Deformation criterion of the strength of plastics in biaxial compression

The deformation at break under uniaxial loading is taken as a criterion of the strength of an anisotropic glass-reinforced plastic in biaxial compression. Formulas are obtained for determining the breaking stresses and their limits of applicability are investigated. The calculated values of the breaking stresses are in agreement with the experimental values for both instantaneous and long-term loading.Mekhanika Polimerov, Vol. 4, No. 2, pp. 276–281, 1968     

Determination of the reliability of glass structures with steady and alternating loads

A method is developed for determining the reliability (nonfailure probability) of glass structures for a prescribed loading duration by alternating loads; an equation is obtained for calculating the reliability of glass structures from material (glass) strength parameters. It is shown that reliability with steady loads is a particular case of reliability with alternating loads. The method developed is based on a correlation established between long-term strength of the material and glass structure, and use of a new criterion of equal reliabilities for alternating loads.Lvov. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 90–97, 1990.     

Long-time strength of isotropic polymers in plane stress state

A criterion of strength of isotropic polymers in the form of the critical work done by stress was postulated and shown, by statistical analysis, to be independent of the time and form of loading. The introduction of the time factor in the existing theories of strength of isotropic materials was postulated and experimentally verified with the aid of this criterion.Mekhanika Polimerov, Vol. 2, No. 6, pp. 837–844, 1966     

Fatigue strength of certain materials used in airframe construction

Conclusions The completed tests show that the fatigue strength of carbon-plastic is 2.5 times greater than that of glass-plastic. Consequently, it is best to use carbon-plastic with ED-20 epoxy resin filled with 4–5m glass microspheres for adhesive purposes in load-bearing components. This makes it possible to significantly reduce the weight of airframes and improve their service properties. It was established that, for the composite materials investigated, stiffness is lost during cyclic loading mainly as a result of damage accumulation; the loss in stiffness may serve as a criterion for evaluating the progress of fatigue fracture.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 451–455, May–June, 1980.     

Comparison of concrete slabs pretensioned with composite bars and steel wires

A test program was set up to study AFRP as prestressing reinforcement for concrete slabs. The paper describes short-term, long-term and cyclic loading tests on ten slabs. The structural behavior of the pretensioned slabs, under these loading conditions, is investigated. Finally, it is concluded that the use of AFRP as prestressing reinforcement can offer promising perspectives.Presented at the Ninth International Conference on the Mechanics of Composite Materials. Riga. October, 1995.University of Ghent. Department of Structural Engineering, Magnel Laboratory for Concrete Research, Technologiepark-Zwijnaarde 9, 9052 Ghent (Belgium). Published in Mechanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 149–157, March–April. 1996.     

Experimental investigation of the stability of glass-reinforced plastic cylindrical shells subjected to long-term axial compression

The results of an experimental investigation of circular cylindrical glass-reinforced plastic shells under long-term axial compression are reported. The experimental method and the experimental apparatus are described. The initial irregularity functions and their evolution during loading and in time at various values of the compressive loads are investigated. The spread of the critical times at a given load level is studied together with the dependence of the critical time on the compressive load. The behavior of the shell after unloading and under alternating loading and unloading is considered. The correlation between the buckled shapes resulting from long-term compression and the initial irregularity functions is examined.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 4, pp. 710–713, July–August, 1973.     

Loading conditions in the local strains theory

Use of the local strains theory [7, 8] makes it possible to extend the loading criterion to complex loading paths if the hardening conditions are related to the local strains on individual small areas. Then the components of the total plastic strain increment are determined by integration over only those local areas on which the given loading condition is satisfied [9]. It is shown that the components of the strain tensor depend significantly on the loading history and the loading condition employed. The changes in the loading zones on the unit sphere are investigated for particular cases of complex loading as a function of the various loading conditions and the loading parameter.Mekhanika Polimerov, Vol. 3, no. 1, pp. 29–34, 1967     

Stability of laminar shells having a viscoelastic binder

Conclusions 1. In loading with a force whose value lies between the long-term and instantaneous critical values, a loss of shell stability by rupture takes place at a certain time after loading. This time is naturally taken as the critical one.2. Numerical estimates show that the level of the initial irregularities has a very great effect on the magnitude of the critical time. Therefore, in a theoretical estimate of the critical time it is necessary to take account of them as accurately as possible.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 2, pp. 277–282, March–April, 1978.     

