Factors influencing the spacings between dipolar walls in cyclic deformation

Scripta METALLURGICA

Vol. 20, pp. 1661-1666, 1986 Printed in the U.S.A.

Pergamon Journals Ltd. All rights reserved

FACTORS INFLUENCING THE SPACINGS BETWEEN DIPOLAR WALLS IN CYCLIC DEFORMATION J. I. Dickson, G. L'Esp~rance and S. Turenne D~parte~ent de g~nie m~tallurgique Ecole Polytechni que C.P. 6079, Succ. "A" Montreal, Quebec, Canada, H3C 3A7 (Received June 20, 1986) (Revised September 16, 1986)

Introduction The spacings between dipolar walls and loop patches in dislocation substructures produced by cyclic deformation of f.c.c, metals are known to depend on the type of dipolar dislocation structures. The largest interwall spacings found are for the {110} walls of the ladder-like dislocation structure within persistent slip bands (i-4). A wall spacing smaller than that between {110} ladder-like walls in persistent slip bands can be found for labyrinth walls (5-10) and for dipolar walls observed in [111] ~ I t i s l i p axis crystals (11,12). As well, the spacings between the walls observed by transmission electron microscopy will be smaller than the true spacings in the case of walls which are not parallel to the beam direction employed in the transmission electron microscopy observations. The correct measurement of spacings between dipolar dislocation structures therefore also depends on identifying properly the orientations of the wall and taking into account both the foil thickness and the angle that the electron beam direction employed makes with the wall or preferably by observing the wall spacing with this angle equal to zero. Reasonable success has been obtained recently (10,13-16) in explaining the orientations and the three-dimensional shape of the dipolar dislocation structures produced in fatigue by considering these dislocation structures as regular stacking networks of dipole loops of the type produced by jog-dragging or edge-trapping mechanisms, with long loop segments on one or two slip systems. One manner in which these considerations can be extended to more than two slip systems is by assuming composite walls consisting of segments, each of which contains dipole loops of one or two slip systems (10,13,14). Figure 1 schematizes the dipolar dislocation configurations in the geometrical model considered by Dickson et al (13,14) for the case of two orientations of loops ( i . e . , long segments belonging to two slip systems). The stacking or effective stacking directions for the dipole loops are perpendicular to the plane containing both orientations of long loop segments, and parallel to directions a and b bisecting the acute and obtuse angles, respectively, between long loop segments. Limited stacking in one of these three directions results in a wall perpendicular to that direction; strong preferential stacking in one direction results in a loop patch elongated in that direction (16). Comparison (10,13-15) of the predictions of this geometrical model with the experimental observations indicates the absence of walls perpendicular to direction a of Figure 1. This result suggests that preferential stacking of dipole loops occurs in this direction. Such preferential stacking also appears to provide a reasonable explanation for the elongation direction of veins or loop patches (16). This preferential stacking can be explained as being mechanistically favoured by the dipole loops being swept into the walls or loop patches by the glide of edge dislocations on the same slip planes as the long segments of the dipole loops. 1661 0036-9748/86 $3.00 + .00 Copyright (c) 1986 Pergamon Journals Ltd.

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b

~

~

~

~

~

~

~

~

~

~

~

I/-~-~

three-dimensional stacking arrangement which can be envisaged for dipole loops of two slip systems, as seen in the plane containing the directions parallel to both orientations of long loops segments. One loop stacking direction is normal to this plane; the other two effective stacking indicateddirecti°ns aareandparallelb, to the directions

o

I t has further been suggested (14) that the tendency for a particular wall to form depend on the angle(s) at which the dipole loops are swept into the walls. The dislocation sweeping angle can be measured as the complement of the angle between the Burgers vector and the direction normal to the wall. A large dislocation sweeping angle (i.e., close to 90°) should favour the occurrence of that wall; a small angle (i.e., close to 0°) should result in that wall being mechanistical ly improbable. Relationship for the Wall Spacin~ This portrait of dipolar walls suggests that the manner in which a wall is initially formed is by the edge dislocations which sweep the dipole loops dumping these loops each time that they stop and reverse their cyclic motion. The dipole loops accumulate at these sites, where they are then stacked into a regular network, giving rise to loop patches or wells. A major factor determining the spacing between walls should be the sweeping distance ds of the edge dislocations. The wall spacing W R (defined more precisely as the width of the channels between walls) resulting from a given valu) of ds Will depend on the dislocation sweeping angle, ~, through a simple geometrical relationship,

W s = ds sin ~.

