Fragmentation of shells

We present a theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material. Experiments were performed on brown and white hen egg shells under two different loading conditions: impact with a hard wall and explosion by a combustible mixture. Both give rise to power law fragment size distributions. A three-dimensional discrete element model of shells is worked out. Based on simulations of the model, we give evidence that power law fragment mass distributions arise due to an underlying phase transition which proved to be abrupt for explosion and continuous for impact. We demonstrate that the fragmentation of closed shells defines a new universality class of fragmentation phenomena.     

Space-time scale invariance in dynamically fragmented quasi-brittle materials

The paper reports on a study to investigate the influence of load intensity and material structure on statistical regularities of fragmentation in ZrO₂-based ceramics differing in porosity. The study was performed on a modified split Hopkinson pressure bar system and allowed a comparative analysis of dynamic stress-strain curves and statistical characteristics of fragmentation such as distributions of emitted light pulses (fractoluminescence) and fragment sizes. It is shown that increasing the ceramic porosity changes both the form of stress-strain curves and the pulse distribution. In ceramic specimens with up to 45% porosity, the pulse distribution is described by a bimodal power law; in ceramic specimens with 60% porosity, by a power law. The fragment size distribution in the material corresponds to a power law with the exponent dependent on porosity and load intensity.     

Characterizing char particle fragmentation during pulverized coal combustion

A particle population balance model was developed to predict the oxidation characteristics of an ensemble of char particles exposed to an environment in which their overall burning rates are controlled by the combined effects of oxygen diffusion through particle pores and chemical reactions (the zone II burning regime). The model allows for changes in particle size due to burning at the external surface, changes in particle apparent density due to internal burning at pore walls, and changes in the sizes and apparent densities of particles due to percolation type fragmentation. In percolation type fragmentation, fragments of all sizes less than that of the fragmenting particle are produced. The model follows the conversion of particles burning in a gaseous environment of specified temperature and oxygen content. The extent of conversion and particle size, apparent density, and temperature distributions are predicted in time.Experiments were performed in an entrained flow reactor to obtain the size and apparent density data needed to adjust model parameters. Pulverized Wyodak coal particles were injected into the reactor and char samples were extracted at selected residence times. The particle size distributions and apparent densities were measured for each sample extracted. The intrinsic chemical reactivity of the char to oxygen was also measured in experiments performed in a thermogravimetric analyzer. Data were used to adjust rate coefficients in a six-step reaction mechanism used to describe the oxidation process.Calculations made allowing for fragmentation with variations in the apparent densities of fragments yield the type of size, apparent density, and temperature distributions observed experimentally. These distributions broaden with increased char conversion in a manner that can only be predicted when fragmentation is accounted for with variations in fragment apparent density as well as size. The model also yields the type of ash size distributions observed experimentally.     

Particle-based modeling of aggregation and fragmentation processes: Fractal-like aggregates

The incorporation of particle inertia into the usual mean field theory for particle aggregation and fragmentation in fluid flows is still an unsolved problem. We therefore suggest an alternative approach that is based on the dynamics of individual inertial particles and apply this to study steady state particle size distributions in a 3D synthetic turbulent flow. We show how a fractal-like structure, typical of aggregates in natural systems, can be incorporated in an approximate way into the aggregation and fragmentation model by introducing effective densities and radii. We apply this model to the special case of marine aggregates in coastal areas and investigate numerically the impact of three different modes of fragmentation: large-scale splitting, where fragments have similar sizes, erosion, where one of the fragments is much smaller than the other and uniform fragmentation, where all sizes of fragments occur with the same probability. We find that the steady state particle size distribution depends strongly on the mode of fragmentation. The resulting size distribution for large-scale fragmentation is exponential. As some aggregate distributions found in published measurements share this latter characteristic, this may indicate that large-scale fragmentation is the primary mode of fragmentation in these cases.     

A model for nuclear matter fragmentation: phase diagram and cluster distributions

We develop a model in the framework of nuclear fragmentation at thermodynamic equilibrium which can be mapped onto an Ising model with constant magnetization. We work out the thermodynamic properties of the model as well as the properties of the fragment size distributions. We show that two types of phase transitions can be found for high density systems. They merge into a unique transition at low density. An analysis of the critical exponents which characterize observables for different densities in the thermodynamic limit shows that these transitions look like continuous second-order transitions.     

