The Effects of Poisson Contraction on Matrix Cracking in Brittle-Matrix Composites

The effects of Poisson contraction on matrix cracking in unidirectional fiber-reinforced brittle-matrix composites are studied in this paper. The fibers, initially held in the matrix by a compressive pressure due to the thermal expansion mismatch, are subjected to frictional slipping over the matrix as soon as a fiber-bridged crack is formed. The friction between the fibers and the matrix is assumed to follow the Coulomb friction law. A shear-lag model, which includes the Poisson contraction and the friction due to the relative fiber/matrix slipping, is adopted to calculate the stress and strain fields in the fibers and matrix. Using the energy balance approach, a relation for the critical matrix cracking stress for propagating of a semi-infinite fiber-bridged crack is derived. The results obtained show that the Poisson contraction has a strong effect on the predicted matrix cracking stress in brittle-matrix composites, especially in composites with a stiff matrix.     

Polypropylene reinforced with aramid and glass fibers

The effect of the chemical nature of the aramid fibers Phenylone, Terlon, Armos, and SVM on the mechanical, thermophysical, and antifriction properties of reinforced polypropylene was investigated. It was found that the composite filled with SVM fibers based on a stiff-chain polymer has high tensile strength and bending modulus. Reinforcement of polypropylene with Phenylone stiff-chain fibers produces a composite with a high impact viscosity. Organoplastics based on polypropylene and aramid fibers have a low density and friction coefficient and high durability. Reinforcement of polypropylene with aramid (SVM) and glass fibers increases the technological properties of the composites. The glass-filled organoplastics developed can be used in instrument making, radio engineering, and machine building as antifriction and construction materials.Ukrainian State Chemical Technological University, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 106–110, January–February, 1996.     

Modification of the mechanical properties of synthetic fibers by grafting vinyl monomers

Graft polystyrene has been synthesized on polypropylene fibers. The isometric heating curves of the grafted fibers have two maxima. The first is associated with the preserved oriented polypropylene structures, the second with the oriented structures formed directly in the process of polystyrene synthesis. The maximum stress corresponding to the latter maximum is proportional to the amount of polystyrene and the degree of orientation of the starting polypropylene and depends on the mechanical stress in the fiber during the process of polystyrene synthesis.Mekhanika Polimerov, Vol. 3, No. 6, pp. 963–969, 1967     

Comments on “Model for cover cracking due to corrosion expansion and uniform stresses at infinity”

This paper presents a discussion on a model for cover cracking due to corrosion expansion and uniform stress at infinity developed by Li et al. [Shu-cai Li, Ming-bin Wang, Shu-chen Li, Model for cover cracking due to corrosion expansion and uniform stresses at infinity, Appl. Math. Modell., doi:10.1016/j.apm.2007.06.003]. The model for cover cracking by the authors uses an equation of the penetration depth of corrosion with time developed from the Faraday’s Law. It is however shown in the discussion that the equation of the penetration depth due to corrosion developed by Li et al. is incorrect. Consequently other equations developed by Li et al. to model cover cracking that use the equation of penetration depth are also incorrect.     

Effect of combined extrusion parameters on mechanical properties of basalt fiber-reinforced plastics based on polypropylene

Basalt fibers are efficient reinforcing fillers for polypropylene because they increase both the mechanical and the tribotechnical properties of composites. Basalt fibers can compete with traditional fillers (glass and asbestos fibers) of polypropylene with respect to technological, economic, and toxic properties. The effect of technological parameters of producing polypropylene-based basalt fiber-reinforced plastics (BFRPs) by combined extrusion on their mechanical properties has been investigated. The extrusion temperature was found to be the main parameter determining the mechanical properties of the BFRPs. With temperature growth from 180 to 240°C, the residual length of the basalt fibers in the composite, as well as the adhesive strength of the polymer-fiber system, increased, while the composite defectiveness decreased. The tensile strength and elastic modulus increased from 35 to 42 MPa and 3.2 to 4.2 GPa, respectively. At the same time, the growth in composite solidity led to its higher brittleness. Thus, a higher temperature of extrusion allows us to produce materials which can be subjected to tensile and bending loads, while the materials produced at a lower temperature of extrusion are impact stable. The effect of the gap size between the extruder body and moving disks on the mechanical properties of the BFRPs is less significant than that of temperature. An increase of the gap size from 2 to 8 mm improves the impregnation quality of the fibers, but the extruder productivity diminishes. The possibility of controling the properties of reinforced polypropylene by varying the technological parameters of combined extrusion is shown. The polypropylene-based BFRPs produced by the proposed method surpass the properties of glass and asbestos fiber-reinforced plastics.Submitted to the 10th International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Ukrainian State University of Chemical Technology, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 845–850, November–December, 1997.     

