Astm stp 519 1973

Since the incremental step test has been used successfully to approximate cyclic stress-strain curves of metals at room temperature, the objective of this study is to evaluate its usef

Committee E-9 on Fatigue

AMERICAN SOCIETY FOR

TESTING A N D MATERIALS

Bal Harbour, Fla 7-8 Dec 1971

ASTM SPECIAL TECHNICAL PUBLICATION 519

L F Coffin and Erhard Krempl, symposium co-chairmen

List price $28.00

04-519000-30

A M E R I C A N SOCIETY FOR TESTING A N D MATERIALS

1916 Race Street, Philadelphia, Pa 19103

9 BY A M E R I C A N S O C I E T Y F O R T E S T I N G A N D M A T E R I A L S 1973 Library of Congress Catalog Card Number: 72-86244

NOTE

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

Printed in Philadelphia, Pa

May 1973

Foreword

The Symposium on Cyclic Stress-Strain Behavior Analysis, Experimen-

tation, and Failure Prediction was sponsored by Subcommittee E09.08 on

Fatigue Under Cyclic Strain of Committee E-9 on Fatigue and held in

Bal Harbour, Fla., 7-8 Dec 1971 L F Coffin, General Electric Co., and

Erhard Krempl, Rensselaer Polytechnic Institute, presided as co-chairmen

Related ASTM Publications

Damage Tolerance in Aircraft Structures, STP 486 (1971), $19.50

Effects of Notches on Low-Cycle Fatigue, STP 490 (1972), $3.00

Stress Analysis and Growth of Cracks, STP 513 (1972), $27.50

Testing for Prediction of Material Performance in Structures and Components, STP 515 (1972), $28.50

Contents

Introduction

Time-Dependent Effects

A Study of Thermal Ratchetting Using Closed-Loop,

Servo-Controiled Test Machines R H STENTZ

Cyclic Stress-Strain Behavior of Two Alloys at High

Temperature C E JASKE, H MINDLIN, AND J S PERRIN

Effects of Temperature and Deformation Rate on Cyclic

Strength and Fracture of Low-Carbon Steel

H ABDEL-RAOUF, A PLUMTREE, A N D T H TOPPER

Intergranular Fatigue Fracture of Chemical Lead at

Room Temperature MASAKl KITAGAWA

Cyclic Deformation and Failure of Polymers

An Automatic Flash Photomicrographic System for

Fatigue Crack Initiation S t u d i e s - - R A L P H PAPIRNO AND

B S PARKER

The Effect of Load Interaction and Sequence on the Fatigue

Behavior of Notched Coupons J M POTTER

Cyclic Inelastic Deformation and the Fatigue Notch Factor

B N LEIS, C V B GOWDA, AND T H TOPPER

Applications of Finite Element Stress Analysis and Stress-Strain

Properties in Determining Notch Fatigue Specimen Defor-

mation and Life D F MOWBRAY A N D J E M C C O N N E L E E

Crack Propagation in Notched Mild Steel Plates Subjected

to Cyclic Inelastic Strains -c v B GOWDA AND T H TOPPER

Cumulative Effects

The Physical Justification of the Term "State of Fatigue of

Materials Under Cyclic Loading" J BURBACH

Cumulative Fatigue Damage Under Complex Strain Histories d

The Role of Cyclic Strain Behavior on Fatigue Damage Under

Engineering Analysis of the Inelastic Stress Response of a Structural

Metal Under Variable Cyclic Strains H R JHANSALE AND

Periodic Overloads and Random Fatigue Behavior P WATSON,

STP519-EB/May 1973

Introduction

Modern machinery is required to perform reliably under a variety of operating conditions Power generation equipment such as nuclear reactors and steam and gas turbines have to respond quickly to the changing power demands of our technological society; aircraft structures and jet engines are

to perform reliably under frequent take off, cruise, and landing operations These are only two examples of the cyclic operating pattern imposed on modern machinery

The cyclic operating pattern, the increasing demands on reliability im- posed by the consumer-oriented society, and the drive for an economic design require sophisticated design methods for critical components sub- jected to severe cyclic loadings An essentially static, time-independent view- point is no longer feasible in these cases It will be necessary to calculate the stresses and strains and assess the accumulated damage by following through the operating history of these critical components Central to this new design approach is the recognition that each severe cycle can cause a permanent damage in the material During the projected lifetime of the machine the total accumulated damage in highly-stressed components will have to be less than the damage which will lead to mechanical failure The objective in the development of a modern design approach for critically- stressed components is therefore the accurate assessment of the damage caused by the elements of the operating history

The Symposium on Cyclic Stress-Strain Behavior Analysis, Experimen- tation and Failure Prediction focuses on three vital aspects of the damage assessment in engineering materials Experimental techniques to determine the cyclic stress-strain behavior and the initiation of cracks in materials are discussed The importance of time (rate) dependent processes as they affect deformation and crack initiation is delineated in various papers Notches and their life-reducing effect are examined from an experimental and analytical point of view In the latter, elasto-plastic computer programs are employed The crack initiation and crack propagation phase are separated

2 CYCLIC STRESS-STRAIN BEHAVIOR

and treated individually The problems of damage definition, damage ac-

cumulation, and life prediction under variable amplitude loading receive

attention in several papers

The reader of these papers will realize the interdisciplinary nature of the

subject, and he will certainly recognize the contributions made by the

metallurgical, materials testing, and analytical disciplines For the develop-

ment of reliable damage assessment and life prediction methods to be used

in the design of modern machinery, an interdisciplinary approach is ab-

solutely essential We want to thank the authors for their contributions and

their willingness to discuss the subject across the boundaries of classical dis-

ciplines We sincerely hope that this Special Technical Publication will be

used by designers and will stimulate further interdisciplinary work towards

the development of rational and reliable life prediction methods for realistic

R H S t e n t z ~

A Study of Thermal Ratchetting Using Closed-Loop, Servo-Controlled Test

Machines

REFERENCE: Stentz, R.H., "A Study of Thermal Ratehetting Using Closed-Loop,

Servo-Controlled Test Machines," Cyclic Stress-Strain Behavior Analysis, Experimen-

tation, and Failure Prediction, A S T M S T P 519, American Society for Testing and

