Problem $5(100$ points$)$

The table below provides Forman Equation material properties for two sheets of aluminum alloys. As an engineer decide which alloy is more suitable to fabricate parts for an environment where fatigue is a dominant failure mode. Use a center$-$cracked panel $($CCP$)$ test to evaluate the damage tolerance characteristics of these two alloys. Evaluate the damage tolerance characteristics of the CCP using the data provided in the table and conclude which material is more desirable for this application. Use panels that are $70"$ wide, ${140}^{\text{'}\text{'}}$ high and ${0\mathrm{.}25}^{\text{'}\text{'}}$ thick. The panel is subject to $15$ Ksi operating cyclic stress with $R=0.$ Also the panel is required to have a residual strength $($due to limit condition$)$ of $22\mathrm{.}5$ Ksi $($it should always be capable of sustaining a minimum stress of $22\mathrm{.}5$ Ksi $).$

Question $1$: a$)$ Plot Linear Elastic Fracture Mechanics $($LEFM$)$ curve for CCP$-$A and $-$B panels $($Frs Vs $2$a$)$ separately.

b$)$ Superimpose Net Section Yield $($NSY$)$ curve on each LEFM curve.

c$)$ Comment on the difference between the two LEFM curves, and the difference between the NSY and the LEFM curves.

Question $2$: a$)$ Determine the critical crack length of each panel for $22\mathrm{.}5$ Ksi required strength

b$)$ Using the Forman Equation and spreadsheet technique $($manual or automated$)$ grow a crack from $2a=0\mathrm{.}1"$ to critical crack length in each panel using $15$ Ksi operating stress.

c$)$ For extra credit, use NASGRO or AFGROW to verify your crack growth analysis

d$)$ Plot the crack growth curve for each panel.

e$)$ Comment on the difference between the crack inspectability in both panels.

Question $3$: Based on your damage tolerance evaluation of CCP$-$A and $-$B panels which material would you pick for this application?

Question $4$: What is the crack growth life for these panels if subjected to $10\%$ higher stresses $($operating and limit$)?$ Comment on the difference in crack growth lives between different stress levels.

Note: the data in this table is similar to the one in Homework, but the crack growth constants are for Forman equation, not for Paris equation

$\backslash$table$[[,$CCP$-1(2024-$T$3$ Sheets$),$CCP$-2(7075-$T$6$ Sheet$)],[K_s,100Ks{i}^{**}{?}^i{n}^{0\mathrm{.}5},72Ks{i}^{**}i{n}^{0\mathrm{.}5}$