ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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Life-fraction summations at failure as low as 0.36 and as high as 2.43 have been reported (Ref 57). The spread
was only from 0.75 to 1.50 for the same tests using damage fractions defined by K(t/t
r
) + (1 - K)(ε/ε
r
), where t
and ε are the time and strain under a period of fixed conditions, for which the rupture time and fracture strain
are t
r
and ε
r
. K is a material constant ranging from zero to 1; the zero limit applies to materials that develop
cracks early in life, and K approaches 1 for materials that exhibit no cracking until rupture is imminent. Typical
values of K (Ref 57) are as follows:
Material and test temperature
K
Copper at 250 °C (482 °F)
0.3
A 286 alloy at 649 °C (1200 °F), solution treated at 1204 °C (2200 °F)
0.47
A 286 alloy at 649 °C (1200 °F), solution treated at 982 °C (1800 °F)
0.43
Inconel X-750 at 732 °C (1350 °F) 0.625
When data are insufficient for determination of K, acceptable results frequently can be obtained with an
empirical rule (Ref 58), by which the life-fractions added are defined by . With any of these
cumulative damage rules, comparison usually is against rupture life from constant-load tests—that is, with
actual stress rising as creep reduces the cross section. When the same specimen undergoes load changes for
different periods, respective stress levels have been based on the initial cross section. This corresponds to using
the same original load if an interrupted test must be restarted. The actual stress at the time of test restart is
(σ
n
(A
o
/A
c
), where σ
n
is the present nominal stress, A
o
is the initial specimen cross section, and A
c
is the
specimen cross section after creep deformation up to the time of the test interruption.
When the specimen for a test in a later portion of creep has been machined from a part that has already
undergone considerable reduction in cross section by prior creep, a corresponding area-modified stress must be
employed for consistent interpretation of the results (Ref 59). The load applied to produce the desired nominal
stress σn, related to the virgin material is calculated to make the actual stress σ
a
= σ
n
(A
o
/A
c
), where the latter
term relates cross-sectional areas of the original part before and after creep. Use of such an area-modified stress
has been reported to improve prediction of remaining life from post-service rupture tests (Ref 59, 60).
An approximation of remaining rupture life for components that have undergone prolonged service can be
calculated by introducing best estimates for operating temperatures and stresses into the above damage rules.
More exact evaluation, however, can be obtained by testing representative samples removed from service.
Measurement of Creep-Rupture Properties After Service. Dependable application of techniques to estimate
remaining life requires that the loading direction for the final test corresponds to the largest principal stress of
service and that the specimen is representative of surface deterioration or other damage present in the part.
Possible temperature and loading gradients in service must be kept in mind when selecting a sampling site and
when applying test results to predictions of further serviceability. Despite these possible additional variables,
assessments of post-service rupture properties require only about the same number and duration of tests as
conventional evaluation of any new lot of familiar material.
Large specimens are recommended to limit relative loss in cross section from oxidation, unless surfaces are
protected from the usual air environment of tests.
For samples from tubes or similar shapes subjected to internal-pressure service and consequent major service
stress in the circumferential direction, uniaxial creep tests are preferred to have the test load act in that
direction. Specimens from tube and pipe can have wedges of similar material welded to the outside-diameter
face near the ends of a ring segment from the sample. Electron-beam welded attachments of imaginative design
make possible the testing of many samples available only in small sizes or inconvenient shapes.
Isostress Tests. A typical study involves testing three or four specimens all at a single stress similar to, or
slightly above, the stress of service, and each at a different temperature higher than that of service. Results are
extrapolated to service temperature on coordinates of log rupture time versus either absolute temperature or its
reciprocal.
The principal drawback of this procedure is that at least some tests must usually be conducted at a higher
temperature than is needed in other evaluation methods.
