Volume 20 - Materials Selection and Design Part 10 pptx

Hickling, "Strain Induced Corrosion Cracking: Relationship to Stress Corrosion Cracking/Corrosion Fatigue and Importance for Nuclear Plant Service Life, paper presented at Third IAEA Spe

content or corrosion potential); (b) measuring the reaction rates for the crack-tip alloy/environment system that corresponds to the "engineering" system; and (c) defining the crack-tip strain rate in terms of continuum parameters such

as stress, stress intensity, and loading frequency Extensive work has been conducted in these areas, which has been reviewed elsewhere (Ref 10)

As a result of these examinations of the tip metallurgical, chemical, and stressing conditions, practical propagation-rate algorithms of the following form have been developed for stainless steels in 288 °C BWR water:

crack-Vt = 7.8 × 10-3 n3.6 ( ct)n (Eq 25)

ct = 6 × 10-14 K4 for constant load (Eq 27)

where is the conductivity of coolant ( S · cm-1), c is the corrosion potential of the steel (mVSHE), EPR is the

measurement of grain-boundary chromium depletion due to heat treatment annealing or welding, K is the stress intensity

(ksi ), app is the applied strain rate (s-1), is the cyclic-loading frequency (s-1), K is the stress-intensity amplitude under cyclic loading, and AR is a parameter that is a function of the mean stress under cyclic loading

Validation of Life-Prediction Algorithms and Their Application. The overall comparison between the observed and theoretical crack-propagation rates in type 304/316 stainless steels in 288 °C water is shown in Fig 41 The laboratory database upon which this comparison was made was obtained under a wide range of stressing (static, monotonically increasing, and cyclic load), material (solution annealed vs various degrees of sensitization) and water composition (<10 ppb O2 to >8 ppm O2, <0.1 to 10 S · cm-1) It is seen that there is a reasonable agreement between observation and prediction

Fig 41 Comparisons between observed and theoretical crack-propagation rates for type 304/316 stainless

steels in 288 °C water This database represents a wide combination of stressing material and environmental

conditions Source: Ref 96

Changes in corrosion potential within the range expected in BWRs can have a significant effect on the cracking susceptibility of type 304/316 stainless steels, especially under constant-load conditions This predicted and observed effect is illustrated in Fig 42 for furnace-sensitized type 304 stainless steel under constant stress intensity (25 ksi )

in water with the conductivity in the range 0.1 to 0.3 S · cm-1 It is seen that over the corrosion potential range -550

mVSHE to +250 mVSHE (spanning "hydrogen-water" conditions to those under "normal" core conditions) the propagation rate can change three orders of magnitude From an operational design viewpoint, therefore, it is seen that considerable benefit may be predicted by developing actions that lower the corrosion potential of the stainless steel structures, thereby highlighting remedial actions that lower the effective concentration of oxidants (oxygen, hydrogen peroxide) in the coolant Solution conductivity is also predicted to have an effect on the cracking susceptibility, as indicated by the three theoretical relationships shown in Fig 42, thereby highlighting the quantitative value of maintaining water-purity control

crack-Fig 42 Observed and predicted sensitivity of stress-corrosion-cracking sensitivity to corrosion potential for

sensitized type 304 stainless steel in 288 °C water The data points are measurements made in the laboratory

or in reactors The curves are the predicted relationships for the indicated conductivities The numbered data points were obtained at the Harwell variable-energy cyclotron The circled numbers were with the proton irradiation turned on, and the uncircled numbers were with the irradiation off Similarly the data point * was obtained under fast neutron irradiation in a boiling-water-reactor core

So far, the comparisons between observation and theory have centered on material/environment systems variables that

affect n in Eq 25 and 26 The effect of stressing/straining conditions on the cracking susceptibility occur primarily

through their effect on the crack-tip strain rate in Eq 27, 28, and 29 It follows that because the crack tip does not

recognize how the strain rate is maintained, the cracking susceptibility for a given material/environment condition should

adhere to the same crack-propagation rate/crack-tip strain-rate relationship, regardless of the stressing/straining mode The truth to this statement is illustrated in Fig 43, which shows the theoretical and observed crack-propagation rate strain-rate relationship for a severely sensitized type 304 stainless steel in 8 ppm O2, 0.5 S · cm-1 water Movement along the strain-rate axis has been achieved by increasing stress intensity under constant-load conditions, increasing applied strain rate under monotonically increasing strain conditions, or cyclic loading under a variety of stress-intensity amplitude, mean stress, and loading frequency conditions The single theoretical relationship line in Fig 43 adequately predicts the cracking under this wide range of loading modes, indicating that the prediction method applies to stress-corrosion cracking (SCC), strain-induced cracking (SIC), and corrosion fatigue (CF)

Fig 43 Predicted and observed crack-propagation rate/crack-tip strain-rate relationships for sensitized type

304 stainless steel in 8 ppm oxygenated, 0.5 S · cm -1 purity water at 288 °C

The old lore that these types of cracking (SCC, SIC, CF) are separate phenomena with, by implication, different mitigation or design modification needs is probably incorrect For instance, it follows from Eq 25 that the sensitivity of the cracking susceptibility to the crack-tip strain rate will be a function of the material/environment conditions that affect

n (Eq 26) Thus, the slope of the crack-propagation-rate/strain-rate relationship will be relatively shallow for severe

environmental and material conditions (e.g., high dissolved oxygen, impure water, and high degrees of grain-boundary sensitization), and the relationship will be steep for less severe material/environmental conditions This predicted and observed (Fig 44) change in propagation-rate/strain-rate dependency with system conditions is significant when evaluating the validity of accelerated tests that are often used for development of design codes For instance, increasing the crack-tip strain rate, and hence cracking susceptibility, by using the "slow-strain-rate test" is a valid test acceleration procedure (because it is accelerating one of the rate-determining steps in the cracking mechanism), but the factor of improvement between a reference condition and a proposed mitigation condition will be less in this test than at the lower stressing or strain-rate conditions expected in the operating plant The relationship (i.e., Fig 44) also gives an explanation for the lore that the cracking susceptibility is more dependent on the specific environmental conditions under constant-load stress-corrosion conditions than under corrosion-fatigue conditions

Fig 44 Predicted and observed crack-propagation rate/crack-tip strain-rate relationships for stainless steels in

a variety of material/environment systems

In summary, therefore, it is apparent that the crack-prediction algorithms are able to quantitatively explain the changes in crack-propagation rates for type 304/316 stainless steel in water at 288 °C for a wide combination of water composition (corrosion, potential, conductivity), material sensitization, and stressing (constant load/displacement, cyclic load) conditions It follows, however, that because the cracking response is so sensitive to changes in combinations of system conditions, it is necessary to combine the predictive method with system-defining sensors and models (Fig 45) Provided this combining is done, it is then possible to make predictions of the extent of cracking in specific plant components (Fig 46) and the increase in life associated with specific system changes (Fig 47)

Fig 45 The integration of system monitors, sensors, and environmental/material models as inputs to a

crack-propagation-rate model

Fig 46 Theoretical and observed intergranular stress corrosion crackdepth vs operational-time relationships

for 28 in diameter schedule 80 type 304 stainless steel piping for two boiling-water reactors operating at different mean coolant conductivities Note the bracketing of the maximum crack depth in the lower-purity plant by the predicted curve, which is based on the maximum residual-stress profile and the predicted absence

of observable cracking in the higher-purity plant (in 240 operating months)

Fig 47 Predicted crack depth vs time response for defected 28 in diameter schedule 80 recirculation piping in

a given boiling-water reactor to defined changes in water purity Also shown is the crack-depth limit that can be resolved by nondestructive testing (NDT)

References cited in this section

10 M.G Fontana, Corrosion Engineering, 3rd ed., McGraw-Hill Book Co., 1986

81 R.L Jones, "Corrosion Experience in U.S Light Water Reactors NACE 50th Anniversary Perspective," Paper 168, presented at Corrosion 93, NACE, 1993

82 R.L Jones, "Critical Corrosion Issues and Mitigation Strategies Impacting the Operability of LWRs," Paper 103, presented at Corrosion 96, NACE, 1996

83 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, J

Roberts and W Berry, Ed., NACE, 1983

84 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, J

Roberts and J Weeks, Ed., ANS, 1985

85 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, J Weeks

and G Theus, Ed., TMS, 1987

86 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, G

Theus and D Cubicciotti, Ed., NACE, 1989

87 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, D

Cubicciotti and E Simonen, Ed., ANS, 1991

88 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, R Gold

and E Simonen, Ed., TMS, 1993

89 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, R Gold

and E McIlree, Ed., NACE, 1995

90 H Okada and R Staehle, Ed., Predictive Methods for Assessing Corrosion Damage to BWR Piping and

PWR Steam Generators, NACE, 1982

91 D.D MacDonald and G.A Cragnolino, Corrosion of Steam Cycle Materials, ASME Handbook on Water

Technology for Thermal Power Systems, P Cohen, Ed., ASME, 1979

92 J.T.A Roberts, Structural Materials in Nuclear Power Systems, Plenum Press, 1981

93 J.C Danko, Corrosion in the Nuclear Power Industry, Corrosion, Vol 13, ASM Handbook, ASM

97 P.L Andresen, Corrosion 47, NACE, 1991, p 917-938

99 F.P Ford, P.L Andresen, M.G Benz, and D Weinstein, On-Line BWR Materials Monitoring and Plant

Component Lifetime Prediction, Proc Nuclear Power Plant Life Extension, American Nuclear Society,

Vol 1, June 1988, p 355-366

100 F.P Ford, "Mechanisms of Environmental Cracking Peculiar to the Power Generation Industry," Report NP2589, EPRI, Sept 1982

101 F.P Ford, Stress Corrosion Cracking, Corrosion Processes, R.N Parkins, Ed., Applied Science, 1982

102 F.P Ford, The Crack Tip System and its Relevance to the Prediction of Environmentally Assisted

Cracking, Proc First International Conf Environment Induced Cracking of Metals, NACE, Oct 1988, p

