Combined bending and compression of circular cylindrically orthotropic plates with low shear strength

Equations are derived for the combined bending and compression of cylindrically orthotropic plates with allowance for shear and without postulating a shear distribution lawf/it(z). Solutions of the equations obtained are given for various boundary conditions. The error introduced by postulating the distribution lawf/it(z) is estimated. The effect of the ratio of the Young's moduli in the circumferential and radial directions E/E_r and the ratio of the Young's modulus E_r and the shear modulus G on the deflection w and the critical load T_cr is investigated. It is shown that for plates made of materials such as oriented glass-reinforced plastics the shear correction is very important. It is noted that buckling (due to shear) can occur even when the Young's moduli of the material are infinite.Mekhanika Polimerov, Vol. 4, No. 1, pp. 116–123, 1968     

Linear Viscoelasticity of Liquid-Crystalline Polymers

A linear (small-amplitude) periodic shear deformation of anisotropic viscoelastic liquids obeying the Akay–Leslie rheological model is considered. The frequency dependences of the real and imaginary components of the complex shear modulus and complex normal-stress coefficient are determined. A comparison between calculation results and test data on the shear flow of poly(-benzylglutamate) in m-cresol is carried out. It is stated that, if the material is characterized by some initial orientation, both components of the complex shear modulus contain a multiplier which depends on the degree of the initial orientation and increases the values of the components compared with those for an initially isotropic material. The model predicts that, in a periodic shear flow, the components of shear and normal stresses are constant and, like the components of shear modulus, are independent of deformation frequency. If the parameter d ₀ of the Akay–Leslie model is equal to zero, the values of its other parameters can be determined from experimental results on periodic shear flow.     

Contact problem for beams made of composite materials

Conclusions 1. In beam sections close to the line of action of a concentrated force the profile of shearing stresses departs appreciably from a quadratic parabola. The magnitude of maximum _xy increases with a lower modulus of elasticity E_y and with a higher shear modulus G_xy.2. With the given values of the anisotropy parameters, typical for glass-plastic and carbon-plastic materials, positive transverse stresses _y become negligible. The zone of local transverse compression extends (accurately within 10% of P/2bh) over the height of the beam section.3. Lowering the transverse stiffness of a material lowers the maximum tensile stresses _x.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 56–62, January–February, 1977.     

Torsion testing of polyvinyl chloride sheet

The behavior of polyvinyl chloride sheet in torsion has been studied. Normal round test pieces were tested at strain rates of 0.3 and 1 rpm. The specimens were cut in the longitudinal and transverse directions of the sheet. The principal strength and plasticity characteristics of the material in torsion were obtained. During the tests torsion diagrams (M_t vs. ) were recorded. The specimens failed in shear. The shear modulus was determined on a special table device. The experiments showed that the shear modulus, limit of proportionality, and tensile strength have the same values in both longitudinal and transverse directions. The values of the angle of twist at failure are large and vary over a wide range.Mekhanika Polimerov, Vol. 1, No. 5, pp. 19–24, 1965     

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.     

Effect of crystallization on the mechanical properties of cellulose triacetate and acetosorbates

The results of an x-ray investigation of the crystallization of cellulose triacetate and acetosorbates with different degrees of esterification (from _c=3 to _c=12) are described. It is shown that the triacetate and the acetosorbates crystallize in the same way. In the amorphous state the strength of the acetosorbates is lower than that of the triacetate, but the former will withstand a greater number of double flexes. The modulus of elasticity decreases as _c increases. Crystallization has almost no effect on the strength of the cellulose triacetate and acetosorbates, but the elongation falls with increase in _c. The number of double flexes and the high-temperature modulus of elasticity sharply increase.Scientific-Research Institute of the Chemistry and Technology of Cotton Cellulose. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 783–786, September–October, 1968.     

Evaluation of Deformation and Strength Characteristics of Composites Based on Low-Density Polyethylene and Linen Yarn Production Waste by the Methods of Mathematical Statistics

The possibilities of using various methods of mathematical statistics for processing and analyzing the results of deformation and strength tests on composites made from a low-density polyethylene and linen yarn production waste are evaluated. The hypothesis that the experimental strength data agree with the Gaussian distribution is examined by the Shapiro–Wilk test (W-test.) It is shown that the Gaussian distribution, both for systems unmodified and modified with diphenylmethane diisocyanate (DIC), is valid only for two parameters: the maximum tensile strength _max and the elastic modulus E _t. For the other parameters (the relative elongation _max corresponding to _max, the specific total work of failure A _b), and the specific work of failure to the tensile strength A _max), a non-Gaussian distribution is observed. An analysis of measurements for different specimens by the Bartlett test shows that the E _t data have equal variances for both systems (with and without DIC), but for the system containing DIC, the _max data have different variances. A two-factor ANOVA analysis reveals that DIC considerably affects the tensile strength and modulus of composites, but the influence of test conditions is a statistically significant factor only for the modulus. The coefficient of variation is considerably lower for _max than for E _t and can be used as a quantitative measure for the degree of heterogeneity of the composites investigated.     

