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    Chapter 13

    Creep and

    Superplasticity

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    Creep Strain vs.Time: Constant

    Temperature

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    Creep Strain vs. Time at Constant

    Engineering Stress

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    Creep machine with variable lever arms to ensure constant stress on

    specimen; note that l2 decreases as the length of the specimen

    increases.

    Creep Machine

    Initial position Length of specimen has increased

    from L0 to L1.

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    Mukherjee-Bird-Dorn Equation

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    Relationship between time to rupture

    and temperature at three levels of

    engineering stress, a, b, and c,

    using LarsonMiller equation (a > b >c).

    Larson-Miller Equation

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    Master plot for LarsonMiller parameter for S-590 alloy (an

    Fe-based alloy) (C= 17).

    (From R. M. Goldhoff, Mater.Design Eng., 49 (1959) 93.)

    Larson-Miller Parameter

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    Relationship between time rupture and temperature at three

    levels of stress, a, b, and c, using MansonHaferd

    parameter (a > b > c).

    Manson-Hafered Parameter

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    Relationship between time to rupture and temperature

    at three levels of stress, a > b > c, using Sherby

    Dorn parameter.

    Sherby-Dorn Parameter

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    Material Parameters

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    Activation energies for creep (stage II) and self-diffusion for a number

    of metals.

    (Adapted with permission from O. D. Sherby and A. K. Miller, J. Eng. Mater.Technol., 101 (1979) 387.)

    Activation Energies for Creep

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    Ratio between activation energy for secondary creep and

    activation energy for bulk diffusion as a function of temperature.

    (Adapted with permission from O. D. Sherby and A. K. Miller, J. Eng. Mater. Technol., 101 (1979) 387.)

    Secondary Creep

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    Fundamental Creep Mechanism

    /G < 10^(-4) Diffusion Creep

    Nabarro Herring

    Coble Creep

    Harper Dorn Creep

    2( ) ( )l

    N H

    D Gb bA

    kT d G

    =&

    3( )( ) ( )c cGb b

    AkT b d G

    =&

    ( )l

    HD HD

    D GbA

    kT G

    =&

    ( )l

    HD HD

    D GbA

    kT G

    =&

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    Flow of vacancies according to (a) NabarroHerring and (b) Coble

    mechanisms, resulting in an increase in the length of thespecimen.

    Diffusion Creep

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    Dislocation climb (a) upwards, under compressive 22

    stresses, and (b) downwards, under tensile 22 stresses.

    Dislocation Climb

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    Different regimes for diffusion creep in alumina; notice that cations

    (Al3+) and anions (O2) have different diffusion coefficients, leading to

    different regimes of dominance.

    (From A. H. Chokshi and T. G. Langdon, Defect and Diffusion Forum, 6669 (1989) 1205.)

    Diffusion Creep

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    Power relationship between and for AISI 316 stainless steel.

    Adapted with permission from S. N. Monteiro and T. L. da Silveira, Metalurgia-ABM, 35 (1979) 327.

    Power Law CreepDislocation (Power Law) Creep: 10^(-2) < /G < 10^(-4)

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    Dislocation overcoming obstacles by climb, according to Weertman

    theory. (a) Overcoming CottrellLomer locks. (b) Overcoming an

    obstacle.

    Dislocations Overcoming ObstaclesWeertman Mechanism

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    Shear stress vs. shear

    strain rate in an aluminum (6061)with 30 vol.% SiC particulate

    composite in creep.

    (From K.-T. Park, E. J. Lavernia, and F. A. Mohamed,

    Acta Met. Mater., 38 (1990) 2149.)

    Shear Stress and Shear Strain Rate

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    Effect of stress and

    temperature on deformation

    substructure developed inAISI 316 stainless steel in

    middle of stage II.

    Reprinted with permission from H.-J.

    Kestenbach, W. Krause, and

    T. L. da Silveira,Acta Met., 26 (1978) 661.)

    Dislocation Glide

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    (a) Steady-state

    grain-boundary sliding with

    diffusional accommodations.

    (b) Same process as in (a), in an

    idealized polycrystal; the dashed

    lines show the flow of vacancies.

    (Reprinted with permission from

    R. Raj and M. F. Ashby, Met. Trans.,

    2A (1971) 1113.)

    Grain Boundary Sliding

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    Grain-boundary sliding assisted by diffusion in AshbyVerralls model.

    (Reprinted with permission from M. F. Ashby and R. A. Verrall,Acta Met., 21 (1973) 149.)

    Ashby-Verralls Model

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    WeertmanAshby map for pure silver, established for a critical

    strain rate of 108 s1; it can be seen how the deformation-

    mechanism fields are affected by the grain size.

    Adapted with permission from M. F. Ashby,Acta Met., 20 (1972) 887.

    Weertman-Ashby Map for Pure Silver

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    WeertmanAshby map for tungsten,

    showing constant strain-rate contours.

    (Reprinted with permission from M. F. Ashby,Acta Met., 20

    (1972) 887.)

    Weertman-Ashby Map for Tungsten

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    Weertman-Ashby Map for Al2O3

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    .(From W.D. Nix and J. C. Gibeling, in Flow and Fracture at ElevatedTemperatures,

    ed, R. Raj (Metals Park, Ohio: ASM, 1985).)

    Mechanisms of intergranular nucleation

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    Transmission electron micrograph of

    Mar M-200; notice the cuboidal

    precipitates.

    (Courtesy of L. E. Murr.)

