S. L. Bazhenov

On the role of friction in energy dissipation upon transverse ballistic impact on fabric

Fabrics based on high-strength nylon and aramid fibers are known to have the ability to strongly dissipate energy upon ballistic impact. This study addresses the causes of this behavior, and it is concluded that the principal contribution to energy dissipation upon transverse ballistic impact is made by friction between multifilament yarns rather than by longitudinal impact waves, as observed in the case of monofilament fibers.

Deformability of Particle-Filled Composites at Brittle Fracture

Strain at the brittle rupture of rubber-particle-filled composites based on polymeric matrices deformed via the neck propagation was found to be equal to the value for the onset of the neck propagation in the initial matrix polymer. This characteristic is important for particle-filled composites, because it determines their ultimate elongation at brittle fracture. Conventionally, caoutchouc particles are introduced into brittle polymers, for example, polystyrene, to increase their shock viscosity and deformability [1]. However, the introduction of caoutchouc or rubber particles into a plastic polymer reduces its ultimate strain [2, 3]. For a certain critical filler content, the composite becomes brittle, more precisely, quasibrittle, which is accompanied by a sharp decrease in the rupture strain by a factor of about 100 [3]. The translation from plastic to brittle fracture of the composite occurs because the formed neck loses its capability to propagate along the sample with a certain content of particles, and it ruptures during the neck formation [4, 5].

Criterion of the Appearance of Diamond-Shaped Pores in Dispersely Filled Polymers

Introduction of a small fraction of large particles often embrittles a polymer, and the rupture of the polymer occurs at small relative elongation. The sharp loss of the deformability of the composite is caused by the appearance of so-called diamond-shaped pores [1] observed previously in [2, 3]. It was shown that the size of particles responsible for the appearance of diamondshaped pores is determined by the critical crack opening and, therefore, by the breakdown viscosity of the matrix polymer. Rupture of particles or their separation from the matrix under tension gives rise to the formation of pores whose shape is determined by the size of particles [1]. Small and large particles form oval pores and diamondshaped pores, respectively. With further tension, the two types of pores that appear behave differently. An oval pore develops only along the material-elongation direction. A diamond-shaped pore grows in three directions, parallel and perpendicular to the sample tension axis, in particular, along the sample thickness, which leads to early failure. In polymers deformed by the propagation of a neck, the problem is compounded, because the growth of pores is often localized in the narrow formed neck. As a result, the material breaks down at small macroscopic strain. Although the fracture process (growth of diamond-shaped pores) is typically plastic at the mesoscale, the material behaves as a brittle material at the macroscale. This work aims to determine the dependence of the critical size of particles at which diamond-shaped cracks appear on the properties of the polymer matrix. Lukoten F 3802 medium-density polyethylene, Lipol A4-70 polypropylene, and 168030-070 low-density polyethylene are used for composites. Polymers were filled with powdered-rubber particles with sizes from 50 to 600 μm. A monodisperse filler was obtained by grading the polymers into grain sizes with a standard set of sieves. Each polymer was mixed with rubber particles in a single-screw laboratory extruder. The filler

The effect of filler content on the lower yield stress of polymer composites

The effect of the concentration of the dispersed elastic filler on the lower yield stress of matrix composites based on plastic polymers is studied. As the matrix polymers, LDPE-HDPE and LDPE-(medium-density PE) are used. The elastic filler is rubber crumb prepared by roll grinding of worn tires or by deformation grinding of ethylene-propylene-diene rubber. Irrespective of the type of filler particles and their adhesion to the polymer matrix, the lower yield stress σd of the composite is described by the linear law σd = σdm(1 − Vf), where σdm is the lower yield stress of the polymer matrix and Vf is the volume content of the filler. Analysis of the published data shows that this relationship is quite general and describes the effect of rigid inorganic particles on the lower yield stress when adhesion between the filler particles and the matrix is poor.

