Propiedades Mecanicas Fractura y Fatiga

62
Chapter 6 - 1 ISSUES TO ADDRESS... Stress and strain: What are they and why are they used instead of load and deformation? Elastic behavior: When loads are small, how much deformation occurs? What materials deform least? Plastic behavior: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? Toughness and ductility: What are they and how do we measure them? Chapter 6: Mechanical Properties

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Conceptos Elementales de Propiedades Mecanicas

Transcript of Propiedades Mecanicas Fractura y Fatiga

  • Chapter 6 - 1

    ISSUES TO ADDRESS...

    Stress and strain: What are they and why are they used instead of load and deformation?

    Elastic behavior: When loads are small, how much deformation occurs? What materials deform least?

    Plastic behavior: At what point does permanent deformation occur? What materials are most

    resistant to permanent deformation?

    Toughness and ductility: What are they and how do we measure them?

    Chapter 6:

    Mechanical Properties

  • Chapter 6 - 2

    Elastic means reversible!

    Elastic Deformation

    1. Initial 2. Small load 3. Unload

    F

    bonds

    stretch

    return to

    initial

    F

    Linear- elastic

    Non-Linear- elastic

  • Chapter 6 - 3

    Plastic means permanent!

    Plastic Deformation (Metals)

    F

    linear elastic

    linear elastic

    plastic

    1. Initial 2. Small load 3. Unload

    p lanes still sheared

    F

    elastic + plastic

    bonds stretch & planes shear

    plastic

  • Chapter 6 - 4

    Stress has units:

    N/m2 or lbf/in2

    Engineering Stress

    Shear stress, :

    Area, A

    F t

    F t

    F s

    F

    F

    F s

    = F s

    A o

    Tensile stress, :

    original area

    before loading

    Area, A

    F t

    F t

    = F t

    A o 2

    f

    2 m

    N or

    in

    lb =

  • Chapter 6 - 5

    Simple tension: cable

    Note: = M/AcR here.

    Common States of Stress

    A o = cross sectional

    area (when unloaded)

    F F

    o

    F

    A

    o

    F s

    A

    M

    M A o

    2R

    F s A c

    Torsion (a form of shear): drive shaft Ski lift (photo courtesy P.M. Anderson)

  • Chapter 6 - 6

    (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM

    o

    F

    A

    Simple compression:

    Note: compressive

    structure member

    ( < 0 here). (photo courtesy P.M. Anderson)

    OTHER COMMON STRESS STATES (1)

    A o

    Balanced Rock, Arches National Park

  • Chapter 6 - 7

    Bi-axial tension: Hydrostatic compression:

    Pressurized tank

    < 0h

    (photo courtesy

    P.M. Anderson)

    (photo courtesy

    P.M. Anderson)

    OTHER COMMON STRESS STATES (2)

    Fish under water

    z > 0

    > 0

  • Chapter 6 - 8

    Tensile strain: Lateral strain:

    Shear strain:

    Strain is always

    dimensionless.

    Engineering Strain

    90

    90 - y

    x = x/y = tan

    L o

    L

    L

    w o

    Adapted from Fig. 6.1 (a) and (c), Callister 7e.

    /2

    L /2

    L o w o

  • Chapter 6 - 9

    Stress-Strain Testing

    Typical tensile test machine

    Adapted from Fig. 6.3, Callister 7e. (Fig. 6.3 is taken from H.W.

    Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of

    Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons,

    New York, 1965.)

    specimen extensometer

    Typical tensile specimen

    Adapted from

    Fig. 6.2,

    Callister 7e.

    gauge length

  • Chapter 6 - 10

    Linear Elastic Properties

    Modulus of Elasticity, E: (also known as Young's modulus)

    Hooke's Law:

    = E

    Linear-

    elastic

    E

    F

    F simple tension test

  • Chapter 6 - 11

    Poisson's ratio,

    Poisson's ratio, :

    Units:

    E: [GPa] or [psi]

    : dimensionless

    > 0.50 density increases

    < 0.50 density decreases (voids form)

    L

    -

    L

    metals: ~ 0.33

    ceramics: ~ 0.25

    polymers: ~ 0.40

  • Chapter 6 - 12

    Mechanical Properties

    Slope of stress strain plot (which is proportional to the elastic modulus) depends

    on bond strength of metal

    Adapted from Fig. 6.7,

    Callister 7e.