Fragment distributions for brittle rods with patterned breaking probabilities

We present a modeling framework for 1D fragmentation in brittle rods, in which the distribution of fragments is written explicitly in terms of the probability of breaks along the length of the rod. This work is motivated by the experimental observation of several preferred lengths in the fragment distribution of shattered brittle rods after dynamic buckling [J.R. Gladden, N.Z. Handzy, A. Belmonte, E. Villermaux, Dynamic buckling and fragmentation in brittle rods, Phys. Rev. Lett. 94 (2005) 35503]. Our approach allows for non-constant spatial breaking probabilities, which can lead to preferred fragment sizes, derived equivalently from either combinatorics or a nonhomogeneous Poisson process. The resulting relation qualitatively matches the experimentally observed fragment distribution, as well as some other common distributions, such as a power law with a cutoff.     

Explosive fragmentation of a thin ceramic tube using pulsed power

This study experimentally examined the explosive fragmentation of thin ceramic tubes using pulsed power. A thin ceramic tube was threaded on a thin copper wire, and high voltage was applied to the wire using a pulsed power generator. This melted the wire and the resulting vapor put pressure on the ceramic tube, causing it to fragment. We examined the statistical properties of the fragment mass distribution. The cumulative fragment mass distribution obeyed the double exponential or power law with exponential decay. Both distributions agreed well with the experimental data. Finally, we obtained universal scaling for fragmentation, which is applicable to both impact and explosive fragmentation.     

Effects of the turnover rate on the size distribution of firms: An application of the kinetic exchange models

We address the issue of the distribution of firm size. To this end we propose a model of firms in a closed, conserved economy populated with zero-intelligence agents who continuously move from one firm to another. We then analyze the size distribution and related statistics obtained from the model. There are three well known statistical features obtained from the panel study of the firms i.e., the power law in size (in terms of income and/or employment), the Laplace distribution in the growth rates and the slowly declining standard deviation of the growth rates conditional on the firm size. First, we show that the model generalizes the usual kinetic exchange models with binary interaction to interactions between an arbitrary number of agents. When the number of interacting agents is in the order of the system itself, it is possible to decouple the model. We provide exact results on the distributions which are not known yet for binary interactions. Our model easily reproduces the power law for the size distribution of firms (Zipf’s law). The fluctuations in the growth rate falls with increasing size following a power law (though the exponent does not match with the data). However, the distribution of the difference of the firm size in this model has Laplace distribution whereas the real data suggests that the difference of the log of sizes has the same distribution.     

Kinetics of a Migration－Driven Aggregation－Fragmentation Process

We propose a reversible model of the migration-driven aggregation-fragmentation process with the symmetric migration rate kernels K(k;j)=K'(k;j)=λkj^υ and the constant aggregation rates I₁, I₂ and fragmentation rates J₁, J₂. Based on the mean-field theory, we investigate the evolution behavior of the aggregate size distributions in several cases with different values of index υ. We find that the fragmentation reaction plays a more important role in the kinetic behaviors of the system than the aggregation and migration. When J₁=0 and J₂ =0, the aggregate size distributions a_k(t) and b_k(t) obey the conventional scaling law, while when J₁>0 and J₂>0, they obey the modified scaling law with an exponential scaling function. The total mass of either species remains conserved.     

Glass transitions in quasi-two-dimensional suspensions of colloidal ellipsoids

We observed a two-step glass transition in monolayers of colloidal ellipsoids by video microscopy. The glass transition in the rotational degree of freedom was at a lower density than that in the translational degree of freedom. Between the two transitions, ellipsoids formed an orientational glass. Approaching the respective glass transitions, the rotational and translational fastest-moving particles in the supercooled liquid moved cooperatively and formed clusters with power-law size distributions. The mean cluster sizes diverge in power law as they approach the glass transitions. The clusters of translational and rotational fastest-moving ellipsoids formed mainly within pseudonematic domains and around the domain boundaries, respectively.     

Power-law statistics of synchronous transition in inhibitory neuronal networks

We investigate the relationship between the synchronous transition and the power law behavior in spiking networks which are composed of inhibitory neurons and balanced by dc current. In the region of the synchronous transition, the avalanche size and duration distribution obey a power law distribution. We demonstrate the robustness of the power law for event sizes at different parameters and multiple time scales. Importantly, the exponent of the event size and duration distribution can satisfy the critical scaling relation. By changing the network structure parameters in the parameter region of transition, quasicriticality is observed, that is, critical exponents depart away from the criticality while still hold approximately to a dynamical scaling relation. The results suggest that power law statistics can emerge in networks composed of inhibitory neurons when the networks are balanced by external driving signal.     

