A study of the effects of mechanical and environmental variables on fatigue crack closure

A STUDY OF THE EFFECTS OF MECHANICAL AND ENVIRONMENTAL VARIABLES ON FATIGUE CRACK CLOSURE P. E. IRVING Divisionof MaterialsApplications,NationalPhysical Laboratory,Teddington,England and J. L. ROBINSON Weld& In@itutc,AbingtonHall, Abington,En&nd and C. J. BEEVERS senior Lcctmer,Dept. of Physical Metallurgyand Sciice of Materials,Universityof Biiingham, Birm@ham,England -Using the potential drop technique,fat@c crack closure has been mo&red in pin loaded SEN specimens of ~-titanium, a titanbm alloy and EN24 steel. Tkc qxcimcns were tested ia tenskm-teasion undar umditbns closely ppproximrdinotophnesbrin,mdclor~wasanlyktectedinvpcurofbetterthn133mNm~‘(1O~‘torr).Nosipaihcant cJosmcwasdetcctedinair.ThcextentofthecmckprcDc4oscdatminimum bad variedwith air pressure,appliedstress, R ntio(RrL~L,),crnekknLth,mataial,Mdlodia%mode.AdditiorulxpcriwatsmdcwithadipgauOcrbowedthet theCOD/PpplkdloPdrrspanseoftbecrsckwasoan-linePIinvacwmabovemi~losdintbcfrtigoecyckcanhnnias tbMcndrClOSUmwaSocCtbt&ItisshownthattaagiMamaterinl,~modemdairprtumc,the~~ofl~snd crackkngthvatiabksoncrackarcacloscdat misimumlfiadcallbcc~~intnnuofthcpYluaater(Kz~-~~, this~proportiolilrltothccslcoktedCODatmipimumloed.TheextmtofcbwreiovsGuumisinltucnced~~~yby this parameta.

INTRODUCTION THEphenomenon of fatigue crack closure under tensile loading was first reporW by Blber[ll. Since then the concept has been invoked to explain a number of observations in the Wd of fatigue crack growth; in particular the effects of R ratio (minimum load/maximum load) [2-4), the occurreruz of threshold values of AK for fatigue crack growthPI, and the effects of a complex loading history on subsequent crack growth[6]. The general hypothesis proposed to explain all these effects is that whenever closure occurs the effective AK at the crack tip, compared with that nominally applied, is reduced and the crack growth rate is consequently decreased. Unfortunately, the situations in which closure has been investigated experimentally are d&rent in certain respects from those in which the concept has been applied. There appears to be little direct experimental evidence for the occurrence of closure in those situations where its manifestation has been invoked. Most of the initial experimental work was performed either on thin sheet where crack tip conditions approximated to plane stress[l, 7, IS], or utilised surface displacement observations[& which will again only be relevant to the plane stress conditions existing at the surface. Methods of crack length measurement which indicate total crack area rather than the surface length, such as the potential drop technique[9] have notably failed to detect sign&ant crack closure, except under conditions of through thickness deformation approximating to plane stress [lO,l I]. Lindley and Richards [ IO] sectioned SEN specimens parallel to the loading axis to reveal the crack profile in the thickness of the specimen. This demonstrated that under plane strain conditions in the centre of the specimen, the crack was open, but was locally closed at the surface, where conditions will approximate to plane stress. Closure therefore only occurs under constant amplitude cycling in plane stress conditions. Hence it appears that simple application of closure concepts to explain R ratio and threshold effects during fatigue crack growth must be made with caution, as these effects are most marked in the low AK region, where it is most usual for plane strain conditions to exist. The situation is further complicated by the work of Irving et al. [ 111and Buck et al. 112,131 619