  • Chapter 6 - 13

    Elastic Shear modulus, G:

    G

    = G

    Other Elastic Properties

    simple

    torsion

    test

    M

    M

    Special relations for isotropic materials:

    2(1 )

    E G

    3(1 2 )

    E K

    Elastic Bulk modulus, K:

    pressure

    test: Init.

    vol =Vo.

    Vol chg.

    = V

    P

    P P P = - K

    V V o

    P

    V

    K V o

  • Chapter 6 - 14

    Metals

    Alloys

    Graphite

    Ceramics

    Semicond

    Polymers Composites

    /fibers

    E(GPa)

    Based on data in Table B2,

    Callister 7e.

    Composite data based on

    reinforced epoxy with 60 vol%

    of aligned

    carbon (CFRE),

    aramid (AFRE), or

    glass (GFRE)

    fibers.

    Youngs Moduli: Comparison

    109 Pa

    0.2

    8

    0.6

    1

    Magnesium,

    Aluminum

    Platinum

    Silver, Gold

    Tantalum

    Zinc, Ti

    Steel, Ni

    Molybdenum

    G raphite

    Si crystal

    Glass - soda

    Concrete

    Si nitride Al oxide

    PC

    Wood( grain)

    AFRE( fibers) *

    CFRE *

    GFRE*

    Glass fibers only

    Carbon fibers only

    A ramid fibers only

    Epoxy only

    0.4

    0.8

    2

    4

    6

    10

    2 0

    4 0

    6 0 8 0

    10 0

    2 00

    6 00 8 00

    10 00 1200

    4 00

    Tin

    Cu alloys

    Tungsten

    Si carbide

    Diamond

    PTF E

    HDP E

    LDPE

    PP

    Polyester

    PS PET

    C FRE( fibers) *

    G FRE( fibers)*

    G FRE(|| fibers)*

    A FRE(|| fibers)*

    C FRE(|| fibers)*

  • Chapter 6 - 15

    Simple tension:

    FL o

    E A o

    L

    Fw o

    E A o

    Material, geometric, and loading parameters all contribute to deflection.

    Larger elastic moduli minimize elastic deflection.

    Useful Linear Elastic Relationships

    F

    A o /2

    L /2

    Lo w o

    Simple torsion:

    2 ML o

    r o 4 G

    M = moment = angle of twist

    2ro

    Lo

  • Chapter 6 - 16

    (at lower temperatures, i.e. T < Tmelt/3)

    Plastic (Permanent) Deformation

    Simple tension test:

    engineering stress,

    engineering strain,

    Elastic+Plastic at larger stress

    permanent (plastic) after load is removed

    p

    plastic strain

    Elastic initially

    Adapted from Fig. 6.10 (a),

    Callister 7e.

  • Chapter 6 - 17

    Stress at which noticeable plastic deformation has occurred.

    when p = 0.002

    Yield Strength, y

    y = yield strength

    Note: for 2 inch sample

    = 0.002 = z/z

    z = 0.004 in

    Adapted from Fig. 6.10 (a),

    Callister 7e.

    tensile stress,

    engineering strain,

    y

    p = 0.002

  • Chapter 6 - 18

    Room T values

    Based on data in Table B4,

    Callister 7e.

    a = annealed

    hr = hot rolled

    ag = aged

    cd = cold drawn

    cw = cold worked

    qt = quenched & tempered

    Yield Strength : Comparison Graphite/ Ceramics/ Semicond

    Metals/ Alloys

    Composites/ fibers

    Polymers

    Yie

    ld s

    tre

    ng

    th,

    y

    (MP

    a)

    PVC

    Ha

    rd to

    me

    asu

    re

    ,

    sin

    ce

    in t

    en

    sio

    n, fr

    actu

    re u

    su

    ally

    occu

    rs b

    efo

    re y

    ield

    .

