NASA 

Contractor Report 175048 , ,. 

USAAVSCOM 

Technical Report 86-C-4 

Thermal-Mechanical Fatigue Behavior 

of Nickel-Base Superalloys 

R.M. Pelloux and N. Marchand 

Massachusetts Institute of Technology 

Cam bridge, Massachusetts 

/ 

March 1986 

Prepared for 

Lewis Research Center 

Under Grant NAG 3-280 

National Aeronautics and 

Space Administration 

d 

e 5 I B c P * -a+ 
Page 

1 .............................. . Introduction 1 

2 . ProgramApproach ............................ 3 

2.1 Task 1:Literature Survey ..................... 

2.2 Task 1I:Problem Definition .................... 5 

2.2.1 Inconel X-750 ...................... 8 

2.2.2 Hastelloy-X ....................... 8 

5 

2.2.3B-l900+Hf ........................ 8 

2.3 Task 1II:Oesign and Construction of Testing Unit 9 

2.4 Task 1V:Mechanical Behavior ................... 9 

2.4.1 Basic Properties ..................... 10 

2.4.2 TMF Testing ....................... 10 

2.4.3 Damage Characterization ................. 11 

2.5 Task V:Data Analysis ....................... 11 

......... 

3 . Main Achievements ............................ 12 

References ................................. 14 

Appendices 

A . Test Equipment & Test Procedures ................. A1 

B . Fracture Mechanics Analysis ................... B1 

C . TMFCG in Inconel X-750 ...................... C1 

0 . TMF In B1900tHf ......................... D1 

E . Summary of the Test Results ................... El 

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a a iw P I f! 
Any component exposed to repeated rapid thermal transients will fail by 

thermal fatigue. Thermal fatigue degradation mechanisms involve 

accumulation of damage, crack initiation, s?ow crack growth and failure b!d fast 

fracture. 

The material properties other than ductility which are important in thermal 

fatigue are hot tensile strength, elastic modulus, thermal conduct-ivity and 

thermal expansion. Oxidation resistance als13 plays an important role in 

thermal fatigue. The interactions betWeen material propert.ies, imposed 

thermal cycle, and component geometry define the ability of a structure to 

resist thermal fatigue. HO'iMVer, the synergistic effect-s between t-hese 

variables are quite complex, and prediction of thermal ffdigue behavior from 

basic properties is difficult. A major objective of most high-temperature 

fatigue programs is to develop and verify models for thermal fatigue by 

comparing experimental dat-a 'iVit-h analytical and/or computer-deri\.red 

predictions of thermal fatigue life. 

Prediction of crack propagation rates in structural components from specimen 

data generated in the laboratory is onlg possihle if i3 parijmeter can be foiund 

which characterizes the severity of the stress and strain r,qcles near the crack 

tip. Such a parameter is needed to match a particular loading and crack lenqth 

in a component with the cclrrect ef$Arii3letit specimen loading and crack length. 

in C~IS~S of cy cl i c 1 oadi ng mai nl 1.j i rivol vi rig 1 i nei3r e 1 as ti 1: de f mi ij t- i 11 ti Ssma 1 1 

scale yielding), the stress intensitg factor (dK) is 3 wiljely used and 

successful parameter. However, the stress lntensity fixt-or may no? be 

d 1 
applicable for some hot section components, since in these areas cracks may 

grow through regions of substantial plastic deformation. 

The prediction of propagation life in engine components requires t-he 

consideration of thermal-mechanical fatigue (TMF) cycles. The problem of 

ttiermomechanically driven crack growth in the presence of significant 

inelastic strains is a challenging problem. In order for a single parameter to 

be useful for predicting thermal-mechanical crack growth in components, it 

should sat-isfy the following conditions: 

1) It should predict crack growth ri3t.e from a single crack growt.h rate 

versus parameter curve. in this way, cracks of different lengths loaded 

in such a way as to yield the same value of the pararrieter., experience the 

same crack growth rate. 

2) It should correctlg predict fat-igue crack growth rates independently 

of part geometry. 

31 It should be calculable for complex real part gearnet-ries. 

Obviously, paramet-ers not satisfying the above requirements would be of 

li rnited value, since component or simulated component test-ing '~;r:i(ould dlWij!-JS 

be required to obtain crack growth rate informatiim. 

In this research program, it was propciseij til asses the suithbility of various 

parameters for correlating high temperature Citid t-hermal -mecfianii:al imck 

growth rates. A parameter was sought which can correlate data for the fir11 

range of conditions from elastic st.ress arid st-rain cgcling to substant.ially 

plastic st.rairi cycling. The ultitnat-e goal of establishing such a psrstneter- is 

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the prediction of the propagation life of real engine components, since it is 

known that cracks initiate earlg in fatigue life. 

As secondary goals, the crack growth data generated were combined with 

outical, SEPl, and TEM observations to assess a sound f!!ndamen!sl mechanist-ic 

understanding of the thermal-mechanical fatigue behavior !if tgpicai nickelbased superalloys. 

Program Amroach 

Fatigue crack growth data in TMF conditions have been obtained on tubul~ 

specimens for many years [ 1 I. This specimen geomet-ry prevents t.he format-ion 

of thermal gradients in the cross section of the materials, thus facilitating the 

dsts reduction step. The TMF crack growth data were reduced 121 using At(,, 

OK, BJ, dCTOD and Tomkin's model. All of them (except ACTOD) failed to 

predict the TMF data within a fact-or of five. One of the main problerrl:; with t.he 

analysis of the fracture mechanics data of tubular specimen is that there is no 

well-established equation which describes the state of st-ress and straln 

3head of a crack when significant plastic deformation takes piace. This is not 

surprising because all the equations developed for this geometry have asslumed 

a pure elastic behavior. 

In order to achieve our main goal , thermal-mechanical fatigue data '+;erg 

obtained on conventional fracture mechanics specimens (SEN) for which wellest-ablished equations to describe the stress-strain field shead of the crack 

exist. The data generated by the t-est procedure (qclinq iinder stress or st-rain 

CCintrol) were analyzed in terms of t-he mechanical st-resses ijtllj :;trains, ijtscl 

3 

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therrnsl stresses and strains, in order to assess their respective influence on 

crack gro'i~th behavior. Using these values and known fracture mechanics 

solutions, various fractim rnechanics pararneters were computed in order to 

estimate which one is the best and how it can be improved for life prediction in 

TMF conditions. 

The material used in this contract were tested in 3 progrijrfi designed to :span 3 

wide range of variables at sufficient dept-h to allow 3 fundamental mechanist.ic 

understanding of the problem. The test program was deslgned to pro?ide 

sufficient data to clearly define the link between the environment and the 

materials. in orljer to achieve the above, t-est. specimens were examined in 

detail after testing. Transmission electron microscopy (TEN) and scanning 

electron microscopy (SEMI analysis as we1 1 as more conventional techniques 

threre used. The main differences between the conventional and the TMF crack 

growth approach used in this program mag be summarized as follows: 

Conventional A~proach 

to TMF Crack Growth 

- Pro p o s e d A p_p ro a c h 

to TMF Crack Frowt-h 

-tubular specimen 

-no thermal gradient 

the cross section 

n 

- complex data reduction 

-na available fractrtre 

rl 

-fracture mechanics specimen 

-small t.herma1 gradient in 

the specimen 

-solutions for t-tie case of 

4 
mechanics solution for 

the case of significant 

inelastic deformation 

-this approach is used 

quali tatively to assess 

the TMF behavior of 

different alloys 

significant plastic deformation 

are available 

-quanti tati !re comparison af 

the crack growth data 

The experimental pragram consisted of five interrelated tasks which were 

achieved in chronological order. 

2.1 Task I: Literature SurveyDuring the first year of this work, an extensive literature sur-ilq of high 

temperature fatigue behavior Waf undertaken, with spec131 emphasis an TNF 

data. The testing procedures relevant to TMF behijvi~~r were a1si:i reviewed; ?t 

was shown that the TMF behavior is a strong function of the controlled 

parameters and the testing procedure. 

2.2 Task I I: Problem Definition 

Testing capability requirements and testing conditions were defi tied in 

collaboration with PWWA engineers for significant hot section cracking 

loC3tions of commercial aircraft engines. These locations include f irst-stage 

turbine vanes., first-stage turbine blades, and combustor liners. Cracking in hilt 

5 
section vanes, blades and combustor liners share many feat.iures in cot-fmii:ln. 

These common features are: 

1. Relatively high temperatures (typical tensperat.ure in the range of 

40O0C to Se;O”C); 

2. Time-dependent nonlinear material behavior; 

3. Variable cyclic strains and t.ernperatiures leading to thermalmechanical fatigue conditions and; 

4. Predominantly thermal loading, leading to a strain-controlled, rather 

than load-controt led si tiistion. 

The similar cracking characteristic between combustors, vanes and blades 

listed above imply that testing capability requirenients and testing prograrns 

for ttie vanes and blades closely parallel t.hose for the ~::omhi~ist.or liners. 

1. Strain control t.0 sitnulate the thermal loading of the cillmponent sime 

most high temperature cornpotients are under st-rain-cijntrotled 

conditions. The niectianical st-rain (t.ut-ij1 st-rain t-riitiim t-het-nlij] st-raiti) 

WBS contro I1 Ed. 

2. Strain hold times tu sirniulate steady state condit.ions trnderqorie 

during normal clperation of tiucleat- redctot- and gas t-urtline enqines. 

6 

d 

L R i q 
Cluring this period the test specimen is undergoing creephlaxation 

behavior. 

3. Controlled transient heating and cooling to simulate the component 

s t rai n c' t emp e ra t UTE f! ha se re 1 a t i on s hi p. 

4. Cimpressive load-carrying capability of the specimen to sustain 

compressive stresses which develop in the heating period sf the cycle. 

5. Crack length measurement capability to obtain crack growth data in 

TRF conditions. 

TfYlF crack propagation included testing of the base metal only, since t-his t.ype 

of criWing is readily studied by 3 fracture mechanics approach. The amount of 

component life spent in starting 3 crack in the coating has to be addressed in 

t-erms of crack initiation techniques. TMF tests should include sever31 t-estiny 

conditons in order to simulate the various strain-temperature t-eiijtions st 

vijrious locations in an actual component. 

Testing included both isothermal tests at the minimum and maximum 

t-emperature of the TMF tests. The following variable^^ 'Tt'erZ included in the 

testing procedures: 

2. mean strain, R = -1 and 0.5 

m 
3. strain rate, set by the maximum transient heating and cooling rate 

that can be experimentally obtained. 

The alloys selected for this reseach program are: 

Inconel E750 is a corrosion and oxidation resistant material with good tensile 

and creep properties at elevated temperatures. Typical applications include 

land-based gas turbine parts, nuclear reactor springs, bolts, bellows and 

forming tools. The tkmperature range of interest. is from 300 t-o 650°C. 

2.2.2 Haste1loy-XThis material is used extensively at Pratt & Whit-riey Aircraft in commercial 

aircraft engine combustor liners. Hastelloy-X is A nickel base alloy 

strengthened by a soilid solution of chramiurn arid rr-iolybdEctium. 

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This material is also used extensively at Pratt h Whitney Aircraft for 

commercial engines; typical applications are ~anes and blades (third stage). B1900 is an advanced conventionally cast nickel base alloy with y/'~(' hardening. 

When casting the test specimens, great c3re is taken to reproduce the 

microstructue encountered in actual companerrt parts. 

2.3 Task 111: Design and Construction of Testing Unit 

The apparatus which was built is a computer-controlled thermal fatigue 

testing system consisting primarily of a closed-loop servo-controlled electrohlJdr8iJlic tension compression fatige machine (MTS 8 10 model 906.061, 3 high 

frequency oscillator for industrial heating (Lepel Plodel T-2.5-?-K(31-5W~~, an 

air compressor for cooling, a low frequency function generator (Exact model 

504), a data acquisition and control system (HP-6942A1, 3 programmable high 

resolution DVM (HP-3478) and a main frame computer (HP 98 165). The system 

is capable of testing specimens of different size and configuratim I:SEN, CT, 

hollow tube, etc.) and to withstand B fatigue loading of 25 000 lhf (1 1 350Kyf). 

The test' specimen is mounted in a verticle plane into two end grips of high 

tensile steel. The specimen alignment is insured by the use of a Wood's metal 

pat which prevents the development of a net bending moment in the specimen. 

Because of DC potential drop technique is used to monitor crack growth, the 

lower grip is electrically insulated from the system by means of ceramic 

coating. The ends of the end grips are water cooled by means of copper coils 

surrounding them. The system and its capabilities are described in iletaii in 

Appendix 1. 

2.4 Task IV: Mechani~xl Behavior 

9 d 
2.4.1 Easi c Properties 

Tensile specimens were tested to qualify the mat.erials. Tests were conducted 

at room temperature and up-to 982°C. Metallographic specimens were taken 

from the Same I~ications to qualify materials. Conventional creep type 

specimens were 1-ested at various temperatures to characterize the 

deformation behavior of the materials. For Hastellq-X and E- 1300+Hf 

complete strain versus time behavior were measured to determine creep rates 

in the primary and steady state regimes. 

2.4.2 TMF t-estingThe TMF response of the materials wi% determined using single-edge-notched - 

(SEN) specimens under stress- or strain-contWo1led testing. The test. prqram 

was designed to evaluate the small scale yielding and fully plastic fat-ig1.1~ 

ct-iXk propagation behavior. 

A series of fatigue tests were perfclrmed using precracked lncorrel X-750 

specittiens imder a constant range of applied loads; the strijin and potential 

‘?!ere measured ijs dep~tidetit variaI3l es. I sothertnal crack growth 1est-s were 

performed at 400°C and 925°C. In-phase cycling (maximum temperature at- 
fully plastic) levels. Measinrement of the opening stress, as determined by the 

potential drop, provided useful information on the influence of environment and 

plasticity on crack propagation rates under TMF conditions. 

2.4.3 Damage Characteri zati on 

The microscopy of failed specimens included detailed TEM and fractbxpphic 

studg of microstructural changes such as yo coarsening, carbine precipi tatisn, 

grain boundary cracking, oxide cracking, and oxide penetration. Microscopic 

studies were performed on both isothermal and TMF failed specimens in order 

tl:f assess differences in microstructural damages associated With thermalmechanical fatigue. 

2.5 Task V: Data Analysis 

In wder to determine the respective influences of thermallg and mechanically 

"driven crack gro'iVth, relevant fracture mechanics parameters were computed in 

terms of thermal strains, mechanical strains and total strains. It was then 

realized that the conventional definitions of the fracture mechanics 

parameters (dK, OK, etc.) canned apply to displacement controlled crack 

growth experirnetit. Proper analytical solutions for hK atid A#, for 

displacement controlled testing were derived. The detail of the derivations are 

given in Appendix 11. 

The results obtained for lnconel X-750 ijre shown in Appendix II!. Res~-iits of 

damage analgsis ccrncernitig €3- 1 SlOO+Hf are shown in Appendix IV. Tfie fPlF 
conditions are shown in Appendix V. A complete anaIgsis of the data is 

discussed in 11 1. 

3. Main Achievements 

The main achievements of this research program are: 

1. Completion of a literatiire survey of the t-hermal-mechanical fatigue 

data published in the open literature. This literature survey covered the 

different experimental procedures for TMF testing. Following this 

review B new approach to the TMF problem was proposed. 

2. Agreement with Pratt. &. Whitney Aircraft. to co0perat.e on TMF 

research. PRWA provided materials and insight. as to determining the 

relevant testing conditions' for TMF. 

3. A fully computerized testing system t.o riun various TMF test was 

built. The software t.o run the isothermal and TMF t.ests, as well as to 

analyze the data were developed. A correction prmdim to the p0tetl?iijl 

drop technique to tnea~tlre crack lengths arid crack opening ( or closure) 

(stress) was 3191 produced. 

4. isotherma? and TMF tests (Yi'ith and without crscksl were perfrmmd. 

Tests were run BS to cover the complete range isf strain ranges, i.e. from 

elastic strain regimes to fiully plastic strain ranges. Special care WBS 

taken to dupl icate the temperature ranges and strai ti t-ijtigeS experi enceil 

b g i n - se r v i c e c o tt-1 p o ne n t s. 

5. Fracture mechanics solutions for displacement controlled SEN 

testing condi tons were cfevel~sped. It was :Sho'~tin that conventional 

4 12 
fracturt! rnechsnics solutions deve!oped for stress-controlled conditions 

overestimated the true driving force for cracking. 

6. Damage under isothermal and TMF conditions were identified for 8- 

1900+Hf. A sound mechanistic understanding of TMF in this allay Was 

achi eved. 

7. Various parameters were computed t.o correlate TMF crack growth 

data. The use of the stress intensit-y factor (derived far displacement 

controlled) corrected for the opening and closing of the crack WAS shown 

to be a successful parameter. 

13 d 
References 

1. N. Marchand: "Thermal-Mechanical Fatigue Behavior i2f Nickel-Base 

Superalloys", Doctoral Dissertation, M.I.T., December 1985. 

2. G.J. f'leeyers, "Fracture Mechanics Criteria for Turbine Engines and Hot Section 

Components", f4kSA LR- 167896, 1982. 

14 d 
Appendix A - Test Equipment 8, Test Procedures 

Submitted to ASTM J. Test & Eval. 

A Computerized Test System for 

Thermal-Mechanical Fatigue Crack Growth 

N. Marchand" and R.M. Pelloux ** 

* Research Assistant, Department of Materiels Science and Engineering, 

M.I.T., Cambridge, MA 02 1351, USA 

*+ Professor, Department of Materials Science and Engineering, M.I.T., 

Gambriage, MA 02 139, USA 

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Abstract 

A computerized testing system to measure fatigue crack growth under 

thermal-mechanical fatigue conditions was built and is described in detail in 

this paper. Built around a servo-hydraulic machine, the system is capable of 

push-pull test under stress or strain controlled conditions in the temperature 

range of 25- 1050°C. Both temperature and mechanical strain are independently 

controlled by the closed loop system to simulate complex in-service straintempera ture re1 uti onshi p. 

