Analysis of the fracture of fiber composites on the basis of the statistical theory of branching processes

A statistical theory of branching processes is used to examine models of the localized and delocalized fracture of fiber composites. It is shown that despite the differences between the two types of models, both can be reduced to the same generalized Markov process. A new fracture criterion to be used for all types of models is proposed. The use of this criterion makes it possible to theoretically describe a new structural effect — the dependence of the breaking stress of a composite specimen on its cross-sectional area. In the limiting case of an infinitely large cross-sectional area, the breaking stress calculated on the basis of the proposed approach turns out to be equal to that calculated using previous models. The breaking stress for specimens of finite dimensions turns out to be lower than for specimens of infinite size. This result is due to the nonlinear dependence of the probability of fiber rupture on the additional overstresses that develop in the composite during local microscopic fractures. The results that are obtained should be taken into account in the calculation of the strength of structurally reinforced composites and small structural elements made of composite materials.Kompozit Research Center, St. Petersburg, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 795–807, November–December, 1996.     

Effect of parameters of the distribution of the length and orientation of short fibers on characteristics of the dynamic viscoelasticity of a polymer composite

Conclusion An algorithm for calculating the dynamic viscoelastic characteristics of a composite reinforced with short fibers was developed and realized in the form of a computer program. An analysis was made of the dependence of the characteristics of the composite on the volume content and length of its fibers, as well as on statistical distributions of fiber length and orientation in the material. It was shown that a change in the parameters of the statistical distributions has a significant effect on both the elastic and the dissi-pative properties of the composite. It was found that ignoring the statistical fiber-length distribution might lead to overestimation of the real component of the complex modulus and underestimation of the mechanical loss tangent.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 13–17, January–February, 1990.     

Elements of structural mechanics of discretely soaked composites with randomly distributed fibers

Conclusions It is evident that the proposed approach is one of the first attempts to construct structural models and carry out examination from the viewpoint of the mechanics of composites of discretely soaked fiber-reinforced filtering materials. The constructed computer structural model and the algorithms of simulations of the processes of loading and failure of these materials are in the stage of experimental verification. At the same time, the approach proposed to examining this new grade of materials for composite mechanics may be of specific interest for widening the possibilities of computer simulation of the processes of deformation and failure of materials on the basis of detailed macrostructural examination and analysis of the results of mechanical tests.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 629–639, September–October, 1993.     

Effect of surface treatment of carbon fibers on the strength properties of carbon fiber plastics

Conclusions The strength characteristics of composites based on carbon fibers having a coating of silicon carbide are in direct dependence on the coating thickness and on the porosity, which makes it possible to assume the possibility of increasing the degree of realization of the strength characteristics of fibers having a coating in a composite by increasing the degree of impregnation of the carbon cord with the binder. The latter finds confirmation also in the fact that at a small coating thickness on the carbon fiber (of the order of 5 nm) the porosity of the composite obtained is equal to the porosity of the material based on the carbon fiber without coating. Moreover, as is evident from Fig. 3c, the casing of silicon carbide does not form a continuous coatting over the whole perimeter of the cord. The presence of these prerequisites, and also the high resistance of carbon fibers having a silicon carbide coating to oxidation [9], open up wide prospects for creating new composite materials based on them.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 603–606, July–August, 1979.     

Mechanical properties of boron fibers

The distribution of the strength of boron fibers is examined on the basis of a large amount of experimental material. The typical defects are isolated and described. The dependence of the average strength on the length of the test fiber is investigated.State Scientific-Research Institute of Chemistry and Technology of Heteroorganic Compounds, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 641–647, July–August, 1973.     

Effect of fiber length on the strength and fracture properties of a fiber-filled silicone composite

The mechanism by which fillers strengthen polymers is discussed, and the effect of fiber length on static and impact bending strength and on the area of the fracture surface is studied with reference to the example of a silicone composite. A correlation is established between the strength properties and the area of the fracture surface. On the basis of the data obtained it is shown that, as the fiber length increases, the fracture mechanism changes from extraction of the ends of the fibers along the fracture path to breakage of the fibers.Moscow Lomonosov Institute of Fine Chemical Technology. Ter-Gazaryan State Scientific-Research Planning Institute of Polymer Adhesives, Kirovakan. Translated from Mekhanika Polimerov, No. 3, pp. 445–449, May–June, 1971.     

