Morphology of impact fragmentation distribution of single spherical and ellipsoidal particles in drop weight experiments

Particle shape is an important factor affecting the fragmentation distribution of the ore particles.To investigate the influence of particle shape on the morphological fragmentation distribution characteristics,the crushable ore particles are defined as prolate,oblate ellipsoid and spherical particles,which have different aspect ratios(AR)and sphericity(S).Based on the drop weight experiment,the influence of the net drop height on the macroscopic mechanical behavior and crushing distribution characteristics of the single spherical and ellipsoidal particles is studied.The results show that different peak-shifting characteristics exist during particle fragmentation.The fragmentation distribution peak shifts left when the increased impact energy is eventually only enough to break medium-sized sub-particles.Conversely,it shifts right when impact energy is increased enough to break largest-sized sub-particles.Besides,regardless of whether the net drop height changes,the maximum continuous fragmentation degree presents"M"-shaped characteristic with the increased AR.Compared with the ellipsoid particles,the single spherical particle is more difficult to be broken by impact,with wider equivalent particle fragmentation distribution.With the increase of particle sphericity,the maximum continuous fragmentation degree of a single ellipsoid particle has an overall trend of initial increase and subsequent decrease.Especially when particle sphericity is 0.9<S<0.95,the maximum continuous fragmentation degree of both prolate and oblate ellipsoid particles is much higher.

Pairing effects on the fragment mass distribution of Th,U,Pu,and Cm isotopes

In this article,a comprehensive study of the fission process of Th,U,Pu,and Cm isotopes using a Yukawa-folded meanfield plus standard pairing model is presented.The study focused on analyzing the effects of the pairing interaction on the fragment mass distribution and its dependence on nuclear elongation.The significant role of pairing interactions in the fragment mass distributions of^(230)Th,^(234)U,^(240)Pu,and^(246)Cm was demonstrated.Numerical analysis revealed that increasing the pairing interaction strength decreased the asymmetric fragment mass distribution and increased the symmetric distribution.Furthermore,the odd-even mass differences at symmetric and asymmetric fission points were examined,highlighting their sensitivity to changes in the pairing interaction strength.Systematic analysis of the Th,U,Pu,and Cm isotope fragment mass distributions demonstrated the effectiveness of the model in reproducing the experimental data.In addition,the effects of the zero-point energy and half-width parameter on the fragment mass distribution for^(240)Pu were explored.Thus,this study provides valuable insights into the fission process by emphasizing the importance of pairing interactions and their relationship with nuclear elongation.

Debris cloud structure and hazardous fragments distribution under hypervelocity yaw impact

This study investigates how the debris cloud structure and hazardous fragment distribution vary with attack angle by simulating a circular cylinder projectile hypervelocity impinging on a thin plate using the finite element-smoothed particle hydrodynamics(FE-SPH)adaptive method.Based on the comparison and analysis of the experimental and simulation results,the FE-SPH adaptive method was applied to address the hypervelocity yaw impact problem,and the variation law of the debris cloud structure with the attack angle was obtained.The screening criterion of the hazardous fragment at yaw impact is given by analyzing the debris formation obtained by the FE-SPH adaptive method,and the distribution characteristics of hazardous fragments and their relationship with the attack angle are given.Moreover,the velocity space was used to evaluate the distribution range and damage capability of asymmetric hazardous fragments.The maximum velocity angle was extended from fully symmetrical working conditions to asymmetrical cases to describe the asymmetrical debris cloud distribution range.In this range,the energy density was calculated to quantitatively analyze how much damage hazardous fragments inflict on the rear plate.The results showed that the number of hazardous fragments generated by the case near the 35°attack angle was the largest,the distribution range was the smallest,and the energy density was the largest.These results suggest that in this case,debris cloud generated by the impact had the strongest damage to the rear plate.

Sensitivity impacts owing to the variations in the type of zero-range pairing forces on the fission properties using the density functional theory

Using the Skyrme density functional theory,potential energy surfaces of^(240)Pu with constraints on the axial quadrupole and octupole deformations(q_(20)and q_(30))were calculated.The volume-like and surface-like pairing forces,as well as a combination of these two forces,were used for the Hartree–Fock–Bogoliubov approximation.Variations in the least-energy fission path,fission barrier,pairing energy,total kinetic energy,scission line,and mass distribution of the fission fragments based on the different forms of the pairing forces were analyzed and discussed.The fission dynamics were studied based on the timedependent generator coordinate method plus the Gaussian overlap approximation.The results demonstrated a sensitivity of the mass and charge distributions of the fission fragments on the form of the pairing force.Based on the investigation of the neutron-induced fission of^(239)Pu,among the volume,mixed,and surface pairing forces,the mixed pairing force presented a good reproduction of the experimental data.

