Mechanism of shear failure of reinforced rings in bending

The mechanism of failure of a ring due to the shear stresses in the matrix is investigated. It is shown that in the process of shear failure the axial displacement distribution is modified and that the shear failure mechanism depends on the type of loading. The load corresponding to the onset of failure of the ring due to the shear stresses in the matrix does not exhaust the carrying capacity of a reinforced ring with respect to this mode of failure.Institute of Hydrodynamics, Siberian Division of the Academy of Sciences of the USSR, Novosibirsk. Translated from Mekhanika Polimerov, No. 3, pp. 435–444, May–June, 1976.     

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.     

Inelastic deformation and fracture of disordered fiber-reinforced composites

Conclusions Simulation of the process of nonlinear deformation and failure in the structure of a unidirectional epoxy glass plastic under transverse loading has indicated that equilibrium regions of failure receiving only hydrostatic compressive loading may form. The development of this region explains the high (up to 40%) nonlinearity of deformation diagrams under transverse biaxial compressive loading. The regions of nonlinear deformation of the epoxy matrix affect less markedly the nonlinearity of the macroscopic s* diagrams. This fact and also the formation and avalanchelike propagation of regions of complete failure explain the linear form of many diagrams corresponding to tensile and shear loading in the transverse plane. The relations of the nonlinear theory of elasticity make it possible to describe with sufficient accuracy the entire set of the calculated diagrams.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 621–628, September–October, 1993.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 5, pp. 621–628, September–October, 1993.     

Experimental evaluation of the strength of one-piece Kapron nuts

The strength of one-piece Kapron nuts has been investigated in static loading tests. Graphs of the load versus the number of turns, which reflect the distribution of the load over the turns, are presented. The types of failure of threads of five standard sizes with different profiles are analyzed. It is concluded that there is an important difference between the usual thread calculation model based on the strength of the turns in shear, bearing and bending and the actual loading of the turns of polyamide nuts cooperating with steel screws.Dnepropetrovsk Metallurgical Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 752–754, July–August, 1968.     

Predicting the transverse strength of unidirectional composites under combination loading

This article presents a mathematical model for predicting the transverse strength of unidirectional fiber composites subjected to combination transverse loading under different conditions. The behavior of the matrix is described by nonlinear physical equations consistent with the strain theory of plasticity for the active loading section. The fibers are assumed to be isotropic and elastic. The boundary-value problem of micromechanics that is formulated includes strength criteria for the matrix and fibers that mark the beginning of their possible failure. The modeling of the fracture process is taken farther through the use of a scheme that reduces the stiffness of the matrix and fibers in the failed regions in relation to the sign of the first invariant of the stress tensor. The method of local approximation is used together with the finite-element method to calculate the stress and strain fields in unidirectional composites with cylindrical fibers in a tetragonal layup. The model is used to study the behavior of an epoxy-based organic-fiber-reinforced plastic subjected to transverse loading in different simple paths — including simultaneous compressive and tensile loads, as well as transverse shear.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 473–481, July–August, 1995.     

Fatigue strength of glass fiber/epoxy angle-ply laminates with different matrix ductility

Conclusion Angle ply laminates made up of glass fiber/epoxy plies have a good static strength for laminate angles up to about 45 °. This is due to the limitation of transverse strain in the plies due to constraints exerted by neighboring plies. At laminate angles of 50 ° and above the transverse and shear strains in the plies are not sufficiently constrained and cause failure in the matrix material. The constraint effect is present in fatigue but since the polymeric matrix material is sensitive to fatigue loading fatigue failure will occur at much lower strain levels than in static loading. This effect cannot be offset by increasing the ductility of the matrix material. Thus, strain to failure under fatigue loading will be only a small fraction of the static strain to failure for angle ply laminates with ply angles up to around 45 ° where the static strength is due to the constraint effect.Published in Mekhanika Kompozitnykh Materialov, No. 5, pp. 632–638, September–October, 1992.     

Evolution of structural damage and macrofailure of inhomogeneous media at the supercritical stage of deformation

The article deals with the evolution of structural damage of an inhomogeneous body as a function of the properties of the loading system whose characteristics are taken into account by supplementing the boundaryvalue problem (1), (2) with the boundary conditions of the third kind (3) and (4). With the numerical solution by the finite-element method these boundary conditions are satisfied in accordance with the Eqs. (6) and (7) by changing the rigidity matrix of the discretized body (8). The material loses its load-bearing capacity at some point of the descending branch of the stress-strain diagram (Fig. 1a) at the instant the conditions of stability (9) are infringed. Normalized correlation functions of a damaged structure plotted for different equilibrium states of a granular composite (Fig. 2) make it possible to identify characteristic stages of failure. Macroscopic failure of material is regarded as the concluding stage of the processes of the onset, localization of structural disruptions, and formation of a macrodefect. Increased rigidity of the loading system makes it possible to stabilize the process of damage calculation, and this leads to an increase of limit deformations. The realization of the supercritical stage of deformation, together with energy dissipation upon structural destruction is the mechanism of adaptation of an inhomogeneous body to the loading conditions.Perm State Technical University, Russia. Translated from Mekhanika Komozitnykh Materialov, Vol. 33, No. 3, pp. 329–339, May–June, 1997.     

