Comminution limit (CL) of particles and possible implications for pumped storage reservoirs

Comminution (fragmentation) of solid particles is important in a range of technologies. An interesting effect is the so-called comminution limit (CL), which is effectively a brittle/ductile transition. Above the CL particles fail by fracture. However, as particle size decreases the amount of stored energy in the particle also decreases and eventually there is no longer sufficient stored energy in the particle to propagate a crack and the particle flows plastically. The CL depends on the hardness, H, and the toughness, K _Ic. In mountainous countries, two-reservoir systems are used to generate and store power. When power is needed, water runs through the turbines to the lower reservoir. If there is excess power, water is pumped to the upper reservoir. This recycling of liquid through the turbines can break up entrained particles. Previous work in this area has been primarily concerned with sedimentation of the particles. The research reported in this paper uses the CL to calculate the particle sizes produced for different materials including different rock types. Interestingly, the particle sizes predicted mainly fall in the range where they sediment near the upper water surface. In such cases, the surface layers become opaque to sunlight and plant and animal life will be affected. It is suggested that the CL provides additional information which would assist research in this area. Where H and K _Ic are not known for a particular rock type they should be measured.     

Oblique impact simulations of high strength agglomerates

Different types of particle compounds like concrete particles can be considered as a model material of high strength agglomerates. It is necessary to investigate and understand fracture behaviour of these agglomerates in order to avoid breakage during storage, handling and transportation. The aim of the research is to examine the comminution behaviour of high strength agglomerates during oblique impact loadings.A two dimensional finite element analysis has been carried out to understand stress pattern distributions before crack initiation. Then a two dimensional discrete element method has been applied to study the fragmentation behaviour of the agglomerates. Concrete particles of B35 strength category have been chosen to represent the high strength agglomerates.Analysis is done with oblique impact loadings at different velocities from 7.7 to 180 m/s. The stressing conditions comprise low flow rate transportation and handling to high speed impacts during fall down in bunker, stock piles, ship loading or stressing in crushers and mill operations. Particle size distributions and new surface generation have also been evaluated in the paper.It is shown that at higher velocities, particle size distributions are identical to each other regardless of impact angle. Increasing impact velocity does not necessarily produce more new surfaces after certain velocity limit.     

A Mineral Liberation Model for Confined Particle Bed Breakage

ABSTRACT

The advent of High Pressure Grinding Rolls technology in the minerals industry has created an interest in the particle bed mode of breakage, not only because of its energy saving qualities, but also due to its apparent enhanced mineral liberating properties. Little scientific evidence exists to substantiate any enhanced liberation properties. Automated image analysis and stereological correction methods have now made it possible to measure mineral liberation quite accurately. A population balance mineral liberation model, based on QEM*SEM liberation data of confined particle bed breakage products of a binary ion oxide core, is presented. The selective breakage observed, due to the differential breakage properties of the respective phases, is described. Preferential breakage is incorporated into a liberation model for the first time.     

垂直轮廓剖面迹线法测定聚合物材料断面粗糙度的研究

运用垂直轮廓剖面迹线法测定了聚合物材料的断面轮廓线粗糙度参数ＲＬ及聚合物材料冲击强度和断口表面粗糙度参数Ｒｓ的关系。实验结果指出：聚合物的面轮廓线粗糙度与试样形状、断裂性质及断口形貌等因素有关。缺口试样断口形貌均衡分布时，试样两表面的测量值相等；断试样表面和心部测量结果相同；韧断试样表面测量结果大于心部测量结果。无缺口试样冲击脆断时，试样表面测量结果与断裂源位置有关，心部测量结果一般大于两表测量平     

Effect of particle size distribution and subgrade condition on degradation of railway ballast under impact loads

Ballasted rail tracks are generally exposed to impact loads generated from abnormal wheel-rail interface as well as sudden variations in support rigidity. These induced impact loads can lead to railway ballast degradation by attrition of the angular edges of the aggregate and breakage of single particle into finer fragments. In the present study, the degradation of ballast particles under impact loads is investigated by considering various fouling and breakage indices. For this purpose, impact test is conducted on ballast aggregates obtained from different quarries (rock types of basalt, marl, dolomite and trachyte) by varying the gradation of ballast aggregates, impact energy and subgrade type. According to the obtained results, the degradation of ballast specimens under impact loading is less for more broadly-graded ballast. In addition, providing a flexible subgrade as support condition leads to reduction in ballast degradation resulted from diminishing impact energy. Furthermore, the axial strain of ballast specimens reduces with decrease in degradation of aggregates under repeated impact loads.     