Materials, 1973, pp 3-12

ABSTRACT: A new testing technique has been devised for studying thermal ratchet-

ting behavior It employs low-cycle fatigue-type specimens (hourglass shape) in conjunc-

tion with two closed-loop, servo-controlled testing machines operating in unison to

provide an exact simulation of the familiar three-bar assembly

Diametral extensometers are employed in conjunction with an analog strain computer

to provide instantaneous values for the total axial strain and to isolate the mechanical

and thermal strain components Stress-strain measurements are recorded continuously

throughout each cycle to provide an extensive evaluation of the response to initial load

level, maximum and minimum cycle temperatures, hold-time effects, different specimen

diameters, and rate of temperature cycling Demonstration tests are described which

employ 304 and 316 stainless steel specimens subjected to an initial stress level of 10 000

psi and a temperature cycle from 1100 to 800 F

KEY WORDS: fatigue (materials), testing equipment, servomechanisms, cyclic temper-

ature, stresses, strains

Thermal ratchetting involves a unidirectional accumulation of plastic deformation resulting from a successive application of a thermal stress This phenomenon has been studied extensively [1-6] 2 , and particular attention has been focused on the use of the three-bar assembly as an analytical model This approach permits an analysis to be made of thermal ratchetting behavior in response to the primary variables of external load and the cyclic temperature profile

Conditions which are pertinent to thermal stress ratchetting and have an important effect in determining the extent of this phenomenon are the following:

1 the amplitude and the rate involved in the temperature cycle,

tVice president, Mar-Test Inc., Cincinnati, Ohio 45215

2The italic numbers in brackets refer to the last of references appended to this paper

4 CYCLIC STRESS-STRAIN BEHAVIOR

2 the thermal conductivity and thermal expansivity of the material or materials contained in the component or structure,

3 the magnitude of the externally applied force,

4 the magnitude of any time-dependent, temperature-dependent or cycle-dependent metallurgical changes or both which may occur in the material, and

5 the geometry of the structure

While most of the above factors are amenable to analysis [1-6], an ac- curate assessment of thermal ratchetting is dependent upon a knowledge of the stress-strain behavior of the material along with a knowledge of any time-, temperature-, and cycle-dependent material changes Experimental procedures which are based on a simulation of the three-bar model are im- portant, therefore, insofar as they identify and evaluate these metallurgical effects which are not easily accommodated in the usual analysis procedures Also of special significance in these types o f experimental studies is that the material behavior which is observed in one member of the three-bar assembly reflects the interaction of this member with the other members of the assembly Such interaction effects include strain-hardening and strain- softening, creep, relaxation and Bauschinger effects, and represent infor- mation which can only be obtained experimentally

Testing Procedure

A new test procedure has been developed which employs two servo- controlled, closed-loop low-cycle fatigue machines operating in unison to provide an exact simulation of the three-bar thermal ratchetting model [1- 6] Two specimens are tested simultaneously; one is held at a constant temperature while the specimen in the second test machine is subjected to a cyclic temperature pattern of preselected amplitude and frequency Reference to the three-bar assembly shown in Fig 1 indicates that Specimen

P FIG 1 Three-bar assembly

STENTZ ON THERMAL RATCHETTING

1 represents the inner bar while Specimen 2 represents the two outer bars

The construction o f the three-bar assembly demands that all bars have the

same length at any instant; it is also required that the summation o f the

forces in the members must always equal the externally applied force, P

Assuming uniform deformation in the members and using strain notation,

the following definitions will be utilized Etota I will represent the

measurable strain in each member and will consist of a c o m p o n e n t caused

by thermal expansion or contraction (o~AT) and a strain c o m p o n e n t (E)

caused by induced stresses in the member Further, using the subscripts 1

and 2 to denote the inner and combined outer bars, respectively, and assum-

ing a temperature change in the outer bars only, the following equations

F I O 2 Three-bar assembly simulation

Hourglass-shaped specimens were employed, and these were heated in-

ductively while precision extensometers were used to measure the diametral

strain at the minimum diameter The extensometer signal together with an

instantaneous force signal from a load cell in series with the specimen were

used in conjunction with an analog strain computer [7] to generate an axial

strain signal This value o f total axial strain is essential to the dynamic

solution of Eq 2 and is also used along with the instantaneous load value to

define the stress-strain behavior t h r o u g h o u t the cycle

6 CYCLIC STRESS-STRAIN BEHAVIOR

A major consideration in this new test technique was the method for

producing the correct thermal behavior in the specimens while accurately

measuring the region of maximum strain It was felt that the combination

of hourglass specimens, induction heating, and diametral extensometers

would provide the best results, since little difficulty is experienced in produc-

ing the required temperature behavior in the relatively short region of the

specimen monitored by the extensometer Of course, the shape of the gage

section also aids in producing the maximum strain in this region

In addition to these points, it was also considered very important to use

an extensometer having very little temperature sensitivity The exten-

someter employed was composed primarily of quartz and invar because of

their low thermal expansion characteristics (both less than 1 • 10 -6 in./in

F) The quartz tips in contact with the specimen also provided a high

resistance to heat flow with a thermal conductivity of about 0.8 B/h-ft-F

It will be evident from the preceding comments that only the minimum

diameter point of the test specimen represents the test section; hence, it is

these regions which represent bars No.1 and No.2 in Fig 1 Furthermore,

the stress-strain behavior is that corresponding to the minimum diameter

point of the test specimen and Eqs 2 and 3 apply in this region of the

specimen

Interconnection of Testing Machines

The interaction between the bars in the three-bar assembly has been in-

dicated by the simultaneous Eqs 2 and 3, and it is this same interaction

which is imposed in the two testing machine approach described Rewriting

these two equations as

e 2 + a A T 2 - e 1 = 0

P - F 1 - F 2 = 0 suggests that the summing junctions of the two servo-controlled systems

could be used to maintain the correct relationships This results in the com-

pound servo loop shown in Fig 3 An analysis of this figure might suggest

that testing machine No 1 operates in strain control and machine No 2

operates in load or force control This condition only exists, however, when

the switches A and B are open as shown Once the compound loop is formed

by closing the switches, the machines can no longer be considered in either

load or strain control; they must simply satisfy the equations by responding

to the externally imposed P, TI (temperature maintained in Specimen 1),

and AT2 along with the interactions between the material properties ex-

hibited by the specimens

For control and recording purposes it is necessary to have electronic

signals representing the total axial strain (~ + c~ A T) as well as the isolated

mechanical (~) and thermal (aAT) strain components These are produced

STENTZ ON THERMAL RATCHETTING 7

/A

F

Force Feedback(F2)

