Reliability of multilayer plastics reinforced in three directions in a two-dimensional random stressed state

Conclusion The method developed permits considering the random character of the components of an applied stressed state and makes it possible to analytically predict the reliability of a three-directional LRP. The possibility of optimization of the material was demonstrated and the corresponding method was developed based on an analysis of the effect of the structure (geometry of the structure of the RES, number of layers), scattering of the loading and strength parameters on the reliability of LRP. The criterion for optimization of the structure of LRP in application to the actual conditions of random loading can be used both for a given loading level and for a required reliability level. Use of the method developed can also be promising in the case of the effect of combined loads.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1037–1045, November–December, 1989.     

Structural-statistical analysis of the strain properties of laminated reinforced plastics

Conclusion The structural relations derived here make it possible to analytically predict the main statistical characteristics of the strain properties of an LRP with allowance for the mutual correlation of the random parameters of the structure. Use of the proposed relations is valid for studying combination loading (bending and a plane stress state), as well as when the structure of the composite is unbalanced. We evaluated the scale effect associated with the presence of multiple layers and determined the impact of this effect on the scatter of the strain properties of the LRP for different types of deformation. We also proposed a method of determining the actual statistical characteristics of layers indirectly — on the basis of experimental testing of multilayered unidirectional plastics. One promising prospect is the use of these results to formulate and solve problems involving optimization of the structure of LRP's on the basis of criteria ensuring the composite's reliability and dimensional stability. Finally, the results can also serve as a basis for establishing scientifically substantiated safety factors for stiffness.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 995–1001, November–December, 1990.     

Effect of stability of the structural parameters of laminated reinforced plastics on their strength properties

Conclusion As a result of the completed analysis, we estimated the effect of scatter of the strength properties of the layers, instability of the layers' strain properties, and instability of the geometry of the structure on the strength properties of multidirectional LRP's in a plane stress state. It was established that instability of the structural parameters produces two negative tendencies: a reduction in the mean values of LRP strength and an increase in their scatter. From the viewpoint of ensuring the reliability of structures (structural elements) made of such materials, these tendencies reinforce one another and are thus even more dangerous. It follows from this that the production method employed should not only (or not even mainly) solve the problem of increasing the values of the parameters of the materials (and their semifinished structural elements), it should also address the problem of alleviating their instability — improving the quality of production.The numerical analysis established the limits at which it is necessary to account for instability of structural parameters in engineering calculations: for the strain properties of the layers — a coefficient of variation of the elastic modulus greater than 10%; for the scatter of the angles of orientation of the layers — a standard deviation greater than 5 °. These numerical results and the computer program developed may prove useful in evaluating the actual properties of structural parameters determined in indirect tests of LRP's, as well as in more adequately comparing empirical data with corresponding calculations based on structural theories. The development of such an approach to analyzing the strength properties of multidirectional LRP's in bending also holds promise.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 659–666, July–August, 1990.     

Structural theory of the strength of reinforced plastics

Conclusions In the present study, we developed structural criteria that make it possible to predict at the component level (polymer binder, fibers) and interface level the long-term strength of laminated reinforced plastics in a plane stress state. The proposed relations make it possible to evaluate the effect of the rheological properties of the components, their volume fractions, and the geometry of the structure of the laminated packet on the long-term strength of reinforced plastics. The relations also permit resolution of the inverse problem: efficiently design the structure of such materials for specific loading conditions.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 833–839, September–October, 1989.     

Dynamic adhesive strength of fiber-polymer systems

A new device for studying the dynamic adhesive strength is created. A procedure for determining the dynamic adhesive strength in fiber—polymer systems under impact loading (pull-out technique) is developed. The adhesive strength of the interface of polymer—steel wire joints formed by polymers of different chemical nature (epoxy resin, polysulfone, and polypropylene) is examined. It is shown that the dynamic adhesive strength grows as the loading rate increases for all the systems under investigation and that the relationship between the adhesive strength and the loading rate, , over a wide range of rates can be described by two straight lines corresponding to the quasi-static and impact loading, respectively. When passing from the quasi-static to dynamic loading, the character of scale relations of the adhesive strength does not change.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 689–700, November–December, 1999.     

