The formation of wither tongue- or ribbon-like extrusions in fatigued copper polycrystals

Acta metall, mater. Vol. 39, No. 7, pp. 1645-1650, 1991

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THE FORMATION OF EITHER TONGUE- OR RIBBON-LIKE EXTRUSIONS IN FATIGUED COPPER POLYCRYSTALS M. BAYERLEIN and H. MUGHRABI Institut fiir Werkstoffwissenschaften, Lehrstuhl I, Universit~it Erlangen--Niirnberg, Martensstr. 5, D-W-8520 Edangen, Fed. Rep. Germany (Received 20 September 1990)

Al~traet--The surface morphology of polycrystalline copper fatigued at temperatures of 107, 298 and 533 K was investigated by scanning electron microscopy (SEM). Both ribbon- and tongue-like extrusions were ob~rved except after fatigue at 533 K, where ribbon-like, complex and needle-like surface structures were apparent. The dependence of the formation of either ribbon- or tongue-like extrusions on the crystallographic orientation of the grains in the direction of the stress axis was investigated by selected area electron channeling patterns in the SEM. The results suggest strongly that the morphology of extrusions formed at emerging PSBs is controlled by the type and the Sehmid factors of the activated slip systems. A model suggested by Polfik et al. [Mater. Sci. Engng 74, 85 (1985)] to explain the formation of the tongue-like extrusions was checked for 20 different grains and found not to be valid in general. R£~m6----On &udie par microscopic 61ectronique fi balayage (MEB) la morphologie superficielle du cuivre polycristallin fatigu~ ~i des temp6ratures de 107,298 et 533 K. On observe fi la fois des extrusions en forme de ruban ou de langue, sauf apr~s fatigue fi 533 K o~ des structures superficielles en forme de ruban, complexes et en forme d'aiguille sont apparentes. Par des diagrammes de canalisation ~lectronique en aire sklectionn6e en MEB, on &udie la fagon dont varie la formation de ces extrusions en forme de ruban ou de langue, en fonction de l'orientation cristallographiqe des grains dans la direction de l'axe de contrainte. Les r~sultats sugg6rent fortement que la morphologie des extrusions form6es sur les BGP ~mergentes est contr616e par le type et les facteurs de Schmid des plans de glissement activ6s. Un module proposk par Polak et coll. [Mater. Sci. Engng 74, 85 (1985)] pour expliquer la formation des extrusions eta forme de langue est test6 pour 20 grains diff6rents; on trouve que ce mod61e n'est pas valable en g6n6ral. Zm,,mmenfmtmg---Die Oberfl/ichenmorphologle von vielkristallinem Kupfer, welches bei 107, 298 und 533 K ermiidet worden war, wurde im Rasterelektronenmikroskop (REM) untersucht. AuBer bei der hohen Temperatur, bei der bandffrmige, komplexe und nadelf6rmige Oberflhchenstrukturen auftraten, wurden bei den anderen Temperaturen band- und zungenf6rmige Extrusionen beobachtet. Die Abh/inglgkeit deren Entstehung vonder kristallografischen Orientierung der jeweiligen K6rner in Richtung der Spannungsachse wurde mit Hilfe yon selected area electron channeling patterns im REM untersucht. Die Ergebnisse lassen vermuten, dab die Morphologle der Extrusionen vom Typ und vom Schmidfaktor der aktivierten Gleitsysteme abh/ingt. Ein von Pol~tk et al. [Mater. Sci. Engng 74, 85 (1985)] vorgeschlagenes Modell zur Entstehung der zungenf6rmigen Extrusionen wurde an 20 verschiedenen Kfrnern gepriift und fiir nicht allgemein zutreffend befunden.

