| dc.description.abstract | Finite element method (FEM) simulations were performed, and
distributions of current density, electromagnetic force, and stress fields due to the self induced electromagnetic forces were evaluated in a pre-cracked thin conductor.
Subsequently, experiments were conducted to validate FEM results, where a custom built
experimental setup was designed that can apply (a) pulse electric current, and (b) a
combination of electric current and mechanical load, at any angle between 0° to 90°
relative to the crack, onto a pre-cracked thin sample. The experimental setup had the
provision of conducting experiments at lowtemperatures by immersing the sample into a
cold bath, such as liquid nitrogen.
A finite sized thin conducting plate with a center crack was investigated under the
presence of an electric current. Firstly, to solve such a coupled multi-physics problem, a
need for using numerical techniques such as finite element method (FEM) was
highlighted in the study. Electric field in a thin conductor with a center crack was
evaluated by performing 2-dimensional (2-D) FEM simulations and results were
successfully bench marked against the available analytical solution. 2-D FEM
simulations were further employed to investigate the stress distribution in a center
cracked conductor due to the self-induced electromagnetic forces. Self-induced
electromagnetic forces due to steady electric current produced significant Poisson‟s
contraction as well as compressive ζxx and ζyy in the vicinity of the crack tip, resulting in
closure of the crack in the center cracked conductor. The observation was slightly
different under transient or pulsed electric current loading, wherein the self-induced
electromagnetic forces opened the crack at the beginning of the transient loading;
however, here also these forces became compressive at latter stage of the loading and
hence eventually acted to close the crack.
Effect of passage of electric current through a finite sized conductor with an edge
crack was further explored for observation of crack propagation. 2-D FEM simulations
showed that self-induced electromagnetic forces due to passage of an electric current can
open the edge crack a thin conductor. Static stress intensity in mode I due to the self induced electromagnetic forces, KIE, was observed to depend on current density, j, and
crack length, a, as KIE = f(a/w)j
2
(πa)
0.5, whereas dynamic K1E depended on j and a as
K1E,d=f(a/w)j
2
(a)
1.5. To corroborate FEM results, experiments were conducted in an edge cracked 12 μm thick Al foil sample. Short duration electric current pulses (without any
external mechanical load), with pulse-width of 50 µs - 0.5 ms, of high current densities,
ranging from 108
-109 A/m2
, were passed and the resultant crack extension after each
pulse was observed in situ using an optical microscope. Crack growth was observed in
the sample due to pure electric current, as long as K1E,dwas higher than the fracture
toughness, K1C, of the material. Moreover, crack propagated by a finite amount per
electric pulse, and it became longer with continued loading. Increase in current density
and performing experiments at higher temperatures resulted in enhanced crack
propagation.
Experiments conducted under the conditions: (i) if normalized crack lengths were
large (e.g., a/w> 0.8), and (ii) when electric current pulses of very high current densities
(e.g., (> 2.08 × 109 A/m2 for a/w of 0.7) were passed, revealed formation of blow holes,
instead of incremental sharp crack, at the crack tip. Upon repetitive electric current pulse
loading the blow holes also propagated in a crack like fashion; however, average velocity
of propagation of blow holes was much higher than the sharp crack propagation. At low
current density blow holes propagated in a zig-zag manner with little splitting, whereas at
higher current density it propagated in a straight path with large number of splitting,
especially originating from the sharp tips of existing frontier blow hole. Formation of
blow holes and their propagation was explained by performing microstructure based
FEM simulations, which revealed that the formation of blow holes at one or multiple
locations depends on the extent and severity of heat affected zone (HAZ). A direct
correlation between the size of HAZ and the size of the blow hole as well as the
propensity of formation of blow hole was established.
After understanding the effect of self-induced electromagnetic force on failure of
pre-cracked conductors, effect of simultaneous electric current and mechanical loading
on the crack propagation behavior in an edge-cracked conductor was explored. FEM
simulation revealed that under combined electromagnetic and mechanical loading, the
components of stress tensor as well as the stress intensity factors due to these two stimuli
can be linearly superimposed to determine the overall stress tensor and stress intensity
factor under combined electromagnetic and mechanical loading. Experiments conducted
under combined electromagnetic and mechanical loading showed that the critical electric
current density required to propagate a sharp crack decreased. Moreover, application of
mechanical load at an angle to the crack faces (i.e., under mixed mode loading), deflected
the crack at an angle upon passage of an electric current. The angle of deflection under
mixed mode conditions was predicted by standard principles of mixed-mode fracture
mechanics.
Implications of the self-induced electromagnetic and electromagnetic-mechanical
loadings were also investigated in context of some real-life applications, such as
microelectronic devices and development of tool-less machining tool. Passage of electric
current pulses of large current density caused catastrophic failure in pre-cracked 300 nm
thick Cu thin films deposited on Si substrate, wherein failure features, such as melting in
the vicinity of crack tip, delamination, splitting of cracks, and formation of blow holes,
were commonly observed. A machining tool based on the electromagnetic-mechanical
fracture was proposed as a constructive application of this rather destructive
phenomenon, which can be used for machining thin metallic samples (≈12 µm) in any
arbitrary shape with very high resolution (< 1 m) | en_US |
