Properties of fiberglass-plastics reinforced with high-modulus fibers

The question of reinforcement of unidirectional fiberglass-plastic with boron or carbon fibers is considered. Static fatigue curves for the Poisson coefficient and the elastic modulus as functions of the volume content of the glass and the high-modulus fibers have been constructed. The theoretical dependences are compared with the experimental data.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Moscow. Translated from Mekhabika Polimerov, No. 1, pp. 68–74, January–February, 1972.     

Deformative characteristics of plastics reinforced with high-modulus anisotropic fibers

The independent elastic constants of plastics unidirectionally reinforced with transversely isotropic fibers have been determined. It has been assumed that the distribution of reinforcement in a transverse section of the plastic is regularly rectangular or hexagonal. To determine the transverse elastic modulus and the shear modulus in the plane of reinforcement, a constancy-of-plane-sections hypothesis was used. Values of deformative characteristics determined by the assumed calculational dependences have been compared with the experimental ones for plastics reinforced with graphite fibers.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 631–639, July–August, 1972.     

Elastic characteristics of ferrocement reinforced by hexagonal grids

The methods of the structural mechanics of composite materials are used to develop a method for predicting the elastic modulus and shear modulus of ferrocement reinforced with hexagonal woven and stamped grids. The method takes into account the elastic properties of the components and the geometry of the reinforcement.Riga Technical University, LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 182–186, March–April, 1997.     

Evaluating the effect of whiskerization of the fibers of composites on the fundamental frequency of a laminated cylindrical shell

Conclusion The calculations showed that whiskerization of the reinforcement of the structural material of multilaminate shells makes it possible in some cases to increase the fundamental vibration frequency of the structure up to 15–20%. In combination with the well-known [1] effect of improved strength characteristics for a whiskerized composite in the transverse and shear directions, this finding allows us to conclude that whiskerized structural materials are more efficient than ordinary laminated composites in shell-type load-bearing structures. Here, the greatest benefit can be expected in the case of whiskers which have higher elastic moduli than the main reinforcement. Since considerably higher reinforcement intensities can be achieved in whiskerized laminated composites than in composites with a reinforcement characterized by an arbitrary three-dimensional structure, it can be concluded on the basis of the results obtained here that, at least for shells of moderate thickness (10 < R/h 50), whiskerized composites are the optimum structural material for load-bearing shells.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1022–1027, November–December, 1987.     

Explicit Elastic Curves

The equilibria of thin rods are given by curves which are critical points of the modified total squared curvature. The critical curves are known as elastic curves. It is shown how all the elastic curves are given explicitly in terms of elliptic functions as soon as a certain set of three parameters is known. Every regular curve can be parametrized to have a constant speed but the parametrization is rarely known explicitly. Remarkably, all the elastic curves are here explicitly parametrized to have a constant speed. Curves with fixed distinct endpoints as well as closed curves are admitted. The tangent direction may be constrained at one, both, or neither of the endpoints. There are three major strands of formulas corresponding to: fixed length L, variable length without tension, and variable length with tension (let > 0 and add a term L to the total squared curvature). In the most complicated cases the three parameters are given as solutions to a non-linear system of three equations. In the least complicated case everything is given explicitly in terms of elliptic functions. If the length is variable and there is no tension, at least one of the parameters is completely determined (the elliptic modulus m = 1/2). Using the same set of parameters explicit formulas are given for: the length when it is variable, the total squared curvature, and the tangent angle along the elastic curve. A number of examples are presented which illustrate the full range of constraints.     

Thermoelastoplastic deformation of complexly reinforced shells

The problem on the elastoplastic deformation of reinforced shells of variable thickness under thermal and force loadings is formulated. A qualitative analysis of the problem is carried out and its linearization is indicated. Calculations of isotropic and metal composite cylindrical shells have shown that the load-carrying capacity of shell structures under elastoplastic deformations is several times (sometimes by an order of magnitude) higher than under purely elastic ones; the heating of shells with certain patterns of reinforcement sharply reduces their resistance to elastic deformations, but only slightly affects their resistance to elastoplastic ones; not always does the reinforcement in the directions of principal stresses and strains provide the greatest load-carrying capacity of a shell; there are reinforcement schemes that ensure practically the same resistance of shells at different types of their fastening. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 707–728, November–December, 2006.     

