Parametric Analyses of High-Temperature Data for Aluminum Alloys

170 Pages·2009·2.62 MB·English

by  J. Gilbert Kaufman

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Copyright © 2008 ASM International®. All rights reserved.
Parametric Analyses of High-Temperature Data for Aluminum Alloys (#05202G) www.asminternational.org
PARAMETRIC ANALYSES
OF HIGH-TEMPERATURE
DATA FOR
ALUMINUM ALLOYS
J. GILBERT KAUFMAN
ASM International®
Materials Park, Ohio 44073-0002
www.asminternational.org
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Copyright ©2008
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Contents
Foreword and Acknowledgments..........................................................iv Data Sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
About the Author....................................................................................v Wrought Alloys
1100-O, H14, H18—Stress Rupture Strength and,
for the 0 Temper, Creep Strengths. . . . . . . . . . . . . . . . . . . . . . . . 23
Introduction and Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2024-T851—Stress Rupture Strength . . . . . . . . . . . . . . . . . . . . . . 41
2219-T6, T851—Stress Rupture Strength. . . . . . . . . . . . . . . . . . . 50
3003-O, H12, H14, H18—Stress Rupture Strength. . . . . . . . . . . . 56
Theory and Application of Time-Temperature Parameters. . . . . . . . 3
3004-O, H32, H34, H38—Stress Rupture Strength. . . . . . . . . . . . 64
Rate Process Theory and the Development of Parametric
5050-O—Stress Rupture Strength. . . . . . . . . . . . . . . . . . . . . . . . . 68
Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
5052-O, H32, H34, H38, and H112—Stress
Larson-Miller Parameter (LMP) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Rupture Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Manson-Haferd Parameter (MHP). . . . . . . . . . . . . . . . . . . . . . . . . . 3
5083-H321 As-Welded with 5083 Filler Alloy—Stress
Dorn-Sherby Parameter (DSP). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Rupture Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Observations on the LMP, MHP, and DSP. . . . . . . . . . . . . . . . . . . . 4
5154-O—Stress Rupture Strength. . . . . . . . . . . . . . . . . . . . . . . . . 82
Illustrative Applications of LMP, MHP, and DSP. . . . . . . . . . . . . . . . 4
5454-O, H32, H34, As-Welded H34—Stress Rupture
Notes about Presentation Format. . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Strength and, for the O Temper, Strength at
Alloys 1100-O and H14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Minimum Creep Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Alloy 2024-T851. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5456-H321 As-Welded with 5556 Filler Alloy—Stress
Alloy 3003-O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Rupture Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Alloy 5454-O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6061-T6, T651—Stress Rupture Strength,
Summary of Parametric Comparisons. . . . . . . . . . . . . . . . . . . . . . . 7
Creep Strength, and Strength at Minimum Creep Rate. . . . . . . 112
Factors Affecting Usefulness of LMP. . . . . . . . . . . . . . . . . . . . . . . . . 7
6063-T5, T6—Strength at Minimum Creep Rate . . . . . . . . . . . . 142
Normal Rupture Test Reproducibility . . . . . . . . . . . . . . . . . . . . . . . 7
Cast Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Testing Laboratory Variability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
A201.0-T7—Stress Rupture Strengths. . . . . . . . . . . . . . . . . . . . . 144
Lot-to-Lot Variability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
224.0-T63—Stress Rupture Strengths. . . . . . . . . . . . . . . . . . . . . 145
Effect of LMPConstant (C ) Selection . . . . . . . . . . . . . . . . . . . . 8
LMP 249.0-T63—Stress Rupture Strengths. . . . . . . . . . . . . . . . . . . . . 147
Choice of Cartesian versus Semi-log Plotting. . . . . . . . . . . . . . . . . 9
270.T7—0.2% Creep Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . 148
Choice of Scales and Precision of Plotting . . . . . . . . . . . . . . . . . . 10
354.0-T61—Stress Rupture Strengths. . . . . . . . . . . . . . . . . . . . . 148
Effect of How the LMPMaster Curves are
C355.0-T6—Stress Rupture Strengths. . . . . . . . . . . . . . . . . . . . . 149
Fitted to the Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Applications When Microstructural Changes
are Involved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Appendix 1: Aluminum Alloy and Temper
Illustrations of Verification and Limitations of LMP. . . . . . . . . . . . . 11 Designation Systems......................................................151
Alloys 1100-O and H14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Alloy 5454-O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Appendix 2: Terminology and Nomenclature..................................153
