Estimation of limit strains in disk-type flywheels made of a compliant elastomeric matrix composite undergoing radial creep

Fiber reinforced elastomeric matrix composites (EMCs) offer several potential advantages for construction of rotors for flywheel energy storage systems. One potential advantage, for safety considerations, is the existence of maximum stresses near the outside radius of thick circumferentially wound EMC disks, which could lead to a desirable self-arresting failure mode at ultimate speeds. Certain unidirectionally reinforced EMCs, however, have been noted to creep readily under the influence of stress transverse to the fibers. In this paper, stress redistribution in a spinning thick disk made of a circumferentially filament wound EMC material on a small rigid hub has been analyzed with the assumption of total radial stress relaxation due to radial creep. It is shown that, following complete relaxation, the circumferential strains and stresses are maximized at the outside radius of the disk. Importantly, the radial tensile strains are three times greater than the circumferential strains at any given radius. Therefore, a unidirectional EMC material system that can safely endure transverse tensile creep strains of at least three times the elastic longitudinal strain capacity of the same material is likely to maintain the theoretically safe failure mode despite complete radial stress relaxation. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 1, pp. 87–94, January–February, 2000.     

Problem of magnetoelasticity for a solid with the spherical cavity

The solution of a static problem of magnetoelastisity for a soft ferromagnetic elastic solid with the spherical cavity is obtained on the base of the linear theory of Brown, Pao and Yeh. It is assumed that the solid has a multi-domain structure, so the hysteresis loss and remanent magnetization are neglected. The solid is affected by a magnetic field which is uniform at infinity and determined by the magnetic induction vector. The cavity causes some distortion of the field distribution near the interface. So the field induces magnetic moments and produces stresses and deformations in the body. The problem is solved for an unperturbed strain state. An approach is discussed to find the perturbed values on the base of the solution obtained. The Fourier variable separation method is used. The stresses are presented via harmonic functions. As a result magnetoelastic stresses are obtained in the closed form. Their distribution in the body is studied and some results of numerical calculations are shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress-strain state in the matrix of stochastically reinforced composites

Conclusion We proposed a method of studying the concentration of stresses and strains in the matrix of composites with a stochastic structure in a three-dimensional formulation. The method is based on the use of tensor operators assigned at the inclusion-matrix interface and results from the theory of effective moduli of stochastically reinforced composites.Advantages of the proposed approach include its relative simplicity and clarity, as well as the fact that it can be used to analyze the three-dimensional stress and strain concentration in the matrix of composites with components having very different properties. However, for high values of the volume concentration of reinforcement c₁ > 0.6, it is necessary to use the results of exact solutions obtained, for example, within the framework of deterministic models. The correction that is introduced here is connected with the average of the stresses and strains over an inclusion. The character of their distribution over the interface remains the same as before.The numerical results obtained here show the significant effect of the relative dimensions of the inclusions on the effective elastic properties and the stress concentration in the matrix. Comparison of theoretical values of the longitudinal elastic modulus with experimental results can serve as grounds for validating the proposed variant of choosing the tensor L₀ in the determination of the corrected characteristics and stress-strain state of the matrix.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 396–402, May–June, 1989     

Predicting the Deformability of Expanded Polystyrene in Long-Term Compression

The interval prediction of creep strain on the basis of 15 years is carried out for slabs of expanded polystyrene (EPS) subjected to a compressive load. The expansion of the confidence interval caused by the discounted prediction information is allowed for by an additional factor. The creep compliance _c (t = 15) of the EPS is determined based on empirically estimating the long-term creep of this material subjected to a compressive stress σ _c = 0.3σ_10% for 15 years. A relationship between _c (t = 15) and EPS density in the slabs is established. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 607–618, September–October, 2005.     

弹性-幂硬化蠕变性材料Ⅱ型界面裂纹准静态扩展的渐近分析

建立了弹性-幂硬化蠕变性材料Ⅱ型界面裂纹准静态扩展的力学模型,求得了在裂纹表面自由和裂纹面有摩擦接触两种情况下,裂纹尖端应力场分离变量形式的渐近解．求解结果表明:Ⅱ型界面裂纹问题的应力、应变具有相同的奇异性;Ⅱ型界面裂纹尖端场不存在振荡奇异性;材料的幂硬化指数n和弹性模量比对裂纹尖端应力场幂硬化蠕变性材料区有着显著的影响,而弹性区仅受幂硬化指数n的影响,当n很大时,蠕变变形占主导地位,应力场趋于稳定,不随n的变化而变化;泊松比对裂纹尖端应力场的影响不明显．     

Deformability of an expanded polystyrene EPS 200 under long-term compression

The results of a study on the creep of EPS 200 plates under compressive stresses σ_c in the interval 0.22 ≤ σ_c/σ_10% ≤ 0.80 are presented. From experimental data, the domain of linear creep of the material in the interval of compressive stresses is determined. Under variations of the stress on the interval 0.22 ≤ σ_c/σ_10% ≤ 0.36, the prognostic value of creep strain of the EPS 200 plates for a lead time of 25 years is found to be 2.4%, with a coefficient of variation equal to 18%.     

