Abstract
The paper deals with viscoelastic, rubber-like material unidirectionally reinforced with discontinuous fibres. The longitudinal storage modulus is calculated not only from an equation based on an existing force balance treatment but also from the elastic strain energy stored in matrix and fibres, using two different models to derive the stress and strain distributions from which the stored energy is calculated. There is very good agreement between all the calculations. The energy calculations reveal that loss modulus is also greatly increased by discontinuous reinforcement and enable its value to be estimated. Experiments on storage and loss modulus are reported and show that the calculations underestimate storage modulus and overestimate loss modulus. In both cases the factor of error ∼ 2, and arises because the amplified matrix strain is underestimated and is partly hydrostatic; the hydrostatic strain is non-dissipative and therefore does not contribute to the loss modulus. Discontinuous reinforcement can increase loss modulus as well as storage modulus by more than 100 times, and this should help sound and vibration deadening. An estimate is made of the wide ratio of compliance ÷ breaking strength available with discontinuous but not with continuous reinforcement, which opens up new design latitude for components hitherto reinforced with continuous fibres.
Similar content being viewed by others
References
N. F. Dow, General Electric Space Sciences Lab. Report R63SD61 (1963).
J. Amirbayat and J. W. S. Hearle, Fibre Sci. and Tech. 2 (1969) 143.
H. L. Cox, Brit. J. Appl. Phys. 3 (1952) 72.
D. McLean, J. Mater. Sci. 7 (1972) 98.
G. E. G. Bagg, M. E. N. Evans and A. W. H. Pryde, Composites 1 (1969) 97.
F. Schwarzl, Acustica 8 (1958) 164.
E. Goens, Ann. Phys. (Leipzig) 11 (1931) 649.
D. H. Ferriss, Conference on Properties of Fibre Composites, National Physical Laboratory — IPC Press (1972) p. 47.
J. W. S. Rayleigh, “Theory of Sound”, Vol. 2 (Macmillan, London, 1896) p. 313; (Dover publications, New York, 1945) p. 313.
R. M. Christensen, “Theory of Viscoelasticity. An Introduction”. (Academic Press, New York and London, 1971) pp. 41–42.
S. T. Mileiko, J. Mater. Sci. 5 (1970) 254.
A. Einstein, Ann. Physik. 19 (1906) 289.
Herr Bacelin, quoted in [14].
A. Einstein, Ann. Physik. 34 (1911) 591.
G. B. Jeffrey, Proc. Roy. Soc. A102 (1923) 161.
G. I. Taylor, ——ibid A103 (1923) 58.
T. B. Lewis and L. E. Nielsen, J. Appl. Polymer Sci. 14 (1970) 1449.
E. Guth, J. Appl. Phys. 16 (1945) 20.
A. Kelly, “Strong Solids” (OUP, 1966) p. 126.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
McLean, D., Read, B.E. Storage and loss moduli in discontinuous composites. J Mater Sci 10, 481–492 (1975). https://doi.org/10.1007/BF00543693
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00543693