Compressive Properties of Pultruded Composites

The compressive properties of E-glass fiber/polyester resin matrix pultruded composites were measured using a short-block compression test fixture. Twenty specimens were tested in the pultrusion (longitudinal) direction and twenty more specimens in the transverse direction. Six specimens were tested at 30, 45, and 60° orientations to the pultrusion direction. Compressive properties such as the compressive modulus, compressive strength, Poisson ratio, and compressive failure strain were measured for both 6.3 and 12.7 mm thick pultruded sheet materials. The test specimens were rectangular with a length of 44.4 mm, width of 25.4 mm, and gage length of 25.4 mm. The test fixture was initially validated by measuring the axial strain distribution across the width of the specimen; from the beginning of loading up to the final failure, the distribution of strains across the specimen width was found to be very uniform. Back-to-back strain gages were also mounted on representative specimens. The end shortening was also measured on all specimens. The compressive strength data were analyzed both for the longitudinal and transverse directions using a two-parameter Weibull, lognormal, and normal distributions. The compressive properties are presented as functions of the specimen orientation angle for both thicknesses.     

Determination of in-plane shear characteristics of composite materials with [±45°] layup

The shear characteristics of a composite with a [±45°] layer layup are measured experimentally by different methods. Investigations were conducted on flat and tubular specimens. The strength and shear modulus were determined by the rail method, the losipescu method, and by applying torsion to thin-wall tubes; only the shear modulus was determined by applying torsion to square plates. Determination of the shear modulus yields quantitatively comparable results, and, at the same time, the scatter of the shear-strength values of the specimens is significant. Maximum strength is achieved on the tubular specimens. The cause of the lower strength values of the flat specimens can be explained by secondary stresses and strains in their effective sections. The influence exerted by the geometry of the specimens on their strength is investigated for specimens tested by the rail and losipescu methods. It is shown that it is possible to increase the strength appreciably by varying the specimen's geometry.Institute of Polymer Mechanics. Latvian Academy of Sciences, Riga, Latvia. AERPAC Company. Netherlands. Translated from Mekhanika Kompozitmykh Materialov, Vol. 32, No. 2, pp. 256–264, March–April, 1996.     

Strength properties of the human aorta and their variation with age

Conclusions 1. The strength of the aorta wall in a direction transverse to the vessel axis exceeds the strength in the longitudinal direction by on average a factor of 1.9 in the thoracic and 1.8 in the abdominal sections.2. The strength of the wall of the thoracic aorta is greater than that of the abdominal aorta. The differences between the strength characteristics of the aortal wall in the transverse direction are statistically reliable (up to 8th decade of life).3. As the organism ages, the strength of the walls of the thoracic and abdominal aortas decreases in the longitudinal and transverse directions. This is indicated by the close inverse correlation between ₁, ₂ and age.4. The strength of the aorta wall changes according to the period or stage of life. In each stage it is approximated by an exponential function.5. The rate of decrease of the strength of the wall is less in the transverse than in the longitudinal direction during the initial or evolutive stage of life.6. The decrease in strength (according to the criteria , , ) indicates more rapid aging of the tissues of the abdominal (relative to the thoracic) aorta. This difference appears after the age of 40 in the transverse and 50 in the longitudinal direction of the aorta wall.Chita State Medical Institute. Translated from Mekhanika Polimerov, No. 1, pp. 104–108, January–February, 1977.     

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.     

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     

Ultrasonic velocity in epoxy resin at temperatures down to 4.2 K

Results are presented from measurements of the velocity of longitudinal and shear elastic waves (f=5 MHz) in ÉD-20 epoxy resin, at temperatures from 4.2 to 293 K. These data were used to calculate the moduli of elasticity E and G. Also, the moduli E (f=250 Hz) and G (f=2 Hz) of the ÉD-20 resin were measured directly. The calculated velocities of the low-frequency elastic waves c_t=(E/p)^1/2 and c_t=(G/p)^1/2 (where p is the density) were compared with the results from the ultrasonic measurements. The frequency dependence of elastic-wave velocity in the epoxy resin was evaluated. It was found that when the frequency was varied by four orders of magnitude, the dispersion of longitudinal-wave velocity was 18% at 4.2 K and 39% at 293 K. A quantitative criterion is proposed for estimation of the dispersion of sonic velocity from the results of measurements at any two frequencies. It was established that the sonic velocity at low temperatures varies linearly with the temperature, and in the case of longitudinal waves changes from c_l-3360 m/sec at 4.2 K to 2820 m/sec at 293 K. The shear-wave velocity changes from c_t=1630 m/sec at 5 K to 1340 m/sec at 293 K. The values of the dynamic Young's modulus E and shear modulus G at 4.2 K are 8.6 and 3.2 GPa, respectively. On a plot of c=f(T) for ED-20, a transition is observed at 180 K, due to reorientational rotation of methyl groups. The activation energy of the relaxation process is 3.6 kcal/mole. Large values are obtained for the dispersion of the dynamic modulus E:37.8% at 4.2 K and 93% at 293 K.Paper presented at 9th International Conference on the Mechanics of Composite Materials Riga, October, 1995.Moscow State Academy of Automotive Vehicle and Tractor Machinery Construction, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 460–466, July–August, 1996.     

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     

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.     

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.     

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.     