I Testing Machine

FIG 3 Testing machine interconnections for thermal ratchetting

by special analog circuits which accept input signals from the diametral ex-

tensometer and a gage section thermocouple in conjunction with the analog

strain computer Figure 4 contains a block diagram which indicates how this

is accomplished Although it is obvious that % + a A T2 can be obtained

directly from an axial extensometer on a uniform gage-length specimen, it is

felt that the disadvantages normally associated with an elevated temperature

axial strain measurement, complicated further by the temperature cycling

requirements of the ratchetting problem, represent experimental difficulties

which are not easily resolved

Test Results

Two specimens of AISI 304 stainless steel were installed in the testing

machines and heated to 1100 F under zero load conditions No interconnec-

tions existed at this time After equilibrium had been obtained, Specimen 1

was brought under strain control while Specimen 2 was brought under load

control The compound loop was then formed by interconnecting the

machines while maintaining zero load on both specimens At this point a

simulated external force of 1000 lb was applied to the system, producing an

initial stress of 10 000 psi in each specimen The temperature control system

was then activated to cycle the temperature of Specimen 2 to 800 F and then

back to 1100 F where a hold period was introduced This procedure was

repeated to yield the test data presented in Table 1 The lengths of the hold

periods at 1100 F were arbitrarily selected in an attempt to show an effect on

the amount of ratchet strain Figure 5 shows the x - y plots of strain versus

load for Specimen 1 The heating and cooling rate for this demonstration

was about 5 F per s

Subsequent exploratory tests on AISI 316 stainless steel exhibited no

ratchetting under the identical conditions For this material it was necessary

8 CYCLIC STRESS-STRAIN BEHAVIOR

FIG 4 - - G e n e r a t i o n o f t o t a l a x i a l s t r a i n andstrain components~na~

TABLE 1 Thermal ratchetting experiment on 304 stainless s t e e l , a

Hold Ratchet Max Tensile Relaxed Ten- Compressive Period, Strain, Stress, sile Stress, Stress,

aData for Spccimcn 1

to increase the initial stress to 20 000 psi to cause ratchetting to occur, thus demonstrating that higher strength materials exhibit greater resistance to thermal ratchetting and that this difference can be clearly evaluated using the present technique No attempt was made in any of these tests to ratchet the specimens to failure

FIG 5 Stress-stra& behavior f o r Specimen 1 in thermal ratchetting test o f 304 stainless steel

Extensions of the Technique

Some recent studies have shown that the test technique described is easily

modified to increase the versatility of this experimental approach In one

modification the control system was extended to allow the temperature of

Specimen 1 to be lowered once the temperature of Specimen 2 attained the

desired lower limit Then when the temperature of Specimen 1 reached that

of Specimen 2, the system reacted to raise the temperature of both

specimens to the original level It was also possible to insert a hold period at

this point to provide a fairly close simulation of the time-temperature

behavior observed in a pipe wall during a temperature transient resulting

from a sudden reduction in the fluid temperature An interesting piece of in-

formation obtainable in this type of test cycle is the stress-time behavior

during the hold period

Another control system modification which has proven to be of some

value relates to the use of a scale factor in conjunction with one test

specimen to cause it to act as though it had a different diameter With this

approach the test specimens can be identical to aid in obtaining identical

thermal response characteristics when both specimen temperatures are be-

ing changed, yet the effect of different diameter (area) ratios on the ratchet-

ting response can be studied This is an important consideration because it

adds increased versatility to the test procedure since several different area

ratios can be evaluated in the same test by merely adjusting the scale factor

10 CYCLIC STRESS-STRAIN BEHAVIOR

Various structures containing interacting forces and strains can be

simulated and studied with the dual-machine approach For example, the

combined relaxation, creep, and unloading behavior of a bolt-flange system

can be difficult to analyze, but can be evaluated effectively with the system

shown in Fig 6 The similarity between this figure and Fig 3 is readily ap-

parent Consequently, the governing equations are of the same form:

force on flange, and external applied force

FIG 6 Testing machine interconnections for bolt-flange simulation

The external force P can be tensile or compressive, constant or variable It

can rtpresent, for example, a variable pressure acting upon the walls of a

pipe or vessel or a centrifugal force in a rotating component The A~/i F

represents the initial differential strain in the system and, in this case,

STENTZ ON THERMAL RATCHETTING 11 provides the means for "tightening the bolt" Possible evaluations could in-

clude the study of the effects of gradual creep or relaxation in the bolt or the

effects of one or more extreme force excursions All forces and strains

would be available for recording and analysis While separate materials

would be needed when the materials of bolt and flange differ, any dimen-

sional differences in area can be accommodated with system scale factors

Future Development Areas

Because of a variation in the values of Young's modulus (E) and Poisson's

ratio (v) as functions of temperature the computed axial strain will be cor-

rect only if the correct material constants are used at the temperature of in-

terest In the demonstration tests, the analog strain computer was calibrated

for operation at 1100 F which resulted in an error of less than 3 percent at

800 F The maximum error could have been reduced by calibrating at an in-

termediate temperature and could have been eliminated for all practical pur-

poses by adjusting the computer material constants as a function of

temperature This technique may be necessary in those tests where a very

large temperature change causes a wide variation of E and v The error likely

to be encountered in a computed axial strain by using the wrong material

constants can be determined from the following equation:

L ' O - 2 v c ) - e ~ ( i - 2 v )

E c 0 - 2v)

where the subscript c denotes the wrong value of the material constant used

in the computation, ea is the diametral strain, and ~ is the instantaneous

stress in the specimen

The heating and cooling rates of 5 F per s were chosen for the pilot tests,

primarily because they were easily within the capability of existing induc-

tion generators and did not require forced cooling Although definite rates

are not required to establish the desired temperature differential between the

specimens, they may be necessary because of associated strain rate and

temperature exposure requirements Increasing the heating rate is generally

less of a problem than increasing the rate at which a specimen cools In the

latter case it may be necessary to use hollow specimens and forced air cool-

ing Any such requirement, of course, would further increase the complexity

of the system

Conclusions

Basically, the effort to date regarding the use of the dual-machine ap-

proach in a study of thermal ratchetting has been to demonstrate the

feasibility of the technique and to identify developmental areas It is felt that

the technique is adaptable to most closed-loop testing machines, and while

12 CYCLIC STRESS-STRAIN BEHAVIOR

somewhat complex to set up and expensive to operate, it will permit a detail-

ed study of component and material interaction, producing a very large amount of data per testing hour

