Elastic Constants Of Composites Research Articles

Determination of elastic constants of composites by time-resolved acoustic microscopy

By using the angular spectrum acoustic microscopy model and the direct global matrix solution for a composite plate, the reflected signal from a time-resolved line focus transducer has been analyzed. The generalized ray solution has been used to decompose the complicated reflected signals into different wave modes. Strategies to determine the elastic constants using time-resolved acoustic microscopy have been discussed. Both the lateral wave and the bulk wave reflected from the bottom surface of a composite plate have been used in the elastic constant determination.

Ultrasonic evaluation of fatigue damage in metal matrix composites

Abstract This paper describes an experimental nondestructive technique for fatigue damage assessment in metal matrix composites by measuring ultrasonic phase velocity and attenuation. A [0/90] SiC/Ti15V3Cr3Al3Sn metal matrix composite is considered as a model system. Cyclic loading at 50 and 70% of the ultimate sample strength were used until failure. The ultrasonic phase velocities and attenuations were measured periodically and found to be very sensitive to fatigue damage. The fatigue-induced changes in the composite elastic constants were calculated from the measured ultrasonic velocity data. For samples heat treated prior to fatigue (815°C) above the matrix β transus (about 760°C), the dominant damage mechanism is debonding of the fiber/matrix interface. We found that when samples were fatigued for less than 50% of the lifetime, the reduction of the composite moduli was linearly dependent on the number of fatigue cycles, which is explained by extension of interfacial partial debonds. This was supported by micromechanical analysis based on a partial disbond model. The rate of decrease in the composite moduli in the second half of the fatigue life was found to be lower, which may serve as a basis for estimation of the remaining fatigue life of the composite from ultrasonic velocity and attenuation measurements. The attenuation data was obtained in directions perpendicular to the fiber. A single-fiber scattering model has been used to explain the effect of the fiber/matrix interface on attenuation. Good correlation between attenuation and moduli measurements was observed.

Elastic Properties of Particle-Occlusion Composites: Measurements and Modeling

We review some of our recent studies on the effective elastic constants of composites where the occluded phase is spherical or spheroidal (oblate or prolate). From constituent properties and phase geometry, we estimated the composites’ effective macroscopic elastic constants using two models: the Ledbetter-Datta scattered-plane-wave ensemble-average model and the Mori-Tanaka effective-field model. We measured elastic constants by three principal methods: resonance, pulse-echo, and acoustic-resonance spectroscopy. We show microstructures, measurements, and model calculations for five representative composites: SiCp/Al, Al2O3-mullitep/Al, Al2O3p/ mullite, graphitep/ferrite (cast iron), voids/Ti.

Generalized Dundurs constants foranisotropic bimaterials

It is well known that when a homogeneous isotropic elastic medium is under a planestrain deformation due to prescribed tractions at the boundary, the stress is independent of elastic constants. In the case of a bimaterial that consists of two dissimilar isotropic materials bonded together along their interface, the stress depends on two composite elastic constants known as Dundurs constants. For anisotropic elastic materials, plane strain deformations are possible for monoclinic materials with the symmetry plane at x 3 = 0. For these materials, the plane strain solution is in terms of two complex variables z 1 = x 1 + p 1 x 2 and z 2 = x 1 + p 2 x 2, where p 1 and p 2 are complex eigenvalues depending on elastic constants. If the boundary conditions are prescribed in terms of tractions, it is shown that the stress is independent of elastic constants except p 1 and p 2. In the case of a bimaterial that consists of two dissimilar monoclinic materials bonded together along their interface, the stress depends on two composite elastic constants α and β (in addition to p 1 and p 2 in both materials). They reduce to Dundurs constants in the isotropic limit. The result remains valid when the interface is not perfectly bonded. We also show that every plane strain solution to a given anisotropic material or bimaterial is applicable to a wider class of anisotropic materials and bimaterials. In particular, every plane strain solution to an isotropic material or bimaterial is applicable to a class of anisotropic materials or bimaterials that may possess no material symmetry. Finally, we show how the results obtained here can be modified for plane stress deformations.

Role of Porosity in Estimates of Composite Elastic Constants

The presence of small amounts of residual void space (on the order of one percent by volume) is sufficient to make estimates of composite elastic constants (obtained while ignoring this porosity) violate the Hashin-Shtrikman bounds in many cases. Experimental values falling below the incorrectly estimated lower bound is the normal direction of violation, but erroneous neglect of porosity in “pure” samples can also lead to experimental values rising above the incorrectly computed upper bound. Examples are presented to illustrate the nature of the error and methods of correcting it for data on composite ceramics. The result is improved agreement between the Hashin-Shtrikman bounds, effective medium theory estimates, and experimental data.