1. INTRODUCTION In fatigued copper mono- and polycrystals two fundamentally different types of extrusions, ribbonand tongue-like extrusions, compare Fig. l(a, b) can be distinguished. The formation of extrusions due to persistent slip bands (PSB) emerging at the crystal surface [2-6] is generally accepted in literature. The dislocation structures in fatigued copper mono- and polycrystals have been widely investigated and the slip processes occurring in the walls and the channels of the PSBs are well documented [4--10]. Several models which describe the formation of extrusions and intrusions, based predominantly on the slip processes of dislocations below the crystal surface,

have been published [11-16]. None of them, however, suggests a mechanism that explains the variety of morphologies observed. A first proposal regarding the morphology of extrusions was made by Pol~k et al. [1], but it was restricted to the formation of tongue-like extrusions. The suggestions of these authors are deduced from an examination of extrusions in a fatigued copper single crystal and are based on models [8, 13, 16] which generally assume extrusions to be related closely to the deformation-induced increase of the point defect density [17, 18]. The point defects prevailing in cyclic saturation are expected to be predominantly of the vacancy-type [8, 16]. One mechanism for the production of point defects, viz. vacancies, is the

1645

1646

BAYERLEIN and MUGHRABI:

FORMATION OF EXTRUSIONS IN FATIGUED Cu the equidistant tongue-like extrusions with the emergence either of the roughly equidistant PSB walls or of the channel material between the walls at the surface [1]. The tongue distance s therefore depends on the distance d between the walls in the PSB and on the angle ~ between the primary Burgers vector and the direction of intersection of the primary slip plane with the surface and is given by [1] d COS

Fig. 1. (a) Ribbon-like extrusions, AEpl= 10-3 , T = 107 K, vacuum, number of cycles N = 50,000, SEM, secondary electrons. (b) Tongue-like extrusions, AEpl= 10-3, T = 107 K, vacuum, number of cycles N = 50,000, SEM, secondary electrons. The stress axis is horizontal. non-conservative motion of jogs on screw dislocations [19]. This mechanism probably operates in the channels of PSBs. An alternative mechanism, suggested more recently, is the collapse of very narrow edge dislocation dipoles. This mechanism has been proposed to occur predominantly in the dense edge dislocation walls of PSBs [16]. Thus, depending on the relative importance of these mechanisms, the rate of vacancy production could be highest either in the channels or in the walls. Vacancy migration in copper is known to occur at temperatures around and above room temperature [20] and the vacancies are expected to diffuse into sinks in the PSB and the surrounding matrix [16]. This results in a net flow of atoms in the opposite direction. Since the vacancies are produced continuously during cyclic deformation, their concentration will reach an equilibrium value when the rates of production and of annihilation are equal [16]. At low temperatures at which vacancies cannot diffuse out of the PSB, their concentration is expected to increase to a saturation value. In the temperature regimes considered the increasing number of vacancies causes the density in the PSB to decrease and consequently compression stresses to occur at the same time. By the extrusion of material to the surface due to slip processes these stresses can be reduced [16]. Pol~ik et al. explain the formation of

The average wall spacing d can be determined by transmission electron microscopy (TEM) and the angle ct can be calculated, if the crystallographic orientation of the surface plane and the slip system are known. Complementary to the above model, Pol~ik et al. point out in the same paper that the tongue-like extrusions could also be caused by a still unknown slip mechanism deduced from the special dislocation configuration of the PSB [1]. With regard to the ribbon-like extrusions, Pol/tk explains their formation in a later paper [2!] in a formal manner and supposes that they are formed, when the diffusion of vacancies occurs in directions perpendicular to the slip plane. The vacancies are expected to move into sinks next to the interface between PSB and matrix and to give rise to a flow of atoms in the opposite direction, causing ribbon-like extrusions or, in some cases, adjacent intrusions [1] to form along the whole PSB. On the other hand, Pol~ik's considerations leave open the question why and under which conditions tongue- and/or ribbon-like extrusions are expected to be formed. The present investigations were performed on fatigued polycrystals in order to exploit the fact that the variety of different orientations of the grains offers the possibility to investigate in a statistical sense the dependence of the extrusion morphology on the orientation. The results show that Pol~ik's model for the occurrence of tongue-like extrusions does not apply generally. Instead, the formation of either ribbon- or tongue-like extrusions appears to depend on the resolved shear stress acting in the activated slip systems. 2. EXPERIMENTAL