139-166

103 R.N Parkins, Environment Sensitive Fracture Controlling Parameters, Proc Third International Conf

Mechanical Behavior of Materials, K.J Miller and R.F Smith, Ed., Pergamon, Vol 1, 1980, p 139-164

104 T.R Beck, Corrosion 30, NACE, 1974, p 408

105 J Hickling, "Strain Induced Corrosion Cracking: Relationship to Stress Corrosion Cracking/Corrosion Fatigue and Importance for Nuclear Plant Service Life, paper presented at Third IAEA Specialists Meeting

on Subcritical Crack Growth, Moscow, May 1990

Design for Corrosion Resistance

F Peter Ford and Peter L Andresen, General Electric Corporate Research and Development Center; Peter Elliott, Corrosion and Materials Consultancy, Inc

References

1 H Uhlig, Chemical and Engineering News, Vol 97, 1949, p 2764

2 Editorial, Corrosion Prevention and Control, Vol 27, 1980, p 1

3 T.P Hoar, Report of the Committee on Corrosion and Protection, Her Majesty's Stationery Office,

London, 1971

4 Proc 1986 Joint Chinese-American Corrosion Workshop, Industrial Technology Research Institute,

Hsinchu, Taiwan, Dec 1986

5 D.A Jones, Principles and Prevention of Corrosion, 2nd ed., Prentice Hall, 1996

6 K.R Trethewey and J Chamberlain, Corrosion for Science and Engineering, 2nd ed., Longman, 1995

7 P Marcus and J Oudar, Corrosion Mechanisms in Theory and Practice, Marcel Dekker, Inc., 1995

8 C.P Dillon, Corrosion Resistance of Stainless Steels, Marcel Dekker, Inc., 1995

9 B.D Craig, Fundamental Aspects of Corrosion Films in Corrosion Science, Plenum Press, 1991

10 M.G Fontana, Corrosion Engineering, 3rd ed., McGraw-Hill Book Co., 1986

11 W.W Kirk and H.H Lawson, Atmospheric Corrosion, ASTM, 1995

12 J.C Scully, The Fundamentals of Corrosion, Pergamon Press, 1975

13 H.P Hack, Galvanic Corrosion, ASTM, 1988

14 S.L Chawla and R.K Gupta, Materials Selection for Corrosion Control, ASM International, 1993

15 P.A Schweitzer, Corrosion and Corrosion Protection Handbook, 2nd ed., Marcel Dekker, 1989

16 G Moran and P Labine, Corrosion Monitoring in Industrial Plants Using Nondestructive Testing and

Electrochemical Methods, ASTM, 1986

17 D.O Northwood, W.E White, and G.F Vander Voort, Corrosion, Microstructure, and Metallography,

American Society for Metals, 1985

18 R.S Treseder, R Baboian, and C.G Munger, Ed., NACE Corrosion Engineer's Reference Book, 2nd ed.,

NACE, 1991

19 R.B Seymour, Plastics vs Corrosives, John Wiley & Sons, 1982

20 M Henthorne, Localized Corrosion Cause of Metal Failure, ASTM, 1972

21 R Baboian, Electrochemical Techniques for Corrosion Engineering, NACE, 1985

22 Corrosion, Vol 13, ASM Handbook (formerly Metals Handbook, 9th ed.), ASM International, 1987

23 S.K Coburn, Corrosion Source Book, American Society for Metals, 1984

24 A.J McEvily, Jr., Atlas of Stress-Corrosion and Corrosion Fatigue Curves, ASM International, 1990

25 L.L Shreir, R.A Jaman, and G.T Burstein, Corrosion Metal/Environment Reactions, Butterworth

Heinenmann, Ltd., 1994

26 R.F Steigerwald and N.D Greene, J Electrochem Soc., Vol 109, 1962, p 1026

27 H.H Uhlig and R.W Rene, Corrosion and Corrosion Control, 3rd ed., John Wiley & Sons, 1985, p 217

28 Z Szklarska-Smialawska, Pitting Corrosion of Metals, NACE, 1986

29 F.P Ford, "Mechanisms of Environmental Cracking Peculiar to the Power Generation Industry," Report NP2589, EPRI, 1982

30 F.P Ford, Stress Corrosion Cracking, Corrosion Processes, R.N Parkins, Ed., Applied Science, 1982

31 R.N Parkins, N.J.H Holroyd, and R.R Fessler, Corrosion, Vol 34, 1978, p 253

32 B Poulson and R Robinson, Corr Sci., Vol 20, 1980, p 707

33 J Congleton, "Some Aspects of Crack Initiation in Stress Corrosion and Corrosion Fatigue," paper presented at Corrosion 88, NACE, St Louis, 21-25 March 1988

34 Conf Proc., Environmental-Sensitive Mechanical Behavior (Baltimore, MD, June 1965), A.R.C

Westwood and N.S Stoloff, Ed., Gordon and Breach, 1966

35 R.W Staehle, A.J Forty, and D Van Rooyen, Ed., The Fundamental Aspects of Stress-Corrosion

Cracking, Ohio State University, Sept 1967

36 J.C Scully, Ed., Theory of Stress Corrosion Cracking, NATO, Brussels, March 1971

37 O Devereaux, A.J McEvily, and R.W Staehle, Ed., Corrosion Fatigue Chemistry, Mechanics and

Microstructure, University of Connecticut, Storrs, June 1971

38 M.P Bastein, Ed., L'Hydrogene dans les Metaux, Science et Industrie, Paris, 1972

39 L.M Bernstein and A.W Thompson, Ed., Hydrogen in Metals, L, American Society for Metals, 1973

40 R.W Staehle, J Hochmann, R.D McCright, and J.E Slater, Ed., Stress-Corrosion Cracking and Hydrogen Embrittlement of Iron-Base Alloys, NACE, 1977

41 A.W Thompson and I.M Bernstein, Ed., Proc Effect of Hydrogen on Behavior of Materials (Jackson

Lake, WY, Sept 1975), TMS, 1976

42 R.M Latanision and J.T Fourie, Ed., Surface Effects on Crystal Plasticity (Hohegeiss, Germany, 1975),

Noordhof-Leyden, 1977

43 P.R Swann, F.P Ford, and A.R.C Westwood, Ed., Mechanisms of Environment Sensitive Cracking of

Materials, The Metals Society, April 1977

44 Corrosion Fatigue, Met Sci., Vol 13, 1979

45 T.R Beck, Corrosion, Vol 30, 1974, p 408

46 R.W Staehle, in Theory of Stress Corrosion Cracking, J.C Scully, Ed., NATO, Brussels, March 1971

47 J.C Scully, Corros Sci., Vol 8, 1968, p 771

48 D.J Lees, F.P Ford, and T.P Hoar, Met Mater., Vol 7, 1973, p 5

49 J.R Ambrose and J Kruger, J Electrochem Soc., Vol 121, p 1974, p 599

50 F.P Ford and M Silverman, Corrosion, Vol 36, 1980, p 558

51 V.R Pludek, Design and Corrosion Control, MacMillan, 1977

52 R.J Landrum, Fundamentals of Designing for Corrosion Control, NACE International, 1989

53 R.N Parkins and K.A Chandler, Corrosion Control in Engineering Design, Department of Industry, Her

Majesty's Stationery Office, London, 1978

54 L.D Perrigo and G.A Jensen, Fundamentals of Corrosion Control Design, The Northern Engineer, Vol 13

(No 4), 1982, p 16

55 Designer Handbooks, Specialty Steel Industry of North America, Washington, D.C.; also publications

relative to design, Nickel Development Institute, Toronto, Canada

56 Guides to Practice in Corrosion Control, Department of Industry, Her Majesty's Stationery Office,

London, 1979-1986

57 Engineering Design Guides, Design Council, British Standards Institute, Council of Engineering

Institutions, Oxford University Press, 1975-1979

58 P Elliott and J.S Llewyn-Leach, Corrosion Control Checklist for Design Offices, Department of Industry,

Her Majesty's Stationery Office, London, 1981

59 P Elliott, Corrosion Control in Engineering Design, audiovisual for Department of Industry, United

Kingdom, 1981

60 O.W Siebert, Classic Blunders in Corrosion Protection, Mater Perform., Vol 17 (No 4), 1978, p 33 and

Vol 22 (No 10), 1983

61 T.F Degnan, Mater Perform Vol 26 (No 1), 1987, p 11

62 P Elliott, Why Must History Repeat Itself?, Ind Corros., Feb/March 1991, p 8

63 P Elliott, Process Plant Corrosion Recognizing the Threat, Process Eng., Vol 65 (No 11), 1984, p 43

64 P Elliott, Understanding Corrosion Attack, Plant Eng., Oct 1993, p 68

65 P Elliott, Corrosion Survey, Supplement to Chem Eng., Sept 1973

66 P Elliott, Catch 22 and the UCS Factor Why Must History Repeat Itself?, Mater Perform., Vol 28 (No

7), 1989, p 70 and Vol 28 (No 8), 1989, p 75

67 Standards for Corrosion Testing of Metals, ASTM, 1990

68 R Baboian, Ed., Corrosion Tests and Standards: Applications and Interpretation, ASTM Manual Series,

MNL-20, 1995

69 H.J.H Wassell, Reliability of Engineered Products, Engineering Design Guide, Design Council, Oxford

University, 1980

70 P Elliott, We Never get Corrosion Problems, Super News, 1974, p 70

71 A Sparks, Steel Carriage by Sea, 2nd ed., Lloyd's of London Press, 1995

72 G Kobrin, Ed., Microbiologically Influenced Corrosion, NACE International, 1993

73 P Elliott, Practical Guide to High Temperature Alloys, Mater Perform., Vol 28, 1989, p 57

74 G.Y Lai, High Temperature Corrosion of Engineering Alloys, ASM International, 1990

75 W Pollock, Corrosion under Wet Insulation, NACE International, 1988

76 "Specification for Wicking-Type Thermal Insulation for Use Over Austenitic Stainless Steel," C 795,

