Astm ds60 1982

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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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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

stress relaxation of metals and alloys of engineering

interest. It contains all data from the previous ASTM

Special Technical Publication No. 187, by the ASTMASME-MPC Joint Committee on Effect of Temperature

on the Properties of Metals.

This current project was sponsored by the Metal

Properties Council, Inc. under the guidance of its

Subcommittee 5 on Stress Relaxation. The data were

compiled and analyzed for the Subcommittee by Dr.

Howard R. Voorhees.

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 contributed services can take pride from the result.

The members of Subcommittee 5 of The Metal

Properties Council are as follows:

M.J. Manjoine, Chairman (Westinghouse

Research Laboratories)

S. F. Collis (Alcoa Research Laboratories)

S. G. Epstein (The Aluminum Association)

R. F. Gill (General Electric Company)

F. Kull (SPS Technologies, Inc.)

R. W. Swindeman (Oak Ridge National Lab.)

H. R. Voorhees (Materials Technology Corp.)

R. C. Westgren (Wean United Inc.)

R. E. Z inkham ( Reynolds Metals Company)

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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 Tm vii

4. 2 Stress relaxation at temperatures above 0.4 Tm vii

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

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Introduction

1. Stress Relaxation of Metals

and Alloys

A bar loaded to an initial stress of, say, 40,000

psi and then held at constant strain and temperature

may after a time period have a remaining stress of

only 30,000 psi. This time-dependent stress reduction of 10,000 psi is called stress relaxation. The

total strain remains fixed but a part of the elastic

strain is replaced with inelastic strain.

Examples of stress relaxation are:

a) loss of preload of a bolt in a rigid flange,

b) decrease of residual stresses, and

c) stress redistribution in a component with complex

geometry.

This book compiles stress relaxation data for

metals and alloys over a range of temperatures and

initial stresses. A comparison of the 1000-hour relaxation strength for several classes of alloys has

been shown in Figure 1. This comparison was made

on an approximately equal basis in the earlier ASTM

compilation. [D1]* Relaxation characteristics of

materials, methods of testing, and the utilization of

relaxation data are reviewed in subsequent sections

of this Introduction.

2. Relaxation Mechanics

In the stress relaxation process, the total strain

is constant and the stress reduction at constant temperature occurs as elastic strain is converted to an

inelastic strain. The types of inelastic strains described below are due to anelasticity, plasticity,

microplasticity, and creep.

2.1 Anelastic strain.

a , is the transient strain for

a stress change and it is recovered when the stress

change is reversed. P* 1] *

Anelasticity results from internal friction and

is a function of stress, o , stress rate, J , temperature, 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,a + a,5 = b,e + b2« ,

where o is the stress, e is the strain, and a and b

are constants.

The anelastic strain is usually only 2 to 5% of

the elastic strain. [Rl, R3] It also influences the

Young's modulus; therefore, the dynamic modulus

is called the unrelaxed modulus while the static

modulus is the relaxed modulus.

The anelastic strain can be out of phase with

the stress and it will contribute to internal heating

during fatigue at high frequencies. P*4]

2. 2 Plastic strain, «p , is the permanent strain

measured when a material is loaded to a stress

above the elastic limit and then unloaded. Since the

elastic limit is a function of the strain rate and the

temperature, this strain for a given stress is also

affected. The plastic strain range for a cyclic stress

range is the difference between the strain range and

the elastic strain range.

2. 3 Mlcroplastic strain, ^p , is the transient

strain for an applied stress and is not fully recovered when the stress is reversed. • ^J Together

with the anelastic strain, it accounts for the timedependent strain observed below the macro-yield

stress and the recovery on stress reversal. The

effects of temperature and strain-rate sensitivity

on this strain are similar to those for the plastic

strain, but the magnitude of the mlcroplastic strain

is usually only 5 to 15% of the elastic strain and

reaches a finite limit at temperatures, T , below

0. 4 of the absolute melting temperature, Tm, of

a material. Since this strain reaches a limit, it

will not be referred to as "creep" which is described below for temperatures above 0. 4 Tm , although it contributes to "primary" creep and recovery. [

6J 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 Tm, the

thermal activation enhances the flow mechanisms.

