Two interfacial shear strength calculations based on the single fiber composite test

The fragmentation of a single fiber embedded in a polymer matrix upon stretching (SFC test) provides valuable information on the fiber-matrix bond strength (), which determines stress transfer through the interface and, thus, significantly affects the mechanical properties of the composite material. However, the calculated bond strength appears to depend on data interpretation, i.e., on the applied theoretical model, since the direct result of the SFC test is the fiber fragment length distribution rather than the value. Two approaches are used in SFC testing for calculation of the bond strength: 1) the Kelly-Tyson model, in which the matrix is assumed to be totally elastic and 2) the Cox model using the elastic constants of the fiber and the matrix. In this paper, an attempt has been made to compare these two approaches employing theory as well as the experimental data of several authors. The dependence of the tensile stress in the fiber and the interfacial shear stress on various factors has been analyzed. For both models, the mean interfacial shear stress in the fragment of critical length (l_c) was shown to satisfy the same formula () = (_cD)/2l_c, where D is the fiber diameter and _c is the tensile strength of a fiber at gauge length equal to l_c. However, the critical lengths from the Kelly-Tyson approach and Cox model are differently related to the fragment length distribution parameters such as the mean fragment length. This discrepancy results in different () values for the same experimental data set. While the main parameter in the Kelly-Tyson model assumed constant for a given fiber-matrix pair is the interfacial shear strength, the ultimate (local) bond strength _ult may be seen as the corresponding parameter in the Cox model. Various _ult values were obtained for carbon fiber-epoxy matrix systems by analyzing the data of continuously monitored single fiber composite tests. Whereas the mean value of the interfacial shear stress calculated in the Cox approach was comparable to the interfacial shear strength from the Kelly-Tyson model, its ultimate value characterizing the true adhesional bond strength appeared to be three or four times greater.To be presented at the Ninth International Conference on the Mechanics of Composite Materials in Riga, Latvia, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 446–461, July–August, 1995.     

A multiscale analysis of the mechanical behavior of a thermo-oxidized c/epoxy lamina

The mechanical behavior of carbon-fiber-reinforced polymer matrix composites having undergone a thermo-oxidation process is studied. The purpose is to perform a multiscale analysis of the consequences of oxidation on the intrinsic mechanical properties of the external composite ply and on the internal mechanical states experienced by the structure under mechanical loads. The effective mechanical properties of oxidized composite plies are determined according to the Eshelby–Kr?ner self-consistent homogenization procedure, depending on evolution of the oxidation process. The results obtained are compared with estimates found by the finite-element method. The macroscopic mechanical states are calculated for a unidirectional composite and laminates. The macroscopic stresses in each ply of the structure are determined by the classical lamination theory and the finite-element method, whereas the local stresses in the carbon fiber and epoxy matrix are calculated by using an analytical stress concentration relation.     

Fracture Model for a Thin Layer of a Fibrous Composite

A model for a flat isolated layer of a unidirectional fibrous composite with a regular structure is constructed to investigate the possible variants of its failure development. An integrodifferential equation for determining the forces in fibers is obtained. Primary attention is focused on examining the failure process after the rupture of one fiber. This causes a drastic redistribution of stresses, which can lead to a failure of adjacent fibers owing to the increased load on them, to an interfacial shear fracture, and to the matrix cracking. It is shown that the development of layer failure is determined by the strength of fibers, the crack resistance of the matrix in axial tension and transverse shear, and also by the adhesion strength of the matrix-fiber interface. The sufficient conditions of applicability of the brittle fracture model are formulated.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Cryogenic mechanical response of multilayer satin weave CFRP composites with cracks

We deal with the thermomechanical response of multilayer satin weave carbon-fiber-reinforced polymer (CFRP) laminates with internal and/or edge cracks and temperature-dependent material properties subjected to tensile loading at cryogenic temperatures. The composite material is assumed to be under the generalized plane strain. Cracks are located in the transverse fiber bundles and extend to the interfaces between two fiber bundles. A finite-element model is employed to study the influence of residual thermal stresses on the mechanical behavior of multilayer CFRP woven laminates with cracks. Numerical calculations are carried out, and Young’s modulus and stress distributions near the crack tip are shown graphically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 479–492, July–August, 2008.     