620

P. E. IRVING, J. L. ROBINSON and C. J. BEEVERS

who have shown using potential drop ahd ultrasonic techniques that environment and specimen geometry can be sign&ant variables iniluencing the occurrence of closure. Using part through cracked specimens (in contrast to the conventional through cracked ones used in all other work) Buck[ 121has shown that closure can be detected under plane strain conditions in air. Further work showed that as the environment became increasingly inert, the degree of closure at minimum load was enhanced[l3], with a maximum being reached in vacuum environments. Similar results have been obtained by Irving et al using SEN specimens tested in tension-tension in vacua of l-33 mN m-’ (lo-’ torr). One feature of the results of Irving and Buck was that in vacuum environments, considerable hysteresis in the load/closure profiles was noted, that is the percentage of the crack closed at a given load depends on whether the load was increasingor decreasing. In addition, under certain conditions, as the load approached maximum a decrease in crack area was again detected. The crack was therefore only fully open around mean load. The present paper examines the inlIuence of a number of variables not discussed in the previous work [ 111on the extent of crack closure in air and vacuum environments. The major conclusions of the previous work were as follows: (1)It was established that variation in the output potential across the crack on fatigue loading in vacuum could be attributed to variation in open crack area with applied load. The form of the area variation is shown in Fii. 1. (2)The fact that the area variation was detected in vacuum and not in air was not thought to be due to insulating layers of oxide making the effect in air. Such a situation is unlikely, as it was observed that the nominal area of crack closed at minimum load, after an air grown crack is cycled in vacuum, is initially greater than the increment of crack grown ln vacuum. (3) On transferringthe crack from air to vacuum and vice ucrsa, about 10‘ cycles were required for the closure to fully develop or fully disappear. (4) Once developed, the form of the closure was unadected by varying the loading frquency from 100Hz to O-01Hz. In conducting preliminary investigationsinto the occurrence of closure in vacuum, it became clear that the effect was controlled by the interaction of many variables,among them being crack length, load ratio R, crack tip plasticity, material, loading mode and air pressure. The present paper is an account of some of the ways in which these modify the extent of closure. In addition it was felt desirable to attempt to sim&aneoWlymonitoracrackparameterinvacuumotherthan crack area. If detectable diderences could be found on comparison with air cents, it would provide additional evidence that crack tip plasticity is dilTerentfrom that in air. It w&s ~~temforeto~0rwithaclipgeugs,~CODvs~lod~inboth~and vacuum.

EXPERIMENTAL

Closure experiments were carried out on an EN24 steel and several titanium alloys. The nominal compositions and yield strengths of these materials are shown in Tabk 1. Tests were

x

$0

IO

I!7

5;

75:

‘sii

2: 36

c

co

$50

0

ii

d

a Time (a) Fig.

1. a-l’i

specimen,load and

AK = 8.5 MNm-‘“;R

Time (b)

nominal percent closure plotted against = 0.35. (b) a/w = Oe43;AK = 1S MN m-‘“;R

time. (a) = 0.35.

O/W

-0.35;

A study of the &cts of mechanicaland environmentalvmiabks on fatiguecrackclosure

621

Table 1.

Material

Composition

Yield strength

Ti-II5

0.095

wt%

0,

260MN

Ti-130

0.160

wtY.

0,

430

MN rn-’

Ti-

0.340

wtY.

o2

630

MN mm2

155

Ti -316

EN24

1900

p.p.m. O,,

0.07

wtY.

Fe.

0.26

wt%

C, 097

I.03

wt%Cr,

wt %

6.26

Al, 3.99

wtY* Mn,

0.26wtY.

I.42

MO, 0.24

I, 000 MN rn-’

wt Y. v.

wt %

Ni.

wt%

Si.

rf2

1,275MN

m

condtuzted on single edge notch pin loaded tension-tension specimens having the dimensions shown in Table 2. These conformed to the requirements of the K calibration in Ref. 15. Fatigue testing was performed on an Amsler Vibrophore fitted with a vacuum chamber. Rotary and oil diffusion pumps combined with a liquid nitrogen cold trap produced a vacuum of l-33 mN m” (10’”torr) in the chamber. Test frequencies were between 70 and 100Hz. Closure of the crack faces was detected using the potential drop method described in detail in[17], and a block diagram of the equipment is shown in Fii. 2. A constant current of 30A through the specimen produced a potential between the probe wires attached to the specimen surface on either side of the crack. Most of the d.c. component of this output was backed OfEwith a precision voltage source, and the remaining ax. and d.c. components amplifiedand fed to one galvanometer in the ultra violet recording osciilograph. To enable variations in the output potential at the fatigue frequency to be correlated with the applied loading on the specimen, part of the aurput fram the impulse generator on the Am&r dynamometer was amplifiedand fed to a second gaivanometer in the recording osciRograph.The phase reMonship between this signal and the load on the specimen had been previously determined by comparing it with the output of a strain gauge attached to a dummy specimen. Any drop on the output potential from a specimen during a loading cycle must he due to contact between previously separated crack faces; that is, crack closure. A second method used to detect crack closure was the measurement of crack opening displacement at the notch mouth. This was done by means of a clip gauge mounted on knife edges machined integral with the specimen. Observations by this method could only be made during slow load cycling using the static load control on -the Asmler. With the clip gauge in position during normal fatigue cycling, large spurious outputs were obtained from vibration of the gauge body relative to the specimen. In order to enable small changes in CODto be detected, clip gauge output was measured by a null defkction method involving an accurate voltage source and a sensitive d.c. voltmeter. Any deviation from linearity in the COD-load record obtained using this equipment would provide strong evidence for contact between the crack faces, this having the effect of changing the compliance of the specimen. Tabk 2. Material Ti-II5 TI -130 Ti-155 Ti-318 EN 24 EN24