    Nylon 6,6

    LDPE

    70

    20

    40

    60 50

    100

    10

    30

    2 00

    3 00

    4 00

    5 00 6 00 7 00

    10 00

    2 0 00

    Tin (pure)

    Al (6061) a

    Al (6061) ag

    Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) hr

    Steel (1020) cd Steel (4140) a

    Steel (4140) qt

    Ti (5Al-2.5Sn) a W (pure)

    Mo (pure) Cu (71500) cw

    Ha

    rd to

    me

    asu

    re,

    in c

    era

    mic

    ma

    trix

    an

    d e

    po

    xy m

    atr

    ix c

    om

    po

    site

    s, sin

    ce

    in

    te

    nsio

    n, fr

    actu

    re u

    su

    ally

    occu

    rs b

    efo

    re y

    ield

    .

    H DPE PP

    humid

    dry

    PC

    PET

  • Chapter 6 - 19

    Tensile Strength, TS

    Metals: occurs when noticeable necking starts. Polymers: occurs when polymer backbone chains are aligned and about to break.

    Adapted from Fig. 6.11,

    Callister 7e.

    y

    strain

    Typical response of a metal

    F = fracture or

    ultimate

    strength

    Neck acts as stress

    concentrator

    en

    gin

    eering

    TS s

    tress

    engineering strain

    Maximum stress on engineering stress-strain curve.

  • Chapter 6 - 20

    Tensile Strength : Comparison

    Si crystal

    Graphite/ Ceramics/ Semicond

    Metals/ Alloys

    Composites/ fibers

    Polymers

    Ten

    sile

    str

    eng

    th,

    TS

    (M

    Pa

    )

    PVC

    Nylon 6,6

    10

    100

    200

    300

    1000

    Al (6061) a

    Al (6061) ag

    Cu (71500) hr

    Ta (pure) Ti (pure) a

    Steel (1020)

    Steel (4140) a

    Steel (4140) qt

    Ti (5Al-2.5Sn) a W (pure)

    Cu (71500) cw

    L DPE

    PP

    PC PET

    20

    30 40

    2000

    3000

    5000

    Graphite

    Al oxide

    Concrete

    Diamond

    Glass-soda

    Si nitride

    H DPE

    wood ( fiber)

    wood(|| fiber)

    1

    GFRE (|| fiber)

    GFRE ( fiber)

    C FRE (|| fiber)

    C FRE ( fiber)

    A FRE (|| fiber)

    A FRE( fiber)

    E-glass fib

    C fibers Aramid fib

    Room Temp. values Based on data in Table B4,

    Callister 7e.

    a = annealed

    hr = hot rolled

    ag = aged

    cd = cold drawn

    cw = cold worked

    qt = quenched & tempered

    AFRE, GFRE, & CFRE =

    aramid, glass, & carbon

    fiber-reinforced epoxy

    composites, with 60 vol%

    fibers.

  • Chapter 6 - 21

    Plastic tensile strain at failure:

    Adapted from Fig. 6.13,

    Callister 7e.

    Ductility

    Another ductility measure: 100 x A

    A A RA %

    o

    f o -

    =

    x 100 L

    L L EL %

    o

    o f

    Engineering tensile strain,

    E ngineering

    tensile

    stress,

    smaller %EL

    larger %EL Lf

    Ao Af Lo

  • Chapter 6 - 22

    Energy to break a unit volume of material Approximate by the area under the stress-strain curve.

    Toughness

    Brittle fracture: elastic energy

    Ductile fracture: elastic + plastic energy

    very small toughness (unreinforced polymers)

    Engineering tensile strain,

    E ngineering

    tensile

    stress,

    small toughness (ceramics)

    large toughness (metals)

    Adapted from Fig. 6.13,

    Callister 7e.

