Dislocation microstructures in fatigued copper polycrystals

Dislocation microstructures in fatigued copper polycrystals

Oool-6160/81/0~735-14102.00/O Copyright Q 1981 Pergamon Press Ltd Arta Mrrclllurgiclr Vol. 29. pp. 735 to 748. 1981. Printed nn Great Britain. All ri...

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Oool-6160/81/0~735-14102.00/O Copyright Q 1981 Pergamon Press Ltd

Arta Mrrclllurgiclr Vol. 29. pp. 735 to 748. 1981. Printed nn Great Britain. All rights reserved

DISLOCATION MICROSTRUCTURES IN FATIGUED COPPER POLYCRYSTALS k

T. \VINTERt,

0. B. PEDERSEN

and

K.V.RAShlUsSEN

Rise National Laboratory, Roskiide, Denmark (Receioed 30 October 1980) Ahatraet-Dislocation structures characteristic of persistent slip bands were observed in the interior of Polycrystalline copper after fatigue. AI low strain amplitudes, within the plateau on the cyclic stressstrain curve, only structures identical to those seen in single crystals were observed. This allows the stress amplitude of the plateau to be calculated. At higher strain amplitudes. above the plateau, more complex structures were found. Further work will be needed to establish the nature of these new structures but it seems clear that the increase in stress amplitude is connected with their appearance. R&u&Nous avons observt des structures ‘de dislocations caractiristiques de bandes de glissement persistantes dans du cuivre polycristallin apr&s fatigue. Aux faibles amplitudes, sur le plateau des courbes contrainte-diformation cyclique, nous n’avons observt que des structures identiques B celles des monocristaux. Au plus fortes amplitudes, audel& du plateau, nous avons trouvt des structures plus complexes. I1 faudra d’autres traveaux pour pr&iser la nature de ces nouvelles structures, mais il semble clair que I’augmentation de I’amplitude de la contrainte est like B leur apparition.

Zusammenfasaung-Die in polykristallinem Kupfer wiihrend der Ermiidung entstandenen Versetzungsstrukturen der persistmten Gleitbiinder wurden untersucht. Bei kleinen Dehnungsamplituden wurden innerhalb des Plateaus der zyklischm Spannungs-Dehnungskurve nur Strukturen beobachtet, die mit den in Einkristallen aufgefundenen identisch sind. Mit Hilfe dieses Befundes liiBt sich die Spannungsamplitude des Plateaus berechnen. Bei htiheren Dehnungsamplituden oberhalb des Plateaus werden komplexere Strukturen beobachtet. Weitere Untersuchungen kiinnten deren Natur aufkl&ren. Es scheint jedoch klar zu sein, daD die ansteigende Spannungsamplitude mit dem Auftreten dieser komplexen Strukturen zusammenh%ngt.

1. INTRODUCI’ION

behaviour was for each surface grain to acquire its own set of bands, commonly on a single slip system. Thompson et al. therefore suggested that PSBs did not spread into the interior grains and were thus able to explain the beneficial effect of electropolishing. The observation that, in a fatique test at constant stress amplitude, the number and extent of the PSBs increase gradually throughout fatigue life is in agreement with work on single crystals [2,3], and, allowing for differences in frequency, the c&i&l stress amplitudes required to form PSBs are in good agreement. When single crystals are fatigued at constant strain amplitude, however, a very different type of behaviour is observed. Under these conditions PSBs first form as the stress amplitude approaches saturation and then propagate rapidly. However, the structure of PSBs soon stabilises and in this stable state the fractional coverage of the specimen surface by PSBs may be very much less than unity. PSBs do not propagate to cover the entire specimen even when the fatigue test is carried to failure. Once formed, the vast majority of PSBs remain active until the end of fatigue testing when the stress amplitude falls as a macroscopic fatigue crack propagates. Evidence for this view is as follows:

Thompson, Wadsworth and Louat [l] showed that the fatigue lives of their polycrystalline copper specimens could be prolonged, apparently indefinitely, by periodic electropolishing to remove the surface grains. They also noted that fatigue cracks nucleated in local regions of the specimen surface which had undergone “some modification of their structure which [caused] them to react differently to the electro-polishing conditions”. Since these regions were able to withstand a short electropolish, sufficient to remove normal slip lines, Thompson et al. named them ‘persistent slip bands’ (PSBs) and this name has passed into general use. They speculated that PSBs might be regions of enhanced oxygen concentration but it was clear that they were associated with (and had their origin in) bands of higher than average strain amplitude which spread slowly across the specimen surface as fatigue testing progressed. This spreading of the slip bands was accompanied by a steady increase in the area of the stress-strain hysteresis loop, an observation which suggests that the slip bands might be spreading through the bulk of the specimen as well as across the surface. However, the PSBs were very reluctant to propagate across the grain boundaries and the usual t Permanent address: Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, England.

