15)
The Paris equation for an aluminum alloy, with ?K in ksi?in, is given below.
$\frac{da}{dN} = 5 \times 10^{-10} (\Delta K)^4 in/cycle$
Non-destructive inspection (NDI) reveals that the largest internal flaw is 0.2 inch long.
The alloy is subject to one of the following two loading conditions:
\begin{tabular}{|l|l|l|}
\hline
Loading condition & Maximum stress & Minimum stress \\
\hline
Reversed loading with R = -1 & 15 ksi & -15 ksi \\
Cyclic loading with R = 0 & 30 ksi & 0 ksi \\
\hline
\end{tabular}
a) Calculate the initial crack growth rate for the two loading conditions.
b) If the fracture toughness of the alloy is $K_{1c} = 25 ksi\sqrt{in}$, under which type of loading is
failure likely to occur sooner?
c) How many cycles will it take for the component to fail under the conditions identified in
part b).
Assume the stress intensity factor under Mode I loading is given by $K_1 = \sigma \sqrt{\pi a}$