Analysis of elastomeric composites based on fiber-reinforced systems 3. Two-directional composites

Results of investigation of deformation of elastomeric composite materials with a two-directional reinforcement scheme are presented. The study is performed on the basis of a structural macroscopic theory. The matrix of the composites analyzed is of a poorly compressible material. The fibers of both reinforcing systems are simulated as compressible bodies. Dependences of the parameters of tensile and shear strains on the strain values for different geometries of fiber arrangement are obtained.State Metallurgical Academy of Ukraine, Dnepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 479–492, May–June, 1999.     

Analysis of elastomeric composites based on fiber-reinforced systems. 1. Development of design methods for composite materials

A method for calculating the elastic properties of fiber-reinforced composites is discussed. The method is based on the structural macroscopic theory for reinforced media [1, 2], which can be used for analysis of stiff and soft composites. As a measure of the elastic properties of composites, the parameters of macroscopic deformations of the base system of Cartesian coordinates are used, with the axes oriented in a certain direction relative to the general reinforcement and loading field. The corresponding macrostresses in the loaded composites are found by a solution of the microboundary problem for a composite macroelement with sides parallel to reinforcement planes of the system. The microboundary-value problem is multiply connected and is formulated based on the information about the homogeneous field of macroscopic displacements specified by the parameters of macroscopic deformation. The problem is solved using the local system of coordinates whose axes are directed along some of the reinforcement trajectories.State Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 733–745, November–December, 1998.     

Structural theory of elastomeric composites based on fiber systems — Invariant description

A three-dimensional theory of elastomeric composites with elastomeric matrices reinforced by systems of fibers is presented. The theory is based on a structural approach in which the matrix and the reinforcement of the composite are considered separately without reduction to a medium having continuously changing characteristics. The approach is based on the idea of a vector field of macroscopic displacements given by the positions of the axial lines of the fibers in the curret (deformed) configuration of the composite. The vector field determines the current macroscopic configuration, the tensor fields of the measures of macroscopic strain, and the field of the macroscopic stress tensor in the composite. The displacement, strain, and stress fields in the elastomeric matrix and the fibers of the reinforcing systems are regarded as derivatives of the field of macroscopic displacements of the medium. Relations are presented to describe the kinematics of the fibers in the current configuration of the composite, including the evolution of their orientation and the frequency of their planar and spatial distribution. Equations are obtained for the macroscopic motion of the fiber-reinforced matrix, and the dynamic variational principle that governs this motion is established. The elastic macroscopic potential of the matrix is found and related to the components of the macroscopic stress tensor. The procedure to be followed in constructing the constitutive equations of the composite is described. The proposed system of equations, relations, and algorithms is closed and can be used to solve problems involving the deformation of products made of fiber-reinforced elastomers and the creation of elastomeric composite products, based on fiber systems, that possess the requisite properties.     

Pultrusion mechanics of fiber-reinforced thermoplastic composites

The associated problem of the rheology of a thermoplastic polymer melt during the pultrusion of fiber-reinforced composites in a plane-slotted die is resolved. The permeabilities of a stochastic fibrous system are determined for the case of a nonlinear (exponential) rheological model of the melt. The pressure distribution in the pultrusion tool is calculated with allowance for the permeability of the fibrous system. The dependence of the pultrusion force on the viscous properties of the melt and on the pull rate of the fibrous layer is established.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. 547–554, July–August, 1995.     

Autohesion of technical elastomeric systems

The compatibility of various plasticizers with the polymers SKN-40 and P-200 and the autohesion of the elastomeric systems obtained by incorporating various plasticizers into these polymers have been studied. For the systems investigated, the strength of autohesion is found to be directly proportional to the compatibility of elastomer and added plasticizer.Mekhanika Polimerov, Vol. 1, No. 2, pp. 15–20, 1965     

Estimation of interface damage of fiber-reinforced composites

The estimation of interface damage of fiber-reinforced composites based on the propagation constants of coherent waves is studied in this paper. First, the relation between the interface damage and the propagation constants is investigated by using the theory of multiple scattering. Next, single and multiple scatterings in the composites in the case of incident P, SV, and SH waves are considered. The propagation constants of coherent waves are computed numerically, and the influence of interface damage on them is discussed. Then, based on the relation between the propagation constants and the interface damage, an inverse method to estimate the interface damage is proposed. Finally, a numerical example is given. The numerical results are obtained by using synthetic experimental data and the genetic algorithm. It is shown by the numerical example that the interface damage can be approximately estimated from the wave propagation constants measured with various degrees of accuracy.     

