Introduction to Fatigue Analysis
fatigue; crack initiation; crack propagation; plastic strain; how cycle fatigue; elastic range; high cycle fatigue; fracture mechanics
In the early 1800’s there were reports of various engineers studying fatigue and failure of railroad equipment. One of the first documented fatigue investigations was reported by a German mining engineer, W. A. S. Albert, who in 1829 performed repeated loading tests on hoist chains. In the 1850’s, August Wohler studied railway axle failures, and subsequently developed design strategies for avoiding fatigue failure under bending, torsion, and axial loads. He also demonstrated that fatigue was affected not only by cyclic stresses but also by accompanying steady (mean) stresses.
Fatigue may be characterized as a progressive failure phenomenon that occurs by the initiation and propagation of cracks to an unstable size. Fatigue failures continue to be a major concern in engineering design. It is estimated that the annual cost of fatigue of materials to the U.S. economy in 1982 dollars is around $100 billion. These costs arise from the occurrence or prevention of fatigue failure for ground vehicles, rail vehicles, aircraft of all types, bridges, cranes, power plant equipment, offshore oil-well structures, and a wide variety of machinery and equipment.
Fatigue failure investigations over the years have led to the observation that the fatigue process actually embraces two domains of cyclic stressing or straining that are significantly different in character, and in each of which failure is produced by different physical mechanisms. One domain of cyclic loading is that for which significant plastic strain occurs during each cycle, which is associated with high loads and short lives, or low numbers of cycles to produce fatigue failure – commonly referred to as low-cycle fatigue. The other domain of cyclic loading is that for which the strain cycles are largely confined to the elastic range, and is associated with lower loads and long lives, or high numbers of cycles to produce fatigue failure – commonly referred to as high-cycle fatigue. Low-cycle fatigue is typically associated with cycle lives from one up to about 10^4 or 10^5 cycles, and high-cycle fatigue for lives greater than about 10^4 or 10^5 cycles.
|This curve shows the typical relationship between stress, strain and cycles to failure (Ref. 5)|
In the design of equipment, it is necessary to avoid fatigue failure for the specified design life. Many components will experience huge number of cycles, and should be designed such that the stress amplitudes are below the fatigue design curves by a margin of safety – and are thus designed for infinite life. Other components may experience stresses above the fatigue strength, and are thus designed for finite life.
At present, there are three major approaches to analyzing and designing against fatigue failures. The traditional approach, which was developed to essentially its present form by 1955, is to base analysis on the nominal (average) stresses in the region of the component being analyzed. The nominal stress that can be resisted under cyclic loading is determined by considering mean stresses and by making adjustments for the effects of stress raisers, such as grooves, holes, fillets, and keyways. This is called the stress-based approach. Another approach is the strain-based approach, which involves more detailed analysis of the localized yielding that may occur at stress raisers during cyclic loading. Finally, there is the fracture mechanics approach, which primarily considers material toughness, crack size and stress levels.
In the stress-based fatigue analysis approach, factors that the designer should consider are:
• The effects of a simple, completely reversed alternating stress on the strength and properties of engineering materials
• The effects of a steady stress with superposed alternating component, that is, the effects of cyclic stresses with a nonzero mean
• The effects of alternating stresses in a multiaxial state of stress
• The effects of stress gradients and residual stresses, such as imposed by shot-peening or cold-rolling
• The effects of stress raisers, such as notches, fillets, holes, threads, riveted joints, and welds
(1) “Mechanical Behavior of Materials – Engineering Methods from Deformation, Fracture and Fatigue” Norman E. Dowling, College of Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 1993, Prentice Hall, NJ 07632
(2)“Failure of Materials in Mechanical Design – Analysis, Prediction, Prevention” J.A. Collins, Ohio State University, 1981, John Wiley & Sons
(3) “Metal Failures – Mechanisms, Analysis, Prevention” Arthur J. McEvily, Professor Emeritus, Department of Metallurgy and Materials Engineering, University of Connecticut, 2002, John Wiley & Sons
(4)“Engineering Against Fatigue” J.H. Benyon, M.W. Brown, T.C. Lindley, R.A. Smith, & B. Tomkins, Eds., 1999, A.A. Balkema, Rotterdam, Netherlands
(5) “Code Design and Evaluation for Cyclic Loading – Sections III and VIII” W.J. O’Donnell, Chapter 39 Companion Guide to the Boiler & Pressure Vessel Code- Criteria and Commentary on Select Aspects of the Boiler Pressure Vessel and Piping Codes, Second Edition, Vol. 1, Ed. K.R. Rao, 2006. ASME
The fatigue design life evaluation procedures in Section III of the ASME Boiler and Pressure Vessel Code were originally developed in the U.S. Naval Nuclear Program. Those involved included Dr. Bill O’Donnell, President, (Bernie) Langer, W.E. (Bill) Cooper and James (Jim) Farr – who, in the late 1950’s and early 1960’s developed the initial formulation of this technology in the Tentative Structural Design Basis for Reactor Pressure Vessels and Directly Associated Components, which became known as “SDB-63.”
Section III of the ASME Code “Vessels in Nuclear Service” was the first to include specific Code rules to prevent low cycle fatigue failure. Its first edition was published in 1963; Section VIII, Division 2, “Alternate Rules for Pressure Vessels” followed in 1968.
Fatigue Analysis Resources
We were requested by a client to perform a stress, vibration and fatigue analysis on a bellows design. The 28-convolution bellows was intended to last for 5 years, or 13.14 billion cycles. The bellows assembly is installed in a vertical orientation with its bottom end stationary. The bellows top end is subjected to a load that causes its top end to move in a circular motion. Both bellows ends remain parallel at a constant distance apart at all times.
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