4. Experimental Details

Random Short Fiber Composite: The specimen whose impedance data are displayed in Fig. 1 was prepared from Type I portland cement at a water-to-cement ratio of 0.4 by weight. Steel fibers (1 % by weight, average length 2 mm, diameter 30 µm) were dry-mixed with the cement in a Hobart planetary mixer for 1 min. The water was added, and mixing continued for 3 min at low speed, followed by hand mixing for 1 min, and 3 additional minutes of machine mixing. The specimen was cast in a rectangular polycarbonate container (25 x 25 x 100 mm) with plain carbon steel (C-1018) electrodes cast in place at a separation of 90 mm. The sample was sealed and stored in a water-saturated environment until impedance measurements were performed.

Oriented Short Fiber Composites: A small-scale ram type extruder was used to produce sheet specimens (25.4 mm wide by 8 mm thick), at a rate of 1.2 mm/min. The overall composition was Type I portland cement with 0.5 vol % carbon fibers (4 mm final length, 8 µm diameter), and 5 % silica fume; 0.6 % superplasticizer and 0.8 % methylcellulose (extrusion aid) were added by weight. The water-to-solids ratio was 0.3. The liquid phase was first mixed with the fibers to distribute them, and then the solid materials were mixed together in a Hobart planetary blender for 10 min. After extrusion, the specimens were cured under a plastic sheet for one day and then cured in 100 % RH for 45 days.

Physical Simulations: Physical simulations were carried out using polycarbonate containers with plain carbon steel (C-1018) electrodes at the ends, but employing tap water as the electrolyte. Our prior work showed that tap water had the appropriate conductivity to simulate the conductivity of mature cement-based specimens. Furthermore, polarization/film impedances form on the surface of steel wires embedded in the tap water, just like in real o composites, resulting in coating impedances that are responsible for the frequency-switchable behavior of conductive fiber composites.

For simulations of fiber pull-out, the apparatus in Fig. 3a was employed. A vertical 50 mm wire (0.5 mm diameter) top electrode was suspended above a graduated cylinder ( ~3.8x10³ mm² cross section) with a copper gauze bottom electrode as shown. The distance between the tip of the wire and the gauze electrode was fixed at 61 mm. Water was added until it just touched the bottom of the tip, and the first impedance measurements were made. Carefully weighed amounts of water were added, from which accurate calculations of the increasing tip submersion were made. Impedance measurements were made as a function of tip submersion. The length of the fiber that was outside the water corresponded to the amount of fiber that would be pulled-out in a mechanical test.

Simulations of fiber debonding were carried out in a polycarbonate cell identical to that employed for the random short fiber composite (25 x 25 x 100 mm), with 90 mm spacing between the electrodes. A 50 mm long 304 steel wire (0.5 mm diameter), coated with an electrically insulating polymer sheath and sealed at the ends, was suspended on insulating supports along the axis of the cell and equidistant from the electrodes. Impedance measurements with and without the supports (in the absence of the wire) showed that these did not contribute to the impedance spectra obtained. Impedance measurements were made with the horizontal coated wire, and subsequently with progressively larger amounts of insulation stripped from each end (2 mm, 5 mm, etc.). The configuration was similar to that represented by Fig. 2a.

Fiber orientation studies were made in a shortened polycarbonate cell (25 x 25 x 31 mm), with a 25 mm bare 304 steel wire (0.5 mm diameter), as shown in Fig. 3b. The shortened cell was used to make it easier to see the fiber arc at large angles between the applied field and the wire, by increasing the value of (or (R_DC – R _CUSP)/R_DC) via minimizing the size of the high frequency arc (the wire-to-electrode contribution). Sufficient distance was maintained between the wire tips and the electrodes in the = 0 configuration (3 mm) in order to avoid end effects. In these studies, impedance spectra were taken as a function of the orientation angle between the wire and the direction of the applied field.

Fiber-orientation measurements were also made on an extruded carbon fiber specimen using the electroding scheme in Fig. 3c. Copper gauze electrodes 6 mm wide and running the width of the specimen were in contact with paper towel strips of the same dimension, which in turn were in contact with the surface of the sample. The paper towel strips were saturated with NaCl solution, to facilitate electrochemical contact with the sample. By shifting the centerlines of the top and bottom electrodes in opposite directions, the angle between the prevailing fiber direction and the direction of applied field was systematically varied, as shown.

