Astm stp 520 1973

It describes the high-temperature fatigue problem as a failure process in a notch in some structure involving nucleation and early growth at the notch root, high-strain crack propagation

FATIGUE AT

ELEVATED TEMPERATURES

A symposium presented at The University of Connecticut Storrs, Conn 18-23 June 1972

A E Carden, A J McEvJly, and C H Wells, editors

List price $45.50 04-520000-30

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( ~ BY AMERICAN SOCIETY FOR TESTING AND MATERIALS 1973 Library of Congress Catalog Card Number: 73-76958

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication

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Foreword

The symposium on Fatigue at Elevated Temperatures held at the Uni-

versity of Connecticut, Storrs, Connecticut, 18-23 June 1972 was organized

because of the growing importance of this topic Committee E-9 on Fatigue

of the American Society for Testing and Materials sponsored the sym-

posium in cooperation with the American Society of Mechanical Engineers

(Materials Division) and the American Society for Metals (Materials

Systems and Design Division) The Steering Committee for this symposium

consisted of L F Coffin, Jr., E G Ellison, M Gell, J C Grosskreutz,

H F Hardrath, G Jacoby, S S Manson, A J McEvily, E M Smith,

S Taira, and C H Wells

The purpose of the symposium was to provide a broad coverage of the

topic in its various aspects, as well as to provide an opportunity for the

presentation of the latest research findings The symposium was organized

on this basis, and this resultant publication is, therefore, of a tutorial as

well as a research nature

The contributions of the session chairmen for their capable performance

gratefully acknowledged These session chairmen were, J C Grosskreutz,

D Hoeppner, R Pelloux, C Laird, H F Hardrath, R Wetzel, R W

Stentz, W H Sharp, E Steigerwald, J W Pridgeon, F VerSnyder, R P

Wei, R Goldhoff, E Krempl, A E Carden, W H Tuppeny, Jr., W L

Greenstreet, A O Schaefer, and B Wei

The contributions of the authors and discussors are also gratefully

acknowledged The contribution of S R Crosby, graduate assistant,

Metallurgy Department, University of Connecticut, who prepared the

index, is likewise gratefully acknowledged

Related ASTM Publications

Probabilistic Aspects of Fatigue, STP 511 (1972),

Correlation of Substructure with the Elevated Temperature

Low-Cycle Fatigue of AISI 304 and 315 Stainless Steels

K D CHALLENGER A N D J MOTEFF

Discussion

Relationship Between Thermal Fatigue and Low-Cycle Fatigue

at Elevated Temperature SHUJI TAIRA

Discussion

Fatigue of Protective Metal Oxides in Combustion Chamber

Exhaust Gases g R DILS

Effects of Frequency and Environment on Fatigue Crack

Growth in A286 at 1100 F H D SOLOMON AND L F

COFFIN, JR

Discussion

Extent to Which Material Properties Control Fatigue Failure at

Elevated Temperatures J WAREING, B TOMKINS, AND G

SUMNER

Discussion

Temperature Dependence of Fatigue Crack Propagation in an

A1-2.6Mg Alloy F JEGLIC, P NIESSEN, AND D J BURNS

Discussion

Derivation of a Failure Law for Creep Under a Cyclic Stress

J A WILLIAMS

Creep-Fatigue Interaction During Crack Growth P N

ATANMO AND A J MCEVILY, JR

Discussion

Thermal-Mechanical Fatigue Crack Propagation in Nickel- and

Cobalt-Base Superalloys Under Various Strain-Tempera-

ture Cycles c A RAU, JR., A E GEMMA, AND G R

Threshold for Fatigue Crack Growth in Ferritic Steels at 300

C L P POOK AND A A BEVERIDGE

General Discussion on Mechanisms of Fatigue

Test Methods

Fatigue at Elevated Temperatures: A Review of Test Methods

A E CARDEN

Discussion of the Test Method and Equipment for the Evalua-

tion of Low-Cycle Creep-Fatigue Failure Criteria

R M SCHNEIDEROVITCH AND A P GUSENKOV

High-Temperature Fatigue Testing of Automotive Valve Steels

- - E T VITCHA

Discussion

Evaluation of Thermal Fatigue Resistance of Metals Using the

Fluidized Bed Technique u g H HOWLS

Discussion

Thermoacoustic Fatigue Testing Facility for Space Shuttle

Thermal Protection System c E RUCKER AND R E

GRANDLE

Fatigue of Supersonic Transport Materials Using Simulated

Flight-by-Flight Loading L A IMIG

Ultrasonic Fatigue in Steam with Small Amounts of Sodium

C h l o r i d e - - A F CONN AND N k NIELSEN

General Discussion on Test Methods

Materials

Fatigue in the Design of High-Temperature Alloys H F

MERRICK, D H MAXWELL, AND R C GIBSON

Discussion

Effects of Grain Size and Temperature on the Cyclic Strength

and Fracture of Iron H ABDEL-RAOUF, T H TOPPER,

AND A PLUMTREE

Discussion

Creep Testing of Alpha Iron During Thermal Cycling D

EYLON, D G BRANDON, AND A ROSEN

CONTENTS vii

High-Strain Fatigue Properties of Cast 1/zCr-Mo-V Steels

W J ELDER, J B MARRIOTT, AND M C MURPHY

Discussion

Effect of Carbon Content on High-Temperature Properties of

2x/~Cr-lMo Steels R R SEELEY AND R H ZEISLOFT

Discussion

Fatigue Crack Propagation in Steel Alloys at Elevated Tempera-

tures H I MCHENRY AND A W PENSE

Low-Cycle Fatigue Behavior of Types 304 and 316 Stainless Steel

at L M F B R Operating T e m p e r a t u r e - - c F CHENG, C Y

CHENG, D R DIERCKS, AND R W WEEKS

Discussion

Combined Low-Cycle Fatigue and Stress Relaxation of Alloy

800 and Type 304 Stainless Steel at Elevated Tempera-

t u r e s - - c E JASKE, H MINDLIN, AND J S PERRIN

Discussion

Effects of Combined Creep and Fatigue Loading on an Austen-

itic Stainless Steel at High T e m p e r a t u r e - - w E WHITE,

R I COOTE, AND I LE MAY

Discussion

Fatigue Crack G r o w t h Characteristics of Several Austenitic

Stainless Steels at High Temperature R SHAHINIAN,

H H SMITH, AND H E WATSON

Discussion

Effect of Several Metallurgical Variables on the Thermal

Fatigue Behavior of Superalloys o n BOONE AND

C P SULLIVAN

Discussion

Thermal Fatigue Characterization of Cast Cobalt and Nickel-

Base Superalloys D F MOWBRAY, D A WOODFORD,

AND D E BRANDT

Discussion

High-Cycle Fatigue Properties of a Dispersion Strengthened

Nickel-Base Superalloy J H WEBER AND M J aOMFORD

Discussion

Effect of Mean Stress on the High-Cycle Fatigue Behavior of

Udimet 710 at 1000 F D M MOON AND G P SABOL

viii CONTENTS

Bend Fatigue of Two Iron-Nickel-Base Superalloys at Elevated

Temperature A J OPINSKY

Combined Creep-Fatigue Behavior of Inconel Alloy X-750

P K VENKITESWARAN, D C FERGUSON, AND D M R

TAPLIN

Discussion

Low-Cycle Fatigue with Combined Thermal and Strain Cycling

- - U S LINDHOLM AND D L DAVIDSON

Low-Cycle Fatigue Behavior of Zircaloy at 573 K R R

HOSBONS

Discussion

Thermal Fatigue Behavior of T - I l l and ASTAR 811C in

Ultrahigh Vacuum K D SHEFFLER AND G S DOBLE

Effect of Interrupting Fatigue by Periods of Heat for Aluminum

Alloy Structural Elements J R HEATH-SMITH AND F E

KIDDLE

Discussion

Test Results of Fatigue at Elevated Temperatures on Aeronauti-

cal Materials G P VIDAL AND P L GALMARD

Effect of Surface Integrity on Fatigue of Structural Alloys at

Elevated Temperatures P.S PREVEY AND W P KOSTER

Thermal Ratchetting

Review of Thermal Ratchetting DAVIO BURGREEN

Discussion

Ratchetting Under Cyclic Axial Strain with Torsional Stress

H YAMANOUCHI, Y ASADA, AND Y WAKAMATSU

Discussion

Analytical and Experimental Study of Thermal Ratchetting

A V A SWAROOP AND A J MCEVILY, JR,

Discussion

Lifetime Predictions and Design

Predicting Service Life in a Fatigue-Creep Environment E (3

