Previous Results

The effect on composite electrical behavior due to the presence of highly conductive fibers is typically discussed with reference to the percolation threshold of the fibers [2,3] . When enough fibers have been added to the matrix, the fibers are above the percolation threshold, which is defined as a characteristic volume or number fraction of fibers at which continuous paths for electrical current exist in the composite. Some of these paths can occur through parts of the matrix where there has been dielectric breakdown between fiber tips, although most of the conduction is probably through touching fibers. The highly conductive fibers dominate conduction.

Uni-directional continuous fiber-reinforced composites also fall in the "percolating fiber" case. For these materials, the conductivity in the fiber direction should scale with the overall cross-sectional area of the fibers. For a time, this relationship was employed in an ASTM standard for assessing the fiber content of unidirectional fiber-resin composites [4]. It has also been utilized to follow the fracture of unidirectional composites in static or dynamic loading [5-7] The conductivity exhibits discontinuities as individual fibers break in loading or during fatigue, leading to "self-monitoring" behavior with respect to permanent damage [7].

Below the fiber percolation threshold, interesting transport behavior is also observed in discontinuous fiber composites. Although the matrix dominates the conduction processes, these processes can be strongly influenced by the highly conducting fibers. Rocha and Acrivos [8] developed a model for the thermal conductivity of a dilute suspension of conducting fibers. By "dilute" is meant a low enough volume fraction of fibers so that the presence of one fiber does not influence the effect of nearby fibers. This model was later extended by Frederickson and Shaqfeh [9] into the semi-dilute regime, where certain of the many-body interactions (influence of fibers on each other) were taken into account. Mackaplow et al. [10] conducted a numerical study of thermal transport in fiber suspensions, incorporating two-body interactions. These models all predicted that the change in composite conductivity should scale as nL³, where n is the number density of fibers of length L. This prediction was confirmed by the recent experimental work of Sundararajakumar and Koch [11]. These authors made isotropic fiber suspensions of chopped carbon fibers in a polyalkylene glycol matrix made moderately conductive by the addition of a small amount of KCl. High frequency conductivity measurements (10⁴ -10⁵ Hz) were employed to eliminate the double layer impedance on the fiber/electrolyte surfaces (see Sec. 3 below), which complicated an earlier DC study [12], thereby allowing true conductive fiber/poorly conductive matrix behavior to be observed.

The most extensive investigation of the electrical behavior of conductive short fiber composites of various kinds has been carried out by Chung and co-workers [7, 13- 15]. This work involved three types of matrices—polymer [13], concrete [14,15] , and ceramic [16]. Strain-induced DC resistance changes were attributed to various factors, including partial pull-out of crack-bridging fibers, changes in contact resistance between fiber and matrix, and changes in fiber alignment/spacing (highly oriented systems), with potential for piezoresistive applications [17] .

A multi-frequency AC conductivity/impedance approach to the study of conductive short fiber composites is a relatively recent development. Fricke [18] derived the first dispersion equations for the conductivity and permittivity of dilute suspensions of conductive ellipsoids in a less conductive matrix, later translated into complex impedance/modulus plots by Bonanos et al. [19]. Two arcs were clearly visible in modulus representation, but not in impedance (Nyquist) representation, most likely due to the absence of polarization/film impedances on the dispersed particles. Han and Choi [20] recently modeled the DC and AC electrical properties of 2-D conductor/insulator composites, obtaining double and even triple arcs in modulus plots, with pronounced fiber orientation effects. Gu et al. [21] observed a single bulk impedance arc in fiber-reinforced cement-based composites, using non-conductive wollastonite micro-fibers.

However, all reports involving conductive fiber composites with a less conducting matrix have exhibited two bulk arcs in Nyquist plots, similar to Fig. 1 [22]. In this instance, 1 % by weight of short steel fibers was added to hydrating cement paste with a 0.4 water-to-cement ratio (for details, see below). We will refer to this figure when discussing the other results from the literature. As can be seen in Fig. 1, the addition of conducting fibers at this level has an insignificant effect on the DC (low frequency) conductivity. Note that the bulk resistance, R_DC , is found at the real axis intersection of the bulk arc(s) and the start of the electrode arc observable on the far right of the diagram. In all impedance plots in this paper, frequency increases from right to left. The presence of conducting fibers clearly subdivides the bulk arc into low frequency and high frequency arcs. We refer to the intersection of the two bulk arcs as R_CUSP. The ratio,

= (R DC - RCUSP ) / RDC

(1)

or the ratio of the low frequency arc size to the overall DC resistance, is an important parameter for characterizing the complex conductivity of conductive fiber composites. For the random short steel fiber-in-cement paste composite of Fig. 1 this parameter is 0.33. Short carbon fiber cement-based composites have been studied [23] and are also the focus of the present work. Two bulk impedance arcs are typically observed for these composites as well (see below). Gerhardt [24] reported Nyquist plots for hot-pressed mullite matrix composites with 10% SiC whiskers. Parallel to the hot-pressing direction (perpendicular to the prevailing whisker orientation) was approximately 0.35. It was greater than 0.90 perpendicular to the hot-pressing direction. Nearly uniaxial fiber orientation was achieved by Wang et al. [25] in extruded/hot-pressed Si₃N ₄ matrix/SiC whisker composites (20 wt % fibers). When measured perpendicular to the fiber axis, was essentially zero (a single bulk arc), whereas it was high (~0.85) in the direction of the fibers.

Fig. 1. Impedance spectra for a random short steel fiber/cement matrix composite vs. the matrix without fibers, at 28 days of hydration. Note the DC resistance values, obtained by separate 4-point measurements.

The preceding examples involved ceramic (cement, oxide, or nitride) matrices. There is evidence that under certain circumstances, polymer matrix composites can exhibit similar two-arc impedance behavior. Kaushik et al. [26] studied the degradation of carbon fiber/vinyl ester composites (20 vol % fibers) submerged in concentrated NaCl solution and subjected to electrochemical potential gradients. The single capacitive feature in Nyquist plots of the pristine composite (due to the resistive polymer matrix) gradually evolved into the dual-arc behavior characteristic of chopped conductive fiber composites, with values of in excess of 0.9. This was interpreted as being due to slow penetration of the electrolyte into microscopic but percolated pores in the polymer matrix, rendering it moderately conductive.