A DC electrical potential method is used to measure crack growth rates. 

The correction procedure of the potential signal to take into account powerline and RF-induced noises and thermal changes, is described in det8i1. It is 

shown that the potential drop technique can be used for physical mechanism 

studies and for modelling of crack tip processes. 

d 

A1 
Introduction 

During the psst two decades, the design criteria 8nd the material 

property requirements for critical structural components of gas turbine 

engines has changed. Until the mid-sixties, most critical components such as 

turbine disks and blades were life limited by the creep and stress rupture 

properties of their materials. However, a demand for improved performance of 

advanced engines has led to marked increases in operatlng temperature 8nd 

stresses. The result has been a transition from creep to low cycle fatigue 8s 

the dominant life limiting factor in over 75 percent of turbine components. 

Law cycle fatigue (LCFkdefined as the initiation, slow crack growth 

and fsilure by fast fracture in less than 5x 104 cycles--is a stochastic process 

having considerable variability. To provide a safe operating llfe, the LCF 

approach has been to use 8 lower bound on the mean cyclic life that is 

equivalent to a probability of 1/1000 of initiating a detectable Crack (1/32 

inch) during the design lifetime of the component. In practice, this translates 

into 999 out of 1000 components, which.are retired from service after 

reaching their design lifetime, although they are still structurally sound. In an 

attempt to utilize the remaining life of these 999 components without 

sacrificing structural safety, the U.S. Air Force and the major aircraft engine 

manufacturers have implemented 8 revised llfe management philosophy n8med 

retirement-for-cause (RFC) or on-condition Iifing. Under RFC, comDonents 

undergo periodic inspections and return to service ff no cracks larger than a 

"critical" size are detected. This procedure relies on two premises. First, the 

Cracks larger than a 'critical" size must be detected with a high degree of 

reliability. Second, the crack growth rates under in-service conditions have to 

- 

A2 
be predicted with high accuracy such that cracks smaller than the 'critical' 

size will not grow to a catastrophic size during one inspection interval. 

implemented Engine Structural lntegri tg Program (ENSIP) is 8 specification for 

future engines that requlres a Usmage tolerant 8ppt-OaCh for 811 critical 

components. Under this program, flaws or defects are assumed to exist in the 

component at the time of production. Design calculations and component 

testing must demonstrate that such defects will not grow to a catdstrophic 

size within the lifetime of the engine. In this scenario, the abillty to measure 

and analytlcelly predlct crack growth under typlcal englne operating conditions 

is a key technology. These conditfons, as shown in Figure 1, Include variation 

in temperature, strain ratio, sustained loadlstrain hold time, as well as 

i r: t eract i ve effects. 

Whereas the RFC is being applied to existing engines, the newly 

There are, at the present time, some sophisticated testing assemblies 

which are Capable of reproducing the compiex stress-strain-temperature 

cycles described in Figure 1 12-41. However, these equipments are very 

expensive, which partly explalns why most of the high temperature fatigue 

tests are stili conducted under isothermal conditions. These test systems use 

tUbUl8r specimen geometry and some fatigue Crack growth data has been 

generated with this geometry in the last ten years 14-71. Unfortunately, this 

geometry Is not easily sultable lor crack growth measurement and It Is no 

surprise that crack growth rates data lower than i@ m/cycle have not been 

measured. Adequate fatigue life prediction relies on the knowledge of 

experimental crack growth dah in the range of 10-lO to 10-6 mhycle under TMF 

ccrndi tiorrs. Therefore, a newer approach to TMF crack growth testirq must be 

considered to meet the requirements of RFC and ENSIP. 

A3 

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The purpose of this paper is to describe a computerized testing unit 

- capable of measurfng thermal-mechanlcal fatigue crack growth (TMFCG) rates 

in the range from 10-10 to lO-3 m/cycle. The control system and the correction 

procedure of the DC potential signal Is described in detail. 

Basic Requirements 

The testing Capability and testing conditions for TMF testing of 

sDecimens are those that allow the duplication of in-service conditions. The 

requirements for testing facilities and test specimens for crack growth TMF 

testing 8re: 

1. Strain control to simulate the thermal loading of the component 

since most high temperature components are under straincontrolled conditions. The mechanical strain (total strain minus 

thermal strain) should be controlled. 

2. Strain hold time to simulate steady state condftions during normal 

operating of gas turbine engines. This period consists of a creep/ 

re ’I ax8 tion behavior. 

3. Cr8Ck length measurement capability to obtain crack growth data 

in TMF conditions. 

4. Controlled transient heating and cooling to simulate a component 

strainl’temperature phase relatlonship similar to the one shown 

In Figure 2. 

5. Compressive load-carrying capattility of the specimen to sustain 

compressive stresses which develcipeb in the heating period of 

the cycie. 

A4 
TMF crack propagation should include testing of the base metal only, 

since this type of cracklng is readily studied by a fracture mechanics approach. 

The amount of component life spent in starting a crack in the coating has to be 

addressed in terms of crack initiation techniques 1101. TMF tests should 

Include several testing conditions in order to simulate the various straintemperature relations at various locations in an actual component. 

Design of test unit 

The aDparatus which w8s assembled is a computer-controlled thermal 

fatigue testing system consisting primarily of a closed-loop servo-controlled 

electro-hydraulic tension compression fatigue m8Chlne (MTS 8 10 model 

906.06), 8 high frequency oscillator for indUStri8l heating (Lepel Eodel T-2.5- 

1-KO 1 -BW), an air compressor for cooling, a low frequency function generator 

(Exact model 504), a data acquisition and control system (HP-6942A), a 

programmable high resolution voltmeter (DVM HP-34781, and 8 main frame 

computer (HP 9816s). Figure 3 shows the control block diagram of this system. 

The system is capable of testlng specimens Of different size and 

configuration (SEN, CT, hollow tube, etc.) and to withstand a fatigue loading of 

25,000 lbf (1 1.350 Kgf). The test specimen is mounted in two end grips of high 

tensile strength steel. The specimen sllgnment Is insured by the use of 6 

Wood's metal pot, which prevents the development of a net bending moment in 

the specimen. Because a DC potential drop technique is used to monitor crack 

growth, the lower grip is electrically insulated from the system by mesns of a 

ceramic coating. The ends of the end grips are water cooted. 

The demand-signal generators 

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The demand-signal generation system provides separate demand signal 

for the control of specimen strain or applied stress and temperature. A 

programmable temperature controller is used to generate the driving signal to 

the high frequency generator and the air valve driver. It is also providing 

trigger signals to the DVM, computer, and function generators (if required). The 

computer and the data acquisition and control system provide the command 

slgnals for the stress and straln controlled cycling. Proper coding and decodlng 

of trigger signals from the temperature controller to the computer allow the 

system to generate any strain/stress/temperature cycling. Feedback signals 

from measuring points on the machine and specimen are compared continuously 

with the demand signals in the electronic control equipment. The difference 

BetweeFi corresponding signals (Le., the error) controls the power delivered to 

the hydraulic actuator or the heatfng circuit unit in such a way that the error in 

the test variable is reduced; careful choice of relative signal magnitudes . 

(amplification) allows adequate control of each variable. 

Control of strain or stress 

Control of specimen strain is achieved by control of the displacement 

between two knife-edges of the strain detector attached to the specimen 

surface. This axial strain extensometer consists of a linear differential 

transformer (LVDT), and a transmitter consisting of two shims which link 

together two sets of invar arms, each supporting an alumina rod. The feedback 

signal from the iVDT is compared with the demand signal and the Oi::erence 

between the two, the error signal, is used to control the drlving signal to the 

servovalve. The command signals (mean strain and amptttude) 8re sent by the 

A6 

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Multiprogrammer (HP 6942A) whlch is controlled by the 98 16s. Figure 4 shows 

a block diagram of the strain controlled closed-loop unit. In the system, the 

set point command (mean stress or Str8ln) is fed dlrectly to the Servo 

controller of the MTS unit. 

The amplitude command signal w8s obtained by feeding the output of a 

twelve bits voltage D/A converter directly into the HTS servocontroller. A 

memory card can be used to continuously supply preloaded data to the D/A. A 

timer card determines the time between each analog voltage change such that 

the changes are perceived in the test as continuous as possible and not as a 

series of step changes. 

Data acquisition and control unit 

The command signals are sent by this data acquisition and control unit 

called Multiprogrammer or HP-6942A. It is composed of an internal main 

microprocessor, memory buffers for I/O and data storage, a real time clock and 

a backplane where separate plug-in cards are connected. Each plug-in 110 card 

is equipped with its own microprocessor. 

Instructions to run the test and values of the stress (in lbs) or strain (in 

%> for the mean and amplitude are typed-ln on the HP-98165 at the beglnnfng of 

the test. These values are then converted into their corresponding binary code 

and voltage are sent to the Multiprograrnmer which in turn decodes them and 

re-programs the appropriate 110 cards. 

With the proper If0 cards, the system has the following capabilities: 

I. data acquisition 

2. measurement ranges 

3. control 

A7 

4 
4. synthesis 

Acquisftion 

Analog measurements from up to 16 channels (can be increased to 960 

channels) may be acquired at 33,000 readings per second, depending upon the 

sc8nner system configuration. Random access to any channel, as well as 

continuous scanning, are easily accomplished. FIgure 5 shows a diagram of the 

scanning system configuration implemented in our system. The signal may be 

digitized 8t rates up to 33 KHz by the A/D and stored on a memory card. Each 

memory card can store up to 64 K re8dlngs. The dllgltizlng process takes place 

independently of all other Multiprogrammer activfty, that is, the d8t8 

scquisition are achieved in parallel without any interruption from the control 

8c t Ivi t tes. 

Measurement Ranges 

Proper switches on the AID converters are used to select and measure 

voltsge range from f 25 mV to 2 1@V full scale in the presence of 250V of 

common-mode voltage. The resolution can then be varied from 12 pV to 5 mV. 

Control and Synthesis 

As stated earlier, twelve bits voltage D/A converters provide outputs for 

analog programmabie instrument and stirnuliis of units under test (mean 

stresslstraln and ampll tude). A memory card can be used to continuously suply 

preloaded data to the OIA card at rates of up to I@ KHz. Any type of wglvefclrms 

A8 
may be loaded into the memory card from the computer and used as stimuli for 

tests. Random fatigue loading can therefore easily be achieved without 

modification to the system (hardware). Any repeatable wave shape (sine, 

square, triangular, etc.) can also be preloaded into a memory card. A timer card 

determined the time between each analog voltage change such that the changes 

we perceived in the test as continuous as possible and to achieve cycling at a 

pre-determined frequency. 

Control of temperature 

The specfmens are heated by a radio frequency unit. For TMF tests, low 

frequency heaters ( 10 KHz) are often used (5-81 because they produce lower 

wall thickness gradients than do the higher frequency (450 KHz) heaters and 

because there are fewer ground-loop problems wf th the 10 KHz heaters than 

with the 450 KHZ heaters. However, It is the author's bellef that high 

frequency induction heating is preferable because of its fast response, making 

It possible to provide hlgh heating rates and Capabale of induclng considerable 

thermal stresses in specimens of small cross-section. In this case, the 

heating mode is close to that encountered in-service, since the heat is 

generated within the surface layer of the specimen. Temperature measurement 

is accomplished by thermocouples welded onto the specfmen. A thermlstor Is 

used with the temperature controller to provide a St8billZed cold junction. 

As pointed out by Carden 191, there is a relationship between the heating 

method, the design of the specimen, and temperature measurement and control. 

Radio frequency induction requires close coil-to-specimen spacing and smell 

grip ends which makes difficult the mounting of additional measurement 

devices and obscures 8ccess to and visibility of the surface for replication, 

A9 
.. .. 

etc.; also, the coil has a high voltage RF potential requiring insulation and 

safety precaution. A temper8ture dlStUrb8nCe occurs at the thermocouple mass 

in the field, as we11 8s at specfmen locations spaced to the coil. Fin8lly, there 

might be possible RF inductton-induced ground loop problems in the 

instrumentation cabling. 

In order to minimlze these potential problems, great care must be taken 

to use properly shielded cables. The coils were machined as to maintain 

constant coil-to-specimen spacing. This was 8ChleVed by using 8 mold having 

oversized dimensions of the specimen. Before each test, the coils were 

carefully positioned around the specimen as to minimize the temperature 

difference between the four faces of the specimen. The temperature variation 

along the gauge length of the specimen has been measured to be less than 10°C 

and accurate to 21°C. 

The amplified signal from the thermocouple (Figure 6) is compared with 

the demand signal which was programmed. A difference between the demand 

and feedback signals caused by the specimen temperature being too low, causes 

an increase in the power supplied to the coil. The increased power passing 

through the coil increases the temperature of the specimen and hence reduces 

the error. If the temperature is too high, the power to the coil is reduced. 

Compressed air is used to cool the specimen during the cool down portion of the 

temperature cycle. The air valve is best controlled by the temperature 

programmer which opens or closes a solid state relay that drlves the power to 

the air valve. With this technique, the air flow is always synchronized to the 

temperature cycle and is repeatable. The cooling rate is controlled by the 

heater ballasting the air blast cooling. 

The lfmits of the system, In terms of heating and maxlmum temperature, 

were also tested. Heating rates in excess of 20°C hec. have been obtained 

A1 0 

d 
wl th the test rig and single edge notch specimen geometry (see Test Rfg 

Ver-lficatlon Procedure). For faster rates, some control accuracy Is sacrificed 

and a detailed thermal analysls has to be performed to determine the timetemperature distribution in the specimen. Using different specimen geometry 

and coil design, control heating rates In excess of 200"Clsec. were achieved 

with an identical heating/cooling unit [ 101. The maximum uniform temperature 

that can be reached is a function of the specimen geometry and specimen-tocoil distance. With the present configuration of specimen and coil design, the 

upper limit of the temperature cycles is 1050T. In the development work, 

specimens were tested between 400 and 925°C. A si% degree per second 

heating 8nd cooling ramp was prOgr'8mmed and run. The dynamic performance of 

the system is shown in Figure 7. Five thermocouples were used and the 

temperature of each thermocouple was always within ten degrees of the 

requested profile throughout the test. 

Crack Growth Measurement 

Crack length measurements during thermal-mechanical fatigue cycling 

under either elastic or plastic strains have been performed mostly by optical 

measurements (5-8, 1 1-13] and by cellulose acetate repllca [MI on tubular 

centered notched specfmens. In these experiments, the surface crack lengths 

must be converted to 8 mean crack length for the tube used (€31 

where a is the mean crack length, R the mean r8diuS of the tube, Do the outer 

diameter of the tube, and 24 the total projected length measured by 

A1 1 

.I 
microscope. This equation applies only if the crack grows symmetrically in a 

fan direction. Although stress and strain lntensfty solutions for thfs geometry 

exist 1151, they require precise messurement of the crack length which is, in 

practice, very difficult to achieve. The resolution claimed [8l for optical 

measurements is In the range of 80- 120 pm, dependlng on the crack tip 

resolutfon and providing the measurements are taken at maximum tensile load. 

There have been few attempts to measure crack length in TMF conditions 

using the potential drop technique If 1 - 121 on a 12.7 mm diameter push-pull 

specimen. Using a starter notch 200 pm deep, experimenters have been able to 

resolve accurately a crack increment of 40 pm, and the corresponding growth 

rates were f~8SUred to better than 10-8 micycle 11 21. The method of potential 

drop has been used satisfactorily for isothermal conditions for numerous 

materials f 16-201 and preliminary experiments by the authors have shcwr: that 

It can be used satlsfactorlly provided that the electrical nofses are adequately 

filtered and that the calibration curve is properly corrected in order .to take 

into account changes of potential with temperature [ 181. 

The electrical noises induced in the potentia? probes by RF heating can be 

ellmin8ted by the use of a band-pass filter centered on a 430-460 KHz 

frequency range. Power line surges, transients, and RF induced power-line 

noises can be taken care of by the following technique. First, a 10 KHz bandpass filter is used to eliminate the Induced-noise of the 10 KHz Master 

oscillator of the MTS console used to provide excitation to the servo-valves 

LVDT's. Second, the DVM is programmed to convert the analog signal in 10 

power line cycles (PLC). In this mode, 1 PLC is used for the runup time, the A/D 

operation repeated ten times. The resultirig teri readings are then averaged afiG 

the answer becomes a slngle readlng. Thfs, with the built-in broad band If? ter, 

greatly reduces the emf noise induced by the power-line fluctuations. A 

A1 2 

d 
schematic of the DC potential system is shown in Figure 8. Because the 

potential, the temperature, the load, and the strain are recorded synchronously, 

It is possible to take into account the thermal variation of the potentlal. The 

procedure is the following. First, the changes in potential as a function of the 

temperature and strain or stress (V(T,a)) Is measured. Then a thermal cycle at 

zero stress is recorded (VCT, a = 0)). The effect of ths applied stress or strain 

is obtained by subtracting V(T,a=O) from V(T,a)) to yield Q(d. The procedure 

is outlined in Figure 9. To assess crack growth, the peak potential of each 

cycle (V(T,o)) fs recorded, and plots of the voltage versus applied number of 

Cycles are obtained. Using well-known solutlons [ 16- 171 relating (V/Vo) to 

(a/ao) for the single-edge notch specimen geometry, the crack lengths versus N 

curves are derived. Improved sensitivity can be achieved through the use of 

reference probes [ 19-2 11 where the ratio (V(t)/Vo) is corrected by multiplying 

by the ratio of the ini tis1 reference probe signal to the reference 

probe signal at time t. The resolution achieved under TMF conditions on single 

edge notch specimens is better than 10 pm. 