Annual Book of ASTM Standards, ASTM

77 "Codes of Practice for Drinking Water Installations (TRWI)," 628.1.033:696.11:620.193, DIN, Teil 7,

1988

78 H.H Uhlig, Corrosion and Corrosion Control, 2nd ed., John Wiley & Sons, 1971, p 314

79 C.G Munger, Corrosion Prevention by Protective Coatings, NACE International, 1984

80 P.E Weaver, "Industrial Maintenance Painting," RP0178, NACE International, 1973, p 2

81 R.L Jones, "Corrosion Experience in U.S Light Water Reactors NACE 50th Anniversary Perspective," Paper 168, presented at Corrosion 93, NACE, 1993

82 R.L Jones, "Critical Corrosion Issues and Mitigation Strategies Impacting the Operability of LWRs," Paper 103, presented at Corrosion 96, NACE, 1996

83 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, J

Roberts and W Berry, Ed., NACE, 1983

84 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, J

Roberts and J Weeks, Ed., ANS, 1985

85 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, J Weeks

and G Theus, Ed., TMS, 1987

86 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, G

Theus and D Cubicciotti, Ed., NACE, 1989

87 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, D

Cubicciotti and E Simonen, Ed., ANS, 1991

88 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, R Gold

and E Simonen, Ed., TMS, 1993

89 Conf Proc., Environmental Degradation of Materials in Nuclear Systems Light Water Reactors, R Gold

and E McIlree, Ed., NACE, 1995

90 H Okada and R Staehle, Ed., Predictive Methods for Assessing Corrosion Damage to BWR Piping and

PWR Steam Generators, NACE, 1982

91 D.D MacDonald and G.A Cragnolino, Corrosion of Steam Cycle Materials, ASME Handbook on Water

Technology for Thermal Power Systems, P Cohen, Ed., ASME, 1979

92 J.T.A Roberts, Structural Materials in Nuclear Power Systems, Plenum Press, 1981

93 J.C Danko, Corrosion in the Nuclear Power Industry, Corrosion, Vol 13, ASM Handbook, ASM

97 P.L Andresen, Corrosion 47, NACE, 1991, p 917-938

98 F.P Ford, "Environmentally Assisted Cracking of Low Alloy Steels," Final Report of Contract C102-1, Report NP7473-L, EPRI, Jan 1992

99 F.P Ford, P.L Andresen, M.G Benz, and D Weinstein, On-Line BWR Materials Monitoring and Plant

Component Lifetime Prediction, Proc Nuclear Power Plant Life Extension, American Nuclear Society,

Vol 1, June 1988, p 355-366

100 F.P Ford, "Mechanisms of Environmental Cracking Peculiar to the Power Generation Industry," Report NP2589, EPRI, Sept 1982

101 F.P Ford, Stress Corrosion Cracking, Corrosion Processes, R.N Parkins, Ed., Applied Science, 1982

102 F.P Ford, The Crack Tip System and its Relevance to the Prediction of Environmentally Assisted

Cracking, Proc First International Conf Environment Induced Cracking of Metals, NACE, Oct 1988, p

139-166

103 R.N Parkins, Environment Sensitive Fracture Controlling Parameters, Proc Third International Conf

Mechanical Behavior of Materials, K.J Miller and R.F Smith, Ed., Pergamon, Vol 1, 1980, p 139-164

104 T.R Beck, Corrosion 30, NACE, 1974, p 408

105 J Hickling, "Strain Induced Corrosion Cracking: Relationship to Stress Corrosion Cracking/Corrosion Fatigue and Importance for Nuclear Plant Service Life, paper presented at Third IAEA Specialists Meeting

on Subcritical Crack Growth, Moscow, May 1990

106 K Osozaawa and H.J Engell, Corros Sci., Vol 6, 1966, p 389

Design for Corrosion Resistance

F Peter Ford and Peter L Andresen, General Electric Corporate Research and Development Center; Peter Elliott, Corrosion and Materials Consultancy, Inc

Selected References

*

• V.A Ashworth and P Elliot, Guide to the Corrosion Resistance of Metals, Metals Reference Book,

5th ed., C.J Smithells and E.A Brandes, Ed., Butterworths, 1976, p 1460

• B.D Craig and D Anderson, Ed., Handbook of Corrosion Data, 2nd ed., ASM International, 1995

• Corrosion Data Survey: Metals Section, 6th ed., NACE, 1985

• Corrosion Data Survey: Nonmetals Section, 5th ed., NACE, 1975

• D.J De Renzo, Ed., Corrosion-Resistant Materials Handbook, 4th ed., Noyes, 1985

• DECHEMA Corrosion Handbook: Corrosive Agents and Their Interaction with Materials, D

Behrens (Vol 1-9) and G Kreysa and R Eckermann (Vol 10-12), Ed., VCH, 1987-1993

• NACE/NIST Corrosion Performance Databases, Corrosion Data Center, National Institute of

Standards and Technology, Gaithersburg, MD

• P.A Schweitzer, Ed., Corrosion Resistance Tables, 3 vol, 4th ed., Marcel Dekker, 1995

• H.H Uhlig, Corrosion Handbook, John Wiley & Sons, 1948

• H.H Uhlig and R.W Revie, Corrosion and Corrosion Control: An Introduction to Corrosion

Science and Engineering, 3rd ed., Wiley, 1985

References cited in this section

5 D.A Jones, Principles and Prevention of Corrosion, 2nd ed., Prentice Hall, 1996

6 K.R Trethewey and J Chamberlain, Corrosion for Science and Engineering, 2nd ed., Longman, 1995

7 P Marcus and J Oudar, Corrosion Mechanisms in Theory and Practice, Marcel Dekker, Inc., 1995

8 C.P Dillon, Corrosion Resistance of Stainless Steels, Marcel Dekker, Inc., 1995

9 B.D Craig, Fundamental Aspects of Corrosion Films in Corrosion Science, Plenum Press, 1991

10 M.G Fontana, Corrosion Engineering, 3rd ed., McGraw-Hill Book Co., 1986

11 W.W Kirk and H.H Lawson, Atmospheric Corrosion, ASTM, 1995

12 J.C Scully, The Fundamentals of Corrosion, Pergamon Press, 1975

13 H.P Hack, Galvanic Corrosion, ASTM, 1988

14 S.L Chawla and R.K Gupta, Materials Selection for Corrosion Control, ASM International, 1993

15 P.A Schweitzer, Corrosion and Corrosion Protection Handbook, 2nd ed., Marcel Dekker, 1989

16 G Moran and P Labine, Corrosion Monitoring in Industrial Plants Using Nondestructive Testing and

Electrochemical Methods, ASTM, 1986

17 D.O Northwood, W.E White, and G.F Vander Voort, Corrosion, Microstructure, and Metallography,

American Society for Metals, 1985

18 R.S Treseder, R Baboian, and C.G Munger, Ed., NACE Corrosion Engineer's Reference Book, 2nd ed.,

NACE, 1991

19 R.B Seymour, Plastics vs Corrosives, John Wiley & Sons, 1982

20 M Henthorne, Localized Corrosion Cause of Metal Failure, ASTM, 1972

21 R Baboian, Electrochemical Techniques for Corrosion Engineering, NACE, 1985

22 Corrosion, Vol 13, ASM Handbook (formerly Metals Handbook, 9th ed.), ASM International, 1987

23 S.K Coburn, Corrosion Source Book, American Society for Metals, 1984

24 A.J McEvily, Jr., Atlas of Stress-Corrosion and Corrosion Fatigue Curves, ASM International, 1990

25 L.L Shreir, R.A Jaman, and G.T Burstein, Corrosion Metal/Environment Reactions, Butterworth

Heinenmann, Ltd., 1994

26 R.F Steigerwald and N.D Greene, J Electrochem Soc., Vol 109, 1962, p 1026

27 H.H Uhlig and R.W Rene, Corrosion and Corrosion Control, 3rd ed., John Wiley & Sons, 1985, p 217

28 Z Szklarska-Smialawska, Pitting Corrosion of Metals, NACE, 1986

68 R Baboian, Ed., Corrosion Tests and Standards: Applications and Interpretation, ASTM Manual Series,

MNL-20, 1995

79 C.G Munger, Corrosion Prevention by Protective Coatings, NACE International, 1984

Note cited in this section

* See also Ref 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,

68, and 79 in the list of numbered references

Design for High-Temperature Applications

David A Woodford, Materials Performance Analysis, Inc

Introduction

APART FROM nineteenth-century steam boilers, machines and equipment for high-temperature operation have been developed principally in the present century Energy conversion systems based on steam turbines, gas turbines, high-performance automobile engines, and jet engines provide the technological foundation for modern society All of these machines have in common the use of metallic materials at temperatures where time-dependent deformation and fracture processes must be considered in their design The single valued time-invariant strain associated with elastic or plastic design analysis in low-temperature applications is not applicable, nor is there in most situations a unique value of fracture toughness that may be used as a limiting condition for part failure In addition to the phenomenological complexities of time-dependent behavior, there is now convincing evidence that the synergism associated with gaseous environmental interactions may have a major effect, in particular on high-temperature fracture

This article reviews the basic mechanisms of elevated-temperature behavior and associated design considerations with emphasis on metals Subsequently, the engineering analysis will be confined to presenting data in the form that a designer might use, with emphasis on design principles rather than detailed design analysis Thus, multiaxial stresses, part analysis, and creep-fatigue interaction are not formally treated However, remaining life assessment and the effect of nonsteady

stresses are covered A broader treatment of most of these aspects can be found in other articles that appear in the ASM Specialty Handbook: Heat-Resistant Materials and in Mechanical Testing, Volume 8 of the ASM Handbook Emphasis

here is placed on developing an appreciation of the uses (and abuses) of creep and rupture testing, data presentation, data analysis, limitations of long-time tests, and alternative approaches to high-temperature design The objective is to provide

a solid foundation for design principles from a materials performance perspective

