packing structure due to the gravity effect. Similar experiments were also performed in a horizontal shear cell where the shear dilation direction of granular materials was against the gravity direction. The dynamic properties are smaller in the horizontal shear cell than those in the vertical shear cell. It is because the horizontal shear cell has the smaller shear rate with the shear dilation direction against the gravity direction.     

脆性材料的亚临界裂纹扩展和双向应力的影响

分析了陶瓷,玻璃等脆性材料的断裂机理和表征.指出了脆性材料的失效过程的三种不同的裂纹发展模式.实验研究了玻璃在静载下的亚临界裂纹扩展特征及其受双向应力的影响.从而为脆性材料的可靠性和寿命评价提供理论基础和手段.     

Quasi-static confined uniaxial compaction of granular alumina and boron carbide observing the particle size effects

The quasi-static confined uniaxial compaction of granular alumina and boron carbide was studied, and the effect of triaxial stress on the materials as a function of increasing particle size was observed. The average particle sizes studied for granular alumina were 170 ± 63, 230 ± 55, 330 ± 67, and 450 ± 83 µm. The average particle size studied for granular boron carbide were 170 ± 40, 190 ± 34, 320 ± 59, and 470 ± 90 µm. The material response at hydrostatic pressure as a function of porosity, the bulk modulus as a function of hydrostatic pressure, and the transmission ratio as a function of applied load was evaluated for increasing particle size. For alumina, the increase in particle size resulted in an increase in strength for a fixed porosity, the bulk modulus of this material did not show clear particle size-dependent trends, and the transmission ratio increased with increase in particle size. Conversely, for granular boron carbide, the hydrostatic pressure-porosity curve shifted to the right with increasing particle size, the change in bulk modulus increased with increasing particle size, and no clear particle size-dependent trends were observed when looking at the transmission ratio during the experiment. Post-experiment scanning electron microscopy revealed that alumina powder fragmented from elongated shapes to block-like structures, while boron carbide powder appeared more circular before the experiments and fragmented into smaller comminuted pieces. This paper discusses the implication of the work in the context of the limited experimental data in the field and the modeling of granular advanced ceramics behavior.     

A dynamic constitutive-micromechanical model to predict the strain rate-dependent mechanical behavior of carbon nanofiber/epoxy nanocomposites

Polymeric materials have wide applications; therefore, it is necessary to develop a dynamic constitutive model to investigate their strain rate-dependent mechanical behavior. In this study, mechanical behavior of neat epoxy and carbon nanofiber (CNF)/epoxy nanocomposites were studied experimentally and analytically. For this purpose, the Johnson–Cook material model has been modified to develop a generalized strain rate-dependent constitutive model to simulate the tensile and shear mechanical behaviors of the neat epoxy at a wide range of applied loading rates. The present model includes three main components: the first component expresses the elastic behavior of polymers using an empirical equation. The second component models the nonlinear behavior of polymers using the modified Johnson–Cook model. Finally, the third component predicts the ultimate strength of polymers under dynamic loading conditions using another empirical equation. Furthermore, by combining the generalized strain rate-dependent constitutive model and the modified Halpin–Tsai micromechanical model, a dynamic constitutive-micromechanical model is presented to predict the strain rate-dependent mechanical behavior of CNF/epoxy nanocomposites. To evaluate the present model, predicted results for the pure epoxy and CNF/epoxy nanocomposites were compared with conducted and available experimental data. It is shown that the present model predicts the strain rate-dependent mechanical behavior of polymeric materials with a good accuracy.     

A theory for the impact behavior of rate-dependent padding materials

A continuum theory is used to describe the rate-dependent behavior of padding materials and is applied to predict the impact behavior of these materials when struck by flat or spherical impactors. Numerical results are given to show the effect of varying the material and geometric parameters. Some implications of the theory to practical situations are discussed.     

