History of Bending Fatigue, Part I

Even after more than a century of bending fatigue investigation, there is still much to be learned.


Bending fatigue life is a principle concern in all wrought and powder metal gearing and all mechanical power transmission components. It is also a concern in polymer gears when the mode of failure is not wear. The first part in this series investigates the historical milestones underlying the study of metal fatigue. The next part will focus on the myriad impending factors that contribute to this type of gear and rotating component failure. The final part of this series will collimate in statistical Probabilistic techniques for the determination of the appropriate survival / failure analysis in experimental design.

Being able to identify all of the contributing material and application influencing fatigue factors and designing intelligent and statistically significant experiments is crucial for the gear and machine design engineer in order to validate materials and geometry that are difficult to calculate with classical methods.

In Germany during the 1850s and 1860s, August Wöhler developed fatigue tests on railway axles. Those experiments are considered to be the first scientific investigations of fatigue. He showed how increasing levels of stress brought on fatigue related failure in a predictable way and, at a certain stress level, a fatigue limit existed with potential for infinite life. The result of Wöhler’s work led to the classic S-N diagram, i.e. stress amplitude versus number of cycles to failure that we use today.

In 1910, using Wöhler’s 50-year-old data, O. H. Basquin showed that alternating stresses in the finite life region could be represented as a log-log linear relationship. Research in the 1920s significantly contributed to the understanding of the combined effects of bending and torsion in multi-axial fatigue and brought about a pioneering understanding in the beginning of fracture mechanics.

In 1945, M. A. Miner devised a rule that had first been proposed by A. Palmgren in 1924. The rule, commonly known as the Palmgren-Miner linear damage theory, states that a body can tolerate only a certain amount of damage and cyclic fatigue, and this is the result of a damage accumulation process in which the material property deteriorates continuously under varying load spectrum. Therefore, the number of stress cycles and their individual amplitudes can be gathered in bins to predict the fatigue life of the body. There are many cautions and admonitions in using this rule. However, no other proposed technique generates a better estimation when done with knowledge and experience.

Between 1929 and 1930, Bernard Haigh, the professor of applied mechanics at the Royal Naval College in Greenwich, England, presented his rational explanation of fatigue when notches are present. He used concepts of notch strain analysis and residual stresses that were later more fully developed by Rudolf Peterson in 1953 and 1974. Peterson’s work in stress concentration factors remains a very significant work even today. Figure 1

During World War II, the loss of Liberty ships and tankers due to brittle fracture renewed a vigorous research into metal fatigue. In the ensuing years leading up to 1952, an amazing 1,289 warships would suffer brittle and structural related fatigue failure in welded joints. Then, in 1954, the first commercial jet dubbed the Comet broke apart in mid-air killing all of its passengers. This failure was due to the compression cycles that initiated a fatigue crack in the corner of an aerial window. Since then, the military, aerospace, and automotive industries have been the leading research proponents of metal fatigue.

The American Gear Manufacturers Association began in 1916 right on the cutting edge of new gear technologies as new gear markets were emerging.  In particular, the automotive industry was pursuing the quiet operation of gears, especially for timing gears. AGMA held its first Annual Meeting in May 1917 with more than 50 members in attendance and discussed subjects of interest and value to its members in the industries they were engaged in. The organization continues in the same manner today. Since that first meeting, a great amount of research still takes place on gear tooth bending and surface contact fatigue. It is a topic of great interest with research and collaboration going on in several current technical committees.

Today, there is much discussion and important work being done to understand and build a predictive model for calculating the bending life of powder metallurgy helical gears. However, even after more than a century of bending fatigue investigation, there is still much to be learned. PM gearing is unique in that the grains of metal powder can be an amalgamate combination of special alloys and metals, consisting of unique combinations of materials and properties. The grain structure of a three-dimensionally sintered surface has a microstructure unique to wrought materials, and its material fatigue properties related to gearing are of especially particular interest. Now, powder metal gears are becoming more and more attractive in automotive applications. A more full and cognizant understanding of the design life of molded, net-shape gear materials will have a profound impact on this industry in the years to come.

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is a senior technical specialist in the development of gearing, drive motors, and power closure devices in the automotive industry. He currently serves on the AGMA Plastic and PM Gearing Committees. Eberle is a master six-sigma black belt and has authored many papers on gearing, measurement system analysis and process statistics. He can be reached at Fred_Eberle@hci.Hi-Lex.com.