A comparative study of fiber-matrix interactions by using micromechanical models

The purpose of this study is to describe the interfacial interactions in terms of stress distributions on short fibers in fiber-matrix unit-cell models. The fiber and matrix are subjected to tensile loading. The study consists of three main parts. First, fiber-matrix cell segments are modeled using a 3D finite-element analysis (FEA) with ANSYS. Three different finite-element geometrical unit-cell models are generated in order to simulate the Cox analytical model: a fiber-matrix combination, a single fiber, and a single matrix element. The second part contains the results of 3D FE analyses, which are applied to the Cox formulations by using a computer program developed. In the last part, the analytical solutions for distributions of normal and shear stresses are investigated. Cox 2D linear elasticity solutions, together with finite-element ones, are presented in detail in graphs. The interfacial interactions between the fibers and matrix are also discussed considering the relative changes in the distributions of normal and shear stresses. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 505–520, July–August, 2008.     

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.     

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.     

Compaction and Consolidation of Aramid and Composite Fibers. 2. Consolidation of Composite Fibers

The transverse compaction and consolidation of composite fibers obtained from blends of rigid-chain aromatic polyamides and a thermoplastic polycaproamide PA-6 are investigated with the aim to predict the fiber behavior during their compression and processing into plastics. Introduction of the aliphatic polyamide PA-6 into aramid fibers considerably increases their transverse compliance and promotes their sintering. A method for calculating the viscosity of the thermoplastic in the interfiber space from the ratio between the volumetric rate of compaction and the porosity of the material is proposed. It is found that the effective viscosity of the PA-6 melt, during its flow in the thin interfibrillar layers under compression, grows with decrease in its content in the composite fibers.     

Stress distribution in an infinite elastic body containing two neighboring locally curved fibers

A method is developed for analyzing the stresses in an infinite elastic body containing two neighboring inphase locally curved fibers located along two parallel lines. The body is loaded at infinity by uniformly distributed nor mal forces in the direction of fibers. The investigation is carried out within the frame work of a piecewise homogeneous body model with the use of the three-dimensional ex act equations of the elasticity theory. Numerical results for stress distributions in the body and for the influence of interaction between fibers on these distributions are given. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 457-478, May-June, 2009.     

Stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers in a composite material

In the present paper, within the framework of a piecewise homogenous body model, with the use of the exact three-dimensional equations of elasticity theory, a method proposed earlier is developed for investigating the stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers located along two parallel planes in an infinite elastic body. The body is loaded at infinity by uniformly distributed normal forces in the direction of fiber location. The self-equilibrated normal and shear stresses caused by the curved fibers are analyzed, and the influences of interaction between the fibers and of the geometric nonlinearity on the distribution of these stresses are studied. Numerical results for this interaction are obtained.     

Long-Term Creep of Hybrid Aramid/Glass-Fiber-Reinforced Plastics

The results of experimental investigation of the long-term creep of SVM aramid fibers, EDT-10 epoxy resin, aramid-epoxy FRP (fiber-reinforced plastics), glass-epoxy FRP, and aramid/glass-epoxy hybrid FRP with different volume fractions of aramid and glass fibers are presented. The long-term tests were continued for 50,000 h (5.7 years). A structural approach for predicting the long-term creep from the properties and content of the components is considered. The effect of hybridization (partial replacement of the aramid fibers by glass fibers) on the inelastic deformation of hybrid FRP is discussed. The redistribution of stresses in the components during long-term creep of the hybrid composites is analyzed.     

Comparison of Mechanical Properties and Effects in Micro- and Nanocomposites with Carbon Fillers (Carbon Microfibers,Graphite Microwhiskers,and Carbon Nanotubes)

The mechanical properties and effects in fibrous composite materials are compared. The materials are based on the same matrix (EPON-828 epoxy resin) and differ in the type of fibers: Thornel-300 carbon microfibers, graphite microwhiskers, carbon zigzag nanotubes, and carbon chiral nanotubes. Two material models are considered: a model of elastic medium (macrolevel model) and a model of elastic mixture (micro-nanolevel model). Mechanical constants of 40 materials (4 types + 10 modifications) are calculated and compared. The theoretical ultimate compression strength along the fibers is discussed. The effects accompanying the propagation of longitudinal waves in the fiber direction are investigated.     

Peculiarities of the Electret State of Melt-Spun and Melt-Blown Fibrous Polypropylene Materials

The charge state of melt-spun and melt-blown polypropylene fibers is investigated. It is shown that the production of fibers by melt-spinning and melt-blowing technologies promotes the formation of a spontaneous polarization charge. Possible mechanisms of fiber polarization are analyzed. The influence of parameters of the melt-spinning technological process and forced electrization of fibers during their formation in stationary and alternating electric fields on the magnitude and stability of the electret charge is examined. It is established that the application of a corona discharge to fiber polarization is more efficient for the electret state formation.     

