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Fatigue-induced shear bands in ferritic single crystals
Acta Mrrullurgtcu Prmted in Great
Vol. 30. pp 273 (0 278. 1982 Brimm All nehts rescned
Copyright
ooO1-61M)~82~010273-06~3.00/0 CD I982 Pcrgamon Press Ltd
FATIGUE-INDUCED SHEAR BANDS IN FERRITIC SINGLE CRYSTALS T. MAGNIN,
A. FOURDEUX
and J. H. DRIVER
Ecole Nationale Superieure des Mines de Saint-Etienne 42023 Saint-Etienne Ctdex. France
158. tours Fauriel
(Recrire$ 18 March 1981)
Abstract-The room temperature cyclic plastic deformation of iron-based bee crystals (Fe-26 Cr-I MO and Fe-3 Sil. oriented close to (Ill ) is shown to lead to the formation of I001 ) (110) shear bands along which cracks are rapidly initiated before final rupture occurs by catastrophic shear. The mechanisms of shear band formation were examined by optical and electron microscopy and X-ray diffraction. The observed slip planes, lattice rotations and dislocation substructures within the bands can be explained by a simple model based on (i) the relative plastic work of $I01 ; (I 10) shear and matrix slip and (ii) the dislocation interactions which give rise to long range stress-free tilt boundaries between the matrix and the bands. It is suggested that this typ of fatigue-induced shear band formation may occur in other alloy systems which. as for the (111) ferritic crystals. exhibit particularly high rates of cyclic hardening. R&sum&-La deformation plastique cyclique a l’ambiante de monocristaux d’alliages de fer (Fe-26 Cr-I MO et Fe-3 Si) d’orientation voisine de (111) conduit a la formation de bandes de cisaillement de type $01: (01 I ). le long desquelles les fissures s’amorcent rapidement avant la rupture finale par cisaillement ‘catastrophique’. Les mecanismes de formation de ces bandes ont ite etudies par microscopies optique et tlectronique et par diffraction X. Les systimes de glissement actifs. les rotations cristallines et les sous-structures de dislocations dans les bandes peuvent dtre expliquts par un mod&e simple base sur (i) les energies relatives de travail plastique pour un cisaillement (001) (I 10) et pour k glissement dans la matrice. et (ii) les interactions de dislocations qui favorisent la formation de joints de flexion .de faible contrainte a longue distance entre la matrice et les bandes. 11 est suggtrt que ce type de formation de bandes ce cisaillement induit par la fatigue peut avoir lieu dans d’autres alliages qui, comme pour les cristaux ferritiques (111). presentent des taux de durcissement cyclique particulierement tlevts.
Zusammenfnssung-Die plastische Wechselverformung bei Raumtemperatur von nahe (111) orientierten Einkristallen der Eisenlegierungen (Fe-26 Cr-1 MO und Fe-3 Si) fuhrt zur Bildung {OOl ) (011) Scherbander. entlang welcher sich Risse sehr schnell entwickeln bevor es zum Bruch durch katastrophenartigen Scherung kommt. Die Mechanismen. die zur Bildung der Scherbander fuhrten. wurden mit Hilfe der Optischen und Rasterelektronenmikroskopie sowie rontgenographisch untersucht. Die beobachteten Gleitebenen Gitterdrehungen und Versetzungssubstrukturen konnten dank eines einfachen Modells. da8 sich auf folgendes begriindet: (il die relative plastische Arbeit von (001 I (I IO) Scherung und Gleiten in der Matrix und (ii) die Versetzungswechselworkung. die die Bildung von spannungsfreien Knickkorngrenzen iiber groBere Entfernungen zwischen der Matrix und den Bandern ermoglicht, beschrieben werden. Es word vermutet. da8 diese Art durch Ermiidung enstandene Scherblndder such in anderen Legierungen, die wie (I 11) orientierte k.r.z. Kristalle. besonders hohe Wechselhartungsverhlltnisse zeigen. vorkommt.
1. INTRODUCT’ION
strain rates or low temperature)
During monotonic testing of bee single crystals. deformation banding is frequently observed either as kink bands in Nb [l], MO [Z] and Fe [3]. or as shear bands in ( 111) Nb crystals deformed at low temperatures [43. Recent fatigue experiments on bee crystals show that deformation banding may also occur during cyclic plastic deformation. For example kink bands have been observed on the surface of fatigued Nb [S. 6. 71 and Fe [6] single crystals oriented for single slip. Mughrabi [8] has also suggested that such deformation banding may be a mechanism for fatigue crack initiation in bee crystals under conditions (high A.M. 30) I---R
273
where classical persistent band formation is inhibited. The present paper describes an unusual form of deformation banding; shear band formation in cyclitally deformed silicon iron and iron-chromium crystals oriented near (111). Some preliminary observations of this behaviour have been previously reported [9]. This paper presents a more detailed description of shear band formation in both single and bicrystals, including a transmission electron microscopy (TEM) study of the band microstructure, together with an interpretation of this form of mechanical instability.
