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UNIVERSITY OF PORTSMOUTH U S AFSOR Study Report

The effects of LCF loadings n HCF rack

growth Annual Report or Phase

FS65 April 998

1 9 9 8 0 5 1 9 0 4 2 Submitted y:

R. . Hall nd B.E.Powell 28 April 998

MECHANICAL EHAVIOUR OF MATERIALS ABORATORY

DEPARTMENT F MECHANICAL ND MA NUF A CTURI NG NGINEERING

Anglesea Building, Anglesea Road

Portsmouth Ol DJ

Phone: 44 0)1705 42324/5 Fax: +44 0)1705 42351

E-mail [email protected]

'DKTiiiBrrnoN T

ATEMENTX

Approved or ublic elease; Distribution Unlimited

'

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REPORT DOCUMENTATION PAGE Form Approved MB No . 0704-0188 Public reporting burden fo r this collection of information is estimated to average ou r per response, including th e t ime fo r reviewing instructions, searching exist ing data sources, gathering an d maintaining th e data needed, an d completing an d reviewing th e collection of information. en d comments regarding this burden estimate or an y other aspect of this collection of information, ncluding suggestions fo r reducing this burden to Washington Headquarters Services, Directorate fo r Information Operations an d Reports, 215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, an d to th e Office of Management an d Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503. 1. GENCY USE ONLY (Leave blank) 2 . EPORT DATE

28 April £ 3. EPORT TYPE AND DATES COVERED

Final Report 4. ITLE AND SUBTITLE

The Effects of LCF Loading on HCF Crack Growth

6. UTHOR(S) R.F . Hall & B.E. Powell

5 . UNDING NUMBERS F6170897W0112

7. ERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University of Portsmouth Anglesea Building Anglesea Road Portsmouth P01 3DJ United Kingdom

8. ERFORMING ORGANIZATION REPORT NUMBER

N/A

9. PONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) EOARD PSC 802 BOX 14 FPO 09499-0200

10 . SPONSORING/MONITORING AGENCY REPORT NUMBER

SPC 97-4021

11 . SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution is unlimited.

12b . DISTRIBUTION CODE A

13 . ABSTRACT (Maximum 200 words) This report results from a contract tasking University of Portsmouth as follows: he contractor will investigate the effects of low-cycle fatigue (LCF) on high-cycle fatigue (HCF) crack growth for aerospace propulsion applications.

14 . SUBJECT TERMS

Structural Dynamics, Structures, Structural Materials

15 . NUMBER OF PAGES 42

16 . PRICE CODE N/A

17 . SECURITY CLASSIFICATION OF REPORT

UNCLASSIFIED

18 . SECURITY CLASSIFICATION OF THIS PAGE

UNCLASSIFIED

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UNCLASSIFIED

20. LIMITATION OF ABSTRACT

UL NSN 7540-01-280-5500 Standard orm 98 Rev. -89)

Prescribed by ANSI Std. 239-18 298-102

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UNIVERSITY OF PORTSMOUTH US AFSOR Study Report

The effects f LCF loadings n HCF crack

growth

Annual Report or Phase

F565 April 998

Submitted y: R . . Hall nd B.E.Powell

28 April 998 MECHANICAL EHAVIOUR OF MATERIALS ABORATORY

DEPARTMENT OF MECHANICAL AN D MANUFACTURING NGINEERING

Anglesea Building, Anglesea Road

Portsmouth POl D J

Phone: 44 0)1705 42324/5 Fax: 44 0)1705 42351

E-mail [email protected]

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The effect of LCF loadings n H C F crack growth

Report or he period 8 April 997- 27 April 998 Report No F 565 Submitted by R. F. Hall and B. E. Powell

Notation CN

CT

HCF

LCF

da/dNHCF

LC F a/dN,

da/dB

da/dBHCF

da/dB, 'LCF

AK

AK ,

AK , HC F

LC F

ax,th

AKon s

AK*

K «.

