Investigation of loading surfaces in the local strains theory

Variants of the application of isotropic, kinematic, and combined strain hardening in the local strains theory are analyzed. The subsequent yield surfaces are determined for biaxial tension and combined torsion and tension and the results are compared with experiment. The theory predicts convex yield surfaces and the dependence of the angle (corner point) of the yield surface at the loading point on the loading path. The expediency of employing the concept of a plastic strain probability factor is demonstrated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 796–800, September–October, 1971.     

Calculation of the long-term strength of thin-walled polymeric tubes under biaxial loading

The problem on calculating the failure time of thin-walled polymer tubes in creep under internal pressure, internal pressure with tension, pure torsion, and torsion with tension is solved. The solution is constructed based on the concept of equivalent stresses. A mixed long-term failure criterion taking into account the sings of principal stresses is used as the equivalent stress. The calculation results are in a satisfactory agreement with experimental data.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 811–826, November–December, 2004.     

Stress relaxation in physically nonlinear polymer materials under simultaneous tension and torsion

Conclusions 1. Application of our method of determining the parameters of physically nonlinear polymer materials from tests in uniaxial tension or in torsion ensures a satisfactory agreement between theoretical and experimental stress-relaxation curves corresponding to other modes of loading.2. Theoretical stress-relaxation curves for shear (tension) calculated on the basis of parameters which have been determined from approximations of stress-relaxation curves for tension (torsion) fall closely within the confidence interval for an individual measurement (with =95%).3. The agreement between theoretical and experimental stress-relaxation curves for a plane state of stress is 2–3 times worse, in terms of the mean-square relative difference, than the agreement between the respective curves for uniaxial tension.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 797–803, September–October, 1977.     

Plane-stress creep of a glass-reinforced plastic

The creep behavior of an orthotropic glass-reinforced plastic based on Polimal'-109 resin and 19-S4 glass fabric is described. A special device for testing tubular specimens in plane-stress creep has been designed. The loading conditions include combined torsion and tension, internal pressure, and loading along the principal directions of anisotropy. Constitutive equations describing creep and recovery are proposed for the two-dimensional case.Warsaw. Translated from Mekhanika Polimerov, No. 3, pp. 398–410, May–June, 1971.     

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.     

Progressive increase in the displacements of a glass-reinforced plastic helicopter blade under the influence of its own weight

The question of the progressive increase in the displacements of a glass-reinforced plastic helicopter blade under its own weight is examined. Integral operators, expressed in terms of fractional-exponential functions, are used for solving the flexural creep problem. The creep curve parameters for simple deformation (tension and torsion) are found for ÉF-32-301 glass-reinforced textolite.K. É. Tsiolkovskii Moscow Aviation Engineering Institute. Translated from Mekhanika Polimerov, No. 5, pp. 943–946, September–October, 1975.     

Comparative analysis of two algorithms for numerical solution of nonlinear static problems for multilayer anisotropic shells of revolution. 1. Account of transverse shear

The discussion focuses on two numerical algorithms for solving the nonlinear static problems of multilayer composite shells of revolution, namely the algorithm based on the discrete orthogonalization method and the algorithm based on the finite element method with a local linear approximation in the meridian direction. The material of each layer of the shell is assumed to be linearly elastic and anisotropic (nonorthotropic). A feature of this approach is that the displacements of the face surfaces of the shell are chosen as unknown functions, i.e., the functions which allows us to formulate the kinematic boundary conditions on these surfaces. As an example, a cross-ply cylindrical shell subjected to uniform axisymmetric tension is considered. It is shown that the algorithms elaborated correctly describe the local distribution of the stress tensor over the shell thickness without an expensive software based on the 3D anisotropic theory of elasticity.Tambov State Technical University, Tambov, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 347–358, May–June, 1999.     

Thermal effects in a glass laminate in tension

The results of a calorimetric investigation of a glass-reinforced textolite in uniaxial tension are presented. The specimens were deformed on the interval of strain rates from 0.3 to 10.5 mm/min at test temperatures from –30 to 80°C. The thermal effects are shown to depend on strain rate and test temperature.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 599–604, July–August, 1971.     

Optimal rigidity of a thin-walled orthotropic cylinder in combined tension and torsion

The problem of optimizing the reinforcement of an orthotropic cylinder in combined torsion and tension is considered in relation to the condition of minimum displacement. A numerical example is given. It is shown that the stiffness depends on the ratio of the normal and shear stresses, the elastic moduli, and the parameters.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1121–1123, November–December, 1973.     

