Fiber-reinforced Elastomers Research Articles

Second-order estimates for the large-deformation response of particle-reinforced rubbers

This paper presents the application of a recently proposed ‘second-order’ homogenization method (J. Mech. Phys. Solids 50 (2002) 737–757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of ‘generalized’ secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin–Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389–1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).

The Response of Fiber-Reinforced Elastomers under Simple Tension

The Response of Fiber-Reinforced Elastomers under Simple Tension

The Response of Fiber-Reinforced Elastomers under Simple Tension

The mechanical behavior and basic response mechanisms of fiberreinforced elastomers (flexible composites) can be significantly different from those of typical advanced “stiff” composites. This paper presents experimental results of elastomer (rubber) matrices, dry and impregnated fibers, and four sets of fiber-reinforced elastomeric composite, summarizes the corresponding initial and nonlinear orthotropic constitutive properties, and sheds light on fundamental response mechanisms. Silicone and urethane rubber were combined with fiberglass and cotton reinforcing fibers. Balanced angle-ply laminates of each material system were fabricated with off-axis angles ranging from 0° to 90° in 15° increments. Dog-boned test specimens, 76 mm (3 in) long, were fabricated with fiber volume fractions ranging from 12% to 62% using a previously documented non-calendering fabrication method [1–3]. The average extensional stiffness of individual twisted cotton fibers increased 74% to 128% when impregnated with an elastomer. Fiber-reinforced elastomer laminate stiffness and nonlinearity can vary significantly with fiber angle. The nonlinear stiffening or softening trends of the silicone and urethane rubbers are reflected in their respective fiber-reinforced elastomers. Longitudinal stiffness at low off-axis angles is a function of the reinforcement stiffness. At high off-axis angles, longitudinal stiffness and strength are functions of fiber type, fiber volume fraction and elastomer.

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.

Axisymmetric deformation of shells of revolution made of fiber-reinforced elastomeric layers

The study of the deformation of shells of fiber-reinforced elastomers is based on a structural approach in which the elastomeric matrix and reinforcement are considered separately, without reduction of the composite to a medium having continuously changing characteristics. The concept underlying this approach was first explained in [1], where a momentless model of deformation was used as the basis for describing a method of designing a rubber shell with a reticular reinforcement and no binder. In [2], calculations were performed for certain shells of revolution made of an elastomer and reinforced along the middle surface using fibers with little or no tensility. The effect of the reinforcement was accounted for by a method employed to analyze momentless shells. Line~-r relations from the theory of elasticity were used in [3] to construct a momentless model of the deformation of a shell with a reticular reinforcement with allowance for the effect of the binder. In [4], a method was presented for solving momentless problems of the deformation of multilayered shells of revolution. Here, the mechanical properties of the reinforcing fibers and binders were described with the use of nonlinear elastic relations. The well-known models of deformation do not consider the moment character of the stress state of composite shells made of elastomeric layers. They are suitable for the design of very thin axisymmetric shells, in which the stress state is of a membrane (momentless) character. Here, we construct a structural model that describes the axisymmetric deformation of moment shells of revolution composed of elastomeric layers unidirectionally reinforced with fibers. The method is based on an iterative procedure for the design of shells of this type and employs the hypothesis of a compressible normal element. In accordance with this hypothesis, a normal element of the shell remains straight and normal to the plane of reference during deformation, undergoing elongations that vary through the thickness of each layer. The volume occupied by the reinforcing fibers is assumed to be small compared to the volume occupied by the binder. In accordance with the smallness of the relative volume of the reinforcement, the cross section of the fibers is assumed to be infinitely small. We will use an iterative method to determine the parameters of the deformed shell at each point of discretization of the given boundary-value problem. 1. We will examine a thin composite shell of N elastomeric layers unldirectionally reinforced with fibers. We will assume that the fibers are crossed (arranged antisymmetrically) in any two adjacent layers to form a reinforcing grid with rhomboid cells. The fibers may be arranged in the meridional direction in one layer and in the circumferential direction in the next layer. Some of the layers have no reinforcing material and are purely elastomeric. The thicknesses of the layers is assumed to be constant or to change smoothly in the meridional direction. We take the internal bounding surface of the shell as the plane of reference (the base coordinate plane). We refer this plane to an orthogonal coordinate system established by the lines of principal curvature. The transverse coordinate z is reckoned along an outer normal to the initial reference plane. As the running meridional coordinate, we take the length t of the generatrix of the coordinate surface from a point on the bounding contour to the current point. We will use the following notation: h is the total thickness of the shell; h k is the thickness of the k-th layer; z k and Zk+ 1 are values of the coordinate z for the lower and upper surfaces bounding the k-th layer; k 1 and k 2 are the principal curvatures of the coordinate surface of the shell; r is the distance from a point on the coordinate surface to the x axis (symmetry axis) of the shell; 0 is the angle between the normal to the coordinate surface and the symmetry axis; vkf is the frequency of fibers in the k-th layer; c~kf is the angle of inclination of the k-th layer fibers to the meridian. Quantities pertaining to the reinforcing