The specimens were machined from a bar of pure 99.99% OFHC copper (Outokumpu, Finland) with an excess of about 0.5 mm in diameter. After removing the deformed surface layer chemically, the final specimens had cylindrical ends and a gauge length of 12 mm with a square cross section of 4.0 x 4.0 mm 2. To obtain a mean grain size of 100/zm (twins not taken into account) specimens were annealed in vacuum at 893 K for 1 h. Prior to cyclic loading the specimens were polished electrochemically. The cyclic deformation was carried out in vacuum at constant temperatures of 107, 298 and 533 K.

BAYERLEIN and MUGHRABI:

FORMATION OF EXTRUSIONS IN FATIGUED Cu

A special chamber which had been built to permit experiments in one and the same gaseous environment or in vacuum at temperatures between 100 and 650 K and which is described elsewhere [22] was used. The specimens were fatigued at a constant plastic strain range A%I = 1 0 - 3 in symmetrical push-pull under plastic strain control, using a closed-loop servohydraulic testing machine (MTS 810). The strain was measured with capacitance probes. After failure, the surfaces of the specimens were examined by scanning electron microscopy (SEM), using a Cambridge 250 Mk instrument. In the present paper we confine ourselves mainly to a discussion of the surface morphology of the specimen fatigued at the lowest temperature (107K), which showed the features of interest most clearly, because the surface profile was least disturbed by irregular surface roughness. This specimen was cycled only till about 0.5% of the fatigue life in vacuum in order to avoid too excessive surface roughening. The surfaces of this specimen were investigated in detail by SEM. Photographs of 20 different grains with tongue- and another 20 different grains with ribbon-like extrusions were taken. In addition selected area electron channeling patterns (SAECPs) of each grain were photographed. It was found that the quality of the SAECPs could be improved significantly by annealing the specimen for 30 min at 413 K. The crystallographic orientation normal to the surface and parallel to the stress axis was determined with SAECPs for each grain using a computer program [23] which had been modified for our purposes. Additionally, Schmid factors for all the octahedral slip systems and the angles between the slip traces of the extrusions at the specimen surface and the stress axis for the four different slip planes were calculated. The active slip plane was determined by comparing the calculated angles with the angle measured on the photograph. The active Burgers vector was determined by assuming that it belonged to the slip system with the highest Schmid factor. Subsequently the Schmid factors of the active slip systems were compared and their mean values were calculated for all grains investigated (with either tongue- or ribbon-like extrusions). From the knowledge of the average distance d between the walls in the PSB measured in the direction of the active "'primary" Burgers vector bp, the expected distance between the tongues of the tonguelike extrusions according to Pol~tk's relation could be calculated for all hypothetically possible slip systems. The spacing d is obtained most reliably from TEM-observations of the (1 ~ 1)-plane (referred to the "primary" slip system (lll)½[i01]) which contains bp = ½[~01] and lies perpendicular to the "primary" slip plane (111). From extensive TEM investigations on specimens with a smaller mean grain size of about 40 # m (twins not taken into account), which had been fatigued under the same conditions, d was determined