ELLISON AND E M SMITH

Discussion

A Realistic Model for the Deformation Behavior of High-

Temperature Materials A K MILLER

CONTENTS ix

Ductility Exhaustion Model for Prediction of Thermal Fatigue

and Creep Interaction J r POLHEMUS, C E SPAETH,

AND W H VOGEL

Discussion

Strain Rate and Holdtime Saturation in Low-Cycle Fatigue:

Design-Parameter P l o t s - - j B CONWAY, J T BERLING,

AND R H STENTZ

Discussion

Comparison of Experimental and Theoretical Thermal Fatigue

Lives for Five Nickel-Base Alloys D A SPERA

Discussion

Temperature Effects on the Strainrange Partitioning Approach

for Creep Fatigue Analysis G R HALFORD, M ft

HIRSCHBERG, AND S S MANSON

Discussion

Kinetic Deformation Criteria of Cyclic Fracture at High Tem-

perature s V SERENSEN, R M SCHNEIDEROVITCH~ AND

AND A P GUSENKOV

Method for Low-Cycle Fatigue Design Including Biaxial Stress

and Notch Effects D c GONYEA

Some Considerations of the Application of Cyclic Data to the

Design of Welded Structures B J L DARLASTON AND

D J WALTERS

Elevated Temperature Test of Welded Furnace Wall Sections

C W LAWTON AND J E BYNUM

Parametric Study to Establish Design Curves and to Evaluate

Design Rules for Ratchetting T R BRANCA AND J L

MCLEAN

Nondestructive Testing in Fatigue: A 1972 Update R B socKY

Codes: Asset or Liability -w E COOPER

The Challenge to Unify Treatment of High Temperature

Fatigue A Partisan Proposal Based on Strainrange

STP520-EB/Aug 1973

Introduction

An increase in the efficiency of a power generating unit, in the rate of

an industrial chemical process, or in the speed of supersonic aircraft, have

in c o m m o n an association with an increase in temperature The technologi-

cal advances, required to obtain such performance increases, are largely

dependent upon the development of new materials and design methods for

structures capable of withstanding the rigors of elevated temperature

service However, before these developments can be put into practice, it is

necessary that the materials be thoroughly characterized with respect to

resistance to stress, temperature, and environment, and that the reliability

of associated design procedures be established These are both formidable

tasks of the utmost importance, especially where long-time service exper-

ience is lacking Consider, for example, the problems associated with the

design of a nuclear reactor c o m p o n e n t of a relatively new alloy which is

expected to be in service at elevated temperatures for forty years or more

Such a design can be made reliable only after the response of the alloy for

the service conditions has been quantified

In addition to this trend toward higher operating temperatures there is

also a trend toward more efficient and economical design This latter goal

can only be achieved through an understanding of the load-structure-stress-

strain-temperature-environment-material interactions Whereas in the past

creep behavior at elevated temperatures may have been the principal

consideration, experience has shown that, in fact, fatigue may often be the

controlling factor All aspects of the fatigue process are modified in the

creep range Mechanisms of crack initiation and growth, test methods,

lifetime predictions, and design methods all are changed In addition new

factors are introduced such as thermal fatigue, thermal ratchetting, and

stress relaxation Each of these serves to make fatigue at elevated tempera-

tures a very complex subject, but it is this very complexity which offers a

challenge to researchers and design engineers concerned with creep-

fatigue interaction

The present volume is intended to provide a comprehensive overview of

this subject, as well as to provide current research findings in four major

subareas:

1 Mechanisms: The processes of crack initiation and growth leading to

creep-fatigue failure

2 Test Methods: The techniques for carrying out elevated temperature

fatigue tests and for analyzing the resultant data

2 INTRODUCTION

3 Materials: A review of the alloys used in elevated temperature creep-

fatigue design, together with the latest data on their properties

4 Prediction Methods and Thermal Ratchetting: A review of current

approaches to creep-fatigue lifetime predictions, including thermal ratchet-

ring, and a consideration of code design procedures and emerging design

philosophies

It is expected that the information contained in this volume will be of use

to metallurgists, materials test engineers, and designers who are concerned

with this important problem It is hoped that interaction between the

various disciplines involved will be promoted, and that this volume will

serve as an impetus for rapid advance in the field of fatigue at elevated

temperatures

L F Coffin, Jr a

Fatigue at High Temperature

REFERENCE: Coffin, L F., Jr., "Fatigue at High Temperature," Fatigue at

Elevated Temperatures, 4STM STP 520, American Society for Testing and

Materials, 1973, pp 5-34

ABSTRACT: This report was prepared as the keynote address given at the 1972

Symposium on Fatigue at Elevated Temperatures at the University of Connecticut,

18-23 June, 1972 It describes the high-temperature fatigue problem as a failure

process in a notch in some structure involving nucleation and early growth at the

notch root, high-strain crack propagation through the plastic zone of the notch,

and elastic crack growth to ultimate failure Several of the important disciplines

bearing on these three steps in the failure process are discussed Particular atten-

tion is given to a description of the high-temperature phenomenology, distinctions

between high- and low-cycle fatigue effects at high temperature, failure criteria

including frequency and holdtime effects, the importance of the environment vis-a-

vis creep in considering time effects on fatigue behavior, high-strain crack propaga-

tion, elastic crack growth, ratchetting effects, and methods for treating notches

KEY WORDS: fatigue (materials), thermal fatigue, fatigue failure, crack initia-

tion, crack propagation, transgranular corrosion, intergranular corrosion, plastic

deformation, elastic deformation, stress analysis

Fatigue at elevated t e m p e r a t u r e s m a y have different m e a n i n g s t o each

p e r s o n w h o e n c o u n t e r s the problem, d e p e n d i n g on their previous training,

c u r r e n t interests, a n d professional responsibilities His w o r k m a y involve

him in a n a r r o w p a r t o f the p r o b l e m f o r which he seeks highly specific

answers, whether it be the u n d e r s t a n d i n g o f fatigue crack initiation, or the

d e t e r m i n a t i o n o f the design life o f a pressure vessel By publishing this

s y m p o s i u m on fatigue at elevated temperatures, the m a n y viewpoints will

be presented so t h a t the reader m a y b r o a d e n his perspective a n d tackle his

w o r k with a b r o a d e r vision

T o e n c o u r a g e a b r o a d e r a p p r e c i a t i o n o f the p r o b l e m a n d t o a t t e m p t to

lower the c o m m u n i c a t i o n barriers, it is a p p r o p r i a t e t o consider the several

physical aspects o f the p r o b l e m , a n d to examine the m a n y disciplines that

are b r o u g h t to bear either to u n d e r s t a n d the problem, to prevent it f r o m

o c c u r r i n g , t o design a r o u n d its complexities, or t o live with it R e f e r r i n g t o