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.     

Compaction and Consolidation of Aramid and Composite Fibers. 1. Compaction of Aramid Fibers

The transverse compaction and consolidation of various aramid fibers used as a reinforcement of plastics are studied with the aim to assess the behavior of the fibers during their processing. The transverse deformation of fiber bundles is considered in the context of viscoplastic flow of the fiber-forming polymer squeezed out into the interfiber space upon the contact interaction of the fibers. This process is analyzed as a flow of a polymer melt having a certain viscosity. A gradual increase in the viscosity with development of transverse deformations is revealed, which corresponds to the morphology of fibers of the skin-core type. It is found that, under these conditions, the transverse deformation and sintering of Terlon fibers are insignificant compared with that of SVM fibers, therefore, they are preferably used for reinforcing heat-resistant thermoplastics.     

Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

Interaction at the Interface of Phosphorus-Containing Carbon Fibers and Diglycidil Ether of Bisphenol-A

Two-component blends of phosphorus-containing carbon fibers (PCF) and diglycidyl ether of bisphenol-A (DGEBA) are investigated. It is found that PCF are better wetted by the epoxy oligomer considered than unmodified carbon fibers. It is stated that the equilibrium work of adhesion of the epoxy oligomer to PCF increases considerably. Heating the two-component blends is accompanied by conversion of epoxy groups and formation of a gel-fraction nonextractable from the fiber surface. The investigation results indicate that chemical bonds are formed at the fiber-oligomer interface, which causes grafting of the DGEBA immediately to the surface of PCF without the use of intermediate compositions usually employed in such cases. It is shown that a transition layer is formed whose morphology differs from that of the fibers and polymer in the blend volume.     

Change in the Surface Properties of Carbon Fibers as a Result of Plasmochemical Modification

The influence of plasmochemical modification of carbon fibers on their surface properties and compatibility with the PTFE matrix is investigated. It is shown that the thin PTFE coating formed on the carbon fiber surface improves the wetting of the fibers by PTFE. As a result, the mechanical characteristics of PTFE-based composites are improved.     

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.     

The Effect of Adhesion Interaction on the Mechanical Properties of Thermoplastic Basalt Plastics

The effect of temperature, adhesion time, and surface treatment of a reinforcing filler on the mechanical properties of thermoplastic basalt plastics based on a high-density polyethylene and a copolymer of 1,3,5-trioxane with 1,3-dioxolan is investigated. An extreme dependence for the adhesive strength in a thermoplastic-basalt fiber system is established and its effect on the mechanical properties of basalt plastics and the influence of the adhesion contact time on the adhesive strength in the system are clarified. The surface modification of basalt fibers in acidic and alkaline media intensifies the adhesion of thermoplastics to them owing to a more developed surface of the reinforcing fibers after etching. It is found that the treatment in the acidic medium is more efficient and considerably improves the mechanical properties of basalt plastics.     

Numerical Calculation of Fiber Orientation in Three-Dimensional Arterial Walls

In this contribution an approach for the fiber reorientation in three-dimensional arterial walls is presented. In detail the load-bearing capacity of the tissue is increased by re orienting the fibers with respect to the principal stresses, cf. [1]. The improved fiber reorientation algorithm is combined with the polyconvex nonlinear anisotropic material model presented in [3]. The results of a three-dimensional finite element simulation, where the reorientation approach is applied to a short segment of a patient-specific arterial geometry, are presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Minimal reduction type and the Kazhdan–Lusztig map

We introduce the notion of minimal reduction type of an affine Springer fiber, and use it to define a map from the set of conjugacy classes in the Weyl group to the set of nilpotent orbits. We show that this map is the same as the one defined by Lusztig in Lfromto, (2011) and that the Kazhdan–Lusztig map in Kazhdan and Lusztig, (1998) is a section of our map. This settles several conjectures in the literature. For classical groups, we prove more refined results by introducing and studying the “skeleta” of affine Springer fibers.     

Relationship of the ultrastructure and mechanical properties in tendinous collagen,a highly ordered macromolecular composite

A relationship has been found between the stress and deformation in tendon and, from an analysis of the data obtained, it was established that there is a major stress-bearing fiber, the diameter of which increases with increasing age of the animal. The relationship of the results obtained with the structure and properties of tendon as well as with the aging process is stressed. Models of the ultrastructure of collagen fibers in rat tail tendon or in other soft connective tissue were prepared by sealing rigid fibers in a considerably softer elastic matrix. Loss of fiber resistance was achieved by contraction of this matrix. These synthetic composite systems exactly reflect a number of the features of the collagen ultra-structure. Models were also used for studying stresses in the matrix about the fibers as this necessary information could not be obtained by a direct study of the biological tissues. Examination of the reaction between tropocollagen and the connective tissue polysaccharides in the process of collagen fiber formation shows that a mechanism exists through which the fibers may lose their resistance also in vivo.