  • Chapter 6 - 23

    Resilience, Ur

    Ability of a material to store energy

    Energy stored best in elastic region

    If we assume a linear

    stress-strain curve this

    simplifies to

    Adapted from Fig. 6.15,

    Callister 7e.

    y y r 2

    1 U

    ydUr 0

  • Chapter 6 - 24

    Elastic Strain Recovery

    Adapted from Fig. 6.17,

    Callister 7e.

  • Chapter 6 - 25

    Hardness

    Resistance to permanently indenting the surface. Large hardness means: --resistance to plastic deformation or cracking in

    compression.

    --better wear properties.

    e.g., 10 mm sphere

    apply known force measure size of indent after removing load

    d D Smaller indents mean larger hardness.

    increasing hardness

    most plastics

    brasses Al alloys

    easy to machine steels file hard

    cutting tools

    nitrided steels diamond

  • Chapter 6 - 26

    Hardness: Measurement

    Rockwell

    No major sample damage

    Each scale runs to 130 but only useful in range 20-100.

    Minor load 10 kg

    Major load 60 (A), 100 (B) & 150 (C) kg

    A = diamond, B = 1/16 in. ball, C = diamond

    HB = Brinell Hardness

    TS (psia) = 500 x HB

    TS (MPa) = 3.45 x HB

  • Chapter 6 - 27

    Hardness: Measurement Table 6.5

  • Chapter 6 - 28

    True Stress & Strain

    Note: S.A. changes when sample stretched

    True stress

    True Strain

    iT AF

    oiT ln 1ln1

    T

    T

    Adapted from Fig. 6.16,

    Callister 7e.

  • Chapter 6 - 29

    Hardening

    Curve fit to the stress-strain response:

    T K T

    n

    true stress (F/A) true strain: ln(L/Lo)

    hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers)

    An increase in y due to plastic deformation.

    large hardening

    small hardening y 0

    y 1

  • Chapter 6 - 30

    Variability in Material Properties

    Elastic modulus is material property

    Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability.

    Statistics

    Mean

    Standard Deviation

    2

    1

    2

    1n

    xxs i

    n

    n

    xx n

    n

    where n is the number of data points

  • Chapter 6 - 31

    Design uncertainties mean we do not push the limit. Factor of safety, N

    N

    y

    working

    Often N is

    between

    1.2 and 4

    Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a

    factor of safety of 5.

    Design or Safety Factors

    4

    0002202 /d

    N,5

    N

    y

    working1045 plain carbon steel:

    y = 310 MPa

    TS = 565 MPa

    F = 220,000N

    d

    L o

    d = 0.067 m = 6.7 cm

  • Chapter 6 - 32

    Stress and strain: These are size-independent measures of load and displacement, respectively.

    Elastic behavior: This reversible behavior often shows a linear relation between stress and strain.

    To minimize deformation, select a material with a

    large elastic modulus (E or G).

    Toughness: The energy needed to break a unit volume of material.

    Ductility: The plastic strain at failure.

    Summary

    Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive)

    uniaxial stress reaches y.

  • Chapter 6 - 33

    ISSUES TO ADDRESS...

    How do flaws in a material initiate failure?

    How is fracture resistance quantified; how do different material classes compare?

    How do we estimate the stress to fracture?

    How do loading rate, loading history, and temperature affect the failure stress?

    Ship-cyclic loading

    from waves.

    Computer chip-cyclic

    thermal loading.

    Hip implant-cyclic

    loading from walking. Adapted from Fig. 22.30(b), Callister 7e.

    (Fig. 22.30(b) is courtesy of National

    Semiconductor Corporation.)

    Adapted from Fig. 22.26(b),

    Callister 7e.

    Chapter 8: Mechanical Failure

    Adapted from chapter-opening

    photograph, Chapter 8, Callister 7e. (by

    Neil Boenzi, The New York Times.)