Structure and properties of ceramic composites based on ZrO2

Monodisperse fine powders of high purity obtained by sol-gel method are used for production of high technical data ceramics. The fiber reinforcement is used for hardening of composite materials. It was of interest to study production possibility of reinforced composite material based on ZrO₂ obtained by sol-gel method with filler from fibers of partially stabilized zirconia. ZrO₂ powders were obtained by precipitation of its hydrated gel from aqueous zirconium oxychloride solution by ammonium hydroxide followed by thermal treatment. For composite reinforcement ceramic partially stabilized (8 mole Y₂O₃) ZrO₂ fibers 0.16–0.67 mm in length and 5–7 m in diameter were used. Content of the fibers in composite was 20 wt.%. From powders and their mixtures with fibers, the samples were pressed as disks, beams and cylinders, and anneal in air at 1100–1600°C temperature range. The investigation has shown that the fibers of partially stabilized zirconia change the composite structure, increase the content of tetragonal modification that promotes its hardening. Treatment temperature of precursor determines physical chemical properties of compositions with fibers. Their high specific surface and reaction ability provides a workability of forming and sintering processes into strong composite material. The ceramics was increased by 2.5–3 times as strength after fibrous filler introduction into ZrO₂ hydrogel matrix.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Presented at the Ninth International conference on the Mechanics of Composite Materials (Riga, October 1995). Institute of General and Inorganic Chemistry of the Academy Sciences of the Belarus. Minsk. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 418–427, May–June. 1996.     

Analysis of elastomeric composites based on fiber-reinforced systems 3. Two-directional composites

Results of investigation of deformation of elastomeric composite materials with a two-directional reinforcement scheme are presented. The study is performed on the basis of a structural macroscopic theory. The matrix of the composites analyzed is of a poorly compressible material. The fibers of both reinforcing systems are simulated as compressible bodies. Dependences of the parameters of tensile and shear strains on the strain values for different geometries of fiber arrangement are obtained.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 479–492, May–June, 1999.     

Some problems in the application of statistical dynamics to shells manufactured from fibrous composites

On the basis of a statistical approach presupposing direct utilization of experimental data produced in modelling operations, a procedure is proposed for computational estimates on composite materials in which allowance is made for the initial defects, the variable properties of the material, and the conditions of use (physical medium). Experimental data on Plexiglas shells which confirm the practical applicability of the procedure are given. Questions relating to the design of tests on composite shells are discussed.Translated from Mekhanika Polimerov, No. 4, pp. 743–745, July–August, 1972.     

Localization of microfailure in fibrous composites

Conclusion When a fibrous composite is loaded, the process of microfailures becomes localized in consequence of the nonuiformity of internal stresses. The degree of localization can be quantitatively characterized by the magnitude of the parameter of localization whose determination was provided in the present work. The dependence of the parameter of localization on the stress applied to the specimen can be measured experimentally from the data on the location of the coordinates of the sources of AE, and it can be calculated theoretically on the basis of the model of failure of the composite. A comparison of the theoretical model with the experimental data makes it possible to determine the magnitude of the overstresses in the fibers of the composite material and the form of the distribution function of these overstresses.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 437–443, May–June, 1989.     

Experimental Evaluation of the Effect of the Structure of Composite Rings on Their Properties in the Radial Direction

Based on the results of bending tests on cut glass-fiber-reinforced plastic rings with a longitudinal-circumferential reinforcement, their radial peel strength is evaluated. The effect of the fiber layout on the properties of the rings in the radial direction is investigated. It is shown that their radial tensile strength only slightly depends on the fiber layout but is basically determined by the properties of the polymer interlayer between the fibers. In radial tension, the presence of fibers in the polymer layer leads to a strain concentration, which results in a premature failure of the polymer phase of the composite. The strain-concentration factor cannot be used for an accurate prediction of the breaking stresses or strains of the composite, because of different failure modes of the pure resin and the composite.     

Method suited for constructing deformation diagrams of composite materials on the basis of the statistical distribution of the strength of the reinforcing fibers

Starting from an analysis of the statistical accumulation of the defects during rupturing of the separate fibers in a composite material, a theoretical method suited for constructing deformation diagrams of composite materials and based on averaging of the stresses in the defect volumes of the material is proposed. The effect of two statistical distribution (Waybul's and uniform) laws of the strength of the original reinforcing fibers on the shape of the deformation diagrams of composite materials is analyzed.     

Intensity of the relaxation processes in statically loaded,highly oriented synthetic fibers

An experimental study of the stress relaxation and creep of a series of synthetic fibers has revealed a reduction in the intensity of these processes as the tensile strain increases. On the basis of a comparison of the relations obtained and the results of previous studies of loaded oriented polymers using small-angle x-ray scattering and NMR techniques it is suggested that the observed effect is attributable to orientational ordering of the through macromolecules in the amorphous regions of the fiber. It is also concluded that in oriented polymers at strains considerably below breaking values the elementary relaxation events are physical (and not mechanochemical) in nature.Kirov Leningrad Institute of the Textile and Light Industries. Translated from Mekhanika Polimerov, No. 1, pp. 154–157, January–February, 1973.     

