Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Fractal approach to the intephase in filled polymers

A fractal model of a filled polymer is proposed. The model allows us to estimate quantitatively the volume of an interphase, to take into account geometrical factors influencing the character and the interphase adhesion level, and to predict the mechanical strength of interfacial bonds. This makes it possible to calculate the size of the critical structural defect and the mechanical properties of filled polymers, which are in agreement with the experimental data. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 1, pp. 3–32, January–February, 2000.     

Viscoelastic properties of a silica-filled styrene-butadiene rubber under uniaxial tension

A model composite — a silica-filled styrene-butadiene rubber with a various filler volume content — was tested for creep and creep recovery at different tensile load levels to evaluate the effect of viscoelasticity on the deformational properties of filled rubbers. A constitutive equation describing the diagram of equilibrium deformation of the composite in quasi-static loading was obtained from an analysis of creep test results. The equation was common for the filled rubber at different filler content. The existence of such a curve has been confirmed by experimental unloading diagrams registered in cyclic loading-unloading tests. It is shown that the phenomenological equations obtained from an analysis of creep recovery test results can be used successfully for describing the hysteresis loops of second and subsequent cycles for cyclic tests with a constant maximum stretch ratio.     

Effects of temperature and moisture on the mechanical properties of polyester resin in tension

The effect of environment on the physical and mechanical properties of composite materials in some cases is determined by the environmental sensitivity of the binder. The results of experimental investigation of the deformability and strength of polyester resin, widely used as a binder in composites, upon the action of stationary and quasi-stationary loads, temperatures, and moisture are presented. The ranges of acceptable values of these services factors are determined. The elastic modulus and tensile strength of the material are obtained from quasi-static tests. The viscoelastic behavior of the resin is investigated in creep tests. From the results of a short-term experiment with stepwise loading up to failure, it is found that the creep of specimens with a moisture content of 0.14% can be described by a linear viscoelastic model for stresses up to 20 MPa (two thirds of the strength). The action of single loading impulses is summarized according to the Boltzmann superposition principle. The temperature and absorbed moisture are considered as factors accelerating the relaxation processes in the material. The creep activation under the action of these factors is described using the methods of time-temperature and time-moisture equivalence. The results of short-term creep tests allow us to determine the relaxation characteristics of the material in stationary conditions. The long-term creep under close-to-service conditions is predicted using these data and quite good agreement with the control test is obtained. The sensitivity of the material characteristics (strength, elastic modulus, and creep strain) to the action of temperature and moisture is estimated. The creep strain is most sensitive to the action of environmental factors. For a fully saturated material (moisture content 1.64 wt.%), after one hour creep, this strain four times exceeds that of a dry one. The same growth in deformability is caused by an 18°C increase in temperature. A quantitative comparison of the characteristics of polyester and epoxy resins allows us to choose the binder for composites and to estimate the expected environmental effect. Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 395–406, May–June, 2000.     

Averaging Special Values of Dirichlet <Emphasis Type="Italic">L</Emphasis>-Series

In this paper we derive estimates for weighted averages of the special values of Dirichlet L-series which generalize similar estimates of David and Pappalardi [1]. The author is partially supported by NSF grant DMS-0090117. 2000 Mathematics Subject Classification: Primary–11M06; Secondary–11G05     

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.     

Dependence of thermooxidative aging parameters on composite properties

An analytical relationship between the thermooxidation rate constants and mechanical properties of composite materials under isothermal and dynamic conditions is obtained. With the example of epoxy-based composites, it is shown that the kinetic parameters of thermooxidation can be used to predict the internal stresses and breakdown voltage of coatings. The calculated drop in the impact toughness exceeds its experimental value by 30%, while the calculated relative breaking elongation is 1.5–2 times greater than the experimental one. A considerable decrease in these indices is observed at a loss of 0.1–1 wt.% of volatile products of thermooxidation. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 237–248, January–February, 2000.     

Effect of aging of the binder on the creep of polymer concrete

Two polyester concretes with diabase and marble fillers and aggregates are used as examples to illustrate the possibility of using a structural approach to evaluate the creep of the composite in the initial state and after preliminary aging under laboratory conditions for a period of 12–13 yrs. Experimental study of the creep of polymer concrete and its structural components (resin and binder) after preliminary aging at elevated temperatures (60, 90°) established that the change that occurs in viscoelastic compliance with aging conforms to the analogy principle with a reduction function that depends on aging temperature and time.Institute of Polymer Mechanics. Latvian Academy of Sciences Riga, Latvia. Central Laboratory of Physico-chemical Mechanics Sofia. Bulgaria. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 787–794, November–December, 1996.     

