## Abstract

Third-order and fourth-order bounds on the effective transverse thermal conductivity k_{e} of fiber-reinforced materials (statistically isotropic in the transverse plane) due to Silnutzer and to Milton, respectively, are evaluated for a distribution of fully penetrable cylinders in a matrix. Both of these bounds involve a multidimensional integral which depends upon the three-point matrix probability function of the model. For nontrivial values of the fiber volume fraction φ_{2} (i.e. 0 < φ_{2} < 1) in the fully penetrable-cylinder model, the third-order bounds always improve upon the second-order bounds due to Hashin and the fourth-order bounds are always more restrictive than third-order bounds. The fourth-order bounds are sharp enough for 0 ≤ φ_{2} ≤ 0.3 to give quantitatively useful estimates of k_{e} even when the conductivity of the fiber phase k_{2} is as much as two orders of magnitude greater than the matrix conductivity k_{1}. For 0.8 ≤ φ_{2} ≤ 1, the Milton bounds are sufficiently restrictive to provide reasonable approximations of k_{e} for an insulating fiber phase such that 0.01 ≤ α ≤ 1, where α = k_{2} k_{1}. The results obtained in this study for k_{e} translate immediately into equivalent results for the axial shear modulus of fiber-reinforced materials.

Original language | English (US) |
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Pages (from-to) | 415-433 |

Number of pages | 19 |

Journal | International Journal of Engineering Science |

Volume | 24 |

Issue number | 3 |

DOIs | |

State | Published - 1986 |

## All Science Journal Classification (ASJC) codes

- Materials Science(all)
- Engineering(all)
- Mechanics of Materials
- Mechanical Engineering