Low amplitude fatigue of copper single crystals—I. The role of the surface in fatigue failure

LOW AMPLITUDE FATIGUE OF GQPPER SINGLE CRYSTALS-l. THE ROLE OF THE SURFACE IN FATIGUE FAILURE Z, S. ~~~NSK~‘~ R. PASCUAL2 and S. 3. BASINSKI’ ‘National Research Council of Canada, Ottawa. Ontario. Canada KIA OR6 and

%stitute Miiitar de Engenharia, Seccao de Ciencia de Materiais, Rio de Janeiro, Brazil (Received

19 Aupst

1982)

Abstract--For low amplitude fatigue of copper single crystals at room temperature, with increasing cumulative strain the PSB voiume fraction increases while the cycle peak stress decreases. The cumulative strain at failure, for the same crystal size and orientation, is independent of applied amplitude. Slip within a PSB is nonuniform at any stage of fatigue. Lo4 strains are at least an order of magnitudelarger than the constant strain in PSI% required by the two phase model. Removal of the rough surface profile rejm+enates a fatigued crystal, indicating that surface geometry determines fatigue life. R&n&--Dam le cas de ia fatigue $ faible amplitude de monocristaux de cuivre zi la temp&rature ambiante, la fraction volumique de bandes de glissement persistantes (BGP) augmente avec ia deformation cumul&e, alors que la contrainte du pit cyclique diminue. La d&formation cum&e a la rupture est indtpendante de l’amplitude appliqu&, pour une taille et une orientation don&es du cristal. Le glissement i I’intbrerieur d’une BGP n’est uniforme d aucun stade de la fatigue. Les deformations locales sont sup&ieums d’au moins un ordre de grandeur li la deformation constante dans les BGP demandct par le modele a deux phases. Si l’on retire le profil rugueux dune surface, on rajeunit un c&al ayant subi une fatigue, ce qui montre que la g&om&ie de la surface d&ermine la dur&e de vie en fatigue. Z~rn~f~~-Werd~ Kupferk~s~lle bei Raumtemperatur mit kleinen ~~~it~en ermiidet, dann sinkt mit zunehmender kumulic~er Abgleitung die maximale Spannung eines Zyktus ab, wghrend der Yotumanteil der persistenten Gkitb&der zunimmt. Die beim Bruch erreichte kumulierte Abgleittmg ist bei gteicher Kristallgr6l3e und -orientienmg unabtingig von der angelegten Amplitude. Die Gleitung in einem persistenten Gl~t~nd ist in szXmtlicheuE~~dungs~~jchen ungl~~rn~~i~ J&ale Ab~~~n~n sind mindestens eine GrMenordnung griil3er als die konstante, vom Zweiphasenmodell geforderte Abgleit~~~. Wird das aufgeraubte O~~~~~profil entfemt, dann entspricht das ~~ndun~~~alten eines Kristalles einem friiheren Stadium. Daraus folgt, daD die Ermiidungsstandzeit von der Oberfl%chengeometrie bestimmt wird.

it has

fangBrett

which ultimately

generaBy recognized that cracks, lead to fatigue failure, are associated

with persistent slip bands (PSBs), or, as they were formerly termed, fatigue striations. it has also been found that electrolytic removal of a surface envelope (30pm) from fatigued polyerystalline specimens extends their fatigue life, and that repeated removal can extend the life apparentiy indefinitely as long as any metal remains [l]. However, PSBs are thought to occur predominantly in the surface grains of pofycrystals !2,3]. For example, Thompson et al. [i] found that when a fatigued potycrystaf is tightly electropolished (2&m), although many of the striations disappeared, some remained, which they therefore called persistent slip bands, the name which has passed into general use. Continued electropolishing eventually removed ail PSBs, none were ever found deeper in the specimen than one grain diameter. Unique illterpret~tion ofthe ef%ct of surface removaf on fatigue fife is not possible from these observations

alone. The enhanced life couId have been due to removal of the PSB structure itself, or to the electrolytic smoothing of the surface profile associated with the PSBs, or to a combination of these. In general, opinion favoured surface roughness as the cause of crack nucleation, and theories were proposed as to how this could happen. Recently, Winter et. al. [4] found using transmission electron microscopy (‘IBM), that ladder structures, the dislocation arrangement characteristic of PSBs, occur in polycrystalline copper in some interior grams, apparently with the same frectuency as in the surface grains. Part of the reason for the apparent discrepancy between this and previous work may be that in the earlier work fatiguing was often carried out using methods which tend to give rise to inhomogeneous stress conditions in the samples, often leading to larger deformation in the surface. For example, the use of reverse plane bending could be responsible for the fact that even in single crystals, Laufer and Roberts f5]. who originatly correlated ‘the dislocation ladder structure with fatigue striations in copper, reported

?I2

BASINSKI

VI (I/.:

