On the formation of deformation bands in fatigued copper single crystal with double slip

Pergamon

ScriptaMetallurgicaet Materialia,Vol. 31, No. 12, pp. 1729-1734, 1994 Copyright©1994ElsevierScienceLtd Printed in the USA. All rights reserved 0956-716X/94 $6.00 + 00

ON T H E F O R M A T I O N O F D E F O R M A T I O N B A N D S IN F A T I G U E D C O P P E R S I N G L E C R Y S T A L W I T H D O U B L E SLIP Shouxin Li, Bo Gong and Zhongguang Wang State Key Laboratory for Fatigue and Fracture of Materials, Institute of Metal Research, Shenyang 1100l 5, China

(Received May 5, 1994) (Revised July 25, 1994) Introduction Cyclic deformation of a copper single crystal oriented for single slip has been intensively studied in the last twenty years for understanding of the fatigue deformation mechansim of [.c.c. metals. However, the deformation of the copper single crystal oriented for multiple slip has not been studied much[I,2]. Among the many features of cyclic deformation of the copper single crystal, probably the occurrence of deformation bands(DBs) is the least understood. An earlier work[3] on the occurrence of DBs in f.c.c, crystals pointed out two types of bands formed in the monotonicaly tensile deformation. One is kink bands, which is normal to the operative slip plane and slip direction. The other is identified as the band of secondary slip, which is almost parallel to the primary slip plane. Though much work has been done on DBs in general, the number of investigations reported in the literature on the deformation band(DB) phenomenon in the context of the fatigue of metals remains small. It should be borne in mind that fatigue crack nucleation is primarily a surface-related effect and the formation of DB could influence not only the process of initiation of fatigue cracks but also their subsequent direction of propagation. Much more attention should be paid to the occurrence of the DBs due to the detrimental effects on the mechanical behaviour of the crystals. Gostelow[4] and Mughrabi[5] observed DBs similar to the kink band in copper single crystals of single slip cycled at a high strain amplitude; Mughrabi attributed this to the relaxation or long range of the internal stress. Saletore and Taggart[6] reported two sets of DBs formed on the 45 ° plane of maximum shear in the [122] copper single crystal under cyclic deformation. They conclude that both the orientation and macroscopic state of stress are responsible for the formation of these bands. Recently, Gong et al.[7] conducted an experiment which revealed that the occurrence of DBs is a general phenomenon in copper single crystals oriented for double slip under cyclic deformation. In the present paper, as a first effort, a simple model was proposed to account for the occurrence of DBs in the copper single crystals oriented for double slip under cyclic deformation. Experimental and results Copper single crystals were grown from O F H C copper of 99.999% purity on CRYSTALLOX MCGS3. Czochralski method was employed with a pulling rate of 40ram / h. The single crystal bars with axes of [034] and [117] orientations were 100~ 150 mm long and 20~ 30 mm in diameter. The orientations are also shown in a crystallographic triangle (Fig.l). The specimens were carefully spark machined from each crystal with a tensile axis parallel to that of the crystal. The size of the specimens was 7 × 5 × 16ram in gauge section. The orientations of specimens were checked by Laue back-reflection technique. Before a fatigue test, the specimens were annealed at 800"C for 1 hr, and carefully electro-polished to ensure that a strain-free and smooth surface layer was obtained on the four sides of the gauge section. Cyclic deformation tests were performed on a Schenck servo-hydraulic testing machine at room temperature in air by a constant plastic strain amplitude ('~p,). A triangle wavelbrm was used with a frequency of 0.2 Hz. The surface of specimens was examined by optical and scan-