The particular model selected for simulation, the three-bar assembly, might not be directly applicable to specific design problems It is felt, however, that material data generated in this manner will have important application in analytical studies of various ratchetting problems While emphasis has been placed on the three-bar assembly, a strong possibility ex- ists that these principles can be applied to the direct simulation of other structural element interactions

It is hoped that the treatment of this specific case may suggest ways of studying other interactions with a similar approach It is only necessary to identify the equations controlling the interactions and to impose these con- ditions upon the testing system

References

[l] Miller, D.R., Journal of Basic Engineering, June 1959, pp 190-196

[2] Bree, J., Journal of Strain Analysis, Vol 2, No 3, 1967, pp 226-238; Vol 3, No 2, 1968, pp

C E J a s k e , 1 H M i n d l i n , ~ a n d J S P e r r i n ~

Cyclic Stress-Strain Behavior of Two

Alloys at High Temperature

REFERENCE: Jaske, C.E., Mindlin, H., and Perrin, J.S., "Cyclic Stress-Straln

Behavior of Two Alloys at High Temperature," Cyclic Stress-Strain Behavior Analysis,

Experimentation, and Failure Prediction, A S T M STP 519, American Society for Testing

and Materials, 1973, pp 13-27

ABSTRACT: The cyclic stress-strain curve is useful in the design of structural com-

ponents that are subjected to cyclic plastic deformation Since the incremental step test

has been used successfully to approximate cyclic stress-strain curves of metals at room

temperature, the objective of this study is to evaluate its usefulness in describing the

cyclic deformation behavior of two alloys at elevated temperature

Constant strain rate incremental step tests were conducted on nickel-iron-chromium

Alloy 800 and Type 304 austenitic stainless steel in air at temperatures between 70 and

1400 F This experimental technique provided a useful method of determining cyclic

stress-strain curves for these two alloys over that temperature range Alloy 800 cyclically

hardened by factors between 2 and 5, with a maximum amount of hardening at 1200 F

Type 304 stainless steel cyclically hardened by factors between 2 and 3, with a maximum

amount of cyclic hardening at 1000 F Strain rate and maximum strain range were

shown to influence cyclic hardening of the Type 304 stainless steel at both 1000 and

1200 F Results indicated that the cyclic stress-strain curve obtained from an incremen-

tal step test is most useful for estimating the cyclic stress-strain response of a material

under variable-amplitude loading

KEY WORDS: fatigue (materials), nickel-containing alloys, austenitic stainless steel,

cycles, hardening (materials), softening, stresses, strains, tests, evaluation, temperature,

cyclic loading, stress strain diagrams

In studies of the low-cycle fatigue behavior of metals, it is important to consider their cyclic stress-strain response Most engineering metals exhibit some degree of cyclic hardening or softening when they are subjected to repeated cyclic plastic deformation Cyclic hardening or softening is usually observed by cyclic changes in stress under strain-controlled conditions It is also evidenced by cyclic changes in strain under stress-controlled conditions The cyclic stress-strain curve is a useful and convenient method of describing and characterizing cyclic stress-strain behavior in direct com- parison with the monotonic stress-strain curve from an ordinary tension

~Senior researcher, division chief, and associate fellow, respectively, Battelle Columbus Laboratories, Columbus, Ohio 43201

14 CYCLIC STRESS-STRAIN BEHAVIOR

test The cyclic stress-strain curve is usually defined [ 1 ]2 as the curve form-

ed by connecting the tips of stable hysteresis loops from constant-amplitude, strain-controlled fatigue tests of several specimens at different strain ranges

In an investigation of alternative procedures for defining the cyclic stress- strain curve, it was found that the incremental step test provides a useful method of experimentally determining the cyclic stress-strain response of several metals at room temperature E2"]

The objective of the present study is to investigate the usefulness of this experimental technique in describing the cyclic deformation response of solution-annealed nickel-iron-chromium Alloy 800 and annealed Type 304 austenitic stainless steel at elevated temperatures These two alloys are used

in pressure vessel and piping system components that may be subjected to significant cyclic strain at temperatures above 800 F, where time-dependent deformation becomes significant Alloy 800 is being considered for use in such applications at temperatures up to 1400 F, and Type 304 stainless steel

is being considered for temperatures up to 1200 F

Experimental Approach

The general experimental approach used in this study was to axially load hourglass-shaped specimens using a servocontrolled, electrohydraulic system operated in closed-loop axial strain control (See Fig 1.)

Equipment

Specimens were heated in air by high-frequency induction, temperature was measured with Chromel-Alumel thermocouples, strain was measured with a special diametral extensometer, and load was measured with a con- ventional load cell Diametral strain and load signals were combined and converted to calculate an axial strain feedback signal using an analog com- puter [3] The strain-time program waveform (Fig 2) was generated using a hybrid digital block programmer with sequential input instructions from punched paper tape

Gripping of the specimens was accomplished using a fixture arrangement patterned after that used in other low-cycle fatigue studies [4] The lower end of the specimen was threaded into an adapter attached to the load cell which was in turn fastened to the hydraulic actuator, and the upper end was attached to the load-frame crosshead through a Wood's metal type of liquid-solid grip [5] Both upper and lower grips were continuously water- cooled

Specimen Preparation

A description of the two alloys used in this investigation is given in Table

I Specimens were machined to the configuration shown in Fig 3 The test

2The italic numbers in brackets refer to the list of references appended to this paper