N,

N ,

n

R,

R,

HC F

LC F

HC F

LC F

comer notched

compact tension

high cycle fatigue

lo w cycle fatigue

crack growth increment resulting ro m the application f a HCF

cycle

crack growth increment resulting ro m the application f a LC F

cycle

crack growth increment resulting ro m the application f a HCF /

LC F loading block

crack growth increment resulting ro m the application f the HCF

cycles within a loading block

crack growth increment esulting ro m the application f the LCF

cycles within a loading block

stress ntensity range

stress ntensity range associated with a HCF cycle

stress ntensity range associated with a LC F cycle, .e. the peak-to- peak load cycle

the value of AK LCF associated

with the onset of HCF

rack growth

threshold value f stress ntensity range

threshold value of maximum tress ntensity

number of HCF ycles n a loading block

number of LCF cycles n a loading block

ratio N HC F N LCF

stress ratio of the HCF ycles

stress ratio of the LCF cycles

1. Introduction The esign f critical otating ero-engine omponents, nd he emonstration f their

structural ntegrity, must nclude n ssessment f their atigue ives n the resence f

significant levels of vibration. In such components a lo w cycle fatigue (LCF) loading arises

from he arge yclic ariation f the onjoint entrifugal nd hermal tresses. n he

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successful, nd where, ue to load nteractions r short crack effects, t has not. n order

to ccommodate oad nteraction ffects, awkyard t l 6 ] av e nalysed he atigue

threshold alues nd ear-threshold rowth ates ssociated ith he CF ycles y

ascribing ll the potential oad history effects to the HCF cycle component f the loading.

Satisfactory crack propagation life predictions were achieved fo r a wide range of HCF/LCF

loadings applied to forged Ti-6A1-4V at room temperature by combining this approach with

a model based n the concept of crack closure. A similar result was obtained by Claridge

an d owell 7] sing ommercial oftware ackage hose lgorithm or rack ife

predictions lso mploys he oncept f crack closure n modelling he fatigue behaviour

of materials. ignificantly, vans et al [8] have used closure corrected data to successfully

predict the crack growth response f IM I 829 at 350°C fo r a range of HCF/LCF oadings.

If the vibrational stresses are of sufficient number an d amplitude, significant reduction in

the fatigue rack growth life is observed, with the transition etween the two growth rate

regimes marking, o r ll ractical urposes, he ffective nd f the rack rowth ife.

Comparisons etween he HCF hreshold alue ssociated ith hi s ransition nd he

threshold alue etermined n constant mplitude oad shedding ests, ave een made n

a range of materials 9-12]. Both agreements nd discrepancies av e been observed. n the

latter case, attempts ave been made to correlate the HCF threshold value at the transition

with the threshold value determined by a method involving a step change in stress ratio (the

jump - in method). n this way improved correlations have been achieved, but more often

they have not. n order to clearly understand this important aspect of material ehaviour,

a systematic tudy of threshold values, derived from the transition between the two growth

rate regimes, oad shedding ests, nd jump-in experiments, s required.

Fundamental tudies nto he ffects f the onjoint ction f HCF/LCF tress ycles

inevitably se tests which involve a substantial implification f the LCF cycle generated

in service. In practice different stress levels will be developed in critical components during

the various tages of each flight. Recent unpublished work conducted t the University of

Portsmouth, as xamined he rowth f racks uring light equence n hich

vibrational oads were uperimposed uring he imulated tages f take-off, limb nd

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cruise. his ork ighlighted he ee d o ccount o r he oad istory ffects hen

assessing he contribution to the overall growth from the HCF ycles. n particular it was

necessary to characterise the crack growth due to superimposed HCF cycles when preceded

by an overload.

1.2 Scope of th e report This report describes three aspects f the present study. irst, the re-analysis f the results

of past studies n the effect of HCF nd LCF loadings, oth when applied eparately nd

in combination, n the fatigue crack growth rate behaviour f forged Ti-6A1-4V. econd,

is he resentation f the redicted atigue rack rowth ates or ombined CF/HCF

loading xperiments nvolving ystematic ariations n the atio f HCF o CF ycles

within ach epeated oading lock. he nalysis llows or verloads within he CF

loading nd onsiders he ffect f heir agnitude. hird, s escription f he

development of the test facility able to apply a wide range of HCF/LCF oadings, achieved

through the modification f the HCF/LCF solation n it an d the nstallation f new load

control nd test monitoring ystems.