The energy of debonding a nanometer-size coating from a rigid substrate

In this study, the shape of an elastic coating upon its debonding from a substrate is theoretically determined. On the basis of this solution, we develop a method of determining the debonding energy (fracture toughness) of the coating. The energies of debonding a carbon film from a glass and a cobalt film from a raw mica were measured. The debonding toughness is close to the energy of the breaking of atomic bonds. This fact made it possible to conclude that the debonding of films of nanometer thickness differs fundamentally from the fracture of macroscopic samples. Recently, the mechanical behavior of two-layer composites composed of a substrate and a thin coating of nanometer thickness have been vigorously studied. Coatings can be used for various purposes, for example, as a shielding layer, for imparting special optical properties, and for storing information. Unfortunately, due to an insufficient adhesion bond, a coating can debond from the substrate. The coating usually either does not debond at all or debonds altogether. In [1], an unusual debonding mechanism involving the progressive intergrowth of sinusoidal-shaped debondings was found. The fracture including the adhesion requires the expenditure of energy on forming a new surface. In samples of macroscopic and microscopic sizes, the typical fracture energy is from hundreds to several thousands of joules per square meter. The fracture energy is the sum of two components, the energy of the breaking of intermolecular bonds and the energy spent on plastically deforming the material near the fracture plane [2]. In metals and polymers, the energy of plastic deformation is three‐five orders of magnitude higher than the energy of the breaking of chemical bonds. For this reason, the bond-breaking contribution is considered as negligible. The fracture energy decreases with the thickness of samples [3]; however, these data were available only for films of thickness from tens of micrometers to several centimeters. For the samples with a thickness of several nanometers, the fracture energy could not be previously measured. This study is devoted to solving this problem. We studied two composites. The first was a glass plate 0.5 mm thick covered by a carbon layer 60 nm thick, and the second was a mica plate covered by a cobalt‐carbon layer 160 nm thick. The cobalt-to-carbon mass ratio was 80 : 20. The surface of composites was studied by a Nanoscope-2 atomic-force microscope (Digital Instruments, Santa Barbara, Calif.) in the contact-force mode. The electron-microscope investigations were carried out on a Hitachi S-520 scanning electron microscope.

Two mechanisms of compression failure of unidirectional carbon-fiber-reinforced plastics

