A simple model to predict the effect of volume fraction,diameter, and length of fibres on strength of fibre reinforced brittle matrix composites

A simplified model is presented to predict the strength variations of brittle matrix composites, reinforced by steel fibres, with the variations of fibre parameters—length, diameter and volume fraction. This model predicts that its tensile and flexural strength increase non‐linearly with the fibre volume fraction. It also predicts that similar non‐linear behaviour should be observed with the reduction of the fibre diameter when other parameters are kept constant. The experimental results support both these theoretical predictions. It is also explained why an increase in the fibre length does not always significantly increase the fracture toughness. The objective of this paper is not to explain and understand in great detail the science of all phenomena responsible for the strength increase of fibre reinforced brittle matrix composites, but to provide a simple engineering explanation as to why its strength increases with the fibre addition, and how this increase can be quantitatively related to the variations in fibre parameters—fibre volume fraction, fibre length and diameter. These simplifying steps are needed to provide a tool that the practicing engineers can use to predict the brittle matrix strength variation with the fibre parameters. In the area of geomechanics, the results presented here can be used to assess and predict the behaviour of fibre‐reinforced earth. Copyright © 2000 John Wiley & Sons, Ltd.