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

A technique for machining thin metallic foils using electromagnetic-mechanical pulsed loading

“…It is important to note here that under above set of experimental conditions neither electrical load nor mechanical load alone would have caused any crack propagation, as the critical a/w-ratios for fracture of 12 μm thick Al foil upon application of only electric current pulses and only far-field mechanical loading were≈0.8 and≈0.65, respectively. These calculations for critical a/w ratios are based on the measured value of K IC of 8.6 MPam −0.5 for 12 μm thick Al foil [11][12][13].…”

“…where B, H and μ are magnetic flux density, magnetic field and magnetic permeability, respectively, the superscripts m and a represent material and air, respectively, and subscripts n and t represent normal and tangential directions, respectively. Equation (10) is a constitutive relation, whereas equations (11) and (12) are the boundary conditions. It should be noted that dD/dt term is neglected while writing equations ( 5) and (9), as electromagnetic wave propagation effects are not relevant for the large time-scale involved in the problem.…”

“…This warrants a need for performing mixed-mode fracture analysis as crack faces are loaded under both Mode I (crack opening mode) and Mode II (in-plane shear sliding mode) [14]. Although electric current pulse always loads the crack faces under Mode I condition [11], the far-field mechanical loading applied at an angle relative to the crack faces would load the sample under mixed-mode (Mode I and II). The failure criterion under such mixed-mode loading condition for an edge-cracked conductor can be given as follows [14]:…”

“…Nevertheless, there is a need of utilizing quantitative description of interaction between stress fields due to electromagnetic forces and far-field mechanical stresses and its impact on the crack propagation for both predicting the crack locus and optimizing the cutting parameters. Interestingly, we recently developed quantitative description of effects of application of electric current pulse and electromagnetic-mechanical loading on failure in thin metallic foils [11][12][13].…”

“…We could not perform any cuts at lower pulse width due to unavailability of the equipment 6. For the detailed formulations required for calculating these optimized conditions, one may refer to our previous works[11][12][13] 7. Nominal current density is calculated by dividing the peak current passed through the sample by the product of the thickness and halfheight of the sample.…”