2. Re-analysis f data fo r Forged Ti-6A1-4V

Forged Ti-6A1-4V is extensively used by all aero-engine manufacturers or critical rotating

components. As a consequence, this material was used in the earliest experiments conducted

at he niversity f Portsmouth nto he atigue rack rowth ehaviour f aero-engine

alloys nder HCF nd CF oadings. nevitably, nd rightly, he ata obtained ormed

base-line gainst which he esponses f more reep esistant lloys were ubsequently

compared. n the light of the renewed interest in the effects of HCF an d LCF loadings, the

present ee d s to extend oth the data-base o r forged Ti-6A1-4V nd the understanding

of its behaviour. hus, it is appropriate to first reassess the data that has been obtained an d

used fo r this purpose n the past 3, 6, 9, 3-15]. Compact ension CT ) nd corner notched CN ) pecimens f forged Ti-6A1-4V were cut

from unused fan an d compressor discs. The applied loads used in their testing consisted of:

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1 . HCF ycles with a stress ratio of 0.7-0.95 nd a frequency f 150 Hz,

2. LCF cycles having a trapezoidal waveform, stress atio of 0.1,

3. Combinations f HCF nd LC F cycles n which the HCF ycles were restricted

to the dwell period at the maximum oad of the LCF cycles.

Full details of the test material, procedures an d data analysis have been reported elsewhere

[3 , 6, 9, 13-15]. 2.1 HCF thresholds nd crack growth ates Th e previously obtained experimental data relating to threshold values fo r Ti-6A1-4V forged

material as been eviewed, e-analysed nd ollated. hus, igures nd 3 ontain he

accumulated hreshold ata, ncluding hat which was derived ro m tests combining HCF

with CF sing process called ack alculation) hich artitioned he verall rack

growth rates into that due to the HCF an d the LCF loading components 16]. The effect of

stress ratio on the threshold value is shown in Figure 2, where a bi-linear representation is

suggested. he oncept f crack losure an e sed o xplain hi s esponse, s or

example n the models of Schmit an d Paris [17] nd Beevers 18]. Each threshold value is

considered to be the sum of the intrinsic barrier to fatigue crack growth an d the resistance

to the crack growth arising from the presence f crack closure. Alternatively, he response

may be explained n terms f the behaviour t the rack tip The nitial all is associated

with a constant value of crack tip opening displacement 19], whilst the limiting threshold

value occurs when maximum tip root radius exceeds critical value, o causing the crack

to behave s a blunt notch 20]. The ame data is presented n Figure 3 n the alternative

form uggested y Marci 21] Marci t l 22] nd Doker 23 ] who uggested hat he

threshold ata fell with an envelope efined y a vertical nd a horizontal ine, which in

this case have been drawn at AK ^ = 2.2 MPaVm an d K^,,, = 6 MPa/m, respectively.

The ear-threshold atigue rack rowth ates ssociated ith HCF ycles ave ee n

determined or tress atios f 0.75, .82 nd .90. wo rocedures er e sed. irst,

measurement ollowing the determination f the fatigue threshold value using HCF cycles

only an d a load shedding equence, nd second, erivation ro m the overall rowth rates

fo r HCF/LCF oadings y he ethod f ack alculation. Generally, here s ood

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agreement between the results of these two procedures, howing that there is no significant

load interaction effect (Figures 4-6). The exception is the case of the retardation evident in

the growth rates derived fo r HCF/LCF test involving a HCF stress ratio (R HCF) of 0.90 with

1000 HCF ycles per LC F ycle. When this particular data se t is removed, he remaining

data fo r HCF=

-90 are seen to be in good agreement Figure 7). he HCF rack growth

rates fo r HCF=

-75 an d 0.82 an d 0.90 have been represented y fits to the data in which

y = da/dBHC F an d x = AK HCF. These representations re visually fitted polynomial equations

whose coefficients show a simple an d small variation with RHCF ; the results being illustrated

in Figure , an d the coefficients eing recorded n Table .

