Compilation of Stress-Relaxation Data for Engineering Alloys

608 Pages·1982·20.82 MB·English

by  Manjoine M. J.

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COMPILATION OF
STRESS-RELAXATION DATA
FOR ENGINEERING ALLOYS
Prepared for
The Metal Properties Council
and ASTM-ASME-MPC Joint Committee on
Effect of Temperature on the
Properties of Metals
by M. J. Manjoine and H. R. Voorhees
ASTM Data Series Publication DS 60
ASTM Publication Code Number (PCN)
05-060000-30
1916 Race Street, Philadelphia, Pa. 19103
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Copyright ® by AMERICAN SOCIETY FOR TESTING AND MATERIALS 1982
Library of Congress Catalog Card Number: 81-70979
NOTE
The Society is not responsible, as a body,
for the statements and opinions
advanced in this publication.
Printed in Baltimore, Md. (c)
September 1982
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Foreword
This book compiles published and known data on The members of Subcommittee 5 of The Metal
stress relaxation of metals and alloys of engineering Properties Council are as follows:
interest. It contains all data from the previous ASTM
Special Technical Publication No. 187, by the ASTM- M.J. Manjoine, Chairman (Westinghouse
ASME-MPC Joint Committee on Effect of Temperature Research Laboratories)
on the Properties of Metals. S. F. Collis (Alcoa Research Laboratories)
S. G. Epstein (The Aluminum Association)
This current project was sponsored by the Metal R. F. Gill (General Electric Company)
Properties Council, Inc. under the guidance of its F. Kull (SPS Technologies, Inc.)
Subcommittee 5 on Stress Relaxation. The data were R. W. Swindeman (Oak Ridge National Lab.)
compiled and analyzed for the Subcommittee by Dr. H. R. Voorhees (Materials Technology Corp.)
Howard R. Voorhees. R. C. Westgren (Wean United Inc.)
R. E. Z ink ham ( Reynolds Metals Company)
The Subcommittee acknowledges with gratitude
those individuals and organizations who contributed
data and services to this effort. The data sources
are referenced in the tables, and those who contrib-
uted services can take pride from the result.
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D o w n l o a d e d / p r i n t e d b y This standard is for EDUCATIONAL USE ONLY.
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Related
ASTM Publications
Formability of Metallic Materials—2000 A.D., STP 753 (1982), 04-753000-23
Fracture Mechanics (13th Conference), STP 743 (1981), 04-743000-30
Stress Relaxation Testing, STP 676 (1979), 04-676000-23
Fatigue Mechanisms, STP 675 (1979), 04-675000-30
Formability Topics—Metallic Materials, STP 647 (1978), 04-647000-23
Selection and Use of Wear Tests for Metals, STP 615 (1977), 04-615000-23
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Contents
Foreword i
Introduction
1. Stress Relaxation of Metals and Alloys v
2. Relaxation Mechanics v
2.1 Anelastic strain v
2.2 Plastic strain v
2.3 Microplastic strain v
2. 4 Creep vi
2.4.1 Primary creep strain vi
2.4.2 Secondary creep vi
2.4.3 Tertiary creep vi
3. Stress Relaxation Testing vi
4. Analyses of Data vi
4.1 Stress relaxation at temperatures below 0.4 T vii
m
4. 2 Stress relaxation at temperatures above 0.4 T vii
m
4. 3 Loss of stress for a bar under constant total strain vii
4. 4 Stress relief by relaxation vii
4.4.1 Thermal treatment viii
4. 4. 2 Mechanical and thermo-mechanical treatment viii
5. Utilization of Stress Relaxation Data viii
5.1 Bolting design viii
5.2 Press-fitted joints, springs, and clamps viii
5.3 Creep-fatigue damage viii
5. 4 Constitutive relationships viii
6. References viii
Fig. 1 - Comparative 1000-hour Relaxation Strengths for Several Classes of Alloys x
Fig. 2 - Relaxation of Solution-annealed Type 304 Stainless Steel xi
Fig. 3 - Relaxation of a 20% Cold-worked Type 304 Stainless Steel from 900 to 1300 F
(482 to 704 C) for an Initial Inelastic Strain of 0.07% xii
Fig. 4 - Remaining Stress for an Annealed Type 304 Stainless Steel Bar at Constant
Strain, as a Function of Temperature and Time xiii
Compilation
Introduction 1
Tabular Data 1
Graphical Presentations 2
Units for Stress 2
Cast Irons 3
Gray Cast Iron 4
Nodular Cast Iron ( Ductile Iron) 20
Carbon Steels (Including carbon-manganese grades) 29
Carbon-Molybdenum Steels (Including copper-molybdenum grades) 77
Chromium-Molybdenum Steels 93
Cr-Mo-V Steels ( Including Mo-V Steels) 137
