Properties for Design of Composite Structures. Neil McCartney

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СКАЧАТЬ cluster of all types of fibre is now considered to be enclosed in a cylinder of radius b such that the volume fraction of fibres of type i within the cylinder of radius b is given by Vfi=niai2/b2. The volume fractions must satisfy the relation

      (4.142)

      It then follows that (4.140) may be written in the form

(4.143)

      The coefficients of the 1/r terms in relations (4.141) and (4.143) must be identical so that

      (4.144)

      It then follows that the effective transverse shear modulus for the multiphase composite is given by

(4.145)

      where

      (4.146)

      On using (4.1), the result (4.145) may also be written in the form

(4.147)

      4.6 Other Effective Elastic Properties for Multiphase Fibre-reinforced Composites

      Four independent effective elastic properties can now be estimated using relations (4.69), (4.67), (4.91) and (4.147), namely, νAeff,kTeff,μAeff,μteff. It is clear that Maxwell’s methodology has not provided an expression for the axial modulus EAeff of a multiphase unidirectionally fibre-reinforced composite. This problem has, however, been overcome [6] by considering a special case of aligned spheroidal inclusions (see Chapter 15 for details and (15.100)) where it has been shown that the effective axial Young’s modulus EAeff may be obtained from the following formula

(4.148)

      where

      (4.149)

      and where values of νAeff and kTeff have already been determined. The transverse Young’s modulus ETeff and transverse Poisson’s ratio νteff can be estimated by making use of the following relations, corresponding to (4.18) and (4.47),

      СКАЧАТЬ