High-precision modeling of deformation of laminated structures

Precise three-dimensional solutions for homogeneous, two- and three-layer plates of symmetric and nonsymmetric structure over their thickness with orthotropic layers in transverse symmetric and antisymmetric loading normal to the surface of the plates are given. It is shown that the character of stressed states under flexural (antisymmetric) and nonflexural (symmetric transverse compression) loading differs greatly. It is noted that the known refined continual models, which take into account the transverse shear and compression, are all essentially flexural and therefore cannot describe the nonflexural deformations well. In particular, continual shear models in symmetric pressure loading lead to zero solutions. A refined nonflexural continual model of deformation of sandwich plates in bilateral symmetric compression is constructed. The general order of resolving differential equations for continual models does not depend on the number of layers. Approximation functions of the transverse coordinate are obtained with the help of well-founded hypotheses. A high-accuracy variant of the flexural continual model is proposed for antisymmetric loading with account of shear and transverse normal strains, as well as a version combining both models mentioned. A method of precise satisfation of all the constitutive relations for the layers, including the conditions of their contact, is proposed, whereas in the known continual models the dependence between the transverse normal stress and strain is satisfied only integrally, or else the Poisson effect is neglected.Ukrainian State Academy of Water Management, Rovno, the Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 13–28, January–February, 1999.     

Investigation of fatigue damage in polymer films by the method of light scattering

Conclusions In cyclic loading of the investigated polyurethane there originates a polydisperse system of microdefects with nonspherical shape, in consequence of which the light scattering increases irreversibly. The method of light scattering is sufficiently sensitive for determining the relative concentrations and dimensions of microdefects that are smaller than the wavelength of light. It was shown that the predominant mechanism of failure of polyurethane is the increased concentration of microdefects whereas their dimensions change only imperceptibly.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 910–917, September–October, 1984.     

Effect of the end conditions on the critical loads for filament-wound glass-reinforced plastic columns

The behavior of glass-reinforced plastic columns with various end conditions has been experimentally investigated. The cross-wound columns had a length to mean diameter ratio of 18–20. Four types of support with different degrees of restraint on end rotation ranging from almost free ends to fixed ends were employed. The possibilities of increasing the critical loads by manipulating the boundary conditions are estimated. Numerical estimates are obtained for the various methods of support. Random imperfections and the number of loadings were not found to have any effect on the critical loads. It is shown that the use of Southwell's method makes it possible to estimate the critical loads for columns with different end conditions from the subcritical loading data.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 54–62, January–February, 1976.     

A refined model for three-point bending of sandwich panels. 1. Deflections and bending stresses

Design formulas for the flexural characteristics of sandwich panels under three-point loading by point forces, taking into account local effects, have been derived. Transverse deformation of the normal in the modified model is deduced in terms of the difference between deflections of face layers. It is considered that the rotation of the normal depends also on shear of the filler. The deflections, local curvatures, and bending stresses, dependent on the face-layer thicknesses and transverse characteristics of the filler, are studied. The danger of initial failure caused by the local moment stresses at the central panel section is shown. Comparative estimates refining the conventional designs are established.Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 747–767, November–December, 1997.     

Structural damage accumulation and stable postcritical deformation of composite materials

The macroscopic failure of composite materials is preceded by complex multilevel processes accompanied by accumulation and localization of damaged centers and formation of a failure cluster. Therefore, the study of these mechanisms is one of the basic problems for the mechanics of modern composite materials used in aerospace engineering. The formation of a theory of the stable postcritical deformation of the work-softening media is considered. The pseudo-plastic deformation affected by structural damage of granular composites is investigated within the framework of the considered two-level structurally phenomenological model of heterogeneous media. The stable evolution of the interconnected processes is accompanied by stress redistributions, partial or complete unloading, and strain or damage localization that are one of the main causes of implementation of the postcritical deformation stage. The numerical calculation results of inelastic deformation and failure of the periodic unidirectional fiber-reinforced composites are presented under conditions of the displacement-controlled transverse proportional loading mode. The main mechanisms of the work-softening behavior for the indicated type of materials are described in the macro-homogeneous stress-strain states. Macroscopically, the failure of heterogeneous media as a result of postcritical deformation and the loss of stability of damage accumulation depends on the stiffness of the loading system. When a deformable body is fixed on the closed surface with sufficiently but not infinitely large coefficients of stiffness, it is possible to observe the equilibrium development of the localized volumes of work-softening and damage. The constitutive equations for the work-softening isotropic, transverse isotropic, and orthotropic media are presented. The effect of the loading system on the stability of deformation, damage accumulation, and failure under monotone and nonmonotone triaxial loading was studied. The growth of failure strains with increase in stiffness of the loading system and unequal resistance of heterogeneous body are registered and investigated. A preventive unloading method is offered for the mathematical modeling of the damage accumulation during the testing of the materials on the servo-controlled systems. The displacement-controlled mode is simulated by a series of soft loading and unloading cycles. The detected phenomenon of failure where the unloading leads to stress-strain diagrams with a negative slope of the descending branch was not found either in the displacement or stress-controlled monotone loading mode.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 234–250, March–April, 1998.     

