History of Fatigue Analysis – Understanding Fatigue Failure
Beginnings – 1920’s
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 loads.
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.
1950’s – Present
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
Two approaches are used to determine a component’s operational fatigue life: Safe Life and Damage Tolerance. They differ in a basic assumption — Safe Life assumes the component starts defect-free, while Damage Tolerance assumes it may already contain a flaw and asks how long that flaw can grow before it becomes critical.
Safe Life
The Safe Life approach designs a component to withstand a specified number of cycles, or the full service life of the equipment, without developing a fatigue crack at all. It relies on S-N test data for the material, combined with a safety factor applied to either the stress or the cycle count, to establish a design life with margin against the scatter inherent in fatigue testing.
Because Safe Life doesn’t assume any pre-existing damage, it typically results in a larger, heavier, and more conservative design than a damage-tolerant one — the safety factor has to cover the full range of uncertainty in material properties, loading, and manufacturing quality. Components designed this way are generally retired at the end of their calculated life regardless of their actual condition, since no inspection scheme is built into the design philosophy to verify remaining life beyond that point.
Damage Tolerance
The Damage Tolerance approach assumes a component may contain a crack-like flaw from manufacturing, handling, or early service, and uses fracture mechanics — rather than S-N data alone — to predict how that flaw grows under cyclic loading. P.C. Paris’ crack-growth relation, which ties the rate of crack extension per cycle to the applied stress intensity range, is the standard tool for this prediction.
Rather than retiring a component at a fixed calculated life, Damage Tolerance sets an inspection interval short enough to detect a crack before it reaches critical size, based on the predicted growth rate. This allows components to remain in service longer, and often lighter, than a Safe Life design would permit — provided the structure remains accessible for inspection and the inspection method is sensitive enough to reliably detect flaws well before they become critical. It’s the standard approach in the aerospace industry, where weight savings justify the added cost of a structured inspection program, and it’s applied more selectively elsewhere, typically where periodic inspection is already practical — pressure vessels and piping under in-service NDE programs, for example.
Choosing Between Them
The choice generally comes down to whether the component can be reliably inspected in service. Safe Life suits components that are inaccessible once installed, or where the consequence of an undetected crack is unacceptable regardless of inspection frequency. Damage Tolerance suits components where periodic inspection is feasible and where the resulting weight or cost savings justify the inspection program. Many designs use both principles together — a Safe Life baseline with damage-tolerant analysis used to justify continued operation past the original design life once inspection data supports it.
Fatigue Analysis References
- “Metal Fatigue in Engineering” – H.O. Fuchs & R.I. Stephens, John Wiley & Sons, 1980
- “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 originated in the U.S. Naval Nuclear Program. Dr. Bill O’Donnell, (Bernie) Langer, W.E. (Bill) Cooper, and James (Jim) Farr developed the initial formulation of this technology in the late 1950s and early 1960s, in the Tentative Structural Design Basis for Reactor Pressure Vessels and Directly Associated Components — later known as “SDB-63.”
Section III, “Vessels in Nuclear Service,” was the first section of the ASME Code to include specific rules preventing low-cycle fatigue failure; its first edition was published in 1963. Section VIII, Division 2, “Alternate Rules for Pressure Vessels,” followed in 1968.
Dr. Bill O’Donnell, Sr. began his career at Westinghouse/Bettis in the Naval Nuclear Program under Admiral Rickover. He later served for several decades as 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 Vibration & Fatigue Analysis on Components including Pressure Vessels and Heat Exchangers.