Specimen

1 1 three point bend specimen

dimensions

140 mm x35

mm x Smm-6mm

2OOmmxbOmmxl0mm

notch

3 mm notch IO mm notch

200

mmx50

mm x25

mm

IO mm notch

P. E. IRVING, J. L. ROBINSON imd C. J. BEEVRRS

622

Fii 2. Block d&am of crack churc emwing

equipment.

Tbc situation existingin the me~~ment of cracklengthby the potential drop method can be simuiat8dusing a conduct&j paper, or metal foil, model.ofthe specimen[l8]. An experiment was carried out to examine the effect on the measured potential of the crack faces touch@ some distance behind the crack tip. This showed that if contact of the faces occurred near the crack moothinstead0fattbetigit~ssifsuv~tines~~~amoruzt0fartalcontacteves occurr& Thus the drop in potential caused by unit area of closed crack de@ on the position of that ama relative to the crack tip. Consequently,without detaikd knowledape of the d&rib&on of cktsurt over the crack face, it is not possible to boy relate the changes in potential observed in the load& to pcrcenw of crack area closed at a ‘jgivcnmoment. The closure observed will therefore be presented as percentage variation in potential output. It was decided that the most couverdent parameter to take as a guide to the way in which closure varied was the totat potential drop during a load cycle from maximumto minimum,expressed as a percentage of the totalpofeatialoutput. This will give an approximateindication of the percentage of crack area closed at miuimum load, and will subsequently be referred to ag nominal &sure.

One of the first variablesto be investigated was that of crack length, as it had been noted that, dPriat~~ofacracLOrowthtest,~~~dsrtPatminlmumIoadvariedastbtClgCL pw across the specimen. Fii 3 shows the forms of the variation with a/w (crack lcugth/specimenwidth) for two tests of Ti-130tested at R = 0.35.The nominal closure rises to a peak of about 10 per cent at a/w = O-3 before gradualIy dc&ning to 2-3 per cent at a/w - 09-06 Similar plots of d&rent titanium alloys tested at the same R ratio and using the same specimen geometry and loading mode exhibit the same general form but with different percentages of nominal closure @ii. 4).

I2 f

ii

t

O(/

l

l

0.3

.

.

efi cTi

13014 I3019

R=@35 R=0.3!5

Acr=32fSMN m-’

0.4

OS

< 6

a/W

Figa 3. Nominal PercentpDt crack clomrc as a function of P/W.‘II-140, R -0.35, variable stress amp&de - 324 MN m-*.

A study ofthe effectsofmechanicaland environmentalvarinbleson fatiguecrackclosure

623

20 o

.a

18-

H

16-

E i

14-

Ti

I lb

Rs0.35

d Ti 153

R 9 0.35

Ti 318

R * 0.35

l

I E

t E E

12r

IO-

co 6 8

5

6

*8

4-

t E :

_ 2 0 0.2

I 0.3

I 0.4

I 0.6

C

i

o/W

F”

4.

Nominalpercentagecrack closureas a functbn of o/w. Ti-115,155,318.Variablestress amphks: 115= 28.3MNm-‘, 155- 26MNm-‘, 318= 30MNm-‘. R - 0.35.