Alloy 6061-T651. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Limitations of Parametric Analyses. . . . . . . . . . . . . . . . . . . . . . . . 12
Presentation of Archival Master LMPCurves. . . . . . . . . . . . . . . . . . 13 Appendix 3: Nominal Compositions and Typical Mechanical
Software Programs for Parametric Analyses of Creep Properties of Some Aluminum Alloys..........................155
Rupture Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Application of LMPto Comparisons of Stress Rupture Appendix 4: SI/Metric Unit Conversions..........................................159
Strengths of Alloys, Tempers, and Products. . . . . . . . . . . . . . . . . . . 15
Comparisons of Stress Rupture Strengths of
Index ....................................................................................................161
Different Tempers of an Alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Comparisons of Stress Rupture Strengths of Different
Products of an Alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Comparisons of Stress Rupture Strengths of Welds
with Parent Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Comparisons of Different Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . 18
Application of LMPto High-Temperature Tensile Data for
Aluminum Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Application of LMPto Microstructural Changes and
Corrosion Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
iii
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Foreword and Acknowledgment
It is the objective of this book to describe the potential usefulness of parametric analyses in ana-
lyzing and extrapolating the properties of aluminum alloys at high temperatures. It is also the intent
to illustrate the use of such methods by presenting a broad spectrum of high-temperature creep data
for aluminum alloys generated from a single source and developed using consistent testing proce-
dures and practices.
The author gratefully acknowledges the support of Alcoa, Inc., and in particular the efforts of Dr.
Gwendolyn Dixon and her management in arranging and approving the release of the information
contained herein. Alcoa, Inc. enabled the author to include many previously unpublished data and
related information from Alcoa’s archives that add immeasurably to the depth and breadth of cover-
age. The archival parametric analyses presented herein are illustrative examples typical and repre-
sentative of the respective alloys and tempers, but have no statistical basis and therefore are not to be
considered as the basis for design.
iv
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About the Author
J.G. (Gil) Kaufman has a background of more than 50 years in the aluminum and materials infor-
mation industries, and remains an active consultant in both areas. In 1997, he retired as Vice Presi-
dent, Technology for the Aluminum Association, Inc., headquartered in Washington, D.C., and is
currently president of his consulting company, Kaufman Associates.
Earlier in his career, he spent 26 years with the Aluminum Company of America, where he man-
aged engineering properties and fabricating metallurgical research at Alcoa Laboratories. Many of
the data presented in this volume were generated over the period when the author was active in
and/or managing Alcoa Laboratories engineering properties research.
Kaufman spent 5 years with ARCO Metals, where he was Director of R&D and, later, Vice Presi-
dent, Research & Engineering.
Kaufman also served for 9 years as President and CEO of the National Materials Property Data
Network where, working with STN International and Chemical Abstracts Service, he established a
worldwide online network of more than 25 numeric materials databases.
Gil is a Fellow and Honorary Member of ASTM and a Fellow and Life Member of ASM Interna-
tional. He has published more than 130 articles, including five books, on aluminum alloys and mate-
rials data systems.
v
Parametric Analyses of High-Temperature Data for Aluminum Alloys Copyright © 2008 ASM International®
J. Gilbert Kaufman, p 1-2 All rights reserved.
DOI: 10.1361/paht2008p001 www.asminternational.org
Introduction and Background
The properties of aluminum alloys are dependent on both the it is appropriate to introduce those that are the focus of this vol-
temperature to which they are exposed and also, for temperatures ume at this point. Anumber of fairly commonly used parameters
above room temperature, to the length of time of exposure at tem- have been developed over the years, and most are based on what
perature. One consequence of this is a need for designers of struc- is termed “rate process theory.” Three versions of such time-
tures intended for very long-life service at high temperatures to be temperature parameters are dealt with herein, notably:
able to anticipate the combined effect of temperature and time at
temperature on the properties for the entire service life based on The Larson-Miller parameter (Ref 1): LMP= T(C+ log t)
data from relatively shorter time experimental testing.