Acknowledgements

Of all the people who have influenced his thinking over the years, the author would like to give special thanks to the late Robert Goldhoff, who directed him into this field of study and research; Louis Coffin, who has provided direct and indirect influence over the years; Edward Hart, a rigorous thinker and writer; Roger Bricknell, an intellectual partner; Michael Henry, a creative materials engineer; the late Chester Sims, a force in superalloys; Joanne Beckman, his first Ph.D student; Donald Van Steele, an outstanding experimentalist; and David Stiles, a supporter of new ideas

Design for High-Temperature Applications

David A Woodford, Materials Performance Analysis, Inc

Historical Development of Creep Deformation Analysis

The phenomenon of time-dependent deformation was referred to as slow stretch by Philips (Ref 1) and as viscous flow by Andrade (Ref 2) at the beginning of this century and subsequently became known as creep There were several seminal ideas in the Andrade work that have had a lasting impact on scientific studies and engineering dogma The initial work was primarily on lead wires at room temperature (a high temperature relative to the melting point for lead) with some additional experiments on a 78.5% Sn 21.5% Pb alloy and copper Andrade noted that after applying a fixed load the rate

of extension initially decreased then became constant for a time, but finally increased and continued increasing until failure He recognized that as the wire stretched, the load per unit area increased Subsequently, he devised a scheme to compensate for this and maintain a constant stress on the wire As a result of this, the extent of viscous flow, that is, extension linearly dependent on time, increased as shown in Fig 1 Andrade also recognized that the length of wire being

experimented on at any time is increasing and thus used the concept of true strain He derived a formula to describe the observed deformation:

where l and lo are the current and initial specimen lengths, t is the time, and and k are constants The initial transient strain (later to be called primary creep) was referred to as beta creep and followed a time to the one-third law, the viscous region (later to be called steady-state creep) was proportional to time, and the accelerating strain region leading to fracture, which was not specifically treated by Andrade, later became known as tertiary creep Much later, in a comprehensive study of creep in copper and aluminum, Wyatt (Ref 3) concluded that there are two types of transient creep in metals:

• At higher temperatures, beta creep predominates as in Andrade's experiments

• At lower temperatures, the strain is proportional to log(time), and the flow is referred to as alpha creep

Fig 1 Creep tests on lead wire In both tests, initial lengths and initial loads were the same Source: Ref 2

From this early work, subsequent studies diverged into two investigative paths The first sought understanding of creep deformation micromechanisms in pure metals and solid-solution alloys in relatively short-term tests, accepted the concept

of steady-state creep (although testing was more often conducted at constant load rather than constant stress), and often assumed implicitly that viscous flow was history independent This means that not only is there a steady creep rate associated with a given applied stress, but that this rate is obtained despite previous deformation at different stresses and temperatures Although this might be a reasonable approximation for pure metals, it is manifestly wrong for most engineering alloys

The second investigative path concentrated on generating long-time creep data on engineering materials The testing was invariably at constant load, and data extracted included times for specific creep strains, minimum creep rates (although the term steady state was often used despite the fact that constant rates cannot be expected when the stress is changing), and time to failure (often referred to as rupture life) This latter measurement was of special significance because it became a basis for design against part failure, and later as a basis for estimating remaining life of operating components

There thus emerged a framework for design against both creep deformation and fracture using a single testing procedure

It formed a basis for what might be called an uncracked body analysis and comprises the major part of this article Analysis of cracked bodies involving fracture mechanics concepts as applied to creeping structures is not covered

although some reference is made as appropriate In particular, the importance of fatigue loading is emphasized in the

article "Creep-Fatigue Interaction" in the ASM Specialty Handbook: Heat-Resistant Materials

Until the last quarter century, virtually all creep and creep fracture studies were on metallic materials However, as early

as 1903, Philips (Ref 1) recognized that the phenomenon was not unique to the metallic bond and that materials with covalent and ionic bonds showed similar effects In fact, creep of polymers is now of considerable importance in plastic automobile components and gas lines, and creep of ceramics is of interest in aerospace applications

References cited in this section

1 F Philips, The Slow Stretch in India Rubber, Glass and Metal Wire When Subjected to a Constant Pull,

Philos Mag., Vol 9, 1905, p 513

2 E.N da C Andrade, The Viscous Flow in Metals and Allied Phenomena, Proc R Soc., Vol A84, 1910, p

1-13

3 O.H Wyatt, Transient Creep in Pure Metals, Proc Phys Soc., Vol 66B, 1953, p 459-480

Design for High-Temperature Applications

David A Woodford, Materials Performance Analysis, Inc

Basic Concepts of Elevated-Temperature Design

Time-dependent deformation and fracture of structural materials at elevated temperatures are among the most challenging engineering problems faced by materials engineers In order to develop an improved design methodology for machines and equipment operating at high temperatures, several key concepts and their synergism must be understood As is described in this section, these include:

• Plastic instability at elevated temperatures

• Deformation mechanisms and strain components associated with creep processes

• Stress and temperature dependence

• Fracture at elevated temperatures

• Environmental effects

Design Phenomenology

The issues of interest from a design basis are the nature of primary creep, the validity of the concept of viscous state creep, and the dependence of deformation on both temperature and stress The simplest and most pervasive idea in creep of metals is an approach to an equilibrium microstructural and mechanical state Thus a hardening associated with dislocation generation and interaction is countered by a dynamic microstructural recovery or softening This process proceeds during primary creep and culminates in a steady-state situation The idea was first presented by Bailey (Ref 4) and subsequently in the following mathematical form by Orowan (Ref 5):

steady-(Eq 2)

where d represents the change in flow stress, / represents the hardening that results from an increment of plastic

strain d , and / t represents the softening due to recovery in a time increment dt

At constant stress (and temperature), the steady-state creep rate is given by:

The concept of steady-state creep has been addressed rigorously in very few publications (Ref 8) From these limited studies, however, it can be stated that a constant creep rate cannot occur during the changing stress conditions of the common constant load test (or, if the creep rate appears constant, it cannot be steady state) Further, it can be said that most engineering alloys undergo purely time-dependent changes at temperature associated with an approach to thermodynamic equilibrium, such as precipitate coarsening With the additional complication of strain-induced changes, it

is unlikely that a steady state could be established It is especially improbable that such a state could be history independent Any search for a true steady state should, therefore, be limited to pure metals or solid-solution alloys and would require constant stress testing and true-strain plotting

Plastic Instability

A major issue in the tensile creep test is the role of plastic instability in leading to tertiary creep Understanding of the nature of plastic instability for time-dependent flow has depended on the theory of Hart (Ref 9) He showed that the condition for stable deformation is:

where m, which equals [( ln )/( ln )] , is the strain-rate sensitivity, and , which equals [( ln )/( )] , is a measure of the strain-hardening rate For steady-state flow, is equal to 0 For constant stress tests, Burke and Nix (Ref 10) concluded that flow must be unstable when steady state is reached according to Hart's criterion but that macroscopic necking is insignificant and that the flow remains essentially homogeneous They concluded that a true steady state does exist Hart himself questioned the conclusions based on their analysis but did not rule out the possibility of a steady state for pure metals (Ref 8) In a very careful experimental analysis, Wray and Richmond (Ref 11) concluded that the concept

of a family of steady states is valid They advocated tests in which two of the basic parameters (stress, strain rate, and temperature) are held constant However, they reported the intrusion of nonuniform deformation before the steady state was reached They also pointed out the complexities associated with uncontrolled and often unmeasured loading paths, which produce different structures at the beginning of the constant stress or constant strain rate portions of the test For constant stress tests in pure metals, although the concept of steady state (viscous flow in Andrade's terminology) is appealing, it appears not yet to have been rigorously demonstrated

In constant load tests, steady-state behavior would of course result in an increasing creep rate after the minimum, as the true stress increases As such, the test is inappropriate to evaluate the concept However, it is by far the most common type of creep test and can be analyzed for instability (Ref 12) The condition for instability may be stated:

where Ä is the second derivative of specimen cross-sectional area with respect to time This in turn leads to a point of

instability expressed in terms of gage length:

(Eq 7)

This criterion is shown in Fig 2 for constant load tests on nickel The instability criterion is fulfilled at a strain very close

to that of the minimum creep rate However, the value of this criterion remains low up to 20 to 25% strain, at which separate measurements of specimen profiles indicate that macroscopic necking occurs In this respect, the results are similar to constant stress results (Ref 10) in that although deformation is potentially unstable at the end of the primary stage, it is not grossly so

Fig 2 Change in the parameter Ä/ with creep strain in nickel at 525 °C (980 °F) and 138 MPa (20 ksi)

Source: Ref 12

Creep Processes

Creep behavior can be characterized either in terms of deformation mechanisms or in terms of strain constituents

Deformation Mechanisms. Creep of metals is primarily a result of the motion of dislocations, but is distinct from time-independent behavior in that flow continues as obstacles, which may be dislocation tangles or precipitate particles, are progressively overcome The rate-controlling step involves diffusion to allow climb of edge dislocations or cross slip

of screw dislocations around obstacles In steady-state theory, there is a balance between the hardening associated with this dislocation motion and interaction, and a dynamic recovery associated with the development of a dislocation substructure Theory for such a process predicts a power-law dependence of creep rate on applied stress For example,

climb-controlled dislocation creep gives an exponent n = 4 in the following equation (Ref 13):

where C is a constant Nothing in this or similar theories allows for history effects, and although the power function

connection may be applicable, the value of n is not only invariably higher, but strongly history dependent in structural

alloys (see the following section)

At very high homologous temperatures (T/Tm) and low stresses, creep may occur in both metals and ceramics by mass transport involving stress-directed flow of atoms from regions under compression to regions under tension In this case,

theory indicates that there is a stress dependence of unity and that the process is controlled either by bulk diffusion (Ref

14, 15) or by grain-boundary diffusion (Ref 16) These various processes of creep (dislocation controlled as well as diffusion controlled) may be represented on a deformation mechanism map to highlight regimes of stress and temperature where each mechanism, based on current theories, may be operating (Ref 17) However, such maps are only as good as the theories on which they are based and give no guidance on deformation path dependence

