Experimental analysis of dynamic mechanical properties for artificially frozen clay by the split Hopkinson pressure bar

A device for impact compression experiments is the split Hopkinson pressure bar with a refrigerating attemperator. Data for incident and reflected waves are obtained by the measuring technique with strain gauges, and data for transmitted waves are obtained by the measuring technique with semiconductor gauges. Static compression tests of frozen clay are conducted at an identical temperature and different strain rates of 0.001 and 0.01 sec ⁻¹ . Dynamic stress-strain curves are obtained at strain rates of 360–1470 sec ⁻¹ . The low and high temperatures correspond to high and low strain rates, respectively. It is shown that both the temperature and strain rate affect the frozen soil deformation process. Different dynamic stress-strain curves obtained at the same temperature but different strain rates are found to converge. The test results indicate that frozen soil has both temperature-brittleness and impact-brittleness.     

Critical Stresses in Spalling and Dynamic Rupture of Metals

Results of dynamic rupture tests of a series of metals obtained using a composite Hopkinson bar and shock-wave loading of plane specimens are described. It is shown that the actual rupture strength at a strain rate of 5 · 10³ sec⁻¹ is very close to the spall strength at higher strain rates. Results of testing the same metals using a composite Hopkinson bar within a temperature range of 20–350°C are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 103–107, November–December, 2005.     

Identification of pulse shapes during transverse impact on composite beams and plates

A test facility for transverse shock loading of beams and plates at small impact velocities (up to 40 km/sec) is described. The impact contact force and unsteady strains are determined for a transverse impact on fiber-layered beams and plates from fiberglass and carbon fiber-reinforced plastic. Pulse shapes are determined for various impact velocities in the range of 5–40 m/sec. The shock loading and unsteady strain of composite beams and plates are calculated by the finite element method. The finite elements take into account transverse shears according to the Timoshenko theory and the viscoelastic material behavior according to the Voigt model.     

Penetration of a rigid shell into a steel obstacle at moderate impact velocities

The effect of the impact velocity and shape of the head of a rigid shell of caliber 20mm on the depth of its penetration into a thick obstacle made of mild low-carbon steel for impact velocities of up to 600m/sec is studied experimentally. Experimental relations between the penetration depth and the impact velocity are obtained for shells with conical and semispherical heads. It is found that for a penetration depth equal to 1 or 2 calibers, the penetration resistance does not depend on the head shape and is characterized by an average stress equal to 2.98GPa. Institute of Experimental Physics, Sarov 607190. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 38–40, January–February, 2000.     

Statistical characteristics of two-phase gas-liquid flow in a vertical microchannel

This paper presents an experimental study of the structure of an upward gas-liquid flow in a vertical microchannel with a cross-sectional dimension of 0.67 × 2.00 mm and a length of 0.5 m. The tests were performed in the ranges of reduced rates of nitrogen 0.04–11.00 m/sec and water 0.07–0.41 m/sec. Using the method of two-beam laser scanning, we identified the main flow regimes (slug-bubble, slug, transient, emulsion, and annular) and determined the statistical characteristics of the two-phase flow. A map of flow regimes was constructed, the dependence of slug velocity on the reduced mixture velocity was obtained, and the friction factor for an upward gas-liquid flow in a microchannel was measured.     

Dynamics of boundary layer formation in a volcano channel in a cavitating high-viscosity magma flow

Based on the full mathematical model of a viscous magma melt flow ascending in the gravity field behind a decompression wave front, an unsteady two-dimensional axisymmetric problem of the melt state dynamics at the initial stage of an explosive volcanic eruption and specific features of the flow in the vicinity of the channel wall for the cases of stationary and dynamically increasing viscosity are studied. The evolution of the boundary layer is numerically analyzed for a constant melt viscosity equal to μ = 10 ³ , 10 ⁵ , and 10 ⁷ Pa · sec. It is demonstrated that a boundary layer is formed on the wall of the channel with a radius of 100 m as the melt viscosity is changed in the range of 10 ³ –10 ⁵ Pa · sec, and the boundary layer thickness increases from 2 to 15 m. As the magma viscosity increases to 10 ⁷ Pa · sec, the boundary layer chokes the major part of the channel, thus, locking the flow in the vicinity of the axis of symmetry of the channel almost over the entire channel length. Substantial changes in the flow structure caused by dynamically increasing viscosity are demonstrated by an example of the melt in the channel with a radius of 10 m. By the time t = 1.1 sec, the boundary layer thickness in the channel cross section at a height of approximately 1000 m reaches almost 8 m, the boundary layer acquires the shape similar to a “diaphragm,” penetrates inward the channel by 200 m (with the mass velocity ranging from 0 to 15 m/sec), and locks the flow in a zone with a radius of approximately 2 m around the axis of symmetry of the channel.     

