Creep and Superplasticity

1
Chapter 13

• Creep and Superplasticity

2
Creep Strain vs.Time Constant Temperature
3
Creep Strain vs. Time at Constant Engineering
Stress
4
Creep Machine
Length of specimen has increased from L0 to L1.
Initial position
Creep machine with variable lever arms to ensure
constant stress on specimen note that l2
decreases as the length of the specimen
increases.
5
Mukherjee-Bird-Dorn Equation
6
Larson-Miller Equation
Relationship between time to rupture and
temperature at three levels of engineering
stress, sa, sb, and sc, using LarsonMiller
equation (sa gt sb gt sc).
7
Larson-Miller Parameter
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.)
8
Manson-Hafered Parameter
Relationship between time rupture and temperature
at three levels of stress, sa, sb, and sc, using
MansonHaferd parameter (sa gt sb gt sc).
9
Sherby-Dorn Parameter
Relationship between time to rupture and
temperature at three levels of stress, sa gt sb gt
sc, using SherbyDorn parameter.
10
Material Parameters
11
Activation Energies for Creep
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.)
12
Secondary Creep
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.)
13
Fundamental Creep Mechanism

• s/G lt 10(-4) Diffusion Creep
• Nabarro Herring
• Coble Creep
• Harper Dorn Creep

14
Diffusion Creep
Flow of vacancies according to (a)
NabarroHerring and (b) Coble mechanisms,
resulting in an increase in the length of the
specimen.
15

• Dislocation Climb

Dislocation climb (a) upwards, under compressive
s22 stresses, and (b) downwards, under tensile
s22 stresses.
16
Diffusion Creep
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.)
17
Power Law Creep Dislocation (Power Law) Creep
10(-2) lt s/G lt 10(-4)
Power relationship between ?e and s for AISI 316
stainless steel. Adapted with permission from
S. N. Monteiro and T. L. da Silveira,
Metalurgia-ABM, 35 (1979) 327.
18
Dislocations Overcoming Obstacles Weertman
Mechanism
Dislocation overcoming obstacles by climb,
according to Weertman theory. (a) Overcoming
CottrellLomer locks. (b) Overcoming an obstacle.
19
Shear Stress and Shear Strain Rate
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.)
20
Dislocation Glide
Effect of stress and temperature on
deformation substructure developed in AISI 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.)
21
Grain Boundary Sliding
(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.)
22
Ashby-Verralls Model
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.)
23
Weertman-Ashby Map for Pure Silver
WeertmanAshby map for pure silver, established
for a critical strain rate of 10-8 s-1 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.
24
Weertman-Ashby Map for Tungsten
WeertmanAshby map for tungsten, showing constant
strain-rate contours. (Reprinted with
permission from M. F. Ashby, Acta Met., 20 (1972)
887.)
25
Weertman-Ashby Map for Al2O3
26
Mechanisms of intergranular nucleation
. (From W.D. Nix and J. C. Gibeling, in Flow and
Fracture at ElevatedTemperatures, ed, R. Raj
(Metals Park, Ohio ASM, 1985).)
27
Heat-Resistance Materials
Transmission electron micrograph of Mar M-200
notice the cuboidal ? precipitates. (Courtesy
of L. E. Murr.)
28
Microstructural Strengthening Mechanism in
nickel-based superalloys
(Reprinted with from C. T. Sims and W. C. Hagel,
eds., The Superalloys (New York Wiley, 1972), p.
33.)
29
Rafting
Rafting in MAR M-200 monocrystalline superalloy
(a) original configuration of gamma prime
precipitates aligned with three orthogonal 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.)
30
Stress-Rupture (at 1000 hours) vs. Temperature
for Heat Resistant Materials
Stress versus temperatures curves for rupture
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.)
31
Gas Turbine
Cross-section of a gas turbine showing different
parts. The temperature of gases in combustion
chamber reaches 1500 ?C.
32
Turbine Blade
(a) Single crystal turbine blade developed
for stationary turbine. (Courtesy of U. Glatzel.)
(b) Evolution of maximum temperature in
gas turbines notice the significant improvement
made possible by the introduction of thermal
barrier coatings (TBCs). (Courtesy of V.
Thien, Siemens.)
33
Creep in Polymers
Springdashpot analogs (a) in series and (b) in
parallel.
34
Maxwell and Voigt Models

• Straintime and
• (b) stresstime predictions for
• Maxwell and Voigt models.

35
Viscoelastic Polymer
Strain response as a function of time for a
glassy, viscoelastic polymer subjected to a
constant stress s0. Increasing the molecular
weight or degree of cross-linking tends to
promote secondary bonding between chains and thus
make the polymer more creep resistant.
36
Creep Compliances
(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 Tg of the polymer. (c) Shift along
the log-time scale to produce a master
curve. (Courtesy of W. Knauss.) (d)
Experimentally determined shift factor.
37
Stress Relaxation
A constant imposed strain e0 results in a drop in
stress s(t) as a function of time.
38
Effect of Crosslinking on Stress Relaxation
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.
39
Electromigration
Metal interconnect line covered by passivation
layer subjected toelectromigration (a) overall
scheme (b) voids and cracks produced by
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.)
40
Superplasticity
Superplastic tensile deformation in Pb62 Sn
eutectic alloy tested at 415 K and a strain rate
of 1.33 10-4 s-1 total strain of 48.5.
(From M. M. I. Ahmed and T. G. Langdon, Met.
Trans. A, 8 (1977) 1832.)
41
Plastic Deformation
(a) Schematic representation of plastic
deformation in tension with formation and
inhibition of necking. (b) Engineering-stress
engineering-strain curves.
42
Strain Rate Dependence
Strain-rate dependence of (a) stress and (b)
strain-rate sensitivity for MgAl eutectic alloy
tested at 350 ?C (grain size 10 µm). (After D.
Lee, Acta. Met., 17 (1969) 1057.)
43
Fracture
Tensile fracture strain and stress as a function
of strain rate for Zr22 Al alloy with 2.5-µm
grain size. (After F. A. Mohamed, M. M. I.
Ahmed, and T. G. Langdon, Met. Trans. A, 8 (1977)
933.)
44
Effect of Strain Rate Sensitivity
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.)
45
Cavitation in Superplasticity
Cavitation in superplasticity formed 7475-T6
aluminum alloy (e 3.5) at 475 ?C and 5 10-4
s-1. (a) Atmospheric pressure. (b) Hydrostatic
pressure P 4 MPa. (Courtesy of A. K. Mukherjee.)
46
Effect of Grain Size on Elongation
(a) Effect of grain size on elongation (A)
Initial configuration. (B) Large grains. (C) Fine
grains (10 µm) (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 of A. K. Mukherjee.)