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.     

Effect of mineral fillers on properties of composite matrix material

The influence of mineral fillers on thermomechanical properties of matrix material of composites is investigated. Different methods to determine elastic properties and thermal expansion coefficients of composite materials have been considered and compared. Injection moulded polyester samples containing varying concentrations of talc filler are tested and properties such as Young 's modulus, thermal expansion coefficients, and volumetric shrinkage during cure are measured. Results obtained by theoretical models and from experiments are compared and discussed.To be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 435–445, July–August, 1995.     

Effect of the structure of a polymer matrix and its area of contact with the surface of the filler on the rigidity of a polyethylene composite

The distribution of the orientation of the macromolecules over the wall cross section of a filled polyethylene tube is analyzed. A direct proportionality is established between the degree of orientation (estimated from the shrinkage) and the elastic modulus. The effect of various fillers on the melting and crystallization of low-density polyethylene is considered. For a specified filler concentration the elastic modulus of the composites depends very considerably on the relative area of contact between the polymer matrix and the surface of the filler.Institute of the Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 387–391, May–June, 1974.     

Stress state calculation of a repair of a uni- or biaxially loaded laminate structure

The growing use of fibre-reinforced plastics requires adequate maintenance and repair behavior of these materials compared with the traditional metallic alloys. Due to the low tensile strength of fibre-reinforced materials perpendicular to the fibre direction, a bonded repair is the most suitable one and it will be considered in this paper. Based on the classical lamination theory, a model for the calculation of the shear stresses in a bonded repair under biaxial loading is developed. In addition to a simple model neglecting the stresses perpendicular to the laminate-plane, which is applied for a uni- and biaxial load case, a more complex model taking these stresses into account is developed. These models allow an estimation of whether a damaged shell can be repaired or must be replaced.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. 351–362, May–June, 1995.     

Nonlinear dynamics of inelastic failure of damaged layered systems

A method of solution is proposed and processes of the formation and development of a failure zone in piecewise-homogeneous rod during impact loading were analyzed. Such properties as being damageable and healing of defects as well as compliance of a barrier are taken into account for the first time. Deformation of the barrier is taken into account by means of a model of a Winkler foundation. The fulfillment of the known failure criterion at the failure front is assumed. The solution is reduced to a system of quasi-linear equations which are hyperbolic in the narrow sense, the right side of which contains integral terms of the hereditary type. As a result of numerical realization for the case of a bilayer rod, when the region contacting the barrier is damaged, it was found that the place and time of formation of the failure zone and time of complete failure depend substantially on compliance of the barrier as well as nonlinearity of the material.Presented at the Ninth International Conference on Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 640–645, September–October, 1995.     

An extended class of minimax generalized Bayes estimators of regression coefficients

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama, W.E. Strawderman, A new class of generalized Bayes minimax ridge regression estimators, Ann. Statist., 33 (2005) 1753–1770] to include non-monotone shrinkage functions.     

New mathematical model for nonuniform deformation of composites

A new mathematical model is suggested for nonuniform deformation of composite materials valid for arbitrary external load gradients. As a basis stochastic equations are suggested for the statics of an elastic microinhomogeneous two-component material with volumetric forces differing from zero. Expressions are obtained for all coefficients in terms of elastic constants of the components and geometric parameters of the structure.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 310–318, May–June, 1995.     

On the problem of mapping deep cracked zones by using seismic observations

The problem of conversion of a slow wave propagating in a cracked collector into a tube wave in a borehole intersecting the collector is considered. The influences of the collector's porosity and of the parameters of the background medium on the dynamics of the tube wave are investigated. It is demonstrated that the elastic response of the medium to the wave incident on the borehole consists of a propagating and a diffusive field.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 123–128.This work was supported by the Russian Foundation for Basic Research under grant Nos. 96-05-66207 and 96-01-00666.     