Modified Cr-Mo-V Steels 207
Steels Containing 0. 6% or More Tungsten 219
Co-Cr-Mo-V Steels and Nb Modifications 219
Ni-Cr-Mo and Ni-Cr-Mo-V Steels 233
iii
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Ultrahlgh Strength Steels 249
Modified H-ll 249
9 Ni - Co Steels 249
18 Ni Maraging Steel 249
AM-350 ; AM-355 249
12% Cr Steels 257
Austenitic Stainless Steels (Including some early superalloys) 319
High-Iron Superalloys 395
Iron-Base Superalloys with Cobalt 415
Cobalt-Base Superalloys 423
Nickel-Base Superalloys 431
Aluminum Alloys 493
Copper Alloys 527
Titanium Alloys 551
Miscellaneous Alloys 571
8. Data Sources 583
iv
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Introduction
1. Stress Relaxation of Metals Anelasticity results from internal friction and
is a function of stress, o , stress rate, J , tem-
and Alloys perature, T , composition, magnetic properties,
degree of order, and elastic fields. Dislocation
dynamics are often used to explain the transient
behavior. •*J A simple model can be used to
describe the general dynamics as follows:
A bar loaded to an initial stress of, say, 40,000
psi and then held at constant strain and temperature a,a + a,5 = b,e + b2« ,
may after a time period have a remaining stress of where o is the stress, e is the strain, and a and b
only 30,000 psi. This time-dependent stress reduct- are constants.
ion of 10,000 psi is called stress relaxation. The
total strain remains fixed but a part of the elastic The anelastic strain is usually only 2 to 5% of
strain is replaced with inelastic strain. the elastic strain. [Rl, R3] It also influences the
Young's modulus; therefore, the dynamic modulus
Examples of stress relaxation are: is called the unrelaxed modulus while the static
modulus is the relaxed modulus.
a) loss of preload of a bolt in a rigid flange,
b) decrease of residual stresses, and The anelastic strain can be out of phase with
c) stress redistribution in a component with complex the stress and it will contribute to internal heating
geometry. during fatigue at high frequencies. P*4]
This book compiles stress relaxation data for
metals and alloys over a range of temperatures and 2. 2 Plastic strain, «p , is the permanent strain
initial stresses. A comparison of the 1000-hour re- measured when a material is loaded to a stress
laxation strength for several classes of alloys has above the elastic limit and then unloaded. Since the
been shown in Figure 1. This comparison was made elastic limit is a function of the strain rate and the
on an approximately equal basis in the earlier ASTM temperature, this strain for a given stress is also
compilation. [D1]* Relaxation characteristics of affected. The plastic strain range for a cyclic stress
materials, methods of testing, and the utilization of range is the difference between the strain range and
relaxation data are reviewed in subsequent sections the elastic strain range.
of this Introduction.
2. 3 Mlcroplastic strain, ^p , is the transient
strain for an applied stress and is not fully recov-
ered when the stress is reversed. • ^J Together
with the anelastic strain, it accounts for the time-
2. Relaxation Mechanics dependent strain observed below the macro-yield
stress and the recovery on stress reversal. The
effects of temperature and strain-rate sensitivity
In the stress relaxation process, the total strain on this strain are similar to those for the plastic
is constant and the stress reduction at constant tem- strain, but the magnitude of the mlcroplastic strain
perature occurs as elastic strain is converted to an is usually only 5 to 15% of the elastic strain and
inelastic strain. The types of inelastic strains des- reaches a finite limit at temperatures, T , below
cribed below are due to anelasticity, plasticity, 0. 4 of the absolute melting temperature, T , of
m
microplasticity, and creep. a material. Since this strain reaches a limit, it
will not be referred to as "creep" which is des-
2.1 Anelastic strain. ea , is the transient strain for cribed below for temperatures above 0. 4 T , al-
m
a stress change and it is recovered when the stress though it contributes to "primary" creep and re-
change is reversed. P* 1] * covery. [R6J D26]
* References with a prefix "D" are from the Data Sources listed in Section 8. Those with a prefix "R" are
listed under "References" in Section 6.