For relatively short-life structures, the need is addressed simply Logt−logt
TheManson-Haferdparameter(Ref5,6):MHP= a
by planning ahead and carrying out a test plan that replicates the T−T
a
intended service conditions. This is quite practical for structures
whose life may be as much as a year, or perhaps even 5 years, but The Dorn-Sherby parameter (Ref 7): DSP= t e(cid:2)A/T
does not generally cover rather typical design lives of 10, 20, or
30 years, or longer. where Tis the temperature, °R; tis the time at temperature; and t,
a
The need for the ability to judge performance for relatively long T, A, and Care constants defined by the respective experimenters.
a
service lives has been addressed for more than 50 years (Ref 1–3) These parameters have been applied with considerable success
through the use of time-temperature parametric equations that per- over the years, especially to stress rupture data for a variety of
mit the folding of data obtained over a variety of temperatures and metals and, to a lesser extent, to creep rates and total accumulated
exposure times into a single relationship. Once that relationship is creep of various amounts. While not necessarily showing a techni-
established with adequate consistency and reliability, it is possible cal advantage over the other two parameters, the Larson-Miller
to extrapolate the available data to anticipate service lives that Parameter (LMP) has become the most widely used, for alu-
substantially exceed the range of test data. This must always be minum alloys at least, primarily in the author’s judgment because
done cautiously and with awareness of the extent of the extrapola- of its ease and simplicity of application. As a result, the bulk of
tion, but it provides a better perspective than simply extrapolating the information presented herein focuses on the LMP.
individual strength life curves. It is timely and useful to consider the value of parametric rela-
The need for some sort of parametric relationship involving tionships not only for creep and stress rupture data but also for
stress, time, and temperature may be visualized readily by observ- elevated temperature tensile property data and even for resistance
ing a representative set of stress rupture strength data for 5454-O in to stress-corrosion cracking. For this purpose we focus on data for
Fig. 5454-1 (Ref 4) plotted as rupture stress as a function of time aluminum alloys, notably those used for ASME Boiler & Pressure
under load at temperature. The data for each temperature appear as Vessel Codes and for other high-temperature applications and also
discrete lines of decreasing rupture stress with increasing time at for alloys subjected through service exposure to long-term high-
temperature. Typically, such curves extend out to between 1000 temperature service.
and 10,000 hours because that represents the practical limits of Briefly, then, the scope of this book includes:
testing time in advance of designing some commercial structure.
Despite the individual lines for each test temperature in Fig. • Review of the theoretical basis for the parametric relationships
5454-1, it appears intuitively that there is some relationship • Some illustrations and comparisons of the application of three
among these curves. It would be highly desirable and helpful in parametric relationships for several aluminum alloys
extrapolating to longer service lives if these curves could be com- • Factors affecting the usefulness of time-temperature parameters
bined and consolidated into a single relationship representing all • Illustrations of the verification and limitations of time-temper-
of the data for all temperatures, as for example in Fig. 5454-2. It is ature-parameters
precisely such consolidation that parametric analyses try to ac- • Presentation of archival Larson-Miller parametric analyses to
complish, and it is the background and application of such analy- stress-rupture data for a variety of aluminum alloys
ses that we discuss in this book. • Presentation of some new analyses of archival data
The theoretical background and development of the time-tem- • Application of LMP to comparisons of the stress rupture
perature parametric relationships are covered in greater depth, but strengths of aluminum alloys, tempers, and products
2 / Parametric Analyses of High-Temperature Data for Aluminum Alloys
• Application of the parametric relationships to high-tempera- aluminum alloys and tempers for which creep rupture data are
ture tensile properties of aluminum alloys presented or referenced in this volume.