MAGNIN
274
2. EXPER~~TAL
et al.: FATIGUE-INDUCED
!&EAR
BANDS
PROCEDURE
Two high purity ferritic alloys have been investigated : Fe--j25 to 3) wt:/, Si containing 3Oppm C and 10 ppm N and Fe-(255 to 26.1) wt% Cr-jO.94 to 1.15) wt% MO containing about 15 ppm C and 25 ppm N. Single crystals were grown by controlled solidification in horizontal furnaces. Bicrystals were produced either by controlled solidification using two seed crystals or by the electron beam welding of two oriented single crystals. Fatigue specimens with a square (4 x 4 mm2) cross section and a 10 mm gauge length, were prepared by spark cutting and heat treated before being brazed into threaded shoulders. The heat treat~nt consisted of a long high temperature vacuum anneal (16 h at 12OO’C)to decrease the total interstitial content to about 4Oppm followed, in the case of the F&r crystals, by a 1 h solution anneal at 950°C and a water quench. Symmetrical tension-compression tests were performed with a ~~ohydraulic machine under total strain control using a triangular waveform signal. The strain was measured by a strain gauge extensometer mounted directly on the specimen gauge length. Further details of the specimen testing techniques have been pubfished elsewhere [IO]. After testing, the crystallography of the slip systems and shear bands were determined by two-surface trace analysis from optical micrographs obtained with interference contrast. Transmission electron microscopy (T.E.M.) was performed on an Fe-Cr specimen using the disc technique on slices cut at 35” to the bands by electro-chemical cutting and subsequently thinned by electro-polishing. 3. RESULTS 3.1.1 Single 1 shows the orientations of all the crystals examined in this study; those orientations grouped around [ill] in which shear bands were formed are represented by open circles. These orientations were always characterized by relatively high rates of cyclic hardening. Other orienta-
J-+
f
011
Fig. I. Orientations of fatigue-tested single crystals. circles indicate the observation of shear bands.
Fig;.%SE.M.
micrograph of shear bands on a [ill] Fe-26 Cr-I MO crystal.
tions such as [I491 [OOl] and (011) tend to harden slightly before saturation and. at low strain rates, the subsequent development of somewhat ill-def%red persistent slip bands, PSBs, parallel to the primary slip plane. For all orientations, the initial cyclic deformation was accommodated by fine homogeneous slip throughout the specimen gauge length. HoGever for orientations close to [iil], macroscopic shear bands were seen to form towards the end of the hardening phase after a cumulative plastic strain which depends on orientation, strain amplitude and strain rate. On continued cycling, other bands appear on systems both parallel (Fig. 2) and inclined to the initial band. In the square section specimens bands are nucleated at the corners then propagate across the crystal at a rate which depends upon the applied strain amplitude (typically = 10 to 100 cycles). Although the stress state at the corners in square specimens undoubtediy facilitates nucleation, identical shear band formation is also observed in cylindrical specimens. At initiation, bands are only about SOitm wide and then widen to about 300-500~m during fatigue. In all cases crack initiation and final rupture take place by shear along the bands. The dependence of shear band formation on parameters such as strain amplitude, strain rate and orientation is shown in Figs 3(a-d). The onset of visible band formation is indicated on these Q (epFu,,,) plots by an arrow at the appropriate value of epFum. Shear band formation occurs rapidly at high strain amplitudes [Fig. 3(a)] when hardening occurs immediately. At low strain amplitudes a slight softening is often observed to extend over substantial cumulative plastic strains before hardening sets in. This cyclic softening at low strain amplitudes is a common feature of cyclic deformation of bee metals containing interstitial elements [8, II, i2J. Irrespective of this behaviour it is clear that the formation of shear bands at both high and low strain amplitudes coincides with
MAGNlN Fe-26Cr-lM0
eI al.:
[ill]
FATIGUE-INDUCED
kTZ2.m-3/S
U
SHEAR 3ANDS
275
N/mm2
1 k
2
1 0
1
3
1
Fc-26Cr-fMo
4
5
* opcum
t
4
[112].
3
WL-m
T=
:0,6%
k-26Cr-lMo, (d)
q,-0.6%
Q b N/mm2
(d
+ L 0
c’ 2
4
s
8
c
0
mw.aJm.
