Below is a plot of the crack velocity vs stress intensity fa

Below is a plot of the crack velocity vs. stress intensity factor for a glass surface in the presence of moist air. a) Assuming that this material is reaction-rate limited, calculate the values of the constants A and n. b) If the applied stress is doubled, by what factor is the crack velocity increased?

10 10 10 10 10 10 0.2 0.3 0.4 0.5 0.6 0.70.8 Stress Intensity Factor K (MPavm)

Solution

a)Can Assume V = AKⁿ ( no rate limit process)

Or, V = Aexp ( nK)      ( Arrhenius type)

Obviously if rate limit, use exp form, then

log V = Log A +n* K

take values from graph: at one xtreme -2 = logA +.65n

and at other extreme -10= logA = .21n

solve for n: =8/.44 =18.2

logA = -13.82 ,==> A = 10 ^(-13.82)

b) applied stress is doubled, the velocity depends only on K so no apparent effect

BEst