The compression failure of a unidirectional carbon-fiber-reinforced plastic containing an epoxy matrix asits base is due to the formation of a so-called kink, i.e.,a slip band oriented at an angle of approximately 45i tothe loading axis [1–5]. It is conventionally consideredthat the kink appearance in a carbon-filled plastic is dueto a violation of the stability of its fibers. This processis similar to the buckling of a rod on an elastic base. Thecritical stress of the fiber buckling in a composite isequal to the elastic modulus G of the composite underan in-plane shear [6]: σ = G . (1) If the fiber concentration in a composite is approxi-mately 50–60 vol %, the shear modulus G of the com-posite is close to Young’s modulus of its matrix and,therefore, the strength due to such a failure mechanismis determined by the rigidity of the matrix.The assumption that the failure is caused by fiberbuckling is confirmed by a certain increase in thestrength for a carbon-fiber-reinforced plastic when theelastic modulus of its epoxy matrix is increased [7].Nevertheless, this is not the only point of view on thefailure mechanism for carbon-fiber-reinforced plastics.Indeed, their strength turns out to be significantly lowerthan the shear modulus. This fact suggests that the com-pression failure is not caused by fiber buckling. Typicalvalues of the shear modulus for carbon-fiber-reinforcedplastics range from 4 to 5 GPa [8, 9]. The compressionstrength of a carbon-fiber-reinforced plastic depends onthe types of both its fibers and its matrix and rangesfrom 1.2 to 1.8 GPa [7]. These values are not greaterthan one-third of the shear modulus.There are two other possible failure mechanisms. Itwas assumed in [10–12] that the failure of a carbon-fiber-reinforced plastic is caused by the fracture of itsfibers and that its strength is determined by a fairly lowfiber strength. The values of the carbon fiber strengthcited in various papers range from 2.4 to 6 MPa [7, 12].Measuring the compressive strength for isolated verythin fibers (6–10 µ m in diameter) is a technicallydemanding task, and, therefore, the values publishedfor the fiber strength are not completely reliable. Thisfact hampers the elucidation of the question raised as towhether a direct correlation exists between the strengthof a carbon-fiber-reinforced plastic and that of its fibers.Another possible mechanism of failure is the split-ting (delamination) of a carbon-fiber-reinforced plasticalong the direction of its fibers [12]. The splitting of acomposite usually involves the origination of longitudi-nal cracks in the matrix or on the fiber–matrix interfaceand the subsequent bending of a separated part of thematerial. The direct formation of the kink by the firstlongitudinal crack is a specific feature of this failuremechanism in carbon-fiber-reinforced plastics; hence,the crushed sample does not look as though it were splitoff. The splitting is caused by the low strengths of boththe matrix and the interface. This mechanism was orig-inally considered only as a possible mode of failure;however, later studies showed that splitting is the mostprobable failure mechanism for carbon-fiber-reinforcedplastics [13]. According to [13], the failure of a carbon-fiber-reinforced plastic can be caused by either the ulti-mate strength attained or longitudinal splitting, depend-ing on the types of fibers and the matrix. Since the fail-ure mechanism for composites is not unambiguouslyestablished at room temperature, failure with kink orig-ination will be here referred to as a shear failure.The aim of this report is to study the temperatureeffect on the compressive failure mechanism for a car-bon-fiber-reinforced plastic containing UKN-5000fibers and an EDT-10 epoxy matrix.Carbon fibers with the trade mark UKN-5000 wereused for reinforcement. An EDT-10 epoxy composition(consisting of an 80 wt % of epoxy ED-20, 10 wt % oftriethanolamine titanate hardener, and 10 wt % of dieth-ylene glycol as a modifier) was used as the matrix. Thefiber was passed twice through a bath with a liquid resinheated to 60 ° C and was then wound on a plane bobbin.The bundle obtained was pulled into a steel cylindrical

Propagation of Longitudinal Acoustic Waves in a Thin Cylindrical Pipe Filled with a Liquid

In [2, 3], the effect of reducing the wave velocity was found for elastic rods made in the form of a thin strip or fiber and immersed in a liquid. A reduction of the velocity is observed only in thin samples with a thickness on the order of a hundred microns. The effect found is caused by the fact that the so-called boundary layer of a liquid vibrates together with the rod. The thickness of this layer depends on the vibration frequency and the density and viscosity of the liquid. When the sound velocity depends on the viscosity, the effect discovered is employed for the determination of the viscosity of liquids. An advantage of this method is its ability to provide high-rate measurements, which makes it possible to control the chemical reactions with a time-dependent viscosity that proceed in liquids. As a sensor, we used metallic strips and fibers with a diameter of approximately 0.1 mm [2, 3], which were immersed in the liquid under investigation. The use, for this purpose, of a thin capillary filled with the liquid presents a number of advantages, among them the possibility of operating with a very small quantity (specified by the capillary volume) of liquid. The problem of the effect of liquid on the propagation of sound in a thin pipe (capillary) has not yet been solved. The goal of this study is to theoretically seek a solution to this problem.