Fig 1, we imagine an engineering structure c o n t a i n i n g a notch T h e struc-

1 Metallurgy and Ceramics Laboratory, General Electric Co., Research and Develop-

ment Center, Schenectady, N Y 12301

5

FIG l Schematic view of high-temperature fatigue problem showing physical stages

in failure process and relevant disciplines

ture might be a turbine rotor, or a pressure vessel, loaded centrifugally, or

by internal pressure, and it presumably has some temperature gradient

acting in the notch region The centrifugal, pressure, or thermal stresses are

cycled, most commonly from zero to tension by start-stop or load-unload

operation of the equipment We then envisage the fatigue process to occur

in three stages: first, nucleation and early growth of cracks within the

plastic zone developed at the notch root; second, crack propagation of a

stable crack through the plastic zone; third, propagation of the crack

through the elastic zone, the crack generating its own plastic zone, until

fracture of the structure results, either by sudden fracture, leakage, or by

excess vibration or deformation These stages are shown in Fig 1

Also in Fig 1 we identify some of the many disciplines which must be

brought to bear on the problem Consider first the plastic zone Identifica-

tion of the appropriate stresses and strains are required through analytical

tools, such as finite element analyses This requires the selection of appro-

priate material information and constitutive equations, heat transfer

analysis, etc With the aid of appropriate failure criteria, the conditions for

the occurrence of microcracks or for nucleation and early growth can be

specified Elastoplastic analysis further aids in the specification of condi-

tions for crack growth through the plastic zone, again coupled with an

appropriate fracture criterion Finally, elastic stress analysis and fracture

mechanics concepts allow the determination of crack growth in the elastic

regime

Along the way we can identify several additional disciplines Included are

environmental effects on nucleation and growth, manufacturing techniques

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for surface preparation in the critical area, choice of material, testing

methods for developing failure criteria, low-cycle fatigue studies, develop-

ment of high- and low-strain crack growth rules, time dependency, frac-

tography, etc Groups of these and other disciplines are lumped together

into such activities as life prediction, design, code development, etc There

is also a whole structure of disciplines directed towards other aspects of the

problem such as metal physics, corrosion and electrochemistry, physical

and process metallurgy, statistics, and others

To obtain some semblance of order among this confusion of disciplines,

it is necessary to keep the physical picture of the problem in mind Too

often, in the interest of obtaining answers, we forget that fatigue failure is

progressive, starting from a single grain or microscopic flaw, gradually

growing to a size where it compromises the integrity of the structure Our

models or criteria should be continually examined to be sure that, indeed,

the physical aspects of the phenomenon have not been lost sight of, or

better yet, are the building blocks for the model or criterion The present

paper is presented with this thought in mind

Plastic Zone and Its Relationship to Low-Cycle Fatigue

The various stages of the fatigue process just described are represented in

Fig 1 Important in this model is (a) an analytical knowledge of the defor-

mation state within the plastic zone and (b) the establishing of a failure

criterion for crack initiation and early growth in terms of the strains so pro-

duced in this zone To be as quantitative as possible it is desirable to have a

complete elastoplastic solution for stresses and strains in the vicinity of the

notch Although rigorous constitutive equations are lacking for such

calculations a recent approach by Mowbray and McConnelee [1,2] 2

appears attractive in attacking this problem They utilize a finite element

analysis where constitutive equations are derived from families of "iso-

cycle" stress-strain curves converted to effective stress-strain curves to

construct a complete stress-strain representation within the plastic zone

Figure 2 shows a typical solution for a notch of Kt = 3.46, and indicates the

plastic zones for various average net section stress amplitudes It would

appear that the analytical tools for treating complex geometries are

developing more rapidly than concomitant material laws [3]

The fatigue literature contains numerous references in which the stabi-

lized or steady-state stress-strain curve is similarly utilized to establish the

local strain distribution at the notch root [4-6] Notch root strains are

commonly and simply determined by the Stowell [7] or Neuber [8] formu-

lation The applicability of these methods to high-temperature problems

will be discussed later

As a result of repeated cyclic plastic strain in the plastic zone microcracks

nucleate and grow to some observable size at the free surface One way to

2 T h e italic n u m b e r s in brackets refer to the list o f references a p p e n d e d to this paper

F I G 2 Progesssion of plastic flow in grooved cylinder test specimen of 21/+Cr-lMo

steel by finite element stress analysis [1 ]

simulate this situation is to imagine a low-cycle fatigue specimen located

as in Fig 1 such that its minimum cross section is some fraction of the

plastic zone Provided suitable corrections are introduced to account for

the different stress states, fatigue failure of this specimen can be made to

approximate the nucleation and early growth of cracks in the c o m p o n e n t

of Fig 1 There is, however, a size and strain gradient problem since, in the

test specimen, the crack is initiated and grows in a uniform strain field to

some fraction of the cross-sectional area, while in the plastic zone this same

process occurs in a strain gradient Hence the concept o f " s m o o t h specimen

s i m u l a t i o n " - - a s M o r r o w et al [9] have named it is sound provided the

plastic zone is sufficiently large relative to the minimum diameter of the

standard low-cycle fatigue test (~-~0.25 in.) and the strain gradient is

acceptably small F o r smaller plastic zones, either proportionally smaller

fatigue specimens, or earlier indications of failure in standard size speci-

mens are required By these arguments, and with the assumption that the

plastic zone of our structure (Fig 1) is large relative to the test specimen,

we can insert the massive volume of low-cycle fatigue information as a

critical link in the chain of events leading to structural fatigue failure

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The foregoing logic may be further generalized with respect to sorting out

specific aspects of the fatigue problem Assuming that the physical picture

is as shown in Fig 1, the usefulness of low-cycle specimen fatigue is clearly

that of determining the nucleation and early growth characteristics of a

metal, a process otherwise difficult to represent quantitatively in our present

state of understanding On the contrary, high-cycle fatigue specimen

testing is, in reality, the combination of all the processes described in

Fig 1 nucleation and early growth, propagation in the plastic zone of the

stress concentration, and stable crack growth a confusion of phenomena

The separation of the study of stable crack growth into a separate discipline,

such as has occurred in recent years, seems fully justified from physical

considerations It is important that this phenomenon be closely related to

the specifics of engineering structures by such methods as linear elastic

fracture mechanics, crack opening displacements, etc Despite the con-

fusion of phenomena, interpretations and failure criteria derived from

total failure information in high-cycle fatigue specimen tests are probably

most useful for the definition of crack nucleation

High-Temperature Low-Cycle Fatigue Testing Methods

From the above rationale we can justify the uniaxial fatigue test as an

appropriate basis for providing both the deformation and fracture infor-

mation needed to establish criteria for crack initiation in real structures

Tests performed under fixed strain limits most closely approximate the

deformation behavior within the plastic zone, although the use of "Neuber

control" has been introduced [10] recently as an alternative approach in

notch geometries Experimental methods for controlled strain testing have

been extensively covered in the recent Manual on Low Cycle Fatigue Test-

with fatigue testing

There are certain techniques which are more significant to high-tempera-

ture fatigue testing than to room temperature Most important of these is

the consideration of time dependency This affects both the deformation

and fracture aspects of the testing program, because it is an important

ingredient of the deformation and fracture aspects of the structure (Fig 1)