1647

to 0.68 #m. The distances between the tongues of the extrusions photographed were measured and compared with the calculated values. 3. RESULTS Independent of the cycling temperature all the specimens investigated revealed ribbon-like extrusions, which were sometimes found to be superimposed by tongues. Tongue-like extrusions could only be observed on specimens fatigued at 107 and 298 K. By comparison, the specimen cycled at 533 K revealed complex surface structures and extrusions which looked like needles. With the exception of extrusions on specimens cycled at the lowest temperature (107K) the extrusions were found to grow continuously with the number of cycles, though at a decreasing growth rate. At the lowest temperature the growth ceased after the initial hardening stage (cf. [24] for more details). With increasing cycling temperature the extrusions appeared less distinct and exhibited a larger surface roughness. The results of the investigation regarding the dependence of the extrusion type on the crystallographic orientation of the grain are presented in Fig. 2, which shows the crystallographic orientation of all grains examined in the direction of the stress axis. The subtriangles characterize the regions in which different secondary slip systems are dominant (compare legend to Fig. 2). A significant difference in the orientation of grains revealing either tongue- or ribbon-like extrusions is apparent. Grains with orientations localized in the subtriangle I of the standard orientation triangle reveal preferentially tongue-like extrusions. By contrast, all grains showing ribbon111

001 • Tongue-like extrusions

011

A Ribbon-like extrusions • Orientotion used by Pol6k et oi.[I] [] Orientotion used by Basinski ond Basinskil25]

Fig. 2. Crystallographic orientations in direction of the stress axis of the investigated grains. In the regions I, II and III the dominant secondary glide systems are the I coplanar glide system (I11)~[I10], the conjugate glide syst tem (rI1)~[011] and (II 1)51 [101]. The notation refers to the primary glide system (lll)~[I01]. The solid and open squares denote the orientations used by Polhk et al. [1] and Basinski and Basinski [25], respectively.

1648

BAYERLEIN and MUGHRABI:

FORMATION OF EXTRUSIONS IN FATIGUED Cu

like extrusions have orientations which are localized without exception outside that subtriangle I. The activated "primary" slip systems of the grains with ribbon-like extrusions, as concluded from the PSBs observed, were found to have a very high Schmid factor with an average value Sr = 0.485. By contrast, the average value St = 0.446 for the grains with tongue-like extrusions is much lower. In the case of tongue-like extrusions the slip system with the second largest Schmid factor was nearly always found to be coplanar with the active slip system, otherwise the difference between the Schmid factor of the most highly stressed coplanar slip system and the Schmid factor of the next highly stressed slip system was only small. The difference between the average Schmid factor of the active systems and the average Schmid factor of the coplanar slip systems was determined to ASc.t = 0.085. Referring to the ribbon-like extrusions, all coplanar slip systems were found to have unfavourably low Schmid factors. For the ribbon-like extrusions, the difference between the average Schmid factor of the active "primary" slip systems and the average Schmid factor of the coplanar slip systems was determined to ASc,f = 0.175. The preferential occurrence of coplanar slip in grains with tongue-like extrusions is also evident from the distribution of the orientations in Fig. 2. In the subtriangle I which contains most of the orientations favouring tongue-like extrusions the dominant secondary slip system is coplanar with the "primary" slip system [23]. The spacings between the tongues calculated with Polfik's relation for all grains that revealed tonguelike extrusions vary from 0.8/~m to 3.8 tim. In one case, a spacing of about 70/~m was also obtained, compare Fig. 3. On the other hand, the average spacings measured are quite different. They vary from 2.8 to 6.2 #m (Fig. 4) and are thus much wider than the calculated spacings. Average spacings of about 17#m were also found in one case. The frequency distribution, Fig. 4, shows that more than 80% of the average spacings measured lie between 2.8 and 4.8#m, whereas the maximum frequency for the calculated values is at about 1/~m, compare Fig. 3. The

50.0 m 400

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200 10.0 00

I

I

Iii

,,,I

10 I

,

m

,,,I

100

'

'

