Linear elastic fracture mechanics:
Brittle solids fracture because the applied stress is amplified by minute cracks (of order 1
Mmin size) which occur naturally as a result of fabrication, solidification, fatigue.
These cracks are termed Griffith cracks.
Wide sheet of thickness B consider an elliptical through thickness crack in an elastic sheet
subject to a stress
in the y – direction causes a stress distribution a long ox1.
Wide or infinite width sheet means W >> 2a or
= maximum stress ; = applied stress; 2 is amplified from to 2 at both tips of the
crack where 2 falls to as x1 increases ( x1 distance from the crack ).
m
The Maximum Stress Amplification at the crack tip:
MSA =
(
For a circle (a = b)
For a thin crack (
) for central crack
MSA = 3
)
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For low applied stress, the stress at the crack tip approach the theoretical strength of the
solid ( inter atomic bonds reach to their breaking point ).
These conditions occur only in materials that is unable to relieve the stress concentration by
plastic flow or other mechanisms of crack blunting such as diamod and ceramics