Fracture behavior and mechanism of highly fragmented steel cylindrical shell under explosive loading

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed.This study investigated the fragmentation performance of a new high-carbon silicon-manganese(HCSiMn)steel cylindrical shell through fragment recovery experiments.Compared with the conventional 45Cr steel shell,the number of small mass fragments produced by the HCSi Mn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model.The fragmentation process of the HCSi Mn shell exhibited more brittle tensile fracture characteristics,with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation.On the one hand,the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite,so that microscopic intergranular fracture reduces the characteristic mass of the fragments;on the other hand,the distribution of alloy carbides can exert a"pinning"effect on the substrate grains,causing more initial cracks to form and propagate along the brittle carbides,further improving the shell fragmentation.Although the killing power radius for light armored vehicles was slightly reduced by about 6%,the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26%based on theoretical assessment.These results provided an experimental basis for high fragmentation warhead design,and to some extent,revealed the correlation mechanism between metallographic structure and shell fragmentation.

Energy consumption in rock fragmentation at intermediate strain rate

In order to determine the relationship among energy consumption of rock and its fragmentation, dynamic strength and strain rate, granite, sandstone and limestone specimens were chosen and tested on large-diameter split Hopkinson pressure bar (SHPB) equipment with half-sine waveform loading at the strain rates ranging from 40 to 150 s- 1. With recorded signals, the energy consumption, strain rate and dynamic strength were analyzed. And the fragmentation behaviors of specimens were investigated. The experimental results show that the energy consumption density of rock increases linearly with the total incident energy. The energy consumption density is of an exponent relationship with the average size of rock fragments. The higher the energy consumption density, the more serious the fragmentation, and the better the gradation of fragments. The energy consumption density takes a good logarithm relationship with the dynamic strength of rock. The dynamic strength of rock increases with the increase of strain rate, indicating higher strain rate sensitivity.

Dynamic fragmentation of microwave irradiated rock

The microwave-assisted rock fragmentation has been proven to be a promising approach in reducing cutting tools wear and improving efficiency in rock crushing and excavation.Thus,understanding the influence of damage induced by microwave irradiation on rock fragmentation is necessary.In this context,cylindrical Fangshan granite(FG)specimens were exposed to microwave irradiation at a power of 6 kW for different durations up to 4.5 min.The damages of the specimens induced by irradiation were quantified by using both X-ray micro-CT scanning and ultrasonic wave measurement.The CT value and Pwave velocity decreased with increase of irradiation duration.The irradiated specimens were then tested using a split Hopkinson pressure bar(SHPB)system to simulate rock fragmentation.A momentum-trap technique was utilized to ensure single-pulse loading on the specimen in SHPB tests,enabling valid fragment size distribution(FSD)analysis.The dependence of dynamic uniaxial compressive strength(UCS)on the irradiation duration and loading rate was revealed.The dynamic UCS increased with increase of loading rate while decreased with increase of irradiation duration.Using the sieve analysis,three fragmentation types were proposed based on FSD,which were dictated by both loading rate and irradiation duration.In addition,an average fragment size was proposed to quantify FSD.The results showed that the average fragment size decreased with increase of loading rate.A loading rate range was identified,where a dramatic reduction of the average fragment size occurred.The dependence of fragmentation on the irradiation duration and loading rate was also discussed.

Fragment spatial distribution of prismatic casing under internal explosive loading

Non-cylindrical casings filled with explosives have undergone rapid development in warhead design and explosion control.The fragment spatial distribution of prismatic casings is more complex than that of traditional cylindrical casings.In this study,numerical and experimental investigations into the fragment spatial distribution of a prismatic casing were conducted.A new numerical method,which adds the Lagrangian marker points to the Eulerian grid,was proposed to track the multi-material interfaces and material dynamic fractures.Physical quantity mappings between the Lagrangian marker points and Eulerian grid were achieved by their topological relationship.Thereafter,the fragment spatial distributions of the prismatic casing with different fragment sizes,fragment shapes,and casing geometries were obtained using the numerical method.Moreover,fragment spatial distribution experiments were conducted on the prismatic casing with different fragment sizes and shapes,and the experimental data were compared with the numerical results.The effects of the fragment and casing geometry on the fragment spatial distributions were determined by analyzing the numerical results and experimental data.Finally,a formula including the casing geometry parameters was fitted to predict the fragment spatial distribution of the prismatic casing under internal explosive loading.