',1111

101

102

Measured tongue spacing [IJm] Fig. 4. Frequency distribution of the averaged tongue spacings measured between tongues of tongue-like extrusions. measured and the calculated values for each grain were compared by determining the quotient Q measured tongue spacing Q = calculated tongue spacing' The measured and the calculated values coincide only in a few cases, hence values of Q of about 1 are very rare, as shown in Fig. 5. Considering all possible errors, Q ought to vary only between 0.5 and 2. However the relative frequency of occurrence of extrusions with Q lying in this range is only about 25%. Ribbon-like extrusions were often observed to extend across the whole grain. Based on Pol~ik's proposal for the formation of tongue-like extrusions, such ribbon-like extrusions could appear if the "primary" Burgers vector, active in the PSBs emerging at the surface, is nearly parallel to the surface. The tongue spacings would then be very wide, so that the tongues could appear as ribbons. This would be supported by the fact that the height of the tongues seemed to decrease with increasing tongue spacing. This possibility was checked by calculating the tongue spacings with Pol~tk's relation for all the grains revealing ribbon-like extrusions. The extension of the ribbon-like extrusions was finally compared with the calculated tongue-spacings for all grains and a quotient Q* was determined Q*= measured extension of the ribbon-like extrusion calculated tongue spacing

50.0

25.0

400

200

" 300

, ~'~

20.0

15,0

.m

LL

0"

100

JL

10.0

u

00

.i 10-1

i ill

iiiii 100

i 101

i .... 102

CaLculated tongue spacing [ I~rnl Fig. 3. Frequency distribution.ofthe mean spacings between tongues of tongue-like extrusions calculated with Pol~ik's relation for the grains that revealed tongue-like extrusions.

00

i

10-1

i

I Irl

'

100

iiI

101

|

,

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0 Fig. 5. Frequency distribution of the quotients Q (measured spacing/calculated spacing) of the tongue-like extrusions.

BAYERLEIN and MUGHRABI:

FORMATION OF EXTRUSIONS IN FATIGUED Cu

30.0

~o >, 0 E

200

0"

100

U_ F

....

l,,

...... 10:

ii ,,lJ

........

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Fig. 6. Frequency distribution of the quotients Q* (measured extension/calculated tongue spacing) of the ribbon-like extrusions.

The results are presented in Fig. 6. There is no correspondence between the calculated and the measured values.

4. DISCUSSION Contrary to Pol~ik who had deduced his model from an investigation on a single crystal, all our investigations were performed on polycrystals. This had the advantage that a variety of grains with different orientations was available for a statistical investigation, whilst the experimental effort was still reasonable. The examination of the surface morphology of specimens fatigued at the different temperatures proved that the ribbon-like extrusions form in the whole temperature range investigated. However, tongue-like extrusions could not be observed at the higher temperature of 533 K at which PSBs are not as frequent as at lower temperatures. This is in contrast to the observations of Basinski and Basinski [25] on copper single crystals fatigued at different temperatures between 4.2 and 350 K. These authors found ribbon-like extrusions to appear at temperatures lower than room temperature and exclusively tongue-like extrusions at higher temperatures. They assumed the formation of the latter to be due to a temperature effect, which could cause thermally activated recovery mechanisms to enter into the total fatigue process [25]. The fact that extrusions stop growing at low temperatures after initial hardening has ceased is in agreement with the predictions of the EGM-model [16]. Growth is expected to cease when the density of vacancies has reached saturation. At temperatures at which vacancies are mobile, the EGM-model predicts the extrusions to grow continuously, as was indeed observed at the higher temperatures [24]. Referring to the shape of the extrusions, they appeared to be more smooth and distinct the lower the cycling temperature was. The surface roughness had been shown to be caused by the irreversibility of slip in the PSBs [26, 27]. Consequently irreversible slip can be assumed to occur to a smaller extent the lower cycling temperature is. A M 39/7--R

