EXAMPLE
First estimate the minimum dimension necessary for plastic effects to be ignored.
From ( 2a) bo = 2.5 ( 50/1400 )2 = 3.2 mm. Although this is less than the ligament length of 6 mm, it exceeds the thickness of 2 mm, so plastic effects are not necessarily negligible and we would expect both failure mechanisms - elastic fracture and plastic collapse - to interact.
Letting the normalised crack length be α = a/w = 4/10 = 0.4, the critical load arising from each of the mechanisms acting independently is as follows :
Plastic Collapse Let σP be the critical load if plastic effects dominate, then from the free body above : | |
σP = Sy ( 1 - α ) = 1400 x 0.6 = 840 MPa | |
Elastic Fracture Let σE be the critical load if elastic effects dominate ( ie. plane strain ), then : | |
KIc = σE Y √( πa ) where, for case ( a) Y = √( sec α π/2 ) = 1.11 and so | |
σE = 50/( 1.11 √( 0.004 π ) ) = 401 MPa don't forget the units ! |