1. Creep and Superplasticity
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 Initial position
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, σa, σb, and σc, using Larson–Miller equation (σa > σb > σc).

7. Larson-Miller Parameter
Master plot for Larson–Miller 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, σa, σb, and σc, using Manson–Haferd parameter (σa > σb > σc).

9. Sherby-Dorn Parameter
Relationship between time to rupture and temperature
at three levels of stress, σa > σb > σc, using Sherby–Dorn 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
σ/G < 10^(-4) Diffusion Creep
Nabarro Herring
Coble Creep
Harper Dorn Creep

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

15. Dislocation Climb Dislocation climb (a) upwards, under compressive σ22
stresses, and (b) downwards, under tensile σ22 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, 66–69 (1989) 1205.)

17. Dislocation (Power Law) Creep: 10^(-2) < σ/G < 10^(-4)
Power relationship between ˙ε and σ 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 Cottrell–Lomer 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-Verrall’s Model
Grain-boundary sliding assisted by diffusion in Ashby–Verrall’s model.
(Reprinted with permission from M. F. Ashby and R. A. Verrall, Acta Met., 21 (1973) 149.)

23. Weertman-Ashby Map for Pure Silver
Weertman–Ashby 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
Weertman–Ashby 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 γ 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 Universit¨at, 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
Spring–dashpot analogs (a) in series and (b) in parallel.

34. Maxwell and Voigt Models
Strain–time and
(b) stress–time 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 σ0. 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 ε0 results in a drop in stress σ(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 Pb–62% 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 Mg–Al 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 Zr–22% 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, Pb–Sr, 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 (ε = 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.)