LOW AMPLITUDE

finding them only in regions less than a few hundred microns from the surface. Clearly. this is not the only factor, since Thompson ef ul. [I] fatigued their specimens in push-pull paying particular attention to achieving uniform stress conditions. They, however, were detecting their PSBs not by TEM but as residual undulations still present after electropolishing. Ladders may thus have been present in the interior grains, but electrolytic dissolution may not effectively reveal them. The possibility is then raised that although transmission electron micrographs of ladder structures from interior and exterior grains appear similar, there may be some difference in their properties. The constraint of surrounding grains might for example inhibit the large scale transfer of material which must be associated with surface extrusions and intrusions. Recently attention has focused on the dislocation substructure which builds up in single crystals fatigued at constant plastic strain amplitude, y. In the low amplitude range (y between about lo-” and IO-? a saturated crystal is divided into matrix and PSB regions whose substructures are now welldocumented 1e.g. 6,7,8]. In copper single crystals the characteristic PSB ladder structure can be found at any depth in the crystal. Examination of a fatigued crystal by eye or by low magnification optical microscopy shows that the bands are usually continuous around the specimen, indicating that composite PSBs form lamellae lying roughly parallel to the primary glide plane. Finney and Laird [9] slit a fatigued copper crystal lengthwise and found the slip line pattern developing on the inside after continued fati~ng to be essentially the same as the exterior one. Therefore, since the PSB structure is not a widely varying function of depth, surface removal experiments on single crystal specimens should provide a means of distinguishing between the internal substructure and surface geometry as a dominating influence on crack fo~ation. To the authors’ knowledge, no systematic study of the effect of surface

eoa

uxl

200 CWUITWE

SHEAR

800

STRAIN

Fig. f. Fatigue hardening curve(S) for crystal of n~entntion shown in the inset (lo“ from II IO]). The two lower curves showf, the volume fraction occupied by PSBs, as n function of cumulative strain for the amplitudes indicated.

FATIGU1

01: C‘OPPI:R-

I

on the fittiguc life of sin@ cryst;lls has bcen rcportcd. Fatigue lives are rc;tsonahly rcproducihle, so that for a given material under specified test conditions, lives are predictable. For single crystal low constant plastic strain amplitude fatigue, the cyclic hardening curve takes the form of a rapidly rising initial portion and a long plateau region which accounts for more smoothing

than 90’%,of the fatigue life of the specimen. In this region, the peak flow stress, cycle shape and even the slip line pattern, reportedly change very little. It seems remarkable that in the absence of any marked change in observable properties, the crystal appears to know within reasonably narrow limits, when it should fail. Most of the available subst~ctural and slip line studies were carried out on crystals still in the earlier part of the plateau region. To complement these, and to look for any apparent change in character with increased cumulative strain, slip line and substructural observations were made later in the plateau region. 2. EXPERIMENTAL Square cross-section crystals (4 x 4)mm2, whose orientation is shown in the inset to Fig. 1, having f54lj axes, and faces paraflei to (123) and (ITT), the cross glide plane, were grown from seed from 99.999% Asarco copper in prepurified graphite molds under a vacuum of > 10m4torr. Thirty five millimetre lengths were spark cut from the as-grown sticks. For the fatigue life experiments the central 1Omm was reduced in cross-sectional area by about 25% by Mitchell polishing [IO] the four faces, leaving the grip ends untouched. The {123) faces only were reduced for the slip line observations. The gauge length of 13.5 mm was defined by an extensometer clipped to the cross glide face. Deformation usually occurred in the reduced cross section, but occasionally PSBs entered the shoulder, in which case the accuracy of the strain measurement would be reduced. The crystals were fatigued in push-pull at room temperature at constant plastic strain amplitude, y, between 5 x 10e4 and 5 x lo-’ in a servo-controlled hydraulic fatigue machine. For some investigations a Reichert optical microscope with Nomarski contrast was mounted near to the specimen, allowing the crystal to be observed and photographed in situ during the fatigue test. To measure the strain in individual slip lines, the fatigue test was stopped either in full tension or full compression, and after all existing slip lines had been polished away, the crystal was given a fatigue half cycle until the opposite stress peak was reached. Step heights were obtained from interference fringe displacements using a Zeiss interference microscope; the width of the lines was obtained by scanning electron microscopy (SEM). The same line could be identi~ed in both instruments by means of its position on it lattice produced by shielding the crystul surface with