Time-stress superposition in nonlinear viscoelasticity

Using low-density polyethylene, whose viscoelastic properties are nonlinear at high stresses, within reasonable limits of stress and time it is possible (under certain conditions) to use time-stress superposition, as well as time-temperature superposition, to predict the long-term creep of polymer materials. A variant of the compact approximation of nonlinear vicoelasticity effects in polymers is proposed.Mekhanika Polimerov, Vol. 4, No. 2, pp. 379–381, 1968Instantaneous elastic strains excluded.     

The effect of radiation modification and of a uniform magnetic field on the deformation properties of polymer composite blends

An experimental study of radiation-modified blends of high-density polyethylene with a chlorinated polyethylene exposed to a constant magnetic field with induction equal to 0.7, 1.0, 1.4, and 1.8 T is presented. A preliminary gamma irradiation has been performed with absorbed doses equal to 50, 100, and 200 kGy. The main attention is devoted to the investigation of deformation (elastic and viscoelastic) properties of the material. Data showing the effect of the absorbed dose of gamma irradiation and the induction of magnetic field on the elastic modulus and creep of the material under a constant stress are obtained.     

Numerical solutions comparison for interval linear programming problems based on coverage and validity rates

In this paper, two-step method (TSM), alternative solution method (SOM-2) and best-worst case (BWC) method are introduced to solve a type of interval linear programming (ILP) problem. To compare the performance of the methods, Monte Carlo simulation is also used to solve the same ILP problem, whose solutions are assumed to be real solutions. In the comparison, two scenarios corresponding with two assumptions of distribution functions are considered: (i) all the input parameters obey normal distribution; (ii) all the input parameters obey uniform distribution. Based on the simulation results, coverage rate (CR) and validity rate (VR) are proposed as new indicators to measure the quality of the numerical solutions obtained from the methods. Results from a numerical case study indicate that the TSM and SOM-2 solutions can cover the majority of valid values (CR > 50%, VR > 50%), compared to the conventional BWC method. In addition, from the point of CR, TSM is more applicable since the solutions of TSM can identify more feasible solutions. However, from the point of VR, SOM-2 is preferred since it can exclude more baseless solutions (this means more feasible solutions are contained in the SOM-2 solutions). In general, TSM would be preferred when only the range of the system objective needs to be determined, while SOM-2 would be much useful in identifying the effective values of the objective.     

Time and temperature dependent deformation of poly(ether ether ketone) (PEEK)

The stress-strain behavior in tension and the effect of temperature on the creep of poly(ether ether ketone) (PEEK) have been studied. At room temperature, 130° below the glass-transition temperature, the material does not become brittle, and the specimens show necking in tension over a wide range of elongation rates. The stress and strain at yield and the strain at break are almost linear functions of the logarithmic elongation rate. The values of stress and strain at yield increase slightly with increasing elongation rate, while the strain at break decreases markedly. The short-term creep tests were conducted at temperatures extending from 20 to 200°C. The glass-transition temperature was found to be about 155°C. The creep of PEEK is greatest at temperatures above 130°C. In the glass region the time dependence of the deformation is much weaker. It has been found that the time-temperature relation for PEEK corresponds well with its thermorheological simplicity in the temperature range investigated. The data on the temperature shift factor below and above the glass-transition temperature may be fitted separately to the Arrhenius and Williams-Landel-Ferry (WLF) equations, respectively. The long-term creep tests show that PEEK has excellent creep resistance at room temperature. After 14-month tests at a stress level of 30 MPa the total strain exceeds the instantaneous elastic strain only by a factor of 1.15.Institute of Polymer Mechanics. Latvian Academy of Sciences, 23 Aizkraukles St., LV-1006 Riga. Latvia. Department of Polymeric Materials, Chalmers University of Technology. S-412 96 Gothenburg, Sweden. Published in Mekhanika Kompozitnykh Materialov, No. 6, pp. 734–746, November–December, 1997.     

Variation of Poisson's ratio in the course of a complete one-dimensional creep cycle

By solving the system of differential equations of a standard solid, expressions are obtained for determining Poisson's ratio with allowance for the characteristics of volume and shear strain. For a material having values of Poisson's ratio in creep (0)<0.5 and ()=0.5, Poisson's ratio in reverse creep (t)^rev>0.5. The volume strains that occur at the beginning of reverse creep have the same magnitude as the creep volume strains, but the opposite sign. The law of disappearance of the volume strains is the same for creep and reverse creep.Mekhanika Polimerov, Vol. 4, No. 2, pp. 227–231, 1968     

Limiting states of rigid polyvinyl chloride in creep

Creep tests at constant stresses have been carried out on crystalline polyvinyl chloride (PVC) at 16, 40, and 60° to determine its limiting states (i.e., states defining its creep strength, complete cessation of creep strain, and the boundary of the range of invariance of the mechanical properties), which are shown to be described by exponential functions. An approximate method of determining creep is developed; in this method the creep strength is defined as the stress corresponding to the point of intersection of the limiting equilibrium curves and the stress/time-to-rupture curves.Mekhanika Polimerov, Vol. 1, No. 3, pp. 81–86, 1965     

Solution of the problem of the plane deformation of a tube made of physically nonlinear quadratic viscoelastic material

An exact solution is obtained for the problem of the plane deformation of a tube of quadratically nonlinear viscoelastic material characterized by four kernels. For given boundary pressures the solution contains functions determined from simple creep and relaxation tests for stresses and strains lying in the region of linearity of the relation. In accordance with the method of approximations for nonlinear materials [9], an approximation is given for a series of convolution integrals of increasing multiplicity in transforms and inverse transforms together with an error estimate.Moscow Institute of Electronic Engineering. Translated from Mekhanika Polimerov, No. 1, pp. 117–123, January–February, 1973.     