Adhesion of Thermoplastic Matrices with Different Molecular Weights to Fibers

The dependence of the interfacial strength in polymer-fiber systems on the molecular weight (MW) of the matrix is investigated. Adhesive joints of poly(phenylene-sulfide sulfones) and polysulfones with a steel wire 150 m in diameter and glass fibers 200-300 m in diameter are examined. The MW of both polymers was controlled during the synthesis process. The shear adhesive strength was determined by the pull-out technique. For all the systems investigated, it is shown that the adhesive strength in relation to the duration t _f of their isothermal formation is described by curves with a maximum, whose values depend on the formation temperature T _f. For each polymer with a given MW, the greatest possible of these values, called optimum and denoted by _opt, are determined. It is found that _opt increases with molecular weight. It is speculated that the effect observed stems from the different packing of polymer chains with distinct lengths in the near-surface layers.     

Experimental determination of the shear modulus of compact bone tissue

Various methods of experimentally determining the shear moduli G₁₂, G₁₃, and G₂₃ of compact human bone tissue have been examined. The results of the study confirm the previous view that compact tissue has properties similar to those of a transversally isotropic material. It has been established that the shear modulus along the diaphysis of the tibia at the level of girdles 9–24 does not change significantly. There is a definite difference in the rigidity characteristics with respect to the regions of the cross section. The highest values for the shear modulus were established in the angle regions of the cross section. There is a linear dependence of the shear stress ₁₂ on the torsional angle ₁ within the experimental range of stresses (₁₂90 kg/cm²).Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 697–705, July–August, 1972.     

Macromechanical Characteristics Deduced from Three-Point Flexure Tests on Unidirectional Carbon/Epoxy Composites

Effects of different factors on the measured values of flexural modulus and flexural strength of unidirectional carbon/epoxy composites are investigated. This allows a correct interpretation of the results of flexural macromechanical properties obtained in three-point flexure tests. The shear deformation, the displacement of neutral axis from the mid-depth of the beam, and the nonuniform distribution of stresses in bent coupons are discussed.     

Calculation of elastic characteristics and creep functions of hollow-sphere plastics by the effective medium method

Conclusion Solutions for the elastic characteristics and the creep functions of a composite containing hollow spherical fillers as applies to the four-phase nucleus/jacket/binder/equivalent-homogeneous-material model are obtained in the study when the method of self-correspondence is used. It is demonstrated that if the two-stage approach (when the elastic characteristics of the nucleus + jacket system, and the composite are calculated in the first and second stages, respectively) yields an exact solution for the bulk modulus K_* of the composite, it is highly approximate when the shear modulus G_* of the composite is determined. The error of determination of G_* increases considerably (by a factor of 2–2.5 when = 0.4) when Kerner's approximate solution (2) is used in lieu of solution (8) for the three-phase model within the framework of the two stage approach. Dzenis and Maksimov [5] establish by comparison with experimental data that the four-phase model provides a rather exact solution for the elastic modulus of a composite when the bulk content of hollow spheres 0.4. It is also demonstrated that use of Kerner's approximate solution (2) within the framework of the two-stage approach in predicting the creep of a composite yields an inadmissibly high error in the region of the principal relaxation transition of the binder from the glassy to the highly elastic state.This work was sponsored at the Iberoamericana University in 1993 by the Mexican National Council of Science and Technology (CONACYT).Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 2, pp. 177–188, March–April, 1994.     

Effect of chemical nature of matrix on the strength of bonds with Armos aramide fibers

This investigation deals with adhesion between high-strength and high-modulus Armos aramide fibers (polyheteroarylene-co-p-phenyleneterephthalamide) and a series of different thermosetting matrices. The effect of the chemical nature of the matrix, time-temperature conditions of bond formation, and test temperature on the strength of the fiber-matrix interface was studied. Modified epoxy and heat-resistant matrices were used as adhesives. As a measure of adhesion, the shear adhesive strength ₀ determined by the fiber pull-out technique was used. It was found that both the adhesive strength and the fracture location in adhesive bonds depended on the nature of the matrix. At room temperature, chlorine-containing epoxy matrices provide the highest values of ₀, while the smallest strength of the interface is observed for bonds with heat-resistant (bismaleimide, oligomethacrylate) matrices. Fracture of adhesive bonds does not always occur at the fiber-matrix interface. A number of the specimens failed near the interface of the fiber. With temperature increase, the values of ₀ decrease. The adhesive strength falls especially drastically in the region of matrix softening. An advantage of heat-resistant matrices is that they retain 60–67% of ₀ value even at 250°C. The strength of unidirectional composites based on the investigated fibers and matrices was also estimated under different loading conditions such as tension, shear, compression, and bending. It was found that the strength in shear and compression did not correlate with the interface strength. The values of _c in bending and tension increased linearly with increase of ₀. The obtained dependences _c–₀ were compared with those of composites based on the SVM polyheteroarylene fibers determined by us earlier.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. 3, pp. 391–406, May–June, 1998.     