IASKE ET AL ON ALLOYS AT HIGH TEMPERATURE 15

FIG l Photograph o f specimen in the test system

FIG 2 Strain-time waveform for 21/2 blocks of an incremental step text

16 CYCLIC STRESS-STRAIN BEHAVIOR

TABLE 1 1dentification of materials

Alloy 800 Type 304 Stainless Steel

Specimen Letter

Code

Condition Hot-finished 1-in diameter bar,

solution-annealed at 2100 F for

lh

Source Huntington Alloy Products Divi- Battelle's Pacific Northwest

sion of the International Nickel Laboratories a Company, Huntington, West

Virginia ASTM grain size

aThe prior history of this material is documented in Ref 6

section o f each s p e c i m e n was p o l i s h e d with successively finer grades o f

silicon c a r b i d e p a p e r to p r o d u c e a surface finish o f 16 u i n r m s or better,

with f i n i s h i n g m a r k s parallel to t h e l o n g i t u d i n a l axis N o heat t r e a t m e n t was

given to the s p e c i m e n s after m a c h i n i n g

Test Procedure

D u r i n g each b l o c k o f l o a d i n g in a n i n c r e m e n t a l step test, axial s t r a i n was

cycled at a c o n s t a n t rate in 20 i n c r e m e n t s of d e c r e a s i n g total s t r a i n r a n g e

f o l l o w e d by 20 i n c r e m e n t s o f i n c r e a s i n g total s t r a i n range, A~ t F i g u r e 2

JASKE ET AL ON ALLOYS AT HIGH TEMPERATURE 17

2.50"

FIG 3 Specimen configuration

shows 289 blocks of such cycling Note that the first quarter cycle was in ten-

sion to obtain a monotonic stress-strain curve The blocks of strain cycling

were repeated until the specimen failed by a complete fracture through the

cross section

Stress-strain hysteresis loops were recorded during the initial half block of

cycling (Fig 4a) and periodically thereafter Cyclic stress-strain curves were

obtained by drawing a curve through the tips of the hysteresis loops for a

stabilized record, such as that shown in Fig 4b

Results

Five specimens of each alloy were tested with a maximum total strain

range of about 3 percent as summarized in Table 2 Both cyclic and

monotonic stress-strain curves that were obtained from these tests are

shown by the solid curves that extend to 0.015 strain in Figs 5 and 6 The

cyclic curve taken from a series of stable hysteresis loops was essentially the

same for both increasing and decreasing increments of cycling The plotted

symbols represent stable cyclic stress-strain values from constant-amplitude,

strain-controlled tests of the present study and of past studies of Alloy 800

[7] and Type 304 stainless steel [8,9], as indicated

Four step tests of Type 304 stainless steel were also performed at 1000 and

1200 F and at maximum total strain ranges of 1 percent as reported in Table

3 The effect of decreasing the strain rate from 4 • 10 to 4 • 10-Ss -~ was in-

vestigated in these tests The cyclic curves for these tests at 4 • 10-3s -~ are

indicated by the solid lines extending to 0.005 strain in Figs 6c and 6d For 4

• 10-Ss - ' , the cyclic and monotonic curves are represented by dashed lines;

the monotonic curve at 1000 F was the same as for 4 X 10-3s -]

A cyclic offset (0.2 percent) yield strength analogous to the conventional

offset (0.2 percent) yield strength was obtained from each of the cyclic

18 CYCLIC STRESS-STRAIN BEHAVIOR

a I n i t i a l c y c l i c h a r d e n i n g d u r i n g B l o c k 1 - d e c r e a s i n g i n c r e m e n t s

b C y c l i c a l l y s t a b l e b e h a v i o r d u r i n g B l o c k 21 - d e c r e a s i n g i n c r e m e n t s

FIG ~-Stress-strain hysteresis loops for an incremental step test o f Type 304 stainless

steel at 1000 F (Specimen SS26)

JASKE ET AL ON ALLOYS AT HIGH TEMPERATURE 19

TABLE 2 Results o f incremental step tests at maximum total strain ranges of

Specimen

Maximum Number of Temperature, Total Strain Blocks of

aspecimen failed at thermocouple weld

stress-strain curves of the step tests to give a quantitative measure of cyclic

hardening behavior Values of the cyclic and monotonic yield strengths are

given in Table 4

Discussion

The cyclic hardening tendencies of these two alloys under constant-

amplitude strain cycling are reflected by the cyclic stress-strain curves from

the step tests (Refer to Figs 5 and 6.) Although the constant-amplitude

data points do not fall exactly on the step test cyclic curves, most of these

data points would be predicted more closely by the step test cyclic curves

than by the monotonic curves Points from the constant-amplitude tests fall

close to or slightly above cyclic curves from the incremental step tests at

high strain amplitudes, but they tend to fall below the curves at lower strain

amplitudes This behavior is most prQnounced for Alloy 800 at 70 F (Fig

5a) and for Type 304 stainless steel at both 70 and 800 F (Figs 6a and 6b)

Based on these results, it is hypothesized that the materials have a

"memory" for cycles applied at high strain levels in the incremental step

tests; thus, subsequent cycles at low strain are then influenced by the prior

history of cylic hardening

a At 7 0 F

Constant Amplitude, Continuous Cycling

[ ] Group A, Heat HH8968A (GEMP-732)

0 Group A, Heal H H 8 9 6 8 A ]

/

9 Group B, Heal HHO9OIA~ presenl study

9 Group C, Heat H H 3 3 1 0 A ) Z~ Group 0, Heat HH:3113A (present study)

FIG %-Comparison o f monotonic and cyclic stress-strain curves.['or incremental step

tests o f Alloy 800 at a strain rate o f 4 • 10 -3 s - ]

Further support for this hypothesis was evidenced by the fact that less

cyclic hardening was observed in the tests of Type 304 stainless steel at 1 per-

cent maximum strain range than in those at 3 percent This difference in

cyclic hardening behavior is shown by the curves in Figs 6c and 6d and by

the cyclic yield strength values in Table 4

At a strain rate of 4 x I0 -s s - I

At a strain rate of 4 x I0 -5 s -I

0 Constant amplitude, continuous cychng (present study) "[ At a strain rate

El Constant amplitude, continuous cycling ( G E M P - 6 4 2 and - 7 5 0 ) I of 4 x I0 -s s - j