Creep is defined as the time-dependent deformation

under applied stress, <j , which persists with time.

Under constant stress or load, three stages of creep

are identified for many materials: Primary, Secondary, and Tertiary.

2.4.1 Primary creep strain, «„ , is the limited

strain which occurs (after loading) with a diminishing rate; £

o can encompass some of the mechanisms

described above. This limited strain has been expressed as:[R7»8]

o = A[exp(-B/T)] ( o/ a0 )* [1 - exp(-Ct)],

where t is the time and A, B,

constants.

C , "o and m are

2.4.2 Secondary creep, '

, accumulates at a creep

rate, j , as long as a stress is applied. This strain,

therefore, is:

«= ft dt

where k is a function of stress and temperature for a

material in a given metallurgical state. Many mechanisms of creep have been postulated^" ^J; one based

on a diffusion process is:

k = a[exp(-Qc/kT)] Sinh ( ° /ae ),

where Qc is the activation constant for creep, a0 can

be a function of temperature, T, and a and * are

constants.

2.4.3 Tertiary creep is one of increasing creep rate

above the minimum secondary rate, up to rupture. It

is a result of the damage processes which accompany

the accumulated strain. The concern here is the reduction of local ductility which can occur in some materials under high constraint, especially multiaxial

stress[R9> 10, 11]. An example is "stress relaxation cracking" or "reheat cracking"[»12] when residual stresses in welds are relaxed.

3. Stress Relaxation Testing

Research on stress relaxation has been dictated

by the following goals:

1. Design data for bolting and spring applications

2. Correlation of creep- and relaxation data

3. Fundamental studies for a given theory

4. Hold-time effects in creep-fatigue damage.

The American Society for Testing and Materials

has developed standard recommended practices for

stress-relaxation tests for materials and structures.

[R13] which allow comparison of data from different

sources. The "relaxed stress" is defined there as the

initial stress minus the remaining (residual) stress

during a stress-relaxation test. Tension tests have

the advantage that the stress can be measured easily and the gage length can be larger for better sensitivity in maintaining constraint with a given extensometer. The relaxation test can be performed by

differing loading procedures:

a) Initial stress at test temperature,

b) Initial total strain at test temperature,

c) Initial total strain at room temperature,

followed by heating to a peak test temperature for a time period,

d) Repeated loadings to selected stress"levels,

e) Holding at a given strain in a cyclic stressstrain loop.

The most common test employed to determine

the stress-relaxation characteristics of materials

is the tension test of a specimen with uniform cross

section, instrumented with a sensitive extensometer,

and employing procedure (a) above. When an initial

strain results from service displacements, procedure (b) can be used to approximate service constraint.

Procedure (c) simulates the loading of a bolt at

room temperature and the subsequent relaxation after elevated service temperature is reached. This

type of loading is used in measuring stress relaxation by the compliance method. [D 70] jn many bolted

flanges, multiple tightenings are employed to prevent

leakage. Design data for frequency of tightening can

be obtained for a given material from tests using

procedure (d).

The "Bauschinger effect" demonstrates that after

initiating flow in a forward direction, the flow stress

in the reverse direction is lower. Therefore, the relaxation characteristics depend on the inelastic strain

history. P^TI Reverse straining can occur from

thermal transients; this type of loading can be studied

by procedure (e). f

106]

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

identified in this compilation.

4. Analyses of Data

As indicated above, relaxation has been studied

to understand the mechanisms of flow, so that analyses can be made for other loading histories or states

of stress. The major effort has been to determine a

correlation between creep and relaxation data, so

that the contributions of the different types of strain

of Section 2 could be evaluated. The early researches

ofKanterf1

14] , Robinson[R14], Boyd[D17], DaVis

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[

D26], Johnson [

D51], Oding [

D75J and others have

been reviewed by Conway[R 16].

4.1 Stress relaxation at temperatures below 0.4 Tm

The stress relaxation at temperatures below about 0. 4 Tm are a result of inelastic strains which

after a time period reach a limit that is a function of

the initial stress and the temperature. These inelastic strains were described in Section 2, and are due

to micro- and macro-plasticity and anelasticity. The

initial stress or strain can be induced in structures

by fabrication loads or service thermal gradients.