Statistical analysis of the bearing capacity of rim-spoke flywheels made of reinforced plastics

Conclusion The suggested numerical method makes it possible to plot the distribution functions of the bearing capacity of RSF at the structural level of their design elements (rim, spokes) with a view to the scatter of the strength and strain properties of the used materials and the geometry of arrangement of the structure. This involves taking into account the random nature of the radial distribution in the rim material of both strain and strength properties, which makes it possible to investigate more fully the processes of failure really occurring in RSF. The suggested method is the basis for stipulating a scientifically substantiated safety factor (the theoretical bearing capacity) in dependence on the required reliability; this makes it possible to use a differentiated approach to problems of devising RSF for actual purposes. Our investigations may serve as the basis for solving problems of optimal planning of RSF according to the conditions of the required reliability.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1041–1047, November–December, 1987.     

Effect of building structure on the distribution of random bending strength of multilaminate reinforced plastics

A probabilistic structural model has been constructed for predicting the bending strength distribution in multilaminate reinforced plastics. The number and random strength/elastic properties of the layers or repeating structural elements are parameters of the structure. The random properties of the repeating structural elements are characterized by the scheme and geometry of the unidirectional layers. Two failure conditions have been analyzed: multistep failure caused by successive failure of separate layers and failure caused by the failure of the weakest component. The effect of the number of layers and the instability of the strength and elastic properties on the basic statistical properties of the bending strength was analyzed numerically for typical structures and for both failure conditions. The quantitative significance of the size effect determined by the thickness of the plastic was investigated. The main theoretical results were checked experimentally for unidirectional reinforced carbon plastic under uniaxial bending. The experimental distribution agrees well with the predicted distribution.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 3, pp. 336–344, May–June, 1993.     

Experimental investigation of the anisotropy of strength of bolted joints of laminated composites upon variation of geometric and design parameters

Conclusion In the present work we investigated the anisotropy of the characteristics of tensile (buckling) strength and elasticity of plates made of KMU-4L in a bolted joint in a wide range of parameters of the material (stacking, number of layers), geometric parameters of the joint, parameters of the fastening element and of design parameters. An analysis of the results showed that the strength of the bolted joint under static loading can be increased for thin plates with h = 1–2 mm by local reinforcement of the zone of the hole by layers with = ±45 °, and also by increasing the moment of preliminary tightening; for plates with h = 3–4 mm the only feasible measure is increasing the moment of preliminary tightening to 20–40 Nm. All the results of the experiment were graphically generalized in the form of surfaces of maximal stress; this made it possible to predict the load bearing capacity of a joint for intermediate values of the parameters by calculating the safety factors.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 268–272, March–April, 1990.     

Temperature dependence of the strength of a woven composite in a plane state of stress

Conclusions On the basis of an analysis of test results obtained by typical patterns of simple momentary quasistatic loading at various temperatures within the 20–150°C range, we have found a family of strength surfaces for a woven organic plastic material in a plane state of stress in the reinforcement plane. These experimentally found strength surfaces can be approximated by the equation of a second-degree surface. It has been established that the range of safe states of stress in the stress space narrows nonuniformly with rising temperature; namely, this narrowing is accompanied by a shift of the center and a reorientation of the axes of the strength ellipsoid. We have revealed and described the temperature dependence of the components of the strength surface tensors involved in the strength criterion. The data can be used for predicting the strength of a composite material under consideration when the latter is subject to simple quasistatic loading patterns in the three-dimensional (₁₁, ₂₂, ₁₂) stress space in the reinforcement plane within a given test range of temperatures.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 452–457, May–June, 1978.     