  • Chapter 6 - 34

    Fracture mechanisms

    Ductile fracture

    Occurs with plastic deformation

    Brittle fracture

    Little or no plastic deformation

    Catastrophic

  • Chapter 6 - 35

    Ductile vs Brittle Failure

    Very

    Ductile

    Moderately

    Ductile Brittle

    Fracture

    behavior:

    Large Moderate %AR or %EL Small

    Ductile fracture is usually

    desirable!

    Adapted from Fig. 8.1,

    Callister 7e.

    Classification:

    Ductile:

    warning before

    fracture

    Brittle:

    No

    warning

  • Chapter 6 - 36

    Ductile failure: --one piece

    --large deformation

    Figures from V.J. Colangelo and F.A.

    Heiser, Analysis of Metallurgical Failures

    (2nd ed.), Fig. 4.1(a) and (b), p. 66 John

    Wiley and Sons, Inc., 1987. Used with

    permission.

    Example: Failure of a Pipe

    Brittle failure: --many pieces

    --small deformation

  • Chapter 6 - 37

    Evolution to failure:

    Resulting fracture

    surfaces

    (steel)

    50 mm

    particles

    serve as void

    nucleation

    sites.

    50 mm

    From V.J. Colangelo and F.A. Heiser,

    Analysis of Metallurgical Failures (2nd

    ed.), Fig. 11.28, p. 294, John Wiley and

    Sons, Inc., 1987. (Orig. source: P.

    Thornton, J. Mater. Sci., Vol. 6, 1971, pp.

    347-56.)

    100 mm

    Fracture surface of tire cord wire

    loaded in tension. Courtesy of F.

    Roehrig, CC Technologies, Dublin,

    OH. Used with permission.

    Moderately Ductile Failure

    necking

    void nucleation

    void growth and linkage

    shearing at surface

    fracture

  • Chapter 6 - 38

    Ductile vs. Brittle Failure

    Adapted from Fig. 8.3, Callister 7e.

    cup-and-cone fracture brittle fracture

  • Chapter 6 - 39

    Brittle Failure

    Arrows indicate pt at which failure originated

    Adapted from Fig. 8.5(a), Callister 7e.

  • Chapter 6 - 40

    Intergranular (between grains)

    Intragranular (within grains)

    Al Oxide

    (ceramic) Reprinted w/ permission

    from "Failure Analysis of

    Brittle Materials", p. 78.

    Copyright 1990, The

    American Ceramic

    Society, Westerville, OH.

    (Micrograph by R.M.

    Gruver and H. Kirchner.)

    316 S. Steel

    (metal) Reprinted w/ permission

    from "Metals Handbook",

    9th ed, Fig. 650, p. 357.

    Copyright 1985, ASM

    International, Materials

    Park, OH. (Micrograph by

    D.R. Diercks, Argonne

    National Lab.)

    304 S. Steel

    (metal) Reprinted w/permission

    from "Metals Handbook",

    9th ed, Fig. 633, p. 650.

    Copyright 1985, ASM

    International, Materials

    Park, OH. (Micrograph by

    J.R. Keiser and A.R.

    Olsen, Oak Ridge

    National Lab.)

    Polypropylene

    (polymer) Reprinted w/ permission

    from R.W. Hertzberg,

    "Defor-mation and

    Fracture Mechanics of

    Engineering Materials",

    (4th ed.) Fig. 7.35(d), p.

    303, John Wiley and

    Sons, Inc., 1996. 3 mm

    4 mm 160 mm

    1 mm (Orig. source: K. Friedrick, Fracture 1977, Vol.

    3, ICF4, Waterloo, CA, 1977, p. 1119.)

    Brittle Fracture Surfaces

  • Chapter 6 - 41

    Stress-strain behavior (Room T):

    Ideal vs Real Materials

    TS

  • Chapter 6 - 42

    Flaws are Stress Concentrators!

    Results from crack propagation

    Griffith Crack

    where

    t = radius of curvature

    o = applied stress

    m = stress at crack tip

    ot

    /

    t

    om Ka

    21

    2

    t

    Adapted from Fig. 8.8(a), Callister 7e.