Allowance for Data Scatter. In an effort to minimize uncertainties from extrapolation procedures, undue
emphasis may be placed on a test with the longest affordable duration. Normal data scatter still limits
evaluation of expected performance from isolated points. Indeed, a more reliable prediction may be obtained
when the same total test time is devoted to performing a greater number of tests with intermediate duration
rather than only a few with extended life. An exception is when instabilities occur only with very long testing.
Some researchers study scatter by running multiple tests at one or more fixed combinations of stress and
temperature. Again, a series of tests, each at different conditions, permits equally good statistical treatment to
evaluate the scatter, while providing a broader indication of the material characteristics. Although emphasis has
been placed on time to rupture, the extra expense of obtaining complete creep deformation data in all tests is
often justified by the insight afforded into the effects of structural changes.
References cited in this section
54. E.L. Robinson, Effect of Temperature Variation on the Creep Strength of Steels, Trans. ASME, Vol 60,
1938, p 253–259
55. P.N. Randall, Cumulative Damage in Creep-Rupture Tests of a Carbon Steel, Trans. ASME J. Basic
Eng., Vol 84 (No. 2), Series D, June 1962, p 239–242
56. D.A. Woodford, Creep Damage and Remaining Life Concept, Trans. ASME J. Eng. Mat. Technol., Vol
101 (No. 4), Dec 1979, p 311–316
57. M.M. Abo El Ata and I. Finnie, A Study of Creep Damage Rules, Trans. ASME J. Basic Eng., Vol 94
(No. 3), Series D, Sept 1972, p 533–543
58. J.W. Freeman and H.R. Voorhees, “Notch Sensitivity of Aircraft Structural and Engine Alloys, Part II:
Further Studies with A-286 Alloys,” Wright Air Development Center, Technical Report 57–58, ASTIA
Document 207,850, Jan 1959
59. R.V. Hart, Concept of Area-Modified Stress for Life-Fraction Summation During Creep, Met. Technol.,
Sept 1977, p 447–448
60. R.V. Hart, Assessment of Remaining Creep Life Using Accelerated Stress-Rupture Tests, Met.
Technol., Jan 1976, p 1–7
Assessment and Use of Creep-Rupture Properties
Howard R. Voorhees, Materials Technology Corporation Martin Prager, Materials Properties Council
References
1. Basis for Estimating Stress Values, Paragraph A-150, Rules for Construction of Power Boilers, ASME
Boiler and Pressure Vessel Code, Section I, American Society of Mechanical Engineers, New York,
1983
2. “Standard Recommended Practice for Conducting Creep, Creep-Rupture, and Stress-Rupture Tests of
Metallic Materials,” E 139, Annual Book of ASTM Standards, Vol 03.01, ASTM, 1984, p 283–297.
3. A.K. Schmieder, Size Effect During Rupture Tests of Unnotched and Notched Specimens of Cr-Mo-V
and Cr-Ni Steels, in Ductility and Toughness Considerations in Elevated Temperature Service,
American Society of Mechanical Engineers, New York, 1978, p 31–48
4. B. Aronsson and A. Hede, Some Observations on the Reproducibility of Creep Rate Determinations, in
High-Temperature Properties of Steel, Iron and Steel Institute, London, 1967, p 41–45
5. D.R. Hayhurst, The Effects of Test Variables on Scatter in High-Temperature Tensile Creep-Rupture
Data, Int. J. Mech. Sci., Vol 16, 1974, p 829–841
6. W. Ruttman, M. Krause, and K.J. Kremer, International Community Tests on Long-Term Behavior of