• Applications of the parametric relationships for anticipating It is also appropriate to note that throughout most of this vol-
microstructural changes in aluminum alloys ume, principal focus is placed on the calculation and presentation
of mechanical properties in the English or engineering system,
It is appropriate to note that throughout this volume, the Alu- rather than the International Standard System of Units (SI) or met-
minum Association alloy and temper designation systems are used ric units. This was done because all of the tabular and graphical
and that the compositions and tensile properties of the materials data presented herein were generated using the English/engineer-
for which data are presented herein met all aluminum alloys spec- ing system, calculated conversions other than when convenient
ifications of the Aluminum Association. Both the alloy and temper would have added the potential for distortion of the presentations.
designation systems and the composition and tensile property For those interested in a more in-depth discussion of SI/metric
specifications for all aluminum alloys are presented in Aluminum units and their use in parametric analysis, see Appendix 4.
Standards and Datapublished by the Aluminum Association and
updated on a regular basis (the current issue at this writing was
REFERENCES
published in 2006) and also in the American National Standards
Institute publications H35.1 and H35.2, published for ANSI by the 1. F.R. Larson and J. Miller, ATime-Temperature Relationship
Aluminum Association. for Rupture and Creep Stresses, Trans. ASME, Vol 74, July
Abrief summary of the Aluminum Association Alloy and Tem- 1952, p 765–771
per Designation Systems is presented in Appendix 1. 2. F.C. Monkman and N.J. Grant, An Empirical Relationship
Alist of the aluminum industry terminology and nomenclature between Rupture Life and Minimum Creep Rate in Creep
used throughout the volume is presented in Appendix 2. Most of Rupture Tests, Transactions of 59th Annual Meeting of ASTM,
the industry terms are those from Aluminum Standards and Data. ASTM, Philadelphia, PA, 1956, p 593–605
There are a few abbreviations used regularly in the text, tables, 3. J.G. Kaufman, Discussion Ref 2 in Transactions of 59th An-
and figures: nual Meeting of ASTM, Philadelphia, PA, 1956, p 606–612
• LMP, Larson-Miller parameter 4. K.O. Bogardus, R.C. Malcolm, and M. Holt, “Extrapolation
• MHP, Manson-Haferd parameter of Creep-Rupture Data for Aluminum Alloys,” presented at
• DSP, Dorn-Sherby parameter the 1968 ASM Materials Engineering Congress (Detroit, MI),
• C , the constant Cin the Larson-Miller parameter D8-100, American Society for Metals, 1968, p 361–390
• T,LtMePst temperature 5. S.S. Manson, “Design Considerations for Long Life at Ele-
• t,time at test temperature vated Temperatures,” Technical Report TP-1-63, NASA, 1963
• AW, as welded 6. S.S. Manson and A.M. Haferd, “ALinear Time-Temperature
• HTAW, heat treated and aged after welding Relation for Extrapolation of Creep and Stress-Rupture Data,”
Technical Note 2890, NACA, March, 1953
Appendix 3 provides for background information the nominal 7. O.D. Sherby and J.E. Dorn, Creep Correlations in Alpha Solid
compositions and typical mechanical properties of all of the Solutions of Aluminum, Transactions of AIME, Vol 194, 1952
Parametric Analyses of High-Temperature Data for Aluminum Alloys Copyright © 2008 ASM International®
J. Gilbert Kaufman, p 3-21 All rights reserved.
DOI: 10.1361/paht2008p003 www.asminternational.org
Theory and Application of
Time-Temperature Parameters
Rate Process Theory and the Development of R(cid:2)(cid:3)1.0
Parametric Relationships
T (cid:2)(cid:3)460 °F or 0 °R
A
Much of the early application and evolution of the high-temper- t (cid:2)the constant Cin the LMP
A
ature parametric relationships to data for aluminum alloys were
carried out during the 1950s and 1960s under the auspices of the Thus, the general equation reduces to:
MPC, then known as the Metals Properties Council (now the Ma-
terials Properties Council). However, the real origins of the rela- P (cid:2) (log t+ C) (T) or LMP(cid:2)T(C+ log t)
tionships go back considerably further.