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2.4 Creep. For temperatures above 0.4 T , the initial stress minus the remaining (residual) stress
m
thermal activation enhances the flow mechanisms. during a stress-relaxation test. Tension tests have
Creep is defined as the time-dependent deformation the advantage that the stress can be measured eas-
under applied stress, <j , which persists with time. ily and the gage length can be larger for better sen-
Under constant stress or load, three stages of creep sitivity in maintaining constraint with a given exten-
are identified for many materials: Primary, Secon- someter. The relaxation test can be performed by
dary, and Tertiary. differing loading procedures:
2.4.1 Primary creep strain, «„ , is the limited a) Initial stress at test temperature,
strain which occurs (after loading) with a diminish- b) Initial total strain at test temperature,
ing rate; £o can encompass some of the mechanisms c) Initial total strain at room temperature,
described above. This limited strain has been ex- followed by heating to a peak test tempera-
pressed as :[R7»8] ture for a time period,
d) Repeated loadings to selected stress"levels,
£o = A[exp(-B/T)] ( o/ a0 )* [1 - exp(-Ct)], e) Holding at a given strain in a cyclic stress-
strain loop.
where t is the time and A, B, C , "o and m are
constants. The most common test employed to determine
the stress-relaxation characteristics of materials
2.4.2 Secondary creep, ' , accumulates at a creep is the tension test of a specimen with uniform cross
t
rate, j , as long as a stress is applied. This strain, section, instrumented with a sensitive extensometer,
therefore, is: and employing procedure (a) above. When an initial
e«= ft dt strain results from service displacements, proced-
ure (b) can be used to approximate service constraint.
where k is a function of stress and temperature for a
material in a given metallurgical state. Many mech- Procedure (c) simulates the loading of a bolt at
anisms of creep have been postulated^" ^J; one based room temperature and the subsequent relaxation af-
on a diffusion process is: ter elevated service temperature is reached. This
type of loading is used in measuring stress relaxa-
k = a[exp(-Qc/kT)] Sinh ( ° /ae ), tion by the compliance method. [D 70] jn many bolted
where Q is the activation constant for creep, a can flanges, multiple tightenings are employed to prevent
c 0
be a function of temperature, T, and a and * are leakage. Design data for frequency of tightening can
constants. be obtained for a given material from tests using
procedure (d).
2.4.3 Tertiary creep is one of increasing creep rate
above the minimum secondary rate, up to rupture. It The "Bauschinger effect" demonstrates that after
is a result of the damage processes which accompany initiating flow in a forward direction, the flow stress
the accumulated strain. The concern here is the re- in the reverse direction is lower. Therefore, the re-
duction of local ductility which can occur in some ma- laxation characteristics depend on the inelastic strain
terials under high constraint, especially multiaxial history. P^TI Reverse straining can occur from
stress[R9> 10, 11]. An example is "stress relax- thermal transients; this type of loading can be studied
ation cracking" or "reheat cracking"[»12] when re- by procedure (e). fD 106]
sidual stresses in welds are relaxed.
The ASTM recommended practice suggests that
the preferred method of relaxation testing should be
similar to that of the intended application of the data.
Thus, bending, torsion and compression data are
3. Stress Relaxation Testing identified in this compilation.
Research on stress relaxation has been dictated
by the following goals:
4. Analyses of Data
1. Design data for bolting and spring applications
2. Correlation of creep- and relaxation data
3. Fundamental studies for a given theory As indicated above, relaxation has been studied
4. Hold-time effects in creep-fatigue damage. to understand the mechanisms of flow, so that anal-
yses can be made for other loading histories or states
The American Society for Testing and Materials of stress. The major effort has been to determine a
has developed standard recommended practices for correlation between creep and relaxation data, so
stress-relaxation tests for materials and structures. that the contributions of the different types of strain
[R13] which allow comparison of data from different of Section 2 could be evaluated. The early researches
sources. The "relaxed stress" is defined there as the ofKanterf1*14] , Robinson[R14], Boyd[D17], DaVis
vi
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[D26], Johnson [D51], Oding [D75J and others have 4. 3 Loss of stress for a bar under constant total
been reviewed by Conway[R 16]. strain
4.1 Stress relaxation at temperatures below 0.4 T The relaxation of the stress in a bar under con-
m
stant total strain can result from a thermal expan-
The stress relaxation at temperatures below a- sion, inelastic flow, and metallurgical changes. The
bout 0. 4 T are a result of inelastic strains which initial stress may be a result of an external load or
m
after a time period reach a limit that is a function of displacement, or from a residual stress due to dif-
the initial stress and the temperature. These inelas- ferential plastic strains. Since the initial strain in
tic strains were described in Section 2, and are due the bar is constant, the stress is a product of the e-
to micro- and macro-plasticity and anelasticity. The lastic strain and the elastic modulus. This modulus
initial stress or strain can be induced in structures decreases with rising temperature; therefore, the
by fabrication loads or service thermal gradients. stress is reduced on heating. The initial stress under
simple tension can be as high as the flow stress for
An example of this relaxation limit is given in the initial total strain.