1
2
3
4
5
6Epcvm
Fig. 3. Cyclic hardening curves [& = 2.10m3 s-’ except for Cc)].(a) The influence of strain amplitude. [ill]
orientation; (b) The influence of alloy composition, [il2] orientation; (c) The influence of strain rate; (d) The influence of orientation, Fe-26 Cr-1 MO, &r/2 = +0.6:,4
a change in slope of the d = f+pc_U,,,) curves and leads to saturation. Orientations e.g. [ 1491, Fig. 3(d), which do not harden significantly do not exhibit shear band formation. For a given strain amplitude bands form particularly rapidly for orientations close to [ir 1J; in the iron--chromium alloy cycled at A+ = 1.2 x lo-’ and i T = 2.10e3 s-l, shear bands are observed at Ed,,,,, values of 0.7,3.5 and 7 for the (11 l), (112) and (234) orientations respectively. Figure 3(b) shows that shear band formation does not appear to be related to the alloy composition. In both alloys the orientation and strain amplitude dependence of band formation are remarkably similar, the only difference being the absolute stress levels. Finally it should be noted that shear band formation is essentially related to cyclic deformation since monotonic tests to rupture of the same crystal orientations do not lead to shear banding.
-1’; ii2
B@
till
00'1
Fig. 4. Fatigue
behaviour
3.1.2. Bicrystals. The single crystal experiments indicated that shear band formation was associated with those orientations close to (111) which exhibit high cyclic hardening rates. To confirm the r61e of the stress level, two different bicrystals, denoted A-A’ and A-B [Fig. 4(a)]. were tested under the. same conditions (A+ = 1.2 x IO-* CT = 2.10m3). A, [i12] and A’ [ill] as single crystals easily form bands while orientation B does not. Figure 4 (b) shows the cyclic hardening behaviour of these two bicrystals together with the critical stress or for shear band formation in a (112) (A) single crystal. Bicrystal A-A’ hardens above o, and in consequence rapidly forms shear bands in both grains. The shear band initiates in the A’ grain and propagates across the bicrystal with a change in angle at the grain boundary. The other bicrystal A-B hardened slightly but the stress level stayed below Q, and shear bands were not
(b)
G
4twnm2
5m_ 400, 3m_ 01
of Fe-Cr bicrystals; (a) orientations &r/2 = 0.6:; ;r = 2.10- 3 s- ‘.
I
1 2
I
3
L’
(b) cyclic hardening
;Epcum curves
t at
276
MAGNIN
er al.:
FATIGUE-INDUCED
Table 1. Slip system and shear band crystallography crystals
Orientation
Alloy
[iii-j
Fe-3 Si
Slip systems
Tension and compression Fe-26 Cr-1 MO
ril2i
Fe-3 Si
of (111).
Schmid factor
(211) [ill] (oil) [iii]
0.314 0.212
(Ill) [ill] -(123) [ill]
0.314 0.309
Fe-26 Cr-1 MO Fe-26 Cr-1 MO
(2i3) [iii]
0.408 0.309
(iol) [ill] (2i3) [ii 1]
0.422 0.239
(ioi) [iii]
detected either in A or B. These results confirm the previous suggestion that a high degree of fatigue strain hardening is necessary for shear band formation.
3.2 Structure of the shear bands Although the matrix slip planes (determined before band formation) in the two alloys are rather different (Table 1) the two sets of bands had identical orientations and always occurred in the following sequence: (i) shear bands with a (matrix) habit plane (001) and shear direction [ilO] (ii) for orientations other than [ill]) bands parallel to the primary slip plane (701) [ill]. For the [ill] orientation the second set of bands was parallel to (010) poi]. The I1 10: (111) bands parallel to an active slip system are similar to coarse slip bands and are probably localized shears which compensate the specimen misalignment due to the formation of the (001 } (110) bands. The (001) (110) bands are in fact made up of fine slip on planes completely different from the matrix, i.e. the (110) planes for a (001) [ilO] shear band (Figs 5 and 6). After shear band formation, the deformation is almost entirely concentrated in the bands as revealed
Fig. 5. Schematic diagram of matrix and shear band slip systems.
( 112) and (234)
Shear bands (0011 (010) -idem--
(001) (101)
(ioi) [fill (011) [ill]
Tension-and compression
[Z34] Tension and compression
SHEAR BANDS
-idem-
($1) (101)
[ilo]
Cl111
by electropolishing
a specimen containing a band and retesting for a few cycles. Microhardness measurements [9] on the (001) bands show that when freshly formed the bands are considerably softer than the matrix but that hardening subsequently occurs within the bands on further cycling. The rumpled appearance of the bands (Fig 6) indicates that a macroscopic band (width 0.3-0.5 mm) is made up of sets of parallel micro-bands. However all bands had a sharp interface with the matrix (Fig. 6). The lattice rotations within the bands were measured by X-ray diffraction using pole figures of both the band and the adjacent matrix. In an FeCr-Mo [ill] > crystal the (001) [ilO] bands were found to be rotated by 1: 30” about the [l lo] axis after a cumulative strain epcuffl= 1.4 (shear band initiation occurred at eycu,,,2 0.7) and A+ = 1.2.10-2. This rotation axis lies in the band habit plane and is normal to the slip traces within the band. Shear bands in a [i12] crystal were similarly rotated by ~20” after a cumulative plastic strain of 5.5 at A+ = 1.2.10-‘. T.E.M. of the bands
A detailed (100 kV) T.E.M. study of the {OOl} (110) bands was performed on a [il2] Fe-Cr crystal after 250 cycles at &r = l.2.1O-2 (epcumz 4.5) and a, = 2.10-3 s-l. Figure 7 shows the dislocation microstructures at the matrix-band interface. Within the matrix a relatively open vein structure typical of
Fig. 6. Optic&l micrograph of a (001) [ilO] shear band and matrix in a [ll l] Fe-Cr crystal (after electropolishing and retesting).
