The fragmentation of wires by pulsed currents: Beyond the first fracture

A theoretical study of the elastodynamic behaviour of wires following fracture due to high pulsed currents is performed. In particular, this paper is concerned with why the fracturing process should continue beyond the first fracture as has been observed in experiments, but which is beyond the scope of previous theoretical studies. We investigate whether the pre-loading the wire undergoes prior to fracture, together with the change in boundary conditions introduced by the fracturing process at the ends of the wire pieces, can be important in explaining this behaviour. The mathematical model used in this study exists within continuum mechanics, and considers a thermal and Lorentz force mechanism for the creation of stress waves in the wire. Axisymmetric solutions are sought for a variety of fracture scenarios following the predictions of previous theoretical studies. For the case of fracture in a wire with initially clamped ends shortly after current switch-on, it is found that large longitudinal tensile stresses are generated in the wire largely as a result of the free-end boundary conditions that are introduced at the fracture surface(s). We also find that the fracturing process may also be expected to continue in a wire with initially free-ends which fractures on the centre-plane due to thermally-induced stresses. In this case, however, the maintenance of high tensile stresses is due to the introduction of stress waves caused by the fracture of the preloaded wire. This paper also considers the evolution from current switch-on of a wire with initially one clamped and one free-end. We find that this asymmetric clamping arrangement produces larger tensile stresses than those predicted by previous theoretical studies, which only considered problems symmetrical about the wire's centre-plane.