Time, through creep or relaxation phenomena, redistributes the stress-strain

profiles in notches, or at crack tips, and consequently changes the stress or

strain inputs or both to our crack nucleation and early growth fracture

criterion Similarly time effects will strongly influence the failure process

as we shall discuss later in more depth Consequently, time is an important

factor in high-temperature fatigue testing and can be introduced through

consideration of strain rate, frequency, holdtimes, strain-range partitioning,

etc The role that it plays in the deformation and fracture process is contro-

versial, and some airing of this important topic will undoubtedly come

forth in this conference

This same matter of time dependency raises important questions of

interpretation from low initial cost testing methods such as bending or

torsion Introduction of holdtimes in these geometries leads to relaxation

processes that do not necessarily occur at constant total strain Nor, in fact

is it easy to ascertain just what the stress-strain-time relationships are in

such geometries Although more costly initially, experiments performed

with statistically determinate specimens under closed loop control gives

more interpretable and meaningful results which, in the long run, justifies

the initial equipment investment

It is instructive to discuss one particular problem that arises in diametral

strain control of hourglass shaped push-pull test specimens It has been

found in certain high-strength, low-ductility cast structures, such as the

nickel-base superalloys, that a pronounced and r a n d o m transverse strain is

produced under both elastic and plastic axial loads The effect is due to the

inherent anisotropy of the individual crystals in the structure and the

comparatively coarse grain size commonly used The behavior is seen in

Fig 3, where a circumferential traverse of the diametral strain is shown for

an as-cast test specimen at a fixed stress range To eliminate scatter in strain

measurements in testing materials of this type, after obtaining such a profile,

we locate two diametral extensometers 90 deg apart in such a position as to

give a response typical of the average transverse strain for the material in

, 0 , o Ro ,oo ,,o ,,o

DIAMETRAL ORIENTATION (DEG)

180

FIG 3 Diametral strain anisotropy in cast and single crystal nickel-base superalloys

under axial loading

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COFFIN ON FATIGUE AT HIGH TEMPERATURE 1 I

It is also interesting to observe in this figure the highly isotropic response

in transverse strain for a single crystal test specimen when the [100] growth

orientation is directed axially, and the highly anisotropic orientation for the

[110] orientation The transverse anisotropy phenomenon is obviously not

confined to cast or single crystal materials [12] nor to high temperature,

but it is particularly applicable to the widely used cast nickel-base super-

alloys

In our own testing work at high temperature, we evaluate the fatigue

behavior of materials not only at several strain ranges (usually with plastic

strain limits) but also at several frequencies For any one temperature a

minimum of nine tests are required three strains and three frequencies for

each strain These test results are then fitted to appropriate fatigue equations,

using a regression analysis procedure, from which six independent co-

efficients are found to characterize the stress range, strain range, and fre-

quency response of the material at the specific temperature selected A more

extensive development of this approach follows

Phenomenological Representation of High-Temperature Fatigue

Before discussing some of the significant aspects of high-temperature

fatigue, it is instructive to characterize the behavior from a phenomenologi-

cal viewpoint One such method employs observations made from controlled

strain range experiments on test specimens of the type shown in the plastic

zone of Fig 1 The work of Berling and Slot [13] on three stainless steels at

three temperatures and at different strains has been widely referenced and is

of value to display the phenomenological viewpoint by combining their

test results with high-temperature fatigue equations developed in recent

years [14-16] These fatigue equations are extensions of equations used for

low-temperature fatigue developed from a strain viewpoint [17,I8], where

the important effects of time are introduced by the frequency of cycling

The first of these equations relates the stress range, the plastic strain range

The quantity n' is the cyclic strain hardening exponent Using Berling and

Slot's data and some unpublished data obtained by our laboratory, the

cyclic stress-strain behavior of AISI 304 stainless steel, a commonly used

material in nuclear application, is shown in Fig 4 Here the frequency effect

is accounted for by rewriting Eq 1, through the combination of the stress

12 FATIGUE AT ELEVATED TEMPERATURES

J

430~ 944,000 0.486 -0.0301 6500C 214,C00 0.259 O.G~31 816"0 63,0O0 0.106 0.0534

F~ ASTIC STNAIN RANGE-~p

FIG 4 Representation of data of Berling and Slot [13] for AISI 304 stainless steel

by Eq 1, showing interaction of frequency and stress range on plastic strain range for several

temperatures

range and frequency, where the term A a v - k l is called the frequency modified

stress range Referring to Table 1, the coefficients of /1, n', and kz are given

It is seen that the cyclic strain hardening exponent decreases rapidly with

increasing temperature, as does A, while kl increases The negative value of

kl at 450 C implies some cyclic strain aging [15]

The use of frequency rather than strain rate for the high-temperature

cyclic stress-strain behavior is consistent with other fatigue equations

introduced in what follows It is, however, more common to use strain rate

in preference to frequency for quantifying high-temperature deformation

behavior, and this is easily done for a triangular waveform if the plastic

strain rate is defined as ~p = 2A~pu Equation 1 then becomes

A ~ = BA~v~,'~vm (2) where B = A / 2 k ~ , n~ = n ' - kz and m = k l Equation 1 or 2 may be useful

in analytical procedures for elastoplastic cyclic stress-strain solutions [1,2]

Further characterization of the high-temperature fatigue behavior can be

accomplished with the aid of two additional equations The first of these is

a high-temperature modification [ 1 4 - 1 6 ] of the low-temperature Coffin-

Manson equation, relating the plastic strain range, fatigue life, and fre-

quency of cycling,

:,~ = C~(N:v~-~)-~ (3) One form of this equation is shown in Fig 5, for AISI 304 stainless steel at

the three temperatures of interest Here the frequency and life are combined

into a term called the frequency-modified fatigue life, a useful parameter

for relating frequency of cycling and cycles to failure Figure 5 shows the

deleterious effect of temperature on fatigue life as expressed in terms of the

plastic strain range Note the increasingly negative slope with increasing

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14 FATIGUE AT ELEVATED TEMPERATURES

I

z 0.1

TENP, COOE

430" o AIR 650' * AIR

816" o AIR

~,,,.~ 816" 9 VACUUM

I I0 100 tO00 t0,000 tO0,O00

FREOUENCY MOOIFIED FATIGUE LIFE - Nfl/K-I

F I G 5 Representation o f data o f Berling and Slot [13] f o r A I S I 304 stainless steel by

Eq 5, showing plastic strain range versus frequency-modified fatigue life at several tempera-

lures in air Vacuum data at 816 C

temperature and the convergence at low life Similar behavior has been

found for several materials [19]

