Theory Of Composite Materials Research Articles

Mechanics of composite materials with a small-scale structural flexure

Thus, a continuum theory of composite materials with regular small-scale structural Texures in the material has been developed in the present paper, making it possible to determine local stresses, self-balanced in each period of the structure. A general method was suggested of solving linear oroblems by the continuum theory developed in an arbitrary approximation, based on the small parameter method. Examples on quasiuniform stress states, admitting exact solution, were studied, thus illustrating the effects under consideration.

On one-dimensional acceleration waves in composite materials modeled as interpenetrating solid continua

A one-dimensional version of a theory of composite materials modeled as interpenetrating solid continua is applied in the analysis of acceleration waves in composites containing two identifiable constituents. As expected, two distinct acceleration waves always propagate except when one of the constituents consists of a chopped fiber. The influence of viscous type damping is included in only the volumetric interaction between the constituents in portions of the treatment. Equations are derived both for the propagation velocities and the varying amplitudes of the disturbance as a function of the state of the material immediately ahead of the wavefront. These rather general results are specialized to the case of a homogeneous steady-state ahead of the fast wave. The various types of behavior possible and the order of the discontinuities occurring across the wavefront are discussed in detail for a number of special cases.

Confirmation of Biot’s theory

Plona’s recent measurements of elastic-wave speeds in a water-saturated porous structure of sintered glass beads are compared quantitatively to the predictions of Biot’s theory. The theoretical predictions lie within the bounds of experimental error (3%) for the fast compressional wave and for the shear wave in all cases. For the slow compressional wave, the theoretically predicted speeds lie within about 10% of the experimental values and increase with increase in porosity as observed. Our model achieves this agreement with no significant free parameters. The frame moduli are estimated using a recently developed self-consistent theory of composite materials. The induced mass of the frame in a water environment is also estimated theoretically.

The change in ultrasonic wave velocities in triaxially stressed brittle rock.

The changes in the ultrasonic wave velocities were measured for granodiorite under axial stress up to failure, and confining pressure up to 1kbar. The velocities begin to decrease at the differential stress of 1-2kbar and show a marked decrease at a stress higher than 70% of the failure strength. The observed decrease of P wave velocity in the minimum stress direction is remarkable (25% maximum) and that of S is somewhat smaller (15% maximum). The decrement of P wave velocity in the maximum stress direction is very small compared with that in the minimum stress direction.The normalized velocity Y(≡υ/υmax, a ratio of the velocity to the maximum one for each run) is empirically represented by a function of normalized differential stress X(=Δσ/σSM, ratio of differential stressΔσ to the strength σSM at the same confining pressure), as follows, Y=√1-a-Xbwhere a and b are constants. An elasticity theory for composite materials was used to interpret this relation.

Biaxial Analogs of Triaxial Stresses

Abstract In the case of composite materials such as concrete and natural rocks, fracture is resisted by internal friction, cohesion of the matrix, and adhesion at the interfaces. Although the behavior of an interface is clearly understood only when it is acted on by tensile forces, rock mechanics is primarily concerned with compressive forces. The apparent difficulty is circumvented by breaking down any given stress system into two components: an isotropic pressure and a tensile biaxial stress. The strength indicated by the latter component is precisely equal to that of the given stress system. Thus a condition of triaxial compression can be transformed into one of biaxial tension. An analysis based on this transformation indicates that the strength of composite materials in equal biaxial compression is considerably greater than in unconfined compression; this relationship becomes the keystone of a strength theory for composite materials.

Mechanical properties of polymer–paper laminates

Tensile mechanical properties of synthetic polymer–paper laminates were measured. The laminates were constructed by hot pressing a sandwich made of a sheet of paper between polymer films. There is complete penetration of the polymer inside the paper; no voids are left. Two different polymer matrices were used: poly(methyl methacrylate) and polyethylene. Several paper samples were utilized: an unoriented holocellulose paper (a strong paper), a highly oriented holocellulose paper, and an unoriented Whatman filter paper (a weak paper). The laminates contain from 0% to 50% of paper. Young's moduli and breaking strengths of the unoriented holocellulose paper laminates can be theoretically predicted from the properties of their constituents using laws of mixtures. The mechanical properties of the Whatman paper laminates are significantly higher than those predicted from the laws of mixtures. This indicates that the polymer increases the strength of the fiber-to-fiber bonds of the weaker sheets, although it does not change the bond strength of a stronger paper such as the holocellulose paper. For the oriented paper laminates, changes in Young's modulus with angle of measurement are explained by the composite materials theories if the angular variations in shear modulus are taken in to account. Changes in breaking strength with angle for the oriented laminates can be analyzed by Tsai and Azzi's theory for composite materials.