Fragmentation Analyses of Granular Explosive Under Drop Weight Impact

Fragmental size and distribution of explosive particles play a more important role in the formation of hot-spot than original particles size under drop weight impact.Because the particles breakage and the hot-spots ignition will form in a sequence between fragments and between the fragments and the drop weight surface under the impact.In this paper,the size and distribution of the cyclotetramethylenete tranitramine(HMX)fragments were analyzed by the Laser Particle Size Analyzer Malvern MS2000.The post-analysis results of fragments showed that size distribution of fragments was strongly dependent on drop height.An empirical formula is established to describe the relationship between the average size and drop height.The volume-based probability distribution of explosive fragments was also studied by experiments and theoretical calculations.

Nonextensivity and Tsallis Entropy in DNA Fragmentation Patterns by Ionizing Radiation

Nonextensive statistical mechanics as in Tsallis formalism was used in this study, along with the dynamical Hamiltonian rod-like DNA model and the maximum entropy criteria for Tsallis’ entropy, so as to obtain length distribution of plasmid fragments, after irradiation with very high doses, assuming that the system reaches metaequilibrium. By intensively working out the Grand Canonical Ensemble (used to take into account the variation of the number of base pairs) a simplified expression for Fragment Size Distribution Function (FSDF) was obtained. This expression is dependent on two parameters only, the Tsallis q value and the minimal length of the fragments. Results obtained from fittings to available experimental data were adequate and the characteristic behavior of the shortest fragments was clearly documented and reproduced by the model, a circumstance never verified from theoretical distributions. The results point to the existence of an entropy which characterizes fragmentation processes and depending only on the q entropic index.

Numerical study on the dynamic fracture of explosively driven cylindrical shells

Research on the expansion and fracture of explosively driven metal shells has been a key issue in weapon development and structural protection.It is important to study and predict the failure mode,fracture mechanism,and fragment distribution characteristics of explosively driven metal shells.In this study,we used the finite element-smoothed particle hydrodynamics(FE-SPH)adaptive method and the fluid-structure interaction method to perform a three-dimensional numerical simulation of the expansion and fracture of a metal cylindrical shell.Our method combined the advantages of the FEM and SPH,avoiding system mass loss,energy loss,and element distortion;in addition,the proposed method had a good simulation effect on the interaction between detonation waves and the cylindrical shell.The simulated detonation wave propagation,shell damage morphology,and fragment velocity distribution were in good agreement with theoretical and experimental results.We divided the fragments into three regions based on their shape characteristics.We analyzed the failure mode and formation process of fragments in different regions.The numerical results reproduced the phenomenon in which cracks initiated from the inner surface and extended to the outer surface of the cylindrical shell along the 45°or 135°shear direction.In addition,fragments composed of elements are identified,and the mass and characteristic lengths of typical fragments at a stable time are provided.Furthermore,the mass and size distribution characteristics of the fragments were explored,and the variation in the fitting results of the classical distribution function under different explosion pressures was examined.Finally,based on mathematical derivation,the distribution formula of fragment velocity was improved.The improved formula provided higher accuracy and could be used to analyze any metal cylindrical shells with different length-to-diameter ratios.

Fractal characteristics of cracks and fragments generated in unloading rockburst tests

True triaxial rockburst experiments with four different unloading rates were performed on four prism specimens of granite sampled from Beishan, China. The damage evolution in the rockburst test was investigated from two aspects including fracture surface crack and fragment characteristics. The scanning electron microscopy was used to observe the micro crack information on fragment surface. Combing binarization and box counting dimensions, the fractal dimensions of cracks were obtained. Meanwhile,the fragments were collected and a sieving experiment was conducted. We weighed the fragments qualities, counted the amount of fragments and measured the fragments length, width and thickness.Utilizing four methods to calculate damage fractal dimensions of fragments, the trend of fractal value changing with unloading rates can be roughly described. It can be concluded from these experiments that the fractal dimension either for crack or for fragment holds a decreasing trend with the decreasing unloading rate, indicating a reduction of damage level.