An estimation of reliability of unidirectional composites by catastrophe theory

In the present work, interest is centered on the theory of fracture and practical approaches to reliability estimation of unidirectional composite materials which are based on it. Fracture mechanics is considered not as a theory of macrocracks but as mechanics of fracture mechanisms of the composites with allowance made for probability estimation. A model of composite material with fibers eliminated from the carrying scheme and parameters specific to the stress-strain-damage state (SSDS) was considered. According to the model, during loading, self-accelerated energy rise is accounted for by structural damages growth — the catastrophe takes place. The model allows us to calculate the critical stress. The composites redistribute forces from overloading zones to neighboring ones by microstructural deformations and damages. It is the effect of reservation of carrying ability. Due to this effect, low-value probability of fracture is sufficiently less for the composite than for homogeneous materials. The approach allows us to evaluate the reliability function for both static loading and fatigue.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Computing Center of the Russian Academy of Sciences, Krasnoyarsk, Russia. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 539–548, July–August, 1996.     

SO(N) invariant Wess-Zumino action and its quantization

A consistent quantization procedure of anomalous chiral models is discussed. It is based on a modification of the classical action by adding Wess-Zumino terms. The SO(3) invariant WZ action for the SU(3) model is constructed. Quantization of the corresponding modified theory is considered in detail for N=3.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 2, pp. 270–291, November, 1995.     

Lattice gauged principal chiral field at largeN

The lattice model of a principal chiral field interacting with gauge fields which have no kinetic term is considered. The complete set of equations for collective field variables is derived in the large N limit. The continuum limit and the phase structure of the model are discussed.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 25–31, July, 1995.     

Dynamic compressive strength of epoxy composites

The strength of laminated and unidirectionally reinforced composite materials was investigated in conditions of dynamic uniaxial compression with a strain rate of 50–1000 sec^–1 using the split Hopkinson pressure bar method. It was shown that in conditions of dynamic compression, glass/epoxy, aramid/epoxy, and carbon/epoxy composites exhibit elastic-brittle behavior with anisotropy of the strength and elastic properties. The effect of the strain rate on the strength characteristics of fiberglass-reinforced plastics was demonstrated.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 776–782, November–December, 1995.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).     

Terminal defects in crystalline polyethylene

Conclusions 1. Possible modes of transverse movement of terminal defects in crystalline polyethylene have been investigated for the three-dimensional case. It has been found that the probability of aggregation of two columns of monovacancies by means of their transverse movement decreases rapidly with increase in the initial distance between defects.2. The process of decrease in volume of a column of vacancies during compression has been investigated. A dependence of the degree of compression of a vacancy on the angle between the external force and the plane of zigzag of the chain has been found.3. Three positions of stable equilibrium of doubling of the three-dimensional model of polyethylene containing a series of vacancies have been observed during loading of the simple shear type.For Communication 1, see [1].Institute for Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 588–595, July–August, 1978.     

Creep simulation in polymer matrix — disperse filler composites

The deformation properties of composites with disperse fillers in close to maximum amounts were investigated. Two types of matrices were selected: epoxy resin with high structural stability in filling, and a crystalline polymer-trioxane-dioxolane copolymer. Materials with a high and low relative surface area-diatomite and ceramic-were used as fillers. The elastic properties were simulated with the Kerner model and creep was simulated with its viscoelastic analog. The model was extended to a matrix-filler-buffer layer model. The possibility of estimating the part of the matrix entering the pores of the filler was examined. Differences in the use of the structural models in predicting elasticity and viscoelasticity were examined. The best results in describing creep were obtained for epoxy resin-ceramic filler composites which have the least interaction between matrix and filler. The possibility of estimating the change in the degree of crystallinity of the matrix and formation of buffer layers in filling with active fillers was examined.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 6, pp. 754–768, November–December, 1995.     

