The effect of the fibre critical length on the thermal expansion of composite materials

The present study shows that both longitudinal and transverse thermal expansions of unidirectional composite materials depend on the length of the fibre. It is suggested that this dependence is through an efficiency factor k, generally used for describing the effectiveness of the reinforcement as expressed by mechanical properties such as modulus and strength. k itself is determined by the ratio of the fibre critical length, l_c, to the fibre length, l, and is expressed by two relationships, one for l≥l_c, and another for l≤l_c. The proposed theory is compared with experimental results obtained for samples comprising continuous short fibres. The length of the fibres was varied by varying the size of the test specimens. The length of the fibre is shown to affect significantly the value of the thermal expansion coefficients. An average l_c value calculated from the experimental results is in close agreement with one found by other investigators from tensile strength testing. It is suggested that the experimental procedure may provide a useful tool for assessing the fibre critical length.