  • Chapter 6 - 43

    Concentration of Stress at Crack Tip

    Adapted from Fig. 8.8(b), Callister 7e.

  • Chapter 6 - 44

    Engineering Fracture Design

    r/h

    sharper fillet radius

    increasing w/h

    0 0.5 1.0 1.0

    1.5

    2.0

    2.5

    Stress Conc. Factor, K t max

    o

    =

    Avoid sharp corners!

    Adapted from Fig.

    8.2W(c), Callister 6e.

    (Fig. 8.2W(c) is from G.H.

    Neugebauer, Prod. Eng.

    (NY), Vol. 14, pp. 82-87

    1943.)

    r , fillet

    radius

    w

    h

    o

    max

  • Chapter 6 - 45

    Crack Propagation

    Cracks propagate due to sharpness of crack tip

    A plastic material deforms at the tip, blunting the crack.

    deformed

    region

    brittle

    Energy balance on the crack

    Elastic strain energy-

    energy stored in material as it is elastically deformed

    this energy is released when the crack propagates

    creation of new surfaces requires energy

    plastic

  • Chapter 6 - 46

    When Does a Crack Propagate?

    Crack propagates if above critical stress

    where

    E = modulus of elasticity

    s = specific surface energy

    a = one half length of internal crack

    Kc = c/ 0

    For ductile => replace s by s + p

    where p is plastic deformation energy

    212

    /

    sc

    a

    Ei.e., m > c

    or Kt > Kc

  • Chapter 6 - 47

    Fracture Toughness

    Based on data in Table B5,

    Callister 7e. Composite reinforcement geometry is: f

    = fibers; sf = short fibers; w = whiskers;

    p = particles. Addition data as noted

    (vol. fraction of reinforcement): 1. (55vol%) ASM Handbook, Vol. 21, ASM Int.,

    Materials Park, OH (2001) p. 606.

    2. (55 vol%) Courtesy J. Cornie, MMC, Inc.,

    Waltham, MA.

    3. (30 vol%) P.F. Becher et al., Fracture

    Mechanics of Ceramics, Vol. 7, Plenum Press

    (1986). pp. 61-73.

    4. Courtesy CoorsTek, Golden, CO.

    5. (30 vol%) S.T. Buljan et al., "Development of

    Ceramic Matrix Composites for Application in

    Technology for Advanced Engines Program",

    ORNL/Sub/85-22011/2, ORNL, 1992.

    6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci.

    Proc., Vol. 7 (1986) pp. 978-82.

    Graphite/ Ceramics/ Semicond

    Metals/ Alloys

    Composites/ fibers

    Polymers

    5

    K Ic

    (MP

    a

    m 0.

    5 )

    1

    Mg alloys

    Al alloys

    Ti alloys

    Steels

    Si crystal

    Glass - soda

    Concrete

    Si carbide

    PC

    Glass 6

    0.5

    0.7

    2

    4

    3

    10

    2 0

    3 0

    Diamond

    PVC

    PP

    Polyester

    PS

    PET

    C-C (|| fibers) 1

    0.6

    6 7

    4 0

    5 0 6 0 7 0

    100

    Al oxide Si nitride

    C/C ( fibers) 1

    Al/Al oxide(sf) 2

    Al oxid/SiC(w) 3

    Al oxid/ZrO 2 (p) 4 Si nitr/SiC(w) 5

    Glass/SiC(w) 6

    Y 2 O 3 /ZrO 2 (p) 4

  • Chapter 6 - 48

    Crack growth condition:

    Largest, most stressed cracks grow first!

    Design Against Crack Growth

    K Kc = aY

    --Result 1: Max. flaw size dictates design stress.

    max

    cdesign

    aY

    K

    amax no fracture

    fracture

    --Result 2: Design stress dictates max. flaw size.

    2

    1

    design

    cmax

    Y

    Ka

    amax

    no fracture

    fracture

  • Chapter 6 - 49

    Two designs to consider...