Shrinkage properties of some rigid polymers

Experimental results from a study of the shrinkage of polymers based on epoxy and polyester resins during the polymerization process are presented. The shrinkage was determined by wire strain gauges from the moment of transition of the polymer into a solid medium. An equation has been found which satisfactorily describes the laws governing chemical shrinkage with time."Plastopolimer" Scientific-Manufacturing Union, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 236–240, March–April, 1972.     

Asymptotic expansions associated with the jackknife functional. II

This paper is a sequel to part I [Ukr. Mat. Zh.,47, No. 4, 443–452 (1995)]. By using the results of the first part, we obtain the initial terms of the asymptotic expansions of the bias and variance for the jackknife estimator of the variance of the error of observations in a nonlinear regressive model.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 731–736, June, 1995.The present work was financially supported by the Ukrainian State Committee on Science and Technology.     

Analysis of the anisotropic properties of honeycomb sandwich plates

A mathematical model has been described and an approach proposed to the diagnostics of the anisotropic properties of the relative elasticity constants of three-layer (sandwich) plates with a honeycomb filler. Compact analytical relationships between the anisotropy coefficients and the geometrical dimensions of the cells have been obtained. A practical approach has been proposed for the selection of rational parameters of the honeycomb structure, at which its anisotropic properties would be in the chosen region of the functional space. The conditions have been formulated at which the constructive anisotropy, inherent to honeycomb structures, degenerates to isotropy for some relative elastic constants.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. 482–487, July–August, 1995.     

Deformability and load-carrying capacity of netted composite rod assemblies with metal fittings

A technology is proposed for making netted rod assemblies with metal joints 3–5 times lighter than existing comparable structures. A procedure was developed for winding assemblies out of carbon-fiber-reinforced plastic (UKN-5000 and binder EKhD-MK). Results are presented from a study of the strain characteristics and load-carrying capacity of assemblies with different reinforcement schemes for different conditions of static damage. It is shown that the design of netted rod assembly proposed here is significantly superior to all known analogs with respect to specific stiffness characteristics and provides great dimensional stability in the case of unilateral heating of the product. The method is most effective if used to develop framework-type structures for use in space — platforms, telescope and antenna supports, and masts.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. 3, pp. 387–392, May–June, 1995.     

Nonsymmetrical temperature fields and stresses in cylinders made of nonuniform composites

The class of problems for determining nonsymmetrical temperature fields and stress in thick-walled hollow nonuniform cylinders is considered. A resolution set of differential equations is constructed for determining steady-state temperature fields, stresses, and displacements in asymmetrically heated cylinders which are arbitrarily nonuniform with respect to thickness with one plane of elastic symmetry. An approach is suggested for effective numerical solution of this class of problems. Problems are analyzed for thick-walled cylinders whose relative volume content of reinforcing elements varies in the radial direction. Known relationships of composite mechanics are used in order to find effective mechanical and thermophysical parameters for the material. Examples are provided for solving specific problems which point to the requirement of considering nonuniformity with respect to thickness.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. 494–500, July–August, 1995.     

Experimental study of the contribution of interfacial friction to the deformation resistance of particle-reinforced polymers

A study has been made of the dissipative properties of heavily filled elastomers as influenced by friction of the elastic matrix on the surface of the solid filler particles. In order to model the frictional surface, specimens were predamaged by cyclic deformation, with strain amplitudes sufficient to cause separation of the matrix from the filler. The predeformation operation was performed by means of a mechanical system having individual particle-matrix bonds, so that it was possible to evaluate the contribution of interfacial friction to the resistance of the polymer. When external pressure was applied to the specimens, the width of the hysteresis loop increased with increasing pressure, obviously reflecting an increase of the surface friction in the matrix. It was established that for a given volumetric fill, the dissipation of mechanical energy increased with decreasing particle size (with increasing frictional surface area). The significant influence of interfacial friction on the level and rate of strain relaxation was demonstrated experimentally.Paper presented at the 9th International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompositnykh Materialov, Vol. 31, No. 5, pp. 579–583, September–October, 1995.