F I G 6 Comparison q f monotonic and cyclic stress-strain curves ,for incremental step

tests o f 7~vpe 304 stainless steel

As shown by the dashed lines in Figs 6c and 6d and by the cyclic yield

strength values in Table 4, decreasing the strain rate from 4 X 10 -3 to 4 X

10 -s s -1 increased the amount of cyclic hardening at 1000 F, and decreased

it at 1200 F The implication of the above results is that the cyclic hardening

mechanism at these temperatures is time-dependent as well as cycle-

dependent, and that the time-dependent effect is opposite at the two

temperatures

The cyclic yield strength of Alloy 800 is relatively constant from 70 to

1200 F, with a maximum value at 1000 F, and drops by a factor of about

two between 1200 and 1400 F For Type 304 stainless steel, it decreases with

increasing temperatures between 70 and 1200 F Based on the ratio of cyclic

to monotonic yield strength (see Table 4), Alloy 800 shows a maximum

22 CYCLIC STRESS-STRAIN BEHAVIOR

T A B L E 3 Results o f incremental step tests o f Type 304 stainless steel at maximum

total strain ranges o f 1 percent

Strain M a x i m u m N u m b e r o f Temperature, Rate, Total Strain Blocks to

a Test was suspended because o f heating unit failure

amount of cyclic hardening at 1200 F, and Type 304 stainless steel shows a

maximum amount of cyclic hardening at 1000 F

It has been shown [1] that the cyclic stress-strain curve can be ap-

proximated by the following function:

where

Act/2 = cyclically stable stress amplitude, ksi

K' = cyclic strength coefficient, ksi

1

n = cyclic strain hardening exponent

From Eq 1 it follows that

lOgl0 (Ao/2) = lOgl0 K' + n' lOgl0 (Aep/2) (2)

Analysis of the step test cyclic stress-strain curves in Figs 5 and 6 showed

that they could be well represented by Eq 2 Values of the cyclic strength

coefficient and cyclic strain hardening exponent (Table 4) were obtained

24 CYCLIC STRESS-STRAIN BEHAVIOR

from a least squares regression analysis of data points from the cyclic

curves Values of Aep/2 were computed from the relation

where E is the modulus of elasticity, ksi An analogous procedure was used

to compute the monotonic strength coefficients and the monotonic strain

hardening exponents listed in Table 4

Because these alloys cyclically harden, the cyclic strength coefficients were

generally greater than the monotonic ones, and the cyclic strain hardening

exponents were generally less than the monotonic ones For Alloy 800,

values of n'were between about 0.09 and 0.12 and showed no significant

trend as a function of temperature For Type 304 stainless steel, values of n'

were between about 0.10 and 0.16; however, n' was 0.16 at 70 F and most of

the values at 800 to 1200 F were between 0.10 and 0.12 The large values of

both monotonic and cyclic strain hardening exponents for the 1.0 percent

maximum strain ;range at 1000 F reflect the tendency of the logarithmic

plots of stress (or Aa/2) versus plastic strain (or h~p/2) to increase in slope

at low strains at this temperature Values of n'for these two alloys fall close

to or within the range 0.10 to 0.20 that has been reported for a variety of

other alloys [2]

Under actual service conditions, materials are usually subjected to com-

plex variable-amplitude loading histories rather than constant-amplitude

cycles Since the previous comparison of constant-amplitude with variable-

amplitude cyclic stress-strain behavior showed that prior cyclic hardening at

higher strain ranges influenced stable stress values at lower strain ranges, it

was reasoned that high strain ranges in a loading spectrum may significantly

affect the stress-strain response throughout the entire spectrum

To examine this type of cyclic stress-strain response, stable stress-strain

values from two-level block-loading tests [10] of the same material used in

this study were compared with corresponding cyclic stress-strain curves

(Fig 7) In these tests, repeated cycles of strain were applied at two alternate

levels with either one cycle at the high level followed by 10 cycles at the low

level, or 10 cycles at the high level followed by 100 at the low level For each

of these tests, two points are plotted in Fig 7 The squares represent the

stable stress-strain response at the high strain level; and the circles, at about

one fourth that strain amplitude, represent the stable stress-strain response

at the corresponding low level The solid lines are the cyclic and monotonic

curves from Figs 6c and 6d, and the dashed lines are the mean curves

through the plotted constant-amplitude points from the same two figures

At both 1000 and 1200 F, the stable stress-strain values from the block

loading tests fall much closer to the cyclic curve from the incremental step

test than to the cyclic curve from the constant-amplitude tests

80

IASKE ET AL ON ALLOYS AT HIGH TEMPERATURE

O Low level ], Stoble amphtudes from two-level [] High levelJ block-looding tests of daske, et el

~" \Cychc curve from

incremental step _test

"Cyclic curve from

incremental step test

FIG 7 Comparison q f cyclic stress-strain response from two-level block-loading tests