MAGNIN
et al.:
FATIGUE-INDUCED
SHEAR BANDS
277
interface. Fe-26 Cr-1 MO (I 12) crystal cycled at kO.69; to eIEv,,,= 4.5.
Fig. 7. T.E.M. montage of a (001) (110) shear band-matrix
bee materials fatigued at moderately ‘high’ strain rates [ 133 is observed, Fig. 8. The band has a completely different cellular structure with a relatively high density of dislodations arranged in both the cell walls and within the cells. In Fig. 7 the matrix plane is parallel to (102) and the band plane -parallel to (i13) corresponding to a rotation of 520” about the [l lo] axis in confirmation of the X-ray results. Electron diffraction revealed that this rotation occurred at the matrix-band interface (or within less than 2 m of the interface), i.e. the interface can be considered almost as a high angle tilt boundary of thickness l-2 m made up of well-developed dislocation cells. This cellular structure at the interface is shown in greater detail in Fig. 9. The band in Figs 7 and 9 had a thickness of 4Opm but several other bands, running parallel to the band, were detected in the thin foil indicating that the macroscopic shear bands (width 300-SOOpm) are in fact made up of a number of micro-bands of width 40 jfm. 4. DISCUSSION The lo01 ) (110) shear bands observed in fatigued (111) crystals appear to be significantly different from either classical P.S.B.s. or deformation bands previously reported in cyclically or monotonically deformed metals. Although kink bands have been observed in fatigued Al [14], Nb [S-7] and Fe 163 crystals, the shear bands differ substantially from kink bands which, according to [lSJ, occur in single slip
Fig. 8. T.E.M. of typical matrix vein structure: same specimen as Fig. 7.
orientations and lie perpendicular to the primary slip plane. Saletore and Taggart [16] have described deformation bands in fatigued (122) Cu crystals oriented for double slip but these bands formed at 245’ to the stress a,xis. From the many detailed studies of deformation banding in tensile deformation the results of Reid et a/. [S] and Asaro [17.18] appear at first sight quite similar, but in fact do not account for the :OOlj (110) shear band orientation. Both authors propose geometrical softening type models to explain the [ 110; (001) bands in pure Nb at 77°K [4] and the shear bands in double-slip oriented Al-Cu crystals [18]. The latter model, based on bifurcation theory, predicts for similar (112) orientations, shear bands inclined at only = 4 or 5” to the slip planes. Moreover both Reid and Asaro observe substantial yield drops at the onset of shear banding in contrast to our fatigue results. In conclusion, to the authors’ knowledge, [OOli (110) bands have neither been experimentally observed nor theoretically predicted. They may, however, be explained quite simply in the following manner. A volume element of a bee crystal can be sheared by an amount d; on (001) [ilO] by slip on a (ilO) plane in 2 directions [l 1 l] and [iil], accompanied by a lattice rotation w = &c clockwise about the [l lo]
Fig. 9. T.E.M. of matrix-band Fig. 7.