Effect of aging creep of polyestermalein resin/mineral filler composites

Long-term (More than 20 years) creep under compression of two polymer concretes, polyestermalein resin/mineral filler composites, was studied. The concretes differ with diabase filler size (d=5–10 mm and d=10–20 mm). It was shown that nonlinearity of viscoelastic properties of concrete increases as the size of filler particle decreases. Aging of the polymer concretes reduces their viscoelastic compliance and shortens the time interval necessary to reach equilibrium conditions under stable loading state.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Institute of Theoretical and Applied Mechanics of the AS CR, Prague 9, Prosecká 74, Czech Republic. Central Laboratory of Physical-Chemical Mechanics of the BAS, Sofia 1113 Acad. Bontchev Street, IV km, Bl. 1. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 2, pp. 190–194, March–April, 1995.     

A Dedekind σ-Complete Banach Lattice into which all Bounded Operators are Regular

We give an answer to a question of Abramovich–Wickstead asked in [Quart. J. Math. Oxford (2), 44 (1993), 257–270] under the axiom ‘measurable cardinal exists’. Mathematics Subject Classification (2000): Primary. 47B60     

Correlation between the strength of fiber-reinforced plastics and the adhesive strength of fiber—Matrix joints

The relationship between the strength (σc) of unidirectional fiber-reinforced plastics in different stressed states and the interfacial strength of their components is investigated. The shear adhesive strength (τ0) of fiber—matrix joints determined by the pull-out technique is used as a measure of the interfacial strength. To obtain the correlation curves betweenσc andτ0, the experimental results are used, where both the plastic and adhesive strength change under the influence of a single factor. In this case, such factors are the fiber surface treatment, nature and composition of polymer matrices, and test temperature. It is shown that the strength of the glass, carbon, and boron plastics increases practically linearly with increased interfacial strength. Such a behavior is observed in any loading conditions (tension, shear, bending, and compression). Sometimes, a small (10–20%) increase in the adhesive strength induces a significant (50–70%) growth in the material strength. Therefore, the interface is the “weak link” in these composites. The shape of theσc—τ0 curves for composites based on the high-strength and high-modulus aramid fibers and different thermoreactive matrices depends on the nature of the fiber and the type of stress state. In many cases, the composite strength does not depend on the interfacial strength. Then, the fiber itself is the “weak link” in these composites. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 291–304, May–June, 2000.     

Comparative Studies on the Mechanical Properties of a Thermoset Polymer in Tension and Compression

Results of an experimental investigation into the mechanical properties of a polyester resin in tension and compression are reported. Features of the stress-strain curves obtained are discussed. Data on the elastic modulus, Poisson ratio, and volume strains are obtained. The results of creep behavior of the material in tension and compression are also presented. It is found that the time-dependent creep obeys a power law, but the nonlinear stress dependence can be described by using the hyperbolic sine function. The effect of load type (tension or compression) on the nonlinearity of the creep is analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 5, pp. 633–650, September–October, 2005.     

聚氯乙烯接近玻璃化转变温度时的蠕变行为研究

利用动态力学分析仪,详细研究了小应力作用下聚氯乙烯（PVC）接近玻璃化转变温度（63℃）时的短期蠕变性能．根据Struik-Kohlrausch (SK)方程及Struik移位方法,分析了物理老化对PVC瞬时蠕变柔量的影响,并提出了基于多松弛机制的新模型定量描述初始蠕变柔量、松弛时间和形状因子．结果表明:SK方程虽可表征不同老化时间下PVC的蠕变性能,但通过Struik移位方法却无法获得理想的主曲线,且初始蠕变柔量、松弛时间、形状因子和蠕变率均受物理老化显著影响,并在双对数坐标下随老化时间呈明显的非线性变化;新模型不仅揭示了物理老化控制参量的演化规律,而且极好地预测了PVC在物理老化进程中的高温蠕变行为．     

Effect of interphase layers on the elastic properties of a carbon-nanotube-reinforced composite

A variant of a stepwise analysis of the elastic properties of a carbon-nanotube-reinforced composite with account of the effect of interphase layers between the nanotubes and the polymer matrix is reported. The preliminary calculation of the elastic constants of a structural element incorporating a nanotube and an interphase layer and the subsequent calculation of independent elastic constants of a composite with such transversely isotropic structural elements oriented in one direction are both performed by using the Mori–Tanaka theory of an equivalent medium. The calculations are carried out for a wide range of ratios between the elastic moduli of the interphase layer and matrix. The elastic constants of a composite with randomly oriented nanotubes are obtained by using the method of orientational averaging.     