BAStNSKl

an ctectron microscope

et

cd.: LOW AMPLl’tXJDE

FATIGUE

OF COPPER-i

591

Nomarski contrast. It appears to be generally true that Fj’SBsbegin to appear when the cyclic hardening and (ITT) faces, were used for these measurements. curve reaches its maximum (as at A in Fig. I). They For some specimens, the dislocation substructure then muit~plyrapidly and increase in width white the was examined by TEM of primary and cross glide stress-strain curve shows pronounced softening. As plane roils. the quasi-equiiibrium region of the hardening curve For some of the slip line work, and for the (plateau) becomes established, the rate of slip band investigations into the effect of surface removaf on growth diminishes. The first PSBs were usuaffy obfatigue life, the crystals were periodically removed served to nucleate near the edge of a {123)-type face, from the machine and electropolished either in cold spread across it, and finally extend across the whole nital or cold %I”/‘,aqueous phosphoric acid solution. crystal. For a given applied plastic strain amplitude, y, the 3. EXPERIMENTAL RESULTS volume fraction, f, occupied by PSBs has been described as constant [9, 11,121, and the cyclic slip as 3. I. Mechanical properties highly reversible [14,15]. This is true to a first apThe cyclic hardening curves obtained at room proximation, however, in the present work, estabtemperature were essentiaEy similar to those prelished PSBs can be seen to widen, and new narrow viously reported for constant plastic strain amplitude fatigue in the low amplit~e region [7,9,tl, 121.A ones appear as defo~ation proceeds. Figure 3 shows typical exam@ is included in Fig. 1 (curve S). After a series of photo~aphs of the same area of a {ID) the initiai period of very rapid hardening, the peak crystal face after 2.5, 5, 10,20,60 and 125 thousand stress per cycle always exceeded the saturation flow cycles for a crystal fatigued at y = k2.1 x 10”. PSB stress, giving rise to a yield point (A in Fig. 1) before multiplication is more obvious in the earlier part of the plateau region is entered. The figure shows that the series, but examination of Fig, 3 shows that the in the plateau region, the peak flow stress per cycle filling up of old sites and the formation of new ones gradually decreases with increasing cumulative strain, continues throughout. Between 60 and 125 thousand so that description of the saturation stress as constant cyctes, activity is evident for example in the lower right corner and near the cycle number. is only approximate. The whole gauge length of some crystis was Figure 2 shows the tot& plastic strain a~~~a~ in crystals fatigued to failure, as a function of the photographed at severai points in the cyclic hardplastic strain amplitude imposed during the test. ening curve, and the percentage of surface area +ence by PSBs There is inevitably a great deal of scatter in a quantity presumably the volume fraction& -pied was estimated. In Fig. 1, $ is shown as a function such as this, but the data obviously indicate that the cumulative strain at failure is not dependent on the of cumulative strain for two crystals fatigued at imposed strain amplitude in this amplitude range. y = f2.1 x IO-’ and 4.2 x IO-‘. As previously reFailure in these particular cyst&s ocours at a cumu- ported [9,11,12], the volumd fraction occupied is lative strain of about go0 (4W = $00, where N is the larger at the higher strain amplitude. Figure 1 also number of cycles to failure). Figure 2 includes a point shows, however, that the volume fraction gradually (F) taken from Finney and L&d sf for a s~gh~y increases with strain ~ron~out the plateau region thicker crysta1 of the same orientation which f&swe8 while the peak stress gradually decreases. Some inwith the present data. These authors give a table of crease inf would be expected from the observations N values for various strain amplitudes but only that represented by Fig. 3. There is an increase in f of quoted in Fig. 2 was obtained by experiment. Their other values were derived assuming that the relation y = 2.18(2N)-*.” obtained for polycrystalline copper [I 31holds also for single crystals. Figure 2 shows that in this respect, single crystals behave differently from poiycrys~ls~ where the cumulative strain at faiture increases with decreasing plastic strain amplutude. The crystals used in the present work were alt of the same orientation and size; a property such as fatigue life would be expected to be dependent on these parameters as well as on many other factors such as prior-treatment, etc. Crystals of the same size, but whose orientation was 20”away from [1IO]on the crass glide plane great circle, had lifetimes about twice as long as the crystals used in this work. onto

it. Crystals

grid

of orientation

while

evaporating

[3211, having

fn

(1%)

During some of the fatigue tests the crystal surface was observed in rirlt using an optical microscope with

Fig. 2. cumulative strain at failure as a function of applied constant plastic strain amplitude.

Fig. 3. PSBs on the same area of a (123)face at increasing numbers of cycles. The numbers, on the same area of each print, are cycle numbers in units of 1000. y =t jc2.1 x 10eJ.

about IOU/,between cumulative strains of 500 and 800 (Fig. I).

The procedure employed was to fatigue a crystal to, number of cycles, polish and remount it in the fatigue machine, and watch the surface carfuffy for the next few cycles. which were usually executed at slower speed. Many photographs were taken in the first few cycles, then occasional ones at successively larger numbers of cycles. Nomarski contrast was used for the in situ work, but unrortunately the set-up did not allow use of it high power objective. To polish slip markings away, the surfaces were lightly Mitchell polished [IO] and then carefully el~tropofished in phosphoric acid solution.

a predetermined

Efectropolishing with no prior treatment tends to leave traces of the PSBs, in agreement with earlier work [I]. In general, for crystals fatigued well into the pfateau region and repolished. newly formed slip fines ~~upied the same sites as those polished away, but their appearance was quite different. There was no observable activity in the matrix, neither in these investigations nor in the observations made later at higher magnification. Figure 4 shows a typical sequence of events occurring in the first cycle after repolishing. The crystal in this case had undergone 39,000 cycles at p = +2. I x IO _‘, the test was stopped at the maximum in tension and the crystal was unloaded, polished and remounted in the machine. Figure 4(a)

BASINSKI PI ul.:

LOW AMPLITUDE

FATIGUE OF COPPER-I

(4

Fig. 4. (a) Successive views of (T25) faceduring first cycle after repolish. Letters mark the same area on each frame and indicate fatigue loop position in (b). (b) Fatigue loop for the first cycle after repolish, showing points where the photographs of (a) were taken in siru during the cycle. 39.000 cycles, y = k2.l x 10-j.

595

j’lh

BASINSKI

L’/ (I/.:

LOW AMPLITUDE

shows irk situ photographs of the same area of the (i23) face taken at points marked in Fig. 4(b) in the first cycle after repolishing. Letters marked on the frames in Fig. 4(a) correspond to positions OR the fatigue cycle in Fig 4(b), and also mark the same point on each frame. In the first quarter cycle, the first features to appear were faint wide bands (frame A). Their contrast was darker than the matrix, they appeared at the same sites as the pronounced rough PSI& which had been polished away. They gradually increased in intensity and, at least at this magnification, appeared to be mainly of uniform contrast, with only occasional darker streaks. As deformation proceeded into the second quarter cycle, some intense btack shp appeared (frame C), ‘This was usually situated both at the interfaces between the uniform bands and the matrix, and at the sites of those PSBs which were still narrow before re-