interface:
specimen
of
278
MAGNIN et ai.:
FATIGUE-INDUCED
axis. This is easily demonstrated by a Bishop and Hill type analysis for constrained shear assuming either slip on I 110: ( 111) or, more appropriately, slip along (111) on the planes of maximum resolved shear stress [19, 20-J. Whether shear occurs on (001) depends upon the relative plastic work terms for (001) shear and matrix slip. The Schmid factors for slip on the (ilo) [Ill] systems for both the [ill] and [il2J crystals are 0.27 compared with values of 0.31 and 0.41 for matrix slip in the [ill] and [i12] orientations respectively (Table 1). Assuming no latent hardening of the systems in the shear band, shear on (001) could then become energetically favourable if the axial stress rises by t 150,” for [ill] and ~50% for [i12]. These values correspond closely to the experimental values of cyclic hardening before the onset of shear band formation, e.g. Fig. 3(d). On this basis, very high rates of cyclic hardening are required for shear band formation in o~entations further than ~30” from [ill], e.g. 8Vd for [i49]; neither shear bands nor substantial cyclic hardening were in fact observed for these orientations. The shear stress criterion based on the absence of latent hardening is also in very good agreement with the bicrystal results. This criterion does not however explain why slip is concentrated in bands rather than distributed homogeneously throughout the matrix. The reason for discrete band formation probably lies in the interactions of the [ill] and [iil] dislocations active on the (ilO) plane. Frank’s expression .for the long range stressfree subboundaries formed by dislocation intersections: ;i 3 (2(? x Qsin6/2 where d is the sum of the Burgers vectors of the dislocations cut by a vector i in the boundary plane, fi the rotation axis and 0 the angle of rotation, can be used to calculate the boundary plane, normal g, created by the intersection of 2 sets of Burgers vectors 6, and -&:iV = H x (6, x 5,) with B = [llOJ. & = [ill] and & = [iil], H = [OOl] which is in fact the experimentally observed interface plane. In other words the interaction of the [ill] and [iii] slip dislocations in the shear band leads to the formation of (001) dislocation subboundaries, which, as shown by optical and electron microscopy, do in fact make up a welldefined interface with the matrix. The above analysis treats the initial stages of band formation but is probably valid for the later stages. The z 30” lattice rotation within the bands rotates the stress axis in the band towards [i13] which tends to reduce the resolved shear stress on the (ilO) slip plane. However if slip is transferred from (ilo) towards the (211) [ill] and (i21) [El] systems the Schmid factor is increased (geometrical softening) while (001) boundaries would still be formed by the interactions of the same dislocation Burgers vectors. In conclusion, a simple model for (001; (110)
SHEAR BANDS
shear band formation in cyclically stressed crystals oriented near (111) is presented and shown to be in good agreement with the experimental observations. The model also implies an absence of latent hardening in cyclically deformed crystals. Shear band formation leads in general to premature failure; the fatigue lives of crystals in which shear band formation occurred were significantly lower (by a factor of = 3) than those of crystals which failed by other mechanisms. Shear bands may be an important feature of fatigue failure in other materials which exhibit very high rates of cyclic hardjening. This is particularly true in the case of high purity b.c.c. metals where classical P.S.B. formation has been shown by Mughrabi [8] to be rather difficult in the low temperature regime (high strain rates or low temperatures). Shear banding may then supersede P.S.B. formation as a fatigue failure mechanism in certain crystal orientations. Rcknowtedgemmfs-The authors are grateful to Professors De Fouquet, Escaig and Goux for helpful discussions and to Dr. H. Mughrabi for access to results prior to publioation
REFERENCES 1. M. S. Duesbery and R. A. Foxall, Phil. Meg. 20, 719 (1969).
2. F. Guiu and P. L. Pratt, Physica storus sofidi 15, 539 (1966). 3. A. S. Keh, Phi/. Msg. 12, 9 (1965). 4. C. N. Reid, R. A. Maynard and M. H. Loretto, Proc. ICSMM, Nancy (1976). Pergamon Press, Oxford, 1, 161 (1976). 5. M. Doner, J. C. Diprimio, E. I. Salkovitz, Acta metal/. 21, 1547 (1973). 6. H. Mughrabi, K. Herz and X. Stark, Int. Journal Fracture, to be published. 7. M. Anglada Ph.D. Thesis, Queen Mary College, Lon-
don (1580). 8. H. Mughrabi, F. Ackermann and K. Hen, Fatigue ‘~ech~isms. ASTM STP No. 675. 69 119791. 9. T. Magnin and 1. H. Driver, Pk. IkSMk, Aachen (1979) Vat. 2, Pergamoa Press, 1213 (1979). 10. T. Magnin and J. H. Driver, Mater. Sci. Engng 39, 175 (1979). Il. P. Lukas and J. Polak, Work Hardening in Tension and Fatigue (edited by A. Thompson) p. 177, A.I.M.M.P.E., New York (1976). 12. T. Magnin and J. H. Driver to be published in an ASTM STP Proc. Int. Conference-on L.ow Cycle Fatiaue and Life Predicrion. Firminv 119801. 13. H. Mughrabi,.K. Hen: and X. Sta;k: Act; metall. 24, 659 (1976). 14. G. Y. Chin and W. A. Backofen. J. inst. Metals 90. 13