Elastic behavior and onset of cracking in cement composite plates reinforced by perforated thin steel sheets

Thin cement mortar plates reinforced by perforated thin steel sheets have been tested in four-point flexure loading. Six kinds of sheet reinforcement and to additional ones (for control) were used. Perforated sheets of the Daugavpils Factory of Machinery Chains differed by their thickness (0.6–1.8 mm), shape (round, rectangular, oval, dumbbell), and mark of steel (St. 08, 50, 70). Dimensions of plantes were 100×20×2 cm. Cements-sand mortar with a 12 ratio of cement PZ35 and river sand of 3 mm grains was used as a matrix. Control specimens of similar dimensions and matrix were reinforced by wire cages and meshes (ferrocement). The testing was performed using an UMM-5 testing machine. Maximum deflection (at the midspan), tension, and shear strains were recorded. The expeimental data are presented in tables and graphs. The testing results showed that the elasticity modulus of material was in good agreement with the admixture rule; an onset of cracking for all types (excluding one) practically did not differ from reference samples; the mode of fracture in typical cases included an adhesion failure and significant shear strains. In one case the limit of the tension strength of the reinforcement was achieved.Presented at the Ninth International Conference on the Mechanics of Composite Materials. Riga. October, 1995.Latvian Building Research Institute. Riga, LV-1012 Latvia. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 195–201, March–April. 1995.     

Two interfacial shear strength calculations based on the single fiber composite test

The fragmentation of a single fiber embedded in a polymer matrix upon stretching (SFC test) provides valuable information on the fiber-matrix bond strength (), which determines stress transfer through the interface and, thus, significantly affects the mechanical properties of the composite material. However, the calculated bond strength appears to depend on data interpretation, i.e., on the applied theoretical model, since the direct result of the SFC test is the fiber fragment length distribution rather than the value. Two approaches are used in SFC testing for calculation of the bond strength: 1) the Kelly-Tyson model, in which the matrix is assumed to be totally elastic and 2) the Cox model using the elastic constants of the fiber and the matrix. In this paper, an attempt has been made to compare these two approaches employing theory as well as the experimental data of several authors. The dependence of the tensile stress in the fiber and the interfacial shear stress on various factors has been analyzed. For both models, the mean interfacial shear stress in the fragment of critical length (l_c) was shown to satisfy the same formula () = (_cD)/2l_c, where D is the fiber diameter and _c is the tensile strength of a fiber at gauge length equal to l_c. However, the critical lengths from the Kelly-Tyson approach and Cox model are differently related to the fragment length distribution parameters such as the mean fragment length. This discrepancy results in different () values for the same experimental data set. While the main parameter in the Kelly-Tyson model assumed constant for a given fiber-matrix pair is the interfacial shear strength, the ultimate (local) bond strength _ult may be seen as the corresponding parameter in the Cox model. Various _ult values were obtained for carbon fiber-epoxy matrix systems by analyzing the data of continuously monitored single fiber composite tests. Whereas the mean value of the interfacial shear stress calculated in the Cox approach was comparable to the interfacial shear strength from the Kelly-Tyson model, its ultimate value characterizing the true adhesional bond strength appeared to be three or four times greater.To be presented at the Ninth International Conference on the Mechanics of Composite Materials in Riga, Latvia, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 446–461, July–August, 1995.     

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.     

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.     

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.     

Composite materials reinforced with a system of three straight,mutually orthogonal fibers

An extension of existing methods of calculating fibrous composites to the case of reinforcement in three mutually perpendicular directions is presented. The basic approach involves the introduction of a "modified" matrix, the properties of which are determined in terms of the elastic moduli of the binder and the reinforcement coefficient in one of the three directions. Approximate expressions are obtained for the elastic characteristics of materials with a high-modulus reinforcing phase. There is a considerable increase in the transverse modulus by comparison with the shear modulus, even for a low reinforcement coefficient in the third direction.     

Relation between the vectors Э and S for a plastic material with a sequence of ray-like loading paths

Two different complex loading paths are investigated in stress space — longitudinal tension with subsequent total unloading and reloading in transverse tension or compression. For these loading paths the local strains theory [4] is used to determine the values of the components of the strain vector {₁, ₂} in five-dimensional space for nonlinearities n=3 and n=5 together with the components of the stress vector S{S₁, S₂}. A relation between the vectors and S is established in terms of the given loading parameter k.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 241–245, March–April, 1970.     

Non-uniformly scaled buckling modes of reinforcing elements in fiber reinforced plastic

We consider a problem about non-uniformly scaled buckling modes of isolated fiber (without accounting of interaction with the surrounding epoxy) or bundle of fibers, which are structural elements of fiber reinforced plastics under the transverse tension (compression) and shear stresses in prebuckling state. Such initial state is formed in fibers and bundles of fibers at tension-compression tests of flat specimens from cross ply composites with unidirectional fibers. For problem statement we use equations recently constructed by reduction of consistent version of geometrically nonlinear equations of theory of elasticity to one dimensional equations of rectilinear beams. Equations are based on refined shear S. P. Timoshenko model with accounting of tension-compression stresses in transverse directions. We give theoretical explanation of developed phenomenon as reducing shear modulus of elasticity of fiber reinforced plastic during the increasing of shear strains. We show that under the loading process of specimens under review uninterruptedly structure reconstruction of composite trough implementation and uninterruptedly changing of internal buckling modes at changing wave parameter is feasible.     

Effect of gamma radiation on the mechanical properties of polyvinylidene fluoride

The variation of the strength and relative elongation at break with radiation dose has been investigated for unoriented block specimens of PVF₂ and for oriented specimens with different crystalline structure ( and ). A certain difference is observed in the behavior of the irradiated oriented specimens and an important difference in the behavior of oriented and unoriented specimens of PVF₂ with the same crystalline structure (). On the basis of the data obtained and the results of a study of the crystalline and supermolecular structure of the irradiated PVF₂ specimens it is concluded that there is a difference in the state of the amorphous regions in the oriented and unoriented PVF₂.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 146–149, January–February, 1973.