polishing. The intense lines were short in comparison with the dimensions of the composite PSB dabs, and their ends often overiapped, as in the case of the narrow sharp PSB in the centre of frame C. The intensities of both the wide bands and the sharp narrow tilts increased to their maximum at the maximum compressive stress (frame D); some of the intense lines even showed Nomarski reversal. When the direction of stressing was reversed the broad diffuse bands Iost their contrast (f-es E, F)* while the intense lines remained essentially unchanged. In the fourth quarter cycle, the intense lines decreased in contrast and some slip of opposite contrast also appeared (frames G, H). Thus, slip in the sense opposite to that occurring in the first half cycle becomes evident not anty as a ~i~tening of contrast but also in the appearance of “white” slip lines which increase in prominence. The sequence described above, development of wide bands of ditTuse contrast in that part of the fatigue cycle where stress is changing rapidly with

strain, foBowed by the appearance of sharp tits where the Bow stress does not change appreciabty with strain, was a very striking feature. The same sequence was common to all crystals repolished in the later plateau region and observed in s&u during continued fatigue. The markings Ieft at the end of the first cycle after repolishing (Fig. da, frame H) represent the irreversible part of the slip occurring in that cycle. As the number of cycles after repolishing increased, the PSI3 sites slowly filled. up and eventually became roughened over their whole width. Figure 5 shows the same area as that in Fig. 4 after an additional 100 and 35,000 cycles. It can be seen that the general roughening has a diKerent appearance from that on crystals fatigued without intermediate polishing. The Pattern is generally finer, and there is often a regularity in the spacing of component slip lines in the quasi-homogeneous band, givntg an overall striped appearance, as shown in Fig. Sb. It is interesting that the stripe spacing is of the order of 1.5jlrn. which is

FATlGlJE

comparable

OF C‘QPPER--I

to the ladder spacing at room tem-

perature, as well as to the ccl! size for high strain amplitude fatigue { Ifi]. Some crystals were removed From the fatigue machine for examination at higher magnification. The broad bands, which at lower magnification appeared to represent quasi-homogeneous deformation, were found to consist of many uniformly distributed fine slip tines. These were different in character from the

intense siip bordering the bands and the occasional isolated intense slip lines. Figure 6(a) shows newly formed PSBs on a crystal fatigued to 70,000 cycles at

-&:2.1x IO-‘, repolished and fatigued another half cycfe from peak to peak. The photograph shows both isolated sharp slip lines and ~n~~~tio~s typical of wide PSBs on repolished crystals. These consist of a band of fine lines of weak contrast bordered on each side by narrow intense lines (two kinds of slip). The superimposed fringes, from a white light interference photograph of the same area, emphasise the large locai strains at intense lines. For the wide band at the teft side of the fringe inset, a displacement of about a thii of a fringe (A/6) occurs at the intense border, while the weak lines inside the band are only just visible as perturbations in the fringes. Winter [I l] assumed that ya, the strain in PSBs, is a constant in the ~~~b~~rn region. His linear plot

BASINSKI

er u/.:

LOW

AMPLITIJDE

CJ). Fig. 6. (a) Optical micrograph of slip on a crystal Fatigued a half cycle in compression after repolish at 70,000 cycles (expected life 100,000 cycles). Superimposed on part of the field of view are white light fringes taken from an inter-

ference photograph of the same area. (b) Scanning electron micrograph of a slip line from a crystal fatigued half a cycle in compression after repolish at 21,000 cycles, y = k2.l x JO-‘. The inset is a thallium light interference photograph of the same area but at different marination, showing the vertical displacement of fringes at the slip line.

of I; the volume Fraction occupied by PSBs, as a function of the imposed strain amplitude, suggests a [l2], who invalue of -0.01 For ye. ~u~rabi vestigated the limits of strain amplitude For the low amplitude region, arrived at a value of 0.0075 for ~a. Figures 4 and 6 show that the strain in PSBs is Far from being uniform, a conclusion also reached by Finney and Laird [9] For lightly Fatigued crystals. Some attempt was therefore made to measure the strain in active regions and compare it with ya. For this purpose it is necessary to know the width of individual slip lines with considerably more accuracy than is possible with optical microscopy. Some crystals were therefore Fatigued to various fractions of their expected life, the test was stopped in Full compression or Fult tension, the crystals repolished and fatigued a half cycle to the opposite peak stress, giving the maximum strain obtainable in one cycle. The resulting slip lines were very difficult to see both on replicas by TEM and by SEM, unlike the Nomarski technique which gives striking contrast but unfortunately not enough width resolution. However, some lines were photographed using SEM and their widths measured. The same areas were then examined by interference microscopy to determine the corresponding step height of the lines. The crystals used

FATIGUE

OF

507

COPPER-I

for this part of the work were of [321) orientation. Figure 6(b) shows an example of a SEM view of a slip line From a repolished crystal previously fatigued 2 1,000 cycles then given another half cycle From peak to peak; the electron beam was parallel to the Burgers vector direction. therel’ore the apparent width of the line represents the true width of the slipped region. The insert shows thallium light interference fringes for the same line (but at lower magnification), showing a vertical displacement of about half a Fringe (A/4) at the slip line. The displacement, along the Burgers vector direction is given by h/cosa, where /r is the measured displacement perpendicular to the crystal surface and a is the angle between this direction and [loll. Table 1 shows some typical examples of the values obtained for the strain amplitude in active intense slip lines (ya), using slip line widths and heights such as those shown in Fig. 6(b), and taking into account the orientation Factor. In the last column of the Table, ys is represented as a multiple of ye (=0.0075). Taking the average of the entries, the strain in the active regions of a PSB is seen to be 1~30 times larger than the constant value of the strain in a PSB suggested by the two phase model. 3.4. Suhslructuraf

observations

The fatigue dislocation structure built up in the earlier part of the plateau region is now well documented. The crystal volume is divided into two easily recognisable regions. The matrix is known to consist of highly disiocated irregularly shaped veins separated by almost perfect material. In the PSBs the fraction of material densely packed with dislocations presents a ladderlike appearance when viewed in cross glide plane sections. In both cases, the dislocations belong predominantiy to the primary system. Later in the plateau region the matrix retains the same characteristic Features. The PSBs however become somewhat modified. Etch pitting the cross glide Face shows that there are Fewer of the narrow welldefined ladders. The bands are usually made up of wider structures in which the component ladders are less well-defined than those at lower cumulative strain. TEM shows that in the late plateau region Table I. n