with cyclic stress-strain curves

These limited results from block loading tests indicate that the incremen-

tal step test may be extremely useful in predicting the cyclic stress-strain

response of such alloys under variable-amplitude loading conditions A

maximum strain amplitude of 1.5 percent with 20 increments of cycling per

26 CYCLIC STRESS-STRAIN BEHAVIOR

half block was chosen for the initial tests based upon the experience of

Landgraf et al [2] When a memory effect was noted in the cyclic strain

hardening behavior, a few additional tests were conducted at a maximum

strain amplitude of 0.5 percent For application to design under variable-

amplitude loading conditions, it would be desirable to use the cyclic stress-

strain curve with a maximum amplitude similar to that anticipated for the

in-service loading spectrum Thus, a family of step test cyclic stress-strain

curves would be required at each temperature For example, in addition to

the curves shown in Fig 6, cyclic curves to maximum amplitudes of 0.25 per-

cent and 1.0 percent would also be desirable for the Type 304 stainless steel

at 1000 and 1200 F

In the present step tests, a linear distribution of the 20 strain increments

was used To study cyclic stress-strain response under conditions that more

closely simulate variable-amplitude service loading, nonlinear distributions

of the strain increments that correspond to the actual distribution of the

loading spectrum should be used

Results of the tests at different strain rates point out that the influence of

time-dependent deformation on cyclic stress-strain behavior also needs to be

investigated further Step tests should be conducted at strain rates as low as

10 -6 to 10-as -1 to simulate those that may be encountered in actual service

Step tests with hold times at peak strain need to be conducted to determine

the influence of hold time on cyclic stress-strain behavior Such tests would

also provide a great deal of information on cyclic stress relaxation behavior

Conclusions

Results of this study showed that the incremental step test can be used to

obtain meaningful data on cyclic stress-strain behavior at elevated

temperature An important advantage of this test is that directly comparable

monotonic and cyclic stress-strain curves were developed by testing a single

specimen Use of one specimen to define the cyclic curve permitted the effect

of important variables, such as temperature, strain rate, and maximum

strain amplitude, to be studied quickly and economically

Alloy 800 cyclically hardened by factors between 2 and 5 (Table 4) over

the temperature range of 70 to 1400 F, with a maximum amount ofhardeh-

ing at 1200 F, Type 304 stainless steel cyclically hardened by factors between

2 and 3 (Table 4) over the temperature range of 70 to 1200 F, with a max-

imum amount of hardening at 1000 F

Strain rate had a significant effect on the cyclic stress-strain response of

Type 304 stainless steel at both 1000 and 1200 F Decreased strain rate

produced increased cyclic hardening at 1000 F and decreased cyclic harden-

ing at 1200 F

Cyclic (and monotonic) curves from the step tests were well described by a

power function relating stress amplitude (stress) and plastic strain amplitude

JASKE ET AL ON ALLOYS AT HIGHTEMPIERATURES 27

(plastic strain) Cyclic strain hardening exponents for this function were between 0.09 and 0.16 for these two alloys

Type 304 stainless steel exhibited different cyclic stress-strain behavior under variable-amplitude loading than under constant-amplitude loading Experimental results indicated that the cyclic stress-strain curve generated from some type of incremental step test may provide the most reasonable es- timate of cyclic stress-strain response for variable-amplitude loading con- ditions that are generally encountered in engineering design applications

A cknowledgmen ts

This investigation was sponsored by the U.S Atomic Energy Commission under Contract W-7405-eng-92 Thanks are also extended to H J Malik and J J Parks for their assistance in conducting the experimental work

References

[1] Morrow, JoDean in Internal Friction, Damping, and Cyclic Plasticity, A S T M S T P 378,

American Society for Testing and Materials, 1965, pp 45-87

[2] Landgraf, R.W., Morrow, JoDean, and Endo, T., Journal of Materials, Vol 4, No.7,

March 1969, pp 176-188

[3] Slot, T., Stentz, R H., and Berling, J T in Manualon Low-CycleFatigue Testing, A S T M

STP 465, American Society for Testing and Materials, 1969, pp 100-128

[4] Feltner, C E and Mitchell, M R in Manual on Low-Cycle Fatigue Testing, A S T M S T P

465, American Society for Testing and Materials, 1969, pp 27-66

[5] Morrow, JoDean and Tuler, F R in Transactions, The American Society of Mechanical Engineers, Series D, Journal of Basic Engineering, Vol 87, No 2, June, 1965, pp 275-289

[6] Claudson, T T., "Fabrication History of Alloys Used in Irradiation Effects on Reactor Structural Materials Program," BNWL-CC-236, Pacific Northwest Laboratory, Richland, Wash., Oct 1965

[71 Conway, J B., "Short-Term Tensile and Low-Cycle Fatigue Properties of Incoloy 800," General Electric Report GEMP-732, Cincinnati, Ohio, Dec 1969

[8] Berling, J T and Slot, T., "Effect of Temperature and Strain Rate on Low-Cycle Fatigue Resistance of AISI 304, 316, and 348 Stainless Steels," General Electric Report GEMP-

642, Cincinnati, Ohio, June 1968

[9] Conway, J B., "An Analysis of the Relaxation Behavior of AISI 304 and 316 Stainless Steel at Elevated Temperature," General Electric Report GEMP-730, Cincinnati, Ohio, Dec 1969

llO] Jaske, C E., Mindlin, H., and Perrin, J S., "Prediction of Fatigue Life Under Complex

Loading Conditions at High Temperature," Symposium on Metallurgical Factors in High-Temperature Life Prediction, American Society for Metals Materials Engineering Congress, Detroit, 18-21 Oct., 1971

H Abdel-Raouf, ~ A Plumtree, t a n d T H Topper 2

Effects of Temperature and Deformation

Rate on Cyclic Strength and Fracture of

Low-Carbon Steel

REFERENCE: Abdel-Raouf, H., Plumtree, A., and Topper, T.H., "Effects of

Temperature and Deformation Rate on Cyclic Strength and Fracture of Low-Carbon

Steel," Cyclic Stress-Strain Behavior - - Analysis, Experimentation, and Failure Predic-

tion, A S T M S T P 519, American Society for Testing and Materials, 1973, pp 28-57

ABSTRACT: Cyclic deformation behavior and fracture mechanisms of Ferrovac E

iron under low cycle fatigue conditions are studied at temperatures ranging from 23 to

540 C, cyclic deformation rates from 4 • 10 4 to 2 x 10 -~ s -~, and strain ranges from

0.010 to 0.040 The stress response during strain cycling shows three stages, primary

hardening, steady state behavior, and secondary hardening Both the onset and duration

of secondary hardening are dependent on deformation rate and temperature through the

process of dynamic strain aging Stress response sensitivity to deformation rate increases

under conditions which permit changes in both internal and effective stress components

There is a variation in the internal stress component at the blue brittleness temperature

(370 C) caused by an increase in total dislocation density due to dynamic strain aging

However, at higher temperatures (485 to 540 C) a variation in the internal stress compo-

nero is caused by accelerated thermal recovery Steady state cyclic deformation in this

temperature range is observed to be consistent with models for steady state creep and

hot-working The fracture mechanism and fatigue life are mainly influenced by the

characteristics of stress and strain redistribution and the inhomogeneity of plastic

strains This inhomogeneity of deformation results from dynamic strain aging effects

during fatigue A parameter which controls stress response, fatigue behavior, and frac-

ture mode under dynamic strain aging conditions is presented

KEY WORDS: stresses, strains, deformation, aging (metallurgy), stress cycle, fatigue