1. At a plastic stra$ amplitude of 3*10m3, the formation of PSBs on a copper crystal is essentially com735

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pleted within the first few thousand (say 5000) cycles at a surface coverage of about 40% (Mughrabi [4]). A crystal was fatigued to failure [S] (2*105 cycles) and the surface coverage measured as 3?%, thus showing that PSBs do not propagate quickly after saturation. A second crystal was fatigued for 1.2. lo5 cycles, repolished to remove PSBs and fatigued to failure (a further 1.1 * 10’ cycles). The surface coverage in this case was 36x, showing that PSBs remained active. 2. PSBs can be removed from the specimen surface by a deep electro-polish but, if fatigue testing is then resumed, they reappear [6]: the new PSB- structure corresponds to the old in all but the &rest detail. It can be deduced that indi~dual PSBs remain active. Rasmussen [7j has established this result for copper polycrystals and in single crystals it holds good even when fatigue testing is resumed at a decreased strain amplitude [S]. The rwo p/tare model In the stable state for single crystals the fractional coverage of the surface by PSBs is linearly related to the plastic strain amplitude. Thus the specimen makes of itself a composite material in which the soft phase (the PSBs) is fatigued at a definite strain amplitude (es) and the harder phase (the ‘matrix’) at a very much smaller strain amplitude (e, 5 zero) the volume fraction (f) of the soft phase is adjusted to suit the plastic strain amplitude of the test (e,,) according to the law of mixtures:

A direct consequence of this behaviour is that this cycle stress-strain curve shows a plateau in the region e, s ep s ebt. Rasmussen and Pedersen [9] have recently shown that a similar model can be used to describe the fatigue of copper polycrystals (grain size h 150 m). In particular, their cyclic stress-strain curve shows a plateau which corresponds with the fatigue limit and also with the plateau for single crystals if a reasonable estimate is made of the stresses required to accommo date the difference in strain amplitude between PSBs and matrix in each grain. The plateau covers the range of e, up to about 1.5*10-3 (i.e. es/S) but the curve then acquires a positive gradient. Rasmussen and Pedersen suggested that this might be due to increased adulation stresses associated with the increased volume fraction of PSBs. Dislocation microstructures The essential difference between the PSBs and the matrix (which leads to the difference in their mechan-

IN PATIGUED P~LYCRYSTALS ical properties) lies in their dislocation microstructures. The matrix contains a dense array of primary dislocation dipoles pierced by irregular, winding channels of relatively undislocated material. The channels have a characteristic width of around 0.8 m. Since this structure is inactive, it can be assumed that the dipolar array is hard and essentially undeformable and inactive. The PSBs contain an array of parallel narrow, equally spaced dipolar walls. The walls themselves contain a very high dislocation density but occupy a small volume fraction ( ~0.1) and their spacing is large (~1.4 F). Thus this is a soft structure, able to accommodate a high plastic strain amplitude. In uniaxially fatigued single crystals there can be little doubt that the PSBs are a bulk rather than a surface phenomenon. Watt [S], and Finney and Laird [IO] have demonstrated inhomogeneous deformation in the centre of their specimens, corresponding to the PSB structure on the surface. Winter [i l] has shown that the wall structure can be found in the middle of the crystal at about the same volume fraction as at the surface. In polycrystals, however, the position is less clear. Pa have certainly been observed in the surface grains of copper both by their external appearance and by observation of the wall structure [12]. In Al-QO/,Cu, Calabrese and Laird Cl33 demonstrated a correlation between surface features very similar to PSBs and defo~ati~ bands in the interior grains. This suggests, as does the mechanical behaviour reported by Rasmussen and Pedersen, that PSBs do occur in the bulk. Against this view, it can be argued that Al+,Cu is very susceptible to cyclic softening and therefore might behave differently from a singlephase materiaL Thompson et al., and Rasmussen and Pedersen both showed that grain boundaries can act as very effective barriers against PSB propagation; thus if PSBs are nucleated at the specimen surface they might not be able to propagate into the interior e;rains. For single phase polycrystals, then, it is still unclear whether PSBs are a bulk or a surface phenomenon. Since PSBs are associated with a very characteristic dislocation microstructure, this problem can be addressed by transmission electron microscopy and this is the p~n~pa1 aim of the present paper. Some evidence already exists concerning dislocation structures in the interior grains [9,14,15] and, by and ‘large, these are only superficially similar to the structures found in single crystals. However, all such work has been performed at relatively high strain amplitudes, above the polycrystal plateau. There is thus a need for investigation at lower strain amplitudes