7

21K

0.002

1K

0.002

70K

0.002 I

W

h

7s

f?,

0.57 0.457 0.2 0.4 0.4 1.143 0.138 0.42 0.5

0.45 0.3 0.5 0.4 0.25 0.9 0.27 0.45 0.4

0.163 0.136 0.516 0.207 0.129 0.163 0.404 0.214 0.165

21.6 18.1 68.9 27.5 17.2 21.7 53.9 18.6 22.0

-

n, number of cycles before repolish; y, plastic strain amplitude; \I’. line width in microns; h, vertical step height in fractions of a fringe; ys, strain amplitude per quarter cycle in active slip lines; m, ys/0.0075.

i’)S

IblSINSKI

01 trl.:

I.OW

AMPLITUDE

FAl‘lGUl~

of 1.5pm.

OF C:OI’f’f:.K.

I

comparable lo the ladder spacing for room

temperature

low amplitude

fatigue.

The cumulative

in these crystals was not necessarily high, so that it is possible that cells are associated with the relatively high strains reached early in a test under high amplitude conditions, and with high accumulated strains under low amplitude conditions. It is interesting that Laufer [ 171reports a structure similar to that represented by Fig. 7, which he aptly describes as a sandwich, with thin layers of ladder structure enclosing a wider layer of misoriented cells. His crystals were fatigued in reverse plane bending to only about I% of their life, so that it is difficult to compare stress and strain conditions with those of the present work. The misoriented cell structure, however, seems to be found in fatigued crystals whose final state has been achieved by a variety of methods. strain

3.5. Enhancement of fatigue life

Fig. 7. Transmission electron micrograph of a cross glide plane foil from a specimen fatigued into the late plateau region showing ladder structures bordering various configurations of miroriented cells, and matrix structure. The average ladder spacing and cell diameters for such specimens is l.5pm.

PSBs often consist of layers of misoriented cells whose diameter is comparable to the ladder spacing. The cells are usually bordered by a thin layer of ladder structure. Figure 7 shows a micrograph of a cross glide plane foil showing an example of the misoriented cells. Comparison of the substructure and slip line observations described above (Fig. 4) suggests that the narrow high strain regions bordering wide PSBs (and the very narrow PSBs) are associated with the ladderlike structure, while the wide band of diffuse slip is associated with misoriented cells. Woods [7] observed isolated patches of misoriented cells in copper crystals fatigued to a cumulative strain of about 120. The PSB structure consisted mainly (95%) of ladders, with some cells. At lower cumulative strain she observed no cells. Gostelow [I61 reports that misoriented cells are an important feature of the substructure in copper crystals fatigued at high amplitude (y = -0.01). The cells had a diameter

In the present work it became apparent that crystals which had been repolished for slip line work and subsequently fatigued to failure, had significantly longer fatigue lifetimes than nominally identical crystals having no intermediate polish. Repolishing experiments were therefore carried out on crystals of the same specifications as those used for the slip line work to investigate this observation further. The crystals were fatigued at room temperature at y = f2.1 x 10m3. At this amplitude in a normal fatigue test the average lifetime is of the order of 10’ cycles. The crystals were electropolished at chosen points on the fatigue hardening curve, about 0.1 mm being removed using ice cold 50% orthophosphoric acid solution. The slip line pattern which developed when fatiguing was continued after repolishing was always finer and smoother than that which had been removed. The repolishing experiments are summarised in Table 2. The specimens fall into three main groups, those repolished at about 30% of their normal lifetime, those repolished at about 80% of their normal lifetime, and those repolished repeatedly. The data in the Table show that specimens repolished either early (30% of life) or later (80%) in the saturation plateau region endured an additional lifetime about twice as long as the normal life of a virgin crystal fatigued to failure, indicating that a fatigued crystal will be rejuvenated and will endure an extra double life if it

Table 2. Length of interval after repolishing (in thousands of cycles)

Last interval

Total life

215 218 186 194 178 163 I44

100 245 253 266 274 380 388 440

Virgin crystal 29.4 35.0 80.0 80.0 50.0 75 40.5

202 I50 80.5

225 120

162

208

296

is repolished at any point in the plateau region. Crystals repeatedly repolished had lifetimes significantly longer than those repolished only once. For example, the last crystal in Table 2 was given live intervals of -40,000 cycles and one of -90.000 cycles. After its sixth repolishing, when it was rather thin and uneven, it endured another 144,000 cycles, thus achieving a total lifetime of more than four

times that normally expected for these crystals. Thus it appears that repeated repolishing could, in principle, extend the fatigue life indefinitely, as in the case of polycrystals. There is some indication from the Table that the