(1961). 15. R. W. K. Honeycombe, 1. Inst. Me&s %o, 45 (1951). 16. M. Saiatore and R. Taggart, Mater. Sci. Engng 36, 259 (19781. \-17. R. J. Asaro, Acta metull. 27, 445 (1979). 18. Y. W. Chang and R. J. Asaro, Acta metall. 29, 241 (1981). 19. P. Penning, Metall. Trans. A 7, 1021 (1976). 20. P. R. Morris and S. L. Semiatin, Text. Cryst. Solids 3, 113 (1979). -I-
Vol. 30. pp 273 (0 278. 1982 Brimm All nehts rescned
Copyright
ooO1-61M)~82~010273-06~3.00/0 CD I982 Pcrgamon Press Ltd
FATIGUE-INDUCED SHEAR BANDS IN FERRITIC SINGLE CRYSTALS T. MAGNIN,
A. FOURDEUX
and J. H. DRIVER
Ecole Nationale Superieure des Mines de Saint-Etienne 42023 Saint-Etienne Ctdex. France
158. tours Fauriel
(Recrire$ 18 March 1981)
Abstract-The room temperature cyclic plastic deformation of iron-based bee crystals (Fe-26 Cr-I MO and Fe-3 Sil. oriented close to (Ill ) is shown to lead to the formation of I001 ) (110) shear bands along which cracks are rapidly initiated before final rupture occurs by catastrophic shear. The mechanisms of shear band formation were examined by optical and electron microscopy and X-ray diffraction. The observed slip planes, lattice rotations and dislocation substructures within the bands can be explained by a simple model based on (i) the relative plastic work of $I01 ; (I 10) shear and matrix slip and (ii) the dislocation interactions which give rise to long range stress-free tilt boundaries between the matrix and the bands. It is suggested that this typ of fatigue-induced shear band formation may occur in other alloy systems which. as for the (111) ferritic crystals. exhibit particularly high rates of cyclic hardening. R&sum&-La deformation plastique cyclique a l’ambiante de monocristaux d’alliages de fer (Fe-26 Cr-I MO et Fe-3 Si) d’orientation voisine de (111) conduit a la formation de bandes de cisaillement de type $01: (01 I ). le long desquelles les fissures s’amorcent rapidement avant la rupture finale par cisaillement ‘catastrophique’. Les mecanismes de formation de ces bandes ont ite etudies par microscopies optique et tlectronique et par diffraction X. Les systimes de glissement actifs. les rotations cristallines et les sous-structures de dislocations dans les bandes peuvent dtre expliquts par un mod&e simple base sur (i) les energies relatives de travail plastique pour un cisaillement (001) (I 10) et pour k glissement dans la matrice. et (ii) les interactions de dislocations qui favorisent la formation de joints de flexion .de faible contrainte a longue distance entre la matrice et les bandes. 11 est suggtrt que ce type de formation de bandes ce cisaillement induit par la fatigue peut avoir lieu dans d’autres alliages qui, comme pour les cristaux ferritiques (111). presentent des taux de durcissement cyclique particulierement tlevts.
Zusammenfnssung-Die plastische Wechselverformung bei Raumtemperatur von nahe (111) orientierten Einkristallen der Eisenlegierungen (Fe-26 Cr-1 MO und Fe-3 Si) fuhrt zur Bildung {OOl ) (011) Scherbander. entlang welcher sich Risse sehr schnell entwickeln bevor es zum Bruch durch katastrophenartigen Scherung kommt. Die Mechanismen. die zur Bildung der Scherbander fuhrten. wurden mit Hilfe der Optischen und Rasterelektronenmikroskopie sowie rontgenographisch untersucht. Die beobachteten Gleitebenen Gitterdrehungen und Versetzungssubstrukturen konnten dank eines einfachen Modells. da8 sich auf folgendes begriindet: (il die relative plastische Arbeit von (001 I (I IO) Scherung und Gleiten in der Matrix und (ii) die Versetzungswechselworkung. die die Bildung von spannungsfreien Knickkorngrenzen iiber groBere Entfernungen zwischen der Matrix und den Bandern ermoglicht, beschrieben werden. Es word vermutet. da8 diese Art durch Ermiidung enstandene Scherblndder such in anderen Legierungen, die wie (I 11) orientierte k.r.z. Kristalle. besonders hohe Wechselhartungsverhlltnisse zeigen. vorkommt.
1. INTRODUCT’ION
strain rates or low temperature)
During monotonic testing of bee single crystals. deformation banding is frequently observed either as kink bands in Nb [l], MO [Z] and Fe [3]. or as shear bands in ( 111) Nb crystals deformed at low temperatures [43. Recent fatigue experiments on bee crystals show that deformation banding may also occur during cyclic plastic deformation. For example kink bands have been observed on the surface of fatigued Nb [S. 6. 71 and Fe [6] single crystals oriented for single slip. Mughrabi [8] has also suggested that such deformation banding may be a mechanism for fatigue crack initiation in bee crystals under conditions (high A.M. 30) I---R
273
where classical persistent band formation is inhibited. The present paper describes an unusual form of deformation banding; shear band formation in cyclitally deformed silicon iron and iron-chromium crystals oriented near (111). Some preliminary observations of this behaviour have been previously reported [9]. This paper presents a more detailed description of shear band formation in both single and bicrystals, including a transmission electron microscopy (TEM) study of the band microstructure, together with an interpretation of this form of mechanical instability.