不同粗糙度岩石-混凝土界面断裂特性研究

界面粗糙度对岩石-混凝土界面断裂特性有重要影响。为研究不同粗糙度岩石-混凝土界面断裂特性,对岩石表面进行刻槽处理获得六种界面粗糙度,采用三点弯曲梁岩石-混凝土复合试件测量界面的断裂参数。运用数值方法计算了界面的起裂断裂韧度K₁ⁱⁿⁱ,并通过P-δ曲线计算界面的断裂能G_f。试验结果表明,所有试件都沿着界面发生破坏,说明岩石-混凝土界面相对于两侧材料属于薄弱面;采用界面刻槽的方式能够获得较大范围的粗糙度数值,当界面粗糙度R_a从0.676 mm增大到2.028 mm时,岩石-混凝土界面起裂断裂韧度KK₁ⁱⁿⁱ从0.362 MPa·m^1/2增加到0.515 MPa·m^1/2,提高了42.3%;界面断裂能G_f从17.928 N/m增加到47.802 N/m,提高了166.7%;同时,K₁ⁱⁿⁱ随着粗糙度的提高一直增大,而G_f随着粗糙度的提高先增大后趋于平缓。     

MIXED-MODE DELAMINATION OF MULTIDIRECTIONAL CARBON FIBER/EPOXY LAMINATES

Scanning electron microscopy was used to identify fractographic features that are characteristic of different modes of interlaminar fracture. The cusp angle and the amount of fiber pull-out on the fracture surface can be used to characterize the different loading modes. A large amount of fiber pull-out is the dominant feature of a mode I fracture, while in mode II large cusp angles and many cusps are the main characteristics. The amount of fiber pull-out, and subsequently brokenfibers, per unit area was investigated and found to vary in proportion to the degree of mode I loading. Such methods can be used to analyze failure and the propagation ofdelamination in structural components. The energy associated with cusp formation constitutes a large proportion of the mode IIfracture toughness component, while the amount of fiber pull-out and fracture has a considerable influence on the mode I fracture component. The cusp angle was seen to provide a quantitative measure of the fracture surface roughness. A failure criterion that takes the fracture surface appearance into account was evaluated. The cusp angle was subsequently used to modify this failure criterion. As a consequence, this provided improved agreement with the experimental data.     

Impact fracture of a ferritic steel in the lower shelf regime

This paper reports the results of a systematic investigation on the fracture of Charpy-V notch A508 steel specimens, tested in the lower shelf regime. The fracture energy has been determined for quasi-static, standard Charpy and one-point-bend impact. The results show a general trend for the fracture energy to increase with the loading rate, at the lower temperature (–160 °C). At this temperature, the roughness of the fracture surface increases markedly with the loading rate. The fractographic analysis shows the presence of 3–4 cleavage initiation sites situated at 100–800 m from the crack front, irrespective of the loading rate. Numerous cleavage microcracks are observed underneath the main fracture plane. The statistical analysis shows that the length distribution of the microcracks is adequately described by Weibull statistics. It is also found that the number of microcracks increases with the loading rate. It is suggested that the larger number of microcracks is responsible for the observed increased roughness and energy dissipation.     

温度对聚氯乙烯缺口冲击强度及断面粗糙度的影响

研究了温度对聚氯乙烯 PVC 缺口冲击强度、断口形貌特征及断面粗糙度的影响。结果表明,PVC 缺口冲击强度和断面粗糙度参数 R_s 随温度变化,在脆化温度 T_h 处存在极小值,前者取决于真实断裂表面积大小;后者受控于局部高强变形及裂纹分叉扩展综合作用。低温冲击断面上易观察到裂纹分叉扩展形成的弧形条纹及分层。     

3D printing of tuneable agglomerates: Strain distribution and effect of internal flaws

The current study presents a novel and reliable method for producing 3D printed agglomerates with different colour distributions and material properties with 2-fold aims: providing feasible and accurate control on compression of agglomerates under different compression angles, and better tracking of individual particle position after agglomerate breakage. Multi-coloured agglomerates in cubic tetrahedral and random sphere shapes were printed with both rigid and soft bonds. The printed agglomerates were analysed thoroughly of their surface and structural properties including surface roughness and printing accuracy. The agglomerate breakage behaviours under static compression were analysed as a function of bond strength, loading rate and loading directions, with strain distribution plotted over the random sphere agglomerate structure. In addition, agglomerate structures with designed internal macro-voids in different positions and sizes were also created for breakage study, in an effort to better understand parameters governing the mechanical properties of agglomerates with cavities and voids which is inevitable in particle industry but poorly understood at present.     

