Ultrasonic determination of the modulus of elasticity of heat-treated thermosets

The results of an ultrasonic investigation of the modulus of elasticity of K-18-2-TsS and K-18-22 phenolics, before and after heat treatment, are examined.     

Investigation of the modulus of elasticity of carbon fibers

A simplified analysis of the dependence of the elastic properties and electrical conductivity of a carbon fiber on its orientation index is presented. The experimentally confirmed inverse correlation between the electrical resistivity and the speed of sound makes it possible to calculate the modulus of elasticity of carbon fibers from data on the bulk resistivity.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 5, pp. 846–850, September–October, 1971.     

Optimization of a member with variable modulus of elasticity

The problem of the optimal (from the weight standpoint) law of longitudinal variation of the modulus of elasticity is considered with reference to a member in axial compression when the limit state is reached as a result of loss of stability. Constraints are imposed on the modulus of elasticity. The problem is solved with the aid of the apparatus of the generalized maximum principle.     

Determination of the complex modulus of elasticity of soft viscoelastic materials

A method of determining the complex modulus of elasticity of soft viscoelastic materials is proposed. This method is based on the measurement of the dynamic characteristics of a three-layer symmetrical bar, in which the investigated material forms the middle layer, and on the subsequent calculation of the characteristics of the soft material from the experimental data obtained.N. E. Zhukovskii Central Aerohydrodynamics Institute, Moscow Branch. Translated from Mekhanika Polimerov, No. 1, pp. 178–181, January–February, 1976.     

Relation between the temperature and deformation dependences of the modulus of elasticity

An analysis of the temperature and deformation dependences of the modulus of elasticity and the rate of stress relaxation has revealed the existence of a strain-temperature analogy. It is suggested that the physical significance of this analogy is associated with the change of volume. The experimental expression of the temperature and deformation dependences of the modulus in terms of change of volume leads to coincidence of the curves in the region above T_g, which confirms the correctness of the conclusion that the temperature-strain equivalence may be associated with the volume changes in that region.     

Effect of fiber curvature on the modulus of elasticity for unidirectional glass-reinforced plastics in tension

The effect of curvature of the fibers on the modulus of elasticity of unidirectional glass-reinforced plastics (GRP) in tension has been investigated on the basis of the theory of layered reinforced media with random initial irregularities [1,2]. It is shown experimentally that relatively minor distortion of the fibers during manufacture may result in important changes in the modulus of elasticity. A model is proposed for determining the effect of fiber curvature on Young's modulus; experiments on specimens with a given regular fiber curvature indicate good agreement with the theory. The effect of prestressing the fibers on the modulus of elasticity has been studied using commercial AG-4S material and the optimum prestress has been established.Mekhanika Polimerov, Vol. 3, No. 2, pp. 243–249, 1967     

Determination of the modulus of elasticity of the amorphous regions of chemical fibers

A method of calculating the orientation index and modulus of elasticity of the elements of a two-phase fiber model is presented. The effect of orientational drawing on the variation of these characteristics has been investigated for nylon [capron] fibers.Mekhanika Polimerov, Vol. 3, No. 3, pp. 409–412, 1967     

Generalized thermoelasticity with temperature dependent modulus of elasticity under three theories

A new model of generalized thermoelasticity equations for isotropic media with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. The present model is described both generalizations, Lord-Shulman (L-S) theory with one relaxation time and Green-Lindsay (G-L) with two relaxation times, as well as the coupled theory, instantaneously. The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, applied to two-dimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in case of temperature-independent modulus of elasticity in each theory.     

Effect of orientation and molecular weight on the modulus of elasticity of polymer materials

The modulus of elasticity of a perfectly crystalline polymer is calculated as a function of the orientation of the crystallites. The calculations are based on the mechanics of a micro-inhomogeneous continuum. The dependence of the modulus of elasticity on crystallite orientation and molecular weight is calculated with reference to the example of crystalline kapron.Moscow-Lenin Pedagogical Institute. Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1002–1007, November–December, 1968.     

Method of determining the modulus of elasticity of epoxies in the initial stages of cure

A method is proposed for determining the temperature-time dependence of the modulus of elasticity of epoxies in the early stages of cure. The kinetics of the time dependence of the modulus of elasticity during the cure are investigated for four epoxy compounds. It is shown that for the polymers investigated the modulus of elasticity characterizes the degree of cure.Technological Institute of the Refrigeration Industry, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 163–165, January–February, 1970.     

Correlation of the elastic characteristics of Arimid PM with the elasticity modulus of its crystal lattice

Studies were made of the elastic characteristics (longitudinal elasticity modulus, elastic recovery) of Arimid PM fibers and of the longitudinal elasticity modulus of the crystal lattice of these samples. The elasticity modulus of the crystallites was determined by x-ray diffraction studies of loaded fibers. It is shown that the studied samples practically instanteneously recover their starting length after removing the load; the sample and its crystal lattice have comparatively low elasticity moduli with nearly identical values. Based on this data, reasons are discussed for the high elastic recovery of Arimid fibers and for the low elasticity modulus of its crystal lattice.Leningrad Branch, All-Union Scientific-Research Institute of Synthetic Fibers. Translated from Mekhanika Polimerov, No. 5, pp. 771–773, September–October, 1972.     

Effect of a dispersed filler on the modulus of elasticity of composites in the glassy state

An expression is proposed for predicting the reinforcement of composites by a dispersed filler in both the rubbery and glassy states with allowance for the internal thermal stresses in the polymer matrix. It is shown that by varying the plasticizer concentration in composites based on polyvinyl chloride it is possible to regulate the thermal stresses in the polymer matrix. The time-stress and time-concentration superposition principles are shown to be applicable to the dependence of the relative modulus of elasticity on filler concentration for glassy composites.     

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.     

Variation of the instantaneous modulus of elasticity of certain types of plastics under long-time static loads

The variation of the elastic characteristics of polymeric materials tested to destruction under long-time static loads has been investigated. Experiments on polymethyl methacrylate, KAST-V glass laminate, and Soviet and Finnish polyester glass-reinforced plastics under constant and intermittent (with "recovery") static tensile loads have shown that their elastic characteristics vary with the loading regime, the type of material, and the stress level. In a number of cases the value of the modulus of elasticity falls by 25–35%. This is attributed to the reduction of the effective cross section of the specimen as a result of damage accumulation.All-Union Correspondence Structural Engineering Institute, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 430–435, May–June, 1971.