Another important deformation process in metallic and ionic polycrystals at high temperature and low stresses is boundary sliding (Ref 18) The resistance to sliding is determined by the mobility of grain-boundary dislocations and by the presence of hard particles at the boundary This sliding leads to stress concentrations at grain junctions, which are important in nucleating cracks In ductile materials, these stress concentrations may be relieved by creep and stress relaxation in the matrix or by grain-boundary migration (Ref 19)

grain-Strain Components. There are several different sources of strain at high temperature in response to an applied stress The elastic strain is directly proportional to stress, and a modulus that is temperature dependent can be determined For metallic materials and ceramics, although there is a strain-rate dependence of elastic modulus, it is small and often ignored For polymers, by contrast, the elastic modulus is ill defined because of viscoelasticity

Plastic strain for all materials may be treated as three separate constituents:

• Time-independent nonrecoverable, which may be thought of as an instantaneous deformation

• Time-dependent nonrecoverable, which may involve any or all of the micromechanisms described above

• Time-dependent recoverable

The first of these is unlikely to be significant in practical applications except in the region of stress concentrations since loading is normally well below the macroscopic yield stress The second is the major source of creep in normal laboratory testing The third constituent is not widely studied or analyzed, but may become very important at low stresses and under nonsteady conditions, that is, high-temperature service It leads to what has been termed creep recovery and anelasticity

At high temperatures, the application of a stress leads to creep deformation resulting from the motion of dislocations, mass transport by diffusion, or grain-boundary sliding These processes in turn lead to a distribution of internal stresses that may relax on removal of the stress This relaxation leads to a time-dependent contraction in addition to the elastic contraction and results in the phenomenon of creep recovery illustrated in Fig 3 In polymers this phenomenon, which may account for nearly all the nonelastic strain, is termed viscoelastic recovery and is associated with the viscous sliding and unkinking of long molecular chains (Ref 21) In metals it is associated with the unbowing of pinned dislocations (Ref 7), rearrangement of dislocation networks (Ref 22), and local grain-boundary motion (Ref 23) In ceramics it appears to

be primarily a grain-boundary phenomenon (Ref 24)

Fig 3 Stress-time step applied to a material exhibiting strain response that includes time-independent elastic,

time-independent plastic, time-dependent creep, and time-dependent anelastic (creep-recovery) components Source: Ref 20

Whereas the importance of creep recovery is well recognized in polymer design, it has often been ignored in design of metallic and ceramic materials A few extensive studies have been reported on metals (Ref 25, 26, 27) that have led to several broad conclusions:

• Creep-recovery strain increases linearly with stress for a fixed time at a given temperature, but is dependent on prestrain

• The rate of creep recovery increases with increasing temperature

• When the stress is low enough, essentially all transient creep is linear with stress and recoverable

• Mathematically, the recovery may be described by a spectrum of spring dashpot combinations with a wide range of relaxation times

Assuming that the measured recovery strain after unloading had made an equivalent contribution to forward creep (Ref 28), it was possible in these studies to separate the anelastic and plastic creep components as shown in Fig 4 Because the anelastic component is linear with stress and the plastic component is a power function of stress (for the same time), at very low stresses the strain is entirely anelastic This observation led to the definition of a plastic creep limit that was time dependent For times up to 100 h in a low-alloy steel tested at 425 °C (800 °F), Lubahn (Ref 26) found this limit to be 140 MPa (20 ksi) (Ref 5); all creep below this stress was fully recoverable In tests on a similar alloy at 538 °C (1000 °F), Goldhoff (Ref 27) found that the creep limit ranged from 150 MPa (22 ksi) for 1 h to zero at 5000 h By plotting the ratio

of anelastic to plastic strain for a fixed time (1000 h) as a function of stress (Fig 5), Goldhoff (Ref 27) showed how the former became dominant at low stresses Figure 5 also shows that a heat treatment that produces low ductility leads to higher ratios, suggesting a link between anelastic deformation and intergranular fracture, which was consistent with microstructural observations of fracture in this alloy

Fig 4 The separation of strain components for a creep test on Cr-Mo-V steel at 538 °C (1000 °F) and 35 MPa

(5 ksi) Source: Ref 27

Fig 5 Effect of ductility on recoverable creep strain for Cr-Mo-V steel after 1000 h creep exposure Source: Ref

27

There have been even fewer systematic studies of creep recovery in ceramics, but silicon carbide fibers have been shown

to recover fully their creep strain between 1000 and 1400 °C (1830 and 2550 °F) (Ref 24) Additionally, provided an appropriate period was allowed for recovery after each stress cycle, tension-tension fatigue resulted in zero cumulative creep strain This indicates the potential importance of anelastic phenomena in damage accumulation for nonsteady conditions Very recent work on large specimens of silicon nitride have shown recovery of most of the accumulated strain after unloading from stress-relaxation tests (Fig 6)

Fig 6 Recovery of creep strain in silicon nitride at 1200 °C (2190 °F) after unloading from a stress-relaxation

test started at 300 MPa (43.5 ksi), showing a time to the one-third dependence

There are strong indications that anelastic phenomena should be included in design considerations Anelastic contraction

as well as extension can occur depending on whether the stress is decreased or increased, whereas plastic shortening never occurs Although several authors have pointed out that, because of the linear stress dependence the analysis should be

much simpler than for plastic creep analysis (Ref 7, 27), accurate measurements at the low stresses of interest for service applications are difficult The possible link with fracture processes is also of great interest, but neither consideration has influenced design practice

Stress and Temperature Dependence

The minimum creep rate in both constant load and constant stress tests is normally represented by a power function of

stress (Eq 8), and the temperature by an Arrhenius expression including an activation energy term (Q) derived from

chemical reaction rate theory (Ref 29):

where S, which is a constant, depends on structure Although an exponential or hyperbolic sine stress function may

provide a better fit in some cases, the power function has generally prevailed and has become strongly linked with mechanistic treatments In pure metals, early studies indicated a stress exponent on the order of four and an activation energy close to that for self-diffusion (Ref 13, 29, 30) For engineering alloys, the stress exponents are generally higher and may not be constant (Ref 31), and the value of the activation energy may be much higher than that for the alloy matrix self-diffusion and may be sensitive to test temperature

Because the basic formulation of Eq 9 is used to correlate much engineering data and is used in creep analysis of components, it is useful to examine critically some of the limitations in this analysis as they apply to engineering alloys It was first shown by Lubahn (Ref 32) that, because of the rapidly decreasing creep rate in the primary stage, a strain-time plot of a portion of this stage always appears to show approximately constant rates at the longest times This has led to

many errors in the literature with false minimum creep rates Some of these errors may lead to apparent n values close to

one and consequent speculations about Newtonian viscous creep (Ref 33) Figure 7 shows results for minimum creep rates in a Cr-Mo-V steel in tests lasting up to 50,000 h Also included are plots where time restrictions on the

measurements were imposed to illustrate this potential for error Nevertheless, the true minimum data points indicate n

values ranging from 3.3 to 12

Fig 7 Effect of test time restrictions on the apparent stress sensitivity of creep rate for a

chromium-molybdenum steel at temperatures of (a) 510 °C (950 °F), (b) 565 °C (1050 °F), and (c) 593 °C (1100 °F) Source: Ref 33

As pointed out by Woodford (Ref 33), the curvature indicates that Eq 9 with S as a constant does not apply over the stress range, and it is meaningless to consider both n and S changing In fact, the slope at any point has no clear physical

significance because the structural state at the minimum creep rate is different for each test because of the different deformation history To approximate a constant structure determination, creep rates have been measured under decreasing stress either by discrete stress drops (Ref 34) or during stress relaxation (Ref 35) The stress exponents measured from

these data are much higher than those obtained from the minimum creep-rate data, but have clear physical significance because they relate to an approximately constant structure An alternative approach for measuring stress dependence at close to constant structure is to monitor the creep rate and corresponding stress increase in constant load tests at strains

beyond those corresponding to the minimum creep rates (Ref 33, 36) In this method n = d log /d log o (1 + ) where

o is the initial stress and the nominal strain Results for the steel data are shown in Fig 8 giving n values for individual

tests between 30 and 100, which are much higher than values estimated from the slopes of the lines drawn through the

minimum creep rates It has been shown that, as in the stress-decrement measurements, the values of n may be related to a

particular structural state The reciprocal of these values gives a measure of strain-rate sensitivity and correlates well with elongation at fracture (Ref 33, 36, 37)

Fig 8 Creep rate for a chromium-molybdenum steel as a function of the true stress showing that the stress

sensitivity measured in a single test is different from that measured in separate tests Source: Ref 33

Although the representation of creep data in the engineering literature has been strongly influenced by the simple correlations reported for short-time tests for pure metals, it is clear that any physical significance is lost for most structural materials The stress dependence of creep determined from the slope of a line drawn through minimum creep-rate data is expected to be quite different from that determined for a stress change on an individual specimen The importance of deformation history is again apparent Likewise, an exponential temperature dependence of minimum creep rates should

be viewed as an empirical correlation Temperature change experiments on a single specimen usually do not give the same activation energy, and because the structural state changes with temperature, a temperature change sequence effect

on the apparent activation energy is also to be expected

Fracture at Elevated Temperatures

As indicated previously, the constant load creep rupture test is the basis for design data for both creep strength (minimum creep rate or time to a specific creep strain) and failure (time to rupture) The various ways in which such data are presented, correlated, and extrapolated are addressed in subsequent sections However, it is useful to note here that the well-known Monkman-Grant relationship (Ref 38) shown in Fig 9 indicates that the time to rupture is reciprocally related

to the minimum creep rate This relationship is commonly observed in ductile materials and has been used to predict one property from the other However, the true significance of the correlation is that the rupture life is principally a measure

of creep strength rather than fracture resistance This leads to a number of inconsistencies in design procedures that are discussed later in this article

