1-s2.0-S092150939700419X-main

~ MATERIALS SCIENCE &

ENGINEERING

A ELSEVIER Materials Science and Engineering A237 (1997) 229-240

Mechanisms of fretting-fatigue of titanium alloys

R.A. Antoniou *, T.C. Radtke Aeronautical and Maritime Research Laboratory, Defence Scierlce and Techology Organisation, PO Box 4331, Melbourne, 1%. 3001, Australia

Received 22 January 1997; received in revised form 30 April 1997

Abstract

The effect of continuous fretting in air at 20C on fatigue performance has been studied for Ti-17 and Ti-6AI4V, high strength titanium alloys used for gas-turbine fan and compressor disks and blades, respectively. The effect of fretting was to reduce the fatigue stress limit from 700 MPa for plain fatigue to 200 MPa for fretting-fatigue. A number of models, supported by metallographic and fractographic evidence, are proposed which explain (i) how the cyclic loading of individual asperities results in crack initiation; (ii) the formation of multiple cracks; (iii) the existence of non-propagating cracks; and (iv) how fretting influences crack propagation once fatigue cracks have formed. 0 1997 Elsevier Science S.A.

1. Introduction

High strength titanium-based alloys are used in critical rotating components in gas-turbine engines due to their high specific strength advantage over other candi- date materials such as Ni-based superalloys and ferritic and martensitic stainless steels. Particular examples include fan and low pressure compressor disks and blades. However, titanium and its alloys are known to be particularly susceptible to fretting-initiated fatigue [l-3] and, in highly stressed locations such as fir-tree roots and blade/disk attachments, the use of these alloys requires particular surface treatments, e.g. shot- peening, hard and soft coatings or solid-state lubricants, that inhibit the initiation of cracks during fretting.

The detrimental effect of fretting on fatigue life has been recognised since early this century [4]. However, despite a broad research effort there are still significant points of contention about the operating mechanisms. Fretting-fatigue failure initially begins as surface and near-surface damage as a result of the fretting action. This damage takes the form of significant plastic strain at the surface [5,6], disruption of the surface films or oxides [7] and material transfer [8]. The disruption of the surface films or oxides through fretting may acceler- ate fatigue failure because (i) it enhances direct metal to metal contact, resulting in micro-welding of the sur-

* Corresponding author.

0921-5093/97/$17.00 8 1997 Elsevier Science S.A. All rights reserved. PI1s0921-5093(97)00419-x

faces, and consequently higher local shear forces, and (ii) the continuous production-destruction cycle of the oxide may produce particles that act as an abrasive third body to produce fretting wear and initiate cracks PI.

The location of cracks may be at the edge of the fretted region, often called the edge of contact (EOC) [lO,l 11, at the boundary between the slip and non-slip regions [12], or at the centre of the specimen [5.13,14]. On a microscopic scale, fretting-initiated cracks have been found to form at the EOC and are initially semi-elliptical in shape when viewed normal to the fretted surface [15]. Some of these cracks propagate while others remain dormant [16]. The propagating cracks generally grow into the specimen at an oblique angle [12,16,17] and their behaviour can be influenced by the fretting action [16,18], the normal pressure [19,20] and the alternating stress. As these cracks ex- tend into the material the influence of the fretting recedes [lo], and the crack growth rate becomes solely determined by the magnitude of the alternating stress.

The susceptibility of titanium alloys to fretting-initiated fatigue has been related to the reactivity of these alloys once the protective surface oxide is damaged [21]. Since this oxide is thin ( - 30 nm) [22] it is reasonable to expect that any action which disrupts the film may have an effect on the fretting-fatigue behaviour. Plain fatigue has some disruptive effect on the surface oxide film but concurrent fretting is likely to have a much greater effect.

230 R.A. Antoniou, T.C. Radtke / Muteriais Science anti Engheering A237 (1997) 229-240

The susceptibility of titanium alloys to fretting fatigue may also be due to a deformation or temperature-induced transformation from a two-phase, u (h.c.p.) plus p (b.c.c.), to a single-phase x (h.c.p.) microstructure which is more brittle. It has been found that deformation due to fretting of a two-phase c1 -t p structure results in the formation of a superficial layer consisting of 20-50 nm crystallites solely of the OL phase [9] and cracks have been found to originate in this fretting-transformed material l6].

