Breakage Behavior Research Articles

Analysis of the Stress Wave Effect During Rock Breakage by Pulsating Jets

Formation, propagation and attenuation of stress waves during rock breakage by pulsating jets are simulated by introducing the Johnson–Holmquist-Concrete nonlinear constitutive model, and using the smoothed particle hydrodynamics approach. The curve of stress over time at different locations of the rock surface under the action of high-velocity pulsating jets is obtained, as well as relationship curve between amplitude of stress wave and distance to jet action spot. Based on the computational results, breakage behavior of rocks under stress wave effect, and impacts of jet velocity and rock properties on stress wave effect are analyzed. The results show that the stress wave effect of pulsating jets is rather strongly localized, and the amplitude of stress wave decreases sharply with increasing distance to jet action spot. The intensity and effect range of stress wave are in direct proportion to jet velocity; besides, there is a threshold velocity regarding macroscopic failure of rocks. Rocks of different lithologies have somewhat different failure modes under stress wave action of pulsating jets; failure mode of low strength rocks like sandstone is mainly crack propagation under tensile stress during rock loading and unloading processes, whereas the failure mode of hard brittle rocks such as limestone and granite is mainly longitudinal failure caused by stress concentration.

Dynamic Spectral Analysis of Jagged Mechanical Signatures of a Brittle Puffed Snack

AbstractThe instrumental evaluation of crispiness and crunchiness of dry and wet cellular foods is challenging. Available texture analysis methods do not always reliably predict sensory analysis results. Temporal sensory integration is suspected to be a key factor in the perception of crispiness and crunchiness. Thus, short‐time Fourier transform, continuous wavelet transform and Hilbert–Huang transform are proposed and applied as dynamic alternatives for analyzing multifracture events. The resulting time–frequency–magnitude spectra graphically show the degree of similarity between the samples. These representations contribute to an understanding of the dynamics of airy foods' jagged mechanical signatures, as demonstrated on corn starch extrudates. In most cases, they finally permit the recognition or discrimination of similarities and differences in the degree of brittleness, corresponding to a specific production process and water content. The analytical techniques should help to determine relevant and objective characteristics that correlate with sensory studies.Practical ApplicationsShort‐time Fourier transform, continuous wavelet transform and Hilbert–Huang transform help to understand the physical processes and the temporal evolution of the breakage behavior of foods. They are powerful tools for analyzing jagged mechanical and acoustic food signatures. Each method offers a different perspective, thereby enabling the exploration of unforeseen characteristics that could lead to better predictions of sensory‐felt crispiness and crunchiness. A food's dynamic fingerprint helps in recognition of similar products that belong to the same family, despite natural individuality, and aids the discrimination between different products. After relating classified food samples to their structure and consumer preferences, food structure design and quality control can be improved. The methods can be applied to multidisciplinary food texture studies that examine air‐conducted crushing sounds, bone‐conducted vibrations, dampening effects of muscles and fatty tissues, or chewing muscle and neural activities. This manuscript intends to make modern techniques of signal analysis more accessible to food scientists.

Application of basic process modeling in investigating the breakage behavior of UG2 ore in wet milling

We carried out wet milling batch tests in a laboratory scale ball mill on a minus 600μm UG2 ore as feed. In this paper, we aim to investigate the nature of the UG2 ore using a simple method that relies only on the breakage kinetic data and knowledge of basic process modeling skills. Our results show that a two component model more accurately predicts the breakage behavior of the UG2 ore when compared to the homogeneous or true first order model. This paper takes the view that due to the effectiveness of the two component model in describing the milling behavior, it may be hypothesized that the ore might best be described as composing material of two different hardness; termed the ‘soft’ and ‘hard’ components. Our results also show that for all solid concentrations investigated, the rates of breakage of the ‘soft’ component are much higher than for the hard component. We also found that at 20% solid content the difference between the rates of breakage of the soft component (0.15 per second) and that of the hard component (0.0159 per second) is 0.1341 per second, while at 50% solids the difference is 0.111.

Numerical modelling of heterogeneous rock breakage behaviour based on texture images

The main objective of this study is to understand rock breakage behaviours which may provide a means to improve fragmentation efficiency. In this study, numerical modelling technology and image analysis are used to investigate the behaviour of actual rocks in the breakage process. A texture-based finite element method (FEM) modelling technique has been developed to present a realistic modelling method for characterizing heterogeneous rock breakage behaviour according to its actual microstructure using integrated microscopic observation, image analysis and numerical modelling.Understanding the role of texture and crack propagation can provide fundamental knowledge for predicting and improving energy-efficiency of comminution. A number of samples were analysed with the aim of providing key information on mineralogical and textural controls which primarily influence preferential liberation.The results in this study demonstrated that mineral distributions and minerals with lower tensile strength play a very important role in the breakage process.