second lifetime of crystals repolished when they had endured 80% of their normally expected lifespan is marginally shorter than for those which had endured only about 30%. Unfortunately, firm conclusions cannot be drawn from so few data; however, it may be that ladders can support longer lifetimes than the cells which are more prevalent in the PSBs of heavily fatigued crystals. There also seems to be a continuous decrease in the length of the last interval before failure from the top to the bottom of the Table. This could be related to the increasing cumulative strain, and hence pliably the increasing preponderance of cells over ladders. However, it is abo possible that the length of the final interval depends on the number of times the crystal had been repolished. Not only will repolishing cause the crystal to become thinner, and therefore less ideal for a fatigue test, but there is also the possibility of introdu&~on of irregularities in the cross-section, and of handling damage. To gain further information on the relation between fatigue life and the surface slip pattern, some crystals were pndeformed in tension to flow stresses beiow the saturation stress. The tensile slip lines were polished away and the crystal was then Fatigued to failure. The fatigue slip lines formed on predeformed specimens were always fine, short, and uniformly distributed in contrast to the PSBs which form on virgin crystals, as previously reported by Winter [18]. The fatigue lifetime of such predeformed crystals was always longer than for virgin crystals. In particular, a crystal predeformed to a flow stress of 1.8 kg/mm2 began to show signs of failing at 5 x IO5 cycles, five times the normal lifespan.

Two theories of fatigue in the current literature depend on models which were developed using available experimental evidence both direct and indirect. For brevity these will be referred to as Modei I, which is due to Brown (I9-ZI], and Model II, due largely to Essmann and Mughrabi [22-241. The reader is referred to the original papers for a full account of the theories. Very brief outlines will be given here only of aspects of the theories which are relevant to the present findings.

In the case of Model f, a sequence of dislocation events is d&cribed which leads to the formation of the characteristic PSB ladder structure, the walls (or ladder rungs) being composed of many small vacancy dipoles, in accordance with the observations of Antonopoulos PI aL f20J. For the purpose of calculating the internal stresses associated with PSBs, Brown shows that such a wall of small dipoles can be replaced by a single large vacancy dipole (which he

labels fictitious) whose components are located at the ends of the wall. The PSB structure is then represented as a system of vacancy dipoles whose components lie along opposite PSB-matrix interfaces; the PSB material is thus in a state of tension parallel to the Burgers vector direction. Calculation of the model stresses showed that they provide a plausible crack-opening force. There appears to be some difficufty with this model in that geometrically it is necessary that vacancy dipoles are balanced by an equal concentration of interstitial dipoles. Very many small vacancy dipoles could be balanced by a few large interstitial dipoles. These would be infrequently encountered in thin foils, also their large separation would make them difficult to reeognise as dipoles. Their presence would therefore not conflict with observation, but as long as they remain in the crystal they would nullify the internal stresses predicted by the theory. It must therefore be implicitly assumed in Model I that inters~tial dipoles in some way glide out of the crystal. In Model II, cyclic straining is described as being accomplished by a superposition of many microscopic slip processes whose glide paths are te~inat~ by dislocation annihilation (and production of point defects in the PSB). In saturation, dynamic equilibrium between annihilation and creation of edge dislocations may be reached in -50 q&s, The processes cause sets of edge dislocations to be deposited at the PSB-matrix interfaces, the interface dislocations being of the same sign at a given boundary. Although very little is known about the nature of point defects in the PSBs, various indirect arguments are examined and it is concluded that these must be predominantly vacancies. In this case, the interface dislocations will be equivalent to a set of interstitial dipoles, and the PSB will be in compression in the Burgers vector direction, in contrast to Model I. The vacancies are then removed from the sphere of influence in some manner dependent upon their mobility. Both Model I and Model II present a fatigued crystal as an essentially nondeforming matrix containing PSB layers which are under stress along the Burgers vector direction, stretched in Model I and compressed in Model II. Such a fibre stress, of whichever sign, would be associated with an inhomogeneous shear stress on the primary system at the PSB-matrix interfaces. During fatigue cycling, considerable cyclic plastic deformation takes place on

(>I)0

BASINSKI

01 rd.:

LOW AMPLITIJDE

the primary system, and the present work indicates

f:ATlGUl;

Ol-’ COPPER--

I

the boundaries of PSBs. Such plastic flow could easily relax any inhomogeneous interface stresses. The models are therefore in need of an additional mechanism which would stabilise the interface dislocations and prevent relaxation by plastic flow of the stress gradient necessary for generating the crack initiation force.

well-documented linear relationship between ,/‘and ; 19, I I, 121implies that the crystal in some way maintains an average strain of the order of 0.01 in its PSBs; locally however. shear strains are at least an order of magnitude higher. If we accept the tentative conclusion (Section 3.4) that the sharp narrow lines are associated with the ladder structure, these must be able to withstand the strain amplitudes shown in Table I (ye).