An example of this relaxation limit is given in

Figure 2 for an annealed Type 304 stainless steel for

which Tm is about 800 deg. F. The remaining stress

reaches a limiting value within 100 hours for temperatures up to 600 F (315 C) and 90% of this relaxation

takes place within 24 hours. The remaining stress is

given in Figure 2 as a function of the initial stress.

This material at room temperature has significant

relaxation which decreases with the initial stress.

Little relaxation is observed for stresses below about

one-half of the yield strength for virgin monotonic

loading. At 600 F ( 315 C ) the amount of relaxation

is greater than that above for a given initial stress,

and no relaxation at stresses below one-half of the

yield strength at this temperature. In this "lower"

temperature range, sufficient stress must be applied

to initiate micro-plasticity. However, after a reversed stress above the proportional limit ( lowest curve

in Figure 2) relaxation is observed for stress levels

below one-half of the yield strength and negative relaxation ( increase in stress) may occur at low forward stresses where the anelastic strain is dominant. [R 17-19]

4.2 Stress relaxation at temperatures above 0. 4 Tm

When creep strain is the dominate inelastic strain,

stress relaxation occurs continually with time and as

a function of the stress and temperature. The majority of the data tabulated in this book are in this "higher"

temperature range, above 0.4 of the absolute melting

temperature.

For a structure which is given an initial strain,

the percent relaxation can be measured as a function

of time at a given temperature, and the data analyzed

to generate constitutive relationships for interpolation

and extrapolation. A parameter P = log t - H/(T -0.4

Tp,) gives good correlation for a cold-worked Type

304 stainless steel in the creep range. t

D7l] The percent relaxation for specimens loaded to an initial 0.07

per cent strain and tested at several temperatures is

plotted as the solid curves in Figure 3. The dashed

curves were obtained using the above parameter with

the constant H being determined by the parameter method.

4. 3 Loss of stress for a bar under constant total

strain

The relaxation of the stress in a bar under constant total strain can result from a thermal expansion, inelastic flow, and metallurgical changes. The

initial stress may be a result of an external load or

displacement, or from a residual stress due to differential plastic strains. Since the initial strain in

the bar is constant, the stress is a product of the elastic strain and the elastic modulus. This modulus

decreases with rising temperature; therefore, the

stress is reduced on heating. The initial stress under

simple tension can be as high as the flow stress for

the initial total strain.

The case for heating a bar of annealed Type 304

stainless steel with an initial stress at room temperature equal to the yield strength of 30 ksi ( 207 MPa)

is illustrated in Figure 4. The top curve in that figure is the reduction of stress due to the change of the

modulus with temperature. The yield strength curve

for a given strain rate is marked °Y. This strength is

less than that due to the modulus change, wherefore

plastic flow will occur on heating and the stress will

be reduced to a value near the yield curve. Since plastic flow is initiated, stress relaxation further reduces

the stress to "the remaining stress for an initial stress

equal to the yield strength".

Below 0.4 T this stress reaches a limit value

within 100 hours. The dashed and lowest curve indicates that if the initial stress is below this curve, no

plastic flow is initiated and no relaxation will occur.

If the temperature is increased above 0.4 Tm,

creep will continue with time and the stress will relax with time of exposure. In Figure 4 the zero-time

curve is shown as the yield strength curve; additional

curves are given for 100 and 1000 hours for temperatures up to 1300 F (704 C).

Similar curves can be generated for other materials by utilizing the data of this book. For materials

which undergo a metallurgical change with time and

temperature, the stress relaxation will be modified.

If precipitation results in a volume decrease, the remaining stress will increase for a time, whereas

volume increases ( such as irradiation swelling) will

cause an additional stress relaxation. Metallurgical

changes also influence the creep strength and this in

turn affects the rate of relaxation.

4.4 Stress relief by relaxation

The residual stress left in a structure from fabrication and processing can be detrimental in service

because of corrosion, distortion, or reduction of the

fatigue and rupture strengths.

vii

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4.4.1 Thermal treatment

The discussion in 4.3 illustrated how thermal

exposure can reduce residual stresses and showed

how the data in this book can be used to evaluate the

magnitude of the reduction. Residual stresses can

be eliminated by reheat treatment but in some cases

this is not practical. Residual stresses may result

from differential thermal expansion in dissimilar

materials.

