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# ASM Metals HandBook Volume 12 - Fractography

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effect on the fatigue crack growth rate will be presented in more detail below.
From a technical standpoint, cyclic frequency (the rate at which the fatigue load is applied) and the wave form (the shape
of the load versus time curve) are two independent variables. They are unrelated because the same frequency can exhibit
different wave forms, such as sinusoidal or triangular. However, from a practical standpoint, the frequency and the wave
form are the only two fatigue parameters that are not load related and are similar enough to be discussed in the same
section.
In addition to discussing \u2206K, frequency, and wave form, the effect of these parameters on the fatigue crack growth rate
and the fracture appearance will be illustrated by using the results of fatigue tests conducted on different materials under
different testing conditions. Each example will contain such data as a description of the material, the testing conditions,
and the results of the tests.
Effect of the Stress Intensity Range, \u2206K. The stress intensity factor, K, is a fracture mechanics parameter that
expresses the stress condition in the material adjacent to the tip of a crack and is a function of the applied load and the
crack shape factor, which for a partial thickness crack is expressed as a function of the depth and length of the crack (Ref
15, 31, 32). A numerically larger K represents a more severe state of stress.
In fatigue, \u2206K represents the range of the cyclic stress intensity factor; however, it is generally referred to as the stress
intensity range. The stress intensity range, \u2206K, is defined as:
\u2206K = Kmax - Kmin (Eq 2)
where Kmax is the maximum stress intensity factor, and Kmin is the minimum stress intensity factor. The values Kmax and
Kmin are calculated by using the maximum and minimum stress (load) associated with each fatigue load cycle. For an
actual fatigue test using an edge-cracked specimen, \u2206K can be calculated directly from (Ref 244):
P aK
BW w
g
D
D =

(Eq 3)
where \u2206P is load amplitude (Pmax - Pmin), B is specimen thickness, W is specimen width (distance from point where load is
applied and the uncracked edge of specimen), a is crack length, and \u3b3(a/W) is the K calibration function.
The fatigue crack growth rate always increases with the value of \u2206K because a numerically larger \u2206K represents a greater
mechanical driving force to propagate the crack. The relationship between the fatigue crack growth rate, da/dN and \u2206K
can be expressed as (Ref 31, 32):
( )mda C K
dN
= D

(Eq 4)
where a is the distance of crack growth (advance), N is the number of cycles applied to advance the crack a distance (a),
da/dN is the fatigue crack growth rate, and C and m are constants. If the fatigue crack propagates exclusively by a
striation-forming mechanism, da/dN represents the average striation spacing, which increases with the value of \u2206K.
The fatigue parameters Kmean and R are defined as:
min max( )
2mean
k kK +=

(Eq 5)
and
max
minKR
K
=

(Eq 6)
By using Eq 2, 5, and 6, it can be shown that Kmean and R are related to \u2206K as follows:
min 2mean
kK k D= +

(Eq 7)
and
max
1 KR
K
D
= -

(Eq 8)
Because Kmean and R are both directly related to \u2206K, by determining the effect of \u2206K on the fatigue crack growth rate, the
effect of Kmean and R can be deduced from Eq 7 and 8.
In the examples given later in this section, the fatigue crack growth rate in a material is sometimes given at low and high
numerical values of \u2206K for moist air as well as the inert environment. As discussed previously, at low fatigue crack
growth rates (low values of \u2206K), the corrosive effects of moist air can result in an increase in the fatigue crack growth rate
above that in the inert environments, but at high fatigue crack growth rates (high values of \u2206K), the moist air environment
has little effect and all environments exhibit similar fatigue growth rates, for these reasons, the span of the fatigue crack
growth rates between the low and high values of \u2206K is generally smaller for the fatigue cracks propagating in the moist
air than an inert environments.
The effect of \u2206K on the fatigue crack growth rate, da/dN, in various materials is summarized below. Unless specified, the
cyclic wave form is sinusoidal and the gas pressures are at or slightly above atmospheric.
Example 1. An API-5LX Grade X42 carbon-manganese pipeline steel with an ultimate tensile strength of 490 to 511
MPa (71 to 74 ksi) was tested under the following conditions: R = 0.1, f = 5 Hz, dry nitrogen gas at a pressure of 69 atm,
at room temperature (Ref 218). The results are listed below:

