For a hole of length L (very ellipsoidal), with radius of curvature
at the ends, R, the energy of the distorted stress region is . Then
. The minimum R is on the level of the atomic size. This means
.
This is too low. creation of cracks involves surface tension. propagation
condition is
. Then
= griffith crack length.
. This means
. Surface
is actually jagged, increasing the real crack length.
=work of fracture
which is typically,
. Then
sometimes, but the crack does not propagate.
propagation condition:
.
There should really be a kinetic term, because the cracks can propagate at the speed of sound.
for
you get the griffith crack length.
. Crack can accelerate over time. Stresses tend to be perpendicular
to the crack. Instability in crack growth is onset at
.