2- %Cr-1%Mo Steel, in High-Temperature Properties of Steel, Iron and Steel Institute, London, 1967,
p 23–29
7. D. Coutsouradis and D.K. Faurschou, “Cooperative Creep Testing Program,” AGARD Report 581,
North Atlantic Treaty Organization, Advisory Group for Aerospace Research & Development, Neuilly-
sur-Seine, France, 1971
8. “Report on the Elevated-Temperature Properties of Stainless Steels,” DS 5-S1, ASTM, 1965
9. “An Evaluation of the Yield, Tensile, Creep, and Rupture Strengths of Wrought 304, 316, 321, and 347
Stainless Steels at Elevated Temperatures,” DS 5-S2, ASTM, 1969
10. “Supplemental Report on the Elevated-Temperature Properties of Chromium-Molybdenum Steels,” DS
6-S1, ASTM, 1966
11. “Supplemental Report on the Elevated-Temperature Properties of Chromium-Molybdenum Steels,” DS
6-S2, ASTM, 1971
12. “Report on the Elevated-Temperature Properties of Selected Super-Alloys,” DS 7-S1, ASTM, 1968
13. “An Evaluation of the Elevated-Temperature Tensile and Creep-Rupture Properties of Wrought Carbon
Steel,” DS 11-S1, ASTM, 1969
14. “Evaluation of the Elevated-Temperature Tensile and Creep-Rupture Properties of C-Mo, Mn-Mo and
Mn-Mo-Ni Steels,” DS 47, ASTM, 1971
15. “Evaluation of the Elevated-Temperature Tensile and Creep-Rupture Properties of Steel,” DS 50,
ASTM, 1973
16. “Evaluation of the Elevated-Temperature Tensile and Creep-Rupture Properties of 3 to 9 Percent Cr-Mo
Steels,” DS 58, ASTM, 1975
17. “Evaluations of the Elevated-Temperature Tensile and Creep-Rupture Properties of 12 to 27 Percent
Chromium Steels,” DS 59, ASTM, 1980
18. “Compilation of Stress-Relaxation Data for Engineering Alloys,” DS 60, ASTM, 1982
19. V.K. Sikka, H.E. McCoy, Jr., M.K. Booker, and C.R. Brinkman, “Heat-to-Heat Variation in Creep
Properties of Types 304 and 316 Stainless Steels,” ASME Paper 75-PVP-26, American Society of
Mechanical Engineers, New York, 1975
20. K.R. Williams and B. Wilshire, Effects of Microstructural Instability on the Creep and Fracture
Behavior of Ferritic Steels, Mat. Sci. Eng., Vol 28, 1977, p 289–296
21. M. Wild, Analysis of Creep Behavior of Heat-Resistant Ferritic Steels at Temperatures from 450 to 600
°C, Archiv. Eisenhüttenwes., Vol 34, Dec 1963, p 935–950 (in German)
22. Private business communication, Materials Technology Corporation data sheets submitted to the Metal
Properties Council for tests under MPC Contract No. 174-1
23. R.L. Klueh, Interaction Solid Solution Hardening in 2.25 Cr-1Mo Steel, Mat. Sci. Eng., Vol 35, 1978, p
239–253
24. J. Glen, The Shape of Creep Curves, Trans. ASME J. Basic Eng., Vol 85 (No. 4), Series D, Dec 1963, p
595–600
25. J.P. Milan et al., Negative Creep in Ni-Cr-Ti Alloys, Fourth Interamerican Conference on Materials
Technology, Caracas, June–July 1975, p 102–106
26. R. Widmer and N.J. Grant, The Role of Atmosphere in the Creep-Rupture Behavior of 80Ni-20Cr
Alloys, Trans. ASME J. Basic Eng., Vol 82 (No. 4), Series D, Dec 1960, p 882–886
27. P. Shahinian and M.R. Achter, Creep-Rupture of Nickel of Two Purities in Controlled Environments,
Joint International Conference on Creep, Institute of Mechanical Engineers, London, 1963, p 7-49 to 7-
57
28. J.H. Bennewitz, On the Shape of the Log Stress-Log Time Curve of Long Time Creep-Rupture Tests,
Joint International Conference on Creep, Institute of Mechanical Engineers, London, 1963, p 5-81 to 5-