A close look at the potential slgnals shown In Figure 9 indicates that 

they can be used to generate information on the mechanisms taking place at the 

crack tip. By noting that V(T,a) and V(T, CT = 0) are also functions of the 

geometry, we can wrl te 

V(a1 = V(T, 0, geo) - V(T, CT = 0, geo). (21 

Therefore, for a given temperature T and zero applied stress, the expected 

value of Q(a) is zero if the geometry of the crack, which include crack length 

and configuration, is unchanged. However, if V(d is not equal to zero at zero 

applied stress, then the geometrg terms in V(T, 0, gec) and NT, G = 0, geo) 

must be different (see Equation 2). Assuming that the Crack increment during 

the thermal cycle is negligible, then the difference associated with the 

A1 3 

d 
geometry term is solely a function of the configuration. The applied stress 

required (see Figure 9.6) to give V(d = 0 represents the minlmum necessary 

stress to re-establish in the specfmen the same crack conflguration. Because 

the transition point where V(a) equal zero corresponds to the transition 

between the tensile and compressive part of the cycle (see Figure 91, it is 

logical to assume that this change in configuration is a change in the opening of 

the crack [ 18-20]. 

From Figure 9 other information can be derived from the analysis of the 

V(a) potential curves. That Is, to determine when the crack is growing within 

one cycle. In Figure 9.b, the V(a) curve for in-phase cycling shows a hump near 

the maximum stress whereas at low OK (Figure 9.8) and lor out-of-phase 

cycling, the V(a) curve is continuous without discontinuity. Such an increase 

in potential usually reflects a sudden increase in crack length 11 6-2 11. 

Therefore, it can be concluded that under this particular condition and speclflc 

loading the crack growth w8s happening at the peak applied loadlstrain. On the 

other hand, for the other conditions shown in Figure 9, it is logical to assume 

that the Crack was growing in a continuous fashion in the tensile going part of 

the cycle (0 < u < urnax). The crack extension during a single cycle can be 

estimated by comparing the values of V(J,a1 at the beginning and at the end of 

the cycle. Local estimate of the crack growth rate wlthin one cycle can be 

computed by dividing the increment in crack length by the time spent in the 

tension going part of the cycle (time interval for which V(a) > 0). if a hump is 

seen on the V(a) the time interval between the hump and V(a) = 0 must be 

taken. .. 

From the above analysis of the V(a) curves it csn be conc:uded that the 

potential drop method has the C8pablllt1~ of monitoring crack extension during a 

cycle, whereas the optical measurement and compliance methods 8re limited 

A1 4 

d 
for- growth measurement to no less than one cycle. Therefore, detailed analysis 

of the crack growth process can be achieved and this Is partlcularly important 

In twlng to determlne the mechanlsms lnvolved wlth TMF crack growth. 

Test Rig Verification Procedure 

TMF and isothermal fatigue crack growth tests were performed under 

straln control on single edge notch specimen (1 1.7 x 4.4) mr$ of cross-se'ction 

wl th a starter notch approximately 1 mm deep which is cut by electrodischarge machining. The specimen were pre-cracked in fatigue at 10 Ht at 

room temperature up to a &K of about 20 MPa m. Axial strain was measured 

with a calibrated LVDT along a gauge length of 12.5 mm. Temperature and 

mechanicai strain were computer-controlled by the same triangular wavefzrms 

shown in Figure 2. The thermal strains (E&) were measured by cycling the 

temperature at zero load. The total strain, computed by adding the E& to 8 preselected mechanical strain (E-) were used for the control. Every five cycles 

the V(T) potentials were re-setted and the thermal stratns checked for any 

drift. The software developed to run the tests is given elsewhere [221. The 

frequency was kept constant at 0.0056 Ht (113 cpm) and the temperature 

cycled between 400 and 925°C. Figure 10 shows E~, qat, and 0 8s 8 

function of time within one cycle for both in-phase and out-of-phase cycling. 

Typic81 hysterisis loop obtained by plotting 0 and E,, are shown in Figure 1 1. 

From the potent181 versus tlme curves simllar to one shown in Figure 9, the 

(ah) vs N curves were derived. The Cr8Ck growth rates were computed using a 

seven-point incremental polynomial method (ASTM E64?-8 1). The AK,, the 

strain intensity factor, were computed using a superposition method derived 

for an edge crack in 8 plate with no bending and fixed-end displacements 122- 

A1 5 
241. The crack growth rates 8s a function of AK, are shown in Figure 12. Oat8 

on the same material but obtained by conventional optical measurements 171, 

%re also reported. As can be seen from Figure 12, the date from the TMFCG setup agrees quite well with data taken from conventional TMFCG test apparatus 

provided the K's are calculated, assuming no free-end rotation af the specimen. 

However, our data covered three orders of magnitude lower than those 

previously reported. As expected from our knowledge of crack growth 

mechanisms in isothermal testing, the TMFCG curves are also characterized by 

8 "threshold' regime which did not exist in the data generated by conventional 

TMFCG methods. 

The crack growth rates are ranked, in terms of severity of damage in the 

following order; isothermal (at T,) In-phase, and out-of-phase cycling. 

However, correction of the K's to take into account closure which has been 

previously defined as the applied stress at which V(a) = 0 (see Figure 9), have 

shown that the stress intensity factor correlates very we?? the testing 

conditions for high strength/low ductility materials like X-750 and 6- 1900+Hf 

11 8,231. Research is under way to determine if similar corrections can be 

applied for the fully-plastic regime [25-261. 

S u rnrn ary 

A thermal-mechanical fatigue test rig has been built around B 

conventional servo-hydraulic machine to simulate complex stress-straintemperature cycles as experienced for in-service components. The system 8nd 

its capabilities have been described in detail. A corrected DC potential drop 

technique used to accurately measure crack lengths w8s shown to yield better 

A1 6 
capabilities for low crack growth rate measurements than the conventional 

methods Used in TMFtt testing. 

It has been shown that solid specimen geometries can be used to 

simulate almost any type of in-service conditions. A1 though these geometries 

might require proper thermal analysis to determine the thermal distribution in 

the cross-section, it has some substantial advantages over the tubular 

geometries. The most important advantage is that it allows deterministic 

crack length measurements and the use of accurate fracture meCh8nlCS 

sol ut ion. 

Further, the choice of fracture mechanics crlterla 8s the failure criteria 

for aircraft components requires a careful monitoring of speclmens durlng 

testing, which obvious1 y increases the experimenter's effort considerably. 

This extra work, however, is justified by the greater relevance of the data 

available to the designer. 

Acknowledgements 

This work was sponsored by the National Aeronautics and Space 

Administration under Grant No. MAG3-280. 

A1 7 
References 

1. J.M. Larsen 8nd T. Nicholas, 'Cumulative Damage Modelling of fatigue 

Crack Growth', presented at AGAR0 Specialists' Meeting of the 

Propulsion and Energetics Panel on Engine Cyclic Durability by 

Analysis and Testing, Lisse, Netherlands, 1984; to be published in 

AGAR0 Conference Proceedings. 

2. S.W. Hopkins, 'Low-Cycle Thermal Mechanicai Fatigue Testing', ASTM 

STP 6 12, 1976, p. 157- 169. 

3. E.& Ellison, "Thermal-Mechanical Strain Cycling 8nd Testing at Higher 

Temperature", in Measurement of High Temperature Mechanical 

Procterties of Materials, ed. by M.S. Lovebay, M.F. Day and 8.F. Dyson, 

NPL, HMSO, 1982, p. 204-224. 

4. M. Okazaki and T. Koizumi, "Crack Propagation of Steels During LowCycle Therm8l-MeChanlCal and Isothermal Fatigue at Elevated 

Temperatures", Met. Trans., Vol. 14A, 1984, p. 1641 - 1648. 

5. A.E. Gemma, E.S. Langer and G.R. Leverant, "Thermal-Mechanical Fatigue 

Crack Propag.8tion in an Anisotropic (Directionelly Solidified) NickelBase Superalloy", ASTM STP 6 12, 1976, p. 199-2 13. 

6. G.R. Leverant, T.E. Strangmen, and 8.5 Langer, 'Parameters Controlling 

the Thermal -Fatigue Properties of Conventional 1 y-Cas t and Directionally-Solidified Turbine Alloys", in Superalloys: Metallurgy and Manufacturers, ed. by 6.H. Kear, D.R. MuZuk8, J.K. Tien, and S.T. Wlodek, 

Claxtor Pub., 1976, p. 265-295. 

7. A.E. Gemm8, F.X. Ashland, and R.M. Masci, The Effects of Stress Owells 

and Varying Mean Strain on Crack Growth During Thermal-Mechanical 

Fatigue', J. Jest. Eval. (JTEVA), Vol. 9, 1981, p. 209-215. 

8. G.J. Meyers, 'Fracture Mechanics Criteria for Turbine Engines and 

Hot Section Components", NASA CR- 167896, 1982. 

9. A.E. Carden, "Fatigue at Elevated Temperatures: A Review of Test 

Methods", ASTM ST? 520, 1973, p. 195-223. 

10. F.A. McClintock, J.W. Holmes and K.S. Ohara, "Thermal Fatigue of Monocrystal Nickel-Base Superalloy", to be presented at ASTM Conference 

A1 8 
11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

on 'Low-Cycle Fatigue - Directions for the Future', Lake George, New 

York, September 30 - October 4, 1985. 

R.P. Skelton, 'Environment Crack Growth in 112 Cr-Mo-V Steel During 

isothermal High Strain Fatigue snd Temperature Cycling", Mat. Sci. 

Eng., Vol. 35, 1978, p. 287-298. 

R.P. Skelton, "The Effect of Microstructure and Tensile Dwell on the 

Growth of Short Fatigue Cracks in 3 16 Steel at 625OC-, Proc. of Conf. 

on Mechanical Behavior and Nuclear ADDlic8tlOn of Stainless Steels at 

Elevated Temoerature, ed. Metals SOC., London, 198 1, p. 191 1 - 191 12. 

R.P. Skelton, "Crack initiation and Growth in Single Metals Components 

During Thermal Cycling', in F8tipe at High Temoerature, ed. by R.P. 

Skelton, App. Sci. Pub., London, 1983, p. 1-62. 

C.A. Rau, A.E. Gemma and G.R. Leverant, Therm8l-Nechanlcal Fatlgue 

Crack Propagation in Nickel and Cobalt Base Super81 logs Under Various 

Strain-Temperature Cycles', ASTM STP 520, 1973, p. 165- 178. 

F. Erdogan and M. Ratwani , 'Fatigue and Fracture of Cylindrical Shells 

Containing a Circumferential Crack', Int. J. Frac. Mech., Vol. 6, 1970, 

p. 379-382. 

M. Hicks and A.C. Pickard, "A Comparison of Theoretical and Experimental 

Methods of Calibrating the Electrical Potential Drop Technique for 

Crack Length Determination', Int. J. Fract., Vol. 20, 1982, p, 91-101. 

M.P. Halliday and C.J. Beevers, "The DC Electrical Potential Method for 

Crack Length Measurement', in The Measurement of Crack Length and 

- Shape During Fracture and Fatigue, ed. by C.J. Beevers, EMAS Pub., 

1980, p. 85-1 12. 

N. Marchand and R.M. Pelloux, "Thermal-Mechanical Fatigue Crack Growth 

in lnconel X-750", in Time-Dependent Fracture, ed. by K. Krausz and A.S. 

I(r8usZJ Martinus Nijhoff, in press. 

T.A. Prater and L.F. Coffin, 'Experimental Cycle An8lysis of Fatigue Crack 

Growth in Compact Type Specimen Geometries', General Electric 

Technical Information Series, Report No. 82CRD039, 1982, 18 pgs. 

R.P. Gangloff, "Electrical Potential Monitorlng of the Formation and 

Growth of Small Fatigue Cracks in Embrittling Environment", in 

A1 9 
Advances in Crack Lenath Measurement, ed. by CJ. Beevers, EMAS Pub., 

1982, p. 175-230. 

2 1. I.P. Vasatis 8nd R.M. Pelloux, "The Application of the DC Potentiel Drop 

Technique in the Creep Stress-Rupture Testing', to be published. 

22. N. Marchand, "Thermal-Mechanical Fatigue Behavior of Nickel-Based 

Superalloys", ScD Dissertation, Mass. Inst. of Technology, Cambridge, 

MA, 1985. 

23. N. Marchand and R.M. Pelloux, "Thermal-Mechanical Fatigue Crack Growth 

in 8- 1900+Hf', to be published in the Proc. of the Conf. on ugh 

- Temperature Alloys for Gas Turbine AEDlication, Liege, Belgium, October 

6-9, 1986. 

24. N. Marchand, D.M. Parks and R.M. Pelloux, "K,-Calculations in Single Edge 

Notch Specimen with Linearty Varying End Displ8cements", submitted 

to Eng. Wac. Mech. 

25. N. Msrehand and R.M. Pelloux, 'Fracture Mechenics Criteria ir: Turbine 

Components Materials", to be published. 

26. N. Marchand, G. L'Esperance and R.M. Pelloux, "Thermal-Mechanical Fatigue 

Responses of Cast 8- 1900+Hf', to be presented at the ASTM Conference 

on "Low Cycle Fatigue - Directions for the Future", Lake George, New 

Yo&, September 30 - October 4, 1985. 
Figure 

Figure 

Figure 1 

Figure 2 

gure 3 

gure 4 

Figure 5 

Figure 6 

Figure 7 

Figure 8 

Figure 9 

0 

1 

Figure 12 

List of faptlons 

Stress-strai n- temperature cycle experienced by turbine 

components 

SChematiC diagram showing waveforms of temperature, strain 

and stress in thermal and isothermal fatigue tests. 

Diagram showing the control system of apparatus used for 

thermal-mechani cal fat i Que test 

Block diagram of the strain-controlled closed-loop unit 

Configuration for sequential scanning with buffered A/D 

Block diagram of the temperature control unit 

Programmed profile and thermtil fatigue system for an d0C/sec. 

triangular waveform 

Schematic of the DC potential system . 

Potential curves V(T,a), V(T) and V(a) for TMFCG tests. (a) 

lnconel X-750,25 MP& %, (b) lnconel X-750;EiO MPa fi 

Stress, mechanical strain, thermal strain and total strain 8s 

a function of time (one cycle). (a) In-phase, (b) Out-of-phase 

Typical hysterisis loop obtained under TMF conditions. (a) 

In-phase, (b) Out-of-phase 

Fatigue crack growth rates under TMF conditions 

A2 1 

d 
TE MER ATUR I 

STRAIN (-E 1 

3 

Gd. 

IDLE CLIMB CRUISE DESCENT 

- 

c 

GROUND 

IDLE 

4 

figure 1 Stress-strain-temperature cycle experienced by turbine 

eomponen t s 

A22 
A2 3 

d 
n 

A24 
*f 

I -- I 

r 

Y 

V 

m 

w 

w 

LL 

w 

IO 

w 

-I 

w 

I/) 

a 

n 

n 

a-- 

.L 

U 

Q) 

c 

c 

El .c, 

c 

0 

0 

1 

C 

Q 

I 

4 

v) 

Q) 

.C 

5 

E 

rc 

0 

a 

I 

m 

W 

-m 

Y 

u 

0 

.C 

Ei 

Q) 

I 

3 

0) 

.C 

LL 

A2 5 
6 

9 

4 

2 

A 

M 

U 

L 

T 

I 

P 

R 

0 

G 

R 

A 

M 

M 

E 

R 

1 I 

1 

(AID BUFFER) I 

DATA-OUT, 

W 

34 AID 

rn 

EOC 1 

ANALOG 

BUSY 

FET -1 SCANNER I INPUT 

INPUT 

1 

ANALOG 

INPUT 

A CHANNELS 

Y 

Figure 5 Configuration for sequential scanning with buffered A/D 

A2 6 
A27 
TMF TEST RIG RESPONSE (G"C/sec) 

IO00 

800 

600 

400 

200 

I I I I 

PROGRAMMED PROF1 LE I 

---- SYSTEM RESPONSE 

0 

-60 

Figure 7 

0 60 t 20 

T I ME (seconds) 

I80 240 

Programmed profile and thermal fatigue system for an d*C/sec. 

triangular waveform 

A28 
+ 

a, 

32 

4 

0 Ea 

>- nfx 

W 

5 

€ 

a: 

A29 
TIME sec 1 

4 I 

4 

04 

02 

0 

-02 

-04 

04 

02 

0 

-02 

-04 

17 

16 

15 

14 

13 

17 

16 

15 

14 

13 

- 

> E 

> 

I 

- 

> 

Figure 9 Potential curves V(T,o), V(T) and V(o) for TMFCG tests. (a) 

lnconel X-7S0025 MPa K0 (b) inconel X-750,SO MP8 fi 

A30 
V' r- -.008 

-.01 

0 20 40 60 80 100 120 140 160 180 

TIME Isec) 

500 

400 

300 

200 

IO0 

0 

-100 

-200 

-300~ -I---, --- :;+ , , I I I , \;:, I I ~-.006 

-400 *----- -.008 

-500 .o I 

Emec 

0 20 40 60 80 100 120 140 160 180 

TIME (sed 

I I I llll[ I1 I 11' .o 1 

- 

- -008 

.006 

- 

8-1900 + Hf 

OUT-OF- PHASE 

T max - 925°C 

T min - 4OOOC 

CYCLE+3650 

A 

/\ 

\ TIME: 14: 46: 19 

P. 

/* '. -/ 

- .\'*. 

- 

-\. '-. 