(1)

Once the walls have formed, one manner in which the dependence of W~ on dR can be expected to be maintained is as follows: The glide of the screw dislocations "threacFing the channels between walls produces dipole loops by a jog-dragglng mechanism, combined with crosssllp and mutual annihilation. The dipole loops thus formed are then swept across the channels by edge dislocations, which bow out of the dipolar walls, in the manner observed by Grosskreutz and Mughrabi (I). This portrait of the formation and sweeping of the dipole loops also would be consistent with the suggestion of Buchinger, Stanzl and Laird (17) that the formation of dipole loops by a jog-dragging mechanism increases in relative importance as the cycling proceeds. Equation 1 indicates that, in the case of a dislocation sweeping angle of O0°, the wall spacing is equal to d+~.~ In the case of a dislocation sweeping angle of 0°, W. is equal to zero, further indicating ~,,~t the occurrence of walls involving a small dislocation sweeping angle is mechanistically improbable.

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The type of roll orientations which can be predicted in f.c.c, crystals depending on the slip systems involved are indicated in Table I (14) along with the associated dislocation sweeping angles. The only wall which involves a dislocation sweeping angle of go ° and thus results in an interwall spacing equal to d s is the {II0} wall perpendicular to the primary Burgers vector. This wall orientation is predlcted for single slip or for combined primary slip and cross-slip. The question then arises as to whether d~ varies significantly with ¢ or not. It can first be noted that, if the initial value of d: determines the site at which a wall starts forming, the growth of the wall in thickness can be expected to decrease de. The size of this decrease should then depend on the tightness of the stacking. This tightness in turn should depend on ¢, since a low angle of ¢ should make tight stacking difficult to achieve. This influence of , on the tightness of the stacking can be related to the result that the appearance of the persistent slip bands is usually accompanied by the first appearance of condensed walls. The {ii0} walls in the persistent slip bands are generally condensed, while the matrix or vein structure remains a loose uncondensed structure. This transition from the matrix structure to the persistent slip band structure, which contains walls perpendicular to the primary Burgers vector, has been shown (17,18) to be associated with a decrease in the amount of secondary slip and with the occurrence of slip involving only a single Burgers vector in the persistent slip bands. The increase in the relative number of dipole loops whose long segments belong to the primary system in the walls should also facilitate tight stacking. It has also been shown (14) that the traces of the channels in the matrix structure in published electron micrographs for single crystals oriented for single slip is in reasonable agreement with the wall orientations which can be predicted for different combinations of pairs of slip systems involving the primary Burgers vector and one of the more probable secondary Burgers vector. This suggests a significant amount of secondary slip activity in the matrix structure, even in the case of single crystals oriented for single slip. With this explanation, the dislocation sweeping angles for the Burgers vectors with respect to the matrix loop patches is thus 60 ° or less (see Table i), in cases where the two values of ~ are equal, and the average angle is less than 60 ° in cases where the two values of ¢ differ. This possible influence of the value of ¢ on the tightness of the stacking can be expected to cause W. to decrease with , more rapidly than predicted by treating ds as a constant in equation i. C~ndensed dipolar walls of orientations other than the {Ii0} perpendicular to the primary Burgers vectors have been shown (5,7,g,i0,II,12,15) to form, which indicates that increasing the strain or stress amplitude results in condensation of the walls even for dislocation sweeping angles less than 90 °. This suggests that another factor contributing to the first appearance of condensed walls within the persistent slip bands is the increased plastic strain amplitude within these bands. The value of dr can also be expected to be influenced by the density of dislocations intersected by the edge aislocatlons sweeping the dipole loops. As already mentioned, truly single slip (combined or not with cross-slip) should result (14) in a dislocation sweeping angle of g0 ° and in [ii0} walls perpendicular to the active Burgers vectors. A dislocation sweeping angle of less than 90 ° should be associated with glide activity of two or more Burgers vectors, with resulting dislocation intersections tending to decrease d s. Thus, based on these arguments, Ws, the spacing between dipolar walls or loop patches should be described by equation i, with the value of ds tending to be less at lower angles of ¢ than it is at 90 ° . Comparison with Published Observations A large number of electron micrographs of dipolar dislocation structures produced by cyclic deformation have been previously published, particularly for f.c.c, copper. In a number of these observations, the active Burgers vectors are known or can be inferred, the wall orientations have been identified with good or reasonably good reliability and the walls have been observed with electron beam directions almost parallel to the wall orientations, making the observed values of W, almost equal to the true values. Available data for copper single or polycrystals tested ai~ room temperature are compared with equation I in Figure 2, by assuming that the value of d s in this equation is 1.5 ~m, the usually accepted (1-4) value of W s for