    Heat-Resistance Materials

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    (Reprinted with from C. T. Sims and W. C. Hagel, eds., The

    Superalloys (New York: Wiley, 1972), p. 33.)

    Microstructural Strengthening Mechanism

    in nickel-based superalloys

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    Rafting in MAR M-200 monocrystalline superalloy; (a) original

    configuration of gamma prime precipitates aligned with threeorthogonal cube axes; (b) creep deformed at 1253 K for 28

    hours along the [010] direction, leading to coarsening of

    precipitates along loading direction.

    (From U. Glatzel, Microstructure and Internal Strains of Undeformed and Creep Deformed Samples of a

    Nickel-Based Superalloy,

    Habilitation Dissertation,Technische Universitat, Berlin,

    1994.)

    Rafting

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    Stress versus temperatures curves forrupture in

    1,000 hours for selected nickel-based

    superalloys.

    (Reprinted with permission from C. T. Sims and W. C. Hagel,

    eds., The Superalloys (New York: Wiley, 1972), p. vii.)

    Stress-Rupture (at 1000 hours) vs.

    Temperature for Heat Resistant Materials

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    Cross-section of a gas turbine showing different parts.

    The temperature of gases in combustion chamber reaches 1500 C.

    Gas Turbine

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    (a) Single crystal

    turbine blade developed for

    stationary turbine. (Courtesyof U. Glatzel.) (b) Evolution of

    maximum temperature in gas

    turbines; notice the

    significant improvement

    made possible by the

    introduction of thermalbarrier coatings (TBCs).

    (Courtesy of V. Thien, Siemens.)

    Turbine Blade

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    Springdashpot analogs (a) in series and (b) in parallel.

    Creep in Polymers

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    (a) Straintime and

    (b) stresstime

    predictions for

    Maxwell and Voigtmodels.

    Maxwell and Voigt Models

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    Strain response as a function of time for a glassy, viscoelastic

    polymer subjected to a constant stress 0. Increasing the

    molecular weight or degree of cross-linking tends to promote

    secondary bonding between chains and thus make the polymer

    more creep resistant.

    Viscoelastic Polymer

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    (a) A series of creep

    compliances vs. time, both on

    logarithmic scales, over a range

    of temperature. (b) The

    individual plots in (a) can be

    superposed by horizontal

    shifting (along the log-time axis)by an amount log aT, to obtain a

    master curve corresponding to a

    reference temperature Tgof the

    polymer. (c) Shift along the log-

    time scale to produce a master

    curve.

    (Courtesy of W. Knauss.)(d) Experimentally determined

    shift factor.

    Creep Compliances

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    A constant imposed strain 0 results in a drop in stress (t) as a function of time.

    Stress Relaxation

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    A master curve obtained in the case of stress relaxation, showing the

    variation in the reduced modulus as a function of time. Also shown is the

    effect of cross-linking and molecular weight.

    Effect of Crosslinking on Stress Relaxation

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    Metal interconnect line covered by

    passivation layer subjected

    toelectromigration;

    (a) overall scheme;

    (b) voids and cracks producedby thermal mismatch and

    electromigration;

    (c) basic scheme used in Nix

    Arzt equation, which assumes

    grain-boundary diffusion of

    vacancies counterbalancing

    electron wind.

    (Adapted from W. D. Nix and E. Arzt.

    Met. Trans., 23A (1992) 2007.)

    Electromigration

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    Superplastic tensile deformation in Pb62% Sn eutectic alloy

    tested at 415 K and a strain rate of 1.33 104 s1; total strainof 48.5.

    (From M. M. I. Ahmed and T. G. Langdon, Met. Trans. A, 8 (1977) 1832.)

    Superplasticity

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    (a) Schematic representation of plastic deformation in

    tension with formation and inhibition of necking. (b)

    Engineering-stress engineering-strain curves.

    Plastic Deformation

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    Strain-rate dependence of (a) stress and (b) strain-rate sensitivity

    for MgAl eutectic alloy tested at 350 C (grain size 10 m).

    (After D. Lee,Acta. Met., 17 (1969) 1057.)

    Strain Rate Dependence

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    Tensile fracture strain and stress as a function of strain

    rate for Zr22% Al alloy with 2.5-m grain size.

    (After F. A. Mohamed, M. M. I. Ahmed, and T. G. Langdon, Met. Trans. A, 8 (1977) 933.)

    Fracture

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    Effect of strain-rate sensitivity m on maximum tensile

    elongation for different alloys (Fe, Mg, Pu, PbSr, Ti, Zn, Zr

    based).

    (From D. M. R. Taplin, G. L. Dunlop, and T. G. Langdon,Ann. Rev. Mater. Sci., 9 (1979) 151.)

    Effect of Strain Rate Sensitivity

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    Cavitation in superplasticity formed 7475-T6 aluminum alloy (=

    3.5) at 475 C and 5 104 s1. (a) Atmospheric pressure. (b)

    Hydrostatic pressure P= 4 MPa. (Courtesy of A. K. Mukherjee.)

    Cavitation in Superplasticity

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    (a) Effect of grain size on

    elongation: (A) Initial

    configuration. (B) Large

    grains. (C) Fine grains (10 m)

    (Reprinted with permission

    from N. E. Paton, C. H.

    Hamilton, J. Wert, and M.

    Mahoney, J. Metal, 34 (1981) No.8, 21.)

    (b) Failure strains

    increase with superimposed

    hydrostatic pressure (from 0 to

    5.6 MPa). (Courtesy ofA. K. Mukherjee.)

    Effect of Grain Size on Elongation