Elastic moduli of two-dimensional composites with sliding inclusions—A comparison of effective medium theories

We study the effective elastic moduli of two-dimensional (2D) composite materials containing sliding circular inclusions distributed randomly in the matrix. To simulate sliding we introduce a sliding parameter, which in two limiting cases gives perfect bonding and pure sliding boundary conditions. We evaluate elastic moduli using four effective medium theories; the self-consistent method, the differential scheme, the Mori-Tanaka method and the generalized self-consistent method. In this paper we focus on two aspects: one is the study of the effect of interface on the elastic constants of composites and the other is a comparison of the results from effective medium theories for the cases of both sliding and perfect bonding. In the discussion we use the recently-stated Cherkaev-Lurie-Milton theorem, which gives general relations between the effective elastic constants of 2D composites. We also compare the results from the effective medium theories with those from numerical simulations.

Determination of macro- and micromechanical and interfacial elastic properties of composites from ultrasonic data

A self-reference ultrasonic bulk wave method for nondestructive measurement of elastic properties of ceramic matrix composites has been developed. The method has the advantage of minimizing the effect of geometrical imperfection of the sample. The experiment has been done on silicon carbide (SiC) fiber-reinforced reaction-bonded silicon nitride (Si3N4) matrix composites. The composite elastic constants are extracted from the experimental phase velocities using a nonlinear optimization procedure to find the best fit between experimental data and the solutions of the Christoffel equation. The effect of individual constituents on the overall composite properties has been investigated. The effects of porosity on the matrix properties and water saturation of pores on the immersion ultrasonic measurements are taken into account using a micromechanical model for two-phase particulate composites. This model is validated by experimental data. A microstructural model for analysis of elastic properties of ceramic matrix composites and their interfaces from experimental data is introduced. The fiber and the interface are modeled by effective fibers with anisotropic properties and a perfect bond between fiber and matrix. The properties of the effective fibers are extracted from the measured composite elastic moduli using a nonlinear optimization procedure. Shear and longitudinal elastic moduli of 3-μm-thick carbon-rich coatings are determined using measured effective and estimated actual elastic properties of the fibers.

On the mechanical behavior of aluminum alloys reinforced by long or short alumina fibers or SiC whiskers

This study was initiated to examine the dispersion of longitudinal and transverse waves in metal matrix composites in order to obtain the dynamic elastic modulus and to evaluate various models for predicting the composite's macroscopic elastic constants from the properties of its constituents. The materials chosen for this investigation were alumina continuous fibers on the one hand and alumina and SiC short fibers on the other hand, all embedded in an aluminum alloy matrix. In addition, some indications have been obtained experimentally for the acoustoelastic effect in the composite.

Calculated elastic constants of composites containing anisotropic fibers

By a wave-scattering method, we derive dispersion relationships for waves propagating perpendicular to continuous fibers that are oriented unidirectionally. In the long-wavelength limit one obtains relationships that predict the composite's effective static elastic constants. We compare these relationships with others derived by energy methods to obtain upper and lower bounds of the effective static moduli. We demonstrate them graphically by plotting for graphite-cpoxy the predicted composite constants over the full range of fiber volume fractions. We consider the fibers to be anisotropic, but transversely isotropic. Under special conditions, the energy-method upper and lower bounds compare identically with the results of this study. The static properties are, of course, special cases of the more general dispersion relationships. Graphs are given for nine elastic constants: axial and transverse Young's and shear moduli, bulk and plane-strain bulk moduli, and three Poisson's ratios.

The elastic constants of carbon-fibre composites

Data on the elastic constants of carbon-fibre composites are presented. It is shown that provided the elastic constants of both the fibre and the matrix are known it is possible to predict the elastic constants of the composite parallel to the fibre axis using either the reduced equations of Halpin and Tsai, based on a self-consistent model, or the exact calculations of Heaton. The properties of the composite perpendicular to the fibres cannot be explained on the basis of the theoretical models considered.

Ultrasonic Elastic Constants of Carbon Fibers and Their Composites

The elastic constants of carbon-fiber-reinforced composites have been measured with an ultrasonic immersion technique. Both carbon and graphite fibers were studied. These fibers were derived from both rayon and polyacrylonitrile (PAN), and had Young's moduli ranging from 6 to 80×106 psi. The composite elastic constants varied with fiber modulus and fiber type (carbon or graphite) but not with the fiber-matrix bond. The fiber elastic constants c11 and c66, corrected for porosity, varied with fiber modulus but not with fiber type. The fiber constants c44 and c13 were independent of fiber modulus but varied with fiber type.

Mechanical Properties of Fiber Reinforced Composites

Theoretical expressions are obtained by means of classical theory of elasticity for determining the composite elastic con stants for fiber reinforced plastics in terms of the elastic moduli and the geometric parameters of the constituents. Infinite series are used for the solution of the differential equations and a com bination of least square method and Fourier method is employed. Although the investigation is made for hexagonal array, the principles are also valid for other fiber arrangements. Numerical examples have been worked out for hexagonal array and compared with an existing analysis.