Properties for Design of Composite Structures. Neil McCartney

Чтение книги онлайн.

СКАЧАТЬ target="_blank" rel="nofollow" href="#ulink_c6e7c743-c080-52e6-99bd-e9201197de4e">4.69), (4.91), (4.147) and (4.152) are generated. Thus, most multiphase properties can be derived from corresponding results for two-phase properties.

      It should be noted that it has not been possible to derive the axial thermal expansion coefficient for a multiphase unidirectional composite, although the concentric cylinder model of a composite generates this property for a two-phase composite (see Appendix B). The challenge now is to determine the property combination P8 (≡αAeff) that enables the two-phase result (B.52) (see Appendix B) to be extended to multiphase composites using a relation of the form (4.158). Following inspection of the multiphase results so far obtained, one might expect that the required mixtures relation for a two-phase composite might have the following form:

(4.159)

      It can be shown that the conjectured relation (4.159) for just two phases is an equivalent form of the result (B.52) derived using the concentric cylinder model of a two-phase unidirectional composite. Relation (4.158) can then be used to generate the following corresponding expression which is conjectured to be valid for multiphase composites:

(4.160)

      4.8 Summary of Results for Multiphase Composites

It is useful to bring together the results that have been derived for multiphase fibre-reinforced composites. The values of the effective properties κAeff, κTeff, EAeff, ETeff, νAeff, νteff, kTeff, μAeff, μteff, αAeff and αTeff of the transverse isotropic unidirectionally fibre-reinforced composite may be obtained from the following set of formulae, obtained from relations (4.10), (4.13), (4.66)–(4.69), (4.91), (4.147), (4.152) and (4.160)

      (4.161)

      СКАЧАТЬ