Fragmentation of metal particles during heterogeneous explosion

Shock Waves - Heterogeneous explosives contain a mixture of standard explosive material and reactive metal particles. The inclusion of metal particles alters the energy density and energy release...     

Simulation of impulse effects from explosive charges containing metal particles

The propagation of an explosive blast wave containing inert metal particles is investigated numerically using a robust two-phase methodology with appropriate models to account for real gas behavior, inter-phase interactions, and inter-particle collisions to study the problem of interest. A new two-phase Eulerian–Lagrangian formulation is proposed that can handle the dense nature of the flow-field. The velocity and momentum profiles of the gas and particle phases are analyzed and used to elucidate the inter-phase momentum transfer, and its effect on the impulsive aspects of heterogeneous explosive charges. The particles are found to pick up significant amounts of momentum and kinetic energy from the gas, and by virtue of their inertia, are observed to sustain it for a longer time. The impulse characteristics of heterogeneous explosives are compared with a homogeneous explosive containing the same amount of high explosive, and it is observed that the addition of solid particles augments the impulsive loading significantly in the near-field, and to a smaller extent in the far-field. The total impulsive loading is found to be insensitive to the particle size added to the explosive charge above a certain cut-off radius, but the individual impulse components are found to be sensitive, and particles smaller than this cut-off size deliver about 8% higher total impulse than the larger ones. Overall, this study provides crucial insights to understand the impulsive loading characteristics of heterogeneous explosives.     

Rheology of a dilute suspension of axisymmetric Brownian particles

Explicit results are presented for the complete rheological properties of dilute suspensions of rigid, axisymmetric Brownian particles possessing fore-aft symmetry, when suspended in a Newtonian liquid subjected to a general three-dimensional shearing flow, either steady or unsteady. It is demonstrated that these rheological properties can be expressed in terms of five fundamental material constants (exclusive of the solvent viscosity), which depend only upon the sizes and shapes of the suspended particles. Expressions are presented for these scalar constants for a number of solids of revolution, including spheroids, dumbbells of arbitrary aspect ratio and long slender bodies. These are employed to calculate rheological properties for a variety of different shear flows, including uniaxial and biaxial extensional flows, simple shear flows, and general two-dimensional shear flows. It is demonstrated that the rheological properties appropriate to a general two-dimensional shear flow can be deduced immediately from those for a simple shear flow. This observation greatly extends the utility of much of the prior Couette flow literature, especially the extensive numerical calculations of Scheraga et al. (1951, 1955).The commonality of many disparate results dispersed and diffused in earlier publications is emphasized, and presented from a unified hydrodynamic viewpoint.     

Analysis of surface crack on forward extruding bar during axisymmetric cup-bar combined extrusion process

In this paper, the kinematically admissible velocity field with surface crack on forward extruding bar is put forward during the axisymmetric cup-bar combined extrusion process, in accordance with the results of model experiments.On the basis of velocity field, the necessary condition for surface crack formation on the forward extruding bar is derived, with the help of upper bound theorem and the minimum energy principle. Meanwhile, the relationships between surface crack formation and combination of reduction in area for the part of forward and backward extursions (ε_b,ε_f) relative residual thickness of billet (T/R₀),frictional factor (m) or relative land length of ram and chamber (l_b|R₀,l_f|R₀) are calculated during the extrusion process. Therefore, whether the surface crack on forward exturding bar occurs can be predicted before extruding the lower-plasticity metals for axisymmetric cup-bar combined extrusion process.The analytical results agree very well with experimental results of aluminium alloy LY12 (ASTM 2024) and LC4 (ASTM 7075).     

Crystal plasticity analysis of texture development in magnesium alloy during extrusion

The texture development mechanism during the extrusion of magnesium alloy is investigated by experimental observation and numerical analysis. First, we perform a finite element analysis of a full extrusion process using a phenomenological constitutive equation, and it is confirmed that the loading condition of the extrusion process near the central axis of the billet is approximated by an equi-biaxial compression mode. Then, the equi-biaxial compression problem is adopted as a simplified boundary value problem to be solved using a crystal plasticity model to clarify the detailed texture development mechanism during the extrusion process. The crystal plasticity analysis of equi-biaxial compression successfully reproduces the texture development from an initial random texture to the final experimentally observed texture. The effects of the deformation modes (i.e. slip and twinning systems) implemented in the calculation and the reference stress ratio of basal to nonbasal slip systems on texture development are studied in detail. Finally, the mechanism of texture development during the extrusion process is discussed in terms of the lattice rotation caused by the activated slip systems.     

The analysis of void growth that leads to central bursts during extrusion

Using large deformation finite element analysis together with Gurson's constitutive model, we have studied the behavior of microvoids nucleated at second phase particles during direct axisymmetric extrusion. Two different die-designs were analyzed. Experiments show that the first die-design results in central burst formation while the second gives a solid product free of central bursts. Comparison of the stress fields of the two die-designs provides a possible explanation of how central bursting initiates and why it appears after several steps of multi-step extrusions. The finite element results are in agreement with experimental observation and show that the finite element method can be successfully used to predict the formation of central bursts during extrusion.     