By eliminating the plastic strain range between Eqs 1 and 3, a high-

temperature form of the low-temperature Basquin equation [ 1 7 , 1 8 ] results,

o r

Ao" A'

where A' = A C 2 n', f3' = ~ n ' , k l ' = f 3 n ' ( k - 1) q- k~ A complete list of

coefficients for several materials found by regression analysis of test data

is given as Table 1 Equations 3 and 4 provide a handy way of representing

high-temperature fatigue, particularly when they are rewritten by com-

bining the strain range and frequency, such that ~epva(k-1) is called the

frequency modified plastic strain range, and AeeV-kl ' is the frequency

modified elastic strain range Using a representation for elastic and plastic

strain ranges suggested by Manson at low temperatures [20], we have

Fig 6, the frequency modified elastic and plastic strain ranges versus cycles

Eqs 3 and 4, showing frequency-modified elastic and plastic strain range at several tempera-

tures in air N~ is transition fatigue life

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to failure, for the three temperatures, 430, 650, and 816 C, for AISI 304

stainless steel

Several features arising from the increasing temperature on fatigue

phenomenology are observed in this figure We see the increasingly negative

slope and decreasing life of the plastic strain cycles to failure representation,

also observed in Fig 5 Increasing temperature and concomitant softening

causes a progressive decrease in the elastic strain (or stress range/elastic

modulus) With increasing temperature the transition fatigue life N t (the

life where the elastic and plastic strain ranges are equal) shifts to lower

values of life More will be said of this term at a later point Increasing

temperature is seen to have a small effect on the exponent/3'

F r o m an engineering design viewpoint the total strain range A~ is a more

commonly used quantity since from it the pseudostress range E2xe can be

derived The total strain range can be found analytically by combining

can be shown Letting k = 1, and k~ = 0, the frequency terms are eliminated

and if C2 = D ~ r = 0.6, n' = 0.2, and A = 3.5~,/D ~ Eq 5 transforms

to Eq 6 Since D is the true fracture strain and a~ is the ultimate strength,

some feeling for the several coefficients of Eq 5 can be established

Equation 5 can be used to show the effect of temperature and frequency

on the total strain fatigue behavior of metals at high temperature Using

AISI 304 stainless steel as an example, with the help of the coefficients of

Table 1, Fig 7 results Two frequencies are considered, 10 and 0.001 cpm,

and the three temperatures Note the increasingly strong frequency effects

as the temperature is raised Further, note the large difference in life at

intermediate strains F o r example at a strain of 0.003, the life at 10 cpm

decreases from 5 X 105 cycles to 7 X 10 ~, a 70 fold decrease, for a change

in temperature from 450 to 816 C At 0.001 cpm on the other hand the

lives are 5 X 105 and 260, a 1900fold decrease It should be pointed out

that this latter comparison is based on an extrapolation of test data to

lower frequencies on the assumption that the frequency exponents of Eq 5

are independent of frequency More will be said about the validity of this

assumption later

Close examination of Fig 7 shows a knee developing in the fatigue

curve as the temperature is increased This knee is a result of a shift or

transition in the dominant strain component of Eq 5 from plastic to elastic

16 FATIGUE AT ELEVATED TEMPERATURES

FIG 7 Representation o f data o f Berling and Slot [13] f o r A I S I 304 stainless steel by

Eq 5, showing total strain range versus cycles to failure f o r two frequencies at several tem-

peratures in air

strain at higher lives (say 10 5 cycles) as the temperature is raised This effect

is also apparent in Fig 6 The transition fatigue life characterizes this

behavior

T r a n s i t i o n F a t i g u e L i f e

Failure by low-cycle fatigue is commonly considered to occur for lives

less than 10 4 or 10 5 cycles This definition arose from early concern in the

low-cycle fatigue phenomenon for metals which were sufficiently ductile

that cyclic effects developed at lives in the order of 10 4 or 10 5 cycles Here

significant plastic strains occurred, and this led to a field of interest apart

from the more classical high-cycle phenomenology It is now apparent that

this definition of low-cycle fatigue is unsatisfactory, particularly when

lower ductility metals are considered from the low-cycle fatigue view and as

a more unified view of the entire fatigue spectrum develops A more

rational definition for separating the high- and low-cycle regimes should be

based on whether plastic effects are important, independent of the strength,

or ductility of the material F o r this reason the transition fatigue life is a

useful concept The transition fatigue life need not be defined as occurring

when the ratio of the plastic to elastic strains are equal; in fact, a ratio of

less than unity might be preferred for reasons to be discussed at a later point

Landgraf [18] has shown how the transition fatigue of steels is changed by

the hardness of the material It is seen by an examination of Fig 5 that

temperature also changes the transition fatigue life A quantitative ex-

pression for Nt can be derived by equating Eqs 3 and 4 Thus

COFFIN ON FATIGUE AT HIGH TEMPERATURE 17

Since ,4' is a measure of strength, C~ a measure of ductility, and 1/(/3' - t3)

is negative, increasing strength and decreasing ductility lower the transition

fatigue life Using the constants of Table 1, at a frequency v = 1 cpm, or

reading directly from Fig 4, Nt = 231 000, 7800, or 2800 cycles for tem-

peratures of 430, 650, and 815 C, respectively Substantially lower transition

fatigue has been found to occur for the cast nickel-base superalloys because

they combine high strength and low ductility For cast Udimet 500 at

816 C, it was found that N~ = 20 [16]

The importance of the knowledge of the transition fatigue life cannot be

overemphasized When compared to a specific life of interest it

distinguishes:

1 Method of testing the material

2 Analytical procedures for attacking the problem

3 Operating initiation and crack growth law

4 Degree to which mean stress and rachetting can be factored into the

problem

Referring to Fig 1, assume that Na is the design life for initiating a crack in

a structure of a size equivalent to that in the specimen test Then if Nd _< N~,

low-cycle fatigue test procedures are required for material evaluation while

if Nd >> Nt, high-cycle fatigue information is more meaningful When

Nd _< Nt, elastoplastic solutions are required for design, but if Nd >> Nt,

linear elastic stress analysis approaches are preferable Again, if N~ < N~,

mean stresses will relax, and rachetting processes are possible [21-23],

while when Nj >> Nt, mean stresses and residual stresses play an important

part in the life of the structure

If N~ represents a design life associated with crack propagation, and

Na <_ Nt, a crack growth law based on gross plastic strains is required, [24]

while if N~ >> N~, elastically controlled crack growth laws are applicable

[25,26]

Failure CrReria at High Temperature

The principal objective in formulating a criterion for fatigue failure at

high temperature is to properly account for the damaging effect of time and

temperature A typical problem facing the designer is how to deal with

extended hold periods with occasional stress reversals Referring again to

Fig 1, pressure or centrifugal elastic stresses in a structure induce in a notch

a constant strain, while removal and reapplication of these stresses leads to

a plastic strain reversal in the notch, and a subsequent stress relaxation

The events are shown in Fig 8 Degradation in fatigue life under such

circumstances can be quite severe as many investigators have shown

Figure 9, from the work of Berling and Conway [27], shows the effect of

tensile strain hold periods on the fatigue life of AISI 304 stainless steel at

650 C

Krempl and Wundt [28], Esztergar and Ellis [29], and Coffin and Goldhoff [30] have reviewed some of these approaches in more detail than

is possible here Briefly, the linear creep-fatigue damage criterion stems from the early work by Lazan on elevated temperature experiments in- volving cyclic stresses with superimposed mean stress [31] The linear

