Inductance and piezoinductance of steel wire rope, with relevance to inductance-based structural self-sensing of stress

Steel wire ropes (cables) are widely used in construction. This work enables unprecedented inductance-based structural self-sensing of stress in steel ropes. Three types of galvanized steel ropes with different rope constructions, namely 1 x 19, 7 x 7 and 7 x 19, were used. The change in the rope inductance due to the applied tension was measured by directly clipping the leads of LCR meter to the rope. The results show that the apparent single-wire inductance (calculated from the measured rope inductance for the reference state of inductors in parallel) is above the inductance of a straight wire (calculated based on the dimensions) by 1-2 orders of magnitude. The model of inductors in parallel does not apply, but the model of resistors in parallel does. This implies that the rope inductance mostly stems from the wire-wire contacts. The structure-related inductance relates to the apparent/calculated single-wire inductance ratio. The inductance increases monotonically with the elastic stress/strain for 7 x 7 and 7 x 19, because tension tightens the wire-wire contacts. However, the inductance decreases upon tension for 1 x 19, because the relatively few wire-wire contact points. Thus, wirewire contact tightening enhances the inductance, whereas wire straightening diminishes the inductance. The importance of these competing mechanisms depends on the stress and rope construction. Above 600 MPa (3.5 x10-3 strain), wire straightening becomes sufficiently hindered by the tightened wire-wire contacts and the inductance reduction upon tension diminishes. The fractional change in inductance per unit strain describes the piezoinductance degree. Its relatively small magnitude for 1 x 19 implies that wire straightening is less influential than wire-wire contact tightening.