Fatigue of Cord-Rubber Composites

Abstract Fatigue failure mechanisms and their dependence on cyclic loading frequency were assessed in the case of a nylon fiber-reinforced elastomer matrix composite representing the actual carcass of bias aircraft tires. Under uniaxial tension, the angle-plied composite specimens were subjected to a considerably large interply shear strain before failure. The composite specimens exhibited infinite fatigue life when stress amplitude was below a threshold level, i.e., fatigue endurance limit. Under cyclic stresses exceeding the endurance limit, localized damage in the form of fiber-matrix debonding and matrix cracking was formed and developed into the delamination eventually leading to gross failure of the composite. The process of damage accumulation was accompanied by a continuous increase of cyclic strain as well as temperature. Fatigue lifetime and the resistance to damage accumulation of aircraft tire carcass composite were strongly influenced by cyclic frequency. The use of higher frequency resulted in shorter fatigue lifetimes at a given stress amplitude and lower endurance limit. The extent of xdynamic creep at gross failure, which is defined as the increase of cyclic strain beyond initial elastic deformation, was roughly independent of stress amplitude under the frequency of 1 Hz, but decreased with higher stress amplitude when the frequency was raised to 10 Hz. Obviously a critical level of dynamic creep exists for gross failure of the composite and this level appears to be independent of the stress amplitude at low frequency. When the frequency is sufficiently high, heat generation due to hysteretic loss is expected to degrade the materials. In this situation, the critical level of dynamic creep for gross failure seems to be reduced by the loss of matrix flexibility as well as fiber-matrix bonding strength, with the degree of reduction becoming greater under higher stress amplitude.

Cumulative Damage of Fiber-Reinforced Elastomer Composites under Fatigue Loading

Fracture mechanisms under fatigue loading were assessed in the case of nylon fiber-reinforced elastomer matrix composite which represents the actual carcass of bias aircraft tires. Under uniaxial tension, the angle-plied carcass composite specimens were subjected to a considerably large interply shear strain before failure. The composite specimens exhibited semi-infinite fatigue life when stress amplitude was below a threshold level, i.e., fatigue endurance limit. Under cyclic stresses exceeding the endurance limit, localized damage in the form of fiber-matrix debonding and matrix cracking was formed and developed into delamination eventually leading to gross failure of the composite. The process of damage accumulation was accompanied by heat generation and a continuous increase of cyclic strain (dynamic creep). Fatigue lifetime and the resistance to damage accumulation of aircraft tire carcass composite were strongly influenced by cyclic frequency. The use of higher cyclic frequency resulted in shorter fatigue lifetime at a given stress amplitude and lower fatigue endurance limit. The extent of dynamic creep at gross failure, which is defined as the increase of cyclic strain beyond initial elastic deformation, was roughly independent of stress amplitude under the frequency of 1 Hz, but decreased with higher stress amplitude when the frequency was raised to 10 Hz. Obviously a critical level of dynamic creep exists for gross failure of the composite and this level appears to be independent of the stress amplitude at low frequency. When the frequency is high enough, heat generation due to hysteretic loss is expected to degrade the materials. In this situation, the critical level of dynamic creep for gross failure may be reduced by the loss of matrix flexibility as well as fiber-matrix bonding strength. The study also examined the effect of load sequence on the damage accumulation process of composite based on dual stress level fatigue testing. Palmgren-Miner's linear damage accumulation theory tended to overestimate the cumulative damage of angle-plied carcass composites. As an alternative to PalmgrenMiner's rule, a linear cumulative damage model based on dynamic creep was utilized. The sum of dynamic creep to gross failure was found to be unity indicating that the level of cumulative damage is independent of the load sequence.

Buckling in Fiber-Reinforced Elastomers

A peculiar phenomenon of in-plane fiber buckling has been observed in rubber beams reinforced with layers of parallel fibers when they are subjected to severe bending with a moment vector perpendicular to the fiber direction parallel to the width of the beam. The shape of the fibers on the inside of the bend, which appears to be independent of the boundary conditions, suggests fiber buckling under elastic support. It is shown here that this buckling phenomenon is unrelated to the case of buckling of an elastically supported rod under pure compression and can be explained only by taking into account the combined action of (a) the support each fiber experiences from fibers in adjacent layers (interlayer support) and (b) the support each fiber experiences from adjacent fibers in the same layer (interlayar support).