An investigation was undertaken of in-service fretting-initiated fatigue cracking between fan/compressor blades and fan/compressor disks due to torsional and longitudinal vibration of the blades. This paper will discuss the fretting-fatigue performance of an uncoated titanium alloy and attempt to elucidate the micro- mechanisms of fretting-fatigue. The testing and evalua- tion of uncoated materials provides a baseline against which coatings and surface treatments can be compared. Particular areas of investigation include (i) the location and mechanism of nucleation of cracks, (ii) the point at which cracks form in the life of a component and (iii) whether fretting influences the initial and longer term rate of fatigue crack propagation.

2. Experimental

A schematic arrangement of the blade/disk configu- ration is given in Fig. 1. The conditions for fretting were simulated in laboratory testing using unidirec- tional fatigue with fretting pads contoured to simulate the blade geometry pressing onto the flat parallel surfaces of the specimen. Details of the fretting pad and loading device are given in Fig. 2(a) and Fig. Z(b). The contact pressure of the pads was applied using a cali-

centrifugal force

blade TL6AMV

blade dovetail/post

lg- rotation of disk

Alternating load

t

I Pad contact pressure -1 tensioning Grew

/

Proving ring

/

Ia) 4 contact pressure

y, -I Position 2 l , Position 1

(position at ffJ * (position at u,,J

(b)

Edge of contact (EbC)

Directmotion

+--- Centre of specimen

Fig. 2. (a) Schematic of fretting-arrangement used for fretting-fatigue testing. (b) Schematic of fretting pad foot.

brated proving ring (Fig. 2(a)) with the magnitude of this pressure (160 MPa) based on calculations of the contact pressure between the blade and disk flats in a gas turbine engine.

Three types of tests were conducted: (i) plain fatigue tests without fretting to produce an S--N curve for the particular specimen geometry, materials and testing environment; (ii) fretting-fatigue tests representing the blade attachment, and (iii) friction tests to determine static and dynamic coefficients.

Fatigue testing was conducted in a servo-hydraulic fatigue testing machine under load control. The tests were conducted under laboratory conditions at 20 + 2C in air at approximately 50% relative humidity, at a frequency of 20 Hz using a sinusoidal loading waveform at an alternating stress ratio (R) of 0.1.

Table 1 Nominal composition of titanium alloys tested (wt.%)

Al V Zr Sn MO Cr Ti

Ti-17 5 Ti-6Al-4V 6

-2 4 -

2 -

4 -

4 -

balance balance

Fig. 1. Disk post cracking location.

Table 2 Mechanical properties of titanium alloys tested

Alloy E CGPa) UTS (MPa) YS,,,? (MPa)

Ti-17 116 1130 1080 Ti-6.41-4V 114 1013 910

The friction tests consisted of sliding a fretting fatigue pad back and forth ( F 100 ym) across the specimen surface at a frequency of 1 Hz. The contact pressure on the pad was 160 MPa and the resultant frictional force was measured via the load cell of the test machine.

The materials used in the tests were (i) for the fatigue specimens, Ti-17, a P-rich, a + /3 alloy with a predominantly Widmanstatten microstructure cut from a pan- cake disk forging, and (ii) for the fretting pads, Ti-6Al-4V, an CL+ p alloy with predominantly equiaxed u grains and fine intergranular p, machined from blade forging bar stock. The compositions and mechanical properties are listed in Table 1 and Table 2, respectively. All fatigue specimen and fretting-pad surfaces were polished to 1200 grade Sic grit with the resultant surface roughness having a centre-line-average (c.1.a.) of 0.52 urn compared to 0.78 urn c.1.a. on disks and 0.84 urn c.1.a. on blades from the second stage of a particular engine of interest. All polishing was parallel to the tensile axis in order to reduce the number of crack initiation sites.