92
29. W.C. Leslie, J.W. Jones, and H.R. Voorhees, Long-Time Creep-Rupture Tests of Aluminum Alloys, J.
Test. Eval., Vol 8 (No. 1), 1980, p 32–41
30. D.J. Wilson and H.R. Voorhees, Creep Rupture Testing of Aluminum Alloys to 100,000 Hours, J. Mat.,
Vol 7 (No. 4), 1972, p 501–509
31. S.P. Agrawal, L.E. Byrnes, J.A. Yaker, and W.C. Leslie, Creep Rupture Testing of Aluminum Alloys:
Metallographic Studies of Fractured Test Specimens, J. Test. Eval., Vol 5 (No. 3), May 1977, p 161–
173
32. D.J. Wilson, Extrapolation of Rupture Data for Type 304 (18Cr-10Ni), Grade 22 (2- Cr-1Mo), and
Grade 11 (1- Cr- Mo- Si) Steels,” Trans. ASME J. Eng. Mat. Technol., Jan 1974, p 22–33
33. R.M. Goldhoff, Appendix
3: Time-Temperature Parameters, Properties and Selection: Stainless Steels, Tool Materials, and
Special-Purpose Metals, Vol 3, Metals Handbook, 9th ed., American Society for Metals, 1980, p 237–
241
34. F.R. Larson and J. Miller, A Time-Temperature Relationship for Rupture and Creep Stresses, Trans.
ASME, Vol 74, 1952, p 765
35. R.M. Goldhoff, Comparison of Parameter Methods for Extrapolating High-Temperature Data, Trans.
ASME J. Basic Eng., Vol 81 (No. 4), Series D, Dec 1959, p 629–644
36. R.L. Orr, O.D. Sherby, and J.E. Dorn, Correlations of Rupture Data for Metals at Elevated
Temperatures, Trans. ASM, Vol 46, 1954, p 113–118
37. R.M. Goldhoff and G.J. Hahn, Correlation and Extrapolation of Creep-Rupture Data of Several Steels
and Superalloys Using Time-Temperature Parameters, in Time-Temperature Parameters for Creep-
Rupture Analysis, American Society for Metals, 1968, p 199–245
38. W.M. Cummings and R.H. King, Extrapolation of Creep Strain and Rupture Properties of Cr- Mo- V
Pipe Steel, Proc. Inst. Mech. Eng., Vol 185, 1970–71, p 285–299
39. S.S. Manson, Time-Temperature Parameters—A Re-evaluation and Some New Approaches, in Time-
Temperature Parameters for Creep-Rupture Analysis, American Society for Metals, 1968, p 1–113
40. S. Manson and C.R. Ensign, “A Specialized Model for Analysis of Creep Rupture Data by the
Minimum Commitment Station-Function Approach,” NASA TM X-52999, 1971, p 1–14
41. S.S. Manson and C.R. Ensign, Interpolation and Extrapolation of Creep Rupture Data by the Minimum
Commitment Method. Part I: Focal-Point Convergence, in Characterization of Materials for Service at
Elevated Temperature, American Society of Mechanical Engineers, New York, 1978, p 299–398
42. S.S. Manson and A. Muralidharen, Analysis of Creep Rupture Data for Five Multiheat Alloys by the
Minimum Commitment Method Using Double Heat Centering Technique, in Progress in Analysis of
Fatigue and Stress Rupture, American Society of Mechanical Engineers, New York, 1984, p 1–46
43. F.C. Monkman and N.J. Grant, An Empirical Relationship Between Rupture Life and Minimum Creep
Rate in Creep-Rupture Tests, Proc. ASTM, Vol 56, 1956, p 593–605
44. H.R. Voorhees, “Determination of Rupture Strength at Temperatures Near the Lower End of the Time-
Dependent Range,” findings reported to the Metal Properties Council, Inc., New York, 1984