Coupling of CFD with PBM for a pilot-plant tubular loop polymerization reactor

A computational fluid dynamics model, coupled with population balance model (CFD–PBM), was developed to describe the liquid–solid two-phase flow in a pilot-plant tubular loop propylene polymerization reactor. The model combines the advantage of CFD to calculate the entire flow field and that of PBM to calculate the particle size distribution (PSD). Particle growth, aggregation and breakage were taken into account to describe the evolution of the PSD. The model was first validated by comparing simulation results with the classical calculated data. Furthermore, four cases studies, involving particle aggregation, particle breakage, particle growth or involving particle growth, breakage and aggregation, were designed to identify the model. The entire flow behavior and PSD in the tubular loop reactor, i.e. PSD, solid holdup and liquid phase velocity distribution, were also obtained numerically. The results showed that the model is effective in describing the entire flow behavior and in tracking the evolution of the PSD.     

Visualization of Impact Damage in Ceramics Using the Edge-On Impact Technique

Projectile impact generates severe fragmentation in ceramics which propagates at high velocities and precedes the penetration of the projectile. The high-speed photographic technique of the Edge-On Impact (EOI) has been developed at the Ernst-Mach-Institute (EMI) in order to visualize dynamic fracture in brittle materials. In a typical EOI test the projectile hits one edge of a specimen and fracture propagation is observed during the first 20 us after impact by means of a Cranz-Schardin highspeed camera. EOI tests allow a characterization of different ceramics by the macroscopic fracture patterns, single crack velocities, and crack front velocities (damage velocities). The phenomenology of damage propagation in several ceramics and a ceramic-metal composite is discussed. The EOI technique is useful for the evaluation of damage models for brittle materials because it enables a direct comparison of model predictions to experimental data obtained during the impact process.     

Evaluation of Strut Strength in Open-Cell Ceramics

The strength of cellular materials is dependent on the strength of the solid making up the cellular structure, but this parameter is often difficult to quantify. In order to better evaluate these materials, a technique has been developed to measure the strength ofthe cell struts in open-cell ceramics. The strut strength was measured in two commercially available, open-cell ceramics and evaluated in terms of a two parameter Weibull distribution. The strut strength distribution was found to be very wide with the Weibull modulusin the range 1 to 3. In addition, it was found that the strut strength was invariant withdensity (at constant cell size) but could be dependent on cell size. This behavior was inqualitative agreement with the failure statistics of brittle materials, once the variations in the microstructural geometry are understood. Based on these data and the observations of flaws within the struts, it is clear that careful processing of these materials could significantly improve the strut strength distribution, in terms of reducing its width and increasing its magnitude. Such microscopic improvements would lead to similar benefits in the strength and toughness of the bulk cellular ceramics.     

A combined experimental-numerical study of the compaction behavior of NaCl

The compaction behavior of NaCl as a model substance is investigated by an integrated experimental and computational approach. The method for characterization of this granular material employs convenient experiments: load-displacement measurements of compaction; measurements of strain on outer circumference of an elastic tubular die; load on bottom and top of the powder compact, as well as compressive strength tests. Related equations for identification of material parameters are derived and are used to characterize powder behavior and powder-die friction. Subsequently, these material parameters are used in simulations with the Drucker-Prager-Cap (DPC) model. For the verification of the computations density distributions are determined based on micro X-ray computer tomography. Good agreement between the spatial density distributions from measurements and simulations is obtained. Restrictions of computer tomography in powder compaction applications are specified. While the study employs NaCl as a model substance, the approach is applicable to a wider array of granular substances.     

A Molecular Mechanism for Stress Corrosion in Vitreous Silica

The mechanical strength of most glasses and ceramics decreases with time under static loading in an ambient environment. This strength loss is associated with slow growth of preexisting surface flaws due to stress corrosion by water from the surrounding environment. We studied stress corrosion in vitreous silica exposed to water and several nonaqueous environments; environments which enhance stress-corrosion crack growth in silica contain active groups with electron donor sites on one end and proton donor sites at the other. These results suggest a detailed chemical model for the interaction of the environment with mechanically strained bonds in the solid at the tip of a crack. The proposed model for stress-corrosion crack growth also has implications for the long-term strength behavior of a wide variety of brittle materials.     