Fig 9 Monkman-Grant relationship between minimum creep rate and time to rupture for a 2 Cr-1Mo steel

Source: Ref 39

At this point, it is appropriate to consider the processes leading to fracture Plastic instability in ductile materials has already been reviewed This process may lead directly to fracture in pure metals and contribute significantly to fracture in engineering materials at moderately high stresses However, of much greater concern are the processes leading to intergranular fracture with reduced ductility at low stresses and high temperatures Here again, many of the basic studies have been conducted on pure metals and solid-solution alloys

Crack Nucleation and Morphology. Two types of cracking have been identified: wedge-shaped cracks emanating from grain-boundary triple points and the formation of cavities or voids on grain-boundary facets often oriented

perpendicular to the applied tensile stress (Ref 40) An example of creep cracks in nickel that appears to show both forms

is given in Fig 10 A fractographic study of creep cavities in tungsten concluded that the different crack morphologies actually reflected differences in growth rate At low growth rates, surface diffusion allowed the cavities to reduce their surface tension by assuming nearly equiaxed polyhedral shapes At higher growth rates, irregular two-dimensional cracks developed that on sectioning appeared as wedge cracks (Ref 42)

Fig 10 Unetched microstructure of nickel samples after air testing at 15.8 MPa (2.3 ksi) and 800 °C (1470 °F)

(a) Low-carbon Ni270 unloaded after 500 h slight cavitation (b) Standard Ni270 after failure in 23 h Source: Ref 41

Although much work continues to model the nucleation and growth of these cracks and cavities (Ref 43), there are uncertainties in the mechanism of nucleation and in the identification of a failure criterion For example, McLean has shown that a stress concentration up to 1000 is needed to nucleate a hole unless it is stabilized by internal pressure (Ref 44) As a consequence, the nucleation stage has been treated with less enthusiasm than has the modeling of growth This issue may well be resolved on the basis of environmental interaction (see the section "Environmental Effects" in this article) Another major problem is the effect of temperature and stress on the extent of cracking at failure Most theories assume that failure occurs at some critical cavity distribution or crack size However, it has been shown that the extent of cavitation at failure or at any given fraction of the failure life is very sensitive to the test conditions (Ref 45, 46) Thus cavitation damage at failure at a high stress may be comparable to damage in the very early stage of a test at low stress For stress-change experiments, there is therefore a loading sequence effect on rupture life, which is discussed later in this article, for engineering alloys

Embrittlement Phenomena. As pointed out previously, rupture life is primarily a measure of creep strength; fracture resistance would be identified better with a separate measure that reflects the concern with embrittlement phenomena that may lead to component failure Most engineering alloys lose ductility during high-temperature service This has been shown to be a function of temperature and strain rate (Ref 47) so that there is a critical regime for maximum embrittlement At a fixed strain rate, for example, ductility first decreases with increasing temperature This is believed to

be caused by grain boundaries playing an increasing role in the deformation process leading to the nucleation of intergranular cracks At still higher temperatures, processes of recovery and relaxation at local stress concentrations lead

to an improvement in ductility Figure 11 is an example of a ductility contour map for a low-alloy steel based on measurements of reduction of area (RA) of long-term rupture tests (Ref 48) Maximum embrittlement occurred in a critical range of temperature and stress (or strain rate) This type of embrittlement generally coincides with a sensitivity to notches, which emphasizes its practical significance For example, Fig 12 shows that the ratio of notch strength to smooth strength for various test times passes through minima corresponding to ductility minima (Ref 49) based on reduction in area at failure in the notch This tendency to develop so-called notch weakening at temperature is of great concern in selecting alloys and monitoring their service performance

Fig 11 Ductility contour map in stress/temperature space for a Cr-Mo-V steel RA, reduction in area Source:

Ref 48

Fig 12 Ratio of notched bar strength to smooth bar strength (a) and notch ductility (b) as a function of test

temperature for various rupture times in a Cr-Mo-V steel Source: Ref 49

The embrittlement phenomena may be associated with precipitation in the alloy that interferes with the ability to accommodate stress concentrations at grain boundaries (Ref 48), with segregation of embrittling species from the grain interior to the grain boundaries (Ref 50, 51), or with intergranular penetration of embrittling species from the environment (Ref 41)

Environmental Effects

It has long been known that test environment may affect creep-rupture behavior Until quite recently, however, the work has been largely empirical with creep tests being conducted in various atmospheres and differences noted in creep rates and rupture lives (Ref 52) The effect on rupture life, in particular, was often less than a factor of ten in environments such

as oxygen, hydrogen, nitrogen, carbon dioxide, and impure helium compared with vacuum In many cases, it was not clear how inert the vacuum was, and little account was taken of specimen thickness Often, effects on ductility were not reported, and there were very few studies of crack propagation

A renewed interest developed in the 1970s as a result of observations of a dominant role played by the environment in high-temperature fatigue crack growth of superalloys (Ref 53) There were subsequent studies of sustained-load crack propagation that also showed very strong effects (Ref 54, 55, 56) In some cases at high stresses, the test environment was

so severe, as in the case of sulfur, that profound changes were seen in smooth bar rupture life Such an example is shown

in Fig 13, in which the time to rupture in common superalloys was reduced by several orders of magnitude in tests in a sulfate/chloride mixture at 705 °C (1300 °F) (Ref 57) These results were explained in terms of grain-boundary penetration of sulfur, which leads to rapid crack propagation The coated specimen was far less susceptible, and the addition of a grain-boundary modifier (in this case, boron) in Udimet 720 gave an enormous improvement relative to Udimet 710

Fig 13 Relative reductions in rupture life due to sulfate/chloride salt at 705 °C (1300 °F) for several

superalloys For RT-22 coated Udimet 710, rupture time in salt for coated alloy divided by time in air for uncoated alloy Source: Ref 57

Embrittling Effects of Oxygen. At about the same time that the ideas on environmental attack at an intergranular

crack tip were being developed, it was also shown that short-term prior exposure in air at high temperature (greater than about 900 °C, or 1650 °F) could lead to profound embrittlement at intermediate temperatures (700 to 800 °C, or 1290 to

1470 °F) (Ref 41, 58, 59, 60, 61) This was shown to be caused by intergranular diffusion of oxygen that penetrated on the order of millimeters in a few hours at 1000 °C (1830 °F) The embrittlement was monitored using measurements of tensile ductility at intermediate temperatures in iron-, nickel-, and cobalt-base alloys (Ref 41) An example of the results for the Fe-Ni-Co alloy, IN903A, is shown in Fig 14, which also confirms the extent of damage penetration from tests in which the specimen diameter of 2.54 mm (0.1 in.) was reduced by half Post-exposure tests on cast alloys showed that this embrittlement could also lead to a reduction in rupture life of several orders of magnitude An example for alloy IN738 is shown in Fig 15

Fig 14 Tensile ductility of IN903A after air and vacuum exposures at 1000 °C (1830 °F) for 100 h as a function

of test temperature in vacuum tests Embrittlement remained after reducing to half the initial diameter Source: Ref 41

Fig 15 Effect of exposure in air at various temperatures on stress-rupture life of IN738 at 800 °C (1470 °F)

and 400 MPa (58 ksi) Source: Ref 59

Using model alloys based on nickel, it was shown that oxygen in the elemental form in high-purity nickel did not embrittle; a chemical reaction was necessary (Ref 41) Three embrittling reactions were confirmed: a reaction with carbon

to form carbon dioxide gas bubbles; a reaction with sulfides on grain boundaries to release sulfur, which does embrittle in the elemental form; and a reaction with oxide formers to form fine oxides that act to pin grain boundaries These phenomena are believed to be the same processes that serve to embrittle the region ahead of a crack tip Thus, oxygen attack may occur dynamically to account for the accelerated advance of a crack in air tests compared with inert environment tests, and it may occur during higher-temperature exposure with or without an applied stress to set up an embrittlement situation Thermal fatigue in combustion turbines is a particularly challenging situation for oxygen attack since maximum strains develop at intermediate temperatures in the cycle, but holding may be at the maximum temperature (Ref 62)

Combined Effects of Oxygen and Carbon. Of special interest relative to the previous discussion of creep cavitation

is the reaction between diffusing oxygen and carbon In nickel, it was found that if this reaction were prevented, creep cavitation could not develop during creep tests Prevention was achieved either by removing the carbon (decarburizing) or

by applying an environmental protective diffusion or overlay coating (Ref 63) Air tests at 800 °C (1470 °F) and at various stresses showed an enormous increase in rupture life (Fig 16) if the gas bubble formation did not occur Since nickel has been used as an archetypical metal for the study of creep cavitation, the confirmation that the cavities are nucleated as gas bubbles now solves the problem of nucleation (Ref 44) The observation that even in superalloys gas bubbles are frequently nucleated at carbides, which may serve as cavity nuclei (Ref 59), and that cavitation during creep

is often concentrated near the specimen surface (Ref 64), points to the likelihood that oxygen attack may be invariably associated with creep cavitation The gas pressures developed in the bubbles appear to be quite adequate for nucleation (Ref 65)

Fig 16 Effect of environmental interaction on rupture life of Ni270 at 800 °C (1470 °F) Longer lives are

obtained by preventing cavitation nucleation from carbon dioxide gas formation This is achieved by decarburizing to eliminate carbon or by coating to prevent oxygen penetration Source: Ref 63

Effect of Other Gaseous Elements. Hydrogen, chlorine, and sulfur may also embrittle as a result of penetration Sulfur is particularly aggressive in that it diffuses more rapidly and embrittles more severely than does oxygen (Ref 66) It

is also frequently found in coal gasification and oil-refining processes as well as industrial gas turbines operating on impure fuel

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26 J.D Lubahn, The Role of Anelasticity in Creep, Tension and Relaxation Behavior, Trans ASM, Vol 45,