The “rate process theory” was first proposed by Eyring in 1936 This analysis has the advantage that log t or Cis the onlyconstant
A
(Ref 1) and was first applied to metals by Kauzmann (Ref 2) and that must be defined by analysis of the data in question, and it is in
Dushman et al. (Ref 3). It may be expressed mathematically as: effect equal to the following at isostress values:
r(cid:2)Ae(cid:3)Q(S)/RT C (cid:2) (LMP/T) (cid:3)log t
where ris the rate for the process in question, Ais a constant, Q(S)
In such a relationship, isostress data (i.e., data for the same stress
is the activation energy for the process in question, R is the gas
but derived from different time-temperature exposure) plotted as
constant, and Tis absolute temperature.
the reciprocal of Tversus log tshould define straight lines, and the
Over the years from 1945 to 1950, several investigators, includ-
lines for the various stress values should intersect at a point where
ing Fisher and McGregor (Ref 4, 5), Holloman (Ref 6–8), Zener 1/T(cid:2)0 and log t(cid:2)the value of the unknown constant C.
(Ref 7), and Jaffe (Ref 8) were credited with recognizing that for
Larson and Miller took one step further in their original pro-
metals high-temperature processes such as creep rupture perform-
posal, suggesting that the value of constant C(referred to as C
ance, tempering, and diffusion appear to obey rate process theo- LMP
hereinafter) could be taken as 20 for many metallic materials.
ries expressible by the above equation.
Other authors have suggested that the value of the constant varies
In 1963, Manson and Haferd (Ref 9) were credited with show-
from alloy to alloy and also with such factors as cold work, ther-
ing that all three of the parametric relationships introduced in the
momechanical processing, and phase transitions or other struc-
section “Introduction and Background” derive from:
tural modifications.
From a practical standpoint, most applications of the LMPare
(logt)σQ−logt
P= A made by first calculating the value of C that provides the best
(T−T )R LMP
A fit in the parametric plotting of the raw data, and values for alu-
minum alloys, for example, have been shown to range from about
where P is a parameter combining the effects of time, tempera- 13 to 27.
ture, and stress; s is stress, ksi; Tis absolute temperature; and T ,
A
log t , Q, and Rare constants dependent on the material.
A Manson-Haferd Parameter (MHP)
For the MHP, Manson and Haferd (Ref 9, 11) chose the follow-
Larson-Miller Parameter (LMP)
ing values for the constants in the rate process equation:
For the LMP, Larson and Miller (Ref 10) elected to use the fol-
lowing values of the four constants in the rate process equation: Q(cid:2)0
Q(cid:2)0 R(cid:2)1.0
4 / Parametric Analyses of High-Temperature Data for Aluminum Alloys
Under these assumptions, the general equation reduces to: relationship assumed of the relationships between log t and 1/T
(Ref 6).
logt−logt As noted in the previous discussions, the LMPassumes that the
P= A
T−T isostress lines converge on the ordinate of a log time versus in-
A
verse temperature plot, while the MHP assumes convergence at
some specific value of both log t and 1/T. The DSPassumes the
In this case, there are two constants to be evaluated, log t and T .
A A isostress lines are parallel rather than radiating from a specific
Manson and Haferd proposed that isostress data be plotted as T
value of coordinates log tand 1/T.
versus log t and the coordinates of the point of convergence be
As representative data illustrated in this book show, the impact
taken as the values for log t and T .
A A of the differences on the results of analyses with the three differ-
It may be noted that the key difference between the LMP and
ent parameters is not very great.
MHPapproaches is the selection of T (cid:2)absolute zero as the tem-
A It is appropriate to note that a number of variations on the three
perature where the isostress lines will converge in the LMPwhile
parameters described previously have been proposed, primarily
in the MHPT is determined empirically, or in effect allowed to
A including such things as letting the values of the various con-
“float.”
stants, such as the C in the LMPand the activations energy A in
the DSP, “float.” None of these have seemed a useful extension of
Dorn-Sherby Parameter (DSP)
the originals. It is common practice to use the available raw data
Dorn and Sherby (Ref 12) based their relationship more directly to calculate or determine graphically the values of the needed con-
on the Eyring rate-process equation: stants, but then once established to hold them constant. Allowing
the constants in any of the relationships to float, for example, the
DSP(cid:2)te(cid:3)A/T activation energy in the DSP, results in a different type of analysis
in which the isostress lines are curves, not straight lines, and con-
where tis time, Ais a constant based on activation energy, and Tis siderably complicates its routine use.
absolute temperature.