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DEFORMATIONBANDSIN Cu

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ning electron microscopy. For [034] crystal,at 7pi< 1.7 x 10-3, primary slipis predominant and secondary slipappears only in some regions near the edges of the specimens, occupying a small fraction of the gauge area. The persistent slip bands(PSBs) of secondary slipare usually very fine with larger spacings betwccn them. While at ,/pt>1.7 × 10-3, sccondary slipbccomcs pronounced, then two types of macro-deformation bands which are denoted as D B I and D B II appear on the four sidesof the specimens(Fig.2). The D B I is almost parallelto primary PSBs on each side of the specimens, and D B II make a certain angle with primary PSBs(see Table I). The changes of surfacc morphologics with the ~l for the [I17] crystal arc similar to those for [034] crystal. Howcvcr, many tiny slipbands collcctcd as stripe which longitudinal direction is parallelto [117] appcar on thc surfaccs of the spccimcn (Fig.3).At ypt> 1.3 x 10-3, two sets of deformation bands also form on the four sides of the crystal.It is noted that D B I does not develop along the primary PSBs and the habit plane of D B I makes about 9 * with the primary plane. Figure 4 schematically illustratesthe surface orientations of the fatigue specimens, favoured slip planes and the deformation band tracesfor [I17],[034] and [122] [6]crystals. A model Rcccnt thcorics of shear banding in mctallic materials can bc divided into two groups. Dillamore ct al.[8], Canova ct al.[9]and Ycung and Duggan[10] have considcred crystallographic modcls which require geometrical softening to explain shear banding. In these theories,a wcU established texture is nccessary if shear band anglcs arc to deviate from the plane of m a x i m u m resolved shear stress.The second group have applied continuum analysisto the shear band problem using differentconstitutiveequations. To our knowledge, no theory has bccn made to account for the formation of D B s in the copper singlecrystals under cyclic loading. Since the mechanisms of formation of D B s in cyclic loading are so complicated, as a firstcffort,only an clcmcntary and simple modcl was proposed here to search the physics insight. The theory presented hcre suggcsts that D B s form in a catastrophic yield-likemanner. Based on thc instabilitycritcriada / d~.0, Dillamorc ct al.[8]have dcrivcd the gcneral instabilitycondition 1 d~r 1 md~. l~n+mdM m d N <~0 (1) wherc N is mobile dislocation density, m, strain rate sensitivity,n, work hardening coefficientand M , Taylor factor. They suggestcd that shcar bands formcd in rolling should be rclated to (l / M ) ( d M / d~). This term corresponds to gcomctrical softening such that instabilityis favoured ifitcauscs a latticerotation into a geometrically softcrorientation. Since the dcformation in cyclic loading is not as large as in rolling,the geometrical softening may not play a major role in the prcscnt modcl. Also the strainrate in fatigue testingdoes not change much, then wc have N ~<0 ~1 d~ =~1 - ~m da-T. (2) Following Lee and Duggan's theory[11], the last term in cq.(2) will be considcrcd in detail. During cyclic deformation, the persistent slip bands(PSBs) are well developed along the primary slip plane (111). When the secondary slip system operates, the slip system which intercepts with the primary PSBs cannot operate easily and their dislocations must pile up against the PSB boundaries. This is particularly true for [117] crystal due to strong interaction o f L o m e r - C o t t r e l l Lock formation(Table 1). As a potential DB at an angle B (Fig.5) operates these pile up dislocations are freed(dislocation avalanche). The density of dislocations treed is given by

N

d N = ---&"sinfl lw where Np is the number of dislocations in the pile up, t, shear band thickness and the strain is given by d~--- S ~,

(3) (4)

where 7, and S, are the shear strain and Schmid factor of the secondary slip system, respectively. The shear strain can be approximately written as Npbsin[3 (5)

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DEFORMATIONBANDSIN Cu

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where ~ is the angle between the secondary slip plane and D B I I (Fig.5), and b is the Burgers vector. Putting eq.(5) into eq.(3) gives 75 dN = ~w Sin(/3 + ~,)

(6)

Substituting eqs.(4) and (6) into the last term in eq.(2), we have m dN m sin(/J + ~,)

N da = N b w

S

(7)

The dislocation avalanche factor [11]

sin(/3 + ~,) A

Since sin{, = IKoon written as

x

A

S$

sin~cos{, + cos~sing~ , =

(8)

S

g I,cos{, = h v , n • K ,sin[3 = [ £ x ff~,n I and cos[3 = L-- h o n n , the eq.(8) can be ~