    Design A --largest flaw is 9 mm

    --failure stress = 112 MPa

    Design B --use same material

    --largest flaw is 4 mm

    --failure stress = ?

    Key point: Y and Kc are the same in both designs.

    Answer: MPa 168)( Bc Reducing flaw size pays off!

    Material has Kc = 26 MPa-m0.5

    Design Example: Aircraft Wing

    Use... max

    cc

    aY

    K

    c amax

    Ac amax

    B

    9 mm 112 MPa 4 mm --Result:

  • Chapter 6 - 50

    Loading Rate

    Increased loading rate... -- increases y and TS

    -- decreases %EL

    Why? An increased rate gives less time for

    dislocations to move past

    obstacles.

    y

    y

    TS

    TS

    larger

    smaller

  • Chapter 6 - 51

    Impact Testing

    final height initial height

    Impact loading: -- severe testing case

    -- makes material more brittle

    -- decreases toughness

    Adapted from Fig. 8.12(b),

    Callister 7e. (Fig. 8.12(b) is

    adapted from H.W. Hayden,

    W.G. Moffatt, and J. Wulff, The

    Structure and Properties of

    Materials, Vol. III, Mechanical

    Behavior, John Wiley and Sons,

    Inc. (1965) p. 13.)

    (Charpy)

  • Chapter 6 - 52

    Increasing temperature... --increases %EL and Kc

    Ductile-to-Brittle Transition Temperature (DBTT)...

    Temperature

    BCC metals (e.g., iron at T < 914C)

    Imp

    act E

    ne

    rgy

    Temperature

    High strength materials ( y > E/150)

    polymers

    More Ductile Brittle

    Ductile-to-brittle transition temperature

    FCC metals (e.g., Cu, Ni)

    Adapted from Fig. 8.15,

    Callister 7e.

  • Chapter 6 - 53

    Pre-WWII: The Titanic WWII: Liberty ships

    Problem: Used a type of steel with a DBTT ~ Room temp.

    Reprinted w/ permission from R.W. Hertzberg,

    "Deformation and Fracture Mechanics of Engineering

    Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and

    Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard,

    The Discovery of the Titanic.)

    Reprinted w/ permission from R.W. Hertzberg,

    "Deformation and Fracture Mechanics of Engineering

    Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and

    Sons, Inc., 1996. (Orig. source: Earl R. Parker,

    "Behavior of Engineering Structures", Nat. Acad. Sci.,

    Nat. Res. Council, John Wiley and Sons, Inc., NY,

    1957.)

    Design Strategy:

    Stay Above The DBTT!

  • Chapter 6 - 54

    Fatigue

    Fatigue = failure under cyclic stress.

    Stress varies with time. -- key parameters are S, m, and

    frequency

    max

    min

    time

    m S

    Key points: Fatigue... --can cause part failure, even though max < c.

    --causes ~ 90% of mechanical engineering failures.

    Adapted from Fig. 8.18,

    Callister 7e. (Fig. 8.18 is

    from Materials Science in

    Engineering, 4/E by Carl.

    A. Keyser, Pearson

    Education, Inc., Upper

    Saddle River, NJ.) tension on bottom

    compression on top

    counter motor

    flex coupling

    specimen

    bearing bearing

  • Chapter 6 - 55

    Fatigue limit, Sfat: --no fatigue if S < Sfat

    Adapted from Fig.

    8.19(a), Callister 7e.

    Fatigue Design Parameters

    Sfat

    case for steel (typ.)

    N = Cycles to failure 10

    3 10

    5 10

    7 10

    9

    unsafe

    safe

    S = stress amplitude

    Sometimes, the fatigue limit is zero!

    Adapted from Fig.

    8.19(b), Callister 7e.

    case for Al (typ.)

    N = Cycles to failure 10

    3 10

    5 10

    7 10

    9

    unsafe

    safe

    S = stress amplitude

  • Chapter 6 - 56

    Crack grows incrementally

    typ. 1 to 6

    a~

    increase in crack length per loading cycle

    Failed rotating shaft --crack grew even though

    Kmax < Kc --crack grows faster as increases crack gets longer loading freq. increases.

    crack origin

    Adapted from

    Fig. 8.21, Callister 7e.