\ 

Figure 10 Stress, mechanical strain, thermal strain and total strain 8s 

8 function of time (one cycle). (a) In-phase, (b) Out-of-phase 

A31 d 
B-I900+HF - A00 IN -PHASE 

T mox = 925°C 

T min = 400°C 

CYCLE 3050 

TIME: 12:58:51 

E TOTAL= 0.4825 % 

- 300 

---300 

.--400 

- -- 500 

STRESS (MPd 

8-1900 + HF 

OUT-OF-RIASE 

Tmaxin = = 400 925°C "Ct: 

CYCLE = 3650 

TIME: 14:46:19 

E ?DTAL=0.4675% / / 

Figure 11 Typical hysterisis loop obt 

In-phsse, (b) Out-of-phase 

ined under TMF condi ions. (a) 

A32 
z 

0 

c 

U 

n 

S 

c 

0 +J 

0 

rb 

G 

cn 

c 

0 

.C 

4 

.C 

.u 

c 

0 

u 

k 

tL 

Q) 

'0 

c 

3 

cn 

a, 

43 

I 

d 

A3 3 
Appendlx B - Fracture Mechanics Analysis 

K -Solutions for Single Edge Notch Specimens under Fixed End 

Displacements I 

by 

N. Marchand*, D. M. Parks** and R. M. Pelloux*** 

Abstract 

The KI solution for a finite length single-edge notch specimen 

Good agreement between the experimental and nuherical 

loaded under fixed end-displacements is derived using a crack compliance analysis. Numerical and experimental checks of the K solution 

are provided. 

solutions is observed. The applicability of conventional fracture 

mechanics to correlate crack growth data generated under displacement 

control is discussed. 

* Research Assistant, Department of Material Science and Engineering, 

Massachusetts Institute of Technology, Cambridge, MA 02139 

** Associate Professor, Department of Mechanical Engineering, 

Massachusetts Institute of Technology, Cambridge, MA 02139 

*** Professor, Department of Material Science and Engineering, 

Massachusetts Institute of Technology, Cambridge, MA 02139 

81 

d 
INTRODUCTION 

The single-edge-notch (SEN) geometry with end constraints has 

received considerable attention in analytical fracture mechanics because 

of its frequent use as a test specimen. The problem of a SEN specimen 

with fixed-end displacements has been studied by several authors [l-31. 

In particular, the formulation of Harris [2] has received much attention 

because of its ease of application. 

bending moments associated with zero far-field relative rotation were 

perhaps more significant than those implied by Harris' solution, and this 

premise motivated the present analysis. 

However, we felt that the closing 

ANALY S f S 

The presence of a crack in a rectangular sheet of thickness B 

loaded by uniform imposed end displacements cause the line of action of the 

applied load to shift relative to the specimen centerline. This shift produces a bending moment that tends to close the crack. 

metries, the only known boundary conditions are the imposed displacements , 

and the applied stresses are not known a priori 

For the SEN geoand must be determined. 

We consider an isotropic linear elastic sub-specimen of length L 

that is 

width (W). The specimen is of thickness B and is subject to opposing 

forces N and moments M as shown schematically in Fig. 1. The line of 

action of the force N is taken as the mid-specimen. The following considerations are restricted to mode I behavior although the argument can be 

"sufficiently long" compared to crack length (a) and specimen 
generalized to include other modes. 

The relative displacement 6 and rot tion e of the specimen ends 

can be taken as the sum of a "crack" and "no-crack" parts: 

[:: 1 + 

The compliance of the "no-crack" beam gives its extension 6nc and rotation 

*nc 

corresponding moment M[4] : 

in terms of the tensile force N acting throughout its center and the 

2 where E' = E(Young's modulus) for plane stress and -E/(l-v ) for plane 

strain, 

3 I = BW /12 and the cross section area A = BW can be substituted into Eq. 2 

to yield: 

w being the Poisson's ratio. The section moment of inertia 

The expression for the "cracked" terns are obtained by considering 

the complementary energy of the specimen U in terms of N and M, 

d 

83 
where the matrix scalar product is indicated. Since the "no-crack'' terms 

given in Eq. 3 are independent of crack length, the energy release rate is 

With the standard relation between G (fracture mechanics energy release 

rate) and KI, 

length a is equal to [SI: 

the change in complementary energy with respect to crack 

The stress intensity factor for combined tension and bending can be obtained 

by superposition of the stress intensity factors applicable to tension and 

bending. Therefore, in matrix form 

Highly accurate functional forms of aK/aN and 3K/;M can be obtained from 

the compilations of Tada et. al. {5] where, for example 

84 

.i 
0.923 i 0.199 (l-sin(F)) 

ab1 Bw2 ra ZW na 

i 1 

(8.2a) 

Note that in Eq. (8.lb, 8.2b), alternative non-dimensional function 

Fl , F2 

terms of a nominal stress "a" as KI = Feo*(ra)1'2. For tension, D = N/BW, 

are introduced in such a manner as to facilitate K-calibrations in 

2 while for bending D = 6M/BW . Now equating Eq. 5 and Eq. 6 and inserting 

Eq. 7 into Eq. 6, one obtains 

i 

2 

- 

2 aK (5) 
Integrating Eq. 9 with respect to "a" provides the "crack" compliance 

matrix: 

where 

(11 1) 

0 

The generalized forces 

displacements Gtot, otot by using Eqs. 1, 3 and 10, providing 

N, M can now be evaluated in terms of imposed 

86 

d 

(11.2) 

(11.3) 
-- M + C2224 + C21N 

'tot E?3W3 

6 =- Z + C N + CZ1M , tot E'BW 11 

or, on multiplying by E'B; 

=- 12L M + B'BCZ2X + E'BC21N 3 W E ' tot 

E'BGtot s 3 id N + E'BCllN + E'BC21fll. 

112.1) 

(12.2) 

(13.1) 

(13.2) 

For fixed-end displacement with no shear force Otot = 0 

Then from Eq. 13.1 we get 

and Gtot = 6. 

while Eq. 13.2 can be re-written 

87 
0. 

On defining the dimensionless cracked compliance Cij as 

A 

Cll = S'ECll 

2 A 

c22 = E'BW c22 

A A 

52 = c21 = E'BBC12 = E'3WCZ1 , 

Eq. 14 simplifies to 

h 

* 'M 12 -c M -= 

w 124) + "22 

while Eq. 15 simplifies to 

AM 

12 i;i * 11) ;N + c LA E'B~ = + r, 

(16.1) 

(16.2) 

(16.3) 

88 
When Eq. 17 is inserted into Eq, 18, the axial force N can be obtained 

as 

The substitution of Eq. 19 into Eq. 17 provides 

Eq. 19 and 20, respectively provide the force N and bending moment M 

applied to the crack in terms of the imposed relative displacement 6 

under conditions of zero relative rotation. Note from Eq. 20 that, since 

the tij are inherently non-negative, the sign of M is indeed negative, 

tending to close the crack. 

99 

d 
The total stress intensity factor for this specimen is, by 

superposition, the sum of that due to tension and that due to bending. 

Due to linearity, 

and on combining Eqs. (8.lb, 8.2b, 19, 20) we obtain 

E'& 

KI = - 

L 

W 1+- L I 

where 6 = a/W. As shown in [SI, the terms e..(<) are normalized 

dimensionless cracked compliances which need be calculated only once. 

the present application, the integrals of Eq. 11 were numerically evaluated 

in increments of dimensionless crack length AE = aa/W of size 0.01 using 

Simpson's rule. 

into Eq. 22, we recover the familiar form 

75 

In 

If we now substitute the nominal stress value (J E E'6/L 
where 

and 5 = a/W, Q = L/W. 

In Fig. 2, plots of G(:, T-I) versus a/U are given for different 

values of L/W. The dimensionless functions F1 and F2 of Tada et. al. [5] 

(see Eqs. 8.lb, 8.2b) for pure tension and pure bending, respectively, are 

also shown for reference purposes. 

stress intensity factor calibration of the SEN specimen due to Harris [Z], 

Finally, Fig. 2 also shows the approximate 

who gives 

with 

61 1 

d 
In the interpretation of Eq. 25a, the nominal stress "a" is 

understood to be N/BW, the nominal far-field stress, which in the present 

application must be determined (analysis) or measured (experiment) in terms 

of the imposed loading parameter 6. 

As can be seen, our solution for G is strongly dependent on 

both relative crack depth and specimen length-to-width ratio and shows a 

local maximum with respect to a/W at some intermediate value of a/W for 

all (LJW) ratios larger than 2. For smaller ratios, the geometric correction factor G shows a monotonic decrease with respect to a/W until 

very deep cracks, a/\/ > .9, are considered. Tada's and Harris' geometry 

correction factors which were derived for tension, F1 and FH, under 

conditions of constant remote uniform tensile stress show a monotone increase 

with increasing a/W. Tada's bending geometry correction factor F2 

shows a slight decrease with increasing a/W, reaching a minimum value near 

a/W = 0.15, followed by a monotonic increase. 

A basic assumption of the preceding analysis is that the specimen 

length 

is sufficiently long in comparison to the appropriate St. Venant decay 

distance for the local stress disturbance introduced by the presence of the 

(1) at which displacement boundary conditions are being imposed 

61 2 
crack. 

"a", so that providing L/W > 1, the analysis should be valid. For very 

deep cracks, the decay length is specimen width W, so L must in that 

case exceed some multiple of W. This analysis cannot precisely quantify a 

requisite minimum value of L/W for any particular maximum value of a/W. 

However, good agreement has been obtained with Bowie and Freese's solution [3] 

for low values of L/W = 2, the agreement between the two solutions was within 

one percent for all values of a/W covered by the analysis. 

For short cracks , a/W << 7, the characteristic decay distance is 

EXPERIMENTAL VERIFICATION 

An experimental check of the solution was provided by performing 

fatigue crack growth tests on SEN specimens subject to imposed displacement 

loading. The dimensions of the specimen are shown in Fig. 3. The notch, about 

1 mm deep, was cut by electro-discharge machining. 

B-l900+Hf, a high-strength/low ductility superalloy with good creep and 

oxidation resistance at elevated temperature. 

reversed strain control condition in the elastic regime (AE = 0.25%) in 

The test material was 

The tests were run under fully 

laboratory air. 

of 12.7 mm which included the crack. The temperature and frequency of the 

tests were 925OC and 0.1 Hz. Before starting the tests, the specimens were 

This nominal axial strain was controlled over a gauge length 

precracked at 10 Hz and room temperature under load-controlled conditions up 

to a AK of about 20 MPa& (Harris' solution) which corresponds to an a/W 

ratio of 0.125. 

ment technique are given elsewhere [7,8]. 

B13 

Details of the experimental set-up and crack growth measured 
Fig. 4 shows the crack growth rates as a function of the strain 

intensity factor AK . The AK is used for convenience because fatigue E s 

at high temperature is a strain-controlled process. It is defined as 

follows [9,10]: 

AK,= AE*G G(a/W) . 

In the above expression, G (a/w) is the same geometric correction term 

derived in connecticn with the stress intensity factor. 

the strain intensity is calculated as A&=& *FH(a/W) with AE = .25%. 

In spite of the fact that bKE, so-defined, lacks a rigorous mechanics 

interpretation, it has been used for correlating crack growth data under 

strain-control led conditions [9-121. 

of fatigue crack growth rate with strain intensity factor range is not to be 

expected in cracks of macroscopic dimension. Thus, the non-monotonic - nature 

of this correlation strongly suggests that there are deficiencies in this 

analysis of the strain intensity factor. 

That is, in Fig. 4, 

Clearly; the non-monotone correlation 

- 

To provide a more rigorous understanding of the result, the AK~ 

were re-defined as 

d 

B14 
where the AK is the stress intensity factor derived for stress-controlled 

(Eq. 25) or displacement-controlled (Eq. 23) conditions. In cases of predominantly elastic behavior, this definition of strain intensity factor is 

consistent with standard fracture mechanics. Fig3 re-plots the fatigue 

crack growth rate versus the cyclic strain intensity factor deduced from 

Eq. 25 and from the current analysis (Eq. 23) using the value of L/W = 2.17 

corresponding to the length of the uniform reduced gauge section of the 

specimen. In the application of Harris' formulation, the nominal stress (I 

was ca'tculated using the tensile force N measured by the load cell. It 

should be noted that the load cell output is insensitive to the shift in 

load line which is associated with longer cracks. Again, the curve indicates 

that the correlation between measured fatigue crack growth rate and inferred 

strain intensity factor is non-monotone. 

relation is somewhat better than that shown in Fig. 4 because the inferred 

range of AK occurring during the tests is reduced. The lower inferred 

range Tn the present case is due to the use of the measured load value, 

which decreases under fixed displacement conditions, due to the increasing 

crack compliance. 

definition of AK& as A&*G - FH(a/W). The importance of load-shedding 

in the determination of the actual driving force has been recognized by Leis 

et. al. [13-141 which also used the measured load in their K calculations. 

Note, however, that the cor- 

& 

This load-shedding is not reflected in the previous 

At this point, it is useful to consider more carefully the mathematical model of an imposed displacement with no rotation over a length "L" 

B15 
as it relates to an actual specimen, such as that in Fig. 3, and its grips. 

Two points need to be reviewed. First, the applicability of the zero 

rotation conditions and secondly, the implication of measuring and controlling 

the imposed displacement at the back face of the specimen. 

In the present case, the zero rotation condition is effectively 

enforced at the base of the threaded ends of the specimen. 

effective value of L/W for the specimen might be expected to be somewhat 

greater than that based on the length of uniform reduced gage section. 

Thus, the 

The 

additional effective length would correspond to the no-crack bending compl iance of the tapered shoulders connecting gage section and threaded ends. 

The tensile part of the additional compliance is not required, since the 

= 2.17.W 25.4 RM. 

gauge 

mean extension 6 is measured over the gauge length of L 

If we let Lb denote the augmented effective bending length of the specimen, 

and nb = Lb/W, then the modified versions of Eq. 22 is (see Appendix). 

where 

rl 

d 

61 6 
and, again, rl = t/W. 

The other point to consider is the consequence of controlling the 

back face displacement , 

the specimen. Because the displacement 6 is controlled at L instead of 

Lb where no-rotation is effectively enforced, the displacement at the back 

face is equal to the displacement at the centerline (6cl) minus the displacement induced by rotation, eL, at L, Le., 

tjBF (see Fig. 3) instead of at the centerline of 

w 

&BF = 6 cl (L)-y 9L' 

Now, using Eq. 30 with tjC1(L) 

KI 

displacement is given by (See Appendix). 

given by Eq. 12.2, the final corrected version 

which takes into account both the effective length (Lb) and back face 

where 

91 7 
with ?I, ?Ib and 5 defined as before. The additional term appearing in 

the denominator of Eq. 32, as compared to Eq. 29, is of litte consequence for 

shorter cracks, and small values of nb-n. 

opposed to 

si gni f i cance . 

Thus, the fact that back face, as 

centerline displacement is monitored is generally of minor 

Based on the assumption that (da/dNImax coincides with a maximum 

in the AK 

a/W were compared with plots of GIc(a/W) versus a/W where 

(i.e., the correlation is monotone), plots of da/dN versus 

€ 

E 

for various values of qb. Note from Eq. 33 that for prescribed 6, AK 

is linearly proportional to GIc(s). The results are plotted in Fig. 6 versus 

relative crack depth, a/W. The maximum growth rate, occurring at a/W = 0.52, 

coincides with the location of maximum GIc (c,n,nb) for the case of qb = 2.5. 

A plot of da/dN versus AK 

+,/w = 2.5 is shown in Fig. 7. 

growth rates and the AK~IS 

reasonable limits of experimental scatter. 

(Eq. 28, 31) correlate the data providing the proper “effective” bending 

inferred from the present analysis with 

E 

A very tight correlation between the crack 

is observed with a monotone correlation, within 

One concludes that our K-solutions 

length is used. It should be pointed out, that an Lb/W ratio of 2.5 (which 

corresponds to a length of 29 mm) is the distance between the mid-shoulders 

of the specimen. 

61 8 

d 
CONCLUSION 

For a given geometry and applied end-displacements, Figs. 4 to 6, 

show that the uncritical use of conventional stress-derived KI solutions 

can substantially overestimate the KI values. While such an eventuality 

is conservative in application, it is non-conservative when testing to obtain 

basic materials behavior. 

In-the present case, the use of the strain intensity factor as 

represented by Eq. 26 seems to have two important limitations, both of 

which grow in importance at higher a/M levels. 

strain intensity factor as crack growth driving parameter does not account 

for the substantial load-shedding associated with the increasing crack compliance. 

monitoring the decreasing load amp1 i tude as the crack extends, and substituting 

this crack-length-dependent load into a tensile loading intensity factor 

calibration. The second major limitation of the traditional strain intensity 

factor defnition is that it fails to account for the development of a closing 

bending moment , associated wi th the prescribed tero-rotati on boundary 

condition. 

driving force. 

specimen is required. When the K-solutions are derived from a line-spring 

analysis and combined with an effective specimen length, good correlations 

are found between 

First, this definition of 

This limitation can, in part, be mitigated (as in Fig. 5), by 

This closing bending moment further reduces the effective crack 

A complete analysis of tension and bending moment in the 

K and the experimental fatigue crack growth data. 

81 9 
ACKNOWLEDGEMENTS 

This work was sponsored by the National Aeronautics and Space Administration under Grant No. NAG3-280. The participation of David M. 

Parks was supported in part by the Office of Naval Research under Grant 

#NO001 4-80-C-0706. 

REFERENCES 

1. 

2. 

3. 0. L. Bowie and C. E. Freese, Engineering Fracture Mechanics, Vol. 14 (1981), 

J. H. Bloom, International Journal of Fracture, Vol. 3 (1967), pp. 235-242. 

D. 0. Harris, Trans. of ASME, Journal of Basic Engineering, Vol. 89, (1969), 

pp. 49-54. 

pp. 519-526. 

4. E. P. Popov, Introduction to Mechanics of Solids, Prentice-Hall, Englewood 

Cliffs (1968). 

5. H. Tada, P. C. Paris, and G. R. Irwin, The Stress Analysis of Cracks 

Handbook, Del Research Corporation, Hellentown '( 1973). 

6. F. A. McClintock, 0. M. Parks, J. W. Holmes and K. W. Bain, Engineering 

Fracture Mechanics, Vol. 20 (1984), pp. 159-167. 

