Problems of the anisotropy of strength

The concept of a strength tensor, analogous to the tensor of elastic constants, has been introduced with a view to using its components for approximate determination of laws governing the variation of strength of anisotropic materials in uniaxial tension or pure shear as a function of the orientation of the stress state. It has been shown that the plasticity condition postulated by Mises can be used as a criterion of strength of many "weakly" anisotropic materials, if one rejects the hypothesis according to which the condition is invariant in respect to hydrostatic pressure. In the case of "strongly" anisotropic materials, wood in particular, the Mises condition is at variance with the results obtained for variously oriented specimens tested in uniaxial tension. A strength condition in the form of a fourth-degree polynomial, based on the assumed existence of a strength tensor analogous to the tensor of elastic constants, has been postulated for these materials. The validity of this criterion has been demonstrated by constructing surfaces of equicritical plane stress states from experimental data obtained for pine wood, plywood, and glass-reinforced plastic laminates.Mekhanika Polimerov, Vol 1, No. 2, pp. 79–92, 1965     

Problems in the prediction of the long-term strength of polymer materials. A review

Conclusions As in the case of the selection of the simplified equations used in the theory of nonlinear viscoelasticity, variants of the equations of the temperature-time dependence of the strength of polymer materials are constructed on the basis of some similarity condition of the experimental lifetime curves. Principles according to which it would be possible to make a prior assignment of a material to some class on the basis of similarity criteria only using, for example, information on chemical composition and structure without testing for long-term strength are lacking. The equations presented in this review may be used for predicting the lifetime only when the nature of the resistance to long-term destruction over time in a given temperature range exactly corresponds to the assumptions inherent in some equation. Thus, the selection of the boundaries of the temperature ranges, in which we may assume uniformity for the deformation and destruction mechanisms leading in the final analysis to identical types of destruction, becomes most significant. Hence, the parametrical methods have a series of advantages since they do not place rigid limitations on the nature of the long-term strength curves at a given temperature.The temperature-time analogy method is the most favored method for predicting long-term strength since this method, without negating other approaches, is their generalization. The use of this method is most promising for cases of a complex stressed state and complex stress pathways. In this case, the temperature -time shift function is most conveniently introduced into the surface strength functionals.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 694–704, July–August, 1979.     

The stressed state in a plate caused by the distortion tensor

The improved plate theory, which makes it possible to determine all the components of the stress tensor, is generalized to the case when the stressed state of a plate is caused by the distortion tensor. The equations obtained can be useful in the study of residual stresses in thinwalled elements, in applications of the method of distortion in the mechanics of failure and elsewhere.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 53–57.     

Strength of an organic/glass fiber-reinforced textolite in plane stress

Conclusions An analysis of the results of testing hybrid glass organic textolites, containing layers of glass and organic fabric reinforcement in various proportions, along characteristic simple short-time quasi-static loading paths served as a basis for determining a family of strength surfaces for plane stress in the plane of reinforcement. The strength of the five materials investigated is described by a second-order surface equation with allowance for the difference in compressive and tensile strengths. The dependence of the strength surface tensor components entering into the strength equation on the structure parameter representing the relative content of organic and glass fabric in the hybrid textolite is investigated and described. The results obtained can be used in practical calculations for determining the optimum ratio of organic to glass fabric in hybrid material with allowance for the specific requirements to be met by the strength properties of the material when used for structural purposes.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1021–1026, November–December, 1979.     

Analysis of the strength of glass-fiber-reinforced shells upon loss of stability

An algorithm is developed for calculating and analyzing the components of the stress tensor on the basis of an experimental function of deflections in the case of buckling of glass-fiber-reinforced shells loaded by a hydrostatic load. Possible sites of fracture of a shell are established qualitatively with the use of Malmeister's strength theory.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 666–673, July–August, 1972.     

The stressed state of a thin coating on an elastic inclusion of optimal shape in an elastic medium

We examine the properties of the stressed state of the thin intermediate zone separating a nonhomogeneous inclusion from the matrix. Explicit expressions are given for the components of the stress tensor in the thin coating depending on the properties of the phases and the load parameters.Simferopol' University. Translated from Dinamicheskie Sistemy, No. 10, pp. 26–30, 1992.     