A specimen of EN24 steel when subjected to similartests produced a curve of the same form but with a peak at a/w of O-4(Fii 5). It may be that this variation results from the different materials, but the measured potential variations in this instance were so small (2CMOrV) in comparison with the noise level in the system (10~1V) that a large degree of scatter is evident in the data points, and precise conclusions not possible. Varying the R ratio has a very marked effect on the form of the nominal closure vs a/w curves. Fii 6 compares the plots obtained from tests at three R ratios (04l7,O.M and 0.70)in T&X30.The curve at R = 0.35 is as descrii above, but at R = O-70,the .pcrcmtage nominal closure was less than 1 per cent. Againthe potentials measured in this instance were so small that it was di6cult to detect any overall trend in the results of this test, although there does appear to be a slight decline in closure with incmasii a/w. In contrast, the test conducted at R = 0-y produced over 10 per cent nominal closure at a/w = 0.25, and this 6gure rapidly increased throughout the test, attaining over 40 per cent at a/w - 05-0~6. Substantial variations in the percentage closure produced at a given a/w could also be produced by varying the applied alternating load, but keeping the R ratio the same. Fii 7 compares the results of three tests on ‘Ii-130 which were conducted at alter&@ stress amplitudes of 43.2,32-Sand 125 MN m-‘. The largest amplitude test produced a curve of similar form to the others discussed previously, but reached a maximum of only 5 per cent nominal closure. The 325 MN m-’ test attained 10 per cent at the same value of a/w, while the test co&cted at the smallest load amplitude (only a liited a/w range was covered) reached 10per cent nominal closure at a/w of O-5.The medium and high amplitude specimens had 4 and 2 per cent respectively at this value of a/w.

I

Pi

EN 24

R = 0.35

5. Nominal percentage crack closure as;f~$c$n

of o/w. ENX Variable stress amplitude-

P. E. IBVING,J. L. ROBINSONand C. J. BEEVEBS

624

4

x ,o

_^ t

R.0.07

o R.O.35 . R80.70

-

Pis.6.~~ofRNtioM~PtdCCM~kc~hTi-lM,pkttedssaAEadionofo/w.Variabk stnu arnpw R = 047, AU= 38.5MNin-‘; R = 0~35.A~= 32.5MNm”; R = O-7,Au = 30.6MNm+.

+ 0

A &o 8 12.5 MN M2 0 Au= 32.5 MN ni2 l Au ~43.2 MN K*

6

Fii 7. EtTect of strewamplitude on nominalpercentcrackclosure.R = 0.35.Plottedasaftmctionof nfw.

As crack length inlbrencesnominal closure, it was thought likely that loading mode might also contriiute. An SEN specimen of EN24 was therefore tested in three point bend at R = 0.35. A small amouut of crack closure could be detected, but the amount was very much less than 1 per cent. The effect of air pressure on nominal closure was examined in a specimen of Ti-130,with the crack length at the beginning of the experiment at a/w of 0.35. The procedure adopted was to cycie for about lo’cycles at a given pressure level, before increasingthe pressure to a new value. The closure reading was taken towards the end of the group of lo* cycles. This figure had been found to be the necessary minimum to maximise closure on changing environments from air to vacuum[ 111.The crack was growingat about lOIsmm/cycle, and hence for 10readings the crack grewabout lmm,froma/w = O-35to a/w = 0.38.From Fig. 3 it can be seen this corresponds to a change in nominalclosure of l-2 per cent. This is a small figurewhen compared with the total size of the environmental effect, and so was ignored. The results of the readings are shown in Fig. 8. There is little variation in closure for pressure reductions from l-33-133mN m-‘. Most of the closure disappeared between 133 and 1330mN m-’ ( 1O-3-1O-’ torr). COD measurements were performed on a specimen of Ti-318 with a crack length of alw = O-35(this tigure was chosen to maximise the effects observed). The procedure adopted was to slowly cycle the load, starting at mean, going up to maximum and then down to m~mum, and was then decreased to zero before being brought back to mean load. This latter operation was

A study of the effects of mechanicaland environmentalvariabks on fatiguecrackclosure C.F?

L

Ol

a - titanium

IO Pressure.

F’ii.

