A statistical model of electrical resistance of carbon fiber reinforced composites under tensile loading

Abstract

The electrical resistance of carbon fiber polymer–matrix composites under tensile loading was measured using both the two-probe and four-probe techniques. Unlike most existing tests, which show an exponential or power relation between the electrical resistance and the tensile strain due to fiber breakage and/or electrical percolation under tensile loading; our results exhibit a more complex response. When the strain is increasing, the electrical resistance increases with a decreasing rate at the beginning, then decreases, and eventually increases exponentially up to the breaking point. To explain this interesting phenomenon, a statistical model based on Weibull distribution function is introduced. Three stages of the electrical resistance versus tensile strain curve have been identified. At the primary and secondary stages, the conductivity of the composite follows a Weibull statistical distribution function. This is mainly due to the increasing number of contact points of the fibers during loading. At the tertiary stage the usual exponential function is obtained, which is controlled by fiber breakage. The results obtained from the theoretical model agree well with the experiment.