The optimal fiber volume fraction and fiber-matrix property compatibility in fiber reinforced composites

Although the question of minimum or critical fiber volume fraction beyond which a composite can then be strengthened due to addition of fibers has been dealt with by several investigators for both continuous and short fiber composites, a study of maximum or optimal fiber volume fraction at which the composite reaches its highest strength has not been reported yet. The present analysis has investigated this issue for short fiber case based on the well-known shear lag (the elastic stress transfer) theory as the first step. Using the relationships obtained, the minimum spacing between fibers is determined upon which the maximum fiber volume fraction can be calculated, depending on the fiber packing forms within the composites. The effects on the value of this maximum fiber volume fraction due to such factors as fiber and matrix properties, fiber aspect ratio and fiber packing forms are discussed. Furthermore, combined with the previous analysis on the minimum fiber volume fraction, this maximum fiber volume fraction can be used to examine the property compatibility of fiber and matrix in forming a composite. This is deemed to be useful for composite design. Finally some examples are provided to illustrate the results

Higher Order Effects in the Dielectric Constant of Percolative Metal-Insulator Systems above the Critical Point

The dielectric constant of a conductor-insulator mixture shows a pronounced maximum above the critical volume concentration. Further experimental evidence is presented as well as a theoretical consideration based on a phenomenological equation. Explicit expressions are given for the position of the maximum in terms of scaling parameters and the (complex) conductances of the conductor and insulator. In order to fit some of the data, a volume fraction dependent expression for the conductivity of the more highly conductive component is introduced.Comment: 4 pages, Latex, 4 postscript (*.epsi) files submitted to Phys Rev.

Bohr-Sommerfeld Quantization of Space

We introduce semiclassical methods into the study of the volume spectrum in loop gravity. The classical system behind a 4-valent spinnetwork node is a Euclidean tetrahedron. We investigate the tetrahedral volume dynamics on phase space and apply Bohr-Sommerfeld quantization to find the volume spectrum. The analysis shows a remarkable quantitative agreement with the volume spectrum computed in loop gravity. Moreover, it provides new geometrical insights into the degeneracy of this spectrum and the maximum and minimum eigenvalues of the volume on intertwiner space.Comment: 32 pages, 10 figure