4.4.2 Mechanical and thermo-mechanical treatment

Residual stresses are self-equilibrated and can

be reduced by imposing for a short time a monotonic

uniform stress sufficiently high to cause plastic flow

in the volumes where the peak stresses are of the

same sign.

Since initiation of plastic flow in the forward direction lowers the yield stress in the reverse direction, cyclic straining with decreasing amplitude can

be employed to reduce residual stresses. This process is similar to that for demagnitization. In roller

leveling of plates or straightening of shafts, reverse

bending with decreasing amplitude can reduce the resudual stresses and redistribute the remaining ones

over the entire cross section so that they will selfequilibrate over a short distance.

Mechanical and thermo-mechanical methods are

used to add favorable residual stresses as well as to

remove distortions or residual stresses. Surface

compressive stresses improve fatigue strength and

can be produced by shot peening, autofrettage or

surface quenching

Shafts can be straightened by local heating techniques to reduce residual stresses or to induce residual stresses which improve the straightness.

Adequate residual bolt loads are required in

bolted assemblies subjected to vibratory loads to

prevent joint opening and the associated higher alternating stress on the bolt.

5.2 Press-fitted joints, springs, and clamps

Other types of assemblies for which the success

of a design depends on the analysis of the load or

interface pressure and its relaxation under service

loads and environment are: press-fitted joints,

springs, and clamps. Uniaxial tensile relaxation

data have been used in analyses of a cylinder on a

rigid shaft [R10] and of a rolled-in tube. [R20]

5. 3 Creep-fatigue damage

The stress-time history of a component for elevated temperature service can be very complex during start-up, operation and shut-down cycles. The

damages from stress and strain histories are a

function of the strain rate, stress state, temperature

and environment. [R 9> 10,11,21,22], However, the

stress redistrubution under multiaxial stresses can

be analyzed using uniaxial relaxation data. [R 22]

The strain damage during relaxation under multiaxial stress can be more severe for some materials. [R 10]

5. 4 Constitutive relationships

Constitutive equations for a material describe

the mechanical-thermal responses of plastic flow,

creep, stress relaxation, and cyclic strain. The

material models assume that the response can be

formulated for multiaxial stress states using effective stresses and strains, and that the time independent part can be separated from the time dependent

part. Relaxation data,^ therefore, are an important

portion of the data base for a material. Comparison

of the relaxation and creep data allow the assessment

of the comparative roles of transient and steady-state

creep in design and analysis. [D26; R8 and 22 J

5. Utilization of Stress Relaxation

Data

5.1 Bolting design.

A principal use of relaxation data is in the design of bolted structures. Leakage at bolted joints

of pressure retaining structures can be prevented

by adequate load of the bolts. The required preload

and the allowance for relaxation can be calculated

from the data presented here.

When a given bolt load is required to prevent

fretting and wear of interfaces, then the allowance

for relaxation must be calculated for the service

period.

6. References

R 1. Zener, C. Elasticity and Anelasticity, University of Chicago Press, Chicago (1948).

R2. LeMay, Iain, Principles of Mechanical Metallurgy, Elsevier North Holland, Inc., New York;

Oxford (1981).

R3. Hill, W. H. , Shimmin, D. L. , and Wilcox, B.A.,

"Elevated Temperature Dynamic Moduli of Metallic Materials", Proc. ASTM, Vol.61, (1961).

R4. Manjoine, M. J. and Landerman, E.I./'Techniques for Fatigue Testing and Extrapolation of

viii

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Fatigue Life for Austenitic Stainless Steels",

ASTM J. of Testing and Evaluation, May 1982.

R5. Microplasticity, C.J. McMahon, Ed., Advances

in Material Research, Vol. 2, John Wiley and

Sons, (1968.)

R6. Creep and Recovery, American Society for

Metals, Cleveland, OH, (1957)

R7. McVelty, P.G. , "Working Stresses for High

Temperature Service", Mech. Engrg. , Vol.