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{II0) walls within ladder-like persistent slip bands. A value of W~ -0.55 pm is obtained for the {i00} labyrinth-llke Walls observed by Jin and Winter (7) for ~their [001] multislip axis single c~stals. In their observations, the value of Ws between uncondensed {i00} walls appears only slightly smaller (, 0.5 ~) than that between condensed Walls and these uncondensed Walls appear to have a condensed outer shell. The dislocation sweeping angles for these Walls is 45 °. A similar value of W~ - 0.55 ~m is obtained for the labyrinth Walls observed in polycrystalline copper by Winter et al (6), which Walls could have either {I00} or (210} or intermediate orientatlons (8,10). For the (210} labyrinth Walls presented by Ackermann et al (8) in their Figure 7, the typical value of W~ between uncondensed walls appears to be Wc -0.7 pro. Close to the persistent slip bands in t~is figure, some more condensed walls of similar orientation appear present with W s - o.g ~m. For this wall orientation, the value of ~ is 39.2 ° . The walls approximately perpendicular to the [III] deformation axis observed by Leplsto (11,12) can be explained (14) as composite (113) walls. The value of ¢ is therefore taken as 60 ° and Ws - 0.45

The traces of the veins observed by Jin and Winter (Ig) in their Figure 3 for a [I12] duplex slip axis crystal agree (13,14) quite well with the predicted (I13) and (Ii0) orientations for the expected duplex slip systems. In these observations W~ , 0.65 ~m for the (113) veins and Ws -0.25 ~ for the thin channels between the (II0) veins. -The respective angles of ¢ are 59.5 and 30 °. In the same micrograph, condensed walls of apparently similar orientations appear in the immediate vicinity of the persistent slip band intersection sites, with variable values of Ws( 1.2 pm for the (113) walls. It can be noted that the narrowness of the condensed walls Which agree with (113) and (Ii0) traces at these sites in fact support these identifications of the wall orientations, both of Which are almost parallel to the [ITI] beam direction. This upper value of 1.2 pm is also plotted in_Figure 2 to give an idea of the maximum value of W~ experimentally observed for condensed (113) walls. This value is seen to approach that e~pected for a dislocation sweeping distance of 1.5 pro. These observations of Jin and Winter (Ig) as Well as those of Ackermann et al (8) suggest that W~ can increase as the tightness of the loop stacking increases, although such an effect was not'clearly indicated by the observations of Jin and Winter (7) on {I00} walls. The experimental data plotted in Figure 2 show that Wc for values of ~
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TABLE 1 Summary of Possible Wall Orientations and Corresponding Dislocation Sweeping Angles for Different Pairs of Slip System Combinations, F.C.C. Metals (14) BV 1 SP 1

BV 2

SP 2

WA

WB

WC

Dislocation Sweeping Angles (in degrees) ¢I ¢2 61 62 71 72

(Perpendicular pair of Burgers vectors) [101] (111) [101] ( ~ 1 1 ) ( 0 2 1 ) ( i 0 0 ) ( 0 1 2 )

18.4

1 8 . 4 4 5 . 0 4 5 . 0 3 9 . 2 39.2

[~01] (1~i) [101] ( 1 1 1 ) ( 0 2 1 ) ( 1 0 0 ) ( 0 1 2 )

18.4

1 8 . 4 4 5 . 0 4 5 . 0 3 9 . 2 39.2

[~01] (111) [101] (~11) (~20) (001) (210)

18.4

1 8 . 4 4 5 . 0 4 5 . 0 3 9 . 2 39.2

[101] (1~I) [101] (111) (120)(001)(210)

18.4

1 8 . 4 4 5 . 0 4 5 . 0 3 9 . 2 39.2

(Non-perpendicular pair of Burgers vectors) [101] (1~1) [011] ( 1 1 1 ) ( 1 1 0 ) ( 1 1 2 ) ( 1 1 1 )

30.0

3 0 . 0 6 0 . 0 60.0

[~01] (111) [011] (~11) (312) (130)(315)