t eb and e, have been measured inde~d~tiy [4,8] withfair agreement. The most reliable values are Mughrabi’s: e,,, = 6,1O-s, e, = 7.5 x 10e3, resolved shear strain per quarter cycle. The resolved stress amplitude of the plateau is 28 MPa, in agreement with the observed critical stress ampfitude for the nucleation of PSBs in copper

single crystals [2,3].

Four polycrystals fatigued by Rasmussen and Pedemen [9] were chosen for study (Table 1). CUE and CuF had been fatigued at low plastic strain

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Table 1. ecvln Specimen

CUE CuF CUB CuA

Aypt 1.13 3.15 6.16 5.13 10.4 8.53

x x x x x x

lo+ lo-.+ lo+ lo+ 1o-4 1O-4

$a) 70.3 76.6 81.8 16.2 loo.3 91.3

f

(=2N&,)

0.037 0.154 0.206 -

24.8 31.5 117.5 33.8

t Unresolved plastic strain per quarter cycle. $ Unresolved stress amplitude at saturation. To relate this to the single crystal plateau stress (28 MPa) the Sachs factor of 2.2 is used: the remnants are probably accounted

for by compatibility stresses.

amplitudes within the plateau region of the cyclic stress-strain curve. CUB and CuA had been fatigued at higher strain amplitudes and in both these cases the strain amplitude had been slightly reduced during fatigue testing. It is not expected that cumulative strain will be an important variable among these specimens. The grain size was about 100-300 pm and before fatigue the specimens contained large numbers of annealing twins. Longitudinal specimens from the surface grains and from various depths beneath the surface were examined on a JEOL-1OOC microscope at 100 kV. The specimens were mounted so that the orientation of each grain relative to the tensile axis of the fatigue test could be determined, although not very accurately (estimated error - +3”). The microscope magnification was calibrated against a carbon replica of a diffraction grating.

3. STRUCTURRS OBSERVED AT LOW STRAIN AMPLITUDES 3.1 PSBs in surface and interior grains PSBs were observed, often as narrow slabs of wall structure (‘ladders’) in both CUE and CuF and in both surface and interior foils (Table 2). No statistically significant dependence of dislocation structure with depth was observed in either set of specimens. Volume fractions occupied by the wall structure were in rough accord with surface observations of PSBs-in particular, CuF contained many more ladders than CUE. Attempts to relate the behaviour of each grain to the tensile axis of the fatigue test were not uniformly successful. The ladders were always found to coincide with the trace of a (111) plane, but in CuF this was not always the primary slip plane. In CUE ladders were rare and only four cases could be analysed; these were all parallel to the trace of the primary slip plane. In CUE there was a tendency for favourably oriented grams to form ladders, whilst harder grains showed only matrix structures (Fig 2), but this observation should be treated extremely cautiously because

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very few grains were analysed and the scope for experimental error is considerable. In CuF, ladders were found even in the most unfavourably oriented grains whilst other, apparently softer grains were entirely occupied by matrix structure. Wall spacings were measured and corrected for projection on the assumption that the walls were perpendicular to the most appropriate (110) direction consistent with the observed slip plane. This assump tion is probably incorrect in some cases [l 13, but is the best that can be made. The corrections are not very large, usually 5 10 or 20%. The average wall spacing was found to be 1.3 pm which is not significantly different from the value for single crystals. Micrographs taken using different reflections usually showed one particular Burgers vector to be heavily predominant in a given grain. Some grains, however, were divided into regions which contained different predominant Burgers vectors (Fig 3). PSBs on more than one system in a single grain were, however. not observed except in a single doubtful case. 3.2 Interaction of PSBs with twins and grain boundaries PSBs were very often found running beside twin boundaries on parallel { 111) planes. Presumably the twin was present before fatigue and helped to nucleate the PSB (Fig. 4) although even in active grains it was possible to find twins which were not associated with PSBs. PSBs were observed to cross subgrain boundaries with only very local modifications to the wall structure, but large angle grain boundaries were usually impervious (Fig. 9 from CUB illustrates the point). The sudden ending of a PSB inside the specimen must be accompanied by rather large compatibility stresses but these seem to be acceptable at a grain boundary. Where PSBs ended within a grain they invariably tapered gradually toward a point, as has been observed in single crystals. 3.3 Dislocation-free