3. Results

3.1. Fatigue cilln~cttirrg-frrtigltc tests

Fig. 3 shows the maximum alternating stress (G& versus cycles to failure (NJ or fatigue limit curves for the fatigue and fretting-fatigue tests. The fatigue limit was defined as the stress level at which failure had not

g 1100 1000

,E 900

vi 800 I c 700 07 P 600

Z 2 500 b

25 Q 400 E z 300

Z 200 2 100

4

0 t s ",'I,,' ~~~"*' s (,,,,,f ' ,-,s*,' ' ",--,' --' 1-j 10' 10; 10' IO5 IO6 10'

Cycles to Failure (NJ

Fig. 4. Overall view of the surface damage at urnax = 200 hlPa. The edge of contact (EOC) is arrowed.

occurred at lo7 cycles. The fatigue limit for plain fatigue was 700 IMPa. The application of fretting at this stress level resulted in a reduction of fatigue life to approximately 10 cycles. as shown in Fig. 3. This

Fig. 5. (a) Fwting-fatigue crack on X-17 specimen. Note the era the edge of the debris build-up (G?,,~% = JO0 MPa). (b) Detail c showing debris within the crack.

ck at If (a)

Fig. 3. Life curves for plain and fretting-fatigue.

232 R.A. Antoniou, T.C. Radrke /Marerials Science and Engineering A237 (1997) 229-240

04

Fig. 6. (@ The edge of contact (EOC; arrowed) at vmmax = 700 MPa. Note the extent of material build-up. (b) Back-scattered electron image of area similar to (a). Note the presence of multiple semi-elliptical cracks (arrowed).

decrease represented a reduction of fatigue life of at least three orders of magnitude. To achieve the fatigue limit with fretting the maximum allowable stress level was reduced from 700 to 200 MPa, i.e. 30% of the plain fatigue limit stress.

3.2. Friction coef$cient tests

The static (~frtatic) and dynamic (~fdSnamic) coefficients of friction of Ti-6Al-4V pads sliding on Ti-17 specimens were measured as 0.85 and 0.70, respectively.

3.3. Swface topogmphq

The appearance of the fretted surface in the region of crack nucleation for four different alternating stress levels is shown in Figs. 4-7. As the alternating stress level was increased the number of cycles to failure decreased rapidly, as shown in Fig. 3. The amount of

Fig. 7. Surface damage at the edge of contact (EOC, arrowed) (%xix = 1000 MPa). Compare the extent of damage with Fig. 4Fig. 5ja)Fig. 6(a).

surface damage was also seen to increase, as seen in Figs. 4-7, and as measured by an increase in the surface roughness (see Table 3).

Cracks were observed to nucleate at the edge of contact (EOC) (see Fig. 2(b)), and these cracks were filled with debris particles (see Fig. 5(b)). Debris particles on the surface are compacted, or fall into the cracks, or are pushed ahead of the pad to rest at the limit of movement (Fig. 5(a)).

Transfer patches are present on the surface (Fig. 6(a) and Fig. S), and these patches are significantly de- formed, showing considerable fragmentation at their edges. Associated with the patches are a number of semi-elliptical cracks (Fig. 6(b)).

3.4. Szrbsurface crack behmiozrr

The behaviour of a crack, once it has initiated, is influenced by the presence of surface frictional forces. In this section we compare the subsurface crack path for plain and fretting-fatigue.

3.4.1. Plain fatigue A typical crack path resulting from plain fatigue is

shown in Fig. 9. Initially the crack forms at or near to

Table 3 Surface roughness measurements of fretting-fatigue tests

amax WW

1200# Sic 0.52 6.2 NA 200 0.43 6.3 1.3 x IO DNF 400 0.81 7.7 49670 700 1.13 14.1 11690 1000 1.38 18.2 5000

R, = arithmetic mean deviation of the roughness profile; R,,, = maximum roughness depth, DNF = did not fail.

Fig. S. Transfer patch of Ti-17 on Ti-6Al-4V pad. Note the flattened and smeared appearance (marked A) of the particle and fragmentation at the edges (arrowd).

the surface and propagates perpendicular to the surface until it reaches a critical length. It was observed thatboth surface and subsurface crack initiation occurred. This observation was in accordance with previous work on titanium alloys [23] with a-phase which has shown that fatigue crack initiation occurs primarily by slip on favourably oriented basal planes, at or near the surface, inclined at between 35 and 55 to the surface. Therefore stage I fatigue crack initiation can be said to occur. Subsequent propagation behaviour was controlled by the effective stress intensity (A&r) and resulted in contin- uum-mode rather than structure-sensitive crack growth [24]. Failure then occurs by ductile overload.