7. N. Marchand and R. M. Pelloux, "A Computerized Test System for ThermalMechani cal Fatigue Crack Growth", submi tted for pub1 i cati on. 

8. N. Marchand and R. M. Pelloux, in Time-Dependent Fracture, Martinus Nijhoff 

(1985), pp. 167-179. 

9. R. C. Boettner, 6. Laird and A. J. McEvily, Trans. of Metallurgical Society 

A. J. McEvily, "Fatigue Crack Growth and the Strain Intensity Factor" in 

Fatigue and Fracture of Aircraft Structures and Materials, AFFDL-TR-70-144 

11970). 

Of AIME, Vol. 233 (1965), pp. 379-387. 

10. 

11. A. E. Gemma, F. A. Ashland and R. M. Masci, ASTM Journal of Testing and 

Evaluation? Vol. 9, (1981), pp. 209-213. 

820 
12. 

13. 

T. Koizumi and M. Okazaki, Fatigue of Engineering Materials and 

Structure, Vol . 1 (1979) pp. 509-520. 

B. N. Leis and T. F. Forte, ASTM STP 743 (1981), pp. 100-124. 

14. B. N. Leis, "Displacement Controlled Fatigue Crack Growth in Elastic 

Plastic Notch Fields and the Short Crack Effect", to appear in a 

forthcoming issue of Engineering Fracture Mechanics. 

821 
APPENDIX 

Consider a specimen of gage length L with its associated shoulders. 

Let's define Lb the effective length at which the zero rotation is enforced 

(elL =o). 

b 

Obvious'ly Lb > L and, as a consequence the back face displacement 

6BF measured at L will be equal to the centerline displacement minus the 

angular displacement at L, i .e., . FeeL. Therefore, the known quantities 

are 6BF (measured at L) and etot across Lb' Equations 12.1 and 12.2 can 

now be written as 

6, = 6 (L) = 6 (L) + 6 (L) - 2 e (L:. tot nc c 

Substitute Eq. 10 into A.l and re-arranging, yielding 

-C12 E'BW 

*N M 

W 

-I: 

12 Ob + Cz2 E'BW 

(A.1) 

(A. 3) 

On using the dimensionless crack compliance defined by Eqns. 16.1 to 16.3, 

Eq. A.3 simplifies to 

822 
A 

A *N -= M -52 

W 

12 'lb + C22 

where n,, = Lb/w. Noting that M(L~) = M(L), the displacement 68F (Eq. A.2) 

is, using Eq. 10 and A.1, 

which, upon re-arranging and using the dimensionless crack compliance 

(Eqns. 16.1-16.3) yields 

Finally, recall ing that 

and upon substitution of Eqns. A.4 and A.6 into A.7, we get 

d 
Equation A.8 corrects for the fact that actual displacements are measured 

at back face instead of the centerline, and for the fact that the zerorotation condition is imposed not at L, but at some distance close 

to the actual grips. 

Lb 

. . 

824 
LIST OF CAPTIONS 

Fig. 1 

Fig. 2 

Fig. 3 

Fig. 4 

Fig. 5 

Fig. 6 

Fig. 7 

Resultant force N and moment M transmitted by the grips to a SEW 

specimen. 

Geometrical factors F1 Fzs F ,, and Eq. 24 as a function of the 

dimensionless crack length. 

Single edge notched (SEN) specimen used for the testing (notch: 

1 mm deep x 0.025 nun wide). 

FCG rates as a function of the strain intensity factor calculated 

using Eq. 22. 

FCG rates as a function of the strain intensity factor calculated 

using Eq. 25. 

FCG rates as a function of a/bJ and Eq. 33 as a function of a/M for 

various nb ratios. 

FCG rates as a function of the strain intensity factor calculated 

using Eq. 32. 

825 

d 
8 

--- 8 

2 

7 

8 

N 

24 

+M 

*W+L 2 2 

zq 

-W2 YM 

N 

THICKNESS = 8 

Fig. 7 Resultant force N and moment M transmitted by the grips to a SEW 

specimen. 

d 

826 
m ln Lp In Q ln Q ln Q b b b b 0 

0 0 m tu N cl( a; 

cc 

0 

ff 

w 

I 

LL 

N 

827 
c 4 

m 

c 

0 

e 

0 

c 

a 

E 

H 

0 

.. 

r 

U 

c, 

0 

t 

W 

cn 

s 

c, 

v) 

QI 

ct 

-1- 

L 

0 

cc 

E: 

E 

nn 

ax 

cn 

a,@ W 

QIU 

-on 

c 

.aFE 

m828 
-.I 

0 

N 

I 

0 m co h m 

Ep 

e4 

Q .-( Q, - b .I. 

& 

.14 

Z 

0 

I- 

(3 

Lf 

Q, 

Q 

Ctl 

41 

u 

tY 

u 

W 

3 

(3 

I-- 

U 

G 

H 

a 

a, 

a 

n 

r. 

0 m co h m 

Ep 

e4 

Q .-( Q, - b .I. 

& 

.14 

Z 

0 

I- 

(3 

Lf 

Q, 

Q 

Ctl 

41 

u 

tY 

u 

W 

3 

(3 

I-- 

U 

G 

H 

a 

a, 

a 

n 

r. 

n 

S 

W 

c 

0 

Y 

0 

id 

G 

x 

Y 

w1 sa 

“C 

0 

+, 

C 

n 

C 

16 

c 

=P 

u) 

c 

829 
.J 

0 

N 

z: 

830 
Nmm 

(UNN 

aaa 

831 

d 
N 

X 

832 

d 
Appendix C - TMFCG in Inconel X-750 

THEftStZI,-?IECHANICXL FATIGUE CRACK CROWTH IN INCONEL X-750 

Norman Marchand* and Regis M. Pelloux** 

*Research Assistant, DeDartment of Materials Scienc.c? 

and Engineering. Massarhusetts Institute of Technology, 

Cambridge, tlA 02139, USA. 

**ProFessor, Department of Haterials Science and 

Engineering, :lassacliiisetts Institute o€ Technology, 

Cambridge, MA 02139. IISA 

Thermal-mechanical fatigue crack growth (TtiFCG) was studied 

in a - , nicke 1 base sripera 1 loy Incone 1 X-750 under cnnt ro1 led 

load amplitude in the temperature range from 300 to 650°C. Inphase (Tmax at .-max), out-of-phase (Tmin at imax) and isatherma1 

tcsts at 650°C were performed on single-edge not\*h hars under 

fully reversed c.yclic conditions. 

4 DC electrical potential method was used to medsurc <.rack 

length. The electrical Dotential response obtained for e,tt It cycle 

of a given wave form and R value yields information on crack (:losure and crack extension per cycle. The macrosL'opic larack growth 

rates &ire! rcuorted as a Function of :.K and the relative m,ignitude 

of the ThlFCG are discussed in the light of the potential drop inforntat ion and of the fractographic obst*rvat ions. 

ISTKODUCT IUN 

d 
~IGINAL P 

WWRQ 

and life predictions techniques are based upon isothermal testing. 

In fact, the study of fatigue has generally bypassed real thermal 

f'itigue loading p'irtly because isotht?rm.il tests are relatively 

siiriple to perform, but also because it has often been felt that 

such tests carried out at the maximum service temperature would 

give worst case results. However, several studies which have compared fatigue resistance under thermal cycling conditions with 

that in isuihrrmal tests have shown that in many cases, the latter, 

rather than giving a worst case situation, can seriously overestinate the real fatigue life [l-151. 

The influence of temperature on low cycle fatigue (LCF) lives 

is welL dclcumentcd [16-191 but the mechanisms by which temperature 

influences the fatigue process are not well understood. Low cycle 

fatigue is generally acknowledged to be directly related to materid ductility; however, as ductility increases with temperature, 

low cycle fatigue life normally decreases. Creep and environmental effects are known to influence LCF behavior, but the relative 

contributions of these two factors are not easily differentiated. 

[17-19, 201. 

The subject of thermal fatigue which involves combined temperature and stress-strain cycling, is less well understood than 

isothermal elevated temperature fatigue and only limited data 

have been gathered on crack growth during thermal-mechanical fatigue (TbfF) under conditions of small plastic strain 12, 5-7, 9, 

13-14]. 

The data obtained from thermal-mechanical testing for.conventionally cast Co- and Ni-based superalloys, and for directionally solidified Ni-based alloy [5-7, 9, 131 have shown faster 

crack growth rates than for the equivalent isothermal conditions 

at T,, . Furthermore, crack growth rates under out-of-phase cycling TTmin at cmax) were found to be faster than under in-phase 

cscling (7 at T~~~). For a 12 Cr-Eio-V-IJ steel thermal-mechically cycleXbetween 300 and 6OO0C, very little difference in 

growth rates for TNF and isothermal tests were found [21], whereas. ,111 inverse behavior was observed on a 304 SS 1151; that is, 

faster crack growth rates under in-phase cycling than under outof-ptins2 cscling. 

ma 

c2 
r, *.$ 11 . ,.. 

tz.nding of TEIF of typical nickel-base superalloys. Second, to 

assess the suitability of variaus parameters for correlating high 

temperature TElFCG rates used for adequate fatigue life predictions 

of engine components. 

EXPERIMENTAL PROCEDURE 

Haterials and Specimen 

The material used in this investigation was a standard chemistry Inconel X-750, a corrosion and oxidation resistant material 

with good tensile and creep properties at elevated temperatures. 

The chemical composition, the heat treatment of the as-received 

annealed material, and the tensile properties at high and room 

temperature are given in Table 1. The grain size is about 0.12 nun. 

Single edge notch tensile bar specimens were used in this investigation. The test specimens have a rectangular cross section of 

11.7 x 4.4 mm2 and a starter notch approximately 1 mm deep which 

is cut by electro-discharge machining. The specimens were precracked in-fatigue at 10 Hz at room temperature under a LK of about 

10-15 MPat'm. All the AK's were calculated with the expression derived by Harris [22]. 

This formula which was derived for an edge crack in a SEN plate 

with no bending is suitable for the testing system. 

Table 1 

(a) Chemical Composition (wt. pct .) 

Xi Cr Fe Ti A1 Nb tin Si C co 

72 15.5 7 2.5 0.7 1 0.5 0.2 0.04 1.0 

(b) Heat Treatment 

Temperature ("C) Time (hr) Quench 

1150 2 air cool 

a50 24 air cool 

700 

>-- 

20 air cool 

(c) Tensile Properties I_ 

' (FIPa) cl (Pct) 

y- UTS P Temp2rature ("C) 7 (NPn) 

6 10 1000 30 

6 16 1000 3' 

5 50 820 7 

c3 
Apparatus 

- and Test Conditions 

The apparatus used in this study was a computer-controlled 

thermal fatigue testing system which consisted of a closed-loop 

servo-cont rolled, elect ro-hydraulic tension-compression fatigue 

machine, a high frequency oscillntnr for induction heating, an air 

compressor for ccwling, a mini-computer, etc. Figure 1 shows the 

L.ontrol block diagram of this system. 

Fig. 1. Diagram showing the control system of apparatus used for 

TEIFCC tests. 

The system is capable of testing specimens of different sizes 

.ind configuration (SEN, CT, hollow tube, etc.) up to loads of 

25,000 lbs. The specimen alignment is insured by the use of a 

liood's metal pot which prevents a bending moment in the specimen. 

Kec-ause a DC potential drop technique is used to monitor crack 

~rtx~tli, the lower grip is electrically insulated from the svstem 

bv me.ins of a ceramic. c*o,iting. The ends of the grips are water 

1'1)o led bv means I) i c-opper (xi i 1 s, 

.- 

c4 
Experimental Condit ions 

c5 
siiirul t,irict)us climge of the net stress .ind tentperatitre fur in-phase 

aid tutt-~~t--ph;ise k.yc.1 ing at low and high ’K. In tlicse figures, 

till, notcntial c-iiange with stress aid tc.mperaturc? v(r. .) and with 

ttmpernture onls V(T) :ire plotted. Tlw tneclisnical driving force 

Y( .) wlii<*li is the difference between V(T,-) and V(T) are also 

plotted. In order to assess crack growth, the peak potential of 

each cycle was recorded and plots of the voltage versus the number 

oi cycle (N) were obtained. Using an esperimental calibration 

L-iirve, the crack lengths versus N were derived. ’The crack growth 

rates were calculated using a seven-point incremental polynomial 

method. Figure $ shows the results as function of LK (R = 0.05) 

iiiid Kmas (R = -1). 

First, it can be seen that the craL.k growth rates are higher 

for T?IF cyL,ling than for tha equivalent isothermal condition (65OOC) 

r;hicli is in agreement with the results obtained on other nickelbase allovs [5-7, 9, 131. Secondly, it is observed (Fig. &) that 

the crack growth rates are higher for R = - 1 than for R = 0.05 

vI1iL.h indiccltes that compressive stresses play an important role 

in the mechanics of TXFCG. Comparison between out-of-phase and 

iii-Dhase at F. = -1 shows that out-of-phase cycling is more damagin; than in-phase cycling at high hK, whereas at low X, the crack 

Erowth rates are the same. The explanation for this behavior can 

be found in Figs. 2 and 3. At low IK the potential curves V(:> 

for out-o f-phase and in-phase are similar which indicates that the 

mechanical driving force for cracking are similar and identical 

crack growth rates are therefore expected. As hK increases, however, tne V(u) potential curves for both in-phase and out-of-phase 

c.ycling display characteristic features (Fig. 3). The in-phase 

17( -> curve shows a smooth increase with Pnet up to the maximum 

followed bs a sharp increase at Jmax. The potential then remains 

stable as :net starts to decrease and sharply falls as -‘net zipproaches zero. In the compression regime the potential smoothly 

decresses, reaches a minimum at “min, and finally increases as the 

stress increases again. On the other hand, the out-of-phase V( ) 

potential curves shows (at the same LK) a smooth increase with 

r;itli .I peak value at -lmilx. The potential then decreases down to a 

minimum value and finally increases agdin with .Tnet. The most import.int feature of these signals is the L.rossover point (denoted 1) 

for which V(.) = 0. The crossover point represents the stress to 

‘ipply tu the specimen For the potential to equal V(T). Because 

Y(T) is mtbasiirrd ‘it - = 0 for the sntire thermal (,vc~L‘, the expected 3crds.s to ‘ipply is J = 0. However, ii the potcntiLil field near 

tilc, L.rL~l%k tip is disturbed either by a non-zeri> rL.sidu,il stressscr.,in fitAld ur by geometrical events suL1i as bluntiria, closure, 

L-~, -, the \:(r, = 0) potc.nticil might not net-essarily cqiicil V(T) 

‘i;i,i .t noii--Lcfro stress is reqtiil-ed tL) c;in, out tlic c.l~ntril)ittian 

,)i t 11 is pliL nt)mcii<i. For tlic! out-oi-pli:is<, potent i.11, tllc - C~L-OSS~~WLit .iIi;.~ys t)ci‘ilrs Lit zero strtass il\r ttiL. io-DliasLh pL)tt,iiti.il. 1%~ 

c~rs .it .i iiegkiti\*cL stress t’ . = -75 k1p-1 .it ‘t; = 50 ?!i’.i~nt), wlierc.is, 

C6 
! \a OR1 E 

OF kl 

02 

0 

-C2 

-u4 

iJ4 

02 

G 

OL 

-(I 4 

9 

a 

7 

6 

Fig. 2. 

Inconel X-750. AR = 25 PlPavm. 

Potential curves V(~,IJ), V(T) and V(J) for TEPCG of 

first assuming that the crossover point occurs near an effective 

closure stress (~~1) it follows that the effective stress intensity factor (2Keff) for crack growth will be higher for out-ofphase than for in-phase cycling (~~1 is negative). If we plot 

the crack growth rates as a function of Ueff, we find that: both 

in-phase and out-of-phase crack growth rates overlap (Fig. 5). 

It is important to note that the absolute amplitude of the 

V(-> signal (see Fig. 3) in the compressive regime of the cycle, 

is much higher for our-of-phase than for in-phase cycling which 

indizcltss that the crack surfaces are in cont.fct on a ntuch larger 

scala than under in-phase cycling. This was confirmed by fractographic observation which shows th,lt otrt -of-pll;lst? c::cLing 1e;lCls 

c7 

d 
Ii 

IT 

ORIGINAL 

OF POOR 

Fin. 3. Potential curves V(T,a). V(T) and V(a) for TXFCC of 

Inconel X-750. AK = 50 War/;;;. 

to transgranular cracking with considerable mating, whereas, inphase cycling leads to intergranular fracture with little evidence 

of mating. The higher crack growth rates at R = -1 than R = 0.05 

.mi the fractographic observations lead to the conclusion that although there should be no cracking at the maximum temperature because of the compressive strc?ss, some form OF severs damage is 

taking place under compressiLre strain. Also, the surface oxide 

film formed at high temperature will rupture at low temperature, 

under maximum tensile stress. This le'ids to a resharpening of the 

crLick tip with each cycle and results in an increase in growth 

r.1 te . 

The rationille for the negative closiire stress in out-fif-ph'ise 

cscling <-.in be frtrind bv assmiin!: that the residii.il stress field ;it 

the cr3L.k tip is oi tensile nature .it ?t'ro applied stress and that 

C8 

d 
a negative stress has to be applied in order to cancel it atid to 

close the crack. This negative : also represents the eifective 

contribution to cracking of the damage taking place durint: tlis 

compression part of the cycle. 

Cl 

"i .i 

I 

I 

Fig. h. TEIFCG of Inronel X-750 as a func.tion of AIL 

i 

-1 i 

-,I 

I 

MP0.mFie. 5. T?fI'CG of Inconel X-750 as a function nf .Xeff 

c9 
The difference in growth rates between the isothermal test 

(650°C) and the TPfF tests were also explained by looking at their 

respective V(*1) potential curves at Low and high K. At low r?K 

no significant differences were observed between V(.) potential 

curves. At higher .'K, however, the isothermal V( potential has 

shown a crossover point taking place at a positive stress. This 

has the effect of reducing the effective driving force for cracking. L-,.I in the computation of .'.K, 

one finds that the crack growth rates in terms of .Xeff fLlr both 

isothermal and TYF tests are similar (Fig. 5). The positice closure stress observed was attributed to the build-up of osides in 

the wake of the crack. This is supported by fractographic observation which shows greater oxidation for isothermal testing than 

for T?fF testing. 