Effectiveness of using hollow fibers to improve the rigidity of glass-reinforced plastics

Calculated and experimental relations between the modulus of elasticity and rigidity of unidirectional glass-reinforced plastics (GRP) and the capillarity coefficient of the hollow fiber reinforcement are presented. It is established that in calculating the flexural rigidity ratio of hollow- and solid-fiber GRP specimens of equal weight it is not permissible to neglect the mass and modulus of elasticity of the resin. The potentialities of hollow fibers as reinforcement for GRP shells subjected to external pressure are demonstrated.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fibers, Moscow Region. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 672–676, July–August, 1968.     

Bending of prestressed glass-reinforced plastic beams

Initial waviness of the fibers and prestressing are investigated in relation to their effect on flexural stiffness and strength for beams with low shear strength. It is shown that prestressing the reinforcement increases the flexural stiffness but at the same time adds to the shear correction as a result of an increase in the modulus of elasticity E_x in the direction of reinforcement and the insensitivity of the shear modulus G_xz to prestress. It is established that prestressing increases the shear strength and the degree of anisotropy . Materials of two types are investigated: unidirectional (AG-4S) and cloth-reinforced (SKT-11).Mekhanika Polimerov, Vol. 3, No. 5, pp. 888–893, 1967     

Elastic constants for a material reinforced in two directions in the planar case

A simplified model is proposed for an elastic material (glass laminate) reinforced in two perpendicular directions. On the basis of an analysis of the cooperation of the reinforcement and the binder in the assumed model, approximate formulas are obtained for the reduced elastic constants of the reinforced material treated as an anisotropic and macroscopically homogeneous body. A slightly different approach to the solution of a similar problem is described in [2, 4]. The formulas obtained are in agreement with the experimental data and the recommendations of other authors.Mekhanika Polimerov, Vol. 3, No. 2, pp. 266–272, 1967     

3-D time-dependent analysis of multilayered cross-anisotropic saturated soils based on the fractional viscoelastic model

The fractional Merchant viscoelastic model is introduced to simulate the viscoelasticity of soil skeleton in this study. According to the elastic-viscoelastic correspondence principle, elastic parameters including shear modulus G_v, horizontal elastic modulus E_h and vertical elastic modulus E_v are replaced by the reciprocal of the flexibility coefficient of viscoelastic media in the Laplace transformed domain. Then, based on the precise integration solutions of multilayered cross-anisotropic elastic saturated soils, 3-D solutions of viscoelastic saturated soils are derived. The final solutions in the physical domain are obtained by the Laplace numerical inversion. The correctness of theories and programs is verified by comparing the numerical results with existing references. Sensitivity analyses are conducted to investigate the effects of viscoelastic parameters, cross-anisotropic parameters and stratification of soils on time-dependent displacement and excess pore water pressure.     

Effect of water sorption on some mechanical parameters of composite systems based on low-density polyethylene and microcrystalline cellulose

Strength-deformation characteristics of low-density polyethylene filled with microcrystalline cellulose Thermocell as a function of the TC content (up to 0.7 parts by weight) are studied. Characteristics such as elastic modulus, relative elongation at break, ultimate strength, and work of failure are determined. Water sorption and change in the size and strength-deformation characteristics of composite specimens during exposure to boiling water (560 min) are also studied. It is shown that with greater filler content it is possible to increase the strength-deformation characteristics of LDPE, such as elastic modulus and tensile strength. The growth of the ultimate strength is associated with the formation of a specific filler framework with increasing filler content. It is found that the main factors which cause a decrease in the elastic modulus and softening of the composite are failure of the filler framework as well as formation of stresses and voids during water sorption by the composite. It is demonstrated that the steady reproducibility of the composition, attainable high filling degrees, and ecological safety make Thermocell a promising filler for polyethylene.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 79–90, January–February, 1999.     