The role of contact friction in the dynamic breakage behavior of granular materials

Based on the discrete element method, a multi-scale model is employed to investigate the role of contact friction in the dynamic compression responses of brittle granular materials. Four numerical granular samples with different particle friction coefficients ranging from 0.0 to 2.0 are tested and the particle breakage extent is quantified with the Einav breakage index. It is observed that the relationship of the breakage extent with the axial stress is apparently non-monotonic concerning the particle friction coefficient. At the same stress level, the breakage extent exhibits a minimum when the particle friction coefficient is around 0.1 but increases significantly with the particle friction coefficient to both sides. The micro physical origin of this non-monotonic behavior is a distinct transition in dominant particle-breakage modes from tension to shear. Moreover, energy analyses also show non-monotonic evolution of the frictional and damping dissipation with the particle friction coefficient. The joint effect of these two dissipation terms contributes to the non-monotonic behavior of particle breakage. In addition, the accuracy and competence of two frequently-used micro quantities, fraction of sliding contacts and average coordination number, are discussed.

Glass - steel hybrid elements under four point bending test

Problems evolving from the brittleness of structural glass result in need of innovative solutions which will improve the post-breakage behaviour of the elements in the structure. As the need of the glass performance gets higher, the fully tempered glass gets in the focus and its usage becomes greater. But although this type of glass gives great performance with its tensile strength and deflection capaciy, it has no residual strength. Due to its breakage pattern into small pieces the collapse of the element may be instant even in laminated glass elements. Thus, increasing the post breakage behaviour is crucial in order to keep the integrity of the tempered glass element. This can be done either by changing the interlayer properties, or including kind of reinforcement in the element structure. This paper presents experimental testing of the performances of steel plate reinforced hybrid glass element under four point bending test. As a result, it shows the improvement in mechanical behaviour of the described hybrid structure concept compared to a monolithic glass element with same dimensions, by means of stress distribution and reinforcement capacity.

In Situ Deformation and Breakage of Silica Particles Inside a SEM

Mechanical properties and particle breakage behavior in the submicron size range are of fundamental importance for many particle related processes and applications. Although many (in situ) studies have been dedicated to materials’ size dependent mechanical characterization, particles as free standing structures have been omitted widely. An important, yet open question is the structure property relationship at small scales. Within this account, the application of a custom built manipulator for particle compression inside a scanning electron microscope (SEM) is presented: Stöber-Fink-Bohn (SFB) particles with mean diameters of 500nm and 1000nm are subjected to heat treatments and their mechanical properties are directly correlated to the internal structure. The as-synthesized SFB particles exhibit a complex and size dependent internal structure. Mechanical properties undermatching the values of fused silica are found and only plastic cracking at large strains is observed: cracks are formed at the surface and propagate in radial direction towards the particle center. Heat treatment leads to densification. The degree of changes is controlled by temperature and treatment time. Starting from initially low values, Young's modulus and hardness are increasing with treatment temperature. Properties of fused silica are approached or even exceeded after a treatment at 1000°C. A significant level of plasticity and high sustained deformations are still found. Whereas small particle show ductile cracking, the heat treated micron sized particles show a brittle behavior. A brittle to ductile transition in the size range of 500 nm to 1000 nm is thus identified.

