Paths swept out by initially slack flexible wires when cutting soft solids; when passing through a very viscous medium; and during regelation

摘要

Flow and fracture of some soft solids may be described by the 'solid' mechanical properties of elastic modulus, yield stress and fracture toughness, all being dependent on rate, temperature and environment. Other soft solids behave more like very viscous materials. When cutting soft solids, friction is often high between the blade and the material, and cutting is made easier when performed with a thin wire. The wire may be held taut in a frame like a fretsaw, but cutting is often done using an initially slack wire pulled into the solid by hand or machine. For both types of material behaviours, we investigate the curved shape taken by a loaded wire, elements along which cut into the material both radially and tangentially. For soft materials displaying solid properties, the treatment is based on the analysis of bi-directional cutting by Atkins et al. (Atkins et al. 2004 J. Mater. Sci. 39, 2761 2766), in which it was shown that the ratio x of tangential to radial displacements strongly influences the cutting forces. The shapes of wires of various lengths arranged as bowstrings, and the loads in the wires, are assessed against experiments on cheddar cheese. The resultant force takes a minimum value for a particular length of the wire, owing to the competition between lower cutting forces, but higher friction at large x and vice versa. Passage of a wire through very viscous materials is flow at very low Reynolds number. To determine the path swept out, we make use of the property of all slender bodies of revolution in highly viscous flow, namely, that the drag exerted across the body is approximately twice as large as along. Comparison is made with the experiments on weighted threads falling under gravity in glycerine. Regelation is another example of passage of a wire through a solid. The mechanism is completely different but, in the context of the present paper, we provide in appendix A the solution for the typical hours-long school demonstration where, unlike most reported studies, non-uniform temperature fields develop in the block of ice. Comparison is made with experiment.