625

loo

1000

mN m-’

8. Effect of vacuum pressure on extent of closure at minimumload. u/w = 0.35438. Variablestress amplitude= 32.5 MN m-‘. R = O-35.

performed to observe closure behaviour beneath minimum load, but with the specimen still in tension. COD, potential and load readings were taken simultaneously.This was Brst done in air. The specimen was then put into vacuum, given the required 10’cycles, and the measurements repeated. The cycling, apart from the deviation to zero load, was performed at R - O-35,and the same applied loads were used throughout. The sequence outlined above was repeated a number of times and the results for a typical run are shown in Fll. 9. In air, the plot of COD against load is linear between maximum and minimum loads. No crack closure is observed in this region. As the load is decreased below minimum, the line becomes mm-linearand closure is observed in the potential output. In vacuum, closure is observed as soon as the load drops below mean, and becomes increasinglyevident as minimum load is approached. As soon as closure was detected on the potential output, the COD line became non-linear. In the vacuum experiment it is also notable that there was hysteresis in the COD measurements, depending on whether the load was bein9 increased or decreased, closure being greatest at a given load for failing load. In air, hysteresis was not observed.

DISCUSSION Theabove results indicate that the presence of an air environment has a considerable effect on the plastic deformation around the tip of a propagatiag fatigue crack. This conclusion should

dan i

Cyclic minlmum 0

400

860 Load.

1200

leoo

kg

sdoo

cyclic n loal

Iwd I

,

600

600

,

,

Load,

lOOa kg

1200

(a) Nominal COD and potential plotted against load for air and vacuum. Ti-318, a/w = O-35.The absolutediierences in COD between the two curves are arbitxary;the two curves are separatedfor clarity. (b) Enlargedportionof (a). Fii. 9.

626

P. E. IRVING, J. L. ROBINSON and C. J. BEEVERS

not be unexpected as in the last few years there have been a number of observations both direct and indirect which have indicated the active role played by air environments in the ~~~~ of crack tip materml. It is well known for instance, that air environments promote fatigue crack growth relative to vacuum environments [e.g. 19-213.Often the morphologyof the fracture face is dependant on the environment in which the test was conducted. It has been reported [22,23]that air environments alter the mechanicalproperties of a thin layer at the surfye of strained materials.Gilmanf24]has advanced the hypothesis that adsorbed species of atoms may influence the extent of crack tip plasticity. Fiiy, Fmnsden et ul.[25] have reported electron microscope observations of dislocation structures obtained during fatigue loading of Ni-Cu alloys in air, oxygen and vacuum environments. Clearly discerned di&rences in dislocation arrangement were found. An important aspect of the present results is that they represent a simpler experimental situation than does testing in an air environment. Any theory which attempts to account for closure ln terms of material plasticity properties, without the compllc&ng effects of air environments must be able to explain its occurrence in both plane stress and plane strain. It is clear from the work OSJindky andRicitards[lO~, thatin airenvy closure occurs in plane stress only, and that Enthick specimens, the internal plane strain region is kept open whiie the plane stress surfaoe region is closed. This observation, whilst ensuring that the closure concept is not avalidonetouse whenattemptingtoexplaincrackgrowthphenomena oCCWhlgillplaM!stlahl in air, does not make it impossible for closure to occur in vacuum. LiadttyandRicbantspointotttthaatsigDiflcantclosuredocsoccurintbep~strain~ minimum of the previous ofthes~n~ttasiie1~iftheloutis~~~balowthe load cycles. The results obtained in the present work would support this view. All that is minimumisachangelnthe necessaryto~clowreatsomGloadinexccssoftheloedcy~ ~~~~~~~,~~~S~~~~~~ ~~~y~~~ The simultaneous observation of fatigue crack closure u&g the potential drop teclmiquc to detect crack area variations, and a clip gauge to detect non-linearityin specimen COD response (Fii. 9) provides a number of further insights into the phenomenon. It will be noted for instance that crack area variation always occurs at the same loads as onset of the non-linear COD variation with applied load. This is true in both air and vacuum, and provides powerful evidence for the occurrence of closure. However, the amount of closure occurring above minimumload in vacuum can be seen to be smail in comparison with the degree of closure produced by reducmg the load below the cyclic minimum. (10per cent nominal closure at minimum load in vacuum, 0 per cent in air, 41 per cent nominal closure at zero load in vacuum, 31 per cent in air). At xero load, the percentage of crack area closed appears to be approa&ing a fixed value, the vacuum one being greater than the air one by 10 per cent, the same amount as was cIosed at minimum load. On the COD curves the vacuum plot tends to exhibit hysteresis, dependant on whether the load is increasingor decreasing,congrmingthe previous observationsof Irving and Buck [11,121. Using the present results, it is possibie to gain some estimate of the proportion of the crack which is closed at any point in the loading cycle. This is possible if it is assumed that the crack closes back from the tip leaving no isolated area of unclosed crack or areas of poor conductivity. The decrease in potential can then be reiated directly to a reduction in open crack length. The