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.     

Modelo numérico del comportamiento histerético de uniones entre forjados reticulares y pilares de fachada

Waffle-flat-plate structures have been widely used for residential and office buildings in the South of Europe between the seventies and nineties of the last century. These buildings were designed with old seismic codes and its vulnerability needs to be evaluated to determine whether they need to be seismic retrofitted or not. This article proposes a simple model that represents the moment transfer between plate and column, for existing exterior connections loaded in the direction normal to the building façade. The model takes into account singularities of existing waffle-flat-plate structures such as the concentration of reinforcement in the direction of the joints, and the existence of punching shear reinforcement. The model consists of frame elements for the columns and shell elements for the slabs, both connected with flexural and torsion hinges. The strength of the flexural hinges is obtained by estimating the portion of longitudinal reinforcement of the plate that transfers directly the unbalanced moment to the column by flexure. The yielding deformations of the flexural and torsion hinges are estimated with simple expressions. The ductility of the flexural hinges is taken from FEMA 356, while infinite ductility is adopted for the torsional hinges in accordance with previous experimental studies. It is shown that the proposed model provides a good approximation of the experimental response of the connection under monotonically increasing lateral displacements, in terms of stiffness, strength and ductility.     

Relation between the interlaminar shear modulus and thermal conductivity of oriented glass-reinforced plastics

The relation between the interlaminar shear modulus G of oriented glass-reinforced plastics and their thermal conductivity in a direction orthogonal to the plane of reinforcement is investigated. It is shown that G can be predicted from the measured values of and the bending deformations from and the propagation velocity of ultrasound.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Makhanika Polimerov, No. 6, pp. 985–989, November–December, 1970.     

Effect of the arrangement of the reinforcement on the stability of circular,cylindrically orthotropic plates with low shear strength

The Bubnov-Galerkin method is used to find the critical loads for cylindrically orthotropic circular continuous and annular plates with different edge conditions in axisymmetric buckling. The effect of the ratio of the Young moduli in the circumferential (E) and radial (E_r) directions and the ratio of E to the interlaminar shear modulus G_rz is investigated. The results are in qualitative agreement with the experimental data of [13].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 275–283, March–April, 1971.     

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.     

Deformation and strength of laminated quasiisotropic carbon-reinforced plastics

Conclusions The stress-strain state and strength of the quasiisotropic carbon-reinforced plastics depend strongly on the lay-up system of the adjacent plies because the magnitude of the interply stresses and their distribution greatly change when the reinforcement system is changed. The highest stress intensity is recorded at the free edge of the specimen. The magnitude of the residual thermal stresses is comparable with that of the mechanical stresses at the instant of formation of cracks in the weak plies of the composite. The first microcracks form inside the plies with the orientation 90 and ±45° in the direction of reinforcement. The IACs start to form at the free edges of the specimen and propagate into the material at strains from 12 to 39% of limiting strain _x ^l . Delamination of the laminated composite starts later than the formation of IACs (40–88% of _x ^l ) because the normal stress _x is higher than _z. The optimum lay-up system of the composite is [0/45/90/-45]_s because this system ensures higher stiffness of the material. The ±45 and 90° plies are not suitable for external surfaces of the composite since they start to crack very early. The quasiisotropic composites are less sensitive to the value of G_{2 3} than the composites with the ply lay-up [±]_s.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 449–454, May–June, 1985.     

Effect of filler on the viscosity and viscoelasticity of melts of low-density polyethylene. Communication 2

Conclusions 1. A filler causes a change in the viscoelastic functions of melts, which in general cannot be described in linearly transformable coordinates.2. With rising filler concentration, the maximum of the frequency of the relaxation spectrum N(s) increases, but the frequency corresponding to the maximum decreases.3. The dynamic viscosity and rigidity of matrices and composites as functions of frequency are satisfactorily described by a three-parameter relationship. The relationship derived contains parameters of the degree of filling. Using the dimensionless viscosity '/_o and deformation frequency '₁ it was possible to obtain a relationship which is invariant with respect to the filler in a limited range of change in and which can be used for approximate calculations.4. The initial shear modulus of a composite with a filler concentration corresponding to formation of a secondary network can be lower than the shear modulus of the matrix.For communication 1 see [13].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 122–126, January–February, 1977.     

Investigation of the dynamic characteristics of composites

The dynamic characteristics E and G and the damping capacity δ* of polymeric resins and composites based on glass, carbon, and boron fibers have been investigated. It is shown that the mechanical losses are correlated with the modulus of elasticity and the shear modulus of the resin and composites with different types of reinforcement. The vibrational strength of various structural materials is estimated.