Interlaminar fracture toughness of graphite fiber-reinforced polyimide composites

Conclusion The present study has proved the effectiveness of the application of viscoelastic polymers with increased fracture toughness to graphite/polyimide composites interlaminar fracture toughness improvement. Thermoplastic polysulphone film and thermoresistant structural adhesive have proved to be inherently more effective for composites' delamination resistance growth than maleimide resin toughening and structural modification. The former inevitably results in increase of the honeycomb delamination resistance (Fig. 1) and its durability.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 6, pp. 848–852, November–December, 1994.     

Averaging the electrical properties of fiber-reinforced metal composites

Using the regular structure model, we average the electrical properties of unidirectional fiber-reinforced metal composites and propose procedures for determination of the effective electrical conductivity tensor of these materials. For the general case of packing of fibers of arbitrary cross section, the problem is reduced to calculation of some functionals determined in solutions of the integral equation of the corresponding boundary current problem for the structure. In the special case of symmetric packing of fibers of circular cross section, the solution is written in the form of series in elliptic functions.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 533–539, July–August, 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.     

Predicting the elastoplastic response of fiber-reinforced metal matrix composites

This paper aims to investigate the effect of microstructure parameters (such as the cross-sectional shape of fibers and fiber volume fraction) on the stress–strain behavior of unidirectional composites subjected to off-axis loadings. A micromechanical model with a periodic microstructure is used to analyze a representative volume element. The fiber is linearly elastic, but the matrix is nonlinear. The Bodner–Partom model is used to characterize the nonlinear response of the fiber-reinforced composites. The analytical results obtained show that the flow stress of composites with square fibers is higher than with circular or elliptic ones. The difference in the elastoplastic response, which is affected by the fiber shape, can be disregarded if the fiber volume fraction is smaller than 0.15. Furthermore, the effect of fiber shape on the stress–strain behavior of the composite can be ignored if the off-axis loading angle is smaller than 30°.     

Predicting the onset of delamination in layered fiber-reinforced composites

In this paper, composite structures are considered which consist of several layers of carbon fiber reinforced plastics (CFRP). For such layered composite structures, delamination constitutes one of the major failure modes and hence predicting its initiation is essential for their design. Evaluating stress-strength relation based onset criteria requires an accurate representation of the through-the-thickness stress distribution, which can be particularly delicate in the case of shell-like structures. Thus, in this paper, a solid-shell finite element is utilized, which allows for incorporating a fully three-dimensional material model, still being suited for application to thin structures. Moreover, locking phenomena are cured by using both the EAS and the ANS concept, and numerical efficiency is ensured through reduced integration. The proposed anisotropic material model accounts for the material's micro-structure by using the concept of structural tensors. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strong influence of a small fiber on shear stress in fiber-reinforced composites

In stiff fiber-reinforced composites, it has been known that the shear stress increases at the rate of as the distance ? between adjacent fibers approaches 0. This paper reveals a strong influence of a combination of a triple fiber, as well as the distance between a pair of fibers, on the blow-up so that the stress concentration can be significantly accelerated by adding a small fiber in-between fibers. Specifically, if a fiber F₂ with a small diameter δ is located in-between fibers F₁ and F₃, ?₁=dist(F₁,F₂) and ?₂=dist(F₂,F₃), then the stress blows up at the exact rates of and between F₁ and F₂ and between F₂ and F₃, respectively. This estimate still holds even when a part of F₂ overlaps with F₃. The magnification factor yields the enormous increase in the stress that greatly surpasses the expectancy by previous methods.     

Averaging the electrical properties of fiber-reinforced metal composites with hollow fibers

We consider the problem of determining the effective electrical conductivity tensor of a metal composite with ideal (biperiodic) packing of the fibers. We assume that the transverse cross sections of the fiber are concentric circular rings and have identical electrical conductivity. We look for a solution in the form of a series in Weierstrassian elliptic functions with subsequent averaging of the electrical properties of the structure.Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 377–383, May–June, 1997.     

The effect of interphase on residual thermal stresses. 2. Unidirectional fiber composite materials

In real composite materials an additional phase may exist between the fiber and the matrix. This phase, commonly known as the interphase, is a local region that results from the matrix bonds with the fiber surface or the fiber sizing. The differing thermal expansions or contractions of the fiber and matrix cause thermally induced stresses in composite materials. In the present study, a four-cylinder model is proposed for the determination of residual thermal stresses in unidirectional composite materials. The elastic modulus of the interphase is a function of the interphase radius and thickness. The governing equations in terms of displacements are solved in the form of expansion into a series [1]. The effective elastic characteristics are obtained using the finite element approach. The effect of the interphase thickness and different distributions of the interphase Young's modulus on the thermal residual stress field in unidirectional composite materials is investigated.For Pt. 1, see [1].Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 200–214, March–April, 1997.