Numerical elastic-plastic simulation of interlaminar stresses in a notched angle-ply thermoplastic composite laminate

A thermoplastic angle-ply AS4/PEEK laminate with a hole is considered. The interlaminar stresses along the hole edge at different interfaces under uniaxial extension are investigated. According to the symmetries of the structure and loading, a suitable finite-element model is developed. Utilizing a three-dimensional elastic-plastic finite-element procedure elaborated previously, a finite-element modeling of the interlaminar stresses in a thick angle-ply composite laminate is carried out. Based on the interlaminar stresses obtained, the dangerous locations of delamination initiation are predicted. The results obtained indicate that there is some relationship between the dangerous locations and fiber orientations in the adjacent layers, and it maybe inferred that the critical locations are near the regions where the hole edge is tangent to the fiber orientation in the layers adjacent to the interface. The interlaminar stresses at the same interfaces are not sensible to distances from the midplane of the laminate. Very high interlaminar tensile stresses are found to exist on the hole edge at the +25°/+25° or –25°/–25° interfaces, and delaminations can initiate there first. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 427-440, May-June, 2009.     

Application of the method of conditional moments to investigating the deformation properties of orthotropic composites with fiber microdamages

A model of deformation of stochastic composites subjected to microdamage is developed for the case of orthotropic materials with microdamages accumulating in the fibers. The composite is treated as a matrix strengthened with elliptic fibers with orthotropic elastic properties. The fractured microvolumes are modeled by a system of randomly distributed quasi-spherical pores. The porosity balance equation and relations for determining the effective elastic moduli for the case of a fibrous composite with orthotropic components are used as the fundamental relations. The fracture criterion is given as a limit value of the intensity of average shear stresses occurring in the undamaged part of the material, which is assumed to be a random function of coordinates and is described by the Weibull distribution. Based on an analytical and numerical approach, the algorithm for determining the nonlinear deformation properties of such a material is constructed. The nonlinearity of composite deformations is caused by the accumulation of microdamages in the fibers. By using a numerical solution, the nonlinear stress–strain diagrams for an orthotropic composite in uniaxial tension are obtained. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 1, pp. 17–30, January–February, 2009.     

Fabrication and thermal expansion behavior of a magnesium-matrix composite with a high content of reinforcing SiC particles

An Mg-based metal-matrix composite reinforced with 50 vol.% SiC particles was fabricated by infiltrating molten metal into porous SiC preforms, and its microstructure and thermomechanical properties were investigated. The effect of thermal processes on the thermal expansion behavior of the composite was investigated by applying 1, 10, and 20 thermal cycles within the range from room temperature to 200°C. The Kerner and Turner analytical models and a 2D unit-cell finite-element model were employed to analyze the thermal expansion behavior of the composite. The coefficient of thermal expansion (CTE) predicted by the 2D unit-cell model was in good agreement with the Kerner model, while the results from the Turner model were significantly lower. The CTE of the composite slightly increased during the thermal cycling and, after a few cycles, agreed well with the Kerner and 2D unit-cell predictions.     

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.     

Superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders

A mathematical model of superposition of large butt-end and coaxial torsional and axial shear deformations of homogeneous and fiber-reinforced thick-wall cylinders is constructed. The macroscopic stresses of the reinforced material are additively determined by matrix stresses and by tensile or constrained compression stresses in the reinforcing fibers. The model is based on the numerical solution of two boundary-value problems, one of which corresponds to the butt-end torsion and the other to the coaxial torsion and axial shear. The boundary-value problem on joint deformations is solved with the use of the displacement field determined from the solution to the boundary-value problem on butt-end torsion. The results obtained by applying this method to homogeneous and axially-radially reinforced thick-wall cylinders subjected to butt-end torsion with subsequent coaxial torsion and axial shear are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 465–492, July–August, 2007.     