Propagation of elastic waves in certain composites

Conclusions 1. Relationships have been obtained for determining nine elastic characteristics of orthotropic composite materials from the properties of the starting components and the assigned reinforcement scheme.2. Formulas are given for calculating the propagation velocity of three types of elastic flat waves for an arbitrary direction in one of the planes of elastic symmetry of a uniform orthotropic material.3. It has been shown that the velocity of the first arrival of a packet of ultrasonic vibrations which is recorded in an experiment is equal to the velocity of motion of the wave front in a limitless medium even for rather thin (5–10 mm) fiberglass-plastic specimens with unidirectional or cross-reinforced schemes.4. The dependences of elastic properties and rates of propagation of elastic vibrations on direction which are calculated theoretically from the properties of the starting components and the reinforcement scheme agree satisfactorily with experimental results.Translated from Mekhanika Polimerov, No. 3, pp. 531–536, May–June, 1978.     

Elastic characteristics of ferrocement reinforced with woven meshes

Applying structural mechanics methods for composite materials, we have worked out a procedure for predicting the elasticity modulus, the shear modulus, and Poisson's ratio for ferrocement taking into account the elastic properties of the components, the wire diameter, the mesh size, and the distance between the meshes. The results make it possible to exploit the potential of such reinforcement to the fullest.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 526–530, July–August, 1994.     

Stability analysis of CFRP-wrapped concrete columns strengthened with external longitudinal CFRP sheets

The external confinement by CFRP wrappings is a very efficient method to increase the load-carrying capacity of round concrete columns. Nevertheless, the serviceability of such columns under loads exceeding the strength of unconfined concrete is limited by different factors. One of them is the reduced stability of the columns due to the significantly reduced tangent elastic modulus inactive loading. To increase the critical load of buckling instability of concrete columns, an additional longitudinal composite reinforcement can be used. In this paper, the stability and strength of concrete columns confined by circumferential wrappings and strengthened with a longitudinal external CFRP reinforcement are studied. Plain and confined columns of length 300 and 1500 mm were tested. Theoretical predictions show that the additional longitudinal reinforcement is efficient in improving the stability of confined columns in the region of moderate slenderness. The prediction for the ultimate strength and stability of the columns coincides rather well with experimental results. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 295–308, May–June, 2005.     

Exact relations for effective tensors of composites: Necessary conditions and sufficient conditions

Typically the elastic and electrical properties of composite materials are strongly microstructure dependent. So it comes as a nice surprise to come across exact formulae for effective moduli that are universally valid no matter what the microstructure. Such exact formulae provide useful benchmarks for testing numerical and actual experimental data and for evaluating the merit of various approximation schemes. They can also be regarded as fundamental invariances existing in a given physical context. Classic examples include Hill's formulae for the effective bulk modulus of a two‐phase mixture when the phases have equal shear moduli, Levin's formulae linking the effective thermal expansion coefficient and effective bulk modulus of two‐phase mixtures, and Dykhne's result for the effective conductivity of an isotropic two‐dimensional polycrystalline material. Here we present a systematic theory of exact relations embracing the known exact relations and establishing new ones. The search for exact relations is reduced to a search for matrix subspaces having a structure of special Jordan algebras. One of many new exact relations is for the effective shear modulus of a class of three‐dimensional polycrystalline materials. We present complete lists of exact relations for three‐dimensional thermoelectricity and for three‐dimensional thermopiezoelectric composites that include all exact relations for elasticity, thermoelasticity, and piezoelectricity as particular cases. © 2000 John Wiley & Sons, Inc.     

Some laws of the elastic properties of oriented fibrous polymers and fibers

The author considers the results of calculations of the limiting values of the elastic properties (modulus of elasticity and load-extension diagram) of the main types of chemical fibers, using a model with "ideal orientation" of the molecules and the derived laws of deformation of polymer chains. A method is proposed for calculating the elastic properties of "ideally oriented" polymers from the velocity of propagation of an elastic deformation pulse and the effective density of the "skeletons" of the polymer chains. Values of the moduli of elasticity of the amorphous regions of the structure of oriented polymers are calculated. The calculated results are compared with experimental data on the elastic properties of fibers.Mekhanika Polimerov, Vol. 2, No. 1, pp. 34–42, 1966Paper read at the XIV All-Union Conference on High-Molecular Compounds, Oriented State.     