Model for cover cracking due to corrosion expansion and uniform stresses at infinity

The mechanical model of the cover layer cracking in reinforced concrete structures due to corrosion expansion of reinforcement and uniform stress at infinity is established in this paper. The principle of superposition and the series expansion technique of the theory of complex potential established by Muskhelishvili are applied. The complex stress potentials are assumed to be in the form of Taylor and Laurent series expansions, and the unknown coefficients are determined by the boundary conditions and the stress state at infinity. Finally the analytical solution for hoop stresses in concrete is derived. Referring to the previous studies in the literature, the equation for time of concrete cracking due to corrosion expansion of reinforcement and uniform stresses at infinity is established. It is found that the change of stress state at infinity may accelerate or decelerate the initiation of crack. In addition, compared with the case without corrosion, the existence of corrosion products can alter the location of cracking. Further analyses indicate that the effect of the ratio between reinforced bar and concrete on the cracking is insignificant, and that the possibility of cover layer cracking increases with increasing penetration of corrosion.     

A 3-D finite-volume method for the Navier-Stokes equations with adaptive hybrid grids

This paper describes the development and application of a numerical scheme for the three-dimensional Navier-Stokes equations of viscous flow using hybrid (prismatic/tetrahedral) grids. Employment of prisms is a relatively new approach towards complex geometry high Reynolds number viscous flow computations. The body surface is covered with triangles, which provides geometric flexibility, while the structure of the mesh in the direction normal to the surface provides better resolution of the viscous stresses. The irregular areas between different prismatic layers covering the surfaces of the domain are filled with tetrahedral elements. Their triangular faces match the corresponding triangular faces of the prisms. A dual adaptation scheme is developed which employs both directional and isotropic local refinement/coarsening of the prisms and tetrahedra. The structure of the prisms is preserved by avoiding interfaces with mid-edge nodes.

Spatial discretization consists of a finite-volume, node-based scheme that is of the central-differencing type. The solution is marched in time using a Taylor series expansion following the Lax-Wendroff approach. The scheme employs a dual cells arrangement for evaluation of the viscous terms, which has the property of suppressing odd-even modes in the solution. A storage-efficient data structure is employed, which utilizes the structure of the prismatic grid in one of the directions.     

On the geodetic number of median graphs

A set of vertices S in a graph is called geodetic if every vertex of this graph lies on some shortest path between two vertices from S. In this paper, minimum geodetic sets in median graphs are studied with respect to the operation of peripheral expansion. Along the way geodetic sets of median prisms are considered and median graphs that possess a geodetic set of size two are characterized.     

Effect of residual stresses on the strength of oriented glass-reinforced plastics

The effect of structural residual stresses on the strength of a glass-reinforced plastic loaded along and across the fibers is investigated. It is established that the residual stresses lead to an increase in the strength of the glass-reinforced plastic across the fibers and to cracking of the polymer matrix in tension along the fibers, but have practically no effect on the combined deformation of the matrix and the fibers in compression.Moscow Ordzhonikidze Aviation Institute. Translated from Mekhanika Polimerov, No. 3, pp. 475–480, May–June, 1969.     

Water uptake and mechanical characteristics of wood fiber-polypropylene composites

The influence of mixing process (in a two-roll mill, high-speed mixer, or twin-screw extruder) on the strength properties of polypropylene/wood fiber composites was studied. The best results were obtained for composites compounded in a twin-screw extruder. The water uptake and the influence of moisture on the flexural strength (σ_fl) and modulus (E_fl) were studied by immersion of the composites in water at 20, 50, and 90°C. Most strongly the moisture affected the value of E_fl, but the degree of water uptake and the change in σ_fl and E_fl also depended on temperature and the presence of a modificator—maleated polypropylene (MAH). MAH improved the strength properties of the composites both in dry and wet states and also decreased the extent of water uptake and swelling in cyclic (soaking/drying) tests. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 101–114, January–February, 2006.     

Note on the Principle of Stationary Phase

The asymptotic expansion by Erdelyi (1955) of integrals of thetype where k is large, is simplified and extended, and put into aform in which three or four terms of the expansion may be writtendown at sight.     

A modified multistage fatigue model to study the fatigue life of forged HS6-5-3 tool steel under high cycle fatigue

DIN type forged HS6-5-3 tool steel (AISI M3:2) is most commonly used in tooling industry and also in some engine parts. Those components are usually exposed to cyclic mechanical stresses and 90% of them failed by fatigue damage. For predicting the life time of this tool steel under high cycle fatigue (HCF) a modified multistage fatigue model found by McDowell is proposed, which leads to reduce effects and cost for predicting life time of this material. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deformation properties and texture of isotactic polypropylene fibers

The deformation properties of isotactic polypropylene fibers are compared with the fraction of crystallites in thea and c textures and with their orientation.Institute of High-Molecular-Weight Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 7–10, January–February, 1971.     