\u2206K
MPa m ksi in
da/dN,
mm/cycle
7 6.5 1 × 10-6
40 36.5 6 × 10-4
The fatigue crack growth rate at \u2206K = 40 MPa m (36.5 ksi in .) was 600 times greater than at 7 MPa m (6.5 ksi in .).
Example 2. A nickel-chromium-molybdenum-vanadium rotor steel (Fe-0.24C-0.28Mn-3.51Ni-1.64Cr-0.11V-0.39Mo)
with an ultimate tensile strength of 882 MPa (128 ksi) was tested under the following conditions: R = 0.5, f = 120 Hz, air
(30 to 40% relative humidity), at room temperature (Ref 220). The results are listed below:

\u2206K
MPa m ksi in
da/dN,
mm/cycle
4 3.5 6 × 10-7
20 18 8 × 10-5
The fatigue crack growth rate at \u3b4K = 20 MPa m (18 ksi in ) was about 130 times greater than at 4 MPa m (3.5
ksi in ).
Example 3. An AISI 4130 steel with an ultimate tensile strength of 1330 MPa (193 ksi) and a hardness of 43 HRC was
tested under the following conditions: R = 0.1, f = 1 to 50 Hz, moist air (relative humidity not specified), at room
temperature (Ref 251). The results are listed below:

\u2206K
MPa m ksi in
da/dN,
mm/cycle
10 9 7 × 10-6
40 36.5 2 × 10-4
The fatigue crack growth rate at \u2206K = 40 MPa m (36.5 ksi in ) was about 30 times greater than at 10 MPa m (9
ksi in ).
Example 4. An AISI 4340 steel with an ultimate tensile strength of 2082 MPa (302 ksi) was tested under the following
conditions: R = 0.1, f = 20 Hz, dry argon gas, at room temperature (Ref 253). the results are listed below:

\u2206K
MPa m ksi in
da/dN,
mm/cycle
15 13.5 7 × 10-5
30 27.5 1.2 × 10-4
The fatigue crack growth rate at \u2206K = 30 MPa m (27.5 ksi in ) was less than twice as great as that at 15 MPa m (13.5
ksi in ).
Example 5. An SUS 410J1 martensitic stainless steel (Japanese equivalent of type 410 stainless steel), which was
tempered at 600 °C (1110 °F) for 3 h, was tested under the following conditions: R = 0, f = 30 Hz, laboratory air (relative
humidity not specified), at room temperature (Ref 233). The results are listed below:

\u2206K
MPa m ksi in
da/dN,
mm/cycle
4 3.5 2 × 10-7
15 13.5 2 × 10-5
The fatigue crack growth rate at \u2206K = 15 MPa m (13.5 ksi in ) was 100 times greater than at 4 MPa m (3.5 ksi in ).
Example 6. An annealed type 316 stainless steel was tested under the following conditions: R = 0.05, f = 0.17 Hz,
vacuum (better than 10-6 torr), at 25 °C (75 °F) Ref 242). The results are listed below:

\u2206K
MPa m ksi in
da/dN,
mm/cycle
35 32 2 × 10-4
70 63.5 7 × 10-3
The fatigue crack growth rate at \u2206K = 70 MPa m (63.5 ksi in ) was 35 times greater than at 35 MPa m (32 ksi in ).
Example 7. Annealed type 301 and 302 stainless steel specimens were tested under the following conditions: R = 0.05, f
= 0.6 Hz, dry argon gas, at room temperature (Ref 217). The results are listed below:

\u2206K Specimen
MPa m ksi in
da/dN,
mm/cycle
50 45.5 4 × 10-4 Type 301
100 90 3 × 10-3
Type 302 50 45.5 6 × 10-4
The fatigue crack growth rate at \u2206K = 100 MPa m (90 ksi in ) was about eight times greater than at```