Table . oefficients f the polynomial its to the HCF rack growth rate data

RHCF x

3 x

2 x

1 x °

0.75 4 x 08

-2 x 07

6.00 x 07

- 1 06

0.82 4 x 08

-2 x 0 7 6.58 x 0

7 -1 0

6

0.90 4 x 0 8 -2 x Q

7 6.95 x 0 7

- 1 0 6

2.2 LCF rack growth ates

The fatigue crack growth rates associated with the application of separate LCF cycles have

been etermined or values f AK LCF n the range 2-50 MPaVm Figure ). he esults

exhibit learly efined ilinear esponse, ith he ransition ccurring t

AK LCF 0 MPaVm. n eeping ith he oncepts roposed y Yoder t l 24-26]

an d Yeun t al 27], good correlation s ound between he alculated eversed lastic

zone iz e nd he rimary lpha rain iz e f he lloy, hese eing 1jj.m nd

23 r n . espectively. he ean f he ata an e epresented y he

relationships:

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da/dN LC F = . 770 0n

AK LC F]5468 or AK LC F = 12-20 ..(1) da/dN LC F .284 0

8 AKLC F ]

3269 or AK LC F = 20-40 ..(2) where a/dNLC F s measured n mm / cycle nd AK LC F n MPa/m

A c tter and as een rawn hat ncompasses 5% f he ata. his catter

band as idth f .7 , hat s o ay , he atio f he atigue rack rowth

rate t he pper ound o hat t he ower ound , o r ixed alue f K , s

2.7

2.3 HCF/LCF rack growth ates The fatigue crack growth rate data fo r combinations f H CF nd LCF cycles re presented

in igure 0-12 , he rowth ate er applied oading lock, a/dB HCF/LCF, eing lotted s

a function of the peak-to-peak stress intensity range, AK LC F, fo r the combined loading. Each

figure shows th e data for a fixed value of RHC F in comparison with the data for LCF cycles

only. p o hree alues f NHC F, he umber f H CF ycles n ach oading lock, re

considered, NLC F eing et at . he majority f the esults re for CT pec imens nd the

remainder for CN specimens. he effect of the different variables ar e as follows. irst, with

regard to RHCF > he lower it s value the lower is the value of AK LC F at which regime 2 growth

is observed, nd the greater the ubsequent nhancement n growth rate relative o that for

LCF cycles only. econd, with regard to the value of n , the greater it s value the greater the

crack growth rate in regime 2. Third, with regard to specimen design, there is n o significant

effect.

3. Predictions f crack growth esponse under combined LCF /HCF oadings

The methodology sed to predict the fatigue crack growth rate for the combined HCF/LCF

loadings f nterest epends pon whether r ot he CF ycles re receded y n

overload cycle. n the absence f an overload, he da/dB values ar e estimated y the linear

summation ule:

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da/dB da/dBHCF + da/dBLCF . .(3) or:

da/dB NHCF x da/dNHCF LCF x da/dN LC F ..(4) The values f da/dNHC F used n these predictions re hose epresented y the polynomial

for RHC F = 0.82 given in Table , whilst the values of da/dNLC F ar e those represented by the

mean f the ata o r RLC F =0.1 iven n quations nd . hen he H CF ycles re

preceded y a overload CF ycle, he Wheeler model s used to modify the ontribution

to the crack rowth from the H C F ycles. All the results re plotted as lo g (da/dB) ersus

lo g (A K HC F), with the results for the LCF component f the loading (da/dBLC F) included for

compar ison.

Figure 3 ives chematic epresentation f the epeated tress im e equences which

have been considered, he various oading locks being classified ccording o th e number

an d orm f the CF ycles. hus:

Type A has single CF ycle which underloads he ollowing H C F ycles,

Type as multiple CF ycles which underload he following H C F ycles,

Type ha s single CF ycle which overloads he ollowing H C F ycles,

Type D ha s multiple CF ycles which verload he ollowing H CF ycles,

Different umbers f H C F ycles within the oading lock re lso onsidered.