Peculiarities of the Electret State of Melt-Spun and Melt-Blown Fibrous Polypropylene Materials

The charge state of melt-spun and melt-blown polypropylene fibers is investigated. It is shown that the production of fibers by melt-spinning and melt-blowing technologies promotes the formation of a spontaneous polarization charge. Possible mechanisms of fiber polarization are analyzed. The influence of parameters of the melt-spinning technological process and forced electrization of fibers during their formation in stationary and alternating electric fields on the magnitude and stability of the electret charge is examined. It is established that the application of a corona discharge to fiber polarization is more efficient for the electret state formation.     

Evaluating the impact of operating conditions on the performance of appointment scheduling rules in service systems

The general practice in implementing an appointment scheduling rule (ASR) is to enforce a certain rule, such as “block appointment”, to schedule customer arrivals in service systems. The operating environments of service systems are expected to affect considerably the performance of a selected ASR. The objective of this paper is to evaluate the impact of the environmental factors which include probability of no-show (ρ), the coefficient of variation (C_ν) of service times, and the number of customers per service session (N). The extent to which a certain environmental factor affects the performance of ASR is examined to see if there is any ASR that performs well under most operating conditions. Under situations characterized by 27 different combinations of the factors ρ, C_ν, and N, the performance of nine scheduling rules are evaluated by a simulation study. The simulation results show that an ASR designed to reduce customer waiting time performs very well in most operating environments considered. One commonly used ASR in real-world service systems, which schedules several customers to arrive at the start of each service session, tends to induce long customer waiting time.     

Fabrication and thermal expansion behavior of a magnesium-matrix composite with a high content of reinforcing SiC particles

An Mg-based metal-matrix composite reinforced with 50 vol.% SiC particles was fabricated by infiltrating molten metal into porous SiC preforms, and its microstructure and thermomechanical properties were investigated. The effect of thermal processes on the thermal expansion behavior of the composite was investigated by applying 1, 10, and 20 thermal cycles within the range from room temperature to 200°C. The Kerner and Turner analytical models and a 2D unit-cell finite-element model were employed to analyze the thermal expansion behavior of the composite. The coefficient of thermal expansion (CTE) predicted by the 2D unit-cell model was in good agreement with the Kerner model, while the results from the Turner model were significantly lower. The CTE of the composite slightly increased during the thermal cycling and, after a few cycles, agreed well with the Kerner and 2D unit-cell predictions.     

Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate deformations at the nanoscale. The resulting ‘nanocomposite’ is subjected to a uniform temperature variation which leads to periodic deformations within the plane perpendicular to the fibers and uniform deformations along the direction of the fibers. These deformation fields are determined by analyzing a representative unit cell of the composite subsequently leading to the corresponding effective thermal expansion coefficients. Numerical results are illustrated via several physical examples. We find that the influence of interface effects on the effective thermal expansion coefficients (in particular that corresponding to the transverse direction in the plane perpendicular to the fibers) decays rapidly as the fibers become harder. In addition, by comparing the results obtained here with those from effective medium theories, we show that the latter may induce significant errors in the determination of the effective transverse thermal expansion coefficient when the fibers are much softer than the matrix and the fiber volume fraction is relatively high.     

Thermal deformation of unidirectionally reinforced hybrid composites. Report no. 1

Conclusion We conducted a dilatometric study of three types of hybrid unidirectionally reinforced composites (organic-glass-, organic-carbon-, and carbon-glass-fiber plastics), each of which was represented by several batches differing in the relative content of the two types of fibers. The tests were performed on a specially-designed laboratory prototype. It was shown that, for the materials studied, the coefficient of linear expansion can be controlled by means of hybridization — by combining several types of fibers with positive and negative values of the coefficient of linear expansion in one composite. Analytic expressions for the coefficient that were obtained by generalizing a three-phase model of a two-component composite with isotropic fibers to the case of a hybrid composite with anisotropic fibers satisfactorily describe the experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 229–236, March–April, 1989.     

Cold flow and melting of plastics under severe friction conditions

Dry friction of a series of crystalline polymers (polypropylene, nylon, PTFE) against steel over a wide range of sliding velocities (4.4–4.4×10^–4 cm/sec) and loads (P=7.5–360 kg) with almost complete mutual overlap of the friction surfaces is studied. It is shown that friction of polymer materials against steel may be accompanied by melting of the crystalline polymer (at high velocities) or cold flow (at low velocities) in the surface layers associated with an orientation effect and the appearance of anisotropy.Mekhanika Polimerov, Vol. 1, No. 5, pp. 95–100, 1965     

Asymptotic Expansions of Multiple Zeta Functions and Power Mean Values of Hurwitz Zeta Functions

Let (s, ) be the Hurwitz zeta function with parameter . Powermean values of the form are studied, where q and h are positive integers. These mean valuescan be written as linear combinations of , where _r(s₁,...,s_r;) is a generalization of Euler–Zagiermultiple zeta sums. The Mellin–Barnes integral formulais used to prove an asymptotic expansion of , with respect to q. Hence a general way of deducingasymptotic expansion formulas for is obtained. In particular, the asymptotic expansion of with respect to q is written down.