45. S. Manson and W.F. Brown, Jr., Discussion to a Paper by F. Garofalo et al., Trans. ASME, Vol 78 (No.
7), Oct 1956, p 143
46. F. Dobeš and K. MiliXXke, The Relation Between Minimum Creep Rate and Time to Fracture, Met.
Sci., Vol 10, Nov 1976, p 382–384
47. D. Lonsdale and P.E.J. Flewitt, Relationship Between Minimum Creep Rate and Time to Fracture for 2-
%Cr-1%Mo Steel, Met. Sci., May 1978, p 264–265
48. M. Gold, W.E. Leyda, and R.H. Zeisloft, The Effect of Varying Degree of Cold Work on the Stress-
Rupture Properties of Type 304 Stainless Steel, Trans. ASME J. Eng. Mat. Technol., Vol 97 (No. 4),
Series H, Oct 1975, p 305–312
49. R.F. Gill and R.M. Goldhoff, Analysis of Long-Time Creep Data for Determining Long-Term Strength,
Met. Eng. Quart., Vol 10 (No. 3), Aug 1970, p 30–39
50. P.L. Threadgill and B.L. Mordike, The Prediction of Creep Life From Transient Creep Data, Z.
Metallkd., Vol 68 (No. 4), 1977, p 266–269
51. F. Garofalo, C. Richmond, W.F. Domis, and F. von Gemmingen, Strain-Time, Rate-Stress and Rate-
Temperature Relations During Large Deformations in Creep, Joint International Conference on Creep,
Institution of Mechanical Engineers, London, 1963, p 1-31 to 1-39
52. P.L. Threadgill and B. Wilshire, Mechanisms of Transient and Steady-State Creep in a γ′-Hardened
Austenitic Steel, in Creep Strength in Steel and High-Temperature Alloys, The Metals Society, London,
1974, p 8–14
53. 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, Trans. ASME J. Basic Eng., Vol 94 (No. 1),
Series D, March 1972, p 1–6
54. E.L. Robinson, Effect of Temperature Variation on the Creep Strength of Steels, Trans. ASME, Vol 60,
1938, p 253–259
55. P.N. Randall, Cumulative Damage in Creep-Rupture Tests of a Carbon Steel, Trans. ASME J. Basic
Eng., Vol 84 (No. 2), Series D, June 1962, p 239–242
56. D.A. Woodford, Creep Damage and Remaining Life Concept, Trans. ASME J. Eng. Mat. Technol., Vol
101 (No. 4), Dec 1979, p 311–316
57. M.M. Abo El Ata and I. Finnie, A Study of Creep Damage Rules, Trans. ASME J. Basic Eng., Vol 94
(No. 3), Series D, Sept 1972, p 533–543
58. J.W. Freeman and H.R. Voorhees, “Notch Sensitivity of Aircraft Structural and Engine Alloys, Part II:
Further Studies with A-286 Alloys,” Wright Air Development Center, Technical Report 57–58, ASTIA
Document 207,850, Jan 1959
59. R.V. Hart, Concept of Area-Modified Stress for Life-Fraction Summation During Creep, Met. Technol.,
Sept 1977, p 447–448
60. R.V. Hart, Assessment of Remaining Creep Life Using Accelerated Stress-Rupture Tests, Met.
Technol., Jan 1976, p 1–7
61. D.A. Woodford, “Accelerated Testing for High Temperature Materials Performance and Remaining
Life Assessment,” EPRI 114045, 1999
62. W.L. Williams, “Parameter and Long-Life Creep Rupture Tests of Type 304 Steel,” ASTM Technical
Report D8-9.6. (Presented at the 1968 Materials Engineering Exposition and Congress, Detroit, 14–17
Oct 1968)
63. V. Biss, D.L. Sponseller, and M. Semchyshen, Metallographic Examination of Type 304 Stainless Steel
Creep Rupture Specimens, ASTM J. Mater., Vol 7 (No. 1), March 1972, p 88–94
64. Independent tests by Materials Technology Corporation, Ann Arbor, MI
65. M. Prager, Development of the MPC Omega Method for Life Assessment in the Creep Range, Pressure
Vessel Technol. (Trans. ASME), Vol 117, May 1995, p 95–103
Assessment and Use of Creep-Rupture Properties
Howard R. Voorhees, Materials Technology Corporation Martin Prager, Materials Properties Council
Selected References
• F.R. Larson and J. Miller, Time-Temperature Relationship for Rupture and Creep Stress, Trans. ASME,
Vol 74, 1952
• S.S. Manson and A. M Haferd, “A Linear Time-Temperature Relation for Extrapolation of Creep and
Stress-Rupture Data,” NACA TN 1890, March 1953
Stress Relaxation Testing
D.A. Woodford, MPa, Inc.