3 .1 ffect f N HCF per block Figure 4 hows he redicted esponse o equence f HCF/LCF oadings nvolving

single CF nderload ycle n ombination with 00 , 00 0 nd 0 00 H CF ycles er

loading block. hese predictions onf i rm the experimental esults for such conditions 14 ] namely, constant value f AK onset, n d within regime , a progressively ncreasing a/dB

with increasing N HC F

3 .2 ffect of N LCF per block Figures 5 nd 6 elate o equence f HCF/LCF oadings nvolv ing multiple CF

underload ycle n ombination it h 00 0 nd 0 00 CF ycles er oading lock,

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respectively. ncreasing he umber f LCF nderload ycles as wo ffects. irst, progressive ncrease n a/dBLCF n ecade teps s NLC F s ncreased n ecade teps.

Second, he ifference etween a/dBLC F an d a/dB ecreases s he roportion N LCF o

N HC F increases.

3 .3 Effect f overload LCF ycles Th e effect of crack growth retardation ue to the presence f a single LCF overload cycle

used n onjunction with 000 nd 0 00 HCF ycles er oading lock s hown n

Figures 17 an d 18 respectively. ach figure show that progressively increasing the Wheeler

constant leads to the reduction an d eventual uppression f the HCF ontribution to crack

growth. igure 19 illustrates the result of multiple LCF overloads. n this case the number

of HCF cycles per block is se t at 1000 an d the Wheeler constant set at 6. Once more there

is both a progressive ncrease n da/dBLC F n decade teps s N LCF s increased n decade

steps; nd the ifference etween a/dBLC F an d da/dB ecrease s the proportion N LCF o

NHC F increases.

4. Development f th e test facility The test facility was designed to apply the repeated oading ndicated as type A in Figure

13, an d it has been modified in order that the loadings ndicated s types B, C an d D, can

be applied. These modifications also enable the determination of fatigue thresholds fo r HCF

crack growth fo r conditions involving either gradual o r substantial load shedding sequences.

Th e two eatures which required alteration were the air bag isolation unit an d the control

system fo r the machine, the latter leading to a new system fo r monitoring the crack growth

test ata. n addition, he ecent K Health nd afety egulations equired he xisting

cooling ystem to be replaced by one which is totally enclosed.

4.1 Modifications o th e isolation nit The function of the ai r bag unit is to decouple the electromagnetic ctuator, which applies

the HCF ycles, ro m the ervohydraulic ctuator, which provides he LCF oading. his

allows the two actuators to function simultaneously an d without interaction. The new design

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incorporates parallel oad path into the isolation unit. When the HCF ycles re applied

this parallel load path is no t engaged, an d the isolation unit functions in the normal manner.

The arallel oad path omes nto peration nly uring he pplication f a LCF ycle

which nvolves n verload. n his ay he equired igh oading s pplied o he

specimen without xcessive ompression f the air bag.

4.3 New control nd monitoring ystem The new system f load control nd data collection s computer based. he development

of the system was achieved by interfacing the computer with the existing analogue control

console [via a D to A interface card], interfacing with a multi-channel igital voltmeter [via

a PIB ard], nd nterfacing ith he C ower upply vi a elay ard]. he

performance f the computer was upgraded an d a data protection facility in the form of an

uninteruptable ower upply American ower onversion] as rovided. estpoint

software [Capital Equipment Corp] was installed an d programs written which would control

an d monitor the tests fo r the various oad - time sequences pecified n the study.

In the previous system the load levels an d ramp rates were se t by analogue controls, whilst

the LCF an d HCF waveforms were fixed. A data logger was used to control the pulsing of

the DCPD crack monitoring ystem, to monitor the test systems an d to record the test data

as hard copy only. With the new system the load levels, ramp rates an d LCF waveform are

all determined by the computer software, which permits manual fine tuning of the selected

load levels. n addition, he computer controls the pulsing f the DCPD rack monitoring

system, the monitoring f the est systems, nd the recording of the test data as Excel an d

text files.

5. Conclusions 1 . he results of past studies on the effect of HCF nd LCF loadings, o th when applied

separately an d in combination, on the fatigue crack growth rate behaviour of forged Ti-6A1-

4V have een re-analysed. quations epresenting he HCF nd CF rack rowth rates

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were determined, together with the limiting values of the maximum stress intensity an d the

range of tress ntensity ssociated with the threshold ondition fo r HCF rack growth.