Analysis of effective elastic properties of unidirectional boron fiber-reinforced plastic by a generalized self-consistent method

A new generalized self-consisrtent method is developed for the statistical mechanics of composites which makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to solution of a simpler averaged problem of an inclusion with a transitional layer in a material with the effective elastic properties sought. The typical size of the transition layer is determined by the correlation radius of the random structure, and its elastic properties are considered as both the close order of the mutual position and the variation of inclusion dimensions in terms of a special averaged indicator function of the structure. A numerical calculation is presented by the generalized self-consistent method for the average indicator function and the transversely-isotropic tensor for effective elastic properties of unidirectional boron fiber-reinforced plastic based on different models for actual random structure in the plane of isotropy. Analysis of the numerical results compared with experimental data and known solutions of other authors demonstrates the high accuracy of the generalized self-consistent method for a broad class of random composite structures.Perm State Mechanical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 747–758, November–December, 1996.     

Some aspects of the behavior of shock-compressed polymers

The changes in the properties of certain polymeric materials subjected to the action of plane shocks of varying amplitude are discussed. Three loading techniques are employed — single, multiple, and high-frequency multiple loading — each accompanied by a different rise in the temperature of the polymeric material. The results show that the change in physicomechanical properties also varies with the loading technique.Volgograd Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 76–80, January–February, 1970.     

Effect of polymers with a conjugation system on the mechanical properties of phenol-formaldehyde resite

Certain mechanical properties of a phenol — formaldehyde resin of the novolac type cured with hexa methylenetetramine in the presence of PCB have been investigated. The curves representing the dependence of the flexural strength, impact strength, and hardness of the specimens on PCB concentration are extremal in character. It is shown by electron microscope techniques combined with oxygen etching of the cleavage surface that the improvement in mechanical properties is associated with a change in the structure of the crosslinked polymer.Communication 108 of the series "Polymers with a conjugation system."Institute of Chemical Physics, AS USSR, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1071–1076, November–December, 1968.     

Strength of an organic/glass fiber-reinforced textolite in plane stress

Conclusions An analysis of the results of testing hybrid glass organic textolites, containing layers of glass and organic fabric reinforcement in various proportions, along characteristic simple short-time quasi-static loading paths served as a basis for determining a family of strength surfaces for plane stress in the plane of reinforcement. The strength of the five materials investigated is described by a second-order surface equation with allowance for the difference in compressive and tensile strengths. The dependence of the strength surface tensor components entering into the strength equation on the structure parameter representing the relative content of organic and glass fabric in the hybrid textolite is investigated and described. The results obtained can be used in practical calculations for determining the optimum ratio of organic to glass fabric in hybrid material with allowance for the specific requirements to be met by the strength properties of the material when used for structural purposes.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1021–1026, November–December, 1979.     

Impregnation of fibrous fillers with polymeric binders 6. Effect of parameters of ultrasound treatment on strength properties of wound fibrous composites

Conclusion Tests of annular PCM specimens — fiberglasses and organoplastics formed by the method of wet winding using low-frequency ultrasound — were conducted. Three alternate US-impregnation schemes were investigated. Optimal alternate schemes and insonification parameters were established experimentally: frequency, amplitude, intensity, and time. Optimization was carried out on the basis of investigation of the relationships between the values of the tensile, compressive, bending, and interlayer-shear strengths, and also the relative content of filler as a function of treatment parameters. It was shown that deviation of insonification parameters from the optimal leads to a reduction in strength characteristics, as well as to a different character of specimen failure in tension and interlayer shear.The effect of US modification in producing PCM is provided by an increase in structural uniformity, and improvement of the strength and production characteristics of the polymer matrix, as well as by a reduction in the composite's effectiveness as a result of a reduction in the content of air inclusions and improvement of the binder's distribution across the section of the filler.For previous communication, see [9].Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 724–731, July–August, 1989.     

Change in the degree of anisotropy of unidirectional glass-reinforced plastics during winding

The change in the degree of anisotropy of the principal elastic and strength properties of unidirectional glass-reinforced plastics during the winding process is described. Two such materials — LSB-F and LSO-R-2M — have been experimentally investigated. The anisotropy of the elastic properties is characterized by the parameter and that of the strength properties by the parameter =/_r.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 953–956, September–October, 1970.     

