Contacting surfaces: A problem in fatigue and diffusion bonding
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I. I N T R O D U C T I O N
A g e f f = Kma x -
A N accurate determination of the crack length, a, is a primary prerequisite for fracture toughness and fatigue crack propagation measurements. For example, in fatigue, the advance of the crack tip is driven by the alternating stress intensity factor A K = g m a x -- Kmi n
[1]
where Kma x and g m i n a r e functions of the applied loads, the crack length, and the part geometry. Besides standard optical techniques, there are now a number of methods available which are capable of performing crack length measurements, including compliance gage, electrical potential, and acoustic techniques, t~'2] However, in applying any one of these techniques to determine the crack length, it becomes immediately apparent that the measurement has to be performed under an applied load such that the crack is fully open. At lower loads, the crack will close down on itself, leading to erroneous crack length measurements. Moreover, this crack closure can have a significant effect o n fatigue crack propagation since closure partially shields the crack tip from the applied driving force on the crackJ 3] At present, the lowest stress intensity factor, Kcl, at the initiation of the first contact between the crack surfaces, is basically the only crack closure information derived from the standard m e a s u r e ments. This then leads to a modification of Eq. [1] to include crack closure effects through an effective stress intensity range t31
O. B U C K , Senior Scientist, R.B. T H O M P S O N , Program Director, and D.K. REHBEIN, Associate Metallurgist, are with A m e s Laboratory, Iowa State University, A m e s , IA 50011. D.D. P A L M E R , a former Graduate Student at A m e s Laboratory, is an Engineer with McDonnell Douglas Corporation, P.O. Box 516, St. Louis, M O 63166. L.J.H. BRASCHE is an Assistant Metallurgist at A m e s Laboratory, Iowa State University, A m e s , IA 50011. This paper is based on a presentation made in the s y m p o s i u m "Nondestructive Evaluation--Predictive and Descriptive Probes of Mechanical Behavior of Metals" presented at the TMS-AIME fall meeting in Cincinnati, OH, October 13, 1987, under the auspices of the T M S Mechanical Metallurgy Committee. METALLURGICAL TRANSACTIONS A
Kcl
[2]
In specific cases, use of Eq. [2] has led to unique relations between the crack propagation rate, da/dN, and A K e f f , independent of stress overload effects or of the applied stress ratio, t41 Unfortunately, the precise determination of Kct is difficult as well as controversial, t4] It has been argued that Kd is not even the correct quantity to be used for the determination of AKeff since contact in the wake of the crack tip does not completely shut off the effect of the externally applied stress on the crack tip. ]5'6'7] Each contact point in the wake of the crack creates its own stress intensity factor. The sum of all stress intensities created by the contacts is called the shielding stress intensity factor. Since any stress intensity factor is geometry dependent, knowle
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