Effect of properties of high-density polyethylene on durability of welded joints

The molecular characteristics of pipe grades of high-density and medium-density polyethylene modified by 1-butene do not affect the durability of welded joints. Their long-term strength depends mainly on the density of the base grade of polyethylene and increases by an order of magnitude when the density is reduced in the investigated range. We have obtained mathematical models approximating the dependence of the durability of welded joints on the most important factors: the degree of crystallinity of the polyethylene and the initial stress in the brittle and mixed brittle-plastic fracture region. The models obtained may be used to assess the quality of the stabilizing system and the effectiveness of the comonomers of ethylene.Kazan State Technological University, Kazan, Tatarstan, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 842–847, November–December 1996.     

Experimental and theoretical modeling of shrinkage damage formation in fiber composites

The cure of a thermoset matrix in the formation of composites is always accompanied by chemical shrinkage that generates internal stresses. In composites with high fiber content, the matrix is cured under three-dimensionally constrained conditions. The results of the previous experimental and theoretical modeling of formation of shrinkage damage under these conditions in epoxy-amine systems are briefly discussed. The effect of the model geometry (tube and plate models), scale factor, cure schedule, and chemical structure of composites is analyzed. A theoretical model for predicting the possibility of formation of shrinkage damage in fiber composites is proposed. A regular square structure was considered. Analysis showed that the maximum level of shrinkage stress in the matrix at the ultimate fiber fraction ⁺ was close to the stress level ⁺ in an experimental long tube model, where the formation of shrinkage damage took place. The experimental results for the short tube model showed that the shrinkage damage in epoxy-amine systems occurred up to approximately ⁺/3. The damage development took place within the whole range of fiber content from ⁺ to ^* (where the shrinkage stress level was about ⁺/3). In the long tube model, cohesive defects always nucleated inside the matrix. The damage grew, reached the inner surface of the tube, and then extended as adhesive debondings. A similar situation is expected in composites with a high fiber content. The damage considered is local, and the total monolithic character of a composite product is conserved.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998. Riga, Latvia.Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka 142432, Moscow Region, Russia. Translated form Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 264–275, March–April, 1998.     

Study of microbuckling of fiber-reinforced composite materials

On the basis of the theory of microbuckling of lamina-reinforced composites and formula predicting the critical composite stress for microbuckling in the shear mode _cs published in the literature, a FORTRAN program for study of the behavior of microbuckling of fiber reinforced composites has been developed. Some types of composite materials (reinforcement of different fibers and epoxy matrix) have been studied. Graphics and curves, accounting for the dependences of the compressive stress at failure _cs from the reinforcement volume k, specimen length L, and shear modulus of resin G_r have been obtained. The comparison of the theoretical diagrams presented here and experimental and theoretical results, published in the literature shows good agreement. The basic conclusion of the work presented here is that the study could be used for other fiber reinforced composites (with different mechanical properties of matrices and fibers).Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 531–538, July–August, 1996.     

Method of estimating the strength of glass-reinforced plastic shells

A combined method of estimating the strength of glass-reinforced plastic shells in the plane stress is described. The method consists in a combination of destructive and nondestructive methods of determining the necessary starting characteristics for use with a criterion of the strength of orthotropic materials in the form of a fourth-degree polynomial.Ritm Scientific-Production Association. Central Scientific-Research Institute of Shipbuilding Technology, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 571–573, May–June, 1972.     

Statistical forecasting for stochastic processes

The main purpose of this paper is to review the efficiency properties of least-squares predictors when the parameters are estimated. It is shown that the criterion of asymptotic best unbiased predictors for general stochastic models is a natural analogue of the minimum mean-square error criterion used traditionally in linear prediction for linear models. The results are applied to log-linear models and autoregressive processes. Both stationary and non-stationary processes are considered.This paper is based on a key note lecture given at the meeting of The Institute of Management Sciences and the Operations Research Society of America, held in Williamsburg, Virginia, January 7–9, 1985.     

Averaging in hyperbolic systems subject to weakly dependent random perturbations

The first initial boundary value problem is considered for a hyperbolic equation with a small parameter for an external action described by some stochastic process satisfying some of the conditions of weak dependence. Averaging of the coefficients over the temporal variable is conducted. The existence is assumed of a unique generalized solution both for the initial stochastic problem and for the problem with an averaged equation, which turns out to be deterministic. For the probability of deviation of a solution of the initial equation from the solution of the averaged problem, exponential bounds are established of the type of S. N. Bernshtein inequalities for the sums of independent random variables.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1011–1020, August, 1992.     

Averaging in parabolic systems subject to weakly dependent random actions. The L2-approach

The first initial-boundary problem for a parabolic equation with a small parameter under external action described by some random process satisfying an arbitrary condition of weak dependence is considered. Averaging of the coefficients over a time variable is carried out. The existence of a generalized solution for the initial stochastic problem as well as for the problem with an averaged equation which turns out to be deterministic is assumed. Exponential bounds of the type of the well-known Bernstein inequalities for a sum of independent random variables are established for the probability of the deviation of the solution of the initial equation from the solution of the averaged problem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 315–322, March, 1991.     