1953, p 787-838

27 R.M Goldhoff, Creep Recovery in Heat Resistant Steels, Advances in Creep Design, A.I Smith and A.M

Nicolson, Ed., John Wiley & Sons, 1971, p 81-109

28 T.S Ke, Experimental Evidence of the Viscous Behavior of Grain Boundaries in Metals, Phys Rev., Vol

31 R Viswanathan, The Effect of Stress and Temperature on the Creep and Rupture Behavior of a 1.25 pct

Chromium-0.5 pct Molybdenum Steel, Metall Trans A, Vol 8, 1977, p 877-993

32 J.D Lubahn, "Creep of Metals," Symposium on Cold Working of Metals, American Society for Metals,

1949

33 D.A Woodford, Measurement and Interpretation of the Stress Dependence of Creep at Low Stresses,

Mater Sci Eng., Vol 4, 1969, p 146-154

34 S.K Mitra and D McLean, Cold Work and Recovery in Creep at Ostensibly Constant Structure, Met Sci.,

Vol 1, 1967, p 192

35 E.W Hart, "Phenomenological Theory: A Guide to Constitutive Relations and Fundamental Deformation

Properties," Constitutive Equations in Plasticity, A.S Argon, Ed., MIT Press, 1975

36 D.A Woodford, Analysis of Creep Curves for a Magnesium-Zirconium Alloy, J Inst Met., Vol 96, 1968, p

371-374

37 D.A Woodford, Strain Rate Sensitivity as a Measure of Ductility, Trans ASM, Vol 62, 1969, p 291-293

38 F.C Monkman and N.J Grant, Proc ASTM, Vol 56, 1956, p 595

39 R Viswanathan, Damage Mechanisms and Life Assessment of High Temperature Components, ASM

International, 1989, p 82

40 F Garofalo, Fundamentals of Creep and Creep Rupture, MacMillan, 1965

41 D.A Woodford and R.H Bricknell, Environmental Embrittlement of High Temperature Alloys by Oxygen,

Embrittlement of Engineering Alloys, C.L Briant and S.K Banerji, Ed., Academic Press, 1983, p 157

42 J.O Steigler, K Farrell, B.T.M Loh, and H.E McCoy, Creep Cavitation in Tungsten, Trans ASM, Vol 60,

1967, p 494

43 A.C.F Cocks and M.F Ashby, On Creep Fracture by Void Growth, Prog Mater Sci., Vol 27, 1982, p

189-244

44 D McLean, The Physics of High Temperature Creep in Metals, Rept Prog Phys., Vol 29, 1966, p 1-33

45 D.A Woodford, A Parametric Approach to Creep Damage, Met Sci J., Vol 3, 1969, p 50-53

46 D.A Woodford, "Density Changes During Creep in Nickel," Met Sci J., Vol 3, 1969, p 234-240

47 F.N Rhines and P.J Wray, Investigation of the Intermediate Temperature Ductility Minimum in Metals,

Trans ASM, Vol 54, 1961, p 117-128

48 D.A Woodford and R.M Goldhoff, An Approach to the Understanding of Brittle Behavior of Steel at

Elevated Temperatures, Mater Sci Eng., Vol 5, 1970, p 303-324

49 W.E Brown, M.H Jones, and D.P Newman, Symp on Strength and Ductility of Metals at Elevated

Temperatures, STP 128, ASTM, 1952, p 25

50 M.P Seah, Grain Boundary Segregation, Metal Phys., Vol 10, 1980, p 1043-1064

51 E.P George, P.L Li, and D.P Pope, Creep Cavitation in Iron Sulfides and Carbides as Nucleation Sites,

Acta Metall., Vol 35 (No 10), 1987, p 2471-2486

52 R.H Cook and R.P Skelton, The Influence of Environment on High Temperature Mechanical Properties of

Metals and Alloys, Int Met Rev., Vol 19, 1974, p 199

53 L.F Coffin, Fatigue at High Temperature, Fatigue at Elevated Temperature, A.E Carden, A.J McEvily,

and C.H Wells, Ed., STP 520, ASTM, 1972, p 5-36

54 K Sadananda and P Shahinian, The Effect of Environment on the Creep Crack Growth Behavior of

Several Structural Alloys, Mater Sci Eng., Vol 43, 1980, p 159-168

55 K.R Bain and R.M Pelloux, Effect of Environment on Creep Crack Growth in PM/HIP René 95, Metall

Trans A, Vol 15, 1984, p 381-388

56 S Floreen and R.H Kane, Investigation of the Creep-Fatigue-Environment Interaction in a Nickel Base

Superalloy, Fatigue Eng Mater Struct., Vol 2, 1980, p 401

57 G.A Whitlow, C.G Beck, R Viswanathan, and E.A Crombie, The Effects of a Liquid Sulfate/Chloride

Environment on Superalloys, Metall Trans A, Vol 15, 1984, p 23-28

58 W.H Chang, Proc Conf Superalloys Processing, Section V, MCIC-7210, AIME, 1972

59 D.A Woodford, Environmental Damage of a Cast Nickel Base Superalloy, Metall Trans A, Vol 12, 1981,

p 299-308

60 R.H Bricknell and O.A Woodford, The Embrittlement of Nickel Following High Temperature Air

Exposure, Metall Trans A, Vol 12, 1981, p 425-433

61 M.C Pandey, B.F Dyson, and D.M.R Taplin, Environmental, Stress-State and Section-Size Synergisms

During Creep, Proc R Soc London A, Vol 393, 1984, p 117-131

62 D.A Woodford and D.F Mowbray, Effect of Material Characteristics and Test Variables on Thermal

Fatigue of Cast Superalloys, Mater Sci Eng., Vol 16, 1974, p 5

63 R.H Bricknell and D.A Woodford, Cavitation in Nickel during Oxidation and Creep, Int Conf on Creep

and Fracture of Engineering Materials and Structures, B Wilshire and R.W Evans, Ed., Pineridge Press,

Inst of Metals, 1991, p 249-262

64 E.C Scaife and P.L James, Met Sci J., Vol 2, 1968, p 217

65 H Reidel, Fracture at High Temperatures, Springer-Verlag, 1987

66 J.P Beckman and D.A Woodford, Gas Phase Embrittlement of Nickel by Sulfur, Metall Trans A, Vol 21,

1990, p 3049-3061

Design for High-Temperature Applications

David A Woodford, Materials Performance Analysis, Inc

Design Methodology

This section describes the basic presentation and analysis methods for creep rupture that are currently widely used In addition to the application of these methods to materials selection and the setting of basic design rules, some consideration will be given to their application to remaining life assessment of operating components The interaction with fatigue will not be included since some discussion of that complex topic is covered in the article "Creep-Fatigue

Interaction" in the ASM Specialty Handbook: Heat-Resistant Materials Also omitted from this discussion are multiaxial

stress effects and sustained load (or creep) crack growth However, it should be recognized that components in service normally operate under multiaxial stress systems, and detailed procedures are used for analysis that are based on effective stresses and strains The considerable amount of work conducted in recent years on sustained-load crack growth, and the

other topics alluded to, are reviewed in several recent texts (Ref 20, 39, 67) and in Mechanical Testing, Volume 8 of the ASM Handbook

Creep Rupture Data Presentation. Laboratory creep tests are typically run between 100 and 10,000 h, although a few are run for shorter times (for example, for acceptance tests), and occasionally some testing is conducted for longer times Since most high-temperature components are expected to last ten years or more, service stresses are obviously lower than those used in the longest creep tests to generate data for most of the alloys used Therefore, to provide data for creep rates and rupture lives that are appropriate for the setting of design stresses, it became necessary to develop methods for extrapolation Over the years, a tremendous amount of effort has gone into optimizing methods of data extrapolation (Ref 68, 69)

One of the major considerations in such procedures must be statistical issues, such as the best estimate of the stress associated with a given median life or creep rate, the use of stress or time as the dependent variable in the data fitting, the treatment of variability among heats of the same alloy, and the analysis of data with run-outs All of these issues have been treated with considerable rigor and shown to be important relative not only to the proper interpretation of data, but to the proper design of experiments (Ref 69) In addition, there are different practices among testing laboratories that may have appreciable effects on results These include specimen geometry, loading procedure, specimen alignment, furnace type, and temperature control

Despite all these concerns regarding proper statistical treatment of data, a methodology has been developed based on time-temperature parameters that is now in widespread use The approach may be used to achieve the following major design objectives:

• It allows the representation of creep rupture (or creep) data in a compact form, allowing interpolation of results that are not experimentally determined

• It provides a simple basis for comparison and ranking of different alloys

• Extrapolation to time ranges beyond those normally reached is straightforward

Based on the Arrhenius rate equation and a previous tempering parameter (Ref 70), Larson and Miller (Ref 71) developed the most commonly used parameter:

where is stress, T is absolute temperature, and tr (or tR) is time to rupture In their original paper, the constant C was set

equal to 20, which provided a good fit for a variety of alloys, and is still widely used today A set of versus log tr data for the alloy Astroloy and the parametric master curve derived from it is shown in Fig 17

Fig 17 Stress-rupture behavior of Astroloy (a) Stress versus time curves (b) Larson-Miller plot Source: Ref

69

Many other parametric forms have been developed (Ref 68, 69), the most common of which are described in the article

"Assessment and Use of Creep-Rupture Data" in the ASM Specialty Handbook: Heat-Resistant Materials The

time-temperature parameter provides the means for interchanging time and time-temperature so that a long time may be computed from a short-time test at higher temperature Figure 18 provides two parametric forms, the shape of which depend on

whether isostress lines are parallel or converge on plots of log t versus 1/T (the Larson-Miller parameter in Fig 18a) or T

(the Manson-Succop parameter in Fig 18b) The Manson-Succop parameter (Ref 72) has been used extensively by the Japanese National Research Institute for Metals in compiling data sheets on a wide range of alloys For example, the data shown in Fig 19 are for Ni-19Cr-18Co-4Mo-3Ti-3Al-B superalloy castings (Ref 73) The rupture data are statistically treated based on a Manson-Succop correlation, and the tensile data show 95% prediction intervals (dashed lines)