A fast and accurate model for the creation of explosion fragments with improved fragment shape and dimensions

Explosion models based on Finite Element Analysis(FEA)can be used to simulate how a warhead fragments.However their execution times are extensive.Active protection systems need to make very fast predictions,before a fast attacking weapon hits the target.Fast execution times are also needed in real time simulations where the impact of many different computer models is being assessed.Hence,FEA explosion models are not appropriate for these real-time systems.The research presented in this paper delivers a fast simulation model based on Mott’s equation that calculates the number and weight of fragments created by an explosion.In addition,the size and shape of fragments,unavailable in Mott’s equation,are calculated using photographic evidence and a distribution of a fragment’s length to its width.The model also identifies the origin of fragments on the warhead’s casing.The results are verified against experimental data and a fast execution time is achieved using uncomplicated simulation steps.The developed model then can be made available for real-time simulation and fast computation.

Comparative population genomics reveals glacial cycles to drive diversifications in tropical montane birds(Aves,Timaliidae)

Many bird species are specialized to live in the broadleaved,evergreen forests in the mountain regions in Southeast Asia.These mountain habitats are not continuously distributed as the different mountain areas are separated by lowlands,which has restricted gene flow and thus contributed to the high biological diversity in this region.The degree of connectivity between mountain areas has fluctuated with the Pleistocene glacial cycles,being largest during the glaciations when the mountain forests spread to lower elevations.Here we study how the intermittent periods of restricted gene flow and connectivity between the populations of five montane species of babblers(Aves,Timaliidae)in Vietnam may be traced in their genomes.The results suggest that the babbler species in the Central Highlands have been isolated from their sister-populations in northern Vietnam for between ca.585 and 380 ky.For two species with populations in both the Central Highlands and the Da Lat region,we found that these split at more or less the same time(440–340 kya).We also found a significant statistical correlation between the time of the splits of these populations and the lowest altitude at which they are known to occur(no similar correlation was found with the geographic distances between populations).The populations in northern Vietnam show higher genetic variation than their counterparts in South-Central Vietnam,supporting the postulate that smaller populations may have lower genetic variation than larger.In accordance with this,we found the lowest genetic variation in the two species with the smallest populations in the Central Highlands.These two populations also show low levels of genomic heterozygosity.Our results show that the south-central populations of the studied babbler species are genetically distinct from their sister-populations in northern Vietnam,providing additional argument for the long-term protection of the evergreen mountain forests in Southeast Asia.

Driving potential and fission-fragment charge distributions

We propose an efficient approach to describe the fission-fragment charge yields for actinides based on the driving potential of the fissioning system.Considering the properties of primary fission fragments at their ground states,the driving potential,which represents the potential energies of the system around scission configuration and closely relates to the yields of fragments,can be unambiguously and quickly obtained from the Skyrme energy-density functional together with the Weizs?cker-Skyrme mass model.The fission-fragment charge distributions for thermal-neutron-induced fission and spontaneous fission of a series of actinides,especially the odd-even staggering in the charge distributions,can be well reproduced.Nuclear dynamical deformations and pairing corrections of fragments play an important role in the charge distributions.

Systematics on fission fragment mass distribution of neutron induced ^(235)U fission

Based on the neutron induced fission fragment mass distribution data up to neutron energy 20 MeV measured with the double kinetic energy method （KEM） and the radio active method （RAM）, the systematics of fission fragment mass distribution was investigated by using 5 Gaussian model and the systematics parameters were obtained by fitting the experimental data. With the systematics, the yields of any mass A and at any energy in the region from 0 to 20 MeV of neutron energy can be calculated. The calculated results could well reproduce the experimental data measured with KEM, but show some systematical deviation from the data measured by RAM, which reflects some systematical deviations between the two kinds of measured data. The error of systematics yield was calculated in an exact error transformation way, including from the error of the experimental yield data to the error of the discrete parameters, then to the systematics parameters, and at last to the yield calculated with systematics.

Fragment distribution in 78,86Kr+181Ta reactions

Within the framework of the isospin-dependent quantum molecular dynamics model, along with the GEMINI model, the86Kr+181Ta reaction at 80, 120 and 160 MeV/nucleon and the78Kr+181Ta reaction at 160 MeV/nucleon are studied, and the production cross sections of the generated fragments are calculated. More intermediate and large mass fragments can be produced in the reactions with a large range of impact parameter. The production cross sections of nuclei such as the isotopes of Si and P generally decrease with increasing incident energy.Isotopes near the neutron drip line are produced more in the neutron-rich system86Kr+181Ta.