1649

The results of the investigation on the dependence of the extrusion type on the crystallographic orientation of the grain allow the conclusion that the formation of either ribbon- or tongue-like extrusions is correlated with the slip systems favoured in terms of the resolved shear stress rather than with the temperature. The circumstance that the average Schmid factor of the grains with tongue-like extrusions is clearly smaller than the corresponding value for the ribbon-like extrusions together with the fact that coplanar slip is much easier in the grains with tongue-like extrusions lead to the conclusion that the formation of tongue-like extrusions is obviously connected with coplanar slip. Vice versa the formation of ribbon-like extrusions seems to be due to single slip, also because slip traces due to secondary slip were not prominent. Other indications concerning the occurrence of coplanar slip in PSBs are inferred from the observations of Laufer and Roberts [7] and Luk/t~ et al. [6] who identified annealed cell walls in PSBs as twist boundaries which must have been formed by coplanar slip. However this cell boundary type was found only rarely. The observations of Pol~ik et al. [1] and Basinski and Basinski [25], who both found ribbon- and tongue-like extrusions on their single crystals, are consistent with our assumption. The orientations of their single crystals are localized near and on the border between the regions in the standard orientation triangle in which ribbon- and tongue-like extrusions dominate, respectively, compare Fig. 2. Thus both types of extrusions can be expected to develop. Pol~k's model could not be verified and is concluded not to be valid in general. The tongue spacings calculated with Polfik's relation [1] coincided only with about 25% of the measured values, as shown in Fig. 5. The peak in the frequency distributions of the calculated spacings is shifted against the peak in the frequency distribution of the measured values by a factor of about 3, cf. Figs 3 and 4. Additionally it was checked whether the formation of ribbonlike extrusions occurs by the same mechanism which Pol~ik had proposed for the tongue-like extrusions. The ribbons might be thought of as tongues with a wide tongue spacing. It was found that the formation of ribbons cannot be explained with Pol~ik's mechanism that describes the formation of tongues (Fig. 6). Further indications that the spacings of tongue-like extrusions are not related to the dislocation wall spacings in PSBs are as follows: (1) in a study on fatigued copper polycrystals, Tbnnessen [28] failed to observe the relationship proposed by Poi~ik; (2) in fatigued or-iron single crystals (with 30 wt ppm carbon) PSBs are observed that do not possess the wall (ladder) structure. Nonetheless, the extrusions are predominantly tongue-like [9]. In conclusion, our observations on fatigued copper polycrystals cannot be explained, using Pohik's model which is based on observations on a fatigued

1650

BAYERLEIN and MUGHRABI:

FORMATION OF EXTRUSIONS IN FATIGUED Cu

copper single crystal. The results presented suggest strongly that the morphology of extrusions formed at emerging PSBs is controlled by the type and the Schmid factors of the activated slip systems. Finally, we remark that caution is in place with respect to the validity of our conclusions concerning the formation of extrusions in single crystals. Since our study was performed on polycrystals, these conclusions are justified only under the condition that the basic mechanism of formation of extrusions in polycrystals does not differ fundamentally from that in single crystals. To date, there is no such indication. The major difference appears to be that the extrusion heights are smaller in polycrystals [16, 24] and that the activation of glide systems in individual grains of a polycrystal are not governed exclusively by the applied stress but also by the internal constraints due to neighbouring grains [10]. 5. CONCLUSIONS 1. Ribbon-like extrusions were found to be formed in copper polycrystals after cyclic deformation at temperatures of 107, 298 and 533 K. 2. Tongue-like extrusions were also observed except on the specimen cycled at 533 K. 3. The surface profile of the extrusions appeared more disturbed by irregular surface roughness the higher the fatigue temperature was. 4. The extrusions were found to grow continuously with the number of cycles at 298 and 473 K, with the growth rate decreasing with the number of cycles. 5. Extrusion growth at 107K ceased after the initial hardening. The dependence of extrusion growth on the temperature coincides with the predictions of the EGM-model. 6. The formation of tongue-like extrusions appears to be connected with favoured coplanar slip in the PSB. 7. The formation of ribbon-like extrusions is favoured when slip occurs on only one "primary" slip system. 8. Pol/tk's model which assumes the formation of tongue-like extrusions to be due to the emergence of either the walls or the channels of a PSB at the surface was found not to be valid in general. Acknowledgements--The support of our work by the

Deutsche Forschungsgemeinschaft (DFG Mu 502/2) is gratefully acknowledged. The authors would also like to thank Outokumpu Finland for supplying the copper free of charge.

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