Showing papers on "Micromechanics published in 1974"

On the Effective Moduli of Isotropic Two-Phase Elastic Composites

Abstract: Let us consider a matrix with elastic moduli K1 and G1 (bulk and shear moduli respectively) in which are embedded particles with elastic moduli K2 and G2. The fractional volume of the particles is c2 and the fractional volume of the matrix is cl (Cl + cz 1 ). This two-phase suspension is assumed to be statistically homogeneous and isotropic. The effective bulk and shear moduli are K’~ and G* respectively. -

Methods for Determining the Elastic and Viscoelastic Response of Composite Materials

Abstract: Two test methods for determining the longitudinal or in-plane shear stress-strain response of a unidirectional composite material are presented. These two methods are the uniaxial tension test on a ′45 deg laminate and the rail shear test on a 0/90 deg laminate. Although these tests are conducted on laminates, the laminates are special cases of geometric construction. It is shown that unidirectional shear properties can be found from the laminate test data. The stress-strain response for both methods agrees very well for glass-epoxy and graphite-epoxy composites. The nonisothermal viscoelastic shear response of a unidrectional composite is determined from tension creep tests on a ′45 deg laminate at temperatures of 81°, 125°, and 150° F. A master shear creep compliance curve is constructed by using the principle of time-temperature superposition. The other unidirectional creep compliances necessary for characterization of an orthotropic material under a state of plane stress are calculated from equations of micromechanics. Agreement is good for a comparison of the shear creep compliance calculated from micromechanics and the ′45 deg laminate. It was found that the behavior of the tensile relaxation modulus of the epoxy resin used in a typical graphite-epoxy composite is similar to the behavior of the epoxy resin used in a typical glass-epoxy. The creep behavior of any laminate can be predicted from laminated plate theory once the unidirectional material is characterized. Viscoelastic interconversion formulas are derived which relate the creep test, constant loading rate test, and dynamic test when the creep compliance can be approximated by a power law in time and linear viscoelasticity theory is valid.

Viscoelastic Characterization of a Nonlinear, Glass/Epoxy Composite Including the Effects of Damage

Abstract: : Isothermal creep and recovery tests were conducted on an epoxy resin and a glass fiber-reinforced composite made from the same bulk resin. The glass/epoxy which was studied included unidirectional and laminated (angle-ply) composites as well as samples removed from a Minuteman III solid rocket motor case. The creep and recovery tests were carried out at a series of stress levels well into the nonlinear region at temperatures of 20,75 and 140 F for several fiber angles. Both the epoxy and glass/epoxy were found to be thermorheologically complex materials with a creep compliance which may be represented by a power law in time. The linear viscoelastic principal creep compliances were determined for the glass/epoxy using fourth-order tensor transformations. Using the Halpin-Tsai relationships and the 'rule of mixtures', the principal creep compliances were compared with those predicted by micromechanics. The experimental results were found to agree very well with the Halpin-Tsai model except at the highest temperatures and were within the upper and lower theoretical bounds on compliance. The nonlinear properties were found to depend primarily on the stress normal to the fiber. Bending tests conducted on glass/epoxy beam and plate specimens brought out a strong influence of the strain gradient.

Thermoelastic Properties of Unidirectional Filamentary Composites by a Semiempirical Micromechanics Theory

Abstract: : A unified, semiempirical micromechanics theory is described which relates the thermoelastic properties of the unidirectional, filamentary composite to the quantities and to the corresponding properties of its constituent materials. The theory treats the composite, the filaments and the matrix as being generally orthotropic, linearly elastic, and accounts for the effect of voids. It is based on the equivalent section concept, on parallel and series connected elements and on the judicious incorporation of certain empirical factors, which reflect the particular fabrication process. Results are presented which demonstrate and verify application of this theory to boron, carbon and glass-filament epoxy-resin composites. Additional results are presented which exhibit the voids and in-situ matrix orthotropicity effects on the thermoelastic properties of the unidirectional composite. Finally, results are included for all the thermoelastic properties of boron, carbon and glass-filament epoxy-resin composites. (Author)

On the determination of physical properties of composite materials by a three-dimensional finite-element procedure

Abstract: In this work the effective moduli of a composite material have been found by employing the finite-element method. The correspondence between the actual composite and its equivalent homogeneous anisotropic material is established on the requirement of equality of the total strain energies for the two media. The method is applied to the unidirectional fiber composites, the short unidirectional fiber composite, and the lamellar composite, and the results compare satisfactorily with available analytical data.

A Finite Element Analysis of Cracks in the Region of a Bi-Material Interface

Abstract: This work was motivated by the fact that the fracture toughness of composite materials is strongly related to the micromechanics of the fracture process. The effects of interfacial bonding, interfacial splitting, fiber pull-out, matrix cracking, fiber failure, etc. on the gross composite strength and toughness have been widely discussed in the literature. This work considers simplified analytical models of some of these mechanisms which permits quantitative evaluations of the roles of material properties as related to microfracture mechanisms. A micro-model of the interfacial region in a two-phase composite is analyzed. The model is a rectangular region loaded at the boundaries. The region is divided into Phase I and Phase II by a vertical line representing the interface. Several crack geometries are modeled including a crack in Phase I approaching the interface and extending to the interface, a crack extending along the interface and a crack penetrating the interface and extending into Phase 11....

Composite material mechanics: thermoelastic micromechanics*

Abstract: This paper is a survey of the principal analytical and experimental developments in the field of composite material mechanics. Emphasis is placed on filamentary-type composite materials. Topics covered are (1) elastic micromechanics, including a great variety of analytical approaches to the problem, and (2) thermal and other transport phenomena, including a number of useful analogies for such phenomena. The survey concludes with a brief discussion of future trends in the field.