Microscopic study of neutron-induced fission process of^(239)Pu via zero-and finite-temperature density functional theory

To study the neutron-induced fission of^(239)Pu,potential energy surface(PES)calculations were performed using zero and finite-temperature density functional theory(FT-DFT)with the Skyrme force.The energy of the incident neutron was simulated by the temperature of the FT-DFT.The variations of the least-energy fission path,fission barrier,total kinetic energy,scission line,and mass distribution of fission fragments with the incident neutron energy were analyzed.It was learned that an increase in the temperature lowers the barrier height,the isomericstate energy,and the ridge between symmetric and asymmetric fission valleys.Additionally,the gaps of the single particle levels become smaller with an increase in the temperature.As the temperature increases,the pre-fission region shrinks,and the scission occurs at smaller deformation around the symmetric fission channel.At low temperatures,the pairing correlations in the collective space are similar to those in zero-temperature DFT,and when the temperature is T>0.3 MeV,the pairing gaps decrease rapidly.Two different methods were used to calculate the fission yields of the neutron-induced fision^(239)Pu(n,)with different incident neutron energies,in the framework of timedependent generator coordinate method(TDGCM).One way to calculate the fission yield of^(239)Pu(n,f)is to solve the collective equation of the TDGCM by using the PES from the FT-DFT with the corresponding temperature.The other involves using the PES from the zero-temperature DFT and adjusting the initial collective energy of the wave packet in the TDGCM according to the incident neutron energy.For the cases of the lower incident neutron energies,these two methods gave similar results and reproduced the experimental peak and width of fission fragment distribution.However,for the highest incident neutron energy considered in this study,the results from the TDGCM using the PES from zero-temperature DFT deviated explicitly from the experimental data,whereas those obtained by using the PES from FT-DFT remained close to the experimental data.This indicated that,with the increase in the incident neutron energy,the shell structure of the compound nuclei changed explicitly;thus,it may not be effective to use the PES from zero-temperature to perform the fission dynamic calculation.

Multi-parameter global calculations of fission fragments using a simplified two-dimensional scission-point model

Exploiting the concept of the dinuclear system,the interaction potential energy of two fragments that are quite close to each other is analyzed.A semi-classical method is used to calculate fission fragment yields using a simplified two-dimensional scission-point model.By considering the tip-to-tip orientation at the scission point of the fission process,we investigate the mass,charge,and kinetic-energy distributions of the fission fragments,for excitation energies in the 0-20 MeV range.Our results show that the fission fragment distributions are reproduced quite well,including the recent experimental results for the isotone chain[D Ramos et al.Phys.Rev.C 97,054612(2018)].Thus,the simplified model is useful for multi-parameter global measurements of fission products.

Influence of the neck parameter on the fission dynamics within the two-center shell model parametrization

The influence of the neck parameter on the fission dynamics at low excitation energy is studied based on the three-dimensional Langevin approach,in which the nuclear shape is described with the two-center shell model(TCSM)parametrization,and the elongation,mass asymmetry,and fragment deformation are set to be the generalized coordinates of the Langevin equation.We first study the influence of the neck parameter on the scission configuration.We find that there is almost no obvious correlation between the neck parameter and mass asymmetryηat the scission point,indicating that has no evident impact on the fragment mass distribution.The elongation Z_(0)=R_(0) and its correlation with the mass asymmetryηat the scission point are clearly influenced by the neck parameter,which has a strong effect on the total kinetic energy(TKE)distribution of the fragments.The pre-neutron emission fragment mass distributions for 14 MeV n+^(233;235;238)U and^(239)Pu are calculated,and then,based on these results,the post-neutron emission fragment mass distributions are obtained by using the experimental data of prompt neutron emission.The calculated post-neutron emission fragment mass distributions can reproduce the experimental data well.The TKE distributions for 14 MeV n+^(235)U fission are calculated for ε=0.25,0.35,and 0.45,and the results show that the TKE distribution cannot be described very well for the three cases.However,the trend of the calculated TKE distribution withεis just as expected from the scission configuration calculations.The results with ε=0.35 present a better agreement with the experiment data compared with the other two cases.