3.4.2. Fretting-fcrtigue The subsurface appearance of the specimens corre-

sponding to the different stress levels where cracks were

Fig. 9. Plain fatigue crack profile at gmax = 825 MPa. Note that initiation (A) is perpendicular to the surface, arrowed (Kellers etch).

Fig. 10. Multiple crack sites at the edge of contact (EOC), showing the presence of debris particles in the main crack (A) and other filled cracks (B) (cman = 400 MPa).

found are shown in Figs. IO- 12. In all tests the near-surface region, at the EOC, had a number of characteristic features in common:

(i) Multiple cracks are present at the EOC. The cracks are of two different types. those marked B in Fig. 10 are generally less than 20 urn long and are filled with compacted debris material. The crack marked A is also filled with debris and has propagated significantly further into the material than the cracks marked B. The microstructure of the compacted debris material is not readily discernible.

(ii) In the initial stage of growth all cracks propagate at an oblique angle to the surface.

(iii) Not all cracks continue to propagate into the material, e.g. the cracks labelled B in Fig. 10. Those cracks that do continue eventually turn to become perpendicular to the direction of the alternating tensile stress (see Fig. 13).

(iv) The upper (oblique) part of each crack is filled with debris particles, most of which appear to be compacted.

4. Discussion

The foregoing results clearly show that fretting, in conjunction with fatigue, results in a considerable reduction in fatigue life for this combination of alloys at the stress levels tested. These results are in good agreement with Betts [2] on Ti-17. The present study shows that the reduction can be considered to be due to surface defects produced by the fretting action. These defects initiate cracks that initially propagate at an oblique angle to the surface (e.g. Figs. lo- 13). After these cracks have grown some distance into the material they propagate perpendicular to the surface under the action of the applied alternating tensile stress.

234

(3) Cc)

Fig. 11. Fractured end of Ti-17 specimen showing secondary cracking, multiple crack initiation and extensive near-surface plasticity, (rmar = 700 MPa). (a) Fracture at A, secondary crack at 3. [b) Initiation site of secondary crack, note the presence of compacted debris. (c) Surface region between main and secondary cracks. Note multiple crack sites and extensive plastic Row (arrowed).

4.1. Mcchnnisrus of cmck ndentim

It has been observed that cracks that cause failure originate from the EOC where surface damage, as indicated by increased surface roughness (Figs. 4-7), is the most severe. Furthermore, as the alternating tensile stress increases, so does the amount of damage at the EOC. It might therefore be expected that, with greater surface damage, the likelihood of a crack initiation site developing earlier would also be greater. However this was clearly not the case in the tests, The greatest reduction in life occurred at the lower stress levels, i.e. 200 and 400 MPa, indicating that, at the higher stress levels, the propensity for crack initiation is not increased by fretting as much as at the lower stresses. A possible explanation for this observation may be that at stress levels close to the tensile yield stress, slip and cross-slip readily occur and result in the formation of persistent slip bands (PSBs) from which a fatigue crack can initiate [X,26]. At lower stress levels the formation of PSBs either takes longer or does not occur and it is the fretting damage that provides the sites for fatigue crack initiation.

Considerable plastic deformation occurs at, and near to, the surface region at the EOC (see Fig. 11(c) and Fig. 12(c)). Once the material in this region is cyclically saturated, further energy is dissipated in crack develop- ment. This may be the reason that work-hardened material is more susceptible to fretting-fatigue than annealed material [17]. Alternatively, it may be that a defect of critical size must be produced before a crack can develop. Either of these processes may be considered as the reason for the existence of a fretting-fatigue life limit or threshold [ I&17,27]. The existence of such a threshold indicates that the total lifetime of the test could probably be influenced by altering the fretting conditions even after some surface damage has occurred.

