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.     

Effect of the geometry of the structure on the strength distribution of multilaminate tridirectional reinforced plastics

Conclusion The proposed analytical method makes it possible to predict the strength distribution of an LRP of the type [0/±]_s from its structure (the geometry of the packet, the number of layers, and the strength properties of the layers) in a plane stress state. Allowance is made for the random character of the strength properties of the layers, which makes it possible to evaluate the reliability of the LRP for both determinate and random loading. A criterion was formulated for the optimum design of the structure of an LRP with respect to ensuring maximum reliability for specific loading conditions. We also evaluated the effect of the parameters of the structure and the characteristics of the plane stress state on reliability. According to the results of a numerical analysis performed with the above-developed structural model of the failure of an LRP — with allowance for the random character of the strength properties of the layers — the imbalance of the laminated packet which occurs during failure can be ignored. The method used to predict the strength distribution of the LRP, involving determination of the strength distribution law of an RSE and subsequent examination of the loading of parallel-connected RSEs, is promising for other reinforcement schemes as well.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 805–812, September–October, 1988.     

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.     

Experimental evaluation of the strength anisotropy of a unidirectionally reinforced organic fiber-reinforced plastic

Conclusions The strength of a unidirectional organic fiber-reinforced plastic has been experimentally determined in various special cases of plane stress. An analysis of the data obtained shows that it is possible to describe the strength of the material in plane stress by means of a second-order surface equation containing linear and quadratic terms. The dependence of the strength in tension and compression on the angle between the directions of loading and reinforcement has been predicted and experimentally confirmed using the values found for the components of the strength surface tensors. The results of the study can be used to estimate the strength of multilayer organic fiber-reinforced plastics in cases where a unidirectionally reinforced layer can be taken as the basic structural element of the material.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 799–803, September–October, 1979.     

Experimental investigation of the strength of glass-reinforced plastics in biaxial compression in three planes of symmetry

Glass-reinforced plastics (GRP) with fiber (wound) and fabric (hot-molded textolites) reinforcement have been investigated in biaxial compression in the three planes of symmetry. The high strength in biaxial compression in the transverse plane, observed for all the GRP investigated, is explained. A method of investigating the tensile strength of the fiber components of the GRP from the results of testing a unidirectional composite in biaxial compression in the transverse plane is proposed. The possibility of a nondestructive estimation of the strength of GRP in biaxial compression at an arbitrary stress ratio is demonstrated.Translated from Mekhanika Polimerov, No. 1, pp. 63–72, January–February, 1976.     

Strength of orthogonally reinforced plastics in uniaxial tension

Failure conditions are proposed for an orthogonally reinforced plastic in uniaxial tension at an arbitrary angle to the directions of reinforcement. The failure conditions are formulated for the case when the strength of the bond between the resin and the reinforcement is greater than the strength of the resin. The strength of the resin, which is in a volume state of stress, is determined by an energy criterion.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 629–633, July–August, 1973.     

Effect of the sign of the shear stresses on the shear strength of reinforced plastics

The effect of the sign of the shear stresses on the shear strength has been investigated for a glass-reinforced plastic of the SVAM type with various ratios of the longitudinal and transverse reinforcement in shear in the plane of reinforcement in axes turned through 45° relative to the direction of reinforcement. More than 80 tubularspecimens were tested. The shear strengths T ₄₅ ⁺ and T ₄₅ ^– corresponding to shear stresses of different signs can be found from uniaxial tests in tension and compression in the direction of the reinforcement.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 262–268, March–April, 1971.     

Influence of vibration on creep in glass-fiber-reinforced plastic in a complex state of stress

The author describes the method and results of tests on tubular specimens of glass-fiber-reinforced plastic for creep under simultaneous torsion (shear in the plane of reinforcement), compression, and vibration in the longitudinal direction. He finds that vibratory creep is not manifested if the amplitudes of the alternating component of the stress are up to 0.1 times the limit of short-term strength and the frequency is 20 kHz.Institute of Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 358–360, March–April, 1974.     