Strength of water under pulsed loading

Experiments were performed to study the strength of water under conditions of pulsed extension, which is typical of the interaction between a triangular compression pulse and a free surface. The tests were performed in a wide (40–1000 MPa) range of rariation in the amplitude of the compression pulse at deformation rates of 10⁴−10⁵ sec⁻¹. It is found that as the compression-pulse amplitude increases from 150 to 1050 MPa, the strength of water decreases from 46 to 22 MPa. The deformation rate was found to have little effect on the strength. The possibility of using the model of homogenous nucleation (formation of cavitation nuclei) to interpret the data obtained is discussed. Institute of Chemical Physical, Russian Academy of Sciences, Chernogolovka 142432. Translated from Prikladmaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 198–205, July–August, 2000.     

Experimental-theoretical study of the penetration of rigid projectiles and identification of soil properties

The parameters of the Grigoryan soil model are determined using an experimental-computational method previously proposed and the results of reversed experiments on penetration of projectiles with flat and hemispherical heads at impact velocities of 50–450 m/sec in sandy soil. It is shown that the quasistationary dependences of the resistance force on impact velocity obtained in the reversed experiment can be used to solve problems of deep penetration of projectile in soil with an error not exceeding the measurement error.     

Optimal Decay Rate of the Compressible Navier–Stokes–Poisson System in {\mathbb {R}^3}

The compressible Navier–Stokes–Poisson (NSP) system is considered in ${\mathbb {R}^3}The compressible Navier–Stokes–Poisson (NSP) system is considered in \mathbb R³{\mathbb {R}^3} in the present paper, and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same L ²-rate (1+t)^{-\frac 34}{(1+t)^{-\frac {3}{4}}} or L ^∞-rate (1 + t)^−3/2 respectively as the compressible Navier–Stokes system, but the momentum of the NSP system decays at the L ²-rate (1+t)^{-\frac 14}{(1+t)^{-\frac {1}{4}}} or L ^∞-rate (1 + t)⁻¹ respectively, which is slower than the L ²-rate (1+t)^{-\frac 34}{(1+t)^{-\frac {3}{4}}} or L ^∞-rate (1 + t)^−3/2 for compressible Navier–Stokes system [Duan et al., in Math Models Methods Appl Sci 17:737–758, 2007; Liu and Wang, in Comm Math Phys 196:145–173, 1998; Matsumura and Nishida, in J Math Kyoto Univ 20:67–104, 1980] and the L ^∞-rate (1 + t)^−p with p ? (1, 3/2){p \in (1, 3/2)} for irrotational Euler–Poisson system [Guo, in Comm Math Phys 195:249–265, 1998]. These convergence rates are shown to be optimal for the compressible NSP system.     

Gas-dynamic spraying. An experimental study of the spraying process

We present results of an experimental study of the specific features of the gas-dynamic formation of coatings from metallic powders (d_p<50 μm) on substrates of various materials depending on the particle velocity (200–1200m/sec), the jet temperature (300–700K), and other parameters. Results of a prospecting study of the implementation of the methods of particle acceleration in supersonic (M=2.0–3.0) rectangular nozzles are described. The rate of bond formation in a cold particle-cold substrate contact occurring in gas-dynamic spraying is estimated within the framework of the concepts applied in analysis of gas-dynamic spraying. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 182–188, March–Apil, 1998.     

Laminar-turbulent transition in the boundary layer on cones in a hypersonic flow at high Reynolds numbers per meter

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M _∞ = 12–14 and pressures in the settling chamber P₀ = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re _1e = (53–200) · 10⁶ m ⁻¹. The transition occurs at Reynolds numbers Re _tr = (2.3–5.7) · 10⁶. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 76–83, May–June, 2007.     

Scherk-Type Capillary Graphs

This paper concerns the regularity of a capillary graph (the meniscus profile of liquid in a cylindrical tube) over a corner domain of angle α. By giving an explicit construction of minimal surface solutions previously shown to exist (Indiana Univ. Math. J. 50 (2001), no. 1, 411–441) we clarify two outstanding questions. Solutions are constructed in the case α = π/2 for contact angle data (γ₁, γ₂) = (γ, π − γ) with 0 < γ < π. The solutions given with |γ − π/2| < π/4 are the first known solutions that are not C² up to the corner. This shows that the best known regularity (C^{1, ∈}) is the best possible in some cases. Specific dependence of the H?lder exponent on the contact angle for our examples is given. Solutions with γ = π/4 have continuous, but horizontal, normal vector at the corners in accordance with results of Tam (Pacific J. Math. 124 (1986), 469–482). It is shown that our examples are C^{0, β} up to and including the corner for any β < 1. Solutions with |γ − π/2| > π/4 have a jump discontinuity at the corner. This kind of behavior was suggested by numerical work of Concus and Finn (Microgravity sci. technol. VII/2 (1994), 152–155) and Mittelmann and Zhu (Microgravity sci. technol. IX/1 (1996), 22–27). Our explicit construction, however, allows us to investigate the solutions quantitatively. For example, the trace of these solutions, excluding the jump discontinuity, is C^2/3.     