zones at grain boundaries

Large angle grain boundaries were frequently found to have associated with them zones of about 1 m width in which the dislocation density was much lower than in the neighbouring matrix structure. Not all boundaries were accompanied. by such zones and for a boundary between two given grains the width of the zone depended on the orientation of the boundary itself (Fig. 5). Twin boundaries parallel to the principal slip plane were never.accompanied by these zones. These dislocation-free zones were as common in CUE as in CuF and occurred in TEM specimens in which no wall structure was found. They are thus not a product of persistent slip. Their most likely function seems to be to assist in the accommodation of the disparate strains in neighbouring grains during fatigue hardening and in this context it is significant that their width is rather similar to that of the channels in the matrix structure (which are believed to deform plastically during fatigue hardening). It might be sug-

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Table 2.

Specimen

Depth/mm

No. of grains studied

No. containing only matrix

15 6

65 16 15 5

7 12 14 56 36 14

0

No. containing ladders or walls

No. containing misoriented cells

5

No. containing labyrinth

Measured wallt spacing/pm

: 1

0 l$ 0 0

0 0 0 0

1.4 1.4 1.4

5 7 6

2 5 7

0 ill 1

8 0

1.2 1.2 1.3

12 16 3

38 15 8

9 4 5

4 3 0

1.3 1.3 1.2

10 1 6 3 3 Details were not recorded but these were similar to the surface grains.

1.1

t kO.2 pm. The apparent variations in wall spacing are probably not significant. $ Where a PSB crossed a subgrain boundary. 5 A transverse specimen. 7 A very small area. For CuF the average correction for projection was 14%.

gested that the zones are produced by diffusion of dislocation debris to the grain boundary, but it is

difficult to reconcile this sort of explanation with the zones’ variable width at some grain boundaries and complete absence from others. The zones are usually not entirely free of dislocations but contain a low density of individual, glissile dislocations which may be of more than one Burgers vector. Presumably, since dislocation debris has not accumulated in these zones, they are not active after satur-

ation, although this possibility can certainly not be ruled out. However. the fact that crack initiation occurs in the PSBs rather than the grain boundaries also suggests that the zones are inactive after saturation. 3.4 Other structures Apart from matrix and wall structures, the only other microstructure observed consisted of an array

of misorientedcells.

This structure was extremely rare

Fig. I. Specimen CUE; depth 1mm. PSB on the primary slip plane (P) in an interior grain at the lowest strain amplitude. T marks the tensile axis of the fatigue test. The observed wall spacing is 1.65 pm but correcting for the angle of projection gives a true spacing of 1.43 pm-as is observed in single crystals (1.38 pm).

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4. DISCUSSION

Fig. 2. Tensile axes of grains from CUE and CuF. 0 rep resents a grain containing only matrix, L a grain showing

one or more ladders.

and the only clear example occurred near the edge of a small grain in CuF. For more details, see the discussion of CUB.

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1. Well developed PSBs have been observed in the interior grains of fatigued polycrystals at a small fraction of fatigue life. Since PSBs cannot propagate across grain boundaries, this implies that they can be nucleated in the interior of the specimen. Twin boundaries have been observed to act as effective nuclei and it is possible that grain boundaries are equally effective. However, the possibility cannot be ruled out that PSBs are able to.form spontaneously from the matrix structure without need for any special nucleation site. This would also be consistent with the observation of small regions of wall structure in the interior of fatigued single crystals[16], although in neither case is the experimental evidence impeccable. Watt [S] reached this same conclusion after studying the distribution of strain in the interior of fatigued single crystals. 2. The nucleation of a fatigue crack must arise from an interaction between a PSB and a free surface. If crack nucleation were solely due to the gradual increase of an internal stress field associated with the PSBs as has been suggested [17], then periodic removal of the surface could not improve fatigue life. It is significant in this context that the beneficial effects of repolishing also occur in single crystals [18]. It is still conceivable, of course, that interaction between a macroscopic stress field and the specimen surface plays a part in crack nucleation.