On the origin of non-linear breakage kinetics in dry milling

While population balance models (PBMs) have described the impact of mechanical interparticle interactions on the specific breakage rate in dry milling processes through a phenomenological effectiveness factor, such models lack particle-scale information and thus a mechanistic basis. In this study, a mechanistic effectiveness factor of the non-linear PBM was derived and calculated by coupling a particle-scale breakage model with interparticle interactions obtained from discrete element method (DEM) simulations of a grinding ball impacting an unconfined particle bed. Mono, binary, ternary, and polydispersed particle beds were simulated to determine the effects of granular composition on breakage kinetics. The effectiveness factor obtained from the DEM simulations shows a reduction in the specific breakage rate for coarse particles in binary mixtures. The origin of this phenomenon, commonly known as cushioning or decelerated breakage in dry milling processes, was explained by the DEM simulations: fine particles in a particle bed increase mechanical energy loss, and reduce and distribute interparticle forces thereby inhibiting the breakage of the coarse component. On the other hand, the specific breakage rate of fine particles increased due to contacts associated with coarse particles. Such phenomenon, known as acceleration, was shown to be less significant, but should be considered in future attempts to accurately quantify non-linear breakage kinetics in the modeling of dry milling processes. The phenomenological effectiveness factor was also assessed and found to accurately describe the impact of mechanical interparticle interactions in binary particle beds as well as predict the non-linear breakage behavior in ternary and polydispersed particle beds. Aside from gaining particle-scale insight into non-linear breakage kinetics, the above findings provide the guidelines for the usage of non-linear PBM framework and are expected to improve the design, control, and optimization of dry milling processes that exhibit non-linear breakage kinetics.

Approach to the breakage behavior of comminuted poplar and corn stover under single impact

Breakage behavior under impact of two different types of biomass resources (poplar and corn stover) is characterized, taking into account the influences of the impact energy, of the number of impacts, of the input particle size and of the material properties itself. Within corn stover, two fractions showed different breakage behavior and they were analyzed separately: corn cob and corn stalk and leaves. Biomass resources present several inherent complexities such as its fibrous non-brittle behavior and the non-spherical shape of their particles. Mastercurve formulation for breakage probability (S) based on the resistance of the particles against fracture (fmat) and on the mass specific energy which a particle can absorb without fracture (Wm, min) was obtained. Moreover, a new formulation of the new particle population generated after the impact (breakage function, B) was developed incorporating two new material parameters (γ and α) to a power law function. Corn cob showed much higher threshold energy for fracture (Wm, min) than corn stalk/leaves and poplar. Furthermore, corn cob presented the highest values of γ and α that represent coarser new particle generation. Corn stalk/leaves and poplar showed more similar material parameters in comparison to corn cob.

Effect of morphology on breakage and liberation characteristics of minerals and coal

Ore morphology plays a vital role during the milling and liberation of minerals. This study was carried out to understand the role of mineral crystallography and mineral interfaces on the milling and liberation processes. Data related to mineral crystallography, Vickers Hardness Number and beneficiation processes were collected from literature, and detailed statistical analysis was conducted to relate these parameters. Review of the crystallographic information of minerals present in ores indicates that molecular weight and cell parameters significantly affect milling and liberation characteristics. Mineral interfaces were classified into the three categories of coherent crystals, semi-coherent and incoherent crystals, and breakage behaviors were studied. The studied cases revealed that these material interfaces control the micropore properties that play a vital role in the initiation of intergranular and intercrystalline fractures which occur in siliceous manganese ores and dolomite as a result of thermal treatment. In contrast, banded hematite jasper and coal exhibited a much more complex fracture pattern due to their coherent interfaces and finer physical associations. This study explains the effect of the various types of interfaces on milling, and the approach can be helpful in developing a methodology to enhance mineral liberation with minimum energy consumption.

Wear and breakage behaviors of PCD small-diameter end-mill: a case study on machining 2A12 aluminum alloy

Small-diameter end-mill is a key element for micro-machining technique. It is a new attempt to manufacture a small-diameter tool with polycrystalline diamond (PCD), which is also a hot issue in the research area of micro-manufacturing. PCD end-mills with small-diameter were fabricated and utilized in micro-milling. With a contact simulation model, the stress distribution and potential crack propagation of the PCD tool was revealed via 2D finite element (FE) analysis of 2Al2 aluminum alloy acting on the tool surface. Thereafter, a series of machining experiments on 2A12 micro-part were carried out with the PCD small-diameter end-mill. The wear characteristics of the rake face and flank face were analyzed, and the wear mechanisms of small-diameter end-mills were carefully investigated by using scanning electron microscope (SEM) and energy dispersive X-ray (EDX) spectroscopy. Three typical breakage morphologies of PCD end-mills were demonstrated while machining the aluminum alloy workpiece, i.e., the breakage of the tool tip, the edge chipping, and the peeling off of PCD layer. The consequent experiment results showed that abrasive wear, adhesive wear, and oxidative wear were the predominant characteristics in the damage region of PCD small-diameter end-mill. The effect mechanisms of various wear characteristics were also analyzed and revealed in detail. The experimental results were discussed according to the simulation results and effects on failure behavior of the PCD tool. The research can provide a better understanding for the wear and breakage behaviors of the downsized PCD tool in machining aluminum alloy and underpin the development of micro-milling process with diamond tool.

