Measurement Technics

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crack propagation and fatiguek1c measurement.

Transcript of Measurement Technics

  • Characterization technics in fracture mechanicsincluding

    K1c test, J1c test and da/dN-K curve measurement

    1

    Jianqiang Chenjchen.map@gmail.com

  • Safety factor and damage tolerance design

    Conventional turbine runner design

    approach: max <

    YS or

    UTS

    Fracture mechanics damage

    tolerance approach: K < K1c, af < ac

    [ALSTOM HYDRO]

    Fracture toughness K1c and fatigue crack growth rates da/dN-K should be known. 2

  • CT specimen(compact tension)

    ( )( )

    2 2 3 3 4 4

    3/ 21/ 2

    (2 a w) 0.886 4.64a w 13.32a w 14.72a w 5.6a wPKBW 1 a w

    + + + =

    B = 0.5W In general

    Fracture toughness K1c test (ASTM E399)

    3

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    USERText BoxK=f() est fonction du stress P et une caracteristique du defaut (B ou a ou W)

  • Fatigue pre-cracking is often used to obtain a sharp crack with small plastic deformation;

    Chevron notch is necessary to initiate a straight crack;

    4

    Fatigue pre-cracking (ASTM E399)

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  • 5Crack mouth opening displacement

    Load

    CMOD

    PQ

    ( )WafWB

    PQ /KQ =

    (c)

    USERText BoxCrack Mouth Opening Displacement

  • Small scale yielding and plane strain conditions:

    YS

    Q

    YS

    Q0

    K2.5B and

    2

    K2.5a

    6

    If not, increase specimen thickness B () or fatigue pre-cracking length a0 ()

    KQ = K1c ?

  • 7KQ = K1c ?

    Even the two previous conditions are met, the recording of force-displacment

    curve could include some non-linarity for two reasons:

    plasticity near the crack tip;

    beginning of stable crack extension.

    if Pmax/PQ < 1.10 and the two previous conditions are met, then KQ = K1C

  • 8Material studied CA6NM steel

    K1c testing - small scale plasticity and plane strain condition

    a = initialcracklength

    B = specimenthickness

    a, B 258 mm !, if a/W = 0.5, W= 516 mm !!

    2

    K2.5Bet 2

    K2.5aYS

    1c

    YS

    1c

    C Mn Si S P Cr Ni Mo

    CA6NM 0.03 0.57 0.37 0.02 0.02 12.68 4.03 0.67

    Chemical composition of the tested material CA6NM (wt. %)

    E (GPa) YS (MPa) UTS (MPa) A (%)

    CA6NM 207 763 837 27.0

    Tensile properties of the tested material

    Fracture toughness

    K1c test is not appropriate for CA6NM steel

  • The Rices J Integral Going back to Griffith ?

    =S

    dSx

    uTwdyJ with = ijijdw

    crack

    [Rice, J Appl Mech 35, p.379, 1968]

    9

    )1( 2=EJK

    )1( 22

    vE

    KGJ ==(plan strain)

  • Linear Elastic Fracture Mechanics (LEFM)

    Stress singularity near a crack tip

    o(r1/2) is higher order stress terms

    )o(r)f(r 2

    K 1/2ij +=

    S

    S

    r

    ax

    K-controlled zone

    Small-scale yielding

    )m(MPa aY K =

    10

    Going back to Griffith ?

    )f(r 2

    Kij =

  • Elastic-Plastic Fracture Mechanics (EPFM)

    Generalisation of the approach with the HRR field near a crack tip

    )(frI

    J ij

    1)1/(n

    nyyij

    +

    =

    S

    S

    a

    J-controlled zone

    Large Scale Yielding

    J represents the elastic-plastic stress fields intensity near a crack tip

    As fo K and Kc, when J reaches a criticalvalue Jc, the crack will propagate stably

    n

    yyy

    +=Ramberg-Osgood

    [Hutchinson, J Mech Phys Solids 16, p.13, 1968] [Rice & Rosengren, J Mech Phys Solids 16, p.1, 1968] 11

    Hutchinson + Rice & Rosengren

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  • Measure of J at begining of a R-curve (initiation of crack extension) Test on SENB and CT specimens; W= 2 inch and B= 1 inch usually; B can be reduced to 0.25 W; Modified geometry for that the extensometer can measure the load-

    line displacement (work)

    Fracture toughness J1c test (ASTM E1820)

    12

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  • Procedure: Fatigue pre-cracking of n specimens (n5) to the same a0 Stop the tests at different af Marking of final crack length

    Break the specimen

    Measurement of af Fitting of J-a curve

    JQ = (BL)(J-a)

    13

    Multi-specimen method

    P-v curve J-a curve

    Long and expensive

  • Procedure:

    Fatigue precracking of one specimen,

    Ductile tearing of specimen with partial unloading to get the elastic compliance,

    After the final unloading, heat tinting to measure a0 and af , and break the

    specimen,

    Results analysis.