Effect of the geometry of the structure on the strength distribution of multilaminate tridirectional reinforced plastics

Conclusion The proposed analytical method makes it possible to predict the strength distribution of an LRP of the type [0/±]_s from its structure (the geometry of the packet, the number of layers, and the strength properties of the layers) in a plane stress state. Allowance is made for the random character of the strength properties of the layers, which makes it possible to evaluate the reliability of the LRP for both determinate and random loading. A criterion was formulated for the optimum design of the structure of an LRP with respect to ensuring maximum reliability for specific loading conditions. We also evaluated the effect of the parameters of the structure and the characteristics of the plane stress state on reliability. According to the results of a numerical analysis performed with the above-developed structural model of the failure of an LRP — with allowance for the random character of the strength properties of the layers — the imbalance of the laminated packet which occurs during failure can be ignored. The method used to predict the strength distribution of the LRP, involving determination of the strength distribution law of an RSE and subsequent examination of the loading of parallel-connected RSEs, is promising for other reinforcement schemes as well.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 805–812, September–October, 1988.     

Optimum stacking sequence of composite laminates for maximum strength

A method is presented for maximum strength optimum design of symmetric composite laminates subjected to in-plane and transverse loadings. The finite element method based on shear deformation theory is used for the analysis of composite laminates. Ply orientation angles are chosen as design variables. The quadratic failure criterion which is meant to predict fracture, is used as an object function for optimum stacking sequence design of a laminated plate. The Broydon-Fletcher-Goldfarb-Shanno optimization technique is employed to solve the optimization problem effectively. Numerical results are given for various loading conditions, boundary conditions, and aspect ratios. The results show that the quadratic failure criterion such as Tsai-Hill theory is effective for the optimum structural design of composite laminates.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 393–404, May–June, 1995.     

Static fatigue of glass-reinforced plastics

Nonlinear damage accumulation rules are usually constructed on the basis of certain hypotheses derived from semiempirical considerations. A method is proposed for constructing an averaged nonlinear damage accumulation rule based on the direct utilization of the results of static fatigue tests on glass-reinforced plastic specimens. Numerical examples of the calculation of the static fatigue strength under repeat loading with a given strength criterion are presented.Sverdlovsk Branch of the Steklov Mathematical Institute, Academy of Sciences of the USSR. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 492–497, May–June, 1969.     

Comparison of the long-term strengths of polymers under uniaxial alternating and pulsating loads

The laws of fracture of PMMA and PS under uniaxial alternating and pulsating cyclic loading have been investigated at several loading frequencies and two test temperatures. An analysis of the dependence of the long-term strength on stress, heating kinetics and the form of the specimen fracture surface has shown that transition from cyclic tension to more complex alternating loading in the tension-compression regime does not change the basic nature of the cyclic fatigue effect and is reflected only in an increase in the local stress concentration and heating.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 483–488, May–June, 1972.     

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.     

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.     

Mechanical behavior of cylindrical laminated plastic shells

The static and dynamic behavior of a cylindrical glass-reinforced plastic shell with an open cross section under long-term loading and unloading has been experimentally and theoretically investigated. The experimental results are compared with the theoretical data obtained using a geometrically nonlinear theory based on the Kirchhoff hypothesis. For calculation purposes the glass-reinforced plastic is assumed to be a homogeneous orthotropic linearly elastic material.Building Research Institute, Prague. Translated from Mekhanika Polimerov, No. 1, pp. 110–115, January–February, 1976.     