results of such a rec~c~tion are shown in Fig. 10 for the case of Ti-130 tested at R = 0.35. Comparison with Fig. 3 shows that general conclusions about the variation of percentage closure with a/w remain essentially unchanged, and that the percentage drop in potential is similarto the percentage of crack area closed. The variables influencing the effects observed in vacuum may be divided into three categories-loading, geometrical and materialparameters.The major loading variableis that of R ratio, and the effects observed are qualitatively the same as those noted by Elber[7’jfor the case of a centre cracked sheet in plane stress; i.e. that closure increased with decreasing R. Eiber however, estimates closure by considering the fraction of the loading cycle for which the crack is closed, ratherthan estimating the fraction of the crack cfosed at a given load, as has been done in this work. He concludes that the former is independent of the crack length and the nominal applied AK. Most of the published work using the crack closure concepts to explain R ratio effects [e.g.

Astudyoftbceffectsofm&anicalanden

vhuncntai

variables on fatigue crack closure

627

6

a/W

PiO.lO.Pacmtcrodranaclosedatminimum~,~~crackcloses~~~kfromthetip. Platted against a/w; Ti-130,R = 0.35. Variable stress amplitude = 32.5 MN m-‘.

3,4,7], use this result coupled with the idea of an effective AK which is the AK acting over that portion of the load cycle for which the crack is open. The present results indicate that vacuum crack closure behaves in substantiallythe same manner as air crack closure in that the portion of the loading cycle for which the crack is totally open depends on R. Some variation with crack length was seen. However, it has been observed that R ratio effects on crack growth rate tend to decrease in vacuum, compand with air experiments [19,201.The extent of closure follows the reverse trend. Hcnceassiaitcrrnbecoacludcdthatthtc~closureconceptis~elyto~emmucbvahiein accounting for R ratio effects. The dlect of loading mode on the extent of nominal closure at minimum load is possibly related to changes in crack tip geometry as the loading mode is varied. Hayes and Turner[26l have used finite element analysis to show that crack tip geometry of SEN specimens is depemknt on whether they are subjected to three point bend or pulled in u&txial tension. Fii 11shows a comparison of the two loading forms, and it will be seen that the three point bend configmation has the crack faces meeting at a higher angle than the uniaxial tension conf@uation for the same dimensionless crack length and the same effective stress. Therefore on a qualitative basis the three point bend contiguration is less likely to exhibit closure than uniaxial tension The majority of the measurements made in this investigation have been concerned with the closure measured at minimum load. It is possible that the effects of crack length, applied stress, and R mtio on the closure can be predicted in terms of their efIect on parameters which determine the COD at minimum load. Clearly,if crack face closure is occurring, then the crack tip COD will be approaching zero, so it will not be possible to relate closure to absohtte values of tip COD. However, it may still be possiik to relate the extent of closure observed to some parameter, proportional to calculated COD at minimum load, and which reflects the influence of crack length, applied stress and R ratio. COD at maximum load is proportional to KL; A COD is proportional to AK’t27.l.Hence COD at minimum load under cyclic loading will be proportional to (K’, - AK?. Both AK and K,, reflect the inlluence of crack length and applied stress. (KL - AK? will be inUuenccdin additkm by R ratio. Pi 12 shows a plot of (KL -AK~againstpeK!entnominalcloaurefor the six specimens of Ti-130 tested. (Figs. 3,6,7). It will be seen that there is a ckar relation between (Kf, -AK’) and closure. Low values of (KL - AK? produced by low R values, low stresses and short crack lengths produce large values of percent closure. High values of (K:, -AK’) produced by high R values, hi& stresses and long crack lengths give small amounts of closure. At low values of (Kk.x - AK?, small changes produce large changes in percentage closure, and it is notable that the greatest scatter is in this region. The points which do not fall on the general curve are the ones at low values of (1/ w,before the peak in Fii. 3,6,7 has been attained. Two explanations may be advanced to account for this. Firstly, at low values of a/w there may be notch effects, as the faces of the notch cannot close. If the crack extended to the edge of the specimen, increased values of percentage closure may have been obtained in this region. Secondly, it may be that the crack must grow some distance in vacuum before an