Transformation due to local heating at asperity contacts may also be a cause of crack initiation. Titanium alloy Ti-6Al-4V has a poor thermal conductivity of 5.S Wm- K-l, compared to a Ni-based superalloy such as Inconel 718 with a thermal conductivity of 11.2 Wm-K-l, and ferritic stainless steels with a thermal conductivity of 25 Wm- K-- ! [ZSJ. This inab- ility to readily conduct heat away from the asperity contacts may result in local temperature increases of a few

235

Fig. 12. Fretting-initiated cracking on Ti-17 fatigue specimen at ~~~~ = 1000 MPa. (a) Edge of contact (EOC). showing clacks at A, B and C. (b) Detail of crack at site A, showing its filled nature, and the presence of debris particles within the crack. (c) Detail of crack at site B. note the plastic flow. (d) Detail of crack at site C. Note the lack of microstructural detail at the mouth of the crack.

hundred degrees [29]. However, in the testing program no temperature measurements of the surface were taken. At elevated temperatures the solubility of oxygen in titanium is significantly greater than at room temperature. At high degrees of deformation, the high disloca- tion densities result in more rapid diffusion at the surface and solution of oxygen is enhanced. On cooling, the oxygen in the surface stabilises the a-phase so that a higher volume fraction of a-phase is present. Since the a-phase (1l.c.p.) is brittle it is possible that cracks are associated with these surface contact points.

The presence of fretting debris can either increase or decrease the probability of initiation. If the debris is oxidised [2,30,31], and hence potentially abrasive, the probability of an initiation site such as a sharp gouge is increased. The abrasive nature of such debris may also act to decrease the probability of initiation by wearing away crack-like defects produced by other mechanisms, such as stress reduction by entrapped particles and removal of fatigued material by fretting wear [32]. However, no direct evidence was presented to support this view. The debris particles can also be incorporated into powder beds in which the relative displacement between the surfaces is accommodated and hence the

particles no longer act as abrasive third bodies. In our tests no significant evidence for gouging, wearing away of defects by abrasion, or the formation of powder beds was found. Instead material transfer was effective in separating the two surfaces from each other, thereby reducing the possibility that oxidised titanium particles could act as abrasive third bodies. Loading was concen- trated on these contact areas, as can be seen in Fig. 8. It has also been shown that oxide particles compact to form a low friction film. as has been found on mild steel [33], or they may form a glaze oxide film as on nickel-based alloys [34]. thereby reducing the shear forces at the contact and decreasing the propensity for crack initiation. No evidence of large scale film formation was found in our experimental program.

4.2. Model of fiettirzg-fatigue ciacli flr{clecrtiorz

A sequence of events which results in the production of fretting-fatigue cracks is proposed as follows:

When two surfaces are brought together they touch only at asperities and have a real area of contact, ilrral? which is only a few percent of the nominal area, A nominal. The value of il,,,, is determined by a range of

236 R.A. Antoniou, T.C. Rnatke ,Matedcds Science and Engineering X37 (1997) 229-240

,

t - .

Fig. 13. Fretting-fatigue crack. Note the initial inclination of the crack at the surface and the gradual turning to become perpendicular within the bulk material away from the influence of fretting.

material properties (e.g. compressive yield stress), surface characteristics (e.g. roughness and surface &-IS) and testing parameters (e.g. applied load). Subsequent small sliding movement between the two surfaces will increase Areal as a result of plastic deformation under combined normal and friction forces, this is termed junction growth [35]. Sliding may also shear any surface &IX present on the surface, such as oxides, lubricants or contaminants (see Fig. 14(a)). Subsequent gross relative movement may then result in shearing along a number of possible planes depending upon the shear strength of the junction formed between the two surfaces, e.g.: (i) at the weak (contaminated, lubricated, etc.) interface between the two surfaces, marked A on Fig. 14(a), (ii) at the film/substrate interface, marked B on Fig. 14 (a), or (iii) within the bulk materials them-

contact pressure

Fig. 15. Optical frdctograph of fracture surface showing multipie fretting-fatigue cracks (arrowed), o,,~ = 700 MPa.

selves: leading to material transfer when the interface is strong, as it would be if microwelding had occurred, marked C on Fig. 14(a).

In case (i) the presence of only weak forces between the two surfaces (Van der Waals, dispersion or hydro- gen bonding) results in only low frictional forces. In case (ii) the film-to-substrate adhesion strength will dictate the friction force. In case (iii) there are strong metallic bonds which must be broken by shear resulting in high frictional forces. The results of friction tests have shown that the coefficients of both static and dynamic friction can be high (~U,,,tic = 0.85 and illdynamic = 0.7) and are indicative of direct metal-to- metal contact.