This relationship, like the others, implies that isostress tests re-
sults at various temperatures should define straight lines when log
Illustrative Applications of LMP, MHP, and DSP
tis plotted against the reciprocal of temperature. However, it dif-
fers from the other approaches in that these straight-line plots are
Several interesting facets of the value and limitations of the
indicated to be parallel rather than converging at values of log t
parametric relationships may be seen from looking at representa-
and 1/T.
tive illustrations for the following four alloys and tempers where
Observations on the LMP,MHP,and DSP all three parameters are applied to the same sets of data.
The essential significance of the differences in the three pa- • 1100-O, commercially pure aluminum, annealed (O)
rameters described previously and applied herein may be illus- • 2024-T851, a solution heat treated aluminum-copper (Al-Cu)
trated by the schematic representations in Fig. 1 based on the
alloy, the series most widely used for high-temperature aero-
space applications. The T851 temper is aged to peak
σ < σ < σ < σ
1 2 3 4 strength, so subsequent exposure at elevated temperatures
σ σ4 results in overaging, and some microstructural changes may
4 t , T
σ a a be expected.
3
σ • 3003-O, a lightly alloyed non heat treatable aluminum-man-
3
ganese (Al-Mn) alloy, widely used for heat exchanger applica-
σ2 σ tions. It is annealed so no further transitions in structures are
4 σ
2 anticipated as it is further exposed to high temperatures.
σ • 5454-O, the highest strength aluminum-magnesium (Al-Mg)
σ 3 σ
1 1 alloy recommended for applications involving high tempera-
tures. Because of the higher alloying, there may be diffusion
σ σ
1 2 of constituent with high-temperature exposure even in the an-
nealed temper.
Many other alloys and tempers are included in the group for
0 1/T 0 T 0 1/T which master parametric relationships are presented in the section
“Presentation of Archival Master LMPCurves.”
It is appropriate to note that some components of the following
Fig. 1 Comparison of assumed constant stress versus temperature
presentations are based on the efforts of Bogardus, Malcolm, and
relationships for Larson-Miller (left), Manson-Haferd (center), and
Holt of Alcoa Laboratories, who first published their preliminary
Dorn-Sherby (right). T, exposure temperature, absolute; t, exposure time, h;
σ, test/exposure stress. assessment of these parametric relationships in 1968 (Ref 13).
Theory and Application of Time-Temperature Parameters / 5
Notes about Presentation Format
Desired service LMP rupture MHP rupture DSP rupture
Temperature, °F rupture life, h strength, ksi strength, ksi strength, ksi
Generally, plots of stress rupture strength or any other property
212 10,000 6.0 5.4 5.9
are presented with the property on the ordinate scale and the pa- 100,000 5.3 4.0 5.0
rameter on the abscissa, as in Fig. 1100-8. From the descriptions 300 10,000 3.7 3.0 3.2
100,000 3.0 2.3 2.7
in Chapter 2, all three of the parameters discussed herein include
400 10,000 2.5 2.4 1.9
both time and temperature, so it is useful to note that the para- 100,000 2.1 1.4 1.5
metric plots can also be presented as in Fig. 2043-3, 2024-6, or 500 10,000 1.1 1.1 1.0
100,000 <1.0 <1.0 <1.0
2024-7, examples of the three parameters in which at the bottom,
abscissa scales showing how the combination of temperature and There is fairly good agreement among the extrapolated values
time are represented. for the three parameters, usually 1 ksi or less variation. It is no-
This type of presentation is often useful for individuals using table that the MHP usually provided the lowest extrapolated
the parameters for extrapolations, but it is not a necessary part of value, while the LMPprovided the highest, usually by less than
the presentation. Therefore, the multiple abscissa axes showing 0.5 ksi.
