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.     

Effect of aggregation of a dispersed rigid filler on the elastic characteristics of a polymer composite

Conclusions We proposed a method for describing the effective elastic characteristics of a polymer composite with a rigid aggregating filler. An important feature of such a medium is the variable coupling of the inclusion phase in relation to its volume content. A change in the degree of coupling of the filler is accounted for by introducing an additional parameter. We examined a method of determining the coupling parameter from the results of statistical modeling of the geometry of the medium. Using the example of a calcite-HDPE composite, we showed that aggregation has a significant effect on the dependence of the elastic modulus on the volume content of filler; satisfactory agreement was obtained between the theoretical and experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 14–22, January–February, 1986.     

Mechanical properties of a composite with a carbonized matrix

The effect of reinforcement schemes that differ in the magnitude of the disorientation angle of neighboring filler layers on the mechanical properties of a "carbon-carbon" composite under extension, compression, or bending is shown.Translated from Mekhanika Polimerov, No. 2, pp. 235–240, March–April, 1976.     

Resistance of bony tissue to tensile fracture

The tensile fracture resistance of compact bony tissue is considered. The relation between specific strain energy and stress level is established. A strength criterion characterizing the degree of deformation is proposed on the basis of a model, according to which compact bony tissue may be regarded as a composite material. The mode of variation of the proposed resistance parameter over the various zones of the cross section of the diaphysis of a human tibia has been experimentally established.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1084–1091, November–December, 1971.     

Scale factor in an experimental model of a highly reinforced composite

Formation of shrinkage defects during isothermal curing of network polymers is considered. The cure was carried out under conditions of adhesive interaction of the polymer matrix with the rigid filler present in the composite. The dependence of the relative mean distance between cohesive defects on the tube diameter in the tube model developed earlier was investigated over more than two orders of magnitude of tube diameters. This distance was found to be constant in the range considered. A similar process of shrinkage defect formation was observed for a plate model.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 163–168, March–April, 1995.The work was financed by the Russian Fund for Basic Research (Project 94-03-09253).     

Elastic unbalance of composite rim flywheels

Elastic unbalance of a composite flywheel is considered to be caused by different strain character of the rotating rim due to the distributed material density homogeneity or the corrective mass balancing it in the static state. An analysis has been carried out on the effect of elasticity of the rim flywheel on the linear elastic unbalance and its magnitude for an actual composite flywheel has been calculated. A procedure has been developed for the elimination of unbalance using two corrective masses. The problem of angular unbalance of a rim flywheel has also been considered. The finite element method has been used for computation.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 552–561, July–August, 1994.     

Safe density ratio modeling

An important problem in logistic regression modeling is the existence of the maximum likelihood estimators. In particular, when the sample size is small, the maximum likelihood estimator of the regression parameters does not exist if the data are completely, or quasicompletely separated. Recognizing that this phenomenon has a serious impact on the fitting of the density ratio model–which is a semiparametric model whose profile empirical log-likelihood has the logistic form because of the equivalence between prospective and retrospective sampling–we suggest a linear programming methodology for examining whether the maximum likelihood estimators of the finite dimensional parameter vector of the model exist. It is shown that the methodology can be effectively utilized in the analysis of case–control gene expression data by identifying cases where the density ratio model cannot be applied. It is demonstrated that naive application of the density ratio model yields erroneous conclusions.     

One dynamic model of a composite material

A model has been constructed for the propagation of waves orthogonally to the layers or fibers of a composite material and based on the Voltaire equation of state with oscillating kernels. The results of treatment of experimental data are presented.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 2, pp. 364–367, March–April, 1976.     

Statistical theory of elasticity of reinforced plastics with internal stresses of shrinkage origin

The statistical boundary value problem of the theory of elasticity of macrohomogeneous composite media in the natural (unstressed) starting state is extended to media with internal stresses of shrinkage origin. It is established that the moduli of elasticity of the composite do not depend on the magnitude of the shrinkage stresses. The conditions, under which shrinkage of the resin in materials of the glass-reinforced plastic type does not lead to warping, are determined. Applications of the results to the computation of structural reliability characteristics are noted.Kirov Ural Polytechnical Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 4, pp. 676–681, July–August, 1970.     

Estimating the parameters of fatigue curve of a composite material

By using the method of maximum likelihood, the parameters of two versions of a mathematical model for fatigue damage accumulation in a laminate are estimated. The models, which are founded on the Markov chain theory, are very simple: they do not take into account the specific structural features of a composite and therefore cannot provide numerical coincidence with experimental fatigue test data, but they can be used for a nonlinear regression analysis of fatigue curves. A simple method is offered for approximately estimating model parameters, some of which characterize the distribution of the local static strength. By using such models, we can predict the relative changes in fatigue curves from known relative variations in the parameters of static strength and also predict the distribution function of fatigue life in program fatigue tests.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 109–120, January–February, 2005.     