    (Fig. 8.21 is from D.J.

    Wulpi, Understanding

    How Components Fail,

    American Society for

    Metals, Materials Park,

    OH, 1985.)

    Fatigue Mechanism

    mK

    dN

    da

  • Chapter 6 - 57

    Improving Fatigue Life

    1. Impose a compressive

    surface stress (to suppress surface

    cracks from growing)

    N = Cycles to failure

    moderate tensile m Larger tensile m

    S = stress amplitude

    near zero or compressive m Increasing

    m

    --Method 1: shot peening

    put surface

    into compression

    shot --Method 2: carburizing

    C-rich gas

    2. Remove stress

    concentrators. Adapted from Fig. 8.25, Callister 7e.

    bad

    bad

    better

    better

    Adapted from

    Fig. 8.24, Callister 7e.

  • Chapter 6 - 58

    Creep

    Sample deformation at a constant stress ( ) vs. time

    Adapted from

    Fig. 8.28, Callister 7e.

    Primary Creep: slope (creep rate)

    decreases with time.

    Secondary Creep: steady-state

    i.e., constant slope.

    Tertiary Creep: slope (creep rate)

    increases with time, i.e. acceleration of rate.

    0 t

  • Chapter 6 - 59

    Occurs at elevated temperature, T > 0.4 Tm

    Adapted from Figs. 8.29,

    Callister 7e.

    Creep

    elastic

    primary secondary

    tertiary

  • Chapter 6 - 60

    Strain rate is constant at a given T, -- strain hardening is balanced by recovery

    stress exponent (material parameter)

    strain rate

    activation energy for creep

    (material parameter)

    applied stress material const.

    Strain rate increases

    for higher T,

    10

    2 0

    4 0

    10 0

    2 0 0

    10 -2 10 -1 1 Steady state creep rate (%/1000hr) s

    Stress (MPa) 427 C

    538 C

    649 C

    Adapted from

    Fig. 8.31, Callister 7e.

    (Fig. 8.31 is from Metals

    Handbook: Properties

    and Selection:

    Stainless Steels, Tool

    Materials, and Special

    Purpose Metals, Vol. 3,

    9th ed., D. Benjamin

    (Senior Ed.), American

    Society for Metals,

    1980, p. 131.)

    RT

    QK cns exp2

    Secondary Creep

  • Chapter 6 - 61

    Creep Failure Estimate rupture time S-590 Iron, T = 800 C, = 20 ksi

    Failure: along grain boundaries.

    time to failure (rupture)

    function of

    applied stress

    temperature

    L)t(T rlog20

    applied

    stress

    g.b. cavities

    Time to rupture, tr

    From V.J. Colangelo and F.A. Heiser, Analysis of

    Metallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John

    Wiley and Sons, Inc., 1987. (Orig. source: Pergamon

    Press, Inc.)

    L)t(T rlog20

    1073K

    Ans: tr = 233 hr

    24x103 K-log hr

    Adapted from

    Fig. 8.32, Callister 7e.

    (Fig. 8.32 is from F.R.

    Larson and J. Miller,

    Trans. ASME, 74, 765

    (1952).)

    L(10 3 K-log hr)

    Str

    ess, ksi

    100

    10

    1 12 20 24 28 16

    data for S-590 Iron

    20

  • Chapter 6 - 62

    Engineering materials don't reach theoretical strength.

    Flaws produce stress concentrations that cause premature failure.

    Sharp corners produce large stress concentrations and premature failure.

    Failure type depends on T and stress:

    - for noncyclic and T < 0.4Tm, failure stress decreases with: - increased maximum flaw size, - decreased T,

    - increased rate of loading.

    - for cyclic :

    - cycles to fail decreases as increases.

    - for higher T (T > 0.4Tm):

    - time to fail decreases as or T increases.

    SUMMARY