Structural theory of the strength of reinforced plastics

Conclusions In the present study, we developed structural criteria that make it possible to predict at the component level (polymer binder, fibers) and interface level the long-term strength of laminated reinforced plastics in a plane stress state. The proposed relations make it possible to evaluate the effect of the rheological properties of the components, their volume fractions, and the geometry of the structure of the laminated packet on the long-term strength of reinforced plastics. The relations also permit resolution of the inverse problem: efficiently design the structure of such materials for specific loading conditions.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 833–839, September–October, 1989.     

An analysis of the thermal stresses in glass elements of electrovacuum devices in the neighborhood of metallic inclusions

On the basis of the improved theory of plates, which makes it possible to determine all the components of the stress tensor, we study the thermally stressed state of a finite round plate with a concentric inclusion of a different material. We obtain the exact analytic solution of the corresponding boundary-value problem for the system of singularly perturbed equations, valid for any ratios between the diameters of the plate and the inclusion. In the contact zones the stresses differ significantly (both quantitatively and qualitatively) from those predicted by the classical plate theories. The results obtained make it possible to draw a number of conclusions that are useful for estimating the strength of electrovacuum devices.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 28, 1988, pp. 1–6.     

Boundary element methods in problems of thermoelasticity for piecewise-homogeneous bodies

Integral representations of the components of the displacement vector and the stress tensor and the corresponding system of boundary integral equations are derived for a piecewise-homogeneous body. A numerical scheme is developed that allows for the specific behavior of the stress fields in the neighborhood of the corner points of the inclusions. As an example, we consider the thermally stressed state of an elastic half-plane with inclusions of various shapes.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 87–98, 1991.     

Optimal reinforcement of a glass-reinforced plastic plate

Relations are derived for the optimal arrangement of the reinforcement in a rectangular glass-reinforced plastic plate supported at the edges and stressed in uniaxial compression by a short-term or long-term, uniformly distributed load. (The optimal arrangement is understood to be that which maximizes the critical load.)All-Union Scientific-Research Institute of Railroad Transport, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 741–744, July–August, 1969.     

Control of the elastic properties of a shell working at stability

This examines a shell with elastic properties varying across the coordinates, which are prescribed by means of scalar functions of the invariants of the elasticity tensor. The basis of the arrangement of the tensor for the elasticity consists of q linear-independent tensors of the fourth range (q is the number of linear-independent components of the elasticity tensor) which are obtained by multiplying and turning the first tensor of the surface and the tensor characterizing the class of symmetry of the medium. The invariants of the elasticity tensor present in the stability equation and their derivatives are taken to be the equations and parameters for the state of the system (shell), and the problem is thus reduced to a problem of optimum equations. As an example we shall examine an orthotropic cylindrical shell with a model varying over the length under the action of external pressure.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 93–100, January–February, 1974.     

Tensile strength of unidirectionally reinforced plates stretched at an angle to the direction of reinforcement

Conditions for the fracture of a unidirectionally reinforced plate under uniaxial tension at an arbitrary angle to the direction of reinforcement are proposed. The fracture conditions are applicable to the case where the adhesion strength between the bond and reinforcement is greater than the strength of the polymer bond. The strength of the polymer bond in the volume stressed state is determined by an energy criterion.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 482–486 May–June, 1973.     

The coupled thermoelasticity problem for thin plates

On the basis of the operator solution of the three-dimensional coupled thermoelasticity problem for a plate we state the main relations of a sharpened version of the theory of thermally stressed thin plates. These relations make it possible to determine all the components of the stress tensor and the corresponding temperature fields.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 1–6.     

Experimental evaluation of the strength anisotropy of a unidirectionally reinforced organic fiber-reinforced plastic

Conclusions The strength of a unidirectional organic fiber-reinforced plastic has been experimentally determined in various special cases of plane stress. An analysis of the data obtained shows that it is possible to describe the strength of the material in plane stress by means of a second-order surface equation containing linear and quadratic terms. The dependence of the strength in tension and compression on the angle between the directions of loading and reinforcement has been predicted and experimentally confirmed using the values found for the components of the strength surface tensors. The results of the study can be used to estimate the strength of multilayer organic fiber-reinforced plastics in cases where a unidirectionally reinforced layer can be taken as the basic structural element of the material.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 799–803, September–October, 1979.     