T

I

f

Fig 3. Specimen CuF; depth 1mm (a) Interface between slip on two different systems-both the Burgers vector and the projected appearance of the matrix structure change. This figure also serves to illustrate the weakness of residual contrast which is not always apparent when no strong contrast is available for comparison. (b) Another region of the same grain showing a persistent slip band. P shows the trace of the primary slip plane, S of a secondary slip plane on which the PSB has formed. Both of these observations indicate that the stress conditions in the polycrystal were far from uniform.

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Fig. 4. SFtimen

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CUE; surface foiL Interaction between a PSB and a smalt twin (left). P marks the t1ace of the primary slip plane which coincides with the twinning plane.

3. PSBs almost always appear as narrow regions of wall structure paraBe to a $111) slip plane. This shape is ideally suited to minimise accomm odation stresses and to allow the PSBs to suffer plastic deformation independent of the elastic matrix which surrounds them. PSBs in a given grain were almost always confined to a single slip system and the wall spacing (which controls the e5erating stress amp&tude of the PSB [19]) is not significantly different from that in single crystala. lbese results support the use of the Sachs model to calculate the stress ampiitude of the potycrystal plateau and bring the calcuiation of Rasmussen and Pedersen [9] into &se agreement with experiment. The single crystal plateau (27 MPa) and the polycrystal fatigue limit (70 MPa) are simply related by the Sachs factor (22) with the small discrepancy being taken up by accommodation stresses. 4. PSBs have been observed to terminate on grain boundaries without tapering to a point. We can only present this as evidence that the resulting accommodation stresses are acceptable. Mistits between n~~bou~ng grains during fatigue hardening are probably accommodated by dislocation-free zones which are often observed to run alongside grain boundaries. The balance of probability is that these zones do not contribute to the plastic strain after saturation. Further studies of the nature of these zones would be desirable. 5. Attempts to relate the slip system active in a particular grain to its orientation with respect to the tensile axis were not always suco3sfuI. This suggests

that quite large locai variations occur in the stress field, presumably arising from plastic deformation in n~~~u~g grains. 5. STRUCTURES OBSERVED AT HIGHER !3TRAIN AMPLXTUDES

All the structures diacusaed above were observed also in CUB and CuA and again there were no marked differences between surface and interior grains. The volume fractions occupied by the wail structure were higher (Fig. 6) and in rough accord with surface observations of PSBs. The wall spacing was again similar to that found in single crystals. Grains showing nothing but matrix structure were easy to find although much rarer than in CuF, aa would be expected. Some grain boundaries were accompanied by dislocation-free zones, exactly as before. Rather many grains showed ladders on more than one slip plane (Fig 7) This can be taken as proof that more than one slip system was operative and since many of these grains were oriented so that the tensile axis was far from any symmetry element (Fig 8), this suggests once again that the stressing conditions in a given gram are determined more by its neighbours than by the tensile axis of the fatigue test. The interactions of PSBs with gram boundaries (Fig 9) and twins were the same as at lower amplitudes, but there are now so many PSBs that it seems not possible for them all to have been nucleated at

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Fig. 5. Specimen CUB: depth 1.5 mm. Foil normal is close to a diad. (a) High angle gram boundary showing a dislocation-free zone .about 1 pm wide. Closer examination would reveal individual dislocations running across the zone, perhaps with more than a single Burgers vector. (b) A different part of the same grain boundary under the same diffraction conditions showing how the width (or even the existence) of the dislocation-free zone depends on the orientation of the boundary. The sudden change in contrast at the boundary shows that it lies normal to the foil rather than at a shallow angle. These observations suggest that the role of the dislocation-free zone is to accommodate disparate strains

between the two grains.

twin boundaries. A single case was also found of a very narrow twin running from the edge of the foil into the specimen until it terminated on one of the dislocation walls. Presumably this twin formed when the thin foil was made. In addition to the PSBs, two other types of structure were found which were not commonly observed in CUE and CuF. Time has not allowed a full investigation of these structures but the following preliminary observations can be made. 5.2 Misoriented cells Extensive areas were occupied by arrays of misor-

iented cells, a structure which has been seen in single crystals [20] and has been analysed in some detail by Laufer and Roberts [21]. These cells are rather often associated with PSBs (Fig. 10). It is usually possible to set the electron diffraction conditions so that the contrast between the cells disappears, leaving only the cell walls. This implies that the misorientations among the cells are all parallel to one axis, the reciprocal lattice vector of the operating reflection. In Fig. 10 the common axis is the normal to the active slip plane, in agreement with the results.of earlier workers [Zl, 223. The cell structure is, rather often associated with regions of multiple slip (Fig. 11).