CONCLL'S IONS 

By taking into account this 

Faster crack growth rates were measured in Inconel X-750 

cycled between 360 and 650°C under out-of-phase conditions than 

under in-phase cycling at R = -1 or R = 0.05. This behavior wds 

rationalized by introducing the concept of an effective closure 

stress which was defined as the applied stress at the crossover 

paint of the V(2) potential curve. ocl should represent the effective contribution to cracking of the damage taking place during 

the compressive part of the cycle. Correlation between TPIFCG rates 

and .X appear to be valid prwided elastic conditions prevailed in 

ths bulk. Correction to the applied stress can be introduced in 

order to take into account damage occurring in the compressive part 

of the last cycle. Further work is needed to assess the suitability 

of CK to more realistic conditions involving TMFCG under cyclic 

plastic strains. 

Acknowledgment: 

Aeronautics and Space Administration under Grant No. Pu'hG3-380. 

This research work was sponsored by the National 

c10 

d 
REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

Sheffler, K. D., Vacuum Thermal-Mechanical Fatigue Behavior of 

Two Iron-Base Alloys, ASTM STP 612, (1976) 214-226. 

Skelton, R. P., Environmental Crack Growth in 1/2Cr-Mo-V steel 

during Isothermal High Strain Fatigue and Temperature Cycling, 

Mat. Sci. Eng., vol. 2, (1978) 287-298. 

Fujino, N. and Tarai, S., Effect of Thermal Cycle on Low Cycle 

Fatigue Life of Steels and Grain Boundary Sliding Characteristics, ICM 3, vol. 2, 1979, 49-58. 

Muwabara, K. and Nitta, A., Thermal-Mechanical Low Cycle 

Fatigue under Creep-Fatigue Interaction in Type 304 Stainless 

Steel, ICM 3, vol. 2, 1979, 69-78. 

Rau, C.X., Gemma,A.E.,Leverant, G.R., Thermal-Mechanical Fatigue Crack Propagation in Nickel and Cobalt Base Superalloys 

under Various Strain-Temperature Cycles, ASTM STP 520 (1973) 

166-178. 

Gemma, A.E., Langer, B.S. and Leverant, G.R., Thermal-Mechanical Fatigue Crack Propagation in Anisotropic Nickel Base 

Superalloys", ASTM STP 612 (1976) 199-213 ~ 

Gemma,X.E., Ashland, F.X. and Masci, R.M., The Effects of 

Stress Dwells and Varying Elean Strain on Crack Growth During 

Thermal Mechanical Fatigue, J. Test. Eval., vol. 9, no.4, 

(1981) 209-215. 

Troshchenko, V.T. and Zaslotskaya, L.A., Fatigue Strength of 

Superalloys Subjected to Combined Nechanical and Thermal 

Loading, ICM 3, vol. 2, (1979) 3-12. 

Eleyers, G. J., Fracture Plechanics Criteria for Turbine 

Engines and Hot Section Components, NASA CR-167896, (1982). 

Jaske, C.E., Thermal Mechanical Low Cycle Fatigue of AIS1 

1010 Steel, ASTN STP 612, (1976) 170-198. 

Westwood, H. J. and Moles, M.D., Creep-Fatigue Problems 

in Electricity Generation Plants, Can. Met. Quart., ~01.18, 

(1979) 215-230. 

Bhongbhobhat, S., The Effect of Simultaneously Alternating 

Temperature and Hold Time in the Low Cycle Fatigue Behavior 

of Steels, Low Cycle Fatigue Strength and Elasto-Plastic 

Behavior of Materials, eds. Rie, K.T. and Harbach, E., DVM 

(1979), 73-82. 
13. Leverant, G. R., Strongman, T.E., and Lacger, B.S., Parameters 

Controlling the Thermal Fatigue Properties of Conventional 

Cast and Directionally-Solidified Turbine Alloys, Superalloys: 

Eietallurgv and Hanufactures, ed., Kear. B.H., Muzuka, D-R-, 

Tien, J.R., and iJlodek, S.T., Claxtors Pub.(1976) 285-295. 

15. Okazaki, hi. and Koizumi, T., Crack Propagation During Low 

Cvcle Thermal-Mechaniczl and lsothermal Fatigue at Elevated 

Temperatures, Plet . Trans. vol. 14A, (1983) 1641-1648. 

15. Kuwabara, K., Nitta, A, and RitamlJr;i, T., Thermal-Mechanical 

Fatigue Life Prediction in High Temperature Component Materials for P1,wcr Plants, Coni. on Advances in Life Prediction 

Xsthods, ASPIE-PlPC, Albany, N.Y. (1983) 131-141. 

16. Itareing, J., Plechanisms of High Temperature Fatigue and CreepFatigue Failure in Engineering Flaterials, Fatigue at High 

Temperature, ed. Skelton, R. P., Applied Sci. Pub. , (1983) 

135-185. 

17. Lloyd, G. J. , High Temperature Fatigue and Creep-Fatigue 

Crack Propagation: Flechanics, Mechanisms and Observed Behavir in Structural Materials, Fatigue at High Temperature, 

ed. Skelton, R.P., Applied Sei. Pub. (1983) 187-358. 

18. Coffin, L. F., Damage Processes in Time Dependent Fatigue - A 

Review, Creep-Fatigue-Environment Interactions, eds. Pelloux, 

R. M. and Stoloff, N.S., AIME (1980) 1-23. 

19. Mills, W. J. and James, L.A., Effect of Temperature on the 

Fatigue Crack Propagation Behavior of Inconel X-750, Fat. 

Eng. Mat. Struct., vol. 3, (1980) 159-175. 

20. Skelton, R.P., The Growth of Short Cracks During High Strain 

Fatigue and Thermal Cycling, ASTM STP 770, (1982) 337-381. 

21. Roizumi, T. and Okazaki, El., Crack Growth and Prediction of 

Endurance in Thermal-Flechanicnl Fatigue of 12 Cr-Flo-V-W Steel, 

Fat. Eng. Mat. Struct., vol. 1, (1979) 509-520. 

22. Harris, D. O., Stress Intensity Factors for Hollow Circumferentially Notched Round Bars, 1. Basic Eng., vol. 89 (1967) 

49-54. 

d 

c12 
Appendqx D - TMF In B1900+Hf 

THE THERMAL-MECHANICAL CYCLIC STRESS-STRAIN 

RESPONSES OF CAST B- 1 goo+tir 

N. Marchan@, G. L’Esperancew and R.M. Pe 1 loux- 

* Research assistant, Department of Material Science and Engineering, 

Massachusetts Institute of Technology, Cambridge, MA 02 139 

W NSERC Research Fellow, Department of Metallurgical Engineering, Ecole 

Polytechnique, Montrdal, Quebec, Canada, H3C-3A7 

jcjcjc Professor, Department of Material Science and Engineerfng, Massachusetts 

institute of Technology, Cambridge, HA 02 139 

d 
Abstract 

A study was undertaken to develop an understanding of the fatigue 

response of superalloy 8- 19OO+Hf under comblned thermal and mechanical 

strain cycling in air. Comparative evaluatlons were made with existing 

themal-mechanical data of 6- 1900 and with results of a comgrehensive study 

of the fatigue behavior of the same alloy under isothermal conditions. The 

thermal-mechanical fatigue (TMF) response was investigated for constant 

amplitude, fully reversed, mechanically strained cycling of uniaxially loaded 

specimens in the temperature range from 400 to 925'C. Experiments were 

conducted both with maximum strain in-phase with maximum temperature, and 

out-of-phase with maximum temperature. 

TMF cycling was observed to cause more cyclic hardening than in 

Isothermal fatigue experiments at the maximum and minimum temperatures. In 

terms of mean stress or plastic strain range, out-of-phase cycling was shown 

to be more deleterlous than in-phase or isothermal cycling. However, few 

differences were observed in terms of the stabilized stress ranges. The 

asymmetrlc cyclic hardeninglsof tening behavlor is explained In terms of 

coarsening of tbe y' and associated strafn field. For TMF cycling, the high 

temperature flow stress depends on the density of the misfit dislocations, 

whereas the low temperature flow stress is controlled by the magnitude and 

sign of the applied stress. The TNF cracking modes are discussed. The results 

show that the fracture criteria under TMF cycling is a stress-base phenomenon. 

KEY WORDS thermal-mechanical fatigue, superalloy, cyclic hardening, damage 

mechanisms, directional coarsening. 
Most high temperature components operate under conditions of cyclic 

mechanical non-isothermal loading. The design of these components must 

consider the effect of plastic strains that are associated with transients as 

well as with the steady state operating stresses and strains that cause time 

dependent failure. Figure 1 [I 1 shows schematically the stress and strain 

cycles to which gas turbine disk and blade materials are subjected to as a 

result of rapid start, steady-state operation and rapid shut-down. These 

stress-strain-temperature cycles produce high strain low cycle fatigue which 

leads to crack initiation, slow crack growth and failure by fast fracture. As a 

consequence, ft Is necessary to fnvestlgate the cyclic stress-strain behavior of 

these structural materials under cyclic temperature conditions. High 

temperature fat@? studfes generally bypass real thermal fatigue loading 

partly because isothermal tests are simpler and much less expensive to 

perform, but also because It was felt that such tests carried out at the 

maximum service temperature would give worst case results. However, 

several studles whfcR Rave compared the fatigue resistance under thermal 

cycling conditions with that of isothermal tests have shown that, in many 

cases, the latter, rather than giving 'the worst case situation, can seriously 

overestfmate the fatlgue lffe [2- 193. 

In the last two decades, a large effort has been made to characterize 

both fatigue crack initiation and fatigue crack propagation behavior of 

materfals at elevated temperature. It fs easy to understand that hlgh 

temperature fatigue is a complex problem because of the time-dependent 

processes which intervene, in add! tion to the cycle-dependent phenomena. At 

D2 

a 
high temperature, factors such as strain-rate or frequency, waveform signal, 

hold time and environment have a strong Influence. Moreover, most nickel-base 

superalloys are metallurgically unstable when they are cyclically deformed at 

hlgh temperature. Therefore, changes tn the flow properties of the materlals 

at the crack tip are expected to induce Changes In the propagation rate. Any 

decrease in the work hardening exponent of the crack tip material caused by an 

increase in strain rate or by an increase in temperature, would cause an 

increase in crack propagation rate. Similarly, stress relaxation reduces the 

effective value of the yield stress. All these phenomena, which are 

temperature-dependent, greatly complicate the prediction of life in real 

components. Isothermal testing, to study the effects of tests parameters, is at 

a disadvantage; new design concepts are needed which are based on the 

knowledge of the cyclic response under thermal cycling if more accurate life 

prediction methods are to be established. 

This paper describes the results of a study where the low cycle fatigue 

behavior of superalloy 8- 1900+Hf was investigated for conditions of combined 

thermal and mechanical strain cycling. Experiments were limited to the two 

extreme conditions of in-phase and out-or-phase cycltng. The objective of this 

study was to obtain information on thermal-mechanical behavior of a commonly 

used superalloy. In turn, this information 1s used to assess the suitability of 

various parameters for correlating high temperature TMF crack growth. 

However, slnce thermal-mechanical fatlgue testing is more time consuming, 

costly, and complicated than isothermal fatigue testing, the approach taken in 

this program was to conduct a limited study of TMF behavior over the 

temperature range of 400 to 925'C for correlatfon with previous isothermal 

work on the same material. 

c- a- i 

D3 
Udoguchf and Wada El, Sheff ler 131, Taira et al. 14-51 and others C6- 191, 

in studies of thermal fatigue of high temperature alloys, have shown that 

thermal fatigue can be shorter than equivalent isothermal fatigue at the 

maximum temperature of the cycle. More specifically, some of the results, 

giving Nf as a function of the plastic strain range for an A-286 steel 131, 

have shown that in-phase cycling (maximum temperature at maximum tensile 

strain) is more damaging than out-or-phase (maximum temperature at 

maximum compressive strain), which in turn caused fracture in fewer Cycles 

than isothermal cycling. This was attributed to extensive cumulative grain 

boundary sliding during thermal cycling. Similar results were obtained for 304 

stainless steel C6, 8-9k, 181. However, when the data is expressed in terms of 

total strain range AE~, Kuwabara and Nitta [8-91 found that isothermal and outof-phase changed rank and that this new order was consistent with the fraction 

of intergranular cracks that was observed. 

dependence of the microstructure under TMF conditions [ 13- 161. 1 t is 

signfficant that rrtF tests between 200 and 600'C have shown that in-phase 

cycling gave higher endurance than the isothermal tests at 600'C [ 13- 151. 

However, when cycled between 300 and 6SO'C, out-of-phase cycling gave 

shorter lives than did Isothermal testing at 650'C [ 161. These results indicate 

that when the temperature embraces a ductility minimum In the material, outof-phase cycling gives shorter lives than Isothermal testing at the maximum 

Studies of Cr-Mo steels have pointed out the strong temperaturetemperature. 

For superalloy IN-738, high strain fatigue tests, In-phase and out-ofphase TMF cycling between 400 and 950'C, all gave tbe same endurances at a 

04 

A 
given A€& level 1201. However, Nitta et al. [ 18- 191 have shown that the 

endurance of IN-738 depends on the applied strain A€&. Their results pointed 

out that thermal fatigue life of nine different nickel-base alloys strongly 

depends upon the strength of the alloy. The data obtained by Lindholm and 

Davidson 171 on conventional 8- 1900, agreed with the previous conclusion. The 

dependence of thermal fatigue on strength may not be restricted to superalloys. 

Jaske 1 11 found that in order to correlate in-phase, out-of-phase, and 

isothermal fatigue data for a low carbon steel, a knowledge of both cyclic 

stress and cyclic strain was necessary. On the basis of stabilized stress range 

versus cycles to failure, little difference was observed in the behavior of 

specimens subjected to in-phase and out-of-phase cycling. However, the cyclic 

hardening characteristics of the alloy tested were very complex, indicating 

difficulty in predicting the stabilized stress range. 

It thus appears that there is no hard and fast rule for relating the 

thermal-mechanical method to isothermal testing. There are many 

uncertainties in comparing total endurances only; for example, the number of 

cycles to initiation may differ, and cracking may be intergranular in isothermal 

tests but transgranular in the cyclic temperature tests. Obviously, low 

endurance data w i I 1 depend on ini t iat ion/propagat ion ratios , duct i 1 i ty, 

including sensitivity to strain rate, hardening behavior, etc. It should be 

emphasized that temperature cycling has a marked effect upon the u-E loop 

shape and deformation mode. The materials tested may or may not accomodate 

differing amounts of deformation before failure, depending upon its 

microstructural condition, which in turn is dependent upon the condition of 

cyclic deformation and temperature history. This points out the importance of 

knowing the temperature and strain history on the instantaneous material 

response to assess the kinetic of damage accumulation. 

D5 

i 
The material for this program was taken from a special quality melt of 

8- 1900+Hf obtained from Certified Alloy Products, Inc., Long Beach, California. 

The chemical analysis, heat treatment, and tensile properties are shown in 

Tables I and II. The structure of the material was documented in both the ascast and fully heat treated conditions. The following observations were made: 

The grain size is about 1 to 2 mm (Figure 2a). The replica technique was 

used to measure and study the gamma prime (y’) size and distribution. The 

fully heat treated material showed the y’ size to be about 0.6-0.9 pm (Figure 

2c). The structure has an interdendritic spacing of about 100 pm and islands 

of y’-eutectic surrounded by a zone of fine y’ (0.9 pm) can be observed (Figure 

2b). MC carbides near the coarse y‘ islands can also be observed. 

Atmaratus and Test Co nditions 

The thermal-mechanical fatigue specimens have a rectangular crosssection of 1 1.7 x 4.4 mm? The test section of each specimen was polished 

with successively finer grades of silicon-carbide paper to produce a bright 

finish, with finishing marks parallel to the longitudinal axis of the specimen. 

Specimens were degreased with trichlorethylene, followed by reagent grade 

acetone before being heated to temperature. 

The thermal-mechanical fatigue experiments were conducted using the 

same basic servocontrolled electrohydraullc test system used for thermalmechanical fatigue crack growth 1231. Details of the equipment, method of 

D6 
heating, gr ipplng and alignment procedure, and general expert mental procedures 

are given elsewhere 122-231. 

Temperature was measured with 0.2 mm diameter chromel-alumel 

thermocouples, which were spot welded along the gauge length. By computer 

control, the temperature in the gauge length was maintained within i5"C of the 

desired temperature for both axial and transverse directions throughout the 

duration of a test. For axial strain measurement, a gauge length of 15 mm was 

selected on the middle part of the specimen and a contact type extensometer 

was employed. Temperature and mechanical strain were computer-control led 

by the same triangular waveform with in-phase or out-of-phase cycling (see 

Figure 3). The mechanical strain was obtained by subtracting the thermal 

strain from the total strain. The thermal strain was measured by cycling the 

temperature at zero load and stored into the computer. The mechanical strain 

(A&) was maintained constant at each strain level. The mechanical strain 

. was increased by approximately 10% of its previous value after saturation of 

the total stress range. This means that for most strain ranges, more than 250 

cycles were performed. The frequency was kept constant at 0.0056 Hr ( 1 /3 

cpm) for all strain ranges which resulted in varying the strain rates between 

0.002 sec-1 and 0.007 sec-1. 

