fracture & yield in polymers

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 w/a= ?
?m = 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 ).
The Maximum Stress Amplification at the crack tip:
MSA = ?_2/?=(1+ 2a/b) for central crack
For a circle (a = b) ? MSA = 3
For a thin crack ( a/b=500 );MSA ? 103
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 diamond and ceramics Fracture of polymers:-
All materials contain small defects of some kind impact and other formsof rapid loading (low strain rate) cause brittle fracture.
-The factors that affect on necking in polymers:-
The type of material, length and thickness of specimen, test conditions especially strain rate.
-The drawing of fibers, films and sheets in forming operations occur at very high strain rates.
-the yield stress depends on strain rate.
-Crazing and shear yielding are affected differently by Temp. and strain rate. In more ductile polymers, the most obvious effect of raising Temp. is to accelerate shear yielding.