time and temperature are not included as a general rule through
this volume unless the archival version included them. Alloy 2024-T851
It is also appropriate to clarify at this stage that the values
Figures 2024-1 and 2024-2 provide graphical summaries of the
shown for the Larson-Miller parameter on the abscissas are in
stress rupture strengths of 2024-T851 over the temperature range
thousands and are presented as LMP/103; thus for example, in Fig.
from room temperature (75 oF, or 535 oR) through 700 oF (1160
1100-8, the numbers from 13 to 21 on the abscissa are actually
oR). The data in Fig. 2024-1 are plotted as rupture strength as a
13,000 to 21,000. For the Manson-Haferd and Dorn-Sherby pa-
function of rupture time for each test temperature, and those of
rameters, the values are as shown.
Fig. 2024-2 are plotted as a function of temperature. The raw test
data are tabulated in Table 2024-1, along with the archival
Alloys 1100-O and H14
isostress calculations.
Table 1100-1 presents a summary of the stress rupture strength LMP for 2024-T851. Table 2024-1 summarizes the isostress
data for 1100-O and 1100-H14; the discussion immediately calculations to determine the LMPconstant C for 2024-T851.
LMP
following focuses on the O temper data. This summary is for The calculations show quite a range of potential values for C ,
LMP
rather extensive tests of single lots of material. Other lots of 1100 ranging from about 13 through 26. It is to be expected that
were also tested, as is illustrated later, but this material was the changes in rate-process-type reactions would be in evidence for
basis of the best documented master curves for 1100-O and H14. 2024-T851, as it had originally been aged to maximum strength;
The data are plotted in the format of stress rupture strength as a subsequent exposure to high temperatures results in increased pre-
function of rupture life in Fig. 1100-1 and Fig. 1100-2 for the O cipitation of alloying constituents at varying rates and, eventually,
and H14 tempers, respectively. recrystallization.
LMP for 1100-O. Figure. 1100-3 shows the archival master The general tendency is for C to decrease with both longer
LMP
LMPcurve developed for 1100-O derived with a value of the Lar- rupture life and also with increasing temperature. Since the long-
son-Miller parameter constant C of 25.3. The isostress calcula- life values tend to best represent the range into which extrapola-
LMP
tions leading to the selection of this value of C no longer exist. tions of data for design purposes are most likely to be needed,
LMP
Scatter and deviations are small, and the curve appears to represent there is a general practice to place greater weight on the values of
the data reasonably well. C for longer lives.
LMP
MHP for 1100-O.The isostress plot of log tand temperature is Figure 2024-3 is a master LMPcurve for 2024-T851 based on
shown in Fig. 1100-4. The isostress lines are not straight nor do an assumed value of C (cid:2)15.9. To facilitate interpretation,
LMP
they seem to converge as projected by Manson and Haferd, but time-temperature pairs are shown along with the LMPvalues on
values of the constants may be judged from projections of the the abscissa.
straight portions of the fitted lines as: log t = 21.66 and T = Several observations can readily be made. The data for room
A A
–500. The resultant master MHPcurve is illustrated in Fig. 1100-5. temperature do not fit with the remainder of the data and are
With the exception of several points obtained in tests at 250 oF, the ignored in the analysis. In addition, for each test temperature,
fit is reasonably good. the higher shorter-life data plots create “tails” off of the resultant
DSP for 1100-O. Calculations of the activation energy con- master curve; these fade into the master curve as rupture life in-
stant for the DSPresulted in a value of 44,100, and the resultant creases. The longer-life and higher-temperature data fit rather
master curve is illustrated in Fig. 1100-6. With the exception of well into a relatively smooth curve, not surprisingly, given the
the data for the lower temperatures, the fit is reasonably good. selection of a value of C deriving most heavily from the longer-
Comparisons of the Parameters. All three parametric rela- life data.
tionships represent data for 1100-O reasonably well. An addi- Figure 2024-4 presents the “extrapolated” curves of stress ver-
tional useful comparison test is the degree of agreement in sus rupture life for 2024-T851 utilizing the value of C = 15.9.
LMP
extrapolated values for predicted rupture life after 10,000 and Additional discussion and illustrations of the effect of varying
100,000 h: the values of Care included later.