Results 

A Cyclic Responses 

Results of all the experiments conducted in this program are summarized 

in Tables 3 and 4, where the mechanical strain range, the number of applied 

cycles at each strain range, the lnlttal and final stress range, and final plastic 

strafn range are listed for both fn-phase and out-of-phase cycling. The plastic 

07 

d 
strain range was taken as the width of the hysteresis loop at zero stress and 

therefore includes both t ime-independent and t ime-dependent inelastic strain 

Components. Figure 4 shows the thermal straln, the mechanical straln, the 

total strain, and the stress amplitude as a function of time (one cycle) for both 

in-phase and out-of-phase cycling. From the load-time and mechanical strain 

(Ew)-time curves the hysteresis loops were obtained. 

Even though strain cycling was fully reversed, the stress cycle was not 

symmetric about zero because the temperature was different at each extreme 

of the cycle. Figure 5 shows examples of the loops obtained for both in-phase 

and out-of-phase cycling. For out-of-phase cycling, a positive (tensile) mean 

stress Is observed and a negative mean stress is observed for the in-phase 

cycling. That is, for the in-phase cycle, the magnitude of peak compressive 

stress was greater than the magnitude of peak tensile stress, or IUminI IUmaxI. 

The opposite was true for the out-of-phase cycle where ICJmaxI IaminJ. Figures 

6a and 6b show the type of stress response for in-phase and out-of-phase 

cycling at a fixed strain range. Figures 7a and 7b summarized the fatigue 

results. From Figures 6 and 7, the following conclusions can be drawn. First, 

one can conclude that the mean stress (.a') does not vary much with the number 

of applled cycles or strain ranges for In-phase cycling. However, 5 does vary 

with N and A€- for out-of-phase cycling. It is also important to notice that 

for similar strain ranges, the absolute value of 5 is higher for out-of-phase 

than for In-phase cycling. Another conclusion that can be drawn is that for all 

A€-, in-phase cycling shows 

unchanged except at high applied strain range. For out-of-phase cycling, Urn, 

hardened and Umin softened. The softening of Umin being more important than 

the hardening of am results in a drift of 5 to higher value of tensile stress. 

On the other hand, because Umin stayed almost unchanged and a- hardened for 

to harden, whereas Umin stayed almost 

D8 
in-phase cycling, the net result is a softening of the mean stress, that is 1551 

decreases. 

As stated before, the "saturation" was defined such that the change in 

stress range (Au), in about fifty cycles, was lower than two percent. The 

values of Om, Umin and 5 are plotted against the strain amplitude (AEmK/2) to 

obtaln the cyclic stress-strain (CSS) curves for in-phase and out-of-phase 

cycling. These curves are shown in Figure 8 along with the isothermal CSS 

curves obtained at 87 1 and 538°C [2 1 I. Interesting conclusions can be drawn 

from Figure 8. First, one can see that the CSS curves of in-phase, out-of-phase 

and isothermal testing coverage at low AE,,/~ (Kl.0012) but diverge as 

A€m,/2 increases. At higher A€mec/2 (but lower than 0.28%), the maximum 

stress (Om= at 925'C) for in-phase cycling is higher than for isothermal 

fatigue at 871°C. For AE-/Z > 0.28%, the inverse behavior is observed, that 

is, a higher hardening rate for isothermal fatigue than for 

cycling. The hardening rate of Omjn of in-phase cycling (T = 4QO'C) is identical 

of in-phase 

to the hardening rate measured for Isothermal fatlgue at 538°C. For out-orphase cycling, Umin (at T = 925°C) also shows a higher hardening rate than 

isothermal fatigue at 871 "C (for AE-/~ < 0.25%), and a lower hardening rate 

for AE-/~ > 0.25% than isothermal fatigue. However, urn= (T = 400°C) for 

out-of-phase shows a higher hardening rate than isothermal fatigue at 538°C. 

compared by plotting u,, of in-phase and bmhJ of out-of-phase, both 

measured at 925°C (Figure 9). Urnin of in-phase cycling and -Urn= of out-ofphase cycling are also plotted. One can see that the hardening rate at 925°C fs 

higher for in-phase (in tension) than for out-of-phase cycling (in compression). 

However, the hardening rate at 4OO'C Is higher for out-of-phase CyCltng (in 

tension) than for fn-phase cycling (in compression) and isothermal testing. 

The hardening behaviors of in-phase and out-of-phase cycling were 

D9 

d 
8. Fractographic and TEM Observations 

In order to clearly identify the cracklng process, the long transverse and 

longitudfnal sections perpendicular to the fracture surface were mounted for 

metallographic observation. For out-of-phase cycling, multiple cracks were 

observed along the gauge length. The propagation path is transgranular 

and appears to proceed interdendri tical ly. 

Examination of the specimen failed under in-phase cycling, revealing a varying 

degree of transgranular and intergranular cracking with a density of 

surface cracks much lower than out-of-phase cycllng. The fracture path, 

however, appears mainly intergranular. These conclusions were 

supported by SEN fractographic observations. 

TEM observations were made on the specimens fatigued to fracture. 

Fcils were taken parallel to the loading axis and observed with a JEOL lQOCX 

operated at 120 KeV. Figures 10 and 1 1 show typical dislocation substructures 

obtained under in-phase and out-of-pRase condftlons. in all cases, coarsening 

of the y’ phase has taken place, being more pronounced under in-phase 

conditions. In some grains of the specimens cycled under in-phase conditions, 

directional coarsening (ratting) was observed (Figure 12). Little or no ratting 

was observed under out-of-phase cycling. A tight dislocation network 

encapsulating the y’ (rafted and unrafted) can be observed in Figures 10 and 12 

(in-phase cycling), whereas a looser dislocation network is observed in Figure 

1 1 (out-of-phase cycling), as can be seen from tRe dislocation spacfng. These 

observatfons indicate that the dislocation density 1s higher under in-phase than 

under out-of-phase cyclfng. The octahedral active systems were found to be 

f 1 1 1 I[ 1 101, (1 1 1 I[ 10 11 and possibly f 1 1 ll[O 1 11 in both cases. Three Burgers 

Dl 0 

d 
vectors were identified using the invisibility criterion and assuming that the 

dislocations were screw in character. These Burgers vectors are a/2[ 1 101, 

a/2[ 10 1 I, and a121 10 11 indicating that at least three slip systems were 

operative. Comparison w I th specimens railed under isothermal cycl ing 12 1 I 

shows that the dislocation density ranked in increasing order; isothermal (Tmin 

and T-) out-of-phase, and in-phase cycling. 

piscuss i on 

The above results show that the two major microstructural features are: 

(1 changes in y’ precipitate morphology (Figures 10- 121, and (2) introduction 

of a dislocation network about the y’ precipitates. It is well known [24-25] 

that coarsening of the y’ precipitates influences the mechanical behavior of 

nickel-base alloys. The task at hand is to separate the relative contribution of 

exh structural feature to the cyclic behavior. In what follows, we will show 

that the increase in the cyclic flow stress during in-phase cycling is due to 

dislocation networks surroundlng the y’, and the lower flow stress under outof-phase cycling and pronounced softening behavior (Figure 6b) is a 

consequence of not only the dislocatfon networks strengthening, but also of the 

dlrectional strain f ield around the y’ precipl tates. 

Cvci ic Hardenina/Softe nina Behavior 

It is generally accepted that coherent particles can be sheared by 

dlslocatfons and consequently, the work done In forcing the first dislocations 

through the particles will be lmportant in determinfng the flow stress. The 

resistance to shear is governed by severai factors: 
1. The interaction of the cuttfng dislocation with the stress field of the 

precipitates. 

2. If the lattice parameters of matrix and Precipitate dfffer, then durlng 

shearing of the particles, misfit dislocations must be created at the 

preclpitate-matrix interface. The magnitude of the Burgers vector of the 

interface dislocation will be the difference between the Burgers vector of the 

slip dislocation in the matrix and in the precipitate, Le., (bm-bp). 

3. If the matrix and precipitate possess dlfferent atomic volumes, a 

hydrostatic interaction would be expected between a moving dislocation and 

the precipitate. 

In the case of superalloys with hfgh volume fraction of y’ (>SOX), y‘- 

shearing is the primary strengthening mechanism. With the mean free edge-toedge distance in the matrix between the precipitates being smaller than the 

average precipitate size itself, dislocation shearing of the particle is favored 

over Oil sl mat l on 1 ooping around the part i c 1 es. 

As previously mentioned, coarsening and rafting of y‘ develop in this 

alloy. Thls feature can be attributed to the large lattice misfit (misfit 

- -0.25% 12611, which generates sufficient interfacial strain to produce misfit 

dislocatfons at elevated temperature. Slgnif icant deformation can occur only 

by dislocatlon penetratjon of the y’ phase and it is postulated that the misfit 

dislocation nets at the interface retards this process. Therefore, more 

hardening should be expected when raf tfng takes place because the dislocation 

networks surrounding the y’ are more Intense (see Figures 10 & 12). On the 

other hand, It has been shown by Shah and Duhl[27] that the flow stress 

decreases as y’ size increases provided the cubic shape of the y’ is conserved. 

These two superimposed phenomena, with opposite effects with regard to the 

flow stress, determine the apparent flow stress. Ffgure 6 shows that the 

01 2 
maximum Stress (a-1 of in-phase cycling (T-) display continuous hardening 

with little appearance of stabllization. On the other hand, the amin curve of 

out-of-phase (T,) displays continuous softening. This behavior has been 

previously observed on 8- 1900+Hf cycled in TMF 1281 where continuous 

hardening of a,, and softening o? Umj, occurred until final fracture without 

evidence of saturation. This raises the question of the validity of the strain 

increment technique for measuring the CSS curves of low stacking-fault energy 

materials where continuous hardening (or softening) is observed until fracture 

128-301 at low applied strain. This behavior is usually rationalized in terms of 

planar configuration of dislocations [29, 3 1 I. At high strain, where cross-slip 

takes place, saturation of the CSS curves is observed. Although B- 1900+Hf is 

also a low stacking fautt energy material, the planar configuration of 

dislocation alone cannot explain the observed cyclic hardeninghof tening 

behavior (Figure 6). 

energy and thermally activated cross slip of the glide dislocations [27,321. 

The directionality of the internal stress field around the y' is small because 

thermal activation is important. Therefore, the flow stress will depend on the 

factors controlling the internal stress. The density of misfit dislocations 

around the y' particles, which depends on the y' size and shape (raft), affect 

the flow stress because it controls the internal stress on the glide 

dislocations. On the other hand, when coarsening takes place, the particle 

At high temperature (T > 600'C) the flow stress depends on the APB 

spacing increases, which leads to weakening because of the increased 

probability of avoiding shearing by Orowan-type mechanisms [34]. Under inphase cycling, coarsening of the y' takes place along with rafting, leading to 

high density of misfit dislocations without significant increase in 

interparticle spacing (Figure 12). The net result is an increase in the flow 

D13 
stress because the internal stress increases faster than the relaxatlon time 

required by the glide distocatfon to overcome the barrier created by the misfft 

dislocations. During out-of-phase cycllng, lsotroptc coarsenfng takes place 

leading to a smaller Increase of misfft dfslocatfons and a more significant 

increase of y’ particle spacing. The net result is a decrease in flow stress. 

At low temperature the directionality of the resultant stress field 

around the y’ particles will also contribute to the internal stress acting on the 

glide dislocations [26,27,331. With coarsening, the hydrostatic tensile stress 

field around the y’ increases and that is one of the reasons why misfit 

dislocations are required. It is well known that the resistance to the 

movement of glide dislocation, i.e., the‘functional force, increases with 

increasing hydrostatic stress 1351. Therefore, the superposition of an external 

hydrostatic stress field will increase or decrease the flow stress depending on 

the magnitude and sign of the applied stress. 1 f an external tensile stress field 

is applied, the frictional stresses increase and so does the flow stress. This 

corresponds to the out-of-phase cycling case where the applied stresses are 

tensile at low temperature (see Figure 6b). When the applied stress field in 

compressive, the flow stress decreases or remains unchanged, depending on the 

magnitude of the net stress field [331. During in-phase cycling, the stresses 

are compressive at Tmin and cancelled with the hydrostatic tensile stress field 

around the y’. The net result is that the frictional forces on the glide 

dislocation are lower and the flow stress does not change much as cycling 

proceeds and coarsening takes place (at TmX), as can be seen in Figure 6a. 

To fully understand the flow behavior with change in sign of the applied 

stress, we must also consider the resolved constrfction stress of partial 

dislocations f27, 321. The direction of the glide force per unit length, F@, will 

reverse upon reversing the applied stress, (J 1271. While thls has no physical 

Dl 4 
meaning in a macroscopic sense, since it only alters the directlon of glide for a 

particular dlslocatlon, reversing the directlon of the glide forces acting on the 

partial diSlOCatiOn,it leads to a distinctly different physical situation. The 

resulting force tends to constrict the partials under an applied tensile stress 

and extend them under a compressive stress [271. Since constriction of the 

partials is required by the cross-sllp process, the flow stress appears stronger 

in tension than in compression where the extended partials retard cross-slip 

activity. The previous argument implles that the flow behavior of 8-1 900+Hf 

is governed by octahedral slip activity. If such is the case, the flow stress can 

be written as 

ua (I/R + Vk), (1) 

where R is the particle size and h the mean free distance between the two 

constricted nodes where the cross-slip event occurs [271. At high temperature, 

h is always smaller than R and the flow stress 1s governed by the dislocation 

network and internal stress which fixed h 127,361. At low temperature, the 

flow stress depends on which of these two parameters (R, A) is the smallest. 

if a tensile stress is applied, the partials tend to be constricted and the mean 

free distance between cross-slip event decreases. If a compressive stress is 

applied, the partials are pulled further apart (A increases), and the flow stress 

is controlled by R, the partlcle size. 

I;yclic Stress-Strain Behavlor 

The cyclic stress-strain curves (Figures 7,8 and 9) show that the flow 

stress, as a function of the strain amplitude (AE~/~), is higher for in-phase 

than out-of-phase or isothermal cycling at the maximum temperature (Tmx). 

Thfs is consistent with the fact that dlslocatlon density lncreases in the order 

of isothermal, out-of-phase and in-phase cycling (see Figures 10- 12). At low 

D15 
temperature (TmiJs because cross-slip is a functlon of the magnitude and slgn 

of applied stress, the flow stress is higher under out-of-phase cycling than 

under in-phase or isothermal cycling (see Figure 9). 

The issue that needs to be addressed now is the cracking mode. 

Fracture is transgranular and proceeds 

interdentritically in out-of-phase cycling and intergranularly under in-phase 

cycling conditions. As expected, fracture is controlled by the favored mode of 

rupture in the tensile part of the cycle. Under in-phase cycling, tension occurs 

at high temperature where the cohesive strength of the grain boundary is low, 

which obviously promotes intergranular cracking. During out-of-phase cycling, 

the specimen is under tensile loading at low temperature and the weakest 

transgranular features (carbide film, secondary dendrites, inclusion stringers, 

etc.) control the rupture mode. The fact that the fracture mode depends on the 

maximum tensile stress, rather than on a critical plastic strain range, 

suggests that the failure criteria for 8-1900+Hf is stress-based rather than 

strain-dependent. In other words, the testing condition (temperature and 

strain relationship) leading to the maximum tensile stress, will determine the 

number of cycles to initiation and the propagation rates. 

. 

As mentioned earlier, the major critical turbine components operate 

under strain-controlled conditions and, more specifically, under displacementcontrol. The stresses are not known a priori. Therefore, if the failure criteria 

in 8-1900+Hf is stress-dependent, the relative crack growth rates for a given 

crack length can be determined from the CSS curves. At 

low strain amplitude ((0.25%) the stress range for TMF cycling is higher than 

for isothermal fatigue. Consequently, faster crack growth rates should be 

obtained for TUF cycling [37]. Under fully plastlc conditions (AE~/~ > 0.25%), 

the isothermal stress range is higher than the stress 

D16 

d 
ranges obtained under TMF cycling and faster crack growth rates are expected 

under isothermal cycling (T-). 

Conclusion 

The cyclic stress-strain behavior under TMF cycting differs from the 

isothermal behavior and shows more hardening, both on a high and low 

temperature basis. This Indicates that it is difficult to predict the cyclic 

stress-strain behavior under realistic conditions (Figure 1) from isothermal 

data. The synergistic coupling between the cyci ic strains and temperatures 

cannot be ignored. 

It was shown that the cyciic flow stress at elevated temperature (Tma) 

is primarily controlled by the density of misfit dislocations, which depends on 

the amount of isotropic and directional coarsening. At low temperature (Tmin) 

the flow stress is controlled by the directionality of the stress field around 

the y', the magnitude of which depends on the sign of the applied stress. The 

cracking modes observed have indicated that TMF fracture is controlled by a 

critical tensile stress (a,) rather than a critical tensile strain. The 

implication of these results on the propagation rates was discussed. 

Acknow iedgement: This research work was sponsored by 

the National Aeronautlcs and Space Administration under 

Grant No. NAG3-280. 

D17 

2 
References 

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3. 

4. 

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8. 

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KO. Sheffler, "Vacuum ThermaI-Mechanical Fatigue Behavior of Two 

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S. Taira, "Relationship Between Thermal Fatigue and Low Cycle 

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N. Fujino and S. Taira, "Effects of Thermal Cycle on Low-Cycle 

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ICM 3, Vol. 2, 1979, pp. 49-56. 

R. N. Stentz, J.T. Berling and J.B. Conway, "A Comparison of Combined 

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US. Lindholm and D.L. Davidson, "Low Cycle Fatigue with Combined 

Thermal and Strain Cycling", ASTM STP 520, 1973, pp. 473-481. 

K Kuwabara and A. Nitta, "Thermal-Mechanical Low Cycle Fatigue 

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K Kuwabara, A Nitta, and T. Kitamura, 'Thermal-Mechanical Fatigue 

life Prediction in High Temperature Component Materials for Power 

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ASME-MPC, Albany, NY, 1 983, pp. 1 3 i - i 4 1. 