2. atigue rack rowth ates or ombined CF/HCF oading xperiments nvolving

systematic variations in the ratio of HCF to LC F cycles within each repeated loading block

have been predicted. he predictions ndicate the manner in which the contribution to the

overall growth rate from the HCF cycles declines as the ratio of HCF cycles to LCF cycles

is reduced, nd overloading f the HCF ycles y the LC F ycles etards the HCF rack

growth.

3. A es t acility ble o pply wide ange f HCF/LCF oadings as een chieved

through the modification f the HCF/LCF solation n it an d the nstallation f new load

control an d test monitoring ystems.

References 1 . owell, . ., all, . . nd awkyard, . The ffect f uperimposed

vibrational stresses on fatigue crack propagation life , In : 1st Int. Conf . n Structural Integrity Assessment , Manchester, 992, 336-345.

2. owell, B. E. Crack rowth in Ti-6A1-4V nder the conjoint action of high an d

lo w cycle fatigue , nt. . Fatigue, 987, 9, 95-202.

3. owell, B. E. Fatigue rack growth behaviour of two contrasting itanium alloys ,

Int. . Fatigue, 995, 7, 221-227.

4. pecht, . . The ow ycle atigue ehaviour f titanium lloys , n: rd Int. Conf . n Low Cycle Fatigue and Elastoplastic Behaviour ofMaterials, Berlin, 1992,

19-24.

5. owell, B. E., Henderson, . nd Duggan, T. V. Th e ffect of combined major an d minor stress cycles on fatigue crack growth , In : 2nd Int. Conf . n Fatigue an d Fatigue Thresholds, irmingham, MAS, Warley, K , 984, 2, 93-902.

6 . awkyard, M., owell, . ., Hussey, . nd Grabowski, . Fatigue rack

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Publishers, Dordrecht, he Netherlands, 996 , 227-235.

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alloy teel ue o major nd minor tress ycles , n: 1th European onf on Fracture, oitiers, rance, 966 . , 281-1286.

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21 . arci, G., Non-propagation conditions ( A K , , , ) nd atigue rack ropagation

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22. arci, G., Castro, D.E. an d Bachmann V., Fatigue crack propagation threshold , Journal of Testing and Evaluation, 989, 7, 28-39.

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25 oder, G.R., Cooley, L.A. and Crooker, T. W ., ngineering Fracture Mechanics, 1979, 1, 05.

26 oder, G.R., Cooley, L.A. an d Crooker, T. W ., Metallurgical Transactions, 977,

8A, 737.

27 uen, ., opkins, . W ., everant, . . nd au, . ., Metallurgical Transactions, 1974, , 833.


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Figures

Figure . Form f fatigue rack rowth ate urve o r imple HCF/LCF oading

combination

Figure 2. Effect f stress atio n he oom emperature atigue hreshold alue f

forged Ti-6A1-4V

Figure . K^ dependence f the room temperature atigue threshold value of forged

Ti-6A1-4V

Figure 4 omparison of back calculated HCF crack growth rates fo r RHCF^ 0-75 from

HCF/LCF ests t 000:1 nd 0 00:1, with rack rowth ata

measured ollowing he etermination f the hreshold alue y oad

shedding rocedure

Figure omparison of back calculated HCF crack growth rates fo r RHCF= 0.82 from

HCF/LCF ests t 000:1 nd 0 00:1, with rack rowth ata

measured ollowing he etermination f he hreshold alue y oad

shedding rocedure

Figure omparison of back calculated HCF crack growth rates fo r RHCF = 0.90 from

HCF/LCF ests at n = 000:1, = 0 000:1 nd n = 00 00:1, with crack

growth data measured following the determination f the threshold value by

a load shedding rocedure

Figure omparison of back calculated HCF crack growth rates fo r RHCF= 0.90 from

HCF/LCF ests with n = 0 000:1 nd n = 00 00:1, with crack rowth

data measured ollowing the determination f the threshold value by a load

shedding rocedure


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Figure omparison f near-threshold rack growth rates representations or RHCF =