An experimental study of the Hertzian contact of surfaces covered with ion-plated films

The results are given of an experimental study of the normal-approachload relationship for steel spheres on steel plates covered with ion-plated lead films. It is found that the degree of plastic deformation is large at high loads for the thickest films (15 μm). With the thinnest films (1 μm) the degree of plastic deformation is of the same order as that associated with the deformation of the surface texture; this suggests that for such thin films an elastic theory for such composite materials is appropriate.

Theoretical predictions of the elastic moduli of polymer‐impregnated hardened cement paste and mortars

AbstractHardened coment pastes with water‐to‐cement (w/c) ratios of 0.4 and 0.6 and hydration times of one, three, seven, and 28 days were oven dried and subsequently impregnated with an epoxy resin formulation which was then polymerized in situ at 75°C. Portland cement mortars containing Ottawa sand and asbestos fibers as filler were also subjected to this impregnation process. Dynamic elastic moduli (E′) were measured at audio frequencies over a range of temperatures (100–400°K). Experimental values were compared with moduli calculated using various theoretical approaches based on two‐phase composite materials theory. Best agreement between experimental and calculated results occurs when Wu's theory for spherical polymer inclusions was applied to a cement‐based matrix. In the case of polymer‐impregnated mortars, experimental and theoretical results are in closest agreement at low temperatures and at low volume fraction of filler.

Solution of Interface Problems by Homogenization. I

The problem of an elliptic differential equation with nonsmooth coefficients is studied. It is assumed that the coefficients are double periodic with the period H and the right-hand side is smooth. The behavior of the solution for $H \to 0$ is investigated and theorems about limiting solution are proved. The study is related to the homogenization ideas used in an intuitive way in the theory of nuclear reactors and theory of composite materials.

Heat-conduction theory for composite materials

The problem of the macroscopic conduction of heat in a composite medium is considered. The medium consists of inclusions of arbitrary geometry embedded in a matrix. Starting with an analysis of the micro-conduction in a suitably defined representative volume, a fourth order equation governing the macro-conduction is deduced together with appropriate boundary conditions. The theory closely resembles the mechanical theory of non-simple materials of grade 2 developed by Toupin [2]. In particular, the well known characteristic material length encountered in stress-gradient theories is evaluated in terms of constituent material properties. It is further shown, as a basis of the theory, that anatural ratio exists between the dimensions of a local representative volume and those of a unit-cell given by the ratio of the classical Voigt and Reuss bounds on the effective diffusivities. In consequence, application of the theory hinges on the evaluation of certain material constants from given information on the inclusion arrangement in a representative volume of specific dimensions. Differences in the behaviour of media with different inclusion distributions depend entirely on the magnitude of such constants.

On the effective moduli of elastic composite materials

A continuum theory for elastic composite materials consisting of a matrix and inclusions is presented. The approximate effective elastic moduli defined dynamically by means of the phase velocities of long plane harmonic waves are obtained for ellipsoid-, needle- and disk-shaped inclusions aligned or oriented at random. The results are compared with the effective moduli obtained by other methods.

A dynamic theory for composite materials

A continuum model is developed for a composite medium consisting of inclusions of arbitrary geometry embedded in a matrix material. The equations are valid up to wave lengths of the order of a unit cell dimension and are found to reduce under special assumptions to Mindlin's equations in the long wave-length approximation. In particular, a pair of characteristic time scales and length scales encountered in stress-gradient theories are evaluated in terms of known constituent material properties. As a basis of the theory, it is shown that adefinite relation exists between the dimensions of a local representative volume and those of a unit cell. The relation is found to depend on the ratio of the maximum and minimum effective elastic impedances. As a consequence, the theory hinges on the evaluation of several material constants that reflect the effect of inclusion arrangement in a local representative volume of definite dimensions.

