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

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 $$K_{\mathrm{IE}}=\upmu l²j²(\uppi a)^0.5f(a/w)$$ , 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 $$K_{\mathrm{IE,d}} \sim f_d(a/w)j²(\uppi a)^1.5$$ . 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 $$\ge $$ $$1.85\times 10⁹\,\hbox {A/m}²$$ 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.