Fig. 3. Schematics of a) the "pull-out" experiments, where the amount of submersion in tap water of a 50 mm long, 0.5 mm diameter, wire was systematically varied, b) the fiber rotation studies, where a 25 mm long steel wire (0.5 mm diameter) was positioned along the axis of a tap water cell equidistant from two electrodes 31 mm apart, and rotated as shown, and c) the composite orientation studies, where varying angles of field application relative to the direction of extrusion were accomplished by shift of the opposing electrodes. Impedance measurements were made in a) between the submerged wire and the copper gauze bottom electrode as a function of wire submersion, in b) between the external steel electrodes as a function of rotation angle, , and in c) between opposing copper electrodes as they were shifted in opposite directions as shown

Impedance Measurements: Impedance studies were carried out using a personal computer-controlled frequency response analyzer (Solartron 1260 with Z60 control software, Schlumberger, Cambridge, UK)* over the frequency range of 0.1 Hz to 10 MHz (10 points per decade). The excitation amplitude was varied from 25 mV to 1.0 V, with no obvious change in bulk spectral features. The spectra were analyzed using the "Equivalent Circuit"* software package [28].

The largest source of error in impedance measurements in inter-electrode spacing, which is estimated to be ± 5%. For a given series of tests, however, the spacing was maintained so as to further minimize uncertainty. In the physical simulations, the conductivity of the tap water can be quite sensitive to extraneous minerals introduced by handling. To confirm that the water had not changed conductivity as a result of testing, its conductivity was measured before and after each series of tests.

Numerical Simulations: Two FORTRAN 77 numerical programs, ac3d.f and elecfem3d.f, were used to carry out pixel-based computer calculations. These programs can be accessed at http://ciks.cbt.nist.gov/garbocz/, Chapter 2, along with a manual in HTML or hard copy format [29]. These programs were designed to compute the electrical properties of random materials whose microstructure can be represented by a 3-D digital image. They can also be used to simulate non-random, but analytically intractable geometries, as in the present study. The program ac3d.f is a finite difference program, for finite frequencies, and was used for all the frequency-dependent computations described in this paper. The program elecfem3d.f is a finite element program, for use in DC problems only. It was used for computations of the fiber pull-out laboratory simulation described above.

Pixels in a 3-D digital image were used to construct representations of each laboratory simulation studied (fiber pull-out, fiber debonding, and fiber orientation). The length scale generally used was 0.5 mm/pixel and the number of pixels used matched the overall sample dimensions. For example, the fiber orientation studies employed a system of 62 x 62 x 62 pixels, closely matching the 25 x 25 x 31 mm sample. The electrode-to-electrode dimension, 31 mm, was the most important dimension to match exactly, as these were close to the fiber tips. The wires were one pixel or 0.5 mm in width, and were suspended in the middle of the sample chamber as in the experimental arrangement. The debonding computations used a 51 x 51 x 182 pixel cell, and a one pixel wire, closely matching the physical size of the experimental cell used. For the pull-out computation, a length scale of 0.1 mm/pixel was used in the finite element program, in a 137 x 137 x 400 pixel system. The size of the computational system, 13.7 mm x 13.7 mm x 40 mm did not, therefore, exactly match the laboratory set-up. However, the size of the cell used, compared to the wire, was large enough, in both laboratory and computational situations, so that the system size should not have significantly affected the final results.

For the orientation and debonding computations, a finite difference node was placed in the middle of each pixel. Bonds were assigned between each pair of nodes, reflecting the conductivities of the materials around each pair of nodes. Both the electrodes and the wires were taken to be highly conductive. No polarization layer was used on the electrodes, so that the electrode arc was not included or computed. A polarization layer was taken on the surface of the wires, however. The admittance of this layer was taken to be that of comparable electrodes (fitted from experimental impedance data), but adjusted for the differences in the size and shape between the wires and the electrodes. In this way, only the time constant (resistance times capacitance) was specified, so that the unknown conductivity, dielectric constant, and thickness of the layer did not need to be individually determined. The water pixels had the correct admittance for the tap water used (~0.03 S/m). The wire was given a bulk DC conductivity approximately 10⁴ times that of the tap water. (The true value would be much larger, but this value was adequate for the computations, which become intractable at much larger values.) Once the model geometry and admittances were set up, a uniform electric field was applied, along the wire in the debonding experiments and at the appropriate angle ( ) to the wire direction for the orientation experiments. For the latter, it was easier to rotate the applied field than to rotate the wire. The frequency was systematically varied, similar to experiment, and the Nyquist plot determined.

In the pull-out computation, the water and air pixels were assigned appropriate conductivities, while the wire, one pixel in width, was assigned a conductivity 1000 times that of the water. There were no coating impedances, as comparison was to be made to the measured value of impedance at a frequency where the wire was highly conducting.