Page 352 - Shigley's Mechanical Engineering Design

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Fatigue Failure Resulting from Variable Loading 327
Collins said it well: “In spite of all the problems cited, the Palmgren linear damage
rule is frequently used because of its simplicity and the experimental fact that other
more complex damage theories do not always yield a significant improvement in fail-
ure prediction reliability.” 26

6–16 Surface Fatigue Strength
The surface fatigue mechanism is not definitively understood. The contact-affected
zone, in the absence of surface shearing tractions, entertains compressive principal
stresses. Rotary fatigue has its cracks grown at or near the surface in the presence of
tensile stresses that are associated with crack propagation, to catastrophic failure. There
are shear stresses in the zone, which are largest just below the surface. Cracks seem to
grow from this stratum until small pieces of material are expelled, leaving pits on the sur-
face. Because engineers had to design durable machinery before the surface fatigue phe-
nomenon was understood in detail, they had taken the posture of conducting tests,
observing pits on the surface, and declaring failure at an arbitrary projected area of hole,
and they related this to the Hertzian contact pressure. This compressive stress did
not produce the failure directly, but whatever the failure mechanism, whatever the
stress type that was instrumental in the failure, the contact stress was an index to its
magnitude.
8
Buckingham 27 conducted a number of tests relating the fatigue at 10 cycles to
endurance strength (Hertzian contact pressure). While there is evidence of an endurance
7
limit at about 3(10 ) cycles for cast materials, hardened steel rollers showed no endurance
8
limit up to 4(10 ) cycles. Subsequent testing on hard steel shows no endurance limit.
Hardened steel exhibits such high fatigue strengths that its use in resisting surface fatigue
is widespread.
Our studies thus far have dealt with the failure of a machine element by yielding,
by fracture, and by fatigue. The endurance limit obtained by the rotating-beam test is
frequently called the flexural endurance limit, because it is a test of a rotating beam. In
this section we shall study a property of mating materials called the surface endurance
shear. The design engineer must frequently solve problems in which two machine ele-
ments mate with one another by rolling, sliding, or a combination of rolling and sliding
contact. Obvious examples of such combinations are the mating teeth of a pair of gears,
a cam and follower, a wheel and rail, and a chain and sprocket. A knowledge of the sur-
face strength of materials is necessary if the designer is to create machines having a
long and satisfactory life.
When two surfaces roll or roll and slide against one another with sufficient force,
a pitting failure will occur after a certain number of cycles of operation. Authorities are
not in complete agreement on the exact mechanism of the pitting; although the subject
is quite complicated, they do agree that the Hertz stresses, the number of cycles, the sur-
face finish, the hardness, the degree of lubrication, and the temperature all influence the
strength. In Sec. 3–19 it was learned that, when two surfaces are pressed together, a
maximum shear stress is developed slightly below the contacting surface. It is postulated
by some authorities that a surface fatigue failure is initiated by this maximum shear
stress and then is propagated rapidly to the surface. The lubricant then enters the crack
that is formed and, under pressure, eventually wedges the chip loose.

26 J. A. Collins, Failure of Materials in Mechanical Design, John Wiley & Sons, New York, 1981, p. 243.
27 Earle Buckingham, Analytical Mechanics of Gears, McGraw-Hill, New York, 1949.