    P-v curve J-a curve

    Single-specimen method

    0.0 0.5 1.0 1.5 2.0 2.5 3.00

    5

    10

    15

    20

    25

    30

    35

    40

    45

    L

    o

    a

    d

    (

    k

    N

    )

    Load line displacement (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0

    0

    100

    200

    300

    400

    500

    600

    700

    data points regression line

    J

    (

    k

    J

    /

    m

    2

    )

    crack extension - a (mm)

    1/C

    Load-unload slope compliance crack length a

    Plastic area under P-v curve + elastic part J integral

    0.0 0.5 1.0 1.5 2.0 2.5 3.00

    100

    200

    300

    400

    500

    600

    700

    J

    (

    k

    J

    /

    m

    2

    )

    crack extension - a (mm)

    J0.2

    0,2mm offset line

    14

  • )(1E

    KJ 22

    el =

    )a(WBA

    J0n

    plpl

    =

    plel JJJ +=

    Force

    Load-line displacement

    15

    Calculation of J and a

    Apl

    depends on specimens geometry

    [ ]5432 677.650355.464106.335u-11.242u4.06319u-1.000196 / uuWai ++=a= ai -a0

    Calculation of J

    Calculation of a

  • For the candidate JQ value is a valid measurement of J1c, several conditions should be met, including:

    B and W-a0 > 10 JQ/Y Straightness of a0 et af, a - aavg < 0.05B a (marking) - a (predicted) < 15%

    e.g. CA6NM steel, K1c = 245 MPa ,YS = 763 MPa, UTS =837 MPa

    B 3.31 mm ! 16

    J-a curve and validation

  • Initial procedure 12.7 mm thick smooth CT specimen

    Problems :

    Significant lateral contraction is observed.

    There are nearly no crack growth at the side surfaces of the specimen while the crack

    front at the center advanced by more than 2 mm.

    KJ1c measured = 452MPa !!! (valid test, K1c = 245 MPa ).

    10 mm

    crack extension direction

    Fracture surfaceSpecimen

    2 mm

    17

  • New procedure 12.7 mm thick side-grooved CT specimen

    Fracture surface

    The crack tunneling is less pronounced by the introduction of side-grooves.

    The crack still grows faster at the center of the specimen compared to the side surfaces.

    The test is not valid according to ASTM E1820 (straightness of af).

    crack extension direction

    BN = 0.8 B

    2 mm

    18

  • 12.7 mm smooth specimen

    Side-grooves effect

    Smooth specimen: invalid test KJ1c = 452 MPa !!!

    Side-grooved specimen: invalid test K1c = 241 MPa .

    12.7 mm side-grooved specimen

    10 mm 10 mm

    19

  • New procedure 25.4 mm thick side-grooved CT specimen

    crack propagation direction

    Fracture surfaceBN = 0.8 B

    The crack extension front is nearly straight, the specimen is in plane strain condition

    (little lateral contraction).

    The test is valid according to ASTM E1820.

    5 mm

    20

  • J-a curve

    0.0 0.5 1.0 1.5 2.0 2.5 3.00

    100

    200

    300

    400

    500

    600

    700

    B = 0.5 inch B = 1.0 inch

    J

    (

    k

    J

    /

    m

    2

    )

    crack extension - a (mm)

    0.2 mm offset line

    Thickness effect 12.7 mm vs 25.4 mm

    Similar fracture initiation toughness J0.2

    values can be obtained on both thin and thick

    specimens even though the test done on thin specimen was not valid according to ASTM

    standard E1820.

    The tearing modulus dJ/da is much higher for thin specimens than thick specimens.

    thickness

    (mm)

    J0.2(kJ/m2)

    KJIc(MPa )

    dJ/da

    (MPa)

    12.7 256 241 215

    25.4 266 245 128

    Measured values

    21

  • 12.7 mm thick specimen 25.4 mm thick specimencrack propagation direction

    5 mm 5 mm

    Thickness effect 12.7 mm vs. 25.4 mm

    J1c 12.7 mm: significant crack front curvature and lateral contraction.

    J1c 25.4 mm: straight crack extension front and little lateral contraction

    However, the measured fracture initiation toughness J0.2

    values are approximately

    equal.

    22

  • fatigue

    precracking

    Microscopic fracture surface SEM observation

    transgranular

    fracture

    intergranular

    fracture

    500 m

    stable crack extension

    dimple ductile

    fracture surface50 m

    23

  • Fracture mechanism in ductile material

    d

    =

    23

    exp21

    RdR

    VM

    H

    =

    Growing crack in a ductile material1Stage 1: Void nucleation

    Stage 2: Void growth

    Stage 3: Void coalescence

    where, R: curre