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.     

Limiting stresses in spatially reinforced composites with components-having different structural geometries nd elastic properties

A model which is proposed for calculating structural stresses in spatially reinforced composites and an invariant-polynomial criterion for evaluating their limiting values are used to predict the effect of the elastic and strength properties of the components and their relative content on the limiting stress-strain state of composites of different structures. Emphasis is given to tri-orthogonal and 4D cubic structures, in addition to structures with hexagonal and angle-ply fiber reinforcement schemes in the plane and perpendicular to it. The types of composite loading typical of standard tests are examined in separate numerical experiments for shear, tension, compression, and their proportional combination. A computational variant of a criterional estimate of the limiting stresses is substantiated for an anisotropic composite of variable strength. The limiting-stress surface is obtained along with contour maps showing stress isolines as a function of the properties of the components and the geometry of the structure. The maps are suitable for practical use. The cases of maximum resistance to shear, tension, compression, and combination loading of 3D and 4D composites are compared to the analogous cases for two-dimensional structures.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 616–639, September–October, 1995.     

One model of a nonlinear viscoelastic medium,taking into account the influence of accumulated damage

We have proposed extremely simple equations for the state of a nonlinear viscoelastic medium of the inherent type, containing the scalar function of the accumulated damage as one of the decisive parameters. The equations take into account the influence of the type of stress pattern; they also contain the long-term strength condition. Equations of this type permit determination of the stress and deformation patterns developing immediately before failure, which is very important for experimental verification of the theory of long-term strength. The proposed model also takes into account the aging of the material.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 8, No. 2, pp. 241–246, March–April, 1972.     

Experimental investigation of the impact strength of Caprolon in linear and plane stress

An apparatus for investigating the impact strength of materials in plane stress is described. The results of testing Caprolon in plane stress and linear tension over a broad range of strain rates are presented.Leningrad Kalinin Polytechnic Institute. Translated from Mekhanika Polimerov, No. 2, pp. 332–334, March–April, 1971.     

Experimental investigation of the strength of anisotropic materials in biaxial and triaxial compression

It is proposed that the strengths in uniaxial and uniform biaxial compression in the direction of the axes of symmetry be used as parameters. The applicability of a strength criterion in the form of a fourth-degree polynomial to glass-reinforced plastics in biaxial compression in the plane of reinforcement and the transversal plane and to wood in triaxial compression has been experimentally confirmed.S. M. Kirov Leningrad Forest Engineering Academy. Translated from Mekhanika Polimerov, No. 6, pp. 991–996, November–December, 1973.     

Strength and deformation properties of fiberglass-plastic in the flat stressed state as a function of reinforcement structure

Conclusion Limiting strength values have been ascertained in the flat stressed state as a function of reinforcement structure. The change in each strength surface tensor component as a function of reinforcement intensity has been approximated by the piecewise-linear approximation method. A strength condition has been derived which can be used in optimization problems. The problem of the optimum reinforcement structure of a composite at various ratios of the stresses ₁₁, ₂₂, and ₁₂ has been examined. By using the strength condition, one can predict strength values for structures which appear in the class of materials in question with various reinforcement intensities. The procedure developed can be used in designing composite materials.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 848–859, September–October, 1978.     

Possibilities of a nondestructive one-parameter method of checking the strength of anisotropic glass-reinforced plastics in uniaxial compression

A nondestructive method of checking the strength of glass-reinforced plastics (GRP) in finished products is proposed. This method is based on the correlation, investigated by the authors, between the modulus of elasticity and the compressive strength determined by a standard method. Various orientations in the plane of reinforcement of glass-reinforced plastics with different ratios of the orthogonally arranged fibers are investigated. It is proposed to determine the modulus of elasticity from the propagation velocity of an ultrasonic pulse measured under conditions of one-sided access to the surface of the product."Ritm" Research-Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 909–919, September–October, 1974.     