Influence of temperature and humidity on the creep of polymeric materials. 4. Prediction on the basis of field test results

Conclusions Comparison was made of the results of prolonged (from 2 to 6 years) control experiments of tubular specimens of PN-3 for creep during tension, torsion, and simultaneous tension and torsion under various temperature-humidity conditions with calculation based on data of short-term (up to 5 h) experiments, in which the creep process was accelerated by increase in temperature and humidity of the material. Calculation of the prolonged creep deformations expected was done from the relationships of viscoelastic properties of a linearly changing solid, generalized for the case of influence of temperature and humidity under the assumption that the volume changes only elastically. On the basis of this generalization, adherence to the temperature-humidity-time analogy is assumed to be experimentally confirmed. Satisfactory agreement of results of prediction and prolonged control experiments is established.For communication 3 see [3].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 982–987, November–December, 1976.     

Yield surfaces of composite media

Yield surfaces with different probabilities of the appearance of plastic strains are obtained for a composite material reinforced in one and two directions. These surfaces (local yield surface density) are obtained using the local strains theory and on the assumption of the inextensibility of the composition material in the directions of reinforcement. The theoretically obtained limit surfaces are shown to be in satisfactory agreement with the experimental data.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 35–40, January–February, 1976.     

Creep of linear unoriented polymers in tension,compression, and torsion

The creep of polymethyl methacrylate, polystyrene, and polyethylene in tension, compression, and torsion has been investigated over a broad interval of temperature below the glass transition point. It is shown that the creep criterion changes depending on the temperature. This is associated with changes in molecular mobility.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 24–28, January–February, 1970.     

Calculation of relaxation spectra from dynamic test data

A procedure is proposed for calculating relaxation spectra from experimental data on uniaxial tension over a broad range of strain rates. The relaxation spectra are calculated for low-density polyethylene and for a fabric-reinforced glass laminate in three directions relative to the reinforcement.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 349–353, March–April, 1971.     

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.     

Relation between the vectors E and S for a plastic material in succesive biaxial tension

The local strains theory is used to determine the values of the components of the vector E{E₁, E₂} in five-dimensional space for a material subjected to successive biaxial tension at degrees of nonlinearity n=3 and n=5. The relation between the vectors E and S and the tangents to the loading and strain trajectories is considered together with the relation between the moduli E of the strains for simple and complex loading.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 975–979, November–December, 1969.     

On the difference in the moduli of elasticity of polyamides subjected to different kinds of deformation

Experiments to determine the moduli of elasticity of polyamides (kapron) in tension and compression are described. A substantial difference in these characteristics was detected. The modulus of elasticity in tension is 0.75–0.80 of the value of the modulus in compresion. This difference is explained by the textural characteristics of the polyamides. The use of values of the modulus of elasticity obtained by testing specimens in tension to determine the stiffness of parts working in compression give overestimated strain values.Mekhanika Polimerov, Vol. 1, No. 4, pp. 47–51, 1965     

Forward and reverse creep of a physically nonlinear polymer material

From tension and torsion experiments under constant load, the authors determine the parameters of a material with physically nonlinear creep. They examine the applicability of these parameters to represent the deformation properties of materials under other loading systems. They give a method of drawing the reverse creep curve (in integral form) with parameters different from those of active creep.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 786–795, September–October, 1973.     

Calculation of thin-wall closed profiles of composite materials under a complex loading

Uniclosed caisson structures with deformable perimeters, which are asymmetric in terms of geometry and stiffness and which are subjected to a complex loading (bending in two planes and torsion with respect to the longitudinal axis) are examined in terms of a cylindrical coordinate system Z, S. The possibility of partitioning the general problem of the stress and strain state into elementary problems by fulfilling conditions of orthogonality is demonstrated. The coordinates of the center of rotation are determined. The need for consideration of the deformation of the cross-sectional perimeter, which defines the warping function and normal bitorque stresses under torsion is indicated. The law governing the distribution of tangential stresses, which contains both a constant component that corresponds to Bredt's theory, and also a part corresponding to Vlasov's theory, is derived.Moscow State Aviation Institute (Technical University), Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 349–359, May–June, 1997.     

Development of the local strain function and the slip function in statistical theories of plasticity

The development of the concept of a local strain function is examined. The principal forms and methods of approximation of the local strain function are described and compared. A generalization of the local strains theory in differential form is proposed. Yosimura's criticism of the slip theory is shown to be invalid. Certain aspects of the local strains and slip theories are compared.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 422–430, May–June, 1969.     

Thermoelasticity of Thin Shells under the Influence of a Moving Heat Source

The thermoelasticity problem for a thin, slightly curved shell under the influence of a point heat source over the surface of the shell is solved, along with the heat-conduction problem under the influence of a local heat source. The temperature is assumed to be distributed linearly along the thickness of the shell, and convective heat transfer obeying Newton's law is assumed to take place from the lateral surfaces of the shell. Fourier and Laplace integral transforms are used to obtain a solution in analytical form. The dependence of the distributions of the temperature field and the components of the stress–strain state of the shell on the time and on the velocity and shape of the heat source is investigated.