The Elastic Constants of Fiber Reinforced Materials

Abstract

The five elastic constants of a composite containing parallel cylin drical fibers are expressed as a series expansion in terms of the volume fraction, c, of the fibers. The coefficients of c² are estimated on the basis of a "reflection" theory: the disturbance in the stress field caused by the presence of a cylinder creates a reaction around a second cylinder, and this in turn has an effect on the stress around the first one. The approximation is made that the reaction of the second cylinder to the said disturbance can be found by treating this disturbance, locally, as a homogeneous field. Although the numerical results of this procedure are not rigorous, it is believed that it correctly describes the role played by the elastic constants of the matrix and of the fiber material. A comparison with some previously published approximations which were derived on the basis of simple models demonstrates that the results for these models are to be used with reserve. This comparison is made in Section IV.