Energy-Size Reduction of Coals in the Hardgrove Machine

To simulate the grinding process in an industrial vertical spindle mill, the Hardgrove mill was fitted with a power-measuring meter to investigate the breakage characterizations of different narrow size fractions of coal. Power consumption in the grinding process was precisely recorded at the sampling frequency of 1 second with the help of sampling software for power. The experimental results indicated that the energy input for grinding decreased with increases in time for each sample. Changes in the weight percentage in the top-size interval showed that the first-order law was not satisfied to describe the total grinding process. The new produced fine coal had a negative effect on the breakage behavior of coarse particles. But removal of −0.09 mm size can help to increase the energy input for grinding and the generating rate of −0.09 mm also accelerated in turn. The relationship between t10 and energy input can be described by the classical breakage function. Specific energy consumed by raw coal with a small size was higher when subjected to the same value of t10, due to the relatively higher specific surface area of ground coal at the same breakage ratio of 10.

Breakage Probability of Stressed Granules Using a Degradation Model

AbstractThe proposed degradation model is verified by experiments to determine the breakage behavior of inhomogeneous granules. The stressing contact points are configured by repeated stressing. The model represents contact point configuration and distributed mechanical properties within a single granule by fitting Monte‐Carlo data. It is applied to fit the cumulative breakage probability with normal, random, and Weibull strength distributions. The drop weight test verifies the model by testing γ‐Al2O3 and Zeolite 4AK granules. A damage accumulation effect by repeated stressing is observed.

Breakage probability of granules during repeated loading

In order to investigate the breakage behaviour of inhomogeneous particulate products such as fine agglomerates i.e. granules, their structural inhomogeneity has to be taken into consideration. In this article, considering the contact at each load during repeated loading, we describe from a micro-mechanical perspective, the differences in the contact area, contact stiffness and fatigue, and from an energetic perspective, the differences in the breakage probability. As model test materials, Geldart D elasto-plastic γ-Al2O3 granules had been selected and tested by quasi-static compression, low-velocity dynamic pendulum double-impact and high-velocity dynamic impact using a pneumatic cannon. Furthermore, we also describe the influence of preloading by double-impact on the breakage probability of granules subsequently loaded by dynamic impact.

Electrical breakdown channel locality in high voltage pulse breakage

An experimental study was conducted, in which synthetic samples made of construction grout and pyrite grains were subjected to high voltage pulses in a single-particle and single-pulse mode, in order to investigate the effect of electrical breakdown channel locality on particle breakage behaviour. The data confirm that the locality of electrical breakdown channel dominates the breakage response of particles. When a breakdown channel passes along the axis of a particle, it generates a finer product and produces more cracks/microcracks on the fragments. The electrical breakdown channel locality is controlled by the grains of minerals with high conductivity/permittivity and their location in a particle under the identical machine settings. The outcomes using the synthetic samples are helpful in understanding the breakage behaviour of natural ore particles in electrical comminution.

A constitutive model for the state-dependent behaviors of rockfill material considering particle breakage

The particle breakage during specimen compaction had more significant influence on the position of the breakage critical-state line (BCSL) of Tacheng rockfill material (TRM) in the e-lnp′ plane than the particle breakage during shearing, based on the large-scale triaxial compression tests on TRM in a wide range of densities and pressures. The state-dependent dilatancy and the plastic modulus were correlated to the breakage index, based on the formulations of the BCSL of TRM in the e-lnp′ plane. The state-dependent model considering particle breakage was proposed for TRM within the framework of the generalized plasticity theory. The proposed model contained fourteen material constants. The test data of TRM from Group A were adopted to determine these material constants, while the test data from Group B were used independently to validate the model predictive capacity. The comparisons between model simulations and test data illustrated that the model with consideration of particle breakage could well represent the stress-strain behaviors of TRM, e.g., the strain hardening and volumetric contraction behaviors at a loose state and the strain softening and volumetric expansion behaviors at a dense state, and also the particle breakage behaviors of TRM.

