STRENGTH PREDICTION AND OPTIMIZATION OF COMPOSITES WITH STATISTICAL FIBER FLAW DISTRIBUTIONS

For continuous fiber reinforced polymeric composites the process dominating tensile strength is fiber fracture. This phenomena results in stress concentrations in adjacent fibers over some distance which is directly associated with the ineffective length. This length is the controlling factor in the theory of bundle strength for polymer-based composites. The associated stress concentration factor. C, is normally associated with fracture propagation in both the matrix and surrounding fibers, and should also be included as an important part of any representation of the mechanism controlling tensile failure in fibrous composites. In this paper, we combine bundle theory with the mechanics of local stress concentration in the development of a mechanistic representation of tensile strength. The resulting analysis is applied to numerical studies of the influence of micromechanical properties and irregular fiber spacing on the tensile strength, and a discussion of optimal design parameters for composites. It is shown that the existence of stress concentrations increases the chance of crack propagation and decreases the strength values predicted by bundle theory. Therefore, these stress concentrations are found to play a significant role in determining the tensile strength of a composite. However, for polymeric based composites, the variation in the strength curve as a function of the constituent material properties is demonstrated to be controlled by the changes in the ineffective length-delta. Therefore, for polymeric composites the optimal design of tensile strength is generally achieved by decreasing the ineffective length. However. for composites with very small values of ineffective length. the relatively larger values of stress concentration are found to result in strength decreases, which provides a maximum (or optimum) value in the strength curve. These calculated strength values are compared with experimental measurements to validate the accuracy of our formulation. This analysis provides designers with adequate tools to choose not only the constitutive materials of the composite, but also the processing techniques which yield various fiber spacings and interface properties.