On the Relative Velocity in a Mixture Theory for Composite Materials

On the Relative Velocity in a Mixture Theory for Composite Materials

A stochastic model for biological tissue elasticity in simple elongation

A mathematical model is described which predicts the effective tangent moduli of biological tissues at each deformed state, which accounts for the contributions of two major load-bearing components — collagen and elastin. The problem is studied from a stochastic point of view based upon the theory of composite materials. It is shown that a simple stochastic model is possible and it can be expressed simply in terms of the volume fractions of collagen and elastin fibers and of the ‘collagen arrival density’. The model is then used in the discussion of stress-strain relationships of the alveolar wall in simple elongation.

Jump conditions and boundary conditions for a multi-continuum theory for composite elastic materials

The jump conditions for mass, momentum and energy across a propagating singularity surface are derived for a theory of mixtures developed for application to bonded composite materials. The jump conditions provide equations necessary for the study of shock and acceleration waves, and are also used to deduce the boundary conditions for the theory.

A multi-continuum theory for composite elastic materials

A continuum theory for composite materials is presented in which the composite constituents are modeled by superimposed continua which undergo thermal and mechanical interactions. Kinematical notions, field equations and a constitutive theory are developed, including consequences of material frame indifference and material symmetry which restrict the form of the response functions. The final result is a set of linearized equations for thermal and mechanical processes in laminated or fiber reinforced composite elastic materials.

The theory of elastic composite materials

A general analysis is given for the determination of the effective elastic constants of a macroscopically isotropic and homogeneous two-phase composite material. Approximate formulae are given and their validity discussed in terms of the general features of the sample geometry.

Toward A Diffusing Continuum Theory of Composite Materials

A theory of composite materials is proposed which is based on the continuum theory of mixtures. The constituents of a composite are modeled as superimposed continua which undergo individual deformations. Effects of structure on dynamical processes in composite materials are then simulated by specifying the coupling between the individual constituent motions. A novel feature of this model is the inclusion of diffusion with relative displacement coupling for perfectly bonded composites. A simple one-dimensional form of such a theory is presented, and, when compared with classical solutions for longitudinal wave propagation in laminated materials, predicts some aspects of the dynamical behavior extremely well.

Composite Material Modeling Of AntebranchialInterosseous Membrane In A Human Forearm

The interosseous membrane (IOM) is a fibrous structure located within the forearm that possesses distinct direction and shape patterns. The definitive function of this structure currently remains undefined. We propose that the IOM functions similarly to a composite material composed of stiff central fibers (longitudinal portion) surrounded by a supporting fibrous matrix (transverse portion). The matrix of the membrane is not actively involved in force transfer, but rather it functions to maintain the orientation of the IOM fibers relative to the radius and ulna. The matrix also transfers applied forces to the load bearing longitudinal fibers. The experimental process consisted of a force being applied by a tensile testing apparatus across the main fiber direction of a prepared IOM sample. The results indicated structural values similar to that of ligaments and provided a quantitative representation of the mechanical properties of the IOM. Using the amount of collagen and elastin and the rule of mixtures theory of composite materials, the theoretical values of the elastic moduli of the IOM were calculated. These values for the longitudinal and transverse portion were then compared to actual values obtained from mechanical testing. The membrane's composite design allows for additional strength in the force transferring direction, while still maintaining its muscular attachments and bony supports. Our experimental results support the composite material theory by demonstrating no difference between the calculated and experimental elastic moduli of the longitudinal and transverse portions of the IOM. Advances in Composite Materials and Structures VII, C.A. Brebbia, W.R. Blain & W.P. De Wilde (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-825-2

The influence of loading age and temperature on the long term creep behaviour of concrete in a sealed, moisture stable, state

Results of long term creep measurements on a number of concretes in a sealed state loaded at ages for 7 days to 400 days at temperatures ranging from 20° to 95° C, show that deformation increases directly with time when both deformation and time are plotted logarithmically. The change in creep rate from this deformation presentation was then related to temperature using a modified Arrhenius expression and indicated that a reasonable correlation existed for sealed, moisture stable, concrete for certain test conditions. Prediction of concrete deformation from multiphase composite material theory is shown to give erroneous long term creep predictions at this stage of its development.