Introduction
THE MAJORITY OF CREEP TESTING, as described in this Volume, uses a fixed load (or stress) at a constant
temperature and measures the increase in strain as a function of time. However, materials may also creep under
constraint with little or no dimensional change. This constraint then approximates a constant total strain, so a
more appropriate test in such situations is one in which the material is deformed to a fixed strain, which is then
held constant. Depending on the application, the corresponding initial stress may be below, at, or above the
yield stress on loading. Whether or not there is permanent plastic strain on loading, there is an elastic strain that,
in linear elastic materials, is proportional to the stress through the appropriate temperature sensitive modulus. If
the temperature and stress are sufficiently high creep will occur, but since the total strain is held constant, this
can only be achieved if the elastic strain decreases with a corresponding decrease in the stress. Creep at a fixed
total strain, therefore, results in a time dependent stress relaxation.
A common practical example where stress relaxation is a major design issue is in high temperature bolting.
After being initially torqued to ensure joint tightness the stress progressively relaxes at a rate that depends on
the creep strength of the material. For major components such as steam turbine shell flanges, it is essential to
avoid leakage by periodic bolt retightening. Alloys have to be used, which will ensure steam tight joints at least
up to normal turbine overhaul periods that may now extend to 50,000 h (Ref 1).
In addition to many such mechanical fastener problems, stress relaxation is important in the wire of prestressed
concrete (Ref 2), all types of springs (Ref 3), electrical contacts (Ref 4), soldered joints (Ref 5), and the relief of
stress gradients induced by differential swelling in in-pile nuclear reactor tubes (Ref 6).
Stress relaxation is not limited to externally applied stresses. Residual stresses caused by metal working (Ref 7)
or welding (Ref 8) may have to be reduced by stress relieving treatments prior to placing parts in service.
Finally, parts such as gas turbine blades with internal cooling may develop severe stress and temperature
gradients in service that will lead to stress redistribution under constraint, and temperature changes in cyclic
operation may lead to residual stresses that relax at temperature. For repeated cycles the accumulated creep
strain may eventually lead to cracking as a result of thermal fatigue (Ref 9).
From this discussion it is clear that stress relaxation and stress redistribution are major manifestations of creep
deformation in practical applications. This is especially true for high-temperature cyclic operation. In many
cases, however, suitable relaxation data does not exist, and analysis has to be made using existing constant load
isothermal creep data. Thus there is much interest in predicting relaxation from creep data and vice versa. The
problem is that most structural materials experience strong deformation path dependence. Thus, a material
creeping under constant load and accumulating strain experiences a different deformation path from one
subjected to a fixed total strain and decreasing stress. To convert one to the other requires a damage law such as
time hardening or strain hardening or a mechanical equation of state, which incorporates one or more internal
state variables (Ref 10). These approaches have varying degrees of success and will not be further considered.
This article concentrates on metallic materials as covered by ASTM E 328 (Ref 11), although stress relaxation
is very important in plastics. For plastics a separate ASTM testing standard (Ref 12) is available that recognizes
the viscoelastic behavior. This means that the creep strain may be mostly or fully recoverable upon removal of
the load. Recent work on engineering ceramics suggests that these materials also show viscoelastic behavior
(Ref 13). Composites of all types are expected to show internal stress redistribution between the components as
well as complex macroscopic stress relaxation depending on the component phases.