Some features of the dynamic bond strength of rubbers in symmetric alternating shear

A power law is obtained for the endurance of the joints in laminated rubber systems, and the relation between the shear stressesf and the strains at joints parallel to the shear direction is shown to be linear for symmetric alternating shear. One consequence of the linearity of the relation betweenf and is the nondependence of the power law coefficient (coefficient of resistance of the joint to repeated loading) on the loading conditions.Mekhanika Polimerov, Vol. 1, No. 2, pp. 114–117, 1965     

Resistance of glass-reinforced plastics to long-term shear failure

The time dependencies of the strength of glass-reinforced plastics in shear under steady, continuous and alternating loads are examined. Failure under steady and continuous loading is depicted by means of an exponential model of the build-up of damage.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 2, pp. 295–302, March–April, 1970.     

Buildup of failures in polymers on micro- and macrolevels

The buildup of damage in polymers has been studied by mechanical and structural—analytical methods. A method of programmed loading has been developed which makes it possible to make an estimate of damage buildup in macroscopic experiments. A comparison has been performed of kinetic curves of failure buildup on molecular and macroscopic levels. It is shown that the kinetic equations where the rate of failure is basically initiated by true stress qualitatively follow the experimental curves for failure buildup on micro- and macrolevels."Plastpolimer" Scientific-Manufacturing Association, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 263–268, March–April, 1976.     

Static strength and failure mechanism of CFRP under biaxial loadings

Tests of cross-ply composite tubes were performed under combined axial and torsional loading up to failure. Strength properties and failure mechanisms were evaluated with reference to the biaxiality ratio of the loading. The scattering of the biaxial strength data was analyzed using the Weibull distribution. The axial contraction of carbon fiber-reinforced plastic (CFRP) tubes under biaxial loading was investigated theoretically and experimentally. Artificial neural networks were introduced to predict the failure strength using the algorithm of the error back-propagation. The prediction was also made by the Tsai-Wu theory using the experimental data and by the combined optimized tensor-polynomial theory. A comparison shows that the artificial neural network has the smallest root-mean square (RMS) error of the three prediction methods. The prediction of the axial contraction of the tubes correlates well with the results of a linear variable differential transformer (LVDT) of the testing machine. From the phenomenological analysis of the failure and the fractographic observations of the fracture surface, three types of failure modes and microscopic failure were investigated, depending on the biaxiality ratio, and the corresponding failure mechanisms are suggested.Submitted to the Tenth International Conference on Mechanics of Composite Materials, Riga, April 20–23, 1998.Department of Mechanical Engineering, Pohang University of Science and Technology, Pohang 790–784, Korea. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 1, pp. 38–56, January–February, 1998.     

Combined bending and axial loading of beams made of materials with low shear strength

The effect of shear stresses on the deflection of glass-reinforced plastic beams in bending with axial loading is investigated in the case of hinged supports. The critical axial compressive load is determined with allowance for shear and the limiting value of the axial tensile load is estimated.Mekhanika Polimerov, Vol. 4, No. 1, pp. 124–130, 1968     

Effect of relaxation parameters on the behavior of rigid polymers in pure shear

The authors have investigated the effect of the relaxation parameters of a rigid polymer corresponding to the individual terms of the relaxation spectrum on the nature of the theoretical curves calculated for creep, strain relaxation and loading at constant strain rate in pure shear on the assumption that the stress-strain relation is described by the generalized Maxwell equation.Institute of Chemical Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 431–436, May–June, 1969.     

Long-term strength of reinforced composites

Conclusion A criterion of long-term strength was proposed for composite materials. The criterion can be used to calculate time to failure for arbitrary loading programs. It was shown that the criterion provides for good agreement with the experimental data not only in the cases of instantaneous and long-term static loadings, but also for fatigue loading in tension, in compression, and in mixed regimes with different asymmetry coefficients.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 16–22, January–February, 1989.     

Experimental investigation of the strength of structural plastics in multiple pulsed bending

Strip-beams of molded fabric-reinforced plastic, unidirectional wound glass-reinforced plastic, and polystyrene and syntactic foam have been tested in pulse bending in a modified electrodynamic testing device. The main stages of the failure process and the nature of the relation between the peak load and the number of cycles to failure have been established. For all the materials tested these relations are similar to the cyclic strength curves obtained at low loading rates. It is shown that for glass-reinforced plastics there is a correlation between the various stages of the failure process.Translated from Mekhanika Polimerov, No. 2, pp. 337–341, March–April, 1971.