Fracture of pre-cracked thin metallic conductors due to electric current induced electromagnetic force

Abstract

We investigated propagation of a sharp crack in a thin metallic conductor with an edge crack due to electric current induced electromagnetic forces. Finite element method (FEM) simulations showed mode I crack opening in the edge-cracked conductor due to the aforementioned (i.e., self-induced) electromagnetic forces. Mode I stress intensity factor due to the self-induced electromagnetic forces, $K_{\mathrm{IE},}$ was evaluated numerically as $K_{\mathrm{IE}}=\upmu l^{2}j^{2}(\uppi a)^{0.5}f(a/w)$, where $\upmu$ is the magnetic permeability, l is the length of the conductor, a is the crack length, j is the current density, w is the width of the sample and f(a / w) is a geometric factor. Effect of dynamic electric current loading on edge-cracked conductor, incorporating the effects of induced currents, was also studied numerically, and dynamic stress intensity factor, $K_{\mathrm{IE,d}}$, was observed to vary as $K_{\mathrm{IE,d}} \sim f_{d}(a/w)j^{2}(\uppi a)^{1.5}$. Consistent with the FEM simulation, experiments conducted using $12\,\upmu \hbox {m}$ thick Al foil with an edge crack showed propagation of sharp crack due to the self-induced electromagnetic forces at pulsed current densities of $\ge$ $1.85\times 10^{9}\,\hbox {A/m}^{2}$ for $a/w = 0.5$. Further, effects of current density, pulse-width and ambient temperature on the fracture behavior of the Al foil were observed experimentally and corroborated with FEM simulations.