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COFFIN ON FATIGUE AT HIGH TEMPERATURE ] 9

damage rule originally proposed by Robinson [32], for varying stress-

rupture life prediction, assumes that the damage fractions ~, for fatigue and

creep, total to unity, or

~fatigue + @ p = 1 (at failure) (8) Various experimenters, including Taira and Ohnami [33], Swindeman [34],

and Manson et al [35], have followed this approach Recently, Lagneborg

and Attermo [36] showed that a linear creep-damage rule did not apply in

experiments on a 20Cr-35Ni stainless steel subjected to cyclic strains and

hold periods and a steady stress at 700 C Rather, an interaction term was

additionally needed, which was the product of the life fraction and time

fraction An explanation for the inadequacy of Eq 8 in representing the

time-dependent fatigue behavior will be discussed in another paper in this

conference [371

The second category of failure criteria, (b) considers the complex strain-

ing as a time-dependent fatigue process Manson and Halford [38] extended

Manson's method of universal slopes [20] to elevated temperature by

introducing a lower bound fatigue life as 10 percent of the life predicted by

Eq 6 A still lower life is predicted, based on creep considerations, given by

Eq 8 More recently, Manson et al [39] have developed a different approach

to account for the time dependent portions of the cycle by separating the

nonelastic cyclic strains into plastic and creep and summing the separate

life fractions to unity They then compare this "strain-range partitioning"

method to their 10 percent rule [38] Timo [40] developed fatigue curves for

constant hold periods by combining low-cycle fatigue tests having different

hold periods with creep-rupture information to obtain high-cycle fatigue

data points on these curves Here the assumption is made that the fatigue

life corresponding to a particular rupture strength is the time to rupture in

the rupture test divided by the hold period of the fatigue test Conway et al

[41] propose that holdtime lives can be predicted from tests for no hold-

times, based on the linearity on a log-log plot of the time to fracture and

the length of this hold period in tension-hold-only tests (such as Fig 9)

from which the time to fracture for any holding time can be calculated

Figure 10 shows such a representation

The concept of Conway et al fits quite naturally into the fatigue Eq 5

It has been suggested [15], that holdtime behavior could be predicted from

Eq 5 by assuming that

1

t / "4- th

where t / is the time for strain reversal and th is the hold period for each

cycle Using the appropriate coefficients of Table l, obtained from the data

of Berling and Slot [13], good agreement with the Conway et al representa-

tion is shown in Fig 10 The dashed lines can be found by cross plotting

20 FATIGUE AT ELEVATED TEMPERATURES

FIG lO -Comparison of period of cycle versus time to failure for holdtime tests with

analytical results derived from Eq 5

Fig 7 at the appropriate total strain range and determining from the

corresponding frequency and life the period and total failure time Conway

et al indicate different slopes for log period versus log time to failure for

different strain ranges These can be found quantitatively by examining

Eqs 3 and 4 Since r = 1/~ and ts = Ns/v, and assuming the strains are

large (Act ~ Aep), Eq 3 becomes

(C2 Y / ~ r ~ (10)

tj = k ~ /

Now assuming the strains are small ( A e t = /Xee), Eq 4 becomes

/ A' \1/~, t/ = 1 - - / r 1-/~'ja') (11)

\E~e/

Using Table 1, for AISI 304 stainless steel at 650 C, the slope ranges from

0.81 at high strains to 0.522 for low strains At intermediate strains the

log t: versus log r relationship is not linear

Kanazawa and Yoshida [42] have investigated the frequency and hold-

time behavior of a 17Cr-10Ni-2Mo austenitic stainless steel They suggest

that strain rate rather than frequency correlates better with holdtime results

Although attention has been drawn to the effect of frequency and hold-

times on the austenitic stainless steels, it is also an important factor in cast

and directionally solidified nickel-base superalloys at high temperature

As indicated earlier, because of their generally low ductility and high

strength, the transition fatigue life for this class of materials is low, such

that in their design life range the behavior is one of high-cycle fatigue

Translated in terms of a phenomenological description of their behavior,

Eq 4 is applicable, while from physical considerations, the failure mecha-

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COFFIN ON FATIGUE AT HIGH TEMPERATURE 21 nism is a result of crack growth in an elastic regime As the temperature is

raised, two effects occur simultaneously: (a) creep deformation becomes an

increasingly important mode of deformation and (b) the fracture mode

becomes increasingly intergranular Since creep deformation leads to

greater strain localization in the plastic zone at the crack tip, and inter-

granular fracture produces a more extended crack for a given plastic strain,

a decreasing frequency can greatly accentuate fatigue failure This be-

havior can be expressed analytically from Eq 4 or

N:~=~I ( v ~ k l ' / ~ '

- - - ( 1 2 )

N/~=~ 2 \ v2 i

Table 2 shows the trend with temperature for two nickel-base superalloys

Here the life ratio N:I/N:= is found when Vl/V= = 10

TABLE 2~Coefficients f o r Eqs 4 and 12

From physical considerations, the central question in high-temperature

fatigue is what causes the degradation of fatigue properties at these tem-

peratures with increasing time Emphasis on creep-fatigue criteria for

failure prediction would suggest that creep and rupture mechanisms play

an important role In fact, fatigue fractographic evidence, generally shows

a tendency towards intergranular fracture with increasing temperatures and

times to failure, and this is consistent with stress-rupture fractography

On the other hand, evidence can be cited to support the position that the

time-dependence of high-temperature fatigue is the result of the environ-

ment, and more specifically, oxygen Not only is there the findings of

several investigators, including White [43], Achter et al [44], and Nachtigall

et al [45], showing the increase in fatigue life in vacuum, but also there is

the tangible evidence that most fatigue cracks produced by slow cycling at

elevated temperature are nearly always filled with oxide products Addi-

tionally, in an investigation of the damage and fracture mechanisms of cast

Udimet 500 in high-temperature fatigue, surface ridging at grain boundaries

was found to be the source of crack nucleation [46] In A286, a highly

localized surface oxidation was identified as the nucleation site for fatigue

cracks under high-temperature low-cycle fatigue [47,48] In Fig 11 surface

22 FATIGUE AT ELEVATED TEMPERATURES

F I G l l - - S u r f a c e markings on 4286 test specimens at 593 C in air ACv = 8 0 0 )< 1 0 - 6 :

FIG 1 2 - - O x i d e growth on fatigue crack nucleus A 2 8 6 at 593 C in air v = 0.2 cpm plus

markings found on A286 hourglass shaped test specimens at 1100 F are

shown to b e c o m e increasingly heavy as the frequency is lowered Examina-

tion of the localized oxide f o r m e d at low frequency reveals the fascinating

structure shown in Fig 12

Recently some controlled strain experiments were conducted on A286 at

1100 F in high v a c u u m and on cast U d i m e t 500 at 1500 F, in push-pull

loading In b o t h of these materials the strong frequency effect found in air

was seen to disappear when the experiments were conducted in a v a c u u m of

10 -8 tort These results are shown in Figs 13 and 14 It was also observed

FIG 13 Plastic strain range versus fatigue life f o r A 2 8 6 in air and vacuum at 593 C N u m -

bets adjacent to test points indicate frequency in cpm S o l i d lines are regression analysis o f

