Breakup of shells under explosion and impact

Fragmentation processes in two-phase materials

We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential stress field is tensile. Cracks initiated in this region grow to form meridional planes. If the collision energy exceeds a critical value which depends on the material's internal structure, cracks reach the sample surface resulting in fragmentation. We show that this primary fragmentation mechanism is very robust with respect to the internal structure of the material. For all configurations, a sharp transition from the damage to the fragmentation regime is observed, with smaller critical collision energies for crystalline samples. The mass distribution of the fragments follows a power law for small fragments with an exponent that is characteristic for the branching merging process of unstable cracks. Moreover this exponent depends only on the dimensionally of the system and not on the microstructure.

Emergence of energy dependence in the fragmentation of heterogeneous materials

The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of universality depending mainly on the dimensionality and on the brittle-ductile mechanical response of the system. Recently, experiments and computer simulations have reported an energy dependence of the exponent increasing with the imparted energy. These novel findings question the phase transition picture of fragmentation phenomena, and have also practical importance for industrial applications. Based on large scale computer simulations here we uncover a robust mechanism which leads to the emergence of energy dependence in fragmentation processes resolving controversial issues on the problem: studying the impact induced breakup of platelike objects with varying thickness in three dimensions we show that energy dependence occurs when a lower dimensional fragmenting object is embedded into a higher dimensional space. The reason is an underlying transition between two distinct fragmentation mechanisms controlled by the impact velocity at low plate thicknesses, while it is hindered for three-dimensional bulk systems. The mass distributions of the subsets of fragments dominated by the two cracking mechanisms proved to have an astonishing robustness at all plate thicknesses, which implies that the nonuniversality of the complete mass distribution is the consequence of blending the contributions of universal partial processes.

Dynamic fragmentation of a ring: predictable fragment mass distributions

We employ a finite element framework, coupled to cohesive elements, to model material decohesion of a uniformly expanding ring. Our study focuses on the average fragment mass, the distribution of fragment masses, and the heaviest fragments. The computed fragment mass distributions are best captured by generalized gamma distributions, regardless of the model parameters. However, the distribution of the heaviest fragments depends on toughness, specimen size, and loading rate.

Particle-based model to simulate the micromechanics of biological cells

This paper is concerned with addressing how biological cells react to mechanical impulse. We propose a particle based model to numerically study the mechanical response of these cells with subcellular detail. The model focuses on a plant cell in which two important features are present: (1) the cell's interior liquidlike phase inducing hydrodynamic phenomena, and (2) the cell wall, a viscoelastic solid membrane that encloses the protoplast. In this particle modeling framework, the cell fluid is modeled by a standard smoothed particle hydrodynamics (SPH) technique. For the viscoelastic solid phase (cell wall), a discrete element method (DEM) is proposed. The cell wall hydraulic conductivity (permeability) is built in through a constitutive relation in the SPH formulation. Simulations show that the SPH-DEM model is in reasonable agreement with compression experiments on an in vitro cell and with analytical models for the basic dynamical modes of a spherical liquid filled shell. We have performed simulations to explore more complex situations such as relaxation and impact, thereby considering two cell types: a stiff plant type and a soft animal-like type. Their particular behavior (force transmission) as a function of protoplasm and cell wall viscosity is discussed. We also show that the mechanics during and after cell failure can be modeled adequately. This methodology has large flexibility and opens possibilities to quantify problems dealing with the response of biological cells to mechanical impulses, e.g., impact, and the prediction of damage on a (sub)cellular scale.

Fragmentation processes in impact of spheres

We study the brittle fragmentation of spheres by using a three-dimensional discrete element model. Large scale computer simulations are performed with a model that consists of agglomerates of many particles, interconnected by beam-truss elements. We focus on the detailed development of the fragmentation process and study several fragmentation mechanisms. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasiperiodic angular distribution. The fragments that are formed when these cracks penetrate the specimen surface give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. This mechanism can only be observed in three-dimensional models or experiments. The results prove to be independent of the degree of disorder in the model. Our results significantly improve the understanding of the fragmentation process for impact fracture since besides reproducing the experimental observations of fragment shapes, impact energy dependence, and mass distribution, we also have full access to the failure conditions and evolution.

Phase transition in liquid drop fragmentation

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl . Upon varying the gas pressure, a critical value is found where the size distribution becomes a pure power law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in nuclear multifragmentation studies. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2 . The sizes of the largest and average fragments, on the other hand, do not go to zero abruptly but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian.

Scaling behavior of fragment shapes

We present an experimental and theoretical study of the shape of fragments generated by explosive and impact loading of closed shells. Based on high speed imaging, we have determined the fragmentation mechanism of shells. Experiments have shown that the fragments vary from completely isotropic to highly anisotropic elongated shapes, depending on the microscopic cracking mechanism of the shell. Anisotropic fragments proved to have a self-affine character described by a scaling exponent. The distribution of fragment shapes exhibits a power-law decay. The robustness of the scaling laws is illustrated by a stochastic hierarchical model of fragmentation. Our results provide a possible improvement of the representation of fragment shapes in models of space debris.

Fragment velocity distribution in the impact disruption of thin glass plates

We present the experimental results of the measurement of fragment velocity in an impact disruption. Cylindrical projectiles impact on a side (edge) of thin glass plates, and the dispersed fragments were observed using a high-speed camera. The fragment velocity did not depend on the mass but rather on the initial position of the fragment; the velocity component parallel to the projectile direction increased with the distance from the impacted side, while the component perpendicular to the projectile direction increased with the distance from the central axis parallel to the projectile direction. It appears that there are two mechanisms for fragment ejection: one is "spallation," where the fragment velocities depend on the particle velocity induced by shock waves, and the other is "elastic ejection," where the velocities are controlled by the strain energy stored in targets and are at most a few tens of meters per second. We performed a one-dimensional numerical simulation of elastic ejection with a discrete element method and obtained the velocity distribution as a function of the initial position. The numerical results are qualitatively consistent with the experimental ones.

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.

Dimensional effects in dynamic fragmentation of brittle materials

It has been shown previously that dynamic fragmentation of brittle D -dimensional objects in a D -dimensional space gives rise to a power-law contribution to the fragment-size distribution with a universal scaling exponent 2-1/D . We demonstrate that in fragmentation of two-dimensional brittle objects in three-dimensional space, an additional fragmentation mechanism appears, which causes scale-invariant secondary breaking of existing fragments. Due to this mechanism, the power law in the fragment-size distribution has now a scaling exponent of approximately 1.17 .