MAGNIN
274
2. EXPER~~TAL
et al.: FATIGUE-INDUCED
!&EAR
BANDS
PROCEDURE
Two high purity ferritic alloys have been investigated : Fe--j25 to 3) wt:/, Si containing 3Oppm C and 10 ppm N and Fe-(255 to 26.1) wt% Cr-jO.94 to 1.15) wt% MO containing about 15 ppm C and 25 ppm N. Single crystals were grown by controlled solidification in horizontal furnaces. Bicrystals were produced either by controlled solidification using two seed crystals or by the electron beam welding of two oriented single crystals. Fatigue specimens with a square (4 x 4 mm2) cross section and a 10 mm gauge length, were prepared by spark cutting and heat treated before being brazed into threaded shoulders. The heat treat~nt consisted of a long high temperature vacuum anneal (16 h at 12OO’C)to decrease the total interstitial content to about 4Oppm followed, in the case of the F&r crystals, by a 1 h solution anneal at 950°C and a water quench. Symmetrical tension-compression tests were performed with a ~~ohydraulic machine under total strain control using a triangular waveform signal. The strain was measured by a strain gauge extensometer mounted directly on the specimen gauge length. Further details of the specimen testing techniques have been pubfished elsewhere [IO]. After testing, the crystallography of the slip systems and shear bands were determined by two-surface trace analysis from optical micrographs obtained with interference contrast. Transmission electron microscopy (T.E.M.) was performed on an Fe-Cr specimen using the disc technique on slices cut at 35” to the bands by electro-chemical cutting and subsequently thinned by electro-polishing. 3. RESULTS 3.1.1 Single 1 shows the orientations of all the crystals examined in this study; those orientations grouped around [ill] in which shear bands were formed are represented by open circles. These orientations were always characterized by relatively high rates of cyclic hardening. Other orienta-
J-+
f
011
Fig. I. Orientations of fatigue-tested single crystals. circles indicate the observation of shear bands.
Fig;.%SE.M.
micrograph of shear bands on a [ill] Fe-26 Cr-I MO crystal.
tions such as [I491 [OOl] and (011) tend to harden slightly before saturation and. at low strain rates, the subsequent development of somewhat ill-def%red persistent slip bands, PSBs, parallel to the primary slip plane. For all orientations, the initial cyclic deformation was accommodated by fine homogeneous slip throughout the specimen gauge length. HoGever for orientations close to [iil], macroscopic shear bands were seen to form towards the end of the hardening phase after a cumulative plastic strain which depends on orientation, strain amplitude and strain rate. On continued cycling, other bands appear on systems both parallel (Fig. 2) and inclined to the initial band. In the square section specimens bands are nucleated at the corners then propagate across the crystal at a rate which depends upon the applied strain amplitude (typically = 10 to 100 cycles). Although the stress state at the corners in square specimens undoubtediy facilitates nucleation, identical shear band formation is also observed in cylindrical specimens. At initiation, bands are only about SOitm wide and then widen to about 300-500~m during fatigue. In all cases crack initiation and final rupture take place by shear along the bands. The dependence of shear band formation on parameters such as strain amplitude, strain rate and orientation is shown in Figs 3(a-d). The onset of visible band formation is indicated on these Q (epFu,,,) plots by an arrow at the appropriate value of epFum. Shear band formation occurs rapidly at high strain amplitudes [Fig. 3(a)] when hardening occurs immediately. At low strain amplitudes a slight softening is often observed to extend over substantial cumulative plastic strains before hardening sets in. This cyclic softening at low strain amplitudes is a common feature of cyclic deformation of bee metals containing interstitial elements [8, II, i2J. Irrespective of this behaviour it is clear that the formation of shear bands at both high and low strain amplitudes coincides with
MAGNlN Fe-26Cr-lM0
eI al.:
[ill]
FATIGUE-INDUCED
kTZ2.m-3/S
U
SHEAR 3ANDS
275
N/mm2
1 k
2
1 0
1
3
1
Fc-26Cr-fMo
4
5
* opcum
t
4
[112].
3
WL-m
T=
:0,6%
k-26Cr-lMo, (d)
q,-0.6%
Q b N/mm2
(d
+ L 0
c’ 2
4
s
8
c
0
mw.aJm.