V.T. Troschenko and L.A. Zaslotskaya, 'Fatigue Strength of Superalloys 

Subjected to Combined Mechanical and Thermal Loading', ICM 3, Vol. 2, 

pp. 3- 12. 

C.E. Jaske, "Thermal-Mechanical Low Cycle Fatigue of AIS1 1020 Steel", 

ASTM STP 6 12, 1976, pp. 170- 198. 

D18 

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12. 

1 3. 

14. 

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17. 

18. 

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21. 

Ak Sheinker, "Exploratory Thermai-Mechanical Fatfgue Results for 

Rene 80 in U1 trahigh Vacuum", NASA CR- 159444, 1978. 

S. Bhongbhobhat, "The Effect of Simultaneously Alternating 

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Low Cycle Fatiaue Strenath and Elasto-Plastic Behavior of Materials, 

ed. by K.T. Rie and E. Harbach, DVM Pub., 1979, pp. 73-82. 

H.J. Westwood and W.K. bee, "Creep Fatigue Crack initiation in 

112 Cr-Mo-V Steel', in CreeD and Fracture of Enaineerina Materials 

and Structure, ed. by 6. Wilshire and W. Owen, Pineridge Press, 

Swansea, UK, 1982, pp. 5 f7-530. 

K.H. Kloos, J. Granacher, H. Barth, and P. Rieth, "Simulation of the 

Service Conditions of Heat Resistant Steels by Creep-Rupture Tests 

Under Variable Stress or Temperature and by Strain Controlled 

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Press, 1982, pp. 2355-2369. 

W.R. Adams and P. Stanley, "A Programmable Machine for Simulated 

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669-673. 

RAT. Dawson, W.J. Eider, G.J. Hill, and AT. Price, "High Strain Fatigue 

of Austenitic Steels", in Thermal and Hiah Stra in Fatiaue, ed. by the 

Metals and Metallurgy Trust, London, 1967, pp. 239-269. 

K. Kuwabara and A. Nitta, 'Effect of High Temperature Tensile Strain 

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ed. by R.M. Curran, ASME-MPC, 1 976, pp. 1 6 1 - 1 77. 

A Ni tta, K. Kuwabara,and T. Kitamura, "The Characteristic of ThermalMechanical Fatigue Strength in Superalloys for Gas Turbines", Proc. 

of Int. Conf. on Gas Turbine, Tokyo, Japan, 1983, 8 pgs. 

M.O. Speidel and A. Pineau, "Fatigue of High Temperature Alloys for 

Gas Turbines", in Hiah TemDerature Atlovs for Gas Turbines, ed. by 

Coutsouradis, Felix, Tischmeister, Habraken, Lindblom and Speidel, 

Applied Sci. Pub., London, 1978, pp. 469-5 12. 

V. Moreno, 'Creep-Fatigue Life Prediction for Englne Hot Section 

Materials", NASA CR- 168228, 1983, 85 pgs. 

D19 
22. 

23. 

24. 

2s. 

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20. 

29. 

30. 

31. 

32. 

N. Marchand and R.M. Pelloux, 'A Computerized Testing System for 

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N. Marchand and R.M. Pel loux, 'Thermal-Mechanical Fatigue Crack 

Growth in lnconel X-750", in Time-Deoendent Fracture, ed. by K. 

Krausz and AS. Krausz, Martinus Ni jhof f Pub. 1985, pp. 167- 178.s 

J.K. Tien and R.P. Gamble, 'Effects of Stress Coarsening on Coherent 

Particle Strengthening', Met. Trans., Vol. 3, 1972, pp. 2 157-2 162. 

D.D. Pearson, F.D. Lemkey, and B.H. Kear, "Stress Coarsening of y' and 

its Influence on Creep Properties of a Single Crystal Superalloy", 

in Proc. of the 4th lntl. SvmD. on Suoerallovs, ed. by J.K. Tien, ASM, 

Metals Park, 1980, pp. 5 13-520. 

L.S. Lin and J.M. Walsh, "Lattice Misf it by Convergent-Beam Electron 

Diffraction--Part 1: Geometry Measurement', in Proc. of 42nd Annual 

Meeting of the EMSA, 1984, pp. 520-523. 

D.M. Shah and D.N. Duhl, "The Effect of Orientation, Temperature and 

Gamma Prime Size on the Yield Strength of a Single Crystal NickelBase Superalloy", in SuDerallovs 1984, ed. by M. Gel1 et al., AIME, 

Warrendale, PA, 1984, pp. 107-1 16. 

J. Hill and R.M. Masci, Private Communication, Pratt & Whitney 

Aircraft, 1985. 

J.O. Nilson, "The Inf hence of Nitrogen of High Temperature Low Cycle 

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K. Hatanaka and T. Yamada, "Effect of Grain Size on Low Cycle Fatigue 

in Low Carbon Steel', Bull. of JSME, Vol. 24, No. 196, 1981 , pp. 1692- 

1699. 

T. Magnin, J. Driver, J. Lepinoux, and L.P. Kubin, "Aspects Microstructturaux de la Deformation Cyclique dans les Metaux et Alliages C. C. et 

C.F.C. 1. Consolidation Cyclique", Rev. Phy. Appl., Vol. 19, 1984, pp. 

467-482 

G.R. Leverant, B.H. Kears and J.M. Oblack, 'Creep of Precipitation020 
Hardened Nickel-Base A1 loy Slngle Crystals at High Temperatures", 

Met. Trans., Vol. 4, 1973, pp. 355-362. 

33. T. Miyazaki, K Nakamura and H. Mori, 'Experimental and Theoretical 

Investigations on Morphological Changes of y'-Precipitates in Ni-AI 

Single Crystals During Uniaxial Stress-Annealing", J. Mater. Sei., 

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34. R.R. Jensen and J.K. Tien, "Temperature and Strain Rate Dependence 

of Stress-Strain Behavior in a Nickel-Base Superal loy", Met. Trans., 

VOl. 16A, i 985, pp. 1049- 1068. 

35. R.W.K. Honeycombe, The Plastic Deformation of Metals, 2nd Ed., Edward 

Arnold Pub., 1984. 

36. M. Geil and D.N. Duhl, "The Development of Single Crystal Superalloy 

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and ProDerties of Advanced Hiah-Temoerature Alloys, June 17- 18, 

1985, ASM Pub., In press. 

37. N. Marchand and R.M. Pel loux, "ThermaI-Mechanical Fatigue Crack 

Growth in 8- 1900+Hf', to be published in the Proc. of the Conf. on 

Hiah - TernDerature allovs for Gas Turbines, Liege, Belgium, Oct. 6-9, 

1986. 

D21 
Figure 1. Stress-strain temperature cycle experienced by 

turbine components. 

Figure 2. Micro-structure of 8- 1900+Hf fully heat treated: 

(a) Grain size (21 X), (b) dendritic structure and two 

zones of yo ( 1 OOX), (c) yo size (3350x1. 

Figure 3. Schematic diagram showing waveforms of temperature, strain and stress in thermal and isothermal 

fatigue tests. 

Figure 4. Stress, mechanical strain, thermal strain, and total 

strain as a function of time (one cycle): (a) in-phase, 

(b) out-of-phase. 

Figure 5. Typical hysteresis loop obtained under TMF conditions: 

(a) in-phase, (b) out-of -phase. 

Figure 6. Typical cyclic hardeninghoftening curves obtained 

under in-phase and outyof-phase cycling. 

Figure 7. Summary of the cyclic hardening behaviors for in-phase 

and out-of-phase cycling. 

Figure 8. Cyclic stress-strain curves obtained under TMF and 

isothermal cycling. 

Figure 9. Comparison of TMF and isothermal cycling. 

Figure 10. Typical dislocation substructures obtained under 

in-phase cycling. 

d 

022 
Figure 1 1. Typical dislocation substructures obtained under 

out-of-phase cycling 

Figure 12. Directional coarsening of the y’-phase during in-phase 

cycling. 

d 

023 
Table 1 

a) Chemical Composition (at %) 

; Cr Co Mo A1 Ti Ta 6 Zr Fe bl Nb Bi Pb Hf Ni 

.09 7.72 9.91 5.97 6.07 0.99 4.21 0.016 0.04 0.17 0.04 0.08 0.1 0.1 1.19 Remaii 

b) Heat Treatment 

Temperature ("C) Time (hr) Quench 

1080 4 air cool 

900 10 air cool 

Table 2 

Tens i 1 e Pro pert i es 

RT 0.005 187.5 

260 0.005 169.6 

538 0.005 149.6 

649 0.005 143.4 

760 0.005 146.8 

871 0.005 138.9 

982 0.005 123.4 

024 

71 4 - 4.9 5.9 

702 888 8.3 10.7 

727 

701 - 7.7 7.2 

709 950 7.9 8.4 

633 785 5.7 6.1 

345 480 7.1 6.9 

- - - 

d 
Table 3 

Summary of Thermal -Mechanical Testing ( In-Phase) 

N AE 

p f (Z) 

0.2000 

0.251 5 

0.3030 

0.3580 

0.3830 

0.4075 

0.4330 

0.4525 

0.4825 

0.5650 

34 7 

337 

556 

388 

490 

303 

340 

280 

160 

54 

3 28 

426 

527 

6Tl 

657 

706 

745 

777 

831 

862 

3 56 

436 

524 

620 

6 64 

7 08 

748 

782 . 

84 2 

880 

0.000 

0 * 000 

0.000 

0.000 

0.005 

0.0120 

0.01 50 

0.0275 

0.0475 

0.0700 

02 5 

d 
Table 4 

Summary of the Thermal-Mechanical Testing 

(Out-o f -Phase) 

N cs 

(MPa 1 

0.1765 

0.1925 

0.2155 

0.2500 

0.2760 

0.2880 

0.3280 

0.3655 

0.4040 

0.4375 

0.4675 

0.5375 

0.6000 

47 5 

426 

31 2 

360 

260 

274 

274 

31 6 

374 

326 

222 

142 

60 

3 04 

450 

41 6 

460 

492 

565 

605 

6 50 

71 1 

7 54 

794 

88 5 

981 

026 

31 0 

369 

4 08 

455 

48 5 

558 

58 5 

640 

684 

745 

78 7 

876 

9 58 

0.0000 

0.0000 

0.0000 

0.0000 

0.0030 

0.0080 

0.01 20 

0.0075 

0.01.45 

0.0145 

0.0325 

0.0485 

0.0880 
TEMPERAWRI 

STRAIN (-E 1 1 

1 

I 

I 

I 

I 

I 

I 

I 

I 

I 

1 

I 

I 

J /. 

/ 

F 

q 

TA 

Figure 1. 

i 

CLIMB1 CRUISE 

GROUND 

IDLE 

L 

: Off REVERSE 

Stress-strain temperature cycle experienced by 

turbine components. 

027 

i 
ORIGINAL PAGE IS 

OF POOR QUALITY 

Figure 2. Micro-structure of 8- 1900+Hf fully heat treated 

(a) Grain size (ZIX), (b) dendritic structure and two 

zones of y' ( 100x1, (c) y' size (33SOX). 

028 
b 

ri 

aJ 

L 

3 

CJ, 

LL 

c 

029 
,7' \\ 

/ \'. 

- 

400 - B - 1900 t Hf - 

300 - 

IN-PHASE - T mx - 925 "C 

T min -400°C 

CYCLE + 3250 - 

- /I;\ 

.008 

.om 

-400 

-500 I I I I 1 I 1 I I, 11 1 II II - .01 

- --- 0- - 

- 't h - -.008 

- - 

0 20 40 60 80 100 120 140 160 180 

TIME (sed 

Figure 4. Stress, mechanical strain, thermal strain, and total 

strain as a function of time (one cycle): (a) in-phase, 

(b) out-of-phase. 

030 
B - I900 f HF 

IN -PHASE 

T max = 925 "C 

T min = 400°C 

CYCLE 3050 

TIME: 12:58:51 

€TOTAL= 0.4825 % 

I I I I s. /I , 

t-"O 

STRESS (MPa) 

8-1900 +HF 

OUT -OF -PHASE 

Tmax = 925 OC 

Tmin = 400°C 

CYCLE- 3650 

TIME: 14:46:19 

E TOTAL= 0.4675% 

SlRAIN 

Figure 5. Typical hysteresis l~op obtained under TMF conditions: 

(a) in-phase, (b) out-of -phase. 

031 

.i 
.04 

.03 

.02 

-01 

c, in 

h 

Y 

8 

CYCLE 

Figure 6. Typical cyclic hardening/softening curves obtained 

under in-phase and outyof-phase cycling. 

032 

d 
m 

400- h 

& 

E 

Y 

300 

200 

100 

0- 

-100 

09 -200 

.E E -300- 

z 

Y 

b 

yloo- 

-500 

-600 

I I I I I1 Ill I I I I I1111 1 I I I I Il1-500 

mec=4825% - 400 

.a3 - 

A€ - 

383 - 300 

-200 

- - - 

- 303 - i$ 

- - L 

-0 

.200 

- -100 0, 

- I I (4 It1 

- t I I 1 I ,,I1 ' ' '"I!. I 0 

- - 

- - -100 

200 - -200 

- - 

- 

9 

33 - CI 

333--x)o 2. 

.43315 - -4oo 3 c 

.e25 - - - -mo 

- I I 1 I I1 Ill I 1 I I I Ill1 I I 1 I I Ili*-~ 

CYCLE 

h 

400- Y 2 300: 

b 

100 

0. 

z 

5 

E 

Y -5 -200 

-300 

b 

Figure 7. Summary of the cyclic hardening behaviors for in-phase 

and out-of-phase cycling. 

033 

a 

- .e75 -r 

.404 -400 - - 

-300 :: 

f 

B 

3279 

.2153 

.276 

- -. Y - .I765 - 

- - 100 

- - 

t: ;:; I I :+ 0 

- - 

- -100 

--200 3q 

.21s'~~ 1 

.276 

- 

f- 

-400- 
CYCLIC STRESS-STRAIN CURVES 

IIII ~~l\~[~~ IIII' 600 600 , 

400 

360 

240 

120 

0 

- 120 

-240 3' 

L 

-300 

- 400 

-600 

3q 

0 

A€ /2 (%) 

WC 

600 

240 

120 

CYCLIC STRESS -STRAIN CURVES 

I I I I I I I I ' I ' I I I/- y' 

8-1900 + Hf 

OUT- OF- PHASE 

Tmax = 925OC 

T min = 400OC 

600 

480 

360 

240 

120 

F X 

Figure 8. Cyclic stress-strain curves obtained under TMF and 

isothermal cycling. 

D34 

i 
F 

D35 
ORIGINAL 

OF pooR 

Figure 10. Typical dislocation substructures obtained under 

in-phase cycling. 

036 

d 
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out-ol-phase cycling. 

d 

037 
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cyclingd 

038 
.. . 2. 

.. . .. 

Appendix E - Summary of the Test Results 

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E51 
2. Government Accession No. 1. Report No* NASA CR-175048 

USAAVSCOM-TR-86-6-4 

4. Title and Subtitle 

March 1986 Thermal-Mechanical Fatigue Behavior of Nickel-Base 

Superalloys 

3. Recipient's Catalog No. 

5. Report Date 

7. Author@) 

R.M. Pelloux and N. Marchand 

9. Performing Organization Name and Address 

Massachusetts Institute of Technology 

Department of Materials Science and Engineering 

Cambridge, Massachusetts 02139 

U.S. Army Aviation Research and Technology Activity - 

AVSCOM, Propulsion Directorate, Lewis Research Center 

Cleveland, Ohio 44135 

12. Sponsoring Agency Name and Address 

Cleveland, Ohio 44135 and NASA Lewis Research Center 

16. Abstract 

This report presents the main achievements of a 36-month research program the main objective of which 

was to gain more insight into the problem of crack growth under thermal mechanical fatigue (THF) 

conditions. This program was conducted at H.I.T. for the period of September 1982 to September 1985 

for the NASA Lewis Research Center under Contract NAG 3-280. The program was arranged into five 

technical tasks. The goal was to identify 

the crack propagation conditions in aircraft engines (hot section) and to assess the validity of 

conventional fracture mechanics parameters to address THF crack growth. The second task defined the 

test facilities, test specimen and the testing conditions needed to establish the effectiveness of 

data correlation parameters identified in Task I. Three materials (Inconel X-750, Hastelloy-X, and 

B-l900+Hf) were chosen for the program. Task I1 was accanplished in collaboration with Pratt & 

Whitney Aircraft engineers. Under Task 111, a camputerized testing system to measure the THF behavior (LCF and CG behaviors) of various alloy systems was built. The software used to run isothermal 

and THF tests was also developed. Built around a conventional servohydraulic machine, the system is 

capable of push-pull tests under stress or strain and temperature controlled conditions in the temperature range of 25OC to 1050°C. A crack propagation test program was defined and conducted under 

Task IV. The test variables included strain range, strain rate (frequency) and temperature. Task V 

correlated and generalized the Task IV data for isothermal and variable temperature conditions so 

that several crack propagation parameters could be compared and evaluated. The structural damage 

(mode of cracking and dislocation substructure) under THF cycling was identified and contrasted with 

the isothermal damage to achieve a swnd fundamental mechanistic understanding of THF. 

Under Task I, the literature of THF data was reviewed. 

8. Performing Organization Report No. 

None 

10. Work Unit No. 

11. Contract or Grant No. 

NAG 3-280 

13. Type of Report and Period Covered 

Contractor Report 

14.SponsoringAgencyCode 

505-63-1 1 

17. Key Words (Suggested by Author@)) 

Fatigue; Crack growth; 

Thermo-mechanical fatigue; 

Superalloys; Mechanisms 

18. Distribution Statement 

Unclassified - unlimited 

STAR Category 26 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 21. No. of pages 22. Price' 

Unclassified 183 A09 

I I I I 

*For sale by.the National Technical Information Service, Springfield, Virginia 221 61 d 

\