Antiplane shear of a strip containing a staggered array of rigid line inclusions

Motivated by the increased use of fibre-reinforced materials, we illustrate how the effective elastic modulus of an Isotropic and homogeneous material can be increased by the insertion of rigid inclusions. Specifically, we consider the two-dimensional antiplane shear problem for a strip of material. The strip is reinforced by introducing two sets of ribbon-like, rigid inclusions perpendicular to the faces of the strip. The strip is then subjected to a prescribed uniform displacement difference between its faces, see Figure 1. It should be noted that the problem posed is equivalent to that of the uniform antiplane shear problem for an infinite two-dimensional material containing a staggered array of rigid inclusions (see [1] for a review of antiplane problems in the literature). The problem is reduced in standard fashion [2–6] to a mixed boundary value problem in a rectangular domain, whose closed form solution given in terms of integrals of Weierstrassian Elliptic functions, is obtained via triple sine series techniques. The effective shear modulus of the reinforced strip can now be calculated and compared with the shear modulus of a strip without inclusions. Also obtained are the stress singularity factors at the end tips of the inclusions. Numerical results are presented for several different reinforcement geometries.     

Influence of edge effects on the state of stress and strength of carbon composites in tension

Conclusions A difference has been found between the theoretical and experimental strength values. The theoretical strength of flat strips with straight edges, obtained on the basis of the two-dimensional solution within the elastic range for a composite with fiber angle < 30°, is higher than the actual strength. The difference is due to the failure to take account of interlaminar shear. The strength tensor is applied to a monolayer with respect to which the internal state of stress and the nature of the interrelationship between the layers are not taken into account. In this connection, it is desirable to supplement the given criterion with a condition which would take account of the difference between the stresses _xy in adjacent layers. If the directions of reinforcement > 30°, then the agreement between the theoretical strength of flat strips of variable width, obtained on the basis of the two-dimensional solution within the elastic range using the tensor strength criterion, is in good agreement with the actual strength obtained experimentally. The big differences between the actual and theoretical strengths for the three-dimensional solution are attributable to the physical and geometric nonlinearity in the boundary zone between the elementary layers of the composite.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 263–270, March–April, 1985.     

Effect of the Rounding Radius of Supports on the Accuracy of Determining the Interlayer Shear Modulus of Reinforced Plastics from Short-Beam Bending Tests

The accuracy of determining the elastic constants of reinforced plastics is estimated based on bending tests of short beams using the results of a numerical experiment with known elastic constants of the specimen material. Several combination variants for the initial values of the shear modulus and support radius are considered. It is shown that the calculation error of the shear modulus is considerably higher than that of the elastic modulus A decrease in the shear modulus increases the accuracy of its determination. The radius of supports affects this accuracy insignificantly.     

水合物沉积物的力学本构模型及参数离散元计算

为有效描述水合物沉积物在不同水合物饱和度与围压情况下的力学行为,该文基于广义Hooke(胡克)定律建立了水合物沉积物的应力 应变关系方程和弹性模量弱化方程;基于三轴压缩试验确定了水合物沉积物的软化系数和软化指数,基于颗粒流程序（PFC3D）开发了水合物沉积物初始弹性模量的离散元算法（DEM）.利用建立的应力 应变关系方程、弹性模量弱化方程和初始弹性模量DEM,数值模拟了水合物沉积物在6种不同水合物饱和度与围压情况下的力学行为.数值模拟结果与三轴压缩试验结果的对比表明,建立的应力 应变关系方程、弹性模量弱化方程和初始弹性模量DEM,能有效预测水合物沉积物的力学行为,可为水合物井筒设计与安全开采提供理论基础和计算方法.