Detonation combustion of hydrogen in an axisymmetric channel with a central body

The problem of initiation and stabilization of detonation combustion of a hydrogen–air mixture injected into an axisymmetric channel with a finite-length central body in a flow with a Mach number M₀ = 5–9 is solved. It is numerically demonstrated that the presence of the central body both in a convergent–divergent nozzle and in an expanding channel leads to stabilization of detonation combustion of a stoichiometric hydrogen–air mixture at free-stream Mach numbers M₀ > 7. Various channel configurations that ensure different values of thrust generated by detonation combustion of a stoichiometric hydrogen–air mixture are compared.     

Combustion of a gas suspension of metal particles

The combustion of a gas suspension of particles reacting in accordance with a heterogeneous mechanism was considered in [1–4]. It was assumed that the reaction rate at the surface of the individual particles does not depend on the thickness of the oxide film, or that a film does not form, i.e., the reaction products are gaseous. With the oxidation of many metals the oxide film formed inhibits the reaction, i.e., with its growth, the rate of the reaction decreases. The special characteristics of the process of the combustion of individual particles of metals arising as a result of the effect of the oxide film were considered in [5], in which it was shown that the dependence of the reaction rate on the thickness of the film has a considerable effect on the laws governing the combustion of individual particles. In the present work, a study was made of the process of the combustion of a gas suspension of particles of metals oxidizing in accordance with the so-called parabolic law (the reaction rate is inversely proportional to the thickness of the oxide film). The results are compared with the laws governing the combusion of a gas suspension of particles reacting in accordance with a purely heterogeneous mechanism in the absence of an oxide film.     

Analysis of a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains

This paper studies a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains. The analytical elastic solution is obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructural parameters and its evolution on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated through examples.     

Tension of a clamped rectangular plate containing a central crack

Using the fundamental solution of a single crack and the Fourier transform solution of an infinite strip, the tension problem of a clamped rectangular plate containing a central crack is reduced to solve a system of singular integral equations. Then, the normal stress on clamped side and the stress intensity factors of the central crack are carried out by means of Gauss-Jacobi integration formulas. The comparison of numerical results is shown in the “table of stress intensity factors”. This work was supported by the Science Fund of the Academy of Sciences of China.     

Mechanism of superdeep penetration of particles into a metal target

A physicomathematical model of superdeep penetration taking into account the strength properties of the target is proposed. Based on this model, the problem of superdeep penetration of tungsten particles into a steel target has been solved for the first time. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 37–46, March–April, 2000.     

Stokes flow in a cylindrical tube containing a line of spheroidal particles

Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for (a) uniform axial translation of the spheroids (b) flow past a line of stationary spheriods and (c) flow of the suspending fluid and spheroids under an imposed pressure gradient. The fluid is assumed to be incompressible and Newtonian. The Reynolds number is assumed to be small and the equations of creeping flow are used. Two types of solutions are developed: (i) an exact solution in the form of an infinite series which is valid for ratios of the spheroid diameter to the tube diameter up to 0.80, (ii) an approximate solution using lubrication theory which is valid for spheroids which nearly fill the tube. The drag on each spheroid and the pressure drop are computed for all cases. Both prolate and oblate spheroids are considered. The results show that the drag and pressure drop depend on the spheroidal diameter perpendicular to the axis of tube primarily and the effects of the spheroidal thickness and spacing are secondary. The results are of interest in connection with mechanics of capillary blood flow, sedimentation, fluidized beds, and fluid-solid transport.     

Flow of a stream containing charged inertial particles past a conducting sphere

The problem of the flow of a hydrodynamic stream containing electrically charged particles past a conducting sphere is solved. The influence of the volume density of the electric charge and the potential of the sphere on the capture coefficient is determined for different values of the inertia parameter of the particles and different drag laws for them. It is shown that for an earthed sphere can appreciably exceed unity. In the formulation of the problem, it is assumed that the region of electrogasdynamic flow is bounded by two electrode grids, which simulate the exit of the source of charged particles and the surrounding electric conditions. The velocity field near the sphere is assumed irrotational. The problem is solved numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 21–26, July–August, 1982.I thank A. B. Vatazhin for assistance in the work.     

Effect of particles on the interaction of two-phase swirling flows in axisymmetric channels

The hydrodynamics of a swirling disperse flow in a cylindrical channel of complex shape is investigated numerically within the framework of a two-velocity two-temperature model of the motion of interpenetrating continua. The principal dimensionless numbers for problems of this type are formulated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 173–175, July–August, 1987.     

Comparative analysis of viscous flows in cavities and channels containing axisymmetric obstacles

The flow past axisymmetric bodies of various shapes in expanding cavities and cylindrical channels is studied on the basis of a numerical solution of the Navier-Stokes equations. For each body shape velocity, pressure and shear stress distributions are obtained. These data are then used for the purposes of a comparative flow analysis in terms of body shape and Reynolds number. The properties characteristic of flows around bodies in channels and cavities with moving boundaries are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 60–66, May–June, 1988.     

Theory of a laval nozzle for a two-phase mixture containing particles of small lag

A two-velocity and two-temperature model is considered for a continuous medium in relation to the flow of a mixture of gas and particles in the subsonic, transsonic, and supersonic parts of a Laval nozzle. It is assumed that the particles are small, and hence that the coefficients f and ^q, which define the interaction with the gas, are large (these coefficients are inversely proportional to the square of the particle radius for a Stokes mode of flow). This means that the velocity or thermal lag of the particles relative to the gas is small. The solution is sought as expansions with respect to the small parameters ₁=1/f and ₂=1/^q.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 89–100, July–August, 1973.