HVOF sprayed Al–Cu–Cr quasicrystalline coatings from coarse feedstock powders

Al–Cu–Cr quasicrystalline (QC) coatings were prepared from coarse feedstock powders by a high velocity oxy-fuel (HVOF) system DJ2700. The contrast experiments were performed by low power atmospheric plasma spray (LPAPS) using the same Al65Cu20Cr15 QC powders, and by HVOF spraying Cu180 powders with the size of 44–61μm. The phase composition, microstructure and microhardness properties of the QC coatings were investigated. XRD results showed that the feedstock and coatings contained a predominant phase, icosahedral quasicrystal (IQC) I-Al65Cu24Cr11, and three minor crystalline phases: α-Al69Cu18Cr13, θ-Al13Cr2 (i.e. Al83Cu4Cr13) and ε-Al2Cu3. A qualitative analysis on the XRD patterns indicated that, a HVOF-sprayed coating contained more IQC and fewer crystalline phases in the one deposited by LPAPS. Moreover, the higher the input heat energy, the fewer IQC and the more crystalline phase the coating contained, for not only HVOF but also LPAPS. As confirmed by experimental results, when the HVOF-sprayed QC particle impacted onto the substrate surface, the unmelted solid part of particle broke up, and the previously deposited coating portion was deformed and densified and even cracked by impingement of the in-flight particles with high velocity; which minified splats and densified the as-sprayed coating. Thus, the HVOF-sprayed coatings from such coarse (61–74μm) QC powders had much smaller splats and much denser microstructures with lower porosity and higher microhardness, compared with those deposited by LPAPS using the same feedstock, although the preferential particle size of feedstock powders for HVOF spraying is conventionally 5–45μm. Furthermore, based on the contrast experimental results, the necessary and sufficient conditions for occurrence of the particle impact breakage behavior in the thermal spray process are: (1) the high brittleness of feedstock and (2) the high velocity and low melting degree of spray particles, respectively.

A New Model for Comminution Behavior of Different Coals in an Impact Crusher

In this study, breakage behavior of three different coals in a laboratory impact crusher was investigated. The laboratory impact crusher carrying three rows of hammers is rotating at 2,840 rpm driven by a 1.1 kW motor. In the evaluation of crushers, t-family curves obtained from pendulum and drop weight test methods are frequently used. It is a known fact that there are many difficulties and problems in these tests. In this study, a new model was developed by t-family value evaluation and Bond grindability approach and the model was tested. As a result, the validity of the model was proved by a high regression value (r2 = 0.945).

Quasi-static diametrical compression of characteristic elastic–plastic granules: Energetic aspects at contact

Comminution processes have traditionally been considered as empirical endeavors, with great difficulties in analyzing, predicting and controlling the observed behavior. Process industries have faced serious problems, ranging from poor product quality control up to managing product quantity losses due to unexpected attrition and breakage events. After a decade of ardent research, there has been a notable advancement in our understanding of granular behavior under mechanical stresses. However, far less is known about the energetic aspects occurring at such conditions.In this article, we present critical information from an energetic perspective concerning the deformation and breakage behavior of characteristic elastic–plastic granules under quasi-static compressive forces, studied using single granule diametrical compression tests at a constant strain controlled loading velocity. The force–displacement behavior has been approximated using the Hertz model (Hertz, 1882) for elastic loading, the Tomas model (Tomas, 2007a) for elastic–plastic loading and the Stronge–Antonyuk correlations (Stronge, 2000; Antonyuk, 2006) incorporated Hertz model (Hertz, 1882) for elastic unloading with additional displacements due to apparent viscous effects. The rate independent specific energy characteristics have been studied and a corresponding energetic coefficient of restitution has been derived. A comparison of the energetic characteristics at primary breakage of fresh and pre-loaded granules has been presented using breakage probability functions. The phenomenon of strain hardening during localized repetitive compressive loadings has also been analyzed. Furthermore, the influences of granule size, moisture content and stressing intensity have been considered in each of the investigated entities.

Numerical study of agglomerate abrasion in a tumbling mixer

A numerical simulation using the Discrete Element Method (DEM) was performed to investigate the phenomena concerning the abrasion and breakage of agglomerates in a diffusion powder mixer. Agglomerates were created by defining a single structure of particles with bonds of different strengths using the Bonded Particle Model (BPM). By comparing the agglomerate size reduction calculated by intact and broken bonds with that agglomerate size calculated by particle number, it was possible to differentiate abrasion and breakage behavior of the agglomerate in the system. The DEM simulations gave support to earlier investigations which concluded that definition of a Stoke abrasion number is a valid approach to predict agglomerate abrasion in a powder blending system.