628

P. E. IRVING, J. L. ROBINSON and C. J. BEEYERS

warkhardoning,

1) CmGk p&ffes Iw pnt~rred trr) piece io tfma fbofnt bendina. Pfon* stmin workhard&fnlng.

eq~b~~ percentage of closure is attained, and the low a/w region is part of the non-equihi portlou. In either case it may only be valid to consider the parts of the curves from the closure maxima onwards to be part of plots such as Fig. 12. It has already been noted that the role of air pressure or enviroument in decreasing closure may be related to changes in crack tip plasticity which in turn produce absolute variations in the COD at ~~ load. COD at ~~~ load in air would then be of such a high vahte that variations in (RL - AK? will not produce detectable crack closure until the load drops below minimum. As the en~o~nt is mademore inert, the absolute value of COD at ~~ load decreases until at some critical pressure closure above minimum load is detectable at very low values of (I& -AK?. If this is so, then the pressure at which closure disappears (Fii 8) will depend on R value, stress amplitude and crack length. CONCLUSXONS (1) Using the potential drop technique to monitor nominal fatigue crack area in Hitanium, a titanium alloy and EN24 steel SEN specin~ens,variation of crack area, of the same frequency,

A studyof the effectsof m&anical and onviromnentalvarhbks on fatiguecrackclosure

629

and in phase with the applied load cycle has been detected in vacua of 1+33mN mm2(lo-’ torr). Closure was not detected in air environments under the same loading conditions. The specimens remained in tension throughout the loading cycle, and plasticity at the crack tip was a close approximation to plane strain (maximum plastic zone size/specimen thickness = 10’3-10’2). (2)The maximum drop in potential corresponded with minimum load in the loading cycle. The potential drop at this point expressed as a percentage of total potential output, could be taken as an approximate indication of the percentage of crack area which closed at minimum load. This was found to vary with R ratio, crack length, stress range, loading mode, specimen material and vacuum pressure. The total range of closure varied from zero to over 40 per cent of the crack area closed at minimum load, depending on the values of the parameters above. (3)For all the materialstested (R-1 15,Ti-130,Ti-155,Ti-318,EN24 steel (The last two bemg in the quenched and tempered condition), the broad trends in behaviour for pin loaded SEN spe&uens can be sununarised as follows: (a) Nominal closure at minimum load increased to a maximum as the crack length increased, at olw = 0*3-0*4.From this point a steady decline occurred up to the ~~a~ of the test at a/w =06. (b) For a given value of a/w, and a given R ratio, nominal closure at minimum load is decreased by increasing stress range and increased by decreasing stress range. (c) Decreasing R ratio from 0.35 to 0.07 produced a massive increase in nominal crack closure at minimum load at all values of a fw (from 10 to 40 per cent at niw = 0.35). Increasing the R ratio from 0.35to 0.70 decreased the closure to less than 1per cent at all values of a/w. (d) No sign&ant closure could be detected in SEN specimens in the three point bend loading mode. (e) Variation of the test material produced d&ring nominal percentages of closure at minimum load. (f) The nominal percentage closure declined with increasing pressure, and had completely disappeared at I.33 N m-’ (10m2 torr) in a specimen of Ti-I30, tested at R = 0.35. (4) Measurement of crack mouth opening with a clip gauge, as the load was cycled, showed that in air, a linear relation between load and COD could be found at loads between minimum and maximum. Below minimum load, the plot became non-linear, and closure could be detected by the potential monitoring equipment. In vacuum the relation between COD and load became non-linear below mean load, and again closure could be detected on the potential equipment. Hysteresis could be observed in the vacuum COD results. (5)The effects of R ratio, stress range and a /w on closure at minimum load in a given material can be shown to be related to their effect on (KL- AK’) (Proportional to COD at minimum load). Effects of loading mode are thought to be related to changes in crack tip geometry, in particular, the angle at which the crack faces meet. (6) The results above are consistant with the view that the air environment profoundly inflmnces the deformation of the material at the crack tip. In inert environments a shift in the balance of forces in the vicinity of the tip can cause reduced CODand meeting of the crack faces over a limited area at loads above minimum, rather than below. Once this has occurred, the effects of (II w, stress range R ratio and loading mode in varying (K’- - AR? cause the observed complex variation in the extent of crack closure.