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,

10pm

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1

‘Fig. 6. Specimen CUB; surface foil PSBs at a higher volume fraction than in CUE and CuF. The ladders are parallel to the trace. of a {II 1) plane and the wall spacing is 1.41 pm. No projection correction is needed.

s’

\

Fig. 7. Specimen CUB; surface foil. PSBs can be seen on two intersecting slip planes. The tensile axis is close to the centre of the stereographic triangle so multiple slip in this particular grain is probably the result of constraints from its neighbours. P shows the trace of the primary slip plane and S the trace of the next most highly stressed { 111) plane. Most of the dislocations are in residual contrast and this is consistent with their having the primary Burgem vector. T‘he PSBs on the secondary plane, however, contain dislocations in strong contrast. (The ladders can be seen most clearly by squinting across the figure.}

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The cell size is usually rather smaller than the wall spacing. Measurements gave an average of about a micrometer without any correction for projection; this may be taken as a slight overestimate. Areas occupied by the cell structure did not neoessariiy take the form of thin plates parallel to { 111j planes. 5.3 Two-dimensional wall structure

Fig. 8. Tensile axes of grains from CUB and GA. The dislocation structures were as follows: O-only matrix; L-iadders; M-ladders on more than one slip plane; C-misoriented cells; K-labyrinth structure. Where a grain showed more than one type of structure, the latest letter in this list is given.

1

1Opm

Two-dimensional wall structures resembling labyrinths were frequently found (Fig. 12). As with the misoriented cells, these were not confined to narrow slabs but sometimes spread to occupy entire grains. Such structures have not been observed in single crystals of copper, but they do resemble the structure revealed by etching the surface of fatigued AgCl crystals where the tensile axis is parallel to a tetrad axis [23,24]. Ladders are sometimes observed running into regions of labyrinth structure and in such cases the dislocation walls in the labyrinth are always inclined to those in the ladder. The wall spacing in the labyrinth is rather small ( ~0.75 m) and occasionally there are appreciable misorientations across individual walls. It is probable that the labyrinth is a product of multiple slip (Fig. 13).

I

Fig. 9. Specimen CUB: surface foil. A PSB approaching a high angte grain boundary. T marks the tensile axis which in this case is very close to a diad; P shows (for the large grain) the trace of one of the highly stressed siip planes. The foil normal is close to a triad axis. The PSB travels right up to the boundary and a dislocation free zone has formed on one side only. These observations are both made frequently. In addition (and much less common) the grain boundary has buckled where the PSB impinges and there is some suggestion of wall structure in the second grain.

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(iii) \

9

Fig. IO. Specimen CUB; surface foil. The structure of misoriented cells. { 1I1 ) operatingrdicctians arc 8s shown and the foil normal was quite close to a diad T marks the tensile axis and P gives the tract of a { 1112plane on which {very untidy) ladders were observed in mather part of the grain. Another active slip plane was also obscrvcd. The ctfl contrast disappears for g = (I I I& implyiog that the mitiultations are all about the same axis. Burgers vector analysis of dislocations in a neighbouring regkn reveakcl at least two active slip systems (see Fig 11). Also note a dislocation-kc zone at the grain boundary.

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Fig I I. Spbnen CUB; surbx foil. Partial Buqers vector analysis of a retion close to the misoriented 0~11sshown in Fig. IO. The orientation is Ihe same as for Fq. IO. S shows the traec of a highly stressed f 1 I 1) plane. Many of the dislocations show residual contrast for q = [I I J) and this is consistent with the mast hvourabk Burgers vector in tht plane 5. However some dislocations beha%%differerknrlyand al

74.5

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Fig. 12. Specimen CuA; depth -.. 1mm. The tw~dimensional wall structure or ‘labyrinth’ structure. Both condensed and uncondensed regions can be seen. The d&cation wails in the labyrinth are paiallel to (001) traces, the foil normal being very close to [OOt]. Note the PSB at bottom right with walis normal to [l lo], as is usual. The wall spacing in the labyrinth is 0.75 m; in the PSB the spacing is I.5 m-again the expected value. The tensile axis (T) is a few degrees away from the tetrad, out of the plane of the micrograph.

