Inductance-dominant impedance of steel wire rope and its change upon elastic tension, with relevance to strain sensing

This work provides the first comprehensive study of the AC impedance (along with the angle θ between the complex impedance and its real part, the resistance) of a metal wire rope (cable, steel, 7 ×7), and its dependence on the elastic tensile strain (≤0.0035). With θ> 45°, the impedance is dominated by the reactance (its imaginary part) rather than the resistance, regardless of the strain, though both reactance and resistance contribute to the impedance. Upon tension, θ decreases slightly (meaning that the degree of reactance dominance decreases slightly) and both reactance and resistance increase, but the fractional increase in resistance exceeds the fractional increase in reactance. The reactance is completely due to the inductance, with negligible contribution of the capacitance. The impedance, reactance, inductance and resistance all increase reversibly upon tension, while θ decreases reversibly. The resistance increase is attributed to a degree of straightening of the wires and the consequent decrease in the number of wire-wire contacts. The inductance increase is attributed to the tightening of the wire-wire contacts and the consequent promotion of the current path tortuosity. In the low-strain regime (≤0.001), the inductance during unloading is lower than that during the prior loading, with hysteresis. The fractional change in inductance per unit strain (up to 5 only) decreases with increasing strain. The resistance is a more sensitive strain indicator than the inductance, reactance, impedance, or θ. The highest gage factor (31) occurs at an intermediate strain (0.001). The strain dependence of the gage factor is reversible but hysteretic.