0.75, 0.82 an d 0.90

Figure atigue crack growth rates fo r LCF cycles at RLCF = 0.1 with representation

of the test data by scatterband

Figure 0 omparison f HCF/LCF rack ropagation ata o r HCF .75 t

1000:1 nd 0 000:1, with the scatterband representing the LCF cycles only

Figure 1 omparison f HCF/LCF rack ropagation ata o r HCF .82 t

1000:1 nd 0 000:1, with the scatterband representing the LCF cycles only

Figure 2 omparison f HCF/LCF rack ropagation ata or RHCF .9 0 t

1000:1, 0 000:1 nd 00 000:1, with the scatterband epresenting he LCF

cycles nly

Figure 1 3 chematic representation f the repeated tress - time sequences onsidered

Figure 4(a) The effect of the number o f HCF cycles - crack growth with a loading block

of n= 00:1

Figure 4(b) The effect of the number of HCF cycles - crack growth with a loading block

of n= 000:1

Figure 4(c) The effect of the number o f HCF cycles - crack growth with a loading block

of n= 0 000:1

Figure 5(a) he effect of the number of LCF cycles - crack growth with a loading block

ofn= 000:1


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Figure 5(b) The effect of the number of LC F cycles - crack growth with a loading block

ofn= 000:10

Figure 5(c) The effect of the number of LCF cycles - crack growth with a loading block

ofn= 000:100

Figure 6(a) The effect of the number of LCF cycles - crack growth with a loading block

ofn= 0 000:1

Figure 6(b) The effect of the number of LCF cycles - crack growth with a loading block

ofn= 0 000:10

Figure 6(c) The effect of the number of LCF cycles - crack growth with a loading block

of n= 0 000:100

Figure 6(d) The effect of the number of LC F cycles - crack growth with a loading block

ofn= 0 000:1000

Figure 7(a) The effect of Wheeler's onstant crack growth with w = nd a loading

block of n= 000:1

Figure 7(b) The effect of Wheeler's onstant crack growth with w = 6 an d a loading

block of n= 000:1

Figure 7(c) The effect of Wheeler's onstant crack growth with w = 2 an d a loading

block of n= 000:1

Figure 8(a) The effect of Wheeler's onstant crack growth with w = nd a loading

block of n= 0 000:1


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Figure 8(b) Th e effect of Wheeler's onstant crack growth with w = 6 an d a loading

block of n= 0 000:1

Figure 8(c) The effect of Wheeler's onstant crack growth with w = 12 an d a loading

block of n= 0 000:1

Figure 9(a) The effect of the number f LCF verload ycles crack rowth with w =

6 an d a loading lock of n = 000:1

Figure 9(b) The effect of the number of LCF overload ycles crack growth with w =

6 an d a loading lock of n = 000:10


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I MIIMIUIIM»

\ ,muiTi\ /

_/ \_ /Regime / •

/ •

z Regime 1 ^̂ ,

o

J

AK onset

Log AK LCF

Figure . o rm f atigue rack rowth ate urve o r imple CF/LCF oading

combination

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Figure Effect of stress rat io on the room temperature fatigue threshold value of forged TJ-6AI-4V

6 r

5-

4-

2 + 2-

0.1 +

o Back calculated from HCF/LCF Load shedding data

— Representa t ion of data 0.2 .3 0.4 .5

Stress Ratio 0.6 .7 .8 .9

Figure 3 Kmax dependence of the room temperature fatigue threshold value of forged T1-6AI-4V