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Fig. 13. Specimen CuA; depth - 1 mm. A partial Burgers vector analysis-of the labyrinth. T marks the tensile axis. Operating reflections as marked are (020) for a; (200) for b; (220) for c; (220) for d. In order to explain the observed effects at least three distinct but possibly coplanar Burgers vectors are required.

6. DISCUSSION

We must ask whether tures

are

active

or

the cell and labyrinth strucpassive. In AgCl, Ogin and

Brown [24] concluded that the labyrinth structure is inactive. In our specimens, both labyrinth and cell structures contain a high volume of undislocated material and in this they resemble the wall structure. On the other hand, the cell size and the wall spacing in the labyrinth are both small and this would suggest a high yield stress. Two qualitative considerations make it seem probable that these are inactive structures. The first, CuA and CUB both contain enough normal PSBs to account for the imposed plastic strain amplitudes; if the cell and labyrinth structures are also active, then the volume fraction of soft material

would be higher than the two-phase model suggests. This, of course, should lead to a reduction in saturation stress rather than the observed increase. Second. the morphology of these structures does not suggest a high plastic strain. amplitude. The labyrinth in particular can occupy large, equiaxed iegions in which the accommodation stresses would be very high. We therefore conclude tentatively that these structures are not active and that their function is to exclude PSBs from sizeable regions of the specimen. Combined with increased accommodation stress attendant on the increasing volume fraction of active material, this could easily lead to the observed increase in stress. Acknowledgements-The authors wish to thank -Mr .I. Lindbo for making thin foil specimens of unusual quality.

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Dr. M. B. Batchelor gave considerable help with analysis of the results. The work was performed at Risa where one author (ATW) was a vising scientist and thanks are due to Dr N. Hansen for provision of laboratory facilities. Dr L. M. Brown made valuable comments upon the manuscript.

REFERENCES 1. N. Thompson, 2. 3. 4. 5. 6. 7. 8. 9. 10.

N. Wadsworth and N. Louaf Phil. Mug. 1. 113 (1956). 0. Helgeland, J. Inst. Metals 93, 570 (1965). W. N. Roberts, Phil. Mag. B-675 (1969). H. Mughrabi. Mater. Sci. Engng. 33, 207 (1978). A. T. Winter, unpublished work. D. P. Watt, Czech. J. Phys. B 19, 337 (1969). K. V. Rasmussen. Ph.D. Thesis. Technical U. of Denmark, September.1980. Available as Rise-M-2241. (In Danish.) A. T. Winter, Phil. Mag. 30, 719 (1974). K. V. Rasmussen and 0. B. Pedersen, Acta metall. 28, 1467 (1980). J. M. Finney and C. Laird, Phil. Mag. 31, 339 (1975).

IN FATIGUED

POLYCRYSTALS

11. A. T. Winter, Phil. Msg. 28, 57 (1973). 12. K. Katagiri, A. Omura, K. Koyanagi, J. Awatani, T. Shiraishi and H. Kaneshiro, Metal& 7kns. A 8. 1769 (1977). 13. C. Calabrese and C. Laird, Mater Sci. Engng 13, 141 (1974). 14. A. T. Winter, Acta metal!. Z& 693 (1980). 15. P. Charsley, Mater. Sci. Engng. To be published. 16. A. T. Winter, Phil. Msg. 37,457 (1978). 17. J. G. Antonopoulos, L. M. Brown and A. T. Winter, Phil. Mag. 34, 549 (1976). 18. Z S. Basinski, private communication. 19. Z S. Basinski, A. S. Korbel and S. J. Basinski, Acta metall. 23, 191 (1980). 20. P. J. Woods, Phil. Mug. 28, 155 (1973). 21. E. E. Laufer and W. N. Roberts, Phi/. Mug. 14, 65 (1966). 22. W. R. ScrobleJr. and S. Weissman, Crys. L&t. Defects 4, 123 (1973). 23. R. W. K. Honeycombe, Proc. R. Sot. A 242,213 (1957).

24. S. L. Ogin and L. M. Brown, Proc. Int. Conj on Dislocation Modelling a/ physical Systems, Gainsville, Florida, USA (June 1980).

Note added in proof-Attention is directed to the work of K. Pohl, P. Mayr and E. Macherauch showing PSB in the interior of fatigued polycrystalline low carbon steel, Scripta metall. 14, 1167 (1980).