Creep of thermally cycled polyethylene

A method for determining creep strains of polymer tube specimens (in three mutually perpendicular directions) tested at constant and cyclically changing temperatures is described. The equipment for the programmed variation of specimen temperature and for the application of complex loads is described. The application of the method is illustrated by the results of creep tests on tube specimens of low-density polyethylene (LDP). The creep strain _c of thermally cycled specimens is noticeably larger than that of specimens tested isothermally at the median temperature of a given thermal cycle, and in time it becomes larger than the strain of specimens tested isothermally at the maximum cycle temperature.Mekhanika Polimerov, Vol. 3, No. 4, pp. 676–685, 1967     

Convergence rate of the solution toward boundary layer solution for initial-boundary value problem of the 2-D viscous conservation laws

In this paper, we study the large time behavior of the solution to the initial boundary value problem for 2-D viscous conservation laws in the space x ? bt. The global existence and the asymptotic stability of a stationary solution are proved by Kawashima et al. [1]. Here, we investigate the convergence rate of solution toward the boundary layer solution with the non-degenerate case where f′(u₊) − b < 0. Based on the estimate in the H² Sobolev space and via the weighted energy method, we draw the conclusion that the solution converges to the corresponding boundary layer solution with algebraic or exponential rate in time, under the assumption that the initial perturbation decays with algebraic or exponential in the spatial direction.     

Modelling the static stress–strain state around the fan-structure in the shear rupture head

The mathematical model of an equilibrium fan-structure in the interface between two elastic blocks, simulating the shear rupture head in a hard rock under high confining pressure, is constructed. The stress–strain state far from the fan-structure is analyzed with the help of a solution of the problem on edge dislocation. The fan length is estimated using this solution. The model of formation of two oppositely directed fans due to the localized action of tangential stress, which pushes two edge dislocations with antiparallel Burgers vectors, is proposed. In complete formulation, the problem on an equilibrium fan-structure in the interface between infinite elastic half-planes is analyzed by means of original method of superposition of dislocations, leading to two nonlinear integral equations in the fan zone. To solve them numerically, the method of successive approximations is applied. Based on this method, fields of stresses and displacements around the equilibrium fan modelling of a deep-seated shear rupture in the seismogenic zone of the Earth’s crust are computed. Such fields can be used, when setting the initial data in the analysis of dynamics of the fan-shaped mechanism.     

A power series solution for vibration and complex modal stress analyses of variable thickness viscoelastic two-directional FGM circular plates on elastic foundations

In the present paper, a power series solution is developed for free vibration and damping analyses of viscoelastic functionally graded plates with variable thickness on elastic foundations. It is assumed that the material properties of the functionally graded material (FGM) vary in the transverse and radial directions, simultaneously. Therefore, the presented solution can be employed for the transversely-graded and radially-graded viscoelastic circular plates, as special cases. In addition to the edge conditions, the plate may be resting on a two-parameter elastic foundation. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A sensitivity analysis including effects of various edge conditions, geometric parameters, coefficients of the elastic foundation, parameters of the functionally graded material, and material loss factor is carried out. In the present paper, concept of the complex modal stresses of the viscoelastic plates is discussed in detail.     

Creep of a thermoplastic cylindrical shell under axisymmetric loading

The solution of the problem of creep of an axisymmetrically loaded thermoplastic cylindrical shell is considered. The strains and stresses for the zero-moment zone and with allowance for the edge effect are predicted on the basis of Kachanov's variational method using a computer. An algorithm is constructed for polyethylene and PVC shells at various values of the load. The analysis of the results obtained is illustrated by the calculation data for individual variants of the program.Leningrad Mozhaiskii Military Engineering Academy. Translated from Mekhanika Polimerov, No. 3, pp. 512–518, May–June, 1969.     

Effect of aligned magnetic field on the steady viscous flow past a circular cylinder

The steady viscous incompressible and slightly conducting fluid flow around a circular cylinder with an aligned magnetic field is simulated for the range of Reynolds numbers 100 ? Re ? 500 using the Hartmann number, M. The multigrid method with defect correction technique is used to achieve the second order accurate solution of complete non-linear Navier–Stokes equations. The magnetic Reynolds number is assumed to be small. It is observed that volume of the separation bubble decreases and drag coefficient increases as M is increased. We noticed that the upstream base pressure increases slightly with increase of M whereas downstream base pressure decreases with increase of M. The effect of the magnetic field on the flow is discussed with contours of streamlines, vorticity, plots of surface pressure and surface vorticity.