During reciprocating sliding, the junction area of asperity contacts increases with each cycle. As the shear strength of each junction is proportional to its area, the shear force required to cause sliding (failure at interface A in Fig. 14(a)) increases with each cycle. Eventually, because of the increase in junction area, the shear strength of the junction may become greater than that of the adjacent material. Two possibilities now exist: (i) material may shear within the bulk (Fig. 14(a) plane C),

contact pressure L -s-c-

-X

-6 + -

Surface film ( eg. oxide, contaminant, lubricant, etc.) 4---r %P

(a) (b)

Fig. 14. Asperity contact and crack initiation.

R.A. htoniou, T.C. Radrke /Materials Scimce and Engineering 4237 (1997) 229-210 337

Crack begins Debris particles Debris Crack opens Further debris to open loosely fill compaction again, more compaction

the open crack (-I&,, is reduced) debris fills WEFr---+ %,j the crack

Fig. 16. Sequence of events for debris-induced closure effect.

and transfer to the opposing surface; or (ii) a crack may initiate at a location (such as X in Fig. 14(b)), due to local stress concentration. Further reciprocal sliding may then cause such a crack to increase in length, since both friction and tensile forces (a,,,) act to open it. As there are many asperity interactions we would expect many such cracks to form, and this is clearly shown in Fig. 6(b), Figs. 10 and 15. Eventually, such defects can link up across the section and produce failure. The fracture surface (Fig. 15) shows multiple crack sites on the same fracture plane which have linked together, while cross-sections such as those in Figs. 10 and 12(a) show that cracks also exist on multiple parallel planes.

4.3. Iq%erice of fretting on propngatioli

Once cracks have formed, their propagation behaviour will be modified by the presence of debris particles, the surface friction forces and other cracks.

4.3.1. In@vzce of debris OH propagation The Ming of the cracks with debris, as shown in Fig.

5(a), (b) and Fig. 10, will progressively decrease the AKCCfO by altering the opening and closing loads for the operating crack. Each fretting cycle will add new debris into the crack, reducing AK,,m until it reaches the stress intensity factor range threshold value AKCth) ,

i.e. AKcefo --f AK(,,,. A seqti&G ZGnts that will result in such a decrease in AK,,, is shown schematically in Fig. 16. The actual compaction of such entrapped debris particles can be seen in Fig. 17(a). The debris particles are in a compacted form at 15-30 pm below the surface, while Fig. 17(b) shows the presence of free debris at a depth of approximately 100 pm below the surface. The process may be thought of as debris-induced crack-closure, similar to oxide-induced crack-closure [36-441. As AKCefO for the operating crack drops towards AKCth, another crack will then become the operating crack.

4.3.2. IrlJ7uerzce of surface friction forces on propagation

Fig. 18(a) shows the load vs. time curves for the specimen. The curve marked far-field is the sinusoidal waveform imposed on the specimen by the servo-hydraulic machine. The curve marked pad/specimen interface is the actual load seen by the specimen at the interface. It should be noted that the friction force is additive to the alternating stress during unloading and subtractive during loading. Furthermore there is a sharp transition about F,,, and Ftin where the relative direction of sliding between the pad and the specimen reverses. This produces a significant jump in the friction force with a magnitude of ~Stat,CN. It could therefore be

238 R.-A. Anronioir, T.C. Ruritkr 1 Mnterinls Science md Enginewing -4237 (1997) 279-&G

expected that cracks would form at the outer edge of the asperity contact, since the friction stress is at its maximum value when the loading cycle passes through F max, and the pad starts moving toward the centre of the specimen.

Cracks that form at the edge of contact (EOC; see Fig. 18(cj), can be considered to behave differently from those closer to the centre (Fig. 18(d)), because the surface friction forces act to open the crack. At this location the EOC crack has a resolved component of the surface friction force acting only on one crack face, thereby enhancing mode I opening. It is thus likely that the rate of crack propagation during mixed mode I and II crack growth is increased in the presence of fretting.

3.3.3. Iirjkwce of shielchg on puopizgrgntion The presence of many closely spaced cracks, as

shown in Figs. 10 and 13(a), may result in shielding of cracks from far-field stresses. For example, the stress

Fig. 17. (a) Free debris particles on the fracture surfxe approximately 100 pm below the surface. (b) Compacted debris approximately 20-30 pm below the surtke.

concentration factor for one oblique edge crack in a semi-iniinite plane under tension [45] is given by:

K= FoJ;rtlcosecO

where LZ is the crack depth, 0 is the far-field nominal stress, Q the angle of inclination of the crack, and F is either F, or F,,, geometrical factors in modes I and II, respectively.

