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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

    AER 606 Fatigue life 1

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    Fluctuating stress

    AER 606 Fatigue life 2

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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).

    AER 606 Fatigue life 3

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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

    AER 606 Fatigue life 4

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    -a

    Sn

    y

    Operating point

    - S Su m- m

    Load line is based onk

    a=

    AER 606 Fatigue life 5

    m

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    -a

    SnSy

    Soderberg line

    - m

    - m

    Soderberg line is based on Sy and Sn 1=+ ma

    AER 606 Fatigue life 6

    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

    AER 606 Fatigue life 7

    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

    AER 606 Fatigue life 8

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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

    AER 606 Fatigue life 9

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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.)

    AER 606 Fatigue life 10

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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

    AER 606 Fatigue life 11

    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.

    AER 606 Fatigue life 12

    , 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

    AER 606 Fatigue life 13

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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

    AER 606 Fatigue life 15

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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.

    AER 606 Fatigue life 16

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    Figure 8.21 (p. 308)

    AER 606 Fatigue life 17

    .

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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

    AER 606 Fatigue life 18

    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

    AER 606 Fatigue life 20

    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.

    AER 606 Fatigue life 21

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    -

    am ,

    Bending load Axial load

    AER 606 Fatigue life 22

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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=

    AER 606 Fatigue life 25

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    as the maximum principle stress resulting

    stresses

    2

    2 mm

    22 mem

    AER 606 Fatigue life 26

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    SF = OP/ONSF = OF/OD

    SF = OC/OA

    When the nature of the overload is unknown,

    AER 606 Fatigue life 27

    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