Figure 2 for an annealed Type 304 stainless steel for
which T is about 800 deg. F. The remaining stress The case for heating a bar of annealed Type 304
m
reaches a limiting value within 100 hours for tempera- stainless steel with an initial stress at room tempera-
tures up to 600 F (315 C) and 90% of this relaxation ture equal to the yield strength of 30 ksi ( 207 MPa)
takes place within 24 hours. The remaining stress is is illustrated in Figure 4. The top curve in that fig-
given in Figure 2 as a function of the initial stress. ure is the reduction of stress due to the change of the
This material at room temperature has significant modulus with temperature. The yield strength curve
relaxation which decreases with the initial stress. for a given strain rate is marked °Y. This strength is
Little relaxation is observed for stresses below about less than that due to the modulus change, wherefore
one-half of the yield strength for virgin monotonic plastic flow will occur on heating and the stress will
loading. At 600 F ( 315 C ) the amount of relaxation be reduced to a value near the yield curve. Since plas-
is greater than that above for a given initial stress, tic flow is initiated, stress relaxation further reduces
and no relaxation at stresses below one-half of the the stress to "the remaining stress for an initial stress
yield strength at this temperature. In this "lower" equal to the yield strength".
temperature range, sufficient stress must be applied
to initiate micro-plasticity. However, after a rever- Below 0.4 T this stress reaches a limit value
sed stress above the proportional limit ( lowest curve within 100 hours. The dashed and lowest curve indi-
in Figure 2) relaxation is observed for stress levels cates that if the initial stress is below this curve, no
below one-half of the yield strength and negative re- plastic flow is initiated and no relaxation will occur.
laxation ( increase in stress) may occur at low for-
ward stresses where the anelastic strain is domin- If the temperature is increased above 0.4 Tm,
ant. [R 17-19] creep will continue with time and the stress will re-
lax with time of exposure. In Figure 4 the zero-time
4.2 Stress relaxation at temperatures above 0. 4 Tm curve is shown as the yield strength curve; additional
curves are given for 100 and 1000 hours for tempera-
When creep strain is the dominate inelastic strain, tures up to 1300 F (704 C).
stress relaxation occurs continually with time and as
a function of the stress and temperature. The major- Similar curves can be generated for other mater-
ity of the data tabulated in this book are in this "higher" ials by utilizing the data of this book. For materials
temperature range, above 0.4 of the absolute melting which undergo a metallurgical change with time and
temperature. temperature, the stress relaxation will be modified.
If precipitation results in a volume decrease, the re-
For a structure which is given an initial strain, maining stress will increase for a time, whereas
the percent relaxation can be measured as a function volume increases ( such as irradiation swelling) will
of time at a given temperature, and the data analyzed cause an additional stress relaxation. Metallurgical
to generate constitutive relationships for interpolation changes also influence the creep strength and this in
and extrapolation. A parameter P = log t - H/(T -0.4 turn affects the rate of relaxation.
Tp,) gives good correlation for a cold-worked Type
304 stainless steel in the creep range. tD7l] The per- 4.4 Stress relief by relaxation
cent relaxation for specimens loaded to an initial 0.07
per cent strain and tested at several temperatures is The residual stress left in a structure from fab-
plotted as the solid curves in Figure 3. The dashed rication and processing can be detrimental in service
curves were obtained using the above parameter with because of corrosion, distortion, or reduction of the
the constant H being determined by the parameter me- fatigue and rupture strengths.
thod.
vii
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