In the case of one edge crack at 45, F1 is 0.705 and F,, is 0.364. For two edge cracks in a semi-infinite plane under tension, the geometrical factors are shown in Table 4 [46]. Comparing two cracks, A and 3, as shown in Fig. 18(b), of equal size and separated by a length equal to twice their depth, FIA is 0.496, FIIA is 0.348, FIB is 0.631 and FrIB is 0.282. The two-crack system shows significant decreases in both the tensile and shear modes.

In summary the influence of fretting on crack propagation is by. a modification of the effective stress intensity as follows: (i) the presence of debris particles withir?_ the crack, Kd~bris (reduction); (ii) the surface friction forces between the pad feet and the specimen, I(friction (enhancement or reduction); and (iii) the presence of multiple cracks which shield each other from the far- field stresses, Kshielding (reduction).

Therefore the total stress intensity is given by

Consequently if a particular crack has a higher effective stress intensity over its adjacent neighbours {e.g. it is in the EOC region or it is not filled with debris or it is slightly longer), then it would shield the adjacent cracks from the far-field stresses with a resultant drop in the effective stress-intensity driving the shielded cracks. Therefore, the combination of the surface friction stress and the shielding would facilitate the opening of cracks within the EOC.

5. Conclusions

The fretting-fatigue behaviour of Ti-17 fatigue specimens with Ti-6A1-4V fretting pads at ambient conditions has been studied, with the following conclusions: 1. fretting dramatically reduces the fatigue life at stress

levels well below the yield stress, due to the increased number of fatigue initiation sites;

2. fretting results in only a small reduction in fatigue life at stresses approaching the yield stress;

3. the initiation of multiple cracks has been shown to be related to individual asperity interactions;

4. a model is proposed incorporating shielding, debris and surface friction forces, which explains the existence of multiple non-propagating cracks and the influence of fretting on fatigue crack propagation.

R.4. Antoniou, T.C. Radtkr / .Materials Science and Etzgiweriug d237 (1997) 229-240 239

t ., I , C, far-field load

Pad Position 1 (am,) (Refer Fig, 2(b))

Crack B Crack A

+x-+

I F t centre of specimen

Time (b) General view of cracks and applied forces

(a) Load versus time behaviour during fretting-fatigue

CN : A PN .p

,z-G= Gal, %p

(c) Forces acting on crack B when the pad is in position 1, and for both cracks A (d) Forces acting on crack A when the

and B when the pad is in position 2, pad is in position I, (NB: Friction

(NB: Friction force is co-directional on force is applied only to the left hand

both faces of the crack ) side crack face)

Fig. 18. Effect of friction on crack behaviour where /is = static coefficient of friction and p(d = dynamic coefficient of friction

Table 4 Geometrical factors for two edge cracks in a semi-infinite plate [39]

0

45 45 45

Gs Gd

1 0.5 1 1.0 1 2.0

L F II.4 F IB F IIB

0.400 0.316 0.619 0.235 0.439 0.332 0.621 0.254 0.496 0.348 0.631 0.282

Referring to Fig. lS(b); c and b are crack depths, d is the crack tip spacing, Q is the crack angle, F, is the geometrical factor for opening mode I and F,, the geometrical factor for shear mode II.

6. Nomenclature

maximum stress minimum stress stress ratio = ~~~~~~~~ stress intensity factor stress intensity (local, due to crack closure) stress intensity (local, due to debris) stress intensity (local, due to friction) stress intensity (local, due to shielding) stress intensity factor range threshold stress intensity factor range effective stress intensity factor range

Acknowledgements

The authors would cott, Dr. S.P. Lynch AMRL for reviewing discussions.

References

like to thank Dr. R.B. Nether- and Dr. B.J. Wicks of DSTO- the manuscript and for helpful

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[3] R.B. Waterhouse, Fretting Fatigue, Applied Science Publishers, London, 1981.

[4] E.M. Eden, W.N. Rose, F.L. Cunningham, Proc. Inst. Mech. Eng. 4 (1911) 539-974.

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