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. .Outline
Constant-life fatigue diagram
a gue a ure cr er on
Stress concentration factor andnotch sensitive factor
Fati ue life rediction
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Fluctuating stress
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Constant Life Diagram Ductile Materials Lines corresponding to constant
106-cycle life, 105-cycle life, etc.
Graphical representation of
m
a in relation to criteria both for
yielding and for fatigue lives.
Fatigue life of interest can be
read from lines CB, DB, EB and
FB (Goodman lines of constant
fatigue life).
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-a,, repeating, cyclic component
(fatigue load) of the fluctuating loadConstant-life
Sn Fatigue strength at a certainlife time
Sy
Goodman line
- S Su
o er erg ne
Operating
pointm
- m
m, static component (static
load) of the fluctuating load
Strength under static
load
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-a
Sn
y
Operating point
- S Su m- m
Load line is based onk
a=
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m
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-a
SnSy
Soderberg line
- m
- m
Soderberg line is based on Sy and Sn 1=+ ma
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yn
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Constant-Life Fati ue Dia rama
SnSy
Goodman line
-m- m
Goodman line is based on Su and Sn 1=+ ma
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un
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a
ma 1=+
SnSy
Goodman line
un
Sn/SF
-SySu /SF m- m
Safe stress line-parallel to the original
Goodman line
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Fatigue-strength diagram for alloy steel, Su = 125 to 180 ksi, axial loading. Average of test
data for polished specimens of AISI 4340 steel (also applicable to other alloy steels, such as
AISI 2330 4130 8630 . Courtes Grumman Aeros ace Cor oration.
Goodman line is more conservative
than experimental data
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Fatigue strength diagram for 2024-T3, 2024-T4, and 2014-T6 aluminum alloys axial
loading. Average of test data for polished specimens (unclad) from rolled and drawn
= = = . u , , u .Sy = 63 ksi. (Courtesy Grumman Aerospace Corporation.)
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Effect of Mean Stress on Fati ue Stren tha
a gue s reng a a
certain life timeS
y
m1, a1
m2, a2
-
As mean stress m increases, allowable alternating
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stress a for a constant life-time decreases.
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Fluctuating Uniaxial Stresses
At (a), = S , is a completely reversed stress, = 0
At (b), a tensile mean stress component exists, a is lessthan Sn in order to have an equal fatigue life (infinite)
At (c) and up, with increasing m, a must corresponding
decrease.
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, max y At (e) and (f), the part is yielded at first load application
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Fatigue Failure Criterion
If 106 cycles is requiredand no yielding is
ermitted sta inside
area AHCGA
Modified Goodman fatigue criterion -
Infinite life and no ield is allowed
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Fatigue Failure Criterion
I 10 cyc es is require
and yielding ispermitted, stay inside
area AHCGB
Infinite life and ieldin is acce table
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No yielding, less6
life time
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_ A round tensile link with negligible stress concentration is
su ec e o a oa uc ua ng e ween an .
is to be a precision member (so that use of CG=0.9 isustified with commerciall olished surfaces C = 0.9 . The
material is to be steel, with Su=150 ksi, Sy=120ksi. A safety
factor of 2 is to be used, applied to all loads.
(b) What diameter is required if only 103 cycles of life are
needed.
Assumptions: Diameter d< 2 in., gross yielding is not permitted.
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Figure 8.21 (p. 308)
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.
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Step 1:
Estimate S-Ncurve
S103 = 0.75 Su = 112 ksi
Sn = 0.5 Su = 75 ksiSn = SnCLCGCSCTCR= 61 ksi
Step 2:
From S-N curve, S104 and S10
5 are
92 ksi and 75 ksi respectively;
diagram (Goodman diagram)
Step 3:SF = 2
A = Cross section area of rod
a = 2(5000 1000)/2 = 4000/A
m = 2(1000 +5000)/2 = 6000/A
a / m = 4000 / 6000 = 0.67
Step 4:From Point 1 on Goodman
Diagram, a = 38 ksi = 4000/A
A = d2/4 = 0.106 in2,
d = 0.367 in or ~ 3/8 in
Step 5:(ANS. a)
o n on oo man agram es
outside the yield line, since gross
yielding is not permitted, Point 3
is selected instead.
a = 48 ksi = 4000/A
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A = d2/4 = 0.083 in2,
d = 0.326 in or ~ 11/32 in (ANS. b)
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Step 1
Draw Goodman diagram from the
-
112ksi
61ksi 103
106
120ksi-120ksi s
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Step 3 Design overload and draw load line
112ksi a120ksi
103
.m
106
Design for 103-cycle4-life, gross yielding
120ksi-120ksi 150ksi
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Design for 106-cycle life
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- Four straight lines
- oo man, o er erg, y e - ne, oa - ne
Which failure criteria to use?
- If onset yielding is allowed, Soderberg will beconservative.
- If ultimate stren th is known with ieldin ermittedthen use Goodman line for 106 cycles.
- If ultimate strength and yield strength are known, withonset ieldin not ermitted, then use Modified
Goodman criterion for 106 cycles.
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-
am ,
Bending load Axial load
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-
Omit the left-half. Use onl the ri ht-half
of the Goodman fatigue diagram
am ,S
a
sn
Goodman
line
Ssy Ssum
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-
stress, em, and equivalent bending alternatingstress, ea, exist in one direction only.
Standard Goodman fati ue dia ram with load-line calculated from equivalent stresses
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calculated from the distortion-energy
combination of existing alternating
22
aaea=
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as the maximum principle stress resulting
stresses
2
2 mm
22 mem
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SF = OP/ONSF = OF/OD
SF = OC/OA
When the nature of the overload is unknown,
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use OP as designed overload line
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Reversed-load fatigue tests, notched versus unnotched specimens.
Kt is the geometric stress concentration factor. In general,
KK
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