10.9

3 4 . 5 1 2 . 9 4 2 . 1 7 3 . 0 28.6

[101] (111) [011] ( 1 1 1 ) ( 3 3 2 ) ( 1 1 0 ) ( ~ 1 3 )

8.7

[~01] (111) [011] ( 1 ~ 1 ) ( 1 3 2 ) ( 3 1 0 ) ( 1 3 5 )

34.5

(Single Burgers vector, 2 slip planes) [~01] (111) [iOl] (111) (010)(i01)

8.7

0

0

3 0 . 0 3 0 . 0 5 9 . 5 59.5

1 0 . 9 4 2 . 1 1 2 . 9 2 8 . 6 73.0

(~01)

0

0

0

0

90

90

(Single Burgers vector, 1 slip plane) [iOl] (111) . . . . . . (121) (111) (~01)

0

---

0

---

90

---

BV: Burgers vector ; SP: Slip plane ; W: Wall ¢I, ¢2; Pl, 62; and yl, y2: Dislocation sweeping angles for Walls A, B and C, respectively

[ "sl

f

I

L _ ~ m.o

l |

i°~-

,,~///o

,

~

,,yo " "://0

, "

L /-o°o o 20

40

6O

1.5

:_'

°"/ /

0

_

~

Fig. 2. Interwall spacings, W c, taken from literature observations (s~e text for details) on copper, plotted versus the dislocation sweeping angle ~ and compared with equation 1 with ds taken as equal to

I00

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Acknowled~Iments Financial support for this research from the FCAR (Quebec) and NSERC(Canada) programs is gratefully acknowledged. The authors are grateful to ~ s . Louise Bisson for typing the manuscript.

References 1.

J.C. Grosskreutz and H. Mughrabi, in Constitutive Equations in P l a s t i c i t y , ed. A. Argon, p. 251, MIT Press (1975). 2. H. Mughrabi, F. Pckermann and K. Herz, Fatigue Mechanisms, ASTM STP 675, p. 69, ASTM Philadelphia (1979). 3. P. Neumann, Physical Metallurgy (3rd Edition), Part 2, p. 1553, North-Holland Physics Publishing, Amsterdam (1983). 4. T. Megnin, J. Driver, J. L~pinoux and L.P. Kubin, Revue Phys. Appl., 19, 483 (1984). 5. P. Charsley, Mater. Sci. Eng., 47, 181 (1981). 6. A.T. Winter, O.B. Pedersen and K.V. Rasmussen, Acta metall., 29, 736 (1981). 7. N.Y. Jin and A.T. Winter, Acta metall., 27, 1173 (1984). 8. F. Ackermann, L.P. Kubin, J. L~pinoux and H. Mughrabi, Acta metall., 32, 715 (1984). g. L. Boulanger, A. Bisson and A.A. Tavassoli, Phil. Mag. A, 51, L5 (1985). 10. G. L'Esp~rance, J.B. Vogt and J . I . Oickson, Mater. Sci. Eng., 79, 141 (1986). 11. T. Lepisto, V. T. Kuokkala and P. Kettunen, Scripta metall., 18, 245 (1984). 12. T.K. Lepisto, V.T. Kuokkala and P.O. Kettunen, Mater. Sci. Eng., 81, 457 (1986). 13. J.I. Dickson, J. Boutin and G. L'Esp~rance, Acta metall., 34, 1505 (1986) 14. J.I. Dickson, L. llandfield and G. L'Esp~rance, Mater. Sci. Eng., 81, 477 i1986). 15. G. L'Esp~rance, J.B. Vogt and J.I. Dickson, in Strength of Metals and Alloys, vol. 2, p. 1423, Pergamon Press, Oxford 1985. 16. J.I. Dickson, L. Handfield, S. Turenne and G. L'Esp~rance, submitted to Mater. Sci. Eng. 17. L. Buchinger, S. Stanzl and C. Laird, Phil. Mag. A, 50, 275 (1984). 18. T. Tabata, H. Fujita, M. Hiraoka and K. Onishi, Phil. Mag. A, 47, 841 (1983). 19. N.Y. Jin and A.T. Winter, Acta metall., 32, 989 (1984). 20. P. Charsley and D. Kuhlmann-Wilsdorf, Phil. Mag. A., 44, 1351 (1981). 21. S.J. Basinski, Z.S. Basinski and A. Howie, Phil. Mag., 19, 899 (1969).