Creep of Heat-Resistant Composites of an Oxide-Fiber/Ni-Matrix Family

A creep model of a composite with a creeping matrix and initially continuous elastic brittle fibers is developed. The model accounts for the fiber fragmentation in the stage of unsteady creep of the composite, which ends with a steady-state creep, where a minimum possible average length of the fiber is achieved. The model makes it possible to analyze the creep rate of the composite in relation to such parameters of its structure as the statistic characteristics of the fiber strength, the creep characteristics of the matrix, and the strength of the fiber-matrix interface, the latter being of fundamental importance. A comparison between the calculation results and the experimental ones obtained on composites with a Ni-matrix and monocrystalline and eutectic oxide fibers as well as on sapphire fiber/TiAl-matrix composites shows that the model is applicable to the computer simulation of the creep behavior of heat-resistant composites and to the optimization of the structure of such composites. By combining the experimental data with calculation results, it is possible to evaluate the heat resistance of composites and the potential of oxide-fiber/Ni-matrix composites. The composite specimens obtained and tested to date reveal their high creep resistance up to a temperature of 1150°C. The maximum operating temperature of the composites can be considerably raised by strengthening the fiber-matrix interface.     

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°.     

Boundary-value problem in the correlative approximation of the method of quasi-periodic components for a unidirectional fiber composite

The boundary-value problem in the correlative approximation of the method of quasi-periodic components and a numerical algorithm based on the boundary element method for determining the nonuniform stress fields in the matrix of a unidirectional fiber composite with a disordered structure are considered. The numerical results and analysis of the probability density function, for example, for normal stresses at some points of the interface of absolutely rigid fibers of the composite are presented. Perm State Technical University, Russia. Translated from Mekhanika Kompozytnykh Materialov, Vol. 35, No. 5, pp. 629–642, September–October, 1999.     

Imperfect interface effect for nano-composites accounting for fiber section shape under antiplane shear

This paper investigates the elastic responses of fibrous nano-composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is the shear lag (or the spring layer) model; the presented nano interfacial stress model is the Gurtin–Murdoch surface/interface model; and the three-phase confocal elliptical cylinder model is the geometry model accounting for the fiber section shape. By virtue of the complex variable method, a generalized self-consistent method is employed to derive the closed from solution of the effective antiplane shear modulus of the fibrous nano-composites with imperfect interface. Five existing solutions can be regarded as the limit form the present analytic expression. The influences of the interface elastic constant, the interfacial imperfection parameter, the size of the elliptic section fiber, the fiber section aspect ratio, the fiber volume fraction and the fiber elastic property on the effective antiplane shear modulus of the nano-composites are discussed. Particularly, numerical results demonstrate that the interfacial elastic imperfection will always cause a significant reduction in the effective antiplane shear modulus; and the fiber interface stress effect on the effective modulus of the fibrous nano-composites will weaken with the interfacial imperfection increases.     

Measuring and modeling the thermal conductivities of three-dimensionally woven fabric composites

The effect of a three-dimensional fiber reinforcement on the out-of-plane thermal conductivity of composite materials is investigated. Composite preforms with different fibers in the thickness direction were fabricated. After in fusion by using a vacuum-assisted resin transfer molding process, their through-thickness thermal conductivities were evaluated. The measured thermal conductivities showed a significant increase compared with those of a typical laminated composite. Although the through-thickness thermal conductivity of the samples increased with through-thickness fiber volume fraction, its values did not match those predicted by the simple rule of mixtures. By using finite-element models to better under stand the behavior of the composite material, improvements in an existing analytical model were performed to predict the effective thermal conductivity as a function of material properties and in-contact thermal properties of the composite. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 241–254, March–April, 2009.     