Angular distributions of photofission fragments of particular mass

Fragment angular and mass distributions have been measured simultaneously for photon energies near the fission barrier of ²³⁶U. Different angular distributions have been observed for particular fragment mass regions. This establishes a clear relationship between the quantum numbers of the transition states and the fragment mass division. The results are discussed within the transition channel concept of the double humped barrier for different fission paths and the more recent model of multi-ecit channels.     

Multiple avalanches across the metal-insulator transition of vanadium oxide nanoscaled junctions

The metal-insulator transition of nanoscaled VO2 devices is drastically different from the smooth transport curves generally reported. The temperature driven transition occurs through a series of resistance jumps ranging over 2 decades in magnitude, indicating that the transition is caused by avalanches. We find a power law distribution of the jump sizes, demonstrating an inherent property of the VO2 films. We report a surprising relation between jump magnitude and device size. A percolation model captures the general transport behavior, but cannot account for the statistical behavior.     

Scale invariance in dynamic fragmentation of quartz

In the work, we studied statistical regularities in fragmentation of cylindrical quartz specimens under dynamic loading. The original equipment used in the study ensured integrity of the specimens after impact for the determination of fragment size distribution (spatial scaling) and allowed recording fractoluminescence pulses at newly formed fracture surfaces for the determination of pulse spacing distribution (temporal scaling). The results of experimental data processing show that the size distributions for both the spatial parameter (fragment size) and the temporal parameter (fractoluminescence pulse spacing) are described by a power function. This enables us to refer dynamic fragmentation of quartz to phenomena exhibiting self-organized criticality.     

Molecular dynamics simulations of jet breakup and ejecta production from a grooved Cu surface under shock loading

Large-scale non-equilibrium molecular dynamics simulations are performed to explore the jet breakup and ejecta production of single crystal Cu with a triangular grooved surface defect under shock loading. The morphology of the jet breakup and ejecta formation is obtained where the ejecta clusters remain spherical after a long simulation time. The effects of shock strength as well as groove size on the steady size distribution of ejecta clusters are investigated. It is shown that the size distribution of ejecta exhibits a scaling power law independent of the simulated shock strengths and groove sizes. This distribution, which has been observed in many fragmentation processes, can be well described by percolation theory.     

Multiply charged neon clusters: failure of the liquid drop model?

We have analyzed the stability and fission dynamics of multiply charged neon cluster ions. The critical sizes for the observation of long-lived ions are n2=284 and n3=656 for charge states 2 and 3, respectively, a factor 3 to 4 below the predictions of a previously successful liquid-drop model. The preferred fragment ions of fission reactions are surprisingly small (2相似文献   

Effects of internal stresses and intermediate phases on the coarsening of coherent precipitates: A phase-field study

Phase stability, topology and size evolution of precipitates are important factors in determining the mechanical properties of crystalline materials. In this article, the Cahn-Hilliard type of phase-field model was coupled to elasticity equations within a mixed-order Galerkin finite element framework to study the coarsening morphology of coherent precipitates. The effects of capillarity, particle size and fraction, compositional strain, and inhomogeneous elasticity on the kinetics and kinematics of coherent precipitates in a binary dual phase crystal admitting a third intermediate stable/meta-stable phase were investigated. The results demonstrated the ability of the model to simulate coarsening under the concomitant action of Ostwald ripening and mismatch elastic strain mechanisms. Using a phenomenological coarsening power law, coarsening rates were determined to depend on precipitate size and volume fraction, compositional strain, and strain mismatch between precipitates and the matrix. Results also showed that the necking incubation time between two neighboring precipitates depends inversely on the precipitate’s initial sizes; however, under fixed volume fraction of precipitates, any increase in the initial sizes of the precipitates mitigates the coarsening. Meanwhile, the compositional strain and the growth of the intermediate stable/meta-stable phase leads to substantial enhancements of precipitate coarsening.     

An appraisal of composite interface mechanics models and some challenging problems

A critical review of previous mechanics models proposed for the evaluation of interfacial properties from single fibre tests is presented with regard to their applicability and limitations. New results which include the effects of some important factors, such as pre-existing fibre flaws. thermal residual stresses and matrix cracks. are provided for a single fibre fragmentation test. By comparing the stress distributions of single fibre fragment and multi-fibre fragment, a basic method to study the multi-fibre composite is introduced in order to relate the interfacial parameters to the mechanical properties of the bulk composite. Some challenging problems on fibre-matrix interfaces are discussed for future research work.