56, p. 149,(1934).

R8. Manjoine, M. J. and Mudge, W. L. , "Creep

Properties of Annealed Unalloyed Zirconium",

Proc. ASTM, Vol. 54,(1954), pp. 1050-1067.

R9. Manjoine, M. J. , "Multiaxial Stress and Fracture", Fracture, Vol. 3: Engineering Fundamentals and Environmental Effects", Academic

Press, New York, (1970).

RIO. Manjoine, M.J. ."Ductility Indicies at Elevated

Temperature", Trans. ASME, J. Engineering

Materials and Technology, Vol. 97, Apr. 1975.

Rll. Manjoine, M. J. ,"Elevated Temperature Mechanics of Metals", 1974 Symposium on Mechanical Behavior or Materials, Society of Material

Science, Kyoto, Japan, (1974).

R18. Swindeman, R. W., "Isocronous Relaxation

Curves for Type 304 Stainless Steel After

Monotonic and Cyclic Strain", ASTMJ. of

Testing and Evaluation, Vol. 2, p. 192,(1979).

R19. Davis, E. A., "Relaxation of a Cylinder on a

Rigid Shaft", Trans. .ASME. J. Applied Mech.,

Vol. 82, Paper No. 59-A-31.

R20. Davis, E.A., "Relaxation of Stress in a HeatExchanger Tube of Ideal Material", Trans.

ASME, Vol. 74, pp.381-385, Apr. 1952.

R21. ASME-MPC Symposium on Creep-Fatigue

Interaction, MPC-3, American Society of

Mechanical Engineers, New York, (1976).

R22. Henderson, J. and Snedden, J. O. , p. 163

in Advances in Creep Design: the A. E. Johnson

Memorial Volume, A.I. Smith and A. M. Nicolson Editors, Applied Science Publishers,

London, (1971).

R23. Lee.D. and Hart, E.W., "Stress Relaxation

and Mechanical Behavior of Metals", Met.

Trans. , Vol. 2, p. 1245, (1971).

R12. Meitzner, C. F. , "Cause and Prevention of

Stress-Relief Cracking in Quenched and Tempered Steel Weldments", Trans. ASME, J. of

Engrg. for Industry, Feb. 1972, pp. 336-342.

R13. "Standard Recommended Practices for StressRelaxation Tests for Materials and Structures",

Annual Book of ASTM Standards, E 328-72,

American Society for Testing and Materials,

Philadelphia, (1982).

R14. Kanter, J. J. , "Interpretation and Use of Creep

Results", Trans., ASM, Vol.24, p. 900, (1936).

R15. Robinson, E. L. , "The Resistance to Relaxation

of Materials at High Temperatures", Trans.

ASME, Vol. 61, p. 543, (1939),

R16. Conway, J.B. , Stentz, R. H. , and Berling,

J.T. , "Fatigue, Tensile, and Relaxation Behavior of Stainless Steels", formerly TID

26135, now available Mar-Test Inc. , 1245

Hillsmith Drive, Cincinnati, OH 45215.

R17. Krempl, E. , "An Experimental Study of RoomTemperature Rate-Sensitivity, Creep and Relaxation of AISI Type 304 Stainless Steel", J^_

Mech. Phys. Solids, Vol. 27, pp. 363-375,

Pergamon Press Ltd. , (1979).

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900 IOOO lira 1200 1300

Temperature, °F

Fig. 1 - Comparative 1000-hour relaxation strengths for several classes of alloys

1500

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Initial Stress, MPa

120 160

o\. Initial Stress, ksi

Fig. 2 - Relaxation of solution-annealed type 304 stainless steel

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(/) 01

L- *-»

"<5

100

I 1 I I | 1 1 I I | 1 1 I I | 1 1 I I | 1 TTT

Experimental

P=Log T-1260

_l I ''I ' I I I I I I I I I I | LJJ I I I I

1300° F

0.01 0.1 1 10

Time, hrs.

100 1000

Fig. 3 - Relaxation of a 20 % cold-worked type 304 stainless steel

from 900 to 1300°F (482 - 704°C) for an initial inelastic strain

of 0.07%

Xll

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