High Temp Behavior of Materials : Mechanical degradation Chemical Degradation

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, tr.

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

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

18. SECONDARY CREEP • Most of component life spent here. • Strain rate is constant at a given T, s --strain hardening is balanced by recovery stress exponent (material parameter) . activation energy for creep (material parameter) strain rate material const. applied stress 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.) • Strain rate increases for larger T, s 24

23. CREEP FAILURE • Failure: along grain boundaries. • Estimate rupture time S 590 Iron, T = 800C, s = 20 ksi g.b. cavities Adapted from Fig. 8.45, Callister 6e. (Fig. 8.45 is from F.R. Larson and J. Miller, Trans. ASME, 74, 765 (1952).) applied stress 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.) 24x103 K-log hr • Time to rupture, tr temperature function of applied stress 1073K Ans: tr = 233hr time to failure (rupture) 25

24. SECONDARY CREEP • Most of component life spent here. • Strain rate is constant at a given T, s --strain hardening is balanced by recovery stress exponent (material parameter) . activation energy for creep (material parameter) strain rate material const. applied stress 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.) • Strain rate increases for larger T, s 24

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

32. The Creep Test:

34. 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.)

35. 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).

36. Material Parameters

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

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 eo 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 eo and conclude whether Coble or Nabarro-Herring creep is dominant.

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

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

48. 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.)

49. 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.)