Fig 18 Two common time-temperature parameters for rupture life (a) Larson-Miller parameter f( ) = TA (lot

t + C) (b) Manson-Succop parameter f( ) = log t - BT Source: Ref 69

Fig 19 Temperature dependence of 0.2% yield stress, tensile strength, and creep rupture strength at 1000

and 10,000 h for a nickel-base superalloy casting Source: Ref 73

At least two approaches have been used to allow a given data set to determine objectively the best of the common parameters or to provide new parametric forms The minimum commitment method (MCM) (Ref 74) and the graphical optimization procedure (GOP) (Ref 75) provide optimal data presentation but lose the advantage of representing different alloys on the same parametric plot The GOP method uses the fact that all parameters are in the form of one variable

expressed as the product of functions of two others, for example, tr = H( )Q(T) or T = H( )C(tr) These functional forms are solved graphically to optimize the parameter For example, Fig 20(a) shows data on Cr-Mo-V steel plotted according

to a Larson-Miller parameter The curves at each temperature are clearly ordered, whereas Fig 20(b) shows the same data

using a parameter determined using the GOP method, which includes the optimized values of the C(tr) function There is

in this case no separation of the isothermal segments The optimized value of the Larson-Miller "constant" actually varied from 28.5 at 10 h to 13.6 at 100,000 h (Ref 76) for this data set

Fig 20 Creep parameters for a Cr-Mo-V steel (a) Larson-Miller plot using a constant of 20 showing

segmenting of the data (b) Same data using an optimized parameter based on the graphical optimization procedure (GOP) method Source: Ref 76

Design rules for high-temperature time-dependent deformation and fracture may be established based on formal codes or

on proprietary manufacturers specifications For example, an ASME code (Ref 77) is used for the design of fossil-fuel boilers and for pressure vessel and piping systems in the petroleum and chemical process industries The allowable stresses are to be no higher than the lowest of:

• 100% of the stress to produce a creep rate of 0.01% in 1000 h

• 67% of the average stress to produce rupture in 100,000 h

• 80% of the minimum stress to produce rupture in 100,000 h

These stresses may be determined from parametric plots or from derived curves, such as those shown in Fig 19 It is of interest to note that it is implicit in these rules that the rupture life provides a measure of creep strength The connection between creep rate and rupture life may be made through the Monkman-Grant relationship (Ref 38) or through the Gill-Goldhoff correlation (Ref 78), which relates stress for rupture with stress for creep to a specific strain for a fixed time and

temperature Both of these methods are described in the article "Assessment and Use of Creep-Rupture Data" in the ASM Specialty Handbook: Heat-Resistant Materials

With nickel-base superalloys, it has been found that surface cracks related to environmental attack may develop at strains

as low as 0.5% (Ref 79) Since these cracks result in severe loss in fatigue life, this is an appropriate failure criterion rather than rupture life Gas turbine blades may therefore be designed on the basis of time to 0.5% creep with a suitable safety factor on stress

References cited in this section

20 N.E Dowling, Mechanical Behavior of Materials, Prentice Hall, 1993

38 F.C Monkman and N.J Grant, Proc ASTM, Vol 56, 1956, p 595

39 R Viswanathan, Damage Mechanisms and Life Assessment of High Temperature Components, ASM

International, 1989, p 82

67 G.A Webster and R.A Ainsworth, High Temperature Component Life Assessment, Chapman and Hall,

1994

68 J.S Conway, Stress Rupture Parameters: Origin, Calculations and Use, Gordon and Breach, 1969

69 R.M Goldhoff, "Development of a Standard Methodology for the Correlation and Extrapolation of Elevated Temperature," EPRI FP-1062, Electric Power Research Institute, 1979

70 J.H Holloman and L.C Jaffe, Time-Temperature Relations in Tempering Steel, Trans AIME, Vol 162,

1945, p 223-249

71 F.R Larson and J Miller, A Time-Temperature Relationship for Rupture and Creep Stresses, Trans ASME,

Vol 74, 1952, p 765-775

72 S.S Manson and G Succop, Stress Rupture Properties of Inconel 700 and Correlation on the Basis of

Several Time-Temperature Parameters, ASTM, STP 174, 1956

73 NRIM Creep Data Sheet, No 34B, National Research Institute for Metals, Tokyo, Japan, 1975

74 S.S Manson and C.R Ensign, "A Specialized Model for Analysis of Creep Rupture Data by the Minimum Commitment Method," Tech Memo TMX 52999, National Aeronautics and Space Administration, 1971

75 D.A Woodford, A Graphical Optimization Procedure for Time-Temperature Rupture Parameters, Mater

Sci Eng., Vol 15, 1974, p 169-175

76 D.A Woodford, Perspectives in Creep and Stress Rupture, Int Conf on Creep, Tokyo, JSME, IMechE,

ASME, ASTM, 1986, p 11-20

77 ASME Boiler and Pressure Vessel Code, Section 1, ASME

78 R.M Goldhoff and R.F Gill, A Method for Predicting Creep Data for Commercial Alloys on a Correlation

between Creep Strength and Rupture Strength, ASME J Basic Eng., Vol 94, Series D, No 1, 1972, p 1-6

79 W.L Chambers, W.J Ostergren, and J.H Wood, Creep Failure Criteria for High Temperature Alloys, J

Eng Mater Technol., Vol 101, 1979, p 374-379

Design for High-Temperature Applications

David A Woodford, Materials Performance Analysis, Inc

Damage Accumulation and Life Prediction

Engineering procedures for life management of operating components assume that the material is progressively degraded

or damaged as creep strain increases and operating time accumulates Damage may be in the form of precipitate changes that may result in softening (overaging) and reduced creep strength, or embrittlement and reduced resistance to fracture The embrittlement may be due to segregation of harmful species, either from the interior or from the external environment, to interfaces, especially grain boundaries Damage may also occur as a result of progressive intergranular cavitation and cracking, as previously described Some of this damage may be reversible by suitable heat treatment or by hot isostatic pressing and may allow the possibility of component rejuvenation However, for the purposes of component life management, which allows decisions to be made regarding part replacement, repair, or rejuvenation, there is a critical need to quantify the accumulation of damage as a function of operating conditions

There are two basic approaches to using the concept of damage accumulation for life assessment:

• Based on a detailed knowledge of the operating conditions, including temperature and stress changes, the remaining life is estimated from the known original properties of the material of construction

• Remaining life estimates are made using post-exposure measurements of microstructural changes, intergranular cavitation, or mechanical properties such as hardness, impact energy, or stress-rupture life

Creep under Nonsteady Stress and Temperature. There are two common approaches to analyzing creep when the temperature and/or the stress change The strain-hardening law assumes an equation of state of the form:

to handle analytically for complex sequences of stress and temperature changes Moreover, if the sequences involve multiple increases and decreases in stress and temperature, the two approaches may produce similar results Modifications

of the laws including normalizing the strain with the fracture strain, normalizing the time with the failure time, or using a mean function have also been used

These same ideas have been extended to predict failure either in terms of strain fractions or time fractions In this case, however, by far the most extensively used in design analysis and life prediction has been the life-fraction approach This concept was first introduced by Robinson (Ref 80, 81) as an accounting system for materials in which the rupture time is

a power function of stress and the log rupture time is a linear function of temperature The analytical solutions for such a material subjected to various temperature and stress cycles were given by Robinson (Ref 81), but the concept is now generally presented in the form:

(Eq 13)

where t is time spent at temperature T or stress , tR is rupture time at temperature T or stress, and n is the number of

temperature or stress changes

Each fractional expenditure of life, or accumulated damage, is considered to be independent of all others Failure is predicted when the sum of the fractions of life equals unity This hypothesis remains a widely used tool for life assessment

Considerable experimental work has attempted to confirm or refute the rule However, when the results of multiple-stress

or temperature-change experiments are analyzed in terms of the life-fraction rule, it is only possible to determine whether

the rule is appropriate, but not why it fails Only when damage is defined in terms of remaining life rather than used life is

it possible to formulate the appropriate damage law (Ref 82) Figure 21 illustrates the procedure schematically for a stress-change experiment where the abscissa is the logarithm of the remaining life The continuous line represents remaining life for the virgin material, that is, the stress-rupture data for the initial condition Point 1 is the remaining life

on two specimens exposed at stress 2 One of these specimens is then tested to failure at 3, and the measured remaining life is represented by point 1A The stress on the second specimen is then reduced to 1, resulting in a measured remaining life indicated by 1B The dashed line drawn through the points 1A, 1, and 1B is then defined as a constant damage line in terms of remaining life Clearly, any number of lines such as 2A, 2, 2B may be constructed

Fig 21 Schematic plot illustrating construction of constant damage curves in terms of remaining life for

different stresses Source: Ref 83

A necessary condition for the life-fraction rule to apply is that the constant damage lines should be displaced horizontally

by a constant distance when remaining life is plotted on a logarithmic scale for both temperature and stress changes For low-alloy steels, the life-fraction rule applies quite well for temperature changes but not for stress changes For stress changes, the curves often converge at low stresses, leading to a loading sequence effect For example, a stress increment leads to a life fraction at failure less than one and a stress decrement leads to a life fraction at failure greater than one This behavior may be combined on a parametric plot (Fig 22), where a sequence of both temperature and stress changes may be represented For detailed discussion on the construction and use of the remaining life curves for nonsteady conditions and component life assessment, see Ref 82, 83, and 84

Fig 22 Schematic plot illustrating construction of constant damage curves in terms of the Larson-Miller

parameter The sequence ABCDE is an example of a particular stress-temperature path Source: Ref 83

Post-Exposure Evaluation. Ideally, a microstructural characterization or mechanical property should change linearly with life fraction and independently of the test conditions, as shown in Fig 23 In fact, the changes are invariably nonlinear and nonunique with life fraction Both cavitation changes and creep strength changes are dependent on the test conditions (Ref 45, 46, 83) Thus, the amount of damage at failure or at a given life fraction is a strong function of the stress in particular

Fig 23 Ideal behavior of a property suitable for damage monitoring as a function of life fraction