Strength of cylindrical shells of laminar composites under dynamic loading

Conclusion The methods described in the present review paper for the computation of cylindrical shells of laminar composites under various types of dynamic loads make it possible to calculate the stress-strain state at any point of the body of the shell at an arbitrary time and to determine the time of the first failure of a layer (including fatigue failure) using strength criterion of an anisotropic body for the case of a plane stressed state, and also the location of the first flaw in the shell. This makes it possible to determine the magnitude of the applied pulse (the amplitude of a pulsed loading), or the amplitude of a vibratory loading for which the first centers of failure appear in the design.Presented at the Second Soviet-American Symposium on the Problem Failure of Composite Materials (Bethlehem, Pa., USA, March, 1981).Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 460–467, May–June, 1982.     

Long-term strength of rigid polyvinyl chloride in the flat stressed state

On the basis of experimental studies it has been established that the time to failure of rigid polyvinyl chloride depends basically on the magnitude of the largest stretching stress and at a long duration of testing deviates considerably from the exponential dependence. A refined formula is suggested for calculating the time to failure, which takes into account some characteristics of the stressed state.A. A. Zhdanov Leningrad State University. Translated from Mekhanika Polimerov, No. 3, pp. 453–457, May–June, 1970.     

The stressed state of glass disks during strength testing

By applying the improved theory of plates, which makes it possible to determine all components of the stress tensor, we study the stressed state of glass disks under axisymmetric bending. We obtain a closed-form solution of the corresponding boundary-value problem for systems of singularly perturbed equations. It is shown that the size of the zone of pure bending-the domain with uniformly stretched surface-differs from those known in the literature. The results obtained make it possible to determine the optimal geometric parameters of the punch-glass disk-support system in strength testing of the glass by the method of axisymmetric bending.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 73–79.     

The problem of strengthening of plastics in polymer solvents medium

It was found that short-term treatment of unstressed acrylate AST-T samples with n-amyl alcohol and butyl acetate leads to a marked improvement in their mechanical properties. The influence of temperature, holding time, and the nature of the solvent on the strength of acrylate AST-T has been studied. The increase in the strength indexes is the result of the thermal effect of the medium on the molecular structure of the surface layers and healing of the surface defects of the material. The great importance of the state of the surface on the physicomechanical properties compared with the temporary plasticizing action of the solvents has been shown.V. I. Lenin Kharkov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 5, pp. 913–915, September–October, 1972.     

Effect of heat treatment on the distribution of residual stresses and the properties of epoxy polymers

Conclusions The analysis of the experimental data showed that heat treatment results in a reduction in the stressed state of a polymer, which affects the tensile strength of the material to a greater degree than the compressive strength. During heat treatment, significant changes take place in sections of the polymer damaged by the effect of residual compressive stresses and sections in which the residual stresses change sign. The quantitative relations in the change in the tensile strength of the material in these two sections make it possible to explain the mechanism of the effect of heat treatment and to predict its character.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 787–790, September–October, 1986.     

Damageability of a material reinforced with unidirectional orthotropic fibers for an exponential function of long-term microstrength

The theory of long-term damageability of a homogeneous material is generalized to the case of an orthotropic fibrous composite material with a stochastic structure. Equations of mechanics of microinhomogeneous media of this structure form the base of the theory. The process of damage of components of a composite is modeled by the formation of stochastically located micropores. The criterion of fracture of a unit microvolume is characterized by its long-term strength determined by the dependence of the time of brittle fracture on the degree of closeness of the equivalent stress to its limit value, which characterizes the short-term strength on the basis of the Huber–von Mises criterion accepted as an arbitrary function of coordinates. Efficient deformation properties and the stress-strain state of an orthotropic fibrous composite with microdamages in components are determined on the base of stochastic equations of elasticity of orthotropic media. For given macrostresses and macrostrains and an arbitrary moment of time, balance equations of damage (porosity) of components are formulated. On the basis of the iteration method, we construct algorithms for calculating dependences of microdamage of components of an orthotropic fibrous material on time and dependences of macrostresses or macrostrains on time and obtain the corresponding curves for the case of a bounded function of the long-term microstrength, which is approximated by an exponential law.