References cited in this section
1. J. Bolton, Design Considerations for High Temperature Bolting, Performance of Bolting Materials in
High Temperature Plant Applications, Institute of Materials, 1995
2. R.J. Glodowski and G.E. Hoff, Stress Relaxation of Steel Tendons Used in Prestressed Concrete under
Conditions of Changing Applied Stress, STP 676, Stress Relaxation Testing, A. Fox, Ed., ASTM, 1978,
p 42–58
3. S.U.V. Idermark and E.R. Johansson, Room Temperature Stress Relaxation of High Strength Strip and
Wire Spring Steels-Procedure and Data, STP 676, Stress Relaxation Testing, A. Fox, Ed., ASTM, 1978,
p 61–77
4. J. Miyake, T. Kimura, and T. Endo, Stress Relaxation of Cu-Ti Alloy C199, Creep and Stress
Relaxation in Miniature Structures and Components, H.D. Merchant, Ed., TMS, 1996, p 57–74
5. H. Mavoori, J. Chin, S. Aaynman, B. Moran, L. Keer, and M. Fine, Creep, Stress Relaxation and Plastic
Deformation in Sn-Ag and Sn-Zn Eutectic Solders, H.D. Merchant, Ed., TMS, 1996, p 173–190
6. J.M. Beeston and T.K. Burr, In-Reactor Stress Relaxation of Type 348 Stainless Steel In-Pile Tube, STP
676, Stress Relaxation Testing, A. Fox, Ed., ASTM, 1978, p 155–170
7. F.T. Geyling and P.L. Key, Stress Relaxation of Residual Metalworking Stresses, STP 676, Stress
Relaxation Testing, A. Fox, Ed., ASTM, 1978, p 143–154
8. R.M. Chenko, Weld Residual Stress Measurements on Austenite Stainless Steel Pipes, Weldments:
Physical Metallurgy and Failure Phenomena, Fifth Bolton Landing Conference, 1978, p 195–206
9. 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 5–43
10. G.A. Webster and R.A. Ainsworth, High Temperature Component Life Assessment,, Chapman and Hall,
1994
11. Standard Methods for Stress Relaxation Tests for Materials and Structures, E 328-86, Annual Book of
ASTM Standards, ASTM, 1991
12. Practice for Testing Stress Relaxation of Plastics, D 2991, Annual Book of ASTM Standards, ASTM
13. D.A. Woodford, Stress Relaxation, Creep Recovery, and Newtonian Viscous Flow in Silicon Nitride, J.
Am. Ceram. Soc., Vol 81 (No. 9), 1998, p 2327–2332
Stress Relaxation Testing
D.A. Woodford, MPa, Inc.
Testing Considerations
Figures 1 and 2 illustrate load characteristics and data representation for stress relaxation testing for the most
convenient and common uniaxial tensile test (Ref 2). The constraint is obtained by the application of the
external load at either a constant strain rate or constant load rate. Figure 3 shows the response in each case for
an initial stress, σ
0
, exceeding the proportional limit. If the stress and temperature are sufficiently high, the
extent of nonelastic strain on loading will depend on the loading rate, which will in turn affect the initial
relaxation rate. The loading rate should therefore be reasonably high. The stress relaxation test starts at t = t
0
when the desired level of constraint is obtained. The relaxation curve can be plotted in the form of remaining
stress (Fig. 2a) or relaxed stress (Fig. 2b), which is the initial stress minus the remaining stress.
Fig. 1 Characteristic behavior during loading period in a stress relaxation test. (a) Constant strain rate.
(b) Constant load rate. Source: Ref 11
Fig. 2 Typical stress relaxation curves plotted for (a) remaining stress and (b) relaxed stress (the initial
stress minus the remaining stress). Source: Ref 11