Problem $4(40$ Points$)$

As a failure expert, you have been called to resolve a dispute between an airline customer and the airplane manufacturer when a rod in the engine mount area failed in service. The customer contends that the rod failed because of a flaw and offers as proof the fact that the fracture surface of the failed part has an obvious crack with an area of $0\mathrm{.}35$ square inch. The manufacturer counters that damage tolerance design concepts were used in the design of the rod, and a crack of this size would not lead to failure. The manufacturer counterclaims that the customer exceeded the maximum load rating of the rod of $1,500lb$ with their engine. To aid in the analysis, you conduct compliance tests with machined flaws of $0\mathrm{.}30$ and $0\mathrm{.}040$ square inch. The test results are plotted below. The rod is made of steel $(E=30,000,000$ and $v=0\mathrm{.}29,K_{IC}=40$Ksi$\sqrt[\phantom{2}]{i}n).$ Using this information who is correct? Justify your answer. $($See discussion about Energy is State of Stress presentations and Energy Principle and R Curve.ppt file$)$

Engine Rod Fracture Surface

Hint

From Eq$.5\mathrm{.}12$ find the GIC ; Then approximate the compliance rate at failure using: $($C: compliance$)\frac{C}{}A.$ Use Eq$.5\mathrm{.}4($remember that $A=B**$ a$,$ where B is thickness$)$ to find P $.$ Compare the P to the load rate by the manufacturer.