256 Effects of Damage on HCF Properties
where 
A
is the fatigue strength at an arbitrary mean stress and depends not only on
temperature but on time in order to account for the time-dependent behavior. This formula
is based on the assumption that the fatigue ratio is a function of the creep rupture strength
only. The formulation goes on to use a “universal” empirical relation between the fatigue
ratio, V
r
, and the normalized creep rupture strength, r,
r =

u
t T

u
20

C
(5.55)
The empirical relationship is of the form
V
r
=A
r
r
−
R (5.56)
By applying this relation to data at two values of stress ratio, R =−1 (fully reversed
loading at zero mean stress) and R =0 (pulsating tension), the coefficients A
r

f
.Ifk
t
is known,
k
t
can be substituted for k
f
for a conservative estimate. This produces the upper curve in
Figure 5.33 for a known k
t
.
s
–1
s y (t,T)
Mean stress
Alternating stress
s
0
Figure 5.32. Haigh diagram of a smooth component in the creep regime (after [37]).
Notch Fatigue 257
s y (t, T )
s
–1
Fictitious mean stress
Alternating stress
k
t
s y (t, T )
k

2
t
3
t
3
> t
2
> t
1
Figure 5.34. Creep rupture curves at elevated temperature.
258 Effects of Damage on HCF Properties
Mean stress/Creep rupture strength
Alternating stress/S
0
Modified Goodman law
Circular arc
Gerber parabola
Figure 5.35. Normalized creep curves (after [20]).
Finally, an alternative empirical relation that involves a straight line Goodman equation
on a Haigh diagram, but using the tensile strength as discussed earlier, can be used
to represent the combined creep and fatigue behavior on a Haigh diagram at elevated
temperatures. For each temperature, a different line represents the data as illustrated in
Figure 5.36 which appears in [35]. The restriction in this method of representing data is
that the static stress does not exceed the creep rupture strength at any temperature. Forrest
claims that the straight line curves, truncated by the creep rupture stress, represent data as
well as the circular arc method at high temperatures and is “a better guide to fluctuating
fatigue strengths at moderate temperatures. That this criterion fits the experimental data
reasonably closely is an indication that in general there is little interaction between the
creep and fatigue processes” (see [20], p. 248).
The discussion above illustrates some of the complexities in designing for fatigue under

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Chapter 6
Fretting Fatigue
6.1. INTRODUCTION
Fretting fatigue is a type of damage occurring in regions of contact where small relative
tangential motion occurs between the two bodies in contact that are under compressive
load. Fretting fatigue typically involves a contact region where both complete and partial
slip occur as discussed below. It is usually associated with loading conditions where

Stick
SlipSlip
Fretting
region
TT + Q
P
Q
2a
Figure 6.1. Schematic of fretting region showing applied forces.
normal and tangential loads are denoted by P and Q, respectively. Under typical stick–
slip conditions, part of the contact region undergoes no relative displacements between
pad and specimen (stick) while the edges undergo slip. The maximum slip occurs at the
deformed edge of contact, at the positions that are at a distance 2a apart in the figure.
Beyond those locations, there is no contact. Under large shear forces, specifically when
the ratio Q/P reaches the value of the average coefficient of friction (COF), the entire
region may undergo slip.
From both experimental observations and theoretical analysis it has been found that
contact conditions in fretting change with increasing displacement amplitude [1]. Three
regions are normally defined under constant normal force and oscillating tangential force.
These regions are referred to as “stick,” “mixed stick–slip,” and “total slip.” Each cor-
responds to a range of displacement amplitudes as depicted schematically in Figure 6.2
taken from [1]. The damage in these three regions can be characterized as low damage
fretting, fretting fatigue, and fretting wear, respectively. As noted in the schematic, the
lowest fatigue lives are associated with the fretting-fatigue region, the subject of this
section. It is noteworthy that the lowest lives are not associated with the lowest or largest
slip amplitudes, but with intermediate values. These values can cover a range of from
about 5 to 50 m, but will depend in general not only on the materials but also on the
contact stresses. In addition to these three regions, a limiting region of large amplitudes
in which wear mechanisms and wear rates become identical to those in unidirectional
sliding is defined as the reciprocating sliding regime [1]. This occurs at the right side of

in Figure 6.3. The failures, as shown, were soon identified as fretting fatigue, and occurred
at average stress levels in the grip area that were considerably lower than the nominal
fatigue strength of the titanium alloy being tested. Only by reducing the nominal stress by
thinning the gage section of the specimen were these failures eventually eliminated. This
experience was certainly not unique since fretting in the grips is a common occurrence
in testing laboratories. This experience, however, and the related observations eventually
led to the design of a fretting-fatigue apparatus used by Hutson and co-workers (see [2]
for example) described later in Section 13 (Figure 6.47). This apparatus made use of
the propensity for fretting-fatigue failures in a contact region under cyclic loading when
gross sliding is not present.
264 Effects of Damage on HCF Properties
N
P
N
A
Figure 6.3. Schematic of uniaxial fatigue test showing fretting fatigue at grip.
One of the more common applications where fretting fatigue is a design issue and
where numerous failures have occurred is the dovetail joint in an engine where the blade
is inserted into a slot as shown schematically in Figure 6.4. Here, the contact interface is
normally composed of two flat surfaces in contact with blending radii in both the blade
and the disk. The general problem is three-dimensional in nature with loading taking
place in the directions shown in the two-dimensional schematic of Figure 6.4 as well as
out of the plane of the figure. The loading can be a combination of LCF due to start up
and shut down of the engine, producing primarily an axial load in the blade as shown,
and HCF due to vibratory motion of the blade, producing lateral cyclic loading as well
as axial or bending (not depicted here) contributions. The contact region, where the flat
surfaces mate, sees both normal and tangential loads as well as bulk loads in both the
blade and the disk. At a contact interface, the normal and shear stresses at any point
Blade
Disk

essentially no relative motion anywhere, small relative displacements can occur in the
region between the rivet and the plate as indicated by the solid lines in the figure. This
very small relative motion, produced by fatigue loading of the joint, is due primarily to
the elastic strains in the adjacent materials at the contact interface. The high stresses that
develop in this contact region can lead to fretting-fatigue crack nucleation and subsequent
propagation due to the bulk loads in the plate as depicted in the figure.
Another common example of a structural configuration where fretting fatigue can occur
is where a hub is press-fitted onto a shaft. A characteristic of this and other applications
where fretting fatigue occurs is the small amplitude of the relative motion between
P
P
2P
Figure 6.5. Schematic of rivet joint showing fretting fatigue region.