RlWEREiNCES [l] W. Elber, hgng. FractureMrch. 2, 37 (1970). [2] R. J. Bucci and P. C. Paris, f. M&n. 7,4Q2 (1972). [3] R. W. Hereberg and E. F. J. Van Euw, Met. Tmns. 4,887 (1973). 141P. C. Paris. R. J. Bucci,E. T. WCS& W. G. Clark and T. R. Mager,Stress analysis and growthof cracks. A,WMSZ’P 513,p. 141(1972). [5l R. J. Bucci, W. G. Clark and P. C. Paris, Stress analysis and growth of cracks. ASTM Srp 513,p. 1?7(1972). [6] E. F. J. von Euw,R W. Hertzbergand R. Roberts,Stressanalysisand growthof cracks.ASTMS’ZP513,p. 230(1972). t7l W. Efber, Damagetokzance in &craft structures. ASTM ST? 486,p. 230(1971).

630

P. E. IRVINQ, J. L. ROBINSON and C. J. BEEVERS

[sl N. J. I. Adams, Jhgng. Fractm Med. 4,543 (1972). [91 W.J.Phmbdge,J.Mam.Sd7,939(1912). [lo] T. C. Li+by aad C. E. Richuds, ‘lltc hllueme of cmk closure ad plastic mm gcomhy on fatiprs crack pqmguwnndnfInrCm~onZ+acrur&Mlaicll1973. [11] P. E. Iwing, J. L. Robineon and C. J. Beam, Znt. J. Fmchm Med. 9, 105 (1973). [12] 0. BlJ& c. L. Ho aad w. L. hhrcw, Eq?lQ?.FInczm Med. 5.23 wn). [13] O.Wlclt,J.D.F~C.L.EIowSH.L.Mucur.TklrdI~Conl.on~S~of~~~MdAUoya,CambriQe, En&d, p. 462 Pub. Ina of Met. LS.1. (1973). [lJl Y. I? Cheq pad H. Bmmef, Zlu.I. mctim Me& (, 431 (1970). [lqa~rpdRA.Scb;8iQ,~.I.~m~A1,168(19R). [lq W. F. Brown ad J. E. SrawIcy, ASTM SlP 410 (1%7). [17) R. J. Cwka and J. L. Robiem, Bina@hm Univmity Research Report (1971). [Is) R. 0. RRchie, 0.0. Cimmtt and J. F. Koott, In& L Fhctm Mcch. 7,462 (1971). [19] M. R. &h&r, F&w ark prop&on. ASTMSTP 415, p. 181(1%7). m] F. J. Bmddmw ad C. Whmbr, trr. J. J’mctm Med. 5,223 (1969). [Zl] R P. Wei. m. Fmcrum bfech 1, 633 (1970). [22] T. R. Kmwr aad A. Kumar, E&a of vacuumenvironments on mechanical behaviour. AFOSR-IR-724734 Feb. (1972)atio aima Corp., Doover, U.S.A. m] T. R. Kmnm ad A. Kunmr, “. “d$m,‘n,‘muimnuioa~ Univ. of Coamht, Jllas (1971),Pub&&cd u NACE2, p. 142. Nathad hocatm [u] J. J. Gluma, PM Mug. 1)1(1972). [ul J. D. Fmaba, N. B. Pa&m d Ii. L. Marcus, Mt. Tmns. I, 1655(1974). [za]D.J.~y~pdC.E.TurPa,Prpsrpn#ntedat~A~y~b~FFccvtvnm~~sof~MdBrittlr Maruid& ulliv. of Leicutcr (1971). [nl~4.Idc$to&tock.t’~1.~~Univ. of colasaicpf Ions (1971)Publhd as NACE2, p.