DBD

S

a

(9)

where L and f f are unit vectors of loading axis and the normal of secondary slip plane, respectively. In eq.(9), L-, K

and S, are already known, Ko# n , the normal of DBTI could be found by solving the eq.(2). F o r iT17]

crystal, L---- ~ 5 1 [i171,

~ =~

tii1}, the critical acumulative shear strain ~/c for formation of DBs are 217],

and Ec=S,pc, S,=0.448, m = 0 . 1 [ l l ] , w = 4 m m , b = 0 . 2 5 n m , N = l . 3 x l 0 1 t m -2 then the Kon n can be found as [0 -0.6

0.80] which isclose to [-0.01

F o r [034] crystal, L-=

_

-0.63 1

[034], n = 7 [ ' [ 1 1 ] ,

0.77] determined by the experiment(Table 1). "~c =4[7], S,=0.457 and if other data are same as above, the

~°an cannot be found correctly. But if a higher mobile dislocation density o l ' N = 3.0xl0nm -2 is used, the h - ~ n can be found as [-0.6 -0.2 0.77] which is close to [-0.59 -0.21 0.78] determined by the experiment. Since the dislocation reaction in [034] crystal is not so strong, the higher mobile dislocation density could be reasonable. As mentioned above, many tiny slip bands appeared on the surface of the [~17] crystal. It could be modeled as following. The PSBs consist of dense primary edge dipoles. Using careful microscopy, Antonopoulos et a1.[12,13] determined that the vacancy type arc about 2 / 3 and the interstitial type about 1 / 3 of the dipoles. Although the PSBs consist of complex dislocation configurations, such as walls and screw segments[14], for simplicity, it could be successfully modeled as two parallel layers of dislocation dipoles[15,16,17]. At first, the PSBs along the primary slip plane are well formed during cyclic deformation, then the PSBs on secondary slip plane are developed. At the beginning, when an arrary of dislocations m o v e on secondary slip plane Sl(Fig.6), it will meet vacancy type P S B at A, the Lomer-Cottrell lock forms and the dislocations pile up there, but when it meets interstitial type P S B at B, the pile up connot exist duc to dislocation anihilation. As rcversc loading, the dislocations on secondary slip plane S 2 will pilc up at B' of vacancy type P S B and not at A' of intcrstitialtype PSB. The dislocations on S l and S 2 could develop as a vacancy type of PSB. F r o m the above analysis, w c m a y say that if a vacancy type P S B meets the same type P S B it will form a pile up and hardening the nearby region of the interception; conversely, if it meets the opposite type PSB, it does not result in pile up and softening the interception area. S a m e argument is available for the interstitialtype of PSB. Since the PSBs consist of 2 / 3 as vacancy type and I / 3 as interstitialtype, we assume that they uniformly distributed both in primary and secondary slip planes as shown in Fig.7. (On a surface of the specimen, theanglc between the traces of primary and secondary slip bands is about 90 * , scc Fig.3. W e study this case.) It can be sccn that small stripes with soft regions could bc formed. In these regions, dislocations m o v e easily and secondary slip traces can be clearly sccn on the surface of the crystal. If thc spacing between well developed PSBs is

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IN C u

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about 7 lain, the spacing between stripes should be about 14~m(Fig.7). This is close to the experimental observation(fig.3a). However, the spacing between PSBs depends on the number of loading cycles and strains, the spacing between stripes is also varied as shown in Fig.3b. Once the dislocations avalanche, probably, some of the freed dislocations will move within DBTI , while some of the dislocations will move close to the primary slip plane to seek the most softening direction to form DBI. The deviation from primary slip plane with a small angle could result as shown in Fig.7. Conclusions The occurrence of DBs is a general phenomenon in copper single crystals oriented for double slip under cyclic deformation. The dislocation avalanche modelling could be used to explain the formation of DBs in copper single crystal under cyclic deformation. The appearance of tiny slip bands can be explained as dislocation reactions between primary and secondary PSBs, particularly for the [717] crystal. The crystal orientation, dislocation reaction, macroscopic and microscopic stress states are all responsible for the formation of DBs. Acknowledgements The authors would like to thank Ms. Y.W.Zhang for her asistance on fatigue testing and Senior Engineer T.Y. Zhang and Prof. G. Y. Li for their support on crystal growth. This work was financially supported by N A M C C under Grant No.5929100 and N N S F C under Grant No.19392300-4. References