Optimal design of reinforced-plastic chord flywheels under reliability limitations

Conclusions The proposed method makes it possible to accomplish optimal design of a CF according to the condition of providing a maximum energy-storing capacity with consideration of the random character of the strength and deformation properties of the plastic being used and the geometry of the composition of the system. In this case, the problem of optimal design reduces to a nonlinear programming problem, where the random values of the objective function and limitations are calculated on the basis of the Monte Carlo method. The requirement of fulfilling the prescribed level of reliability of the CF is the condition of optimal design, which makes it possible to take into account the variation of the load-bearing capacity of the structure, variation of the energy-storing capacity, and conditions of the planned purpose. The effect of the structural parameters was analyzed for the example of the optimal design of a FGRP CF and the interrelation and difference of the stochastic and deterministic solutions was shown. The investigations can be useful in the practice of using effective reinforced plastics in the production of mechanical energy storages.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 908–914, September–October, 1988.     

Effect of kinematic heterogeneity on the critical stability parameters of cylindrical laminar shells

Conclusions In engineering computations, involving the stability of thin laminar designs of the plate and shell type, to determine the critical stability parameters (P_cr ¹, m_cr, and n_cr), use of the kinematically homogeneous model of a laminar packet (the classical hypothesis of a straight line) is permissible when R/h 25 for physically heterogeneous orthotropic packets irrespective of their structure, and for orthotropic hybrid packets provided that the elastic characteristics of the hard layers in the axes of layer symmetry do not exceed the corresponding characteristics of the soft layers by more than 10–15 times.In all of these cases, use of the kinematically homogeneous model produces estimates of the critical axial compressive force on the high side by not more than 3% (a hybrid quasiregular three-layer packet) with respect to values computed on the basis of the kinematically heterogeneous model of a laminar packet (broken-line hypothesis).Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 271–278, March–April, 1982.     

Fatigue strength of certain materials used in airframe construction

Conclusions The completed tests show that the fatigue strength of carbon-plastic is 2.5 times greater than that of glass-plastic. Consequently, it is best to use carbon-plastic with ED-20 epoxy resin filled with 4–5m glass microspheres for adhesive purposes in load-bearing components. This makes it possible to significantly reduce the weight of airframes and improve their service properties. It was established that, for the composite materials investigated, stiffness is lost during cyclic loading mainly as a result of damage accumulation; the loss in stiffness may serve as a criterion for evaluating the progress of fatigue fracture.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 451–455, May–June, 1980.     

Generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures

The feasibility of using a generalized self-consistent method for predicting the effective elastic properties of composites with random hybrid structures has been examined. Using this method, the problem is reduced to solution of simpler special averaged problems for composites with single inclusions and corresponding transition layers in the medium examined. The dimensions of the transition layers are defined by correlation radii of the composite random structure of the composite, while the heterogeneous elastic properties of the transition layers take account of the probabilities for variation of the size and configuration of the inclusions using averaged special indicator functions. Results are given for a numerical calculation of the averaged indicator functions and analysis of the effect of the micropores in the matrix-fiber interface region on the effective elastic properties of unidirectional fiberglass—epoxy using the generalized self-consistent method and compared with experimental data and reported solutions.Perm State Technical University. Translated from Mekhanika Kompozitmykh Materialov, Vol. 33, No. 3, pp. 289–299, May–June, 1997.     

A generalized self-consistent method for composites with random elastic properties of inclusions

The generalized self-consistent method is extended to the problems of statistical mechanics of composites with random elastic properties of inclusions. This approach makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to a sequence of simpler homogenized boundary-value problems for solitary inclusions with inhomogeneous elastic transition layers in a homogeneous effective elastic medium and with the corresponding boundary conditions. The elastic properties of a solitary inclusion for the gth homogenized problem are found from the solutions of the gth and (g+1)th homogenized problems. The elastic properties and sizes of the transition layers account for the random distribution, random sizes, and random elastic properties of inclusions in the composite. A test problem of predicting the effective elastic properties of a transversely isotropic layer composite with random elastic properties of some layers is solved by using the method proposed. The solution obtained coincides with the known exact solution [1].Perm State Technical University, Perm, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 785–796, November–December, 1999.