Experimental investigation of the impact breakage characteristics between grinding media and iron ore particle in ball mills

The particle breakage of the ball mill is an extremely complicated breakage process. It is difficult to quantify and describe the particle breakage behavior. In this study, a drop-ball experimental setup was developed to demonstrate the impact process of grinding media on ore particles. The quantitative analysis of the effects of particle size, impact energy, and the number of impacts on particle breakage behavior was performed separately. The results show that the breakage probability model and product size distribution model used can be excellent to predict the particle breakage behavior for the single-particle impact experiments. The breakage probability of particles is highly sensitive to impact energy and particle size, exponentially increasing with the increase of impact energy. In addition, the application of the t_n-t₁₀ relationship provides a convenient means to characterize and predict the particle size distribution. In multi-layer particle impact experiments, the captured thickness of ore particles is approximately 2 layers during the crushing process. The broken mass of iron ore particles is proportional to the number of concessive impacts at different impact energies. This paper provides theoretical and methodological support for the evaluation and optimization of particle breakage in ball mills.     

Influence of interface properties on fracture behaviour of concrete

Hardened concrete is a three-phase composite consisting of cement paste, aggregate and interface between cement paste and aggregate. The interface in concrete plays a key role on the overall performance of concrete. The interface properties such as deformation, strength, fracture energy, stress intensity and its influence on stiffness and ductility of concrete have been investigated. The effect of composition of cement, surface characteristics of aggregate and type of loading have been studied. The load-deflection response is linear showing that the linear elastic fracture mechanics (LEFM) is applicable to characterize interface. The crack deformation increases with large rough aggregate surfaces. The strength of interface increases with the richness of concrete mix. The interface fracture energy increases as the roughness of the aggregate surface increases. The interface energy under mode II loading increases with the orientation of aggregate surface with the direction of loading. The chemical reaction between smooth aggregate surface and the cement paste seems to improve the interface energy. The ductility of concrete decreases as the surface area of the strong interface increases. The fracture toughness (stress intensity factor) of the interface seems to be very low, compared with hardened cement paste, mortar and concrete.     

Impact–fatigue behaviour of unidirectional carbon fibre reinforced polyetherimide (PEI) composites

Impact fatigue properties of unidirectional carbon fibre-reinforced polyetherimide (PEI) composites was evaluated by subjecting standard izod impact samples to low velocity impact loading at energy levels ranging 0.16–1.08 J by using Ceast Model Resil 25, a pendulum type instrumented impact test system. The effect of the previous low velocity impacts on the impact properties of the laminates was investigated. On the other hand materials were subjected to repeated low velocity impact tests up to fracture. Results of repeated impact study are reported in terms of peak load, absorbed energy and number of impacts. Fractographic analysis revealed the fracture by primary debonding, with fibre breakage and pullout in the tensile zone, but a shear fracture of fibre bundles in the compressive zone of the specimen.     

The influence of target geometry on the high velocity impact response of CFRP

The influence of geometrical parameters on the high velocity impact response of CFRP has been studied. Impact velocities between 10 m/s and 500 m/s were obtained using a high pressure nitrogen gas gun. The resulting impact damage was assessed visually, by optical microscopy and by thermally deplying specimens in an oven at 420°C.It has been shown that increasing the flexural stiffness of a target by varying the fibre stacking sequence or increasing its thickness changes the mode of initial fracture from a lower surface flexural failure to a top surface contact failure. For a given incident energy, increasing the target thickness results in a lower level of damage as detected by ultrasonic inspection. Further, changing the specimen geometry in this way leads to significant increases in the perforation threshold energy. Increasing the surface area of the target by varying its length or width does not alter the amount of damage incurred under high velocity impact loading. Indeed, it appears that smallscale test coupons are fully capable of reproducing damage levels incurred by operational structures when subjected to high velocity impact by a light projectile.     

Study of the Comminution Characteristics of Coal by Single Particle Breakage Test Device

Single-particle breakage tests of South Blackwater and Ensham coal from the Bowen Basin area in Queensland were conducted by a computer-monitored twin-pendulum device to measure the energy utilization pattern of the breakage particles. Three particle sizes (-16.0 + 13.2 mm, -13.2 + 11.2 mm, -11.2 + 9.5 mm) of each coal were tested by a pendulum device at five input energy levels to measure the specific comminution energy. When particles were tested at constant input energy, the variation of comminution energy between the same size broken particles of Ensham coal was minimal, because Ensham coal is a softer and higher friability coal, which absorbs more input energy than harder coal during breakage tests. For different particle sizes, the specific comminution energy increases linearly with the input energy and the fineness of the breakage products increases with the specific comminution energy.The size distribution graphs are curved but approach linearity in the finer region. At a constant input energy, the twin pendulum breakage product results show that the fineness of the products increases with decrease in particle size and South Blackwater coal produced finer products than the Ensham coal. The t-curves are the family of size distribution curves, which can describe the product size distribution of the breakage particles during single-particle breakage tests.     

