Problem $3$: A single$-$edge$-$cracked plate is loaded in tension and has dimensions $($b $=75$ mm$,$ t $=5$ mm$,$ large h$).$ It has an initial crack

length of ai $=4$ mm$.$ It is cyclically loaded with Pmin $=0$ and Pmax $=20$ kN and the material is such that

KIC $=200$ MPa m$,$ C $=3\mathrm{.}28$ x$10-9$ mm$/$cycle

$$MPa meter $$m $,$ andm $=3\mathrm{.}13$

For the correction factor F use the method of Goss & Brown as given in The Stress Analysis of Cracks Handbook.

Note: The Yield Strength of the material is neither given nor considered. Depending on the material$$s Yield Strength it is possible

that failure by ligament yielding could occur before Fast Fracture. For proper component design this possibility would need to be

comprehensively explored.

a$.$ Convert the value of C to have consistent MKS units

b$.$ At what crack length will fast fracture occur?

c$.$ How many cycles can be applied before failure by fast fracture occurs?