High Temp Behavior of Materials : Mechanical degradation Chemical Degradation

• High Temp Behavior of Materials:Mechanical degradationChemical Degradation

• Gas Turbine and jet Turbine• Nuclear reactors• Power plants• Spacecraft • Chemical processing

• Homologous temperature:• Th = (tcreep+273)/(tmelting +273)• Th > 0.5 Creep is a concern

• Creep test: measure dimensional changesFocuses on early deformation stages Creep conducts: Const Load Engineering purpose

Stress Rupture test: effects of Temp on long time load bearing characteristics, r.

• 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.

• 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.

• Andrade’s Model• 1.Sudden strain, 2.Transient creepwith

strain rate decrease with time,• 3. const rate creep

• Garofalo Model:

22

• Elevated Temperature Tensile Test (T > 0.4 Tmelt).

• Generally,

time

creep test

xslope = ss = steady-state creep rate.

ssceramics ssmetals sspolymers. . .

MEASURING ELEVATED T RESPONSE

timeelastic

primary secondary

tertiary

T < 0.4 Tm

INCREASING T

0

strain,

• Occurs at elevated temperature, T > 0.4 Tmelt• Deformation changes with time.

23

Adapted fromFigs. 8.26 and 8.27, Callister 6e.

CREEP

0 t

• 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 rateactivation energy for creep(material parameter)

applied stressmaterial const.

• Strain rate increases for larger T,

102040

100200

Steady state creep rate (%/1000hr)10-2 10-1 1s

Stress (MPa)427C

538C

649C

Adapted fromFig. 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.)

s K2nexp

QcRT

.

SECONDARY CREEP

• Failure: along grain boundaries.

25

time to failure (rupture)

function ofapplied stress

temperature

T(20 logtr ) LL(103K-log hr)

Stre

ss, k

si

100

10

112 20 24 2816

data for S-590 Iron

20appliedstress

g.b. cavities

• Time to rupture, tr

• Estimate rupture time S 590 Iron, T = 800C, = 20 ksi

T(20 logtr ) L1073K

24x103 K-log hr

Ans: tr = 233hr

Adapted fromFig. 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

• 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 rateactivation energy for creep(material parameter)

applied stressmaterial const.

• Strain rate increases for larger T,

102040

100200

Steady state creep rate (%/1000hr)10-2 10-1 1s

Stress (MPa)427C

538C

649C

Adapted fromFig. 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.)

s K2nexp

QcRT

.

SECONDARY CREEP

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

The Creep Test:

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

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

Material Parameters

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

Diffusion Creep

• 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

• 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.

Dislocation climb (a) upwards, under compressive σ22stresses, and (b) downwards, under tensile σ22 stresses.

Dislocation Climb

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

Dislocations Overcoming ObstaclesWeertman Mechanism

(a) Steady-stategrain-boundary sliding withdiffusional accommodations.

(b) Same process as in (a), in anidealized polycrystal; the dashedlines show the flow of vacancies.

(Reprinted with permission fromR. Raj and M. F. Ashby, Met. Trans.,2A (1971) 1113.)

Grain Boundary Sliding

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

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

• 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

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

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

Plastic Deformation

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

Tensile fracture strain and stress as a function of strainrate 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

Effect of strain-rate sensitivity m on maximum tensileelongation 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

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

(a) Effect of grain size on elongation: (A) Initial configuration. (B) Largegrains. (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 strainsincrease with superimposed hydrostatic pressure (from 0 to 5.6 MPa). (Courtesy ofA. K. Mukherjee.)

Effect of Grain Size on Elongation

Microstructure of a Creep resistant steel

Heat Resisting SteelPrecipitates

M23C6 , M7 C3 , M2X ,

M3 C , M6 C , M X

IntermetallicsLaves Phase, Z-Phase

Alloying ElementsSubstitutional :

Cr, V, Nb, Mo,W, Cu, Mn

Interstitial : C, N

Creep Resistant Steel

MicrostructureTempered Martensite, Bainite

Resistance to Creep

Solid solution hardening Precipitate hardening Microstructure