Differences in dry and wet grinding with a high solid concentration of coking coal using a laboratory conical ball mill: Breakage rate,morphological characterization,and induction time

This study explored the influence of wet and dry grinding conditions on breakage rate, shape factor and surface roughness of ground particles, induction time (the threshold for particle–bubble attachment to occur), and flotation recovery. The experimental results indicated that the dry grinding breakage rate was much higher than the wet grinding one. The first-order region was limited to a relatively short grinding time, where it was considered that little or no secondary breakage occurred. With the increasing time, the dry grinding breakage rate increased, while it decreased for wet grinding (solid concentration of 70 vol.%). The differences in shape factor and surface roughness of the wet- and dry-ground samples were attributed to different breakage mechanisms and grinding energy amounts generated by those two types of procedures. The wet-ground particles were characterized by more irregular shape factors and smoother surfaces, and thus presented shorter induction times and higher floatation recoveries compared to the dry-ground ones.     

Scale-up procedure of parameter estimation in selection and breakage functions for impact pin milling

This paper presents a scale-up procedure of parameter estimation in the selection function and breakage function from single particle impact breakage to inform the predictions at the process scale of an impact pin mill. The selection and breakage functions used in population balance model (PBM) for particle breakage in the literature are briefly reviewed. Single particle breakage tests are conducted in a vertical impact tester subject to varying impact velocities. The single particle breakage results further serve to provide the database for the parameter estimation in Vogel and Peukert model (Vogel and Peukert, 2005). The estimated parameters in the particle level are upscaled in an impact pin mill using the population balance model, which is implemented in the software gPROMS (Process Systems Enterprise, UK) (gPROMS® 4.1 Release Notes, 2016). The impact milling tests were carried out in an impact pin mill UPZ100 subject to four feed rates, providing the dataset for model validation. The sensitivity analysis of the PBM parameters was conducted to help identify their leverage on the particle size distribution. The scale-up procedure by specifying the parameters from single particle level to the process level of PBM demonstrates an approach to help predict the size reduction process subject to the prevailing mechanism in an impact pin mill and other milling processes alike.     

Selection function of particles under impact loads: The effect of collision angle

The current work investigates the effect of collision angle on the breakage of particles under impact loads. The experiments were performed using a homemade experimental system that accelerates the particles horizontally toward the target using compressed air. The design of the system allows the angle of the target and the air velocity, both adjustable to check different collision angles at different impact velocities; and the tested material that was blown to the target to be collectible for measuring the percentage of broken particles for the analysis. In this study, six different materials were tested by conducting experiments with different collision angles and impact velocities. As expected, the results showed that the collision angle affects the breakage of the particles. When the collision angle becomes acute, i.e., less than 90° (perpendicular collision with the target), it results in less breakage of the particles for all tested materials and at all tested velocities. Consequently, an empirical model got established. This model can predict the median impact velocity that causes half of the particle population to break, depending upon collision angle and particle size.     

Influence of particle breakage on the dynamic compression responses of brittle granular materials

The dynamic compression responses of dry quartz sand are tested with a modified spilt Hopkinson pressure bar (MSHPB), and the quasi-static compression responses are tested for comparison with a material testing system. In the experiments, the axial stress–strain responses and the confining pressure of the jacket are both measured. Comparison of the dynamic and the quasi-static axial stress–strain curves indicate that dry quartz sand exhibits obvious strain-rate effects. The grain size distributions of the samples after dynamic and quasi-static loading are obtained with the laser diffractometry technique to interpret the rate effects. Quantitative analyses of the grain size distributions show that at the same stress level, the particle breakage extent under quasi-static loading is larger than that under dynamic loading. Moreover, the experimental and the theoretical relationships of the particle breakage extent versus the plastic work show that the energy efficiency in particle breakage is higher under quasi-static loading, which is the intrinsic cause of the strain-rate effects of brittle granular materials. Using the discrete element method (DEM), the energy distributions in the brittle granular material under confined compression are discussed. It is observed that the input work is mainly transformed into the frictional dissipation, and the frictional dissipation under dynamic loading is higher than that under quasi-static loading corresponding to the same breakage extent. The reason is that more fragmentation debris is produced during dynamic breakage of single grains, which promotes particle rearrangement and the corresponding frictional dissipation significantly.     

A grain-scale study of spall in brittle materials

The evolution of spall for a brittle material is investigated under variance of anisotropy, grain boundary fracture energy, and loading. Because spall occurs in the interior of the specimen, fundamental studies of crack nucleation and growth are needed to better understand surface velocity measurements. Within a cohesive approach to fracture, we illustrate that for anisotropic materials, increases in the fracture energy cause a transition in crack nucleation from triple-points to entire grain boundary facets. Analysis of idealized flaws reveals that while crack initiation and acceleration are strong functions of the fracture energy, flaws soon reach speeds on the order of the Rayleigh wave speed. Finally, simulated surface velocities of spalled configurations are correlated with microstructural evolution. These fundamental studies of nucleation, growth, and spall attempt to link atomic separation to the macroscopic spall strength and provide a computational framework to examine the evolution of spall and the impact on the simulated surface velocity field.