Sunday, June 10, 2012
A compelling failure analysis case history
Some presentations are so compelling that you can remember them, even four decades later. I still recall how back in fall 1971 Jack Low began a case history in his Mechanical Behavior of Materials II class at Carnegie Mellon University.
He passed around a prop - a transparent one-inch wide plastic box containing a sheet of clear plastic. Jack explained that was a replica (copy) of the surface to a broken hinge from the variable-sweep wing of an F-111 fighter-bomber. Both crewmen were killed when that plane crashed at low altitude on December 22, 1969. Then the whole fleet of F-111s was grounded - until General Dynamics could tell the US Air Force what had happened, and how to not have it ever happen again.
On the replica there was a thumbnail-shaped crack which had escaped detection during inspection after forging. In less than a hundred hours of flying it grew to a critical size, and resulted in the left wing falling off. It took Jack four or five classes to lead us through the whole detective story. A brief summary of it appears in John W. Lincoln’s 2000 article about the Effect of Failures on USAF Structural Requirements on pages 3 to 6. What made the story for this case history compelling?
First, it was a real world case which treated us like adults - not an oversimplified example that just used what was inside a textbook. We couldn’t just look up an equation, put in some numbers from a handy table, and get an answer in a few minutes.
Second, Jack introduced us to a new topic, linear elastic fracture mechanics. For homework he gave us photocopies of lecture notes used to teach it to engineers in the nuclear industry. In fracture mechanics there is a criterion for brittle fracture called the critical stress intensity factor, K1c.
You can measure K1c by testing a material in the laboratory. (Jack was on the committee that created the standard test for K1C). For a particular crack geometry you can calculate the stress intensity factor, K1 based on the applied stress and the crack depth. A safe design has K1 less than K1c. The stress analysis course we’d had the previous year taught us how to get from service loads to the applied stress. The crack depth is based on what you can detect via nondestructive evaluation of the product or component.
A safe design has to allow for cracks growing from repeated loading during service - a process called fatigue. (Sometimes you can see the fatigue crack-advance markings called striations on a fracture surface). Laboratory tests can measure the fatigue crack growth rate versus changes in the stress intensity factor. The interval between inspections would be chosen based on being able to detect a crack before it could cause failure.
Third, figuring out how to avoid having another failure had required creative thinking. Three different nondestructive test methods were used on the F-111. All had failed to detect that crack in the wing hinge. But, K1c is lower at below room temperature, so they set up to load the wings with each plane sitting in a room at a frosty -40 F. If the wings didn’t break during this cold proof test then fracture mechanics calculations said they also wouldn’t break in flight. Cold proof tests were repeated after every 1500 hours of flying time. The Royal Australian Air Force kept operating F-111 aircraft long after the US had retired theirs, and they continued using the cold proof test.
The image of three F-111 aircraft came from Wikimedia Commons.