Tensile strength of unidirectionally reinforced plates stretched at an angle to the direction of reinforcement

Conditions for the fracture of a unidirectionally reinforced plate under uniaxial tension at an arbitrary angle to the direction of reinforcement are proposed. The fracture conditions are applicable to the case where the adhesion strength between the bond and reinforcement is greater than the strength of the polymer bond. The strength of the polymer bond in the volume stressed state is determined by an energy criterion.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 482–486 May–June, 1973.     

Theoretical and experimental investigation of anisotropic damage in textile-reinforced composite structures

In the present work, a phenomenological plane-stress damage-mechanics-based model for textile-reinforced composites is presented and its predictive capability is evaluated by carrying out a series of experimental tests. Damage variables are introduced to describe the evolution of the damage state and, as a subsequence, the degradation of material stiffness. For calculating the nonlinear stress and strain distribution of complexly loaded composites with a textile reinforcement, a special emphasis has to be placed on the interaction between the fiber failure due to the stress in the fiber direction and the matrix failure due to the transverse and shear stresses. This demands the formulation of realistic failure criteria taking into account the microstructural material behavior and different fracture modes. The new failure criteria, like the fracture mode concepts, consider these fracture modes, as well as further fracture types, in the reinforcement plane. The failure criteria are based on equations for failure surfaces in the stress space and damage thresholds in determining the stiffness degradation of the composite. The model proposed was used to characterize the strength and the failure behavior of carbon-fiber-reinforced composites. For this purpose, several unidirectional and bidirectional tests were performed to determine the specific properties of the material. The specimens were investigated by using acoustic emission techniques and strain-controlled tension and torsion tests.Russian translated published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 791–810, November–December, 2004.     

Equilong-term strength surfaces of organic textolite in the plane stressed state

Conclusion Long-term strength tests of textolite were conducted for seven different particular cases of the plane stressed state. Maximum times to failure for which experimental data were obtained reach 2500 h. It is established from analysis of the test results that the experimental long-term strength curves for the types of stressed state under consideration are closely similar. The condition of long-term strength in the general case of the plane stressed state for constant levels of stresses is taken as the equation of the short-term strength surface in which the time factor is introduced parametrically; in this case, the apparent observance of similarity between equilong-term strength surfaces makes it possible to express the tensor components characterizing the long-term strength by tensor components of the short-term strength surface and a certain monotonically decreasing time function, which is independent of the form of stressed state.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 51–56, January–February, 1979.     

Static and vibrational creep of a fabric-reinforced plastic in shear in the plane of the reinforcement

The results of a comparative experimental investigation of the short-term static and vibrational creep of a fabric-reinforced plastic in shear in the plane of the reinforcement are presented. The experimental procedure is described in detail. It is shown that on the investigated ranges of temperature, stress, and amplitude-frequency parameters the effect of an additional vibrational load on the creep process is unimportant.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 605–610, July–August, 1971.     

Problems of the anisotropy of strength

The concept of a strength tensor, analogous to the tensor of elastic constants, has been introduced with a view to using its components for approximate determination of laws governing the variation of strength of anisotropic materials in uniaxial tension or pure shear as a function of the orientation of the stress state. It has been shown that the plasticity condition postulated by Mises can be used as a criterion of strength of many "weakly" anisotropic materials, if one rejects the hypothesis according to which the condition is invariant in respect to hydrostatic pressure. In the case of "strongly" anisotropic materials, wood in particular, the Mises condition is at variance with the results obtained for variously oriented specimens tested in uniaxial tension. A strength condition in the form of a fourth-degree polynomial, based on the assumed existence of a strength tensor analogous to the tensor of elastic constants, has been postulated for these materials. The validity of this criterion has been demonstrated by constructing surfaces of equicritical plane stress states from experimental data obtained for pine wood, plywood, and glass-reinforced plastic laminates.Mekhanika Polimerov, Vol 1, No. 2, pp. 79–92, 1965