Introduction to Fatigue Analysis

Keywords: fatigue; crack initiation; crack propagation; plastic strain; Low 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. Later, 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. Read more about the History of Fatigue Analysis.


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 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 when significant plastic straining occurs during each cycle, which is associated with loads exceeding the material elastic limit and subsequent 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 when 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 cyclic 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.

Sample Fatigue Analysis Curve
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. Components that experience large number of cycles should be designed such that the stress amplitudes are below the fatigue design curves by a margin of safety –  thus designed for infinite life. Other components that experience stresses above the fatigue strength 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.

The second 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 stress
• 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

Fatigue Failures

Fatigue is the most common cause of fatigue failure in mechanical and thermal processing equipment, accounting for an estimated 70 percent of such failures.

The basic reason relates to the myriad of the causes of failures which include deficiencies in design, materials, processing complexities and owner/operator error. Failures have been traced to corrosion, material defects, stress risers, structural hot spots, dynamic loads, variable weather conditions and other factors not adequately covered by Design, Safety and Fabrication Codes & Standards.


(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


Fatigue Analysis Resources

ASME Standards
ASME Committee on Design Methods
ASTM Fatigue Standards and Fracture Standards
ASM Handbook, Volume 19: Fatigue and Fracture

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,

O’Donnell Consulting performs vibration and fatigue analysis – as well as thermal fatigue analysis on components for clients in industries including petrochemical, manufacturing and energy.

(412) 835-5007

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