4.2. The strain in PSBs

4.3. Surface removul

It has been shown [9,11,12] by measuring the crystal surface area covered with slip bands, that the volume fraction occupied by PSBs, A is a linear function of the imposed constant plastic strain amplitude, y. Winter [l I], assuming that there is a definite constant plastic strain associated with PSBs, proposed his two phase model, in which matrix material is converted into PSB structure as required by the current plastic strain amplitude. The method of measuring coverage by slip lines gave in the present work volume fractions comparable to those in the literature, but also showed that at a given y the volume fraction is not truly constant, but increases very slowly with increasing accumulated strain throughout the saturation region (Fig. 2). A plot off vs y is thus not as straightforward a matter as it at first appears. Some provision must be made to measure f under comparable conditions for each crystal, but since the measurements themselves are not very precise and even somewhat subjective, these considerations may not be of great importance. The repolishing experiments in the late plateau region showed that there are two types of strain in PSBs (Figs 4 and 6) One, observed in the first quarter cycle, is weak and quasi-uniform and fills the wider bands. The other, observed in the second quarter cycle, is very intense, and occurs as narrow lines at the borders of the wide PSBs and as isolated narrow PSBs. Description of PSBs as a single phase, at least in the late plateau region, may therefore be not strictly correct. The strain associated with the intense slip lines (Table I) is at least an order of magnitude larger than the constant strain assigned to the PSB structure on the basis of the two phase model. Finney and Laird [9], also using a repolishing technique but at much lower cumulative strains (<30), showed that PSBs rather than being sites of uniform strain, comprise short narrow slip lines separated by inactive areas. In order for their f/y plot to agree with those obtained without intermediate repolish, they used the total width of a macroband to determine f, including the inactive regions. The interferograms of Finney and Laird also show some evidence of higher shear strains being associated with the edges of bands, indicating that the tendency is there even at this early stage of fatigue. Clearly, the strain in a PSB is nonuniform, both in the early and in the late plateau region. However, the

It was mentioned in the Introduction that electrolytic surface removal can extend the life of fatigued polycrystals apparently indefinitely. Wowever, it has long been thought that PSBs formed only in the surface grains [e.g. 2,3]. It was thus not possible to say whether surface removal was effective because the PSB structure was removed or because the surface profile was smoothed, or both. There have been varying opinions about the concentration of PSBs with depth not only in polycrystals but also in single crystals, but it is now accepted that PSBs may extend throughout a single crystal cross section. Thus, the effect of surface removal can be used to distinguish between surface topography and dislocation substructure as a cause of fatigue failure in single crystals. Very recently, however, Winter et al. [4] showed convincingly that ladder structures occur in some grains inside a polycrystal. This may have been sufficient indication that removal of intrusions and extrusions extended fatigue life, were it not for the possibility that the ladder structures formed under the constrained conditions of the interior may be in some way different from those at the surface (see Section 1). The large scale transfer of material resulting in the formation of extrusions and intrusions is free to take place in surface grains but not in interior ones. Unique conclusions can thus be drawn only from single crystal data. The present work showed that removal of a thin surface envelope gave a fatigued crystal a new lease on life, its new lifetime being about twice as long as that expected by a virgin crystal. This rejuvenation occurred whether the crystal was repolished near the beginning or near the end of its fatigue life. It may be inferred from these data that (a) surface geometry is responsible for failure (since the substructure and internal stresses remain unchanged by electropolishing), and (b) the most damaging profile forms early in the fatigue test. The PSB substructure is relevant only in that it provides the site at which surface serrations are generated. The fact that the PSB substructure itself changes character somewhat between the early and late plateau region, but that electropolishing in either of these stages gives the same rejuvenation, reinforces the conclusion that surface topography is the basic cause of failure. The rough PSB surface is known to consist of extrusions and intrusions; the early observations are summarised in Thompson and Wadsworth’s review

that this is particularly

pronounced

in the vicinity of

BASINSKI

et al.:

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article 121. in particular,

Cottrell and Hull [25] who made replicas of fatigued copper surfaces, state that intrusions and extrusions occur in comparable abun-

dance and with

similar

dimensions.

It is to be ex-

petted that stress concentrations associated with individual initiation

iI~trusi~~ns

might

be

responsible

for

lhc

of cracks.

The current theories of fatigue (Section 4.1) predict surface profile will consist of a general surface bulge, or net extrusion with a superimposed statistical surface roughening. Vacancy production accompanied by a swelling of PSB material in the direction of the primary Burgers vector is responsible for the net extrusion [23,24]. Statistical roughening is a consequence of many random microscopic slip processes. The interferograms of Finney and Laird [9] are often quoted as evidence for a net bulge at PSBs, but these authors themselves were careful to point out that the instrumental factors were such that an apparent continuous wide ridge could have represented a serrated profile with notches of any depth. Similarly, Mughrabi and Wang [26] cite a SEM view of a fatigued crystal surface as evidence for elongation parallel to the Burgers vector direction. However, viewing the exterior of a crystal can only reveal bunches of closely spaced extrusions, giving the appearance of a rough bulge and concealing any other features the profile might have. It is necessary to take replicas, or employ some appropriate sectioning technique, in order to see the full extent of intrusions into the bulk or to know whether a net bulge exists. Assuming that the model interface stresses mentioned in Section 4.1 are in some way stabilised, the theories predict large surface stresses at the lines of intersection of the PSB-matrix interfaces with the surface. Crack initiation is envisaged at one side of the bulge at the interface of each pair where there are tensile stresses tending to tear the PSB and matrix apart [21]. Since the stress states are opposite, the prime crack nucleation sites would be at opposite interfaces in the two models. However, removal of a thin surface layer from ~n~gurations such as those proposed in the models should not cause drastic changes in the stress pattern, since the boundaries of the strained PSB, which penetrate the whole crystal, are the entities giving rise to the surface stress fields. The spectacular rejuvenation demonstrated in the present work is very difficult to explain on such models, it thus appears more likely that stress concentrations associated with the sharp surface serrations at PSBs are responsible for crack initiation, and hence failure. Some preliminary work (271, in which sections were taken through RSBs parallel to the cross glide plane and examined by SEM, showed that cracks formed at PSB-matrix interfaces and also anywhere within the wide PSBs. Cracks were also often seen outside the PSBs where only isolated single intrusions could be detected. There appeared to be no preference for one that the PSB