Globally Optimized Spherical Point Arrangements: Model Variants and Illustrative Results

The well-balanced distribution of points over the surface of a sphere is of significant interest in various fields of science. The quality of point configurations is typically expressed by criterion functions that have many local optima. A general global optimization framework is suggested to solve such problems. To illustrate the viability of this approach, the model development and solver system LGO is applied to four different model versions. Numerical results – including the visual representation of criterion functions in these models – are presented. The global optimization approach can be tailored to specific problem settings, and it is also applicable to a large variety of other model forms.     

Thermal creep of polyethylene in the presence of thermal cycling

The temperature-time dependence of Poisson's ratio and the volume relaxation of LDP is investigated in the case of uniaxial tension. It is established that at elevated temperatures and loads the material becomes denser and Poisson's ratio exceeds 0.5. It is shown that the (t) curves and the temperature dependence of the instantaneous Poisson's ratio are nonmonotonic, while the nature of the (t) relaxation changes qualitatively as a certain temperature region is entered and the stress is increased.Mekhanika Polimerov, Vol. 4, No. 3, pp. 421–427, 1968     

Temperature dependence of the strength of a woven composite in a plane state of stress

Conclusions On the basis of an analysis of test results obtained by typical patterns of simple momentary quasistatic loading at various temperatures within the 20–150°C range, we have found a family of strength surfaces for a woven organic plastic material in a plane state of stress in the reinforcement plane. These experimentally found strength surfaces can be approximated by the equation of a second-degree surface. It has been established that the range of safe states of stress in the stress space narrows nonuniformly with rising temperature; namely, this narrowing is accompanied by a shift of the center and a reorientation of the axes of the strength ellipsoid. We have revealed and described the temperature dependence of the components of the strength surface tensors involved in the strength criterion. The data can be used for predicting the strength of a composite material under consideration when the latter is subject to simple quasistatic loading patterns in the three-dimensional (₁₁, ₂₂, ₁₂) stress space in the reinforcement plane within a given test range of temperatures.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 452–457, May–June, 1978.     

Rubber life over a broad interval of stresses and aggressive medium concentrations

A generalized dependence of rubber life on stress and the concentration of the aggressive medium is proposed for a broad interval of variation of stresses and concentrations. The known expressions for the life in air and aggressive media as functions of stress (at large values of ) and concentration at constant stress are obtained as special cases. At zero concentration the proposed relation goes over into Zhurkov's equation with =(). The proposed equation and the graphic construction can be used, in particular, for determining rubber life in air at low stresses, i.e., under conditions similar to those encountered in service.The experiments were performed by N. L. Novikova.Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1020–1025, November–December, 1968.     

Averaging in parabolic systems subject to weakly dependent random actions. The L2-approach

The first initial-boundary problem for a parabolic equation with a small parameter under external action described by some random process satisfying an arbitrary condition of weak dependence is considered. Averaging of the coefficients over a time variable is carried out. The existence of a generalized solution for the initial stochastic problem as well as for the problem with an averaged equation which turns out to be deterministic is assumed. Exponential bounds of the type of the well-known Bernstein inequalities for a sum of independent random variables are established for the probability of the deviation of the solution of the initial equation from the solution of the averaged problem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 315–322, March, 1991.     

Study of stress intensity factors near cracks in plates made of linearly viscoelastic fiber composites

For the first time a method is proposed for determining the stress intensity factors (SIF) near cracks in linear viscoelastic fiber composites using the data from polarization-optical measurements. The character of the change in the SIF in time near cracks in plates made of optically sensitive viscoelastic fiber composites exposed to constant tensile stresses (creep) was investigated. In describing the mechanical and optical properties of the materials, the composite was considered a homogeneous linearly viscoelastic orthotropic body. Equations were derived which correlate the fringe ordersm(t) with SIFK _j (j=1,2) and the longrange field stress _Ox in the vicinity of the apex of a crack whose direction coincides with the main direction of the axis of orthotropy. The SIF near linear cracks whose direction forms angles =90° and =45° with the direction of the tensile stresses were determined. It was found that the character of the change in SIF in time near cracks in creep, is a function of the angle between the direction of the crack and the direction of the tensile stress.Scientific-Research Institute of Mechanics, M. V. Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 321–328, May–June, 1997.     

Lifetime and relaxation processes in solid polymers

The relationship between relaxation processes and the fracture of solid polymers is examined with reference to the example of repeat loading with recovery. An investigation of polymethyl methacrylate, KAST-V glass laminate, and a Finnish polyester glass-reinforced plastic has shown that this lifetime may be considerably (several orders) shorter than that at the same level of constant stress. This is attributed to the time dependence of the structure-sensitive coefficient in the lifetime equation and is illustrated by means of a model that includes a Regel' fracture element.Moscow Lenin State Pedagogical Institute, Problem Laboratory of Polymer Physics. Translated from Mekhanika Polimerov, No. 4, pp. 629–635, July–August, 1969.     