“Fundamental” and “practical” adhesion in polymer-fiber systems

The relationship between adhesion and bond strength in thin fiber-polymer matrix systems was studied. Adhesive interaction in composite materials was analyzed within the scope of thermodynamic and molecular-kinetic theories of adhesion. Methods based on wetting are shown to give poor estimation of the work of adhesion in fiber-polymer systems, which is due to their low sensibility to donor-acceptor interactions taking place at the interface. Important information about the acidity and basicity of contacting surfaces can be obtained by using inverse gas chromatography to investigate the thermodynamics of adsorption. The calculation of the work of adhesion including acid-base interactions shows the best agreement with the bond strength in the same systems. The local (ultimate) interfacial shear strength is proposed to characterize the quality of fiber-matrix bonding. Analysis of the relationship between the work of adhesion and adhesive pressure for various systems allowed us to differentiate the dispersive and acid-base components of the local bond strength as well as to estimate distances characteristic of these twoTypes of interaction. For dispersive forces, our estimation gives 7–8Å, i.e., of an order of magnitude of the center-to-center distance for van der Waals interactions. At the same time, the acid-baseInteractions have a characteristic range of 4–5Å and can be attributed to hydrogen bonding. The agreement between the calculated distances and literature data is evidence for the applicability of the proposed method to the analysis of the adhesive interaction in fibrous polymer composites.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 431–446, July–August, 1998.     

Failure of composite tubes in the Chinese lantern mode under a weight-type load

The failure of unidirectional composite tubes in the Chinese lantern mode is analyzed in the case of a tube compressed by a weight type load, which retains its magnitude after splitting of the tube. Calculation formulas are derived for predicting the critical load. The main regularities of the solution obtained are illustrated with specific examples. It is shown that the nature of the acting load must be considered in the analysis of unidirectional composite tubular bars with axial reinforcement.Bauman Moscow State Technical University, Russia. Scientific Research Institute of Mechanical Engineering, Moscow, Russia. Translated from Mekhanika Komspozitnykh Materialov, Vol. 35, No. 3, pp. 319–324, May–June, 1999.     

Aging of polymer composite materials exposed to the conditions in outer space

A comprehensive investigation is made of glass, carbon, organic fiber-reinforced plastics, and epoxy-based hybrid composite materials employed in Salyut-type spacecraft which remained in space for up to 1501 1501 days. In particular, the properties, aging mechanism, and strain-strength variations in these materials due to exposure to the conditions in outer space were studied. After a series of tests were performed in space the standard strain and strength parameters as well as the mass, density, and thickness changes in the composite materials were estimated. Electron-microscopic and dynamic-mechanical analyses were performed, and the thermal expansion was estimated for a wide range of temperatures. The principal, dominant process occurring due to the continuous presence in outer space was found to be post-curing of the resin materials, which in turn affected the mechanical characteristics of the composite materials. After 456–1501 days in space the room-temperature strength of the composite materials (except for organic plastics) did not decrease, while at high temperatures it even increased. The post-curing and restructuring of some composite materials lowered their dynamic shear moduli in the glassy state of the resin. Due to consolidation of the surface layer of hybrid composite materials irradiated and subjected to thermal cycles, failure during bending varied from transverse fracture to delamination. The negative effect of the post-curing process was expressed as higher internal tension in the hybrid composite materials with different linear thermal expansion coefficients. The magnitude of this effect depended on the amplitude of the thermal cycles. The unprotected surface of the composites bombarded by atomic oxygen, microparticles, and space garbage were subjected to pickling and microerosion, the maximum effect occurring at the initial stage of exposure. Desorption of moisture and low-molecular products during the first 100–200 days of thermal cycling in the vacuum of near-earth orbit must be considered when estimating the total mass loss of composite materials. Data from microscopic, dynamic-mechanical, and other types of analyses revealed that the outer-space factors improved the supermolecular order of the resin volume, while the subsurface layer structure of the composite materials had loosened. Microcracks formed in the plastic's surface during 1501 days in outer space did not, in general, affect the mechanical parameters of the composite materials. Most of the observed effects of exposure to conditions in outer space were less pronounced for plastics protected by aluminum foil or other plastic coatings. The data obtained can be used for designing external elements of spacecraft by selecting materials with specified and predictable properties for long-term service.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 457–467, July–August, 1993.In conclusion we thank I. G. Zhigun and R. P. Shlits for assisting in determining the mechanical properties of PCM as well as the crew of the Salyut-6 and Salyut-7 space stations for setting up, monitoring, and delivering samples to earth.     