Conditions of the ductile-brittle transition in failure of polymer materials

Conclusions The polymer materials are characterized by the transition from ductile to brittle fracture with increasing loading rate and decreasing temperature. The brittle fracture susceptibility of the material can be determined on the basis of the critical size of the defect/ crack. The measure of the cracking resistance of plastics can often be represented by the material scale of the crack length. The quality of the critical size of the defect/crack to the material scale of the crack length can be used as a criterion determining the conditions of transition from ductile to brittle fracture.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 779–785, September–October, 1988.     

Generalized criterion of the long-term strength of viscoelastic materials

A long-term strength condition of the same type as the Il'yushin [2] or Moskvitin [1] nonlinear criterion is proposed. A method is suggested for determining the stress and time functions forming part of the proposed criterion from the long-term strength diagrams and from the data of pulsed or stepped loading tests. It is shown, on the basis of the experimental data, that the proposed criterion, which in a particular case is identical with the Moskovitin criterion, describes the experimental results better than the Bailey criterion.     

Deformation of cylindrical composite shells under combined dynamic loading

Conclusions A procedure has been shown for calculating the stress-strain state of cylindrical multilayer shells made from composite materials under the combined action of dynamic axial compression and dynamic external pressure, as well as with different variants of combined loading with static and dynamic forces. An investigation has been made of the effect on the mode of the buckled shell surface of the ratio of the application rate of dynamic loads; ranges of loading rates have been established in which stresses predominate caused either by axial compression or external pressure. It has been shown that, as a result of preliminary static loading, a marked change occurs in the initial imperfections of the shell mode which affects subsequent dynamic buckling. To calculate the time when the first defect occurs and its location in the shell body, a procedure has been devised for layer-by-layer strength analysis employing a tensor-polynomial criterion. It was demonstrated that the level of preliminary static loading noticeably affects the time until the first failure of the layer, not only a reduction of this time being possible with an increase in the static loads, but also an increase in it.We should also point out the work in [10] where it is shown that it is possible to weaken the susceptibility of the shell to initial imperfections when internal pressure is applied.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 461–473, May–June, 1981.     

Modeling the mechanical behavior of metal-reinforced plastic pipes under internal pressure

Numerical nonlinear models for the mechanical behavior of the metal-reinforced plastic pipes (MRP) in destructive tests are developed to analyze the stress-strain state (SSS) in such pipes during loading. The influence of contact conditions at the polyethylene-steel boundary on the SSS of the metal-reinforced plastic pipes at normal temperatures is considered. A criterion of ultimate state of MRP is suggested to predict the load-carrying capacity of the pipes under internal pressure. The behavior of a welded butt joint of the MRP is studied, a stress redistribution phenomenon in the reinforcing skeleton is revealed, and the results obtained in destructive tests of butt joints are explained.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 57–70, January–February, 2005.     

Construction of fatigue curves in hard high-cycle loading of reinforced plastics

Conclusions The determination of the instant of failure of specimens in hard loading on the basis of load relaxation, the reduction of the elastic properties, of the length of surface cracks to some constant value is not associated with the process of high-cycle fatigue of the composites. It is recommended that the strength criterion of failure in the hard regime should be represented by the rapid reduction of the load in the last 1000–2000 cycles to 10% of its previous value. Endurance in hard loading depends strongly on the form of the specimen and the method of maintaining the given regime and, consequently, these data must be considered in constructing the fatigue curves. It was shown that the fatigue curves in the -log N coordinates in the soft and hard regimes with the symmetric cycle are positioned equidistantly on the axis. This relation may be used for constructing the -log N curves for hard loading from the fatigue curves for soft loading or, vice versa, at a reduced volume of tests. The error in determining the fatigue limits by this method for N10⁶ cycles does not exceed ±5%.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 457–463, May–June, 1987.