Certain Families of Elliptic Functions Defined by <Emphasis Type="Italic">q</Emphasis>-Series

We introduce certain families of elliptic functions involving the Weierstrass ℘-function via q-series systematically and investigate their analytic and algebraic properties. Especially, we give examples of non-linear algebraic ordinary differential equations satisfied by some such elliptic functions. 2000 Mathematics Subject Classification: Primary–11M36, 33E05     

Estimation of the long-term strength of polymer materials under arbitrary loading histories

A nonlinear version of the phenomenological theory of long-term strength of polymer materials (viscoelastic bodies) is proposed. It is based on the introduction of a function accounting for the damage accumulation connected with changes in the load intensity. The form of this function may be determined from the results of testing the material with a load changing with time in a certain way, for instance, periodically. As a parameter, the function contains the rate of the changing load or the frequency for periodic loads. For a quasi-isotropic material, the basic relationships of the theory proposed are generalized to the case of combined stresses. The durability (failure time) calculations of the material based on this theory are compared with experimental data for a number of polymer and composite materials in a wide range of loading modes. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 5, pp. 585–594, September–October, 1999.     

Multifibre polymer composites: Prediction of deformation and thermophysical properties

Conclusions A theoretical and experimental investigation was carried out to examine the possibilities of a structural approach for prediction of elastic constants, creep functions and thermophysical characteristics of hybrid polymer composites reinforced with anisotropic fibres of several types. The theoretical solutions were obtained by generalizing the self-consistent method for the case of a three phase model. The effects of brittle fibre breakdown under tension in the direction of reinforcement of a unidirectional hybrid composite were studied under conditions of a short-term loading and a long-term creep. It has been shown that a creep of viscoelastic fibres plays a principal role in creep of the hybrid composite. It is just this creep that significantly increases the fibre damage during creep of the composite.A variant of the solution has been proposed for predicting the thermorheologically complex behavior of hybrid composites containing not only elastic but also viscoelastic thermorheologically simple components with different temperature-time shift factors. The peculiarities of thermal expansion of hybrid composites and the possibilities for a purposeful control of thermal expansion coefficients by hybridization were studied. The considered thermal interval included a region of transition of the polymer matrix from a glass state into a viscoelastic one.The control tests were performed for specimens of organic/glass, organic/carbon, glass/carbon and organic/boron polymer composites with different ratios of fibre volume contents. On the whole, the obtained accuracy of predicting the characteristics of the examined hybrid composites may be considered as acceptable for engineering applications.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 299–313, May–June, 1994.     

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.     

Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials

The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 195–214, March–April, 2000.     

Determining <Emphasis Type="Italic">p</Emphasis>-values for systems cointegration tests with a prior adjustment for deterministic terms

Following Doornik (J Econ Surv 12:573–593, 1998) I present a procedure to approximate the asymptotic distributions of systems cointegration tests with a prior adjustment for deterministic terms suggested by Lütkepohl (Econometrica 72:647–662, 2004), Saikkonen and Lütkepohl (Econometric Theory 16:373–406, 2000a, J Business Econ Stat 18:451–464, 2000b, Time Series Anal 21:435–456, 2000c) and Saikkonen and Luukkonen (J Econ 81:93–126, 1997). These tests rely upon different assumptions as to the inclusion of deterministic components such as a constant, a linear trend or a level shift. The asymptotic distributions, which are functions of Brownian motions, are approximated by Gamma distributions. Only estimates of the mean and variance of the asymptotic test distributions are needed to fit the Gamma distributions. Such estimates are obtained from response surfaces. The required coefficients to compute the asymptotic moments are presented in this paper. Via the fitted Gamma distributions one can, then, easily derive p-values or arbitrary percentiles.