Eq 5 [481

24 FATIGUE AT ELEVATED TEMPERATURES

J

O

10 4 I0

FIG 14 Test results o f stress amplitude versus fatigue life f o r cast Udimet 500 in air

vacuum at 816 C (lower curve) Air tests both stress and strain control; vacuum tests stress

control only Frequency-modified stress amplitude versus fatigue life f o r same test results,

after Eq 4 [48]

that the mode of fracture in this medium for each of these materials was

transgranular in contrast to the intergranular fractures found in air Based

on these and other observations, it was concluded that, for the frequencies

employed, the degradation in fatigue life found in air at elevated tempera-

ture with decreasing frequency is a result of the environment

A subsequent study [49] has revealed additional information on the effect

of high vacuum on the low-cycle fatigue behavior of A286, Nickel A,

C1010 steel, and AISI 304 stainless steel F o r example, there appears to be

little difference in the plastic strain range-life behavior of A286, Nickel A,

and AISI 304 stainless steel between room temperature and elevated tem-

perature This is shown in Fig 13 for A286 Additionally in Fig 5 for

AISI 304 stainless steel, high-vacuum tests at 816 C show a substantial

improvement over similar tests in air and exceed in life those tests con-

ducted in air at 430 C A summary figure of the high-temperature vacuum

test results is shown in Fig 15 It also includes test results obtained many

years ago [50] for annealed 1100 aluminum, O F H C copper, C1018 steel,

AISI 347 stainless steel, Nickel A, and 2024 T6 aluminum in air at room

temperature as open points Further, the results of Swindeman [51] on

D43 columbium at 20, 871, and 1093 C are included since these tests were

also performed in high vacuum Also, data on the fatigue behavior of

tantalum [52] at 315, 593, and 732 C in high-purity argon have been added,

on the basis that the environment of these experiments was sufficiently

inert to be considered applicable in the present comparison A single test

point for In 718, a nickel-base superalloy, tested at 648 C, is also included

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OPEN POINTS-ROOM TEMP-AIR "~" ~ "" ~ -

CLOSED POINTS-ELEVATED TEMP-VACUUM ~ ' ~

OR ARGON ~ !

L i l i , , , , t l l i i i ~ , - - I , , , , H I , i , , H , , t i , , , H , , I ,

CYCLES TO FAILURE

F I G 1 5 - - S u m m a r y plot o f plastic strain range versus cycles to failure f o r several metals

The dashed lines of Fig 15 define the broad scatterband of the data

(excluding the tensile ductility of 2024T6) and are drawn with a slope

of - ~ It is readily seen that the high-temperature, high-vacuum results

are a continuation of the room-temperature results This compilation of

data strongly suggests that in the absence of environmental influences, the

two-slope plastic strain range-life relationship, typically shown in Fig 5,

disappears and is replaced by a single slope, narrow scatterband, straight

line of slope/3 = 0.5 for all the materials considered

It is important to note that in all the tests used in the plotting of Fig 15,

failure was produced by fatigue cracks which propagated transgranularly

This observation is consistent with a model proposed earlier [19] suggesting

that the two-slope behavior of Fig 5 is the result of a progressive transition

in fracture mode from transgranular to intergranular with elevated tem-

perature in air Decreasing frequency and plastic strain aid in this transition

Assuming a reaction zone at the tip of a propagating crack due to oxidation

increasing temperature and decreasing frequency enhance this zone, while

decreasing plastic strain confines the crack advance to the more damaged

portion of this zone It is further argued that the reaction zone is selective

to grain boundaries because of the greater activity due to stress, concentra-

tion gradients, precipitates, etc Finally, for a given plastic strain, inter-

granular cracks advance further than transgranular cracks all else being

equal Thus, in Fig 5, higher temperatures, lower plastic strains, and lower

frequencies lead to decreased lives Now, if the crack propagation is at all

times transgranular, as is observed in all the high-vacuum experiments,

this is the result of the elimination of a reaction zone, and its deleterious

influence on crack propagation

26 FATIGUE AT ELEVATED TEMPERATURES

One interesting consequence of Fig 15 is its relation to models predicting

the exponent/3 of Eq 3 M o r r o w [53] has proposed that/3 = 1/(Sn' -+- 1)

where n' is the cyclic strain hardening coefficient; while Tompkins [54] has

developed a theory for crack propagation from which /3 = 1/(2n' + 1)

Knowing n' to be a function of temperature and material, and assuming

it to be independent of environment, it is difficult to reconcile the predicted

values of/3 with the constant value shown in Fig 15 The implication here

is that it is the mode of cracking rather than the cyclic strain hardening

exponent that governs fatigue life

High-Strain Crack Propagation

Referring again to Fig 1, following initiation and early growth, the crack

grows by propagation through the plastic zone Methods for considering

this aspect of the problem are not well developed; however, the work of

Boettner et al [55], Weiss [56], and Tompkins [54] have proposed models for

crack growth A c o m m o n fracture of these models is that the crack growth

rate dc/dN is proportional to crack length c or log c is proportional to N

Solomon [24] has studied the growth of cracks from single side notch plane

stress specimens subjected to a constant plastic strain range as a function of

temperature and frequency Based on results from 1018 steel at tempera-

tures from 25 to 350 C and A286 at 1100 F he has developed a crack growth

law

de r A~,)

v k-1 (13)

dN ~s"'

where ~o and a' are constants, a = 1//3 from Eq 5, +I is the fracture ductility

The format of this relationship follows closely the frequency-modified

fatigue law, Eq 5 This work will be discussed in more detail in another

paper presented at this conference [37]

High-strain crack propagation experiments are particularly useful in

evaluating the effect of a broad frequency range on fatigue behavior It will

be shown [37] that, at least for A286 at 1100 F, three failure regimes appear

to exist, depending on the frequency At very low frequencies, the behavior

is time dependent, but not cycle dependent Here k = 0 in Eq 13 The

physical processes involved may be associated with stress-rupture or

environmental damage At low to intermediate frequencies the failure

process is the result of an environmental interaction, as determined by

comparative crack growth measurements in air and vacuum Here k 0.49

Finally, at very high frequencies, a time-independent, cycle-dependent

failure process dominates This is based on studies by Organ and Gell [57]

on wrought Udimet 700 at 1400 F and Tien and Gamble [58] who found

that single crystals of Mar-M200 at room temperature behave in air at

20 000 cpm in a manner comparable to specimens cycled at 10 Hz in vacuum

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COFFIN O N FATIGUE AT HIGH TEMPERATURE 27

Crack Growth in the Elastic Regime

The literature abounds with papers dealing with fatigue crack growth

through an elastic stress field and numerous crack growth laws relating

d c / d N to AK or K the stress intensity range or the maximum stress

intensity to some power have been proposed At temperatures sufficiently

high for time dependent effects to be important, it has been shown that

crack growth rates can be similarly represented provided time effects have

been properly taken into account James [59], for example, has found that,

for AISI 304 stainless steel at 1000 F, at low values of AK a crack growth

law in the form of

dc

= B ( A K ) m (14),

exists where B is a function of frequency Popp and Coles [25] have studied

the effect of holdtimes on crack growth of In 718 at 1000 F and find that

the coefficient B in Eq 14 can be represented by a Larson-Miller type

parameter relating temperature and holdtime per cycle

Greater emphasis needs to be placed on the development of crack

growth laws in the elastic regime at high temperature As was pointed up

earlier, when applications are such that N~ >> Nt, such approaches con-

stitute the only rational way to treat the fatigue problem It might further

be pointed up that many aircraft engine materials exhibit transition fatigue

lives in the order of 100 cycles at temperature such that at design lives of

10 000 cycles elastic crack growth concepts apply

Deformation and Fracture Aspects of Ratchetting

Since the subject of ratchetting will be dealt with at some length in this

symposium, it would be well to discuss this briefly here It has been ob-

served frequently that, in the presence of cyclic plastic strain, simul-

taneously applied mean stresses cause progressive monotonic deformation,

or ratchetting [21-23] Other manifestations of this same phenomenon are

plastic instabilities or shape changes in ductile metals subjected to large

cyclic plastic strains, [21] or, for mixed cyclic and monotonic strains, a

resulting flow stress for monotonic strain which, in the limit, is determined

by the stress range of the stabilized hysteresis loop [60] Although little

work has been done to describe the flow rules for such processes, it has

been suggested [23] that the ratchetting rate, ip (strain advance per cycle)

can be expressed as

Aep

~ = A~m • - - (15)