Fracture of a composite material based on a uniformly deformable polymeric matrix and rubber particles

In the case of tension in thermoplastic polymers filled with mineral particles at a certain filler content, an abrupt drop of the material deformability occurs, caused by the transition from plastic to brittle fracture [1‐5]. In the present study, we have established that the embrittlement of filled thermoplastics is associated with the formation and propagation of a neck in the matrix polymer under tension. If the matrix polymer is deformed macrouniformly and the neck does not form, then introducing a filler does not result in the embrittlement of the composite material. In order to prepare composite materials, we used a copolymer of ethylene and vinyl acetate (CEVA) of the 11306-075 trademark. A rubber powder was used as a filler. The powder consisted of about 50, 10, and 10 wt % of isoprene; divinyl; and methylstyrene caoutchoucs, respectively, as well as 30 wt % carbon black. The size of rubber particles was 100 < d < 500 μ m. Mixing the CEVA with rubber particles was performed in a single-worm laboratory extruder. The concentration of the rubber powder varied within the limits from 1.7 to 88 vol % (2 to 90 wt %). From the mixtures obtained, plates 2 mm thick were prepared by pressing. Two-sided blades with working surfaces of 5 〈 35 mm were cut out from these plates. Mechanical tests of the composites were carried out with the help of a 2038P-005 dynamometric facility at the deformation rate of 20 mm/min. The CEVA crystalline structure and CEVA-based composites were studied at a heating rate of 10 K/min by the method of differential scanning calorimetry with the use of a TA 4000 thermal analyzer manufactured by the Mettler Company. Calorimetric analysis has shown that the presence of rubber particles does not change the crystallinity degree or melting temperature of the polymeric matrix. Therefore, the elastic filler does not affect the crystalline structure of the material, and it is identical with the original structure of the unfilled CEVA.

Deformation Properties of High-Density Polyethylene-Filled with Rubber Particles

The composite material was obtained by mixing in a melt with the help of a single-screw laboratory extruder. The filler concentrations were taken within the range between 2 and 95 wt % (1.8‐94.5 vol %). We used the material obtained to make 2-mm-thick plates through hot pressing at 160 ° C and under 10-MPa pressure followed by cooling under pressure to room temperature. Next, for our investigations, we cut out samples in the form of a double-ended spade with dimensions of the useful part of 5 〈 35 mm. The mechanical properties of the composites were determined by a 2038 R-005 tension testing machine at room temperature. The deformation rate was 20 mm/min. After testing, the fracture surface was examined with the help of an MBS-9 optical microscope.

Propagation of longitudinal acoustic waves in a thin elastic strip coated by a layer of a viscous liquid

In [1, 2], we observed an effect of decreasing prop-agation velocity of longitudinal sound waves in a fineelastic rod after its immersion in a liquid. The decreasein the sound velocity is governed by the so-calledboundary layer of the liquid, which vibrates togetherwith the rod as an associated mass. The thickness ofthis layer depends on both the vibration frequency andboth the density and viscosity of the liquid. At a soundsignal frequency of about 100 kHz, the typical value ofthe boundary layer thickness for technical oils is 10 to50 µ m [1]. Therefore, the decrease in the sound veloc-ity is considerable only for thin samples, i.e., sampleswhose thickness does not exceed a few hundreds ofmicrons.Since the thickness of the boundary layer dependson the viscosity of a liquid, it is appropriate to employthe above effect for determining the viscosity. Anadvantage of this method is the possibility of perform-ing high-rate viscosity measurements that attain a rateof up to several thousands per second. Such high ratesmake it possible to measure the viscosity even in thecase when it varies with time.The problem of the effect of a liquid on the propa-gation velocity and the damping of acoustic waves in athin strip immersed into an infinite volume of a liquidwas solved analytically [1]. However, there exists theproblem of controlling the behavior of polymeric resinsdeposited in liquid form on a metal surface and solidi-fied on it.The goal of this study is to theoretically solve theproblem related to the propagation of a longitudinalharmonic acoustic wave in a thin elastic strip coated bya layer of an incompressible Newtonian liquid.We introduce a system of coordinates such that thefree surface of a liquid coincides with the plane X = 0.The longitudinal vibrations of the elastic strip along the Y -axis are described by the equation [3–5] (1) Here, u is the displacement of a small strip elementfrom the equilibrium position; ρ