Three-dimensional reinforced fabric materials

Three-dimensional materials whose principle of construction is based on marked curvature of the fibers of multilayered three-dimensionally woven fabric are discussed. The effect of the law and degree of curvature of fibers on the deformative properties of the composite material is investigated on the basis of the model proposed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 311–318, March–April, 1970.     

Resistance to interlayer shear of plastics on a carbon filament base

Conclusions 1. An equation has been derived for the strength during interlayer shear along reinforcing fibers of a composite material of unidirectional texture which allows calculation of this index as a function of composition of the material and state of the interphase boundary. Experimental confirmation of this equation has shown that the effectiveness of surface treatment of the reinforcing filler can be estimated by its use.2. It has been shown that the strength during interlayer shear of an epoxy-phenol plastic can be increased by a factor of more than 3, and during bending by a factor of 1.3, as the result of treatment of high-modulus carbon fibers in nitric acid.3. A correlation has been established between changes in electrical resistivity of the carbon fiber and the molecular component of adhesion to it of consolidated epoxy-phenol binder.Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 445–451, May–June, 1977.     

An interphase layer in organic fibrous composites

Conclusions In this work, it was attempted to demonstrate the special features of polymer fibers manifested primarily in a special mechanism of formation of the interphase layer during formation of the composite material. The role of the interphase layer in this case is not reduced just to dissipation of the energy generated during rupture of a fiber. It can also play the role of an element of the structure of the composite acting as a possible source of initial cracks. From this viewpoint it would be useful to re-examine the micromechanics of failure of the composite and attempt to take into account the role of the interphase layer in a real system of many fibers, not just in the fiber-interphase layer-matrix triad.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 1, pp. 10–18, January–February, 1993.     

Effect of the morphology of the organic fibers on the mechanical behavior of composites

Scanning electron microscopy and x-ray diffraction analysis are used to study the morphology of several aramid and polyimide fibers developed in Russia and to determine their strain-strength characteristics. It is shown that the supermolecular structure of the fiber in large part determines the character of its interaction with the matrix and behavior during failure of the fiber composite (FCP). In the case of aramid fibers, composite failure is accompanied by intensive fibrillation leading to lamination on a microscopic scale and a deterioration in the service characteristics of the composite. The stability of the investigated polyimide fibers against fibrillation and microlamination, in combination with good heat resistance, makes them promising as reinforcing materials for FCPs.Submitted for the Tenth International Conference on the Mechanics of Composites (Riga, April 1998).Institute of High-Molecular-Weight Compounds of the Russian Academy of Sciences (St. Petersburg, Russia) and the Khimvolokno Scientific-Industrial Association (Mytishchi, Russia). Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, 656–669, September–October, 1997.     

Relationship between strength characteristics of unidirectional glass-reinforced plastics and their composition

The article discusses the effect of the amount of binder present and the porosity of the glass reinforced plastic on the usable strength of the glass fibers, the tensile strength, and the elasticity module in stretching. It is shown that a relationship exists over the whole range tested between the volume ratio of the components (binder and glass fiber), certain strength characteristics, and porosity. A method is suggested for the comparison of glass-reinforced plastics according to their usable fiber strength which can be used for the selection of the best binder, the glass material, the glass composition, glass fibers, the lubricant, the technological scheme, etc.Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 477–480, May–June, 1970.     

Statistical theory of defect buildup in composite materials and the scale-factor effect in reliability

A statistical theory of fracture based on the concept of defect buildup is applied to composite materials with a definite fiber orientation. On the premise that the concentration of defects that precede a fracture is sufficiently low, asymptotic distributions of defectiveness are established and asymptotic expressions for the reliability function are derived. It appears feasible to use this theory for predicting the reliability and the scale-factor effect for structures made of oriented composite materials.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 247–255, March–April, 1976.     

Study of microbuckling of fiber-reinforced composite materials

On the basis of the theory of microbuckling of lamina-reinforced composites and formula predicting the critical composite stress for microbuckling in the shear mode _cs published in the literature, a FORTRAN program for study of the behavior of microbuckling of fiber reinforced composites has been developed. Some types of composite materials (reinforcement of different fibers and epoxy matrix) have been studied. Graphics and curves, accounting for the dependences of the compressive stress at failure _cs from the reinforcement volume k, specimen length L, and shear modulus of resin G_r have been obtained. The comparison of the theoretical diagrams presented here and experimental and theoretical results, published in the literature shows good agreement. The basic conclusion of the work presented here is that the study could be used for other fiber reinforced composites (with different mechanical properties of matrices and fibers).Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 531–538, July–August, 1996.