Aa where am is the mean stress, 2xE~ the plastic strain range, and Aa the cyclic

stress range Equation 15 is similar to a plasticity solution derived by

Swift [61] for the progressive growth of a cyclically bent beam subjected

simultaneously to an axial stress Equation 15 can be also expressed as

ip = B~m X A~ (16)

Aee Thus the process is a low-cycle fatigue phenomenon, and the transition

fatigue life (where A~e = A~) characterizes the regime where a particular

material will be sensitive to the phenomenon F o r a given plastic strain

and mean stress, as the temperature is raised, Aa and A~, decrease, and the

ratchetting rate becomes more significant Further, at high vacuum, the life

is extended, as is the total ratchetting strain ~r = ~pNj Hence large ratchetting

strains can be expected, and this is confirmed as seen in Fig 16 where a

pronounced specimen shortening and minimum diameter fattening (except

at the diameter measuring probes) is observed

FIG 16 Appearance o f specimen o f A I S I 304 stainless steel following vacuum test at

COFFIN ON FATIGUE AT HIGH TEMPERATURE 29 Similar arguments can be used to consider mean stress or residual stress

relaxation It is apparent from Eq 16 that the ratio of plastic to elastic

strain must be very low to prevent mean stress relaxation

Many situations occur in practice where cyclic strains and mean stresses

are superimposed and where ratchetting processes or mean stress relaxation

can occur There is little experimental work or predictive approaches

developed to account for these situations, particularly from strain con-

siderations The work of Yamanouchi [62] is of interest here He reports

fatigue studies on thin tubes involving steady torsion, an axial cyclic strain,

and a cyclic temperature for three m a t e r i a l s - - A S T M 302-B, AISI 304, and

SCM 3, a 1Cr-0.2Mo steel He finds that, despite torsional strain ratchetting,

there is no effect of these strains on the low-cycle fatigue resistance of the

material Further, the ratchet strain increases with the repetition of axial

strain, the magnitude of the steady torsional stress, and axial strain

amplitude

A related study [60] on Nickel A at room temperature was conducted

with a mixed cyclic and monotonic strain program Specific ratios were

maintained of total cyclic strain range to the longitudinal strain advance

per cycle until failure, and from these tests a failure criterion was found,

where

\ Nso l ~so

where

NI = fatigue life for a total mean strain es,

Nj0 = pure fatigue life, and

~s0 = fracture ductility in simple tension

Also

= 0.563 for Nickel A at room temperature

According to Eq 17, for strain ratios less than 0.05, the effect on fatigue life

would be small, in accord with Yamanouchi

Another way to consider the effect of cyclic and m o n o t o n i c strain is to

compare the ratio of the mean or creep strain to the accumulated cyclic

plastic strain after m a n y cycles When this ratio is small, the corresponding

mean stress will likewise be small and the effect on fracture negligible

Unfortunately, this question has not been studied systematically at elevated

temperature

Notches

Although the literature abounds with various treatments o f the notch

problem at room temperature, relatively little work has been done on the

elevated temperature low-cycle fatigue resistance of notched bars where

30 FATIGUE AT ELEVATED TEMPERATURES

time-dependent effects are important Although not directly related to the

question of time, of interest are the experiments of Krempl [63] on notched

bars of three low-strength structural steels, a 2.25Cr-1Mo steel and AISI 304

stainless steel subjected to fully reversed loads at room temperature and

550 F Since the notch root undergoes cyclic plastic strain, comparisons of

the strain in this region with smooth bar data are suggested N o t c h root

strain measurements were compared with smooth bar fatigue results for

equivalent lives It was found that neither the axial strain range nor esti-

mates of the effective strain range based on the octahedral shear strain or

the maximum shear strain correlated well On the other hand M o w b r a y

and McConnelee [1,2] have applied finite element analysis techniques to

these geometries, using cyclic stress-strain curves and find good agreement

with smooth bar results

An approach which follows that of T o p p e r et al [9] is currently being

studied at our laboratory F r o m Neuber's rule it can be shown that

where AS is the nominal stress range applied to a notched member whose

fatigue concentration factor is KI and AG and A~ are the local stress and

strain ranges in the notch root By assuming conditions at the notch root

to be equivalent to those in a smooth bar, the quantity (AaA~E) a)2 can be

evaluated from smooth bar data for a particular life, and AS determined

F o r high temperature where time dependency must be considered, it is

attractive to combine the high-temperature fatigue Eqs 4 and 5 with Eq 18,

after rewriting or

Since time effects are introduced through the frequency in Eqs 4 and 5,

Eq 18 or 19 provide means for evaluating frequency and holdtime effects in

notches

Figure 17 shows some preliminary results from the utilization of this

technique Here specimens of three different cylindrical notch geometries,

Kt = 1.5, 2.0, and 3.0, were prepared and subjected to fully reversed

uniaxial loads at several stress levels and frequencies The material was

A286 at 1100 F This figure compares the notch bar fatigue results (the

individual test points) with smooth bar data expressed in the form of Eq 18

or 19, using Eqs 4 and 5 and the appropriate coefficients of Table 1 F r o m

each test for a specific notch geometry a value of KI is found from Eq 18 by

equating the actual and predicted life, from which a mean value of KI was

determined for each notch Hence Fig 17 really shows the applicability of

this mean K s for various stress ranges and frequencies of cycling

An important consideration that arises in translating from the nominal

stresses applied to the actual structure to those in the local notch is the role

of the nominal mean stress Nominal stresses in the structure are often

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FIG 17 Comparison o f test results on notched bars o f A286 at 593 C at several stress

amplitudes and frequencies with calculated notch stress amplitude (unpublished data)

cycled between zero to tension, while uniaxial data are most often strain

limited and fully reversed The applicability of uniaxial data of this type will

depend on the degree to which mean stress relaxation can occur in the

notch root Here again the transition fatigue life serves as the guide Thus

when Ni = Nt, that is, where the cycles for initiation is of the order of the

transition fatigue life, mean stress relaxation of the applied stresses occurs

in the notch, and fully reversed uniaxial data are applicable When Ni >> Ne,

mean stresses as determined by stress analysis must be taken into account

in predicting initiation life

S u m m a r y R e m a r k s

Many important aspects of the high-temperature fatigue problem such as

mechanisms for fatigue nucleation and growth, metallurgical aspects,

material selection, and thermal fatigue have been omitted from this paper

because of space Despite this, it has been my intent to treat the high-

temperature fatigue problem as a failure process in a notch in some struc-

ture in terms of nucleation and early growth at the notch-root, high-strain

crack propagation through the plastic zone of the notch, and elastic crack

growth to ultimate failure and to discuss the role that some of the im-

portant disciplines play in treating the problem A number of points have

been made throughout the paper and are summarized here:

1 In developing models employing constitutive equations and failure

criteria for structural design more attention needs to be paid to fatigue as a

process of failure by nucleation and growth

2 Greater attention should be given to the transition fatigue life in

determining the approach taken to the problem both in testing and design