Thermal conductivity of unidirectionally reinforced hybrid composites

Conclusion The thermal conductivity of organic-glass, organic-carbon, and carbon-glass plastic in dependence on the volumetric content of organic, glass, and carbon fibers was experimentally investigated. The solution for transverse thermal conductivity of unidirectional hybrid composite, obtained in [8] by generalizing the method of self-congruence to the case of a triphase model, is in satisfactory agreement with the experimental data.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 817–822, September–October, 1990.     

Microstress fields and the mechanical properties of disordered fiber composites

Conclusion The effective elastic moduli and Poisson's ratios and the mean characteristics of the stress fields in the components of unidirectional fiber composites with a stochastic structure are nearly the same as the corresponding values calculated for a regular model of the composite. Relatively small increase (up to 6%) is seen in the transverse shear moduli with the transition from a regular structure to a stochastic structure. In the latter, there is a substantial increase in the stress concentration factor. Here, the difference between the stochastic structure and the regular structure increases with an increase in fiber stiffness and is particularly great (with a difference of two to three orders of magnitude) in the case of shear loading. The probability of the occurrence of microscopic fracture in the binder of the investigated materials is higher in transverse tension, but the difference from the results obtained for the regular models is more significant in the case of shear loading. Microscopic fracture nuclei will be formed in the matrix of the composite with the stochastic structure at considerably lower macroscopic stresses than are required for the regular structure.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 860–865, September–October, 1990.     

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.     

Application of CFRP as a rotor shaft material

Conclusions Theoretical analysis and tests performed on rotors with composite shaft show that there is a sufficiently wide rotation stability region in the rotor parameter space despite comparatively high damping of a polymeric composite with respect to steel. Optimum parameters of the shaft (lay-up, thickness) and bearing (radial stiffness, damping) can be found within this region for each given rotor ensuring a low vibration level at critical frequencies.If rotor system parameters are far enough from the instability threshold, maximum vibration level is observed when rotor passes the first eigenfrequency zone. Further increase of rotation frequency leads to a rotor self-centering, and vibration level does not change passing the second eigenfrequency zone. The rotor response is not sensitive to small changes in rotor system parameters. If rotor system parameters are close to the instability threshold, vibration level at the second eigenfrequency dominates, and a small variation of bearing parameters causes significant changes in the vibration level.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 227–240, March–April, 1995.     

Long-term strength of reinforced composites

Conclusion A criterion of long-term strength was proposed for composite materials. The criterion can be used to calculate time to failure for arbitrary loading programs. It was shown that the criterion provides for good agreement with the experimental data not only in the cases of instantaneous and long-term static loadings, but also for fatigue loading in tension, in compression, and in mixed regimes with different asymmetry coefficients.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 16–22, January–February, 1989.     

Fracture propagation in a boron-aluminum composite

Conclusions 1. Application of the linear mechanics of fracturing to composites of the boron-aluminum type is justified, since it has proven possible to determine in an experiment the value of the fracture strength which characterizes the resistance of the material to fracture.2. The fracture strength of boron-aluminum turns out to be higher than the same characteristic of the matrix material. Boron-aluminum is a material with a high resistance to fracture, whose surface is normal to the direction of the fibers. The fracture work of boron-aluminum with a fiber content of 50% is approximately three times higher than the fracture work of the unreinforced matrix.3. At present there is no computational model of a composite which would permit reliably estimating the value of the fracture strength and optimizing a composite for this characteristic. Such a model should intrinsically take account of the statistical characteristics of a fiber.4. The data obtained can also be interpreted as confirmation of the existence of a scaling dependence of the strength of a composite in the case of supercritical reinforcement.Institute of Solid-Body Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1010–1017, November–December, 1976.     

Evaluation of porosity in composite aircraft structures

Conclusion The use of an analytical model for determining the moduli of elasticity of composite laminates made of woven or unidirectional plies with different porosity levels was described. The analysis of aircraft composite parts with different levels of voids (porosity) was based on a method which utilizes the results of state-of-the-art nondestructive testing methods (ultrasonic through transmission, loading, or pulse/echo) as the starting data for the analytical model. The porosity distribution over the volume of the material and correlations for the nondestructive testing methods were determined for epoxy-carbon laminates with standard and stiffened binders and corroborating experiments were conducted. It was shown that the moduli of elasticity of composite laminates decrease with an increase in the porosity levels. The type, thickness, and layup of the laminate are the basic factors that affect the decrease in the elastic properties of porous composite laminates.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 6, pp. 813–830, November–December, 1994.