History of Fatigue Analysis
Keywords: A. Wohler; Gerber; Goodman; J. Bauschinger; O. Basquin; H. Gough; H. Moore & J. Kommers; A. Griffith; L. Coffin; S. Manson; P. Paris; M. Brown; K. Miller
The history of fatigue analysis originated with the study of the catastrophic failure of rail axles. These early investigations determined that failures occurred at the axle shoulders – and that the elimination of large geometric discontinuities helped to alleviate the issue. At this time the word “fatigue” was introduced to describe failures occurring from repeated stresses.
In Germany, during the 1850s, August Wöhler performed many laboratory rail axle fatigue tests under repeated stresses – and is now considered the “Father” of fatigue testing. Using stress vs. life (S-N) diagrams, he showed how fatigue life decreased with higher stress amplitudes, and that below a certain stress amplitude, the test specimens did not fracture – introducing the concept of an “endurance limit” of a material. Wöhler further concluded that the cyclic stress range was more important than peak stress.
During the 1870s, Gerber and others investigated the influence of mean stress and Goodman proposed a simplified theory concerning mean stresses. In 1886, Bauschinger showed that the yield strength in tension or compression was reduced after applying a load of the opposite sign that caused inelastic deformation. This was the fore-runner of understanding cyclic softening and hardening of metals.
In 1910, Basquin showed that alternating stress vs. number of cycles to failure in the finite life region could be represented on a log-log linear relationship. In the 1920s, Gough and others discovered the effects of bending and torsion (multiaxial fatigue). In 1927 Moore and Kommers published the first American book on the fatigue of metals. In 1920, Griffith published the results of his theoretical experiments on brittle fracture using glass. He found that the strength of the glass depended on the size of microscopic cracks. If (S) is the nominal stress at fracture and (a) is the crack size at fracture – the relation is S √a = constant. Through his pioneering work on the importance of cracks, Griffith became the “father” of fracture mechanics.
After crashes of de Havilland Comets in 1954, efforts were made to mitigate the initiation and growth of cracks. The aerospace industry thus initiated a concentrated effort to learn the criticality of fatigue, stress risers, and crack initiation and growth. Further progress was made during the 1950s toward understanding the fatigue process by L.F. Coffin and S.S. Manson. They demonstrated the ability to explain fatigue crack-growth in terms of plastic strain just ahead of the crack tip as the cracks propagated into the material. Plastic deformation occurs just ahead of the crack tip leading to the propagation of the crack with each load cycle.
The prediction of fatigue life came in the 1960s when P.C. Paris proposed methods for predicting the rate of growth of individual fatigue cracks. He demonstrated the rate of change in the crack length versus the number of cycles.
Over the past several decades, much progress has occurred in understanding the effects of cyclic loading and the mechanism of propagation of cracks in metallic structures. Numerous scientists have been involved in these historical advances. During the 1980s, Brown and Miller investigated the complex problem of in-phase and out of phase multiaxial fatigue. The small crack problem was noted at this time, and many others worked to understand this problem. The small crack problem was complex and important, since these cracks grew faster than longer cracks based on the same driving forces. Fatigue of materials continues to be studied in order to design components to last their intended design lives.
METHODS OF DESIGN
There are two approaches used during the design of a component to determine its useful, or operational, fatigue life: (1) Safe Life and (2) Damage Tolerance.
(1) Design a component to not fail within a certain period of time or to last nearly forever during the service life of a component under a given set of operating conditions.
(2) Design a component to a specific life based on using crack growth prediction methods.
Safe Life requires testing and analysis to estimate the service time of a component. Additionally, a safety factor is added to ensure that catastrophic failures will not occur. This approach subsequently makes the component larger, heavier, and possibly more expensive to manufacture.
Damage Tolerance assumes a crack or cracks already exist in the component. In this approach, the fracture load where the component will fail is known as the critical crack size. Assuming the size of the existing cracks, the period of time for a crack to grow to this critical crack size is predicted. Damage Tolerance utilizes da/dN curves for the material of the component. Cracks can initiate from internal defects or from surface defects. Thus it is required to understand the effects of alloy composition, processing effects and subsequent microstructure.
Fatigue Analysis References
1) “Metal Fatigue in Engineering” – H.O. Fuchs & R.I. Stephens, John Wiley & Sons, 1980
2) “Metal Fatigue in Engineering, 2nd Edition” – Ralph I. Stephens, Ali Fatemi, Robert R. Stephens, Henry O. Fuchs, John Wiley & Sons, 2001
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, (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.Our company President, Bill, Sr. began his career at Westinghouse/ Bettis in the Naval Nuclear Program under Admiral Rickover. For several decades, he served as the Chairman of the ASME Subgroup on Fatigue Strength, and has published numerous papers on design, fatigue and fracture.
O’Donnell Consulting performs engineering design and analysis – including fatigue analysis on components including pressure vessels and heat exchangers.