Non-uniformly scaled buckling modes of reinforcing elements in fiber reinforced plastic

We consider a problem about non-uniformly scaled buckling modes of isolated fiber (without accounting of interaction with the surrounding epoxy) or bundle of fibers, which are structural elements of fiber reinforced plastics under the transverse tension (compression) and shear stresses in prebuckling state. Such initial state is formed in fibers and bundles of fibers at tension-compression tests of flat specimens from cross ply composites with unidirectional fibers. For problem statement we use equations recently constructed by reduction of consistent version of geometrically nonlinear equations of theory of elasticity to one dimensional equations of rectilinear beams. Equations are based on refined shear S. P. Timoshenko model with accounting of tension-compression stresses in transverse directions. We give theoretical explanation of developed phenomenon as reducing shear modulus of elasticity of fiber reinforced plastic during the increasing of shear strains. We show that under the loading process of specimens under review uninterruptedly structure reconstruction of composite trough implementation and uninterruptedly changing of internal buckling modes at changing wave parameter is feasible.     

Analytical and numerical techniques for predicting the interfacial stresses of wavy carbon nanotube/polymer composites

By introducing a new simplified 3D representative volume element for wavy carbon nanotubes, an analytical model is developed to study the stress transfer in single-walled carbon nanotube-reinforced polymer composites. Based on the pull-out modeling technique, the effects of waviness, aspect ratio, and Poisson ratio on the axial and interfacial shear stresses are analyzed in detail. The results of the present analytical model are in a good agreement with corresponding results for straight nanotubes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 299-306, March-April, 2009.     

The Effect of Surface Treatment of F-12 Aramid Fibers with Rare Earths on the Interlaminar Shear Strength of Aramid/Epoxy Composites

Solutions of a rare-earth modifier (RES) and the epoxy chloropropane (ECP) grafting modification method are used for the surface treatment of F-12 aramid fibers. The effects of RES concentration on the interlaminar shear strength (ILSS) of F-12 aramid fiber/epoxy composites are investigated in detail, and the fracture surfaces of ILSS specimens are analyzed by SEM. It is shown that the RES surface treatment is superior to the ECP grafting treatment in promoting the interfacial adhesion between aramid fibers and the epoxy matrix. However, the tensile strength of single fibers is almost unaffected by the RES treatment. The optimum ILSS is obtained at a 0.5 wt.% content of rare-earth elements.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 265–272, March–April, 2005.     

Equal-stressed reinforcement of metal-composite plates with fibers of constant cross section in steady-state creep

The problem on equal-stressed reinforcement of metal-composite plates with fibers of constant cross section, loaded in their plane and operating under the conditions of steady-state creep, is formulated. A qualitative analysis of the corresponding system of resolving equations and boundary conditions is performed. An important case of the problem is considered, where both the reinforcing fibers and the matrix are equally stressed. A method for numerically solving this problem is developed. Particular analytical and approximate solutions are discussed, with the example of which changes in the reinforcement structure in relation to the stress level in the reinforcing fibers are clarified. It is shown that nonunique solutions to such problems can exist. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 11–34, January–February, 2008.     

Assessment of transmission of the shear stress in potted anchors for composite rods 1. Sleeve of constant thickness

The key problem facing the application of fiber-reinforced polymer (FRP) stay cables and tendons is the anchorage. Potted (bond-type) anchors have been used more extensively than anchors of any other type. The main aim in the design of anchors is to minimize the peak shear stress at the FRP rod-pottant interface. To this end, parametric analyses of the stress state in the anchors are carried out. Since parametric studies can not be easily performed by the finite-element method, an analytical model of the anchor is proposed. The model involves significant simplifying assumptions and allows one to obtain a relatively simple analytical solution for shear-stress distributions at the FRP rod-pottant interface. The use of this solution at various boundary conditions and various geometrical and mechanical parameters of anchor components enables one to search for and evaluate, at least qualitatively, different methods for decreasing the peak interfacial shear stress in the anchor. In this part of the investigation, an anchor consisting of a sleeve of constant thickness is considered. Russian tanslation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 321-346, May-June, 2009.