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OF COPPER-i

601

particular interface, which would be required by the theories, or for any other exclusive site. In the same work an attempt was made to investigate the question of a net bulge at PSBs. So far, however, no firm conclusions could be drawn since some PSBs bulged at the surface while others did not, even on the same specimen. The experiments with prestretched crystals are compatible with the conclusion that the jagged surface profile provides sites for crack initiation. Predeformation in tension increased the fatigue life of a crystat by a factor of five. The surface slip markings on fatigued predeformed crystals were liner than in normal PSBs, and were uniformly distributed rather than being bunched into bands. The damaging profile formed early in the life of a normal fatigue specimen is avoided and the life therefore extended. 5. SUMMARY For copper crystals of single slip orientation fatigued at room temperature at constant plastic strain amplitude in the low amplitude range: (1) in the saturation plateau region the apparent volume fraction of crystal occupied by PSBs slowly increases, and the saturation peak flow stress per cyde slowly decreases with increasing cumulative strain (Fig. 1). (2) The crystals, of 15411 orientation, fail at an average cumulative strain of about 800, independent of the imposed strain amplitude (Fig. 2). (3) There was no observable slip in the matrix. (4) The cyclic appearance and disappearance of slip markings on repolished specimens was largely reversible, but irreversible processes led to the reformation of new PSBs on the same sites as the original ones (Fig. 5). (5) The strain in a PSB is nonuniform both early and later in fatigue. In the late plateau region, in situ optical (Nomarski) microscopy of repolished crystals shows that in the first quarter cycles, PSBs deform over their whole width by low level, quasi-uniform defo~ation. In the next quarter cycle very intense slip also occurs, as sharp narrow lines at the PSBmatrix interfaces, and in very narrow PSBs. The diffuse slip appears in that part of a cycle in which stress is a rapidly varying function of strain, while intense slip occurs when stress changes very little with strain. The strain in intense slip lines (Table 1) is about 30 times the constant strain in PSBs predicted by the two phase model. (6) When the surface of a fatigued crystal is smoothed by electropolishing at any point in the plateau region, its new life expectancy is about twice that for a virgin crystal. Such rejuvenation can be repeated (Table 2) as long as enough crystal remains. Since the PSB substructure can be found at any depth in the crystal, fatigue life must be dependent on that property which exists only at the surface, namely the rough PSB surface profile.

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(7) Predeformation in tension enhances fatigue life. Slip is tine and uniformly distributed, so that the usual damaging fatigue profile is avoided. Acknowledgements-Two

of the authors (Z.S.B. and S.J.B.)

would like to thank members of the Metal Physics group at the Cavendish Laboratory, Cambridge, for stimulating and enlightening discussions during their sabbatical year. The authors especially wish to thank Dr L. M. Brown for giving them a copy of the manuscript on his theoretical model for fatigue (Rd [Zl]), and Dr H.-Mu~mbi for a manuscript of reference 23 orior to publication. They also thank Mr J. W. Fisher for growing the crystals used in this work, and Messrs H. G. Champion, H. J. Broome and J. Riddell for technical help.

FATIGUE

OF COPPER-I

I. I’. J. Woods, Phil. Msg. 28. I55 (1973). 8. Z. S. Basinski, A. S. Korbcl and S. J. Basinski, Acw mrruii. ta I91 (1980). 9. J. M. Finney and C’Laird, Phil. Mug. 31, 339 (1975).

IO. J. W. Mitchell. J. C. Chevrier. B. J. Hockcv and J. P. Monaghan, C&. J. Phys. 45,453 (1967). II. A. T. Winter, Phil. Mug. 30, 719 (1974). 12. H. Mughrabi, Muter. Sci. Engtzg 33, 207 (1978). 13. P. Lukas and M. Klesnil, Muter. Sci. Eagng If, 345 (1973). 14. D. F. Watt, J. D. Embury and R. K. Ham, Phil. Msg. 17, 199 (1968). 15. D. F. Watt, Czech. J. Phys. Bt9, 337 (1969). 16. C. R. Gostelow, Melals Sci. 5, 177 (1971). 17. E. E. Laufer, Czech. J. Phys. B19, 333 (1969). 18. A. T. Winter, Phil. Mag. 31, 411 (1975). 19. L. M. Brown. Metals Sci. 11. 315 (19771.

20. J. G. Antonopoulos, REFERENCES I. N. Thompson, 1, I I3 (1956). 2. N. Thompson (1958). . 3. H. Mughrabi, 4. A. T. Winter.

N. Wadsworth and N. Louat, Phil. Mng. and N. J. Wadswo~h, Ads. fhys. _ 7.72

scriplo metail. 13, 479 (1979). 0. B. Pedersen and K. V. Rasmussen. Acta metall. 29, 735 (1981). 5. E. E. Laufer and W. N. Roberts, Phil. Mag. IO, 883

(1964). 6. A. T. Winter, Phil. Mug. 2.8, 51 (1973).

L. M. Brown-and A. T. Winter,

Phil. Mug. 34, 549 (1976).

21. L. M. Brown, private communication. 22. H. Mughrabi, ICSMA3, Vol. 3, 1615 (1979). 23. U. Essmann, U. Gosele and H, Mu~rabi, Phil. Mag. A44, 405 (1981).

24. U. Essmann, Phil. Mug. A45, I71 (1982). 25. A. H. Cottrell and D. Hull, Proc. R. Sot. h242, 211 (1957). 26. H. Mughrabi and i. Wang, Int. Symp. Defects and Fracture, Tuczno, Poland. Martinus Nijhoff, The Hague (1982). 21. Z. S. Basinski and S. J. Basinski. To be. published.