1. High Temp Behavior of Materials : Mechanical degradation Chemical Degradation Gas Turbine and jet Turbine Nuclear reactors Power plants Spacecraft Chemical processing

2. Homologous temperature: Th = (tcreep+273)/(tmelting +273) Th > 0.5 Creep is a concern Creep test: measure dimensional changes Focuses on early deformation stages Creep conducts: Const Load Engineering purpose Stress Rupture test: effects of Temp on long time load bearing characteristics,  r.

3. Creep is the tendency of a solid material to slowly deform permanently under the influence of stresses. It occurs as a result of long term exposure to levels of stress that are below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods, and near the melting point. Creep always increases with temperature. The rate of this deformation is a function of the material properties, exposure time, exposure temperature and the applied structural load. Depending on the magnitude of the applied stress and its duration, the deformation may become so large that a component can no longer perform its function — for example creep of a turbine blade will cause the blade to contact the casing, resulting in the failure of the blade.

4. Creep is usually of concern to engineers and metallurgists when evaluating components that operate under high stresses or high temperatures. Creep is a deformation mechanism that may or may not constitute a failure mode. Moderate creep in concrete is sometimes welcomed because it relieves tensile stresses that might otherwise lead to cracking.

12. Andrade’s Model 1.Sudden strain, 2.Transient creepwith strain rate decrease with time, 3. const rate creep

13. Garofalo Model:

16. 22 Elevated Temperature Tensile Test (T > 0.4 T melt ). Generally,... MEASURING ELEVATED T RESPONSE

17. Occurs at elevated temperature, T > 0.4 T melt Deformation changes with time. 23 Adapted from Figs. 8.26 and 8.27, Callister 6e. CREEP

18. Most of component life spent here. Strain rate is constant at a given T,  --strain hardening is balanced by recovery 24 stress exponent (material parameter) strain rate activation energy for creep (material parameter) applied stressmaterial const. Strain rate increases for larger T,  Adapted from Fig. 8.29, Callister 6e. (Fig. 8.29 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.). SECONDARY CREEP

23. Failure: along grain boundaries. 25 time to failure (rupture) function of applied stress temperature applied stress g.b. cavities Time to rupture, t r Estimate rupture time S 590 Iron, T = 800C,  = 20 ksi 1073K 24x10 3 K-log hr Ans: t r = 233hr Adapted from Fig. 8.45, Callister 6e. (Fig. 8.45 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).) 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.) CREEP FAILURE

24. Most of component life spent here. Strain rate is constant at a given T,  --strain hardening is balanced by recovery 24 stress exponent (material parameter) strain rate activation energy for creep (material parameter) applied stressmaterial const. Strain rate increases for larger T,  Adapted from Fig. 8.29, Callister 6e. (Fig. 8.29 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.). SECONDARY CREEP

31. The Creep Test: a typical creep curve showing the strain produced as a function of time for a constant stress and temperature. Apply stress to a material at an elevated temperature Creep: Plastic deformation at high temperature

32. The Creep Test:

34. 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.) Larson-Miller Parameter

35. Relationship between time to rupture and temperature at three levels of engineering stress, σa, σb, and σc, using Larson–Miller equation (σa > σb > σc). Larson-Miller Equation

36. Material Parameters

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

43. Coble creep: a form of diffusion creep, is a mechanism for deformation of crystalline solids. Coble creep occurs through the diffusion of atoms in a material along the grain boundaries, which produces a net flow of material and a sliding of the grain boundaries. Coble creep is named after Robert L. Coble, who first reported his theory of how materials creep over time in 1962 in the Journal of Applied Physics. The strain rate in a material experiencing Coble creep is given by: where σ is the applied stress d is the average grain boundary diameter Dgb is the diffusion coefficient in the grain boundary − QCoble is the activation energy for Coble creep R is the molar gas constant T is the temperature in Kelvin

44. Note that in Coble creep, the strain rate   is proportional to the applied stress σ; the same relationship is found for Nabarro-Herring creep. However, the two mechanisms differ in their relationship between the strain rate and grain size d. In Coble creep, the strain rate is proportional to d − 3, whereas the strain rate in Nabarro-Herring creep is proportional to d − 2. Researchers commonly use these relationships to determine which mechanism is dominant in a material; by varying the grain size and measuring how the strain rate is affected, they can determine the value of n in   and conclude whether Coble or Nabarro-Herring creep is dominant.

45. Dislocation climb (a) upwards, under compressive σ22 stresses, and (b) downwards, under tensile σ22 stresses. Dislocation Climb

46. Dislocation overcoming obstacles by climb, according to Weertman theory. (a) Overcoming Cottrell–Lomer locks. (b) Overcoming an obstacle. Dislocations Overcoming Obstacles Weertman Mechanism

48. (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

49. 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.) Ashby-Verrall’s Model

58. Deformation mechanism maps These are graphs in typically stress-temperature space (but also grain size- temperature and others) which show which deformation mechanisms dominate under which conditions

59. Deformation mechanism maps These are graphs in typically stress- temperature space (but also grain size- temperature and others) which show which deformation mechanisms dominate under which conditions

66. 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.) Superplasticity

67. (a) Schematic representation of plastic deformation in tension with formation and inhibition of necking. (b) Engineering-stress– engineering-strain curves. Plastic Deformation

68. 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.) Strain Rate Dependence

69. 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.) Fracture

70. 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.) Effect of Strain Rate Sensitivity

71. 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.) Cavitation in Superplasticity

72. (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.) Effect of Grain Size on Elongation

82. Microstructure of a Creep resistant steel

83. Heat Resisting Steel Precipitates M 23 C 6, M 7 C 3, M 2 X, M 3 C, M 6 C, M X Intermetallics Laves Phase, Z-Phase Alloying Elements Substitutional : Cr, V, Nb, Mo,W, Cu, Mn Interstitial : C, N Creep Resistant Steel Microstructure Tempered Martensite, Bainite

84. Resistance to Creep  Solid solution hardening  Precipitate hardening  Microstructure