1
2
3
4
5
6Epcvm
Fig. 3. Cyclic hardening curves [& = 2.10m3 s-’ except for Cc)].(a) The influence of strain amplitude. [ill]
orientation; (b) The influence of alloy composition, [il2] orientation; (c) The influence of strain rate; (d) The influence of orientation, Fe-26 Cr-1 MO, &r/2 = +0.6:,4
a change in slope of the d = f+pc_U,,,) curves and leads to saturation. Orientations e.g. [ 1491, Fig. 3(d), which do not harden significantly do not exhibit shear band formation. For a given strain amplitude bands form particularly rapidly for orientations close to [ir 1J; in the iron--chromium alloy cycled at A+ = 1.2 x lo-’ and i T = 2.10e3 s-l, shear bands are observed at Ed,,,,, values of 0.7,3.5 and 7 for the (11 l), (112) and (234) orientations respectively. Figure 3(b) shows that shear band formation does not appear to be related to the alloy composition. In both alloys the orientation and strain amplitude dependence of band formation are remarkably similar, the only difference being the absolute stress levels. Finally it should be noted that shear band formation is essentially related to cyclic deformation since monotonic tests to rupture of the same crystal orientations do not lead to shear banding.
-1’; ii2
B@
till
00'1
Fig. 4. Fatigue
behaviour
3.1.2. Bicrystals. The single crystal experiments indicated that shear band formation was associated with those orientations close to (111) which exhibit high cyclic hardening rates. To confirm the r61e of the stress level, two different bicrystals, denoted A-A’ and A-B [Fig. 4(a)]. were tested under the. same conditions (A+ = 1.2 x IO-* CT = 2.10m3). A, [i12] and A’ [ill] as single crystals easily form bands while orientation B does not. Figure 4 (b) shows the cyclic hardening behaviour of these two bicrystals together with the critical stress or for shear band formation in a (112) (A) single crystal. Bicrystal A-A’ hardens above o, and in consequence rapidly forms shear bands in both grains. The shear band initiates in the A’ grain and propagates across the bicrystal with a change in angle at the grain boundary. The other bicrystal A-B hardened slightly but the stress level stayed below Q, and shear bands were not
(b)
G
4twnm2
5m_ 400, 3m_ 01
of Fe-Cr bicrystals; (a) orientations &r/2 = 0.6:; ;r = 2.10- 3 s- ‘.
I
1 2
I
3
L’
(b) cyclic hardening
;Epcum curves
t at
276
MAGNIN
er al.:
FATIGUE-INDUCED
Table 1. Slip system and shear band crystallography crystals
Orientation
Alloy
[iii-j
Fe-3 Si
Slip systems
Tension and compression Fe-26 Cr-1 MO
ril2i
Fe-3 Si
of (111).
Schmid factor
(211) [ill] (oil) [iii]
0.314 0.212
(Ill) [ill] -(123) [ill]
0.314 0.309
Fe-26 Cr-1 MO Fe-26 Cr-1 MO
(2i3) [iii]
0.408 0.309
(iol) [ill] (2i3) [ii 1]
0.422 0.239
(ioi) [iii]
detected either in A or B. These results confirm the previous suggestion that a high degree of fatigue strain hardening is necessary for shear band formation.
3.2 Structure of the shear bands Although the matrix slip planes (determined before band formation) in the two alloys are rather different (Table 1) the two sets of bands had identical orientations and always occurred in the following sequence: (i) shear bands with a (matrix) habit plane (001) and shear direction [ilO] (ii) for orientations other than [ill]) bands parallel to the primary slip plane (701) [ill]. For the [ill] orientation the second set of bands was parallel to (010) poi]. The I1 10: (111) bands parallel to an active slip system are similar to coarse slip bands and are probably localized shears which compensate the specimen misalignment due to the formation of the (001 } (110) bands. The (001) (110) bands are in fact made up of fine slip on planes completely different from the matrix, i.e. the (110) planes for a (001) [ilO] shear band (Figs 5 and 6). After shear band formation, the deformation is almost entirely concentrated in the bands as revealed
Fig. 5. Schematic diagram of matrix and shear band slip systems.
( 112) and (234)
Shear bands (0011 (010) -idem--
(001) (101)
(ioi) [fill (011) [ill]
Tension-and compression
[Z34] Tension and compression
SHEAR BANDS
-idem-
($1) (101)
[ilo]
Cl111
by electropolishing
a specimen containing a band and retesting for a few cycles. Microhardness measurements [9] on the (001) bands show that when freshly formed the bands are considerably softer than the matrix but that hardening subsequently occurs within the bands on further cycling. The rumpled appearance of the bands (Fig 6) indicates that a macroscopic band (width 0.3-0.5 mm) is made up of sets of parallel micro-bands. However all bands had a sharp interface with the matrix (Fig. 6). The lattice rotations within the bands were measured by X-ray diffraction using pole figures of both the band and the adjacent matrix. In an FeCr-Mo [ill] > crystal the (001) [ilO] bands were found to be rotated by 1: 30” about the [l lo] axis after a cumulative strain epcuffl= 1.4 (shear band initiation occurred at eycu,,,2 0.7) and A+ = 1.2.10-2. This rotation axis lies in the band habit plane and is normal to the slip traces within the band. Shear bands in a [i12] crystal were similarly rotated by ~20” after a cumulative plastic strain of 5.5 at A+ = 1.2.10-