6-,

4-

* 3 <

1

—i—

10

o Back calculated from HCF/LCF Load shedding data

— Representa t ion of data

—i— 15

—i— 20

—i 25

Kn

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8/13/2019 A 344374


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8/13/2019 A 344374


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8/13/2019 A 344374


Figure 14(a) The effect o f the number o f H CF cycles - crack growth with a loading block

ofn= 00:1

1.00E-01

o 1.00E-02

fa u p a -a

1.00E-03

ö 1.00E-04

13 1.00E-05

1.00E-06 10

AKHCF

Figure 14(b) Th e effect o f the number o f H CF cycles - crack growth with a loading block

of n = 000:1

2 I.UUC-UI

o 1.00E-02 p a g J ,

1.00E-03 Jp a O e s -a „

1.00E-04 W -a e s

1.00E-05

1.00E-06 10

AKHCF

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Figure 14(c) The effect of the number of HCF cycles - crack growth with a loading block

ofn = 0 000:1

1.00E-01

§ 1.00E-02

S t, j

P 5 9

p q

1.00E-03

1.00E-04

1.00E-05

1.00E-06 10

AKHCF

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Figure 15(a) The effect of the number of LCF cycles - crack growth with a loading block

ofn= 000:1

1.00E-01

u o

s 1.00E-02

1.00E-03 to U p a «

e a T3

1.00E-04

-o .00E-05

1.00E-06 1

T

1

._.._ _ rl-iMTT da/dBLCF

10

AKHCF

Figure 15(b) The effect o f the number o f LCF cycles - crack growth with a loading block

ofn=

000:10

1.00E-01

iA g 1.00E-02 s a s 1.00E-03 ü «

03 1.00E-04

1.00E-05

1.00E-06

g i

/

: di/rlR da/dBLCF

10

AKHCF

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15(c) The effect o f the number o f LCF cycles - crack growth with a loading block Figure ofn= 1000:100

1.00E-01

1.00E-06 AKHCF

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Figure 16(a) The effect of the number o f LCF cycles - crack growth with a loading block

ofn= 0 000:1

o 3

1.00E-01

1.00E-02

1.00E-03 E fa u 1 1.00E-04 «

'S 1.00E-05

1.00E-06 10

AKHCF

Figure 16(b) The effect of the number of LCF cycles crack growth with a loading block

ofn= 0 000:10

1.00E-01

1.00E-02 3

1.00E-03 u p a e ä -a

•a 1.00E-04 1.00E-05

1.00E-06 10

AKHCF

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Figure 16(c) The effect o f the number of LCF cycles - crack growth with a loading block

ofn= 0 000:100

1.00E-01

ä 1.00E-02

1.00E-06 AKHCF

Figure 16(d) The effect o f the number o f LCF cycles - crack growth with a loading block

o f n =

0 000:1000

1.00E-01

1.00E-06 AKHCF

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Figure 17 (a ) The effect of Wheeler's constant - crack growth with w = n d a loading

block of n= 000:1

l.UUt-UI

j£ 1.00E-02

Ö 1.00E-03

p a

B 1.00E-04

5

1 nriF-os

da/dF

1.00E-06

da/dBLCF

1 0

AKHCF

Figure 17(b) The effect of Wheeler's constant - crack growth with w = an d a loading

block of n= 000:1

1.00E-01

1.00E-06 AKHCF

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Figure 17(c) The effect of Wheeler's constant - crack growth with w = 2 an d a loading

block o f n= 000:1

1.00E-01

1.00E-06 AKHCF

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Figure 18(a) The effect o f Wheeler's constant - crack growth with w = an d a loading

block of n= 0 000:1

1.00E-01

1.00E-06 AKHCF

Figure 18(b) The effect of Wheeler's constant - crack growth with w = 6 an d a loading

block of n= 0 000:1

1.00E-01

-3 1.00E-02 o s to U P Q -a

1.00E-03

£ 1.00E-04

a 1.00E-05

1.00E-06 AKHCF

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Figure 18(c) The effect of Wheeler's constant - crack growth with w = 2 an d a loading

block of n= 0 000:1

1.00E-01

1.00E-02 S Eb u p a

p a -a

1.00E-03

1.00E-04

1.00E-05

1.00E-06

1 10

AKHCF

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Figure 19(a) The effect o f the number o f LCF overload cycles crack growth with w =

an d a loading block o f n = 000:1

1.00E-01

o 1.00E-02 3

to 1.00E-03 u «

1.00E-04 p a «

1.00E-05

1.00E-06 10

AKHCF

Figure 19(b) The effect o f the number of LCF overload cycles - crack growth with w -

an d a loading block of n = 000:10

1.00E-01 F

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