Numerical investigation of crack initiation,propagation and suppression in robot-assisted abrasive belt grinding of zirconia ceramics via an improved chip-thickness model

Motivated by the prevailing assisted techniques in wheel grinding of brittle and hard materials, an attempt is made in this paper to identify the feasibility of robot-assisted abrasive belt grinding of zirconia ceramics. Owing to the flexible machining system, the challenge of this attempt resides in achieving the required profile accuracy and surface quality, in which the evolution of grinding-induced micro-cracks is prioritized. The single-grit scratching simulation based on an improved chip-thickness model that incorporates elastic modules of tool-workpiece engagement is employed to explore the damage mechanism in terms of the initiation, propagation and suppression of micro-cracks. The simulation results demonstrate that the critical depth of cut for brittle-to-ductile transition of zirconia ceramics is determined as 0.42 μm according to the tentative maximum undeformed chip thickness (UCT) values. In ductile-regime grinding, the zirconia surface morphologies are independent of the abrasive particle velocity. Lateral cracks begin to initiate especially when the maximum UCT exceeds 0.42 μm, and the brittle removal becomes dominant. In brittle-regime grinding, high abrasive particle velocity could help substantially enhance the workpiece surface integrity by suppressing the median/radial cracks that initiate once the maximum UCT approaches 0.8 μm. Experiment concerning the force-controlled robotic belt grinding of zirconia ceramics is conducted to verify the simulation results via the microscope observation of ground surface morphologies. The findings are likely to provide experimental evidence on the feasibility of belt grinding of brittle and hard materials with a flexible industrial robot.     

Chipping of ceramic-based dental materials by micrometric particles

Chipping caused by micrometric particles poses a threat to the structural integrity of modern dental prosthetic materials. It can degrade their fracture strength and cause wear of both artificial crowns and antagonist teeth. Here, surface chipping of the main types of commercial ceramic-based dental materials at the microcontact/particle level is investigated by means of indentation tests. Conical tips of different sizes (radii 20 and 200 μm) under axial and sliding loading are employed to simulate individual microcontacts. Both decreasing particle size and adding a lateral contact force decrease the chipping load below typical bite forces. Specific damage mechanisms are identified as predominantly brittle fracture in ceramics with small, equiaxed crystals, with significant quasi-plastic damage in ceramics containing large, elongated crystals and composites. Critical loads for the occurrence of chipping are quantified (lowest values in equiaxed glass–ceramics; greatest in zirconia) and analyzed within the framework of fracture mechanics. The brittleness index (BI) is proposed as a simple indicator of the resistance to chipping of dental materials—the lower the BI, the greater the resistance. Special attention is paid to the effect of the materials’ microstructure, which can result in transformation toughening (as in zirconia) or quasi-plastic behavior (as in lithium disilicate), both highly beneficial to increasing the chipping resistance. Finally, practical implications for the selection of current dental materials as well as for the development of novel materials with improved durability are discussed.     

Classification of ceramics and glass (edge chipping and fracture toughness)

The standard classification of advanced ceramics is based on their strength, although in many cases the performance of products made of such materials is controlled by their deformation behavior and fracture resistance. In this article, ceramics and glass are classified according to their edge chipping resistance (EF-method). Such a classification is based on the idea of a baseline (direct proportionality between edge chipping resistance and fracture toughness of ceramics that are similar to the model material of linear elastic fracture mechanics). Use was made of various elastic and inelastic, oxide and non-oxide ordinary ceramics, composite ceramics capable and incapable of retarding cracks and intended for engineering and biomedical applications. Attention is also given to silicate glass.