Deduction of Saint-Venant"s Principle for the Asymptotic Residue of Elastic Rods

Let u(ε) be a rescaled 3-dimensional displacement field solution of the linear elastic model for a free prismatic rod Ω^ε having cross section with diameter of order ε, and let u ⁽⁰⁾ –Bernoulli–Navier displacement – and u ⁽²⁾ be the two first terms derived from the asymptotic method. We analyze the residue r(ε) = u(ε) − (u ⁽⁰⁾ + ε² u ⁽²⁾) and if the cross section is star-shaped, we prove such residue presents a Saint-Venant"s phenomenon near the ends of the rod. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamical deformation of a flat liquid–liquid interface

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo ₁/Mo ₂ ∈ [2 × 10⁻⁵–5 × 10⁴] and Re ₁/Re ₂ ∈ [2 × 10⁻³–5 × 10²].     

On asymptotic properties of solutions of linear differential functional equations with linearly transformed argument

We establish new properties of C ¹[−1, +∞)-solutions of the linear functional differential equation ẋ(t) = ax(t) + bx(qt) + hx(t−1) + cẋ(qt) + rẋ(t−1) in the neighborhood of the singular point t = +∞. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 170–177, April–June, 2006.     

Shear-strain-rate effects in a high-strength aluminum alloy

Methods of investigating the plastic flow of materials at high rates are reviewed, and experiments are described in which thin-walled tubular specimens were subjected to dynamic torsional loading. These experiments were performed using a modified version of a torsional Hopkinsonbar apparatus used in earlier work. The results show that, at strain rates of order 10³ sec⁻¹, the stress-strain curve of the alloy tested does not differ significantly from that found at 10⁻³ sec⁻¹. In tests involving the propagation of a stress increment, however, it was found that the speed of propagation was that of elastic shear waves, indicating that the initial response of the material is essentially rate dependent.     

Rheostructural studies of a discotic mesophase pitch at processing flow conditions

The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from 20 to 1,100 s^− 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal wall shear rates ranging from 500 to 2,500 s^− 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: r–θ (cross section) and r–z (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as a few micrometers), where shear rate is highest. Furthermore, as observed in the r–θ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus, the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the r–z plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow of pitch through the die.     

Molecular dynamics of the glass relaxation process of the soft phase in block copolymers: effect of molecular architecture

To determine the impact of molecular architecture on the molecular dynamics of the glass relaxation processes of soft blocks in different types of block copolymers, model block copolymers with a variation in both molecular architecture and chemical composition were studied. Four block copolymer models, namely, two styrene–butadiene–styrene (S-B-S) block copolymers and two styrene–styrene butadiene–styrene (S-SB-S) were chosen. In each pair of block copolymers, one is linear triblock and the other is star asymmetric. For the sake of comparison, two polybutadiene (PB) homopolymer samples, having similar chain lengths of the PB blocks present in the S-B-S block copolymers, have been investigated. Dynamic mechanical measurements have been carried out for the real and imaginary parts of the complex shear modulus (G′, G”) in the temperature and frequency ranges from −110 to 30 °C and from 10⁻² to 15.9 Hz, respectively. Complete master curves have been constructed for all samples investigated. Moreover, broadband dielectric spectroscopy has been carried out to cover wide temperature and frequency windows, −120 to 0 °C and 10⁻¹ to 10⁷ Hz, respectively. The results showed that the molecular dynamics of the glass relaxation process of the PB or statistical PSB soft phases in the block copolymers is dramatically changed when compared to the PB homopolymer. In addition, the molecular architecture is found to be an important factor in determining the molecular mobility of the soft blocks. The results are discussed in terms of the applied confinement of the counter PS hard phase, block lengths, domain thicknesses and the type of end-to-end junctions between the different polymeric blocks. Paper presented 3rd Annual European Rheology Conference (AERC 2006) April 27–29, 2006, Crete, Greece.     

Rheological properties of binary associating polymers

Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains) of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G ^′ and G ^″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω _x , and an extremely strong effect of added free stickers (fC) on the dynamics. This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006.     

Specific features of microparticle deformation upon impact on a rigid barrier

Based on experimental data and numerical modeling, it is shown that a lamina of melted metal of thickness of order0.01 d, in which the temperature is close to the melting point of the particle material, can be formed upon high-speed impact (v ₀≈500–1200 m/sec) of a fine metal particle (d=1–50 μm) on a rigid undeformable barrier near the contact surface. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 1, pp. 204–209, January–February, 2000.