(I) (2) (3) C4)

(5) (6) (7) (8) • (9)

(I0) (II) (12) (13) (14) (15) (16) (17)

A.S. Cheng and C. Laird, Mater. Sei. Eng., 51(1981)55. N.Y. Jin and A.T. Winter, Acta Metall., 32(1984)989. E.A. Caiman, Aeta Crystall., 5(1952)557. C.R. Gostelow, Met. Sci. J., 5(1971)177. H. Mughrabi, Mater. Sci. Eng., 33(1978)207. M. Saletore and R. Taggart, Mater. Sci. Eng., 36(1978)259. B. Gong, Z.G; Wang and Y.W. Zhang, Submitted to Mater. Sci. Eng., 1994. I.L. Dillamore, J.G. Roberts and A.C. Bush., Metals Sei., 13(1979)73. G.R. Canova, U.F. Koeks and M.G. Stout, Scripta Metall., 18(1984)437. W.Y. Yeung and B.J. Duggan, Acta Metall., 35(1987)541. C.S. Lee and B.J. Duggan, Acta Metall. Mater., 42(1994)857. J.G. Autonopoulos and A.T. Winter. Phil. Mag., 33(1976)87. J.G. Antonopoulos, L.M. Brown and A.T. Winter, Phil. Mag., 34(1976)549. U. Essmann, U. Gosele and H. Mughrabi, Phil. Mag., 44(1981)405. D. K u h l m a n n - W i l s d o r f and C. Laird, Mater. Sci. Eng., 27(1977)137. K. Tanaka and T. Mura, J. Appl. Mech., 48(1981)97. G. Venkatarman, Y.W. Chung and T. Mura, Acta Meta]l., 39(1991)2621. TABLE 1 Angles between (a) DBI & DB TI Normals of Dislocation Loading Favoured (b) DBII & loading axis, DBI & DBTI reaction axis slip system s (e) DBI & (111)

[~171 [034]

[i22]

Lomer-Cottrell

DBI [0.65 0.60 0.46]

(111)[011]

lock

DBTI [-0.01 -0.63 0.77]!

(III)[I01]

Sessile

(i11)[ioi]

jog

DBII [-0.59 -0.21 0.78]!

(111)[i01]

Glissile in

DBI [0.47 0.69 0.55]

(lll)[il0]

(111)

BDH [-0.27 -0.05 0.96]

(I

1 l)[iO I ]

(a)

(b)

(c)

92 *

42 *

9*

91 °

30 o

4 °

69 °

44 °

9 °

DBI [0.54 0.64 0.56] I i

Vol. 31. No. 12

DEFORMATION BANDS IN Cu

22

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Fig.l Orientation of crystals investigated • present experimental

001

01~

x refer to [6].

\

X

Fig.2 Deformation bands in [034] crystal.

(a)

(b)

Fig.3 Deformation bands and tiny slip bands collected as stripes in [117] crystal.

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DEFORMATION BANDS IN Cu

[843 5]

Iti~7] [o4ij

Vol. 31, No. 12

[~017

Fig.4

i1°

Illustration

of

surface orientations and d e f o r m a t i o n bands i n f a t i g u e specimens.

v0c0r~ type

,,
Fig.5 Geometry

PSB

~

7

of

primary PSBs

Fig.6

and secondary

Schematic

slip plane with a potential

of hardening

deformation

and softening

band.

areas.

Fig.7 The s o f t e n i n g a r e a s c o l l e c t e d as s t r i p e s in which the secondary slip traces are much clear. If the spacing a between PSBs is about

i

#.

7~m, t h e s p a c i n g d between s t r i p e s

w i l l be

about ( 3 / 2 ) ~ a f 1 4 p m . V'VOC

P~ i" intl

PSL

of

the formation