Journal of Composite Materials

The requirements on the boundary conditions of the assumed series in a Ritz solution for anisotropic plates is discussed for classical and elastically restrained boundary conditions. A convenient method is indicated for handling elastically restrained boundary conditions which satisfies the natural boundary conditions for orthotropic or iso tropic plates and which utilizes the integration formulas given in a previous paper. Extensive numerical results are presented to illus trate the solution method for series satisfying only the geometrical boundary conditions and for series satisfying both natural and geo metrical boundary conditions.

Advanced composites are now vying with well-established metals, glass, and ceramics in load bearing applications. The economic success of these composites depends upon the cost-property index, B/P where B is the price per pound of the composite and P is the specific property of the composite critical to the load bearing ap plication. Until this index approaches those for commonly-used materials, advanced composites will be utilized only in applications where there is a premium for light weight, such as transportation.

A two-dimensional dynamic photoelastic investigation was con ducted of crack growth in glass-plastic composite models. The models used were idealized fiber-reinforced composites and consisted of al ternating layers of glass and polyester resin. A crack configuration was introduced in the central glass reinforcing bar to insure crack initiation at that point. A falling weight system producing dynamic tension in the direction of the reinforcing bars was used. This dynamic loading was coordinated with the triggering of a high-speed Cranz-Schardin multiple-spark camera. Transient isochromatic fringe patterns during crack propagation were recorded with this camera operating at a rate of 200,000 frames per second. Some characteristic phenomena were observed. Precursor traces appeared before the crack. These traces did not indicate any evidence of cracking in tests where the crack was arrested and subsequent crack extension followed these traces faithfully. The arrested crack in the matrix phase had a peculiar horseshoe shape. Its propagation velocity was much lower than ex pected. Upon reaching the interface with the glass element the crack showed appreciable hackle dividing into many branches.

The effect of boundary conditions on the bending, vibrations, and buckling of unsymmetrically laminated rectangular plates is in vestigated. Five sets of boundary conditions corresponding to various clamped and simply-supported edges are treated. The effect of in- plane boundary conditions is shown to be a function of fiber orienta tion within the laminate. Numerical results also show that the effects of bending-extensional coupling can be severe for all the boundary conditions considered. The applicability of the reduced-bending- stiffness approximation is also explored.

An analysis of interlaminar shear stresses is performed for a lami nate under generalized plane stresses. The laminate is modeled as a set of anisotropic layers separated by isotropic adhesive layers. The corresponding equilibrium differential equations are developed and solved for laminates of infinite and finite width. In the first case, it is shown that the interlaminar shear stress is zero everywhere, while in the latter case, this stress attains finite maximum values at the edges of the strip. These results are important when interpreting strength data obtained from uniaxial tests.

A dislocation model is used to study the propagation of elastic- plastic shear cracks in composite materials. It is found that the ex tension of plastic zones in ductile matrices is governed by both the yield strength and rigidity of the matrix phase. Knowing the length of plastic zone, the crack opening displacement can be found. For a constant length of plastic zone, the crack opening displacement in creases as the rigidity of the matrix material decreases. Suppose the fracture of the two-phase system under consideration is caused by reaching a critical crack opening displacement at the crack tip, the critical fracture strength can be determined from the knowledge of fracture toughness of the matrix material.

The resonant frequencies of unidirectional graphite epoxy com posite beams were found to deviate markedly from classical beam theory predictions at higher modes of vibration. Timoshenko beam theory was used to account quantitatively for the dependence of ex perimental resonant frequencies on mode of vibration, length/thickness ratio, and the ratio of Young's modulus/shear modulus of the com posite beam. By using reasonable values for the longitudinal-trans verse shear moduli, the longitudinal Young's modulus of anisotropic composite beams under vibration agreed well with values determined by static tests and became independent of mode of vibration and L/t. The vibrating beam test method was employed for the deter mination of E₁₁, E₂₂, and G₁₂.

This paper is concerned with determining the elastic properties of a composite material composed of hollow spherical inclusions em bedded in a matrix. Both inclusions and surrounding material are taken to be isotropic and elastic.

As the result of a straightforward extension of Hashin's work, upper and lower bounds have been developed for the gross shear modulus of the composite. In addition, a closed form expression is presented for the gross bulk modulus of the material. Numerical results have been presented illustrating the effect of wall thickness of the inclusion upon the elastic constants of the composite. As illus trated by example, control of the properties and geometry of the inclusions permits "design" of a material with prescribed elastic behavior.

A membrane theory for thin, single layer, generally orthotropic, cylindrical shells experiencing harmonic, axi-symmetric motion is established. Shear-coupling in the plane of the middle surface of the shell results in coupled motion occurring in three dispersive modes of propagation. Long and short wavelength velocity limits in the three modes are analogous to those of an isotropic shell, however, the short wavelength limits are reversed in the first and second modes. Three discrete frequencies occur for which: (1). motion is predominantly radial; (2). motion becomes uncoupled in the first and second modes; (3). the type of wave changes from extension-shear to shear-extension (or vise-versa) for most off-angle orientations. These events occur within the range of wavelengths, established in the membrane theory for isotropic shells, which render the theory accurate. When the shell is specially orthotropic, the in-plane motion is uncoupled; the first mode is a non-dispersive shear mode, while the second and third are dispersive extensional modes.

The development of a submicron boron nitride coating for boron filaments has made possible the production of boron-aluminum com posites by a continuous casting technique. The tensile properties of aluminized boron filaments, as well as composite modules and tapes, fabricated by this liquid infiltration process are evaluated in this investigation. Tensile strengths up to 297 ksi were obtained for 65 volume percent nitrided boron-6061 aluminum alloy composite modules. Thermomechanical treatment in air of early 16-filament modules showed no degradation in strength after one hour at 1050°F, or 1000 hours at 570°F. Seven inches square panels, fabricated by diffusion bonding 20 mil diameter modules, exhibited longitudinal tensile strengths as high as 187 ksi and transverse strengths up to 15 ksi for fiber volume fractions of approximately 50 percent. The use of Ti cladding on aluminum-boron panel surfaces increased the trans verse strength to 33 ksi.