(materials), creep properties, hot working, fatigue life, damage, crack propagation, frac-

tography

Nomenclature

Stress response

Ae Total strain range

~Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario,

Canada

2Department of Civil Engineering, University of Waterloo Ontario, Canada

28

Number of cycles Internal stress components Thermal stress component

Cyclic deformation behavior of carbon steels is complicated by the effect

of strain aging on the resistance to plastic deformation [1] 3 Many research

workers [2,3,4,5] have shown the dependence of fatigue limit on the amount

of interstitials present in o~-iron solid solution and that aging occurs dynamically For coarse grain steels, Oates and Wilson [5] observed exten- sive plastic deformation below the fatigue limit stress They suggested that the diffusion rate and precipitation of interstitial solutes may be enhanced during plastic deformation and that the fatigue limit observed in this case was due to dynamic strain aging rather than to initial dislocation locking At temperatures above 100 C, fatigue life improved with temperature reaching

a maximum at various temperatures between 200 and 400 C, depending on

the testing frequency [6,7] This increase in life was attributed to dislocation

locking by carbon and nitrogen and also to the formation of finely dispersed

precipitates of carbides and nitrides [6,7] Two aging reactions were

reported to occur during fatigue of steel at room temperature, one of which involved dissolved carbon in ferrite and the other involving the resolution of iron carbides [8] More evidence concerning the influence of dynamic strain aging on low cycle fatigue properties was reported by Coffin [9] who showed

a strong dependency of stress response on the amount of interstitials present

in the ferrite phase

The type of substructure generated during fatigue of carbon steels is dependent on the cyclic stress level At low stress amplitudes, patches of dis- location loops are observed, but a cell structure is formed at high stress 3The italic numbers in brackets refer to the list of references appended to this paper

30 CYCLIC STRESS-STRAIN BEHAVIOR

amplitudes [10] The size of these dislocation cells is dependent on cyclic

strain amplitude [11] Holden.[12] showed that microcracks were formed at

the fatigue generated subboundaries in polycrystalline iron thus estab-

lishing a link between the initiation of fatigue cracks and fatigue formed

substructures The density of dislocations and their arrangement in the sur-

face layer were found to be distinctly different from those of the bulk

material [13] Higher dislocation densities observed near the surface

suggested that surface layer characteristics control fatigue behavior

Aging effects in fatigue arise from the interaction of point defects with

dislocations These interactions inhibit plastic flow and therefore play a role

in both initiation and growth of fatigue cracks [14] Recently, Wilson et al

the tendency for the plastic strains to concentrate in active slipbands leading

to crack initiation

This paper presents the results of an investigation of the effects of

temperature and deformation rate on cyclic deformation behavior and frac-

ture mechanism of low-carbon steel Special attention has been given to

dynamic strain aging as a fatigue strengthening mechanism

Experimental

Material and Specimens

The material used in this investigation was Ferrovac E iron, of the

chemical composition given in Table 1 Rolled bars of 0.5 in in diameter

were annealed for 1 h at 700 C in vacuum, and subsequently furnace-cooled

giving a final grain size of about 80 m# Fatigue specimens were machined

as indicated in Fig 1, surface ground, and finally chemically polished [16]

T A B L E 1 Chemical composition o f Ferrovac E iron

ABDEL-RAOUF ET AL ON TEMPERATURE AND DEFORMATION RATE

0"i

31

05" @ N

FIG l Fatigue specimen

Apparatus and Procedure

Fatigue testing was done in a closed loop servocontrolled testing machine

equipped with a commercial load cell and a displacement transducer in the

ram A self-aligning molten metal grip attached to the ram minimized self

stresses in specimen setup [17] Stainless steel grips which attached to the

load cell at the upper and the molten metal grip at the lower end were water

cooled The threaded ends of specimens were coated with a high

temperature lubricant before being locked in the grips An electrical

resistance furnace with a proportional controlling unit surrounding the

specimen maintained desired temperatures for various tests During heating,

the machine in load control was set to maintain zero load In this case, the

stroke signal changes as thermal expansion occurs in the specimen and the

grips A steady state stroke signal which is reached somewhat later than the

desired oven temperature indicates dimensional stability in all heated com-

ponents has been achieved

32 CYCLIC STRESS-STRAIN BEHAVIOR

Axial strains were controlled and measured using a clip-on extensometer

at room temperature and a stroke transducer mounted on the ram at

elevated temperature The techniques used in obtaining a satisfactory

stroke-strain calibration is of some interest A special stainless steel clip-on

extensometer with high temperature strain gages was first calibrated at all

temperatures of interest With this transducer a reference specimen was then

strained at the combinations of strain amplitude and temperature chosen for

this project and stroke-strain hysteresis loops similar to those of Fig 2 ob-

tained The line connecting the tips o f hysteresis loops in this figure in-

dicates a linear relationship between stroke amplitude and total strain

pB

) RAM STROKE (in)

F I G 2 Stroke-strain relationship

amplitude in the range o f strains investigated While cyclic hardening of the

material increases the load response of a specimen throughout a test, the

stiffness of the components in series with the specimen is great enough that

changes in the linear relationship between stroke and strain are too small to

be measured The results also indicated that this calibration is not affected

by temperature over the range investigated It is important to point out that

stroke-strain hysteresis loops were very sensitive to specimen design and

that specimen dimensions were selected to give minimum hysteresis Stroke

measurements and this calibration were used t h r o u g h o u t the testing

program to estimate specimen strain Since there is no extensometer in con-

tact with the specimen, the advantage of a free fracture without any effects

due to knife edges is attained

Independent testing variables were strain range, temperature, and cyclic

deformation rate The material was cycled sinusoidally at three relatively

high strain ranges of 0.010, 0.020, and 0.040 The other two variables

(temperature and cyclic deformation rate) were chosen such that a wide

variation of stress response due to dynamic strain aging effects would be at-

tained F o r this purpose, interrupted tests were carried out at different

temperatures with cyclic frequency being changed over a wide range for

each temperature level On this basis, temperatures of 23, 205, 370, and 540

C and four deformation rates of 4 • 10 -4, 1.6 X 10 -3, 8 • 10 -3, and 2 X 10 -~

s -~ were chosen for this study To examine the effect of cyclic deformation

rate, the test frequency was decreased as the strain range increases (6 =

2Ac f s -1) [20] Where @ is the average deformation rate t h r o u g h o u t a strain

cycle In a given test, a specimen was cycled to failure at a single combina-

tion of strain range, temperature, and deformation rate

Surface damage and fracture surfaces were examined using scanning

electron microscopy

Results

The cyclic stress response at room temperature is shown in Fig 3 During

cycling, the material shows a primary hardening period followed by steady