The stressed state and certain fracture characteristics of glass-reinforced plastics loaded in tension at an angle to the direction of reinforcement

The stressed state of glass-reinforced plastic specimens with various structures is investigated experimentally in the case of tensile loads acting at 45° to the direction of reinforcement. A relation is established between the stress distribution over the cross section and the scale factor associated with the relative width of the understressed zones along the edges of the specimen. The fracture characteristics of GRP specimens with different structures are analyzed. Recommendations are given for testing GRP with different structures in tension at an angle of 45° to the direction of reinforcement.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1030–1034, 1967     

New Potentialities in Producing Composites Reinforced with High-Strength High-Modulus Polyethylene Fibers

A concept of physical and chemical stages of interaction between the matrix and reinforcing fibers during the production of composite materials is introduced. A strong bond between these constituents is formed at the stage of chemical interaction, which is characterized by a certain value of activation energy. The activation energy of such an interaction for high-strength high-modulus polyethylene fibers used for reinforcing composites is estimated. Based on these estimates, conditions for fiber activation with cold plasma are found. The application of plasma-activated polyethylene fibers for reinforcing an epoxy matrix allows one to produce light-weight composites with high physicomechanical indices. The failure mode of such composites points to a high strength of the bond between the fibers and matrix. The data on treating the fiber surface with cold plasma above the activation energy of chemical interaction may be utilized to create new types of organic composites from other kinds of organic fibers and matrices.     

Influence of edge effects on the state of stress and strength of carbon composites in tension

Conclusions A difference has been found between the theoretical and experimental strength values. The theoretical strength of flat strips with straight edges, obtained on the basis of the two-dimensional solution within the elastic range for a composite with fiber angle < 30°, is higher than the actual strength. The difference is due to the failure to take account of interlaminar shear. The strength tensor is applied to a monolayer with respect to which the internal state of stress and the nature of the interrelationship between the layers are not taken into account. In this connection, it is desirable to supplement the given criterion with a condition which would take account of the difference between the stresses _xy in adjacent layers. If the directions of reinforcement > 30°, then the agreement between the theoretical strength of flat strips of variable width, obtained on the basis of the two-dimensional solution within the elastic range using the tensor strength criterion, is in good agreement with the actual strength obtained experimentally. The big differences between the actual and theoretical strengths for the three-dimensional solution are attributable to the physical and geometric nonlinearity in the boundary zone between the elementary layers of the composite.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 263–270, March–April, 1985.     

Modeling of Structures in the Mechanics of Composites

One possible general statement of a quasi-static problem in the mechanics of composites is considered. It is assumed that a composite is characterized not only by the heterogeneity of a regular structure, but also by the presence of imperfections, impurities, cracks, and the roughness of surfaces, which are partly taken into account by introducing appropriate couple stresses. Two statements, in displacements and in stresses, are considered together with the statement of the same problems in the case where the constitutive relations are linear integral operators. The boundary-value problem remains nonlinear due to the nonlinearity of a scattering function which enters into the heat equation. The theory of effective moduli for a nonpolar medium is discussed in more detail. The equilibrium equations for a homogeneous medium with reduced characteristics and the equation of heat inflow, introduced in nonlinear (in an explicit form) and linear variants, are examined. For a simple laminated composite, all effective mechanical and thermophysical characteristics are found in an explicit form. The effective material functions for a transversely isotropic medium are constructed on the basis of a unique dimensionless relaxation kernel with the use of several Il'ushin kernels. Based on the known solution of the boundary-value problem for the reduced medium, the stress and strain concentration tensors, at any point of a simple laminated composite, are also constructed in an explicit form. In this case, the changes in the structure are taken into account.     

Numerical Analysis of the Efficiency of Using Theories of Thin and Thick Composite Shells in Stress Concentration Problems

The feasibility of overcoming cutoff effects in four versions of the theory employing classical and mixed functionals is analyzed for sample problems involving the stress concentration near a hole in composite spherical shells with different thicknesses and transverse shear rigidities. Recommendations on the choice of theory are given depending on the shell parameters. A class of not very thick shells with a low shear rigidity is found for which all the versions of the theory yield an acceptable computational accuracy.     

Deformation and fracture of composites by the methods of speckle-holographic interferometry

Summary The holographic method described makes it possible effectively to investigate complex problems of the deformation mechanics of composites, and obtain new precise information on their fracture process. The high sensitivity (to 0.1m) and the almost unlimitedly small strain measuring bases make it convenient to use the method described to investigate the reliability of the hypotheses and assumptions of theoretical calculation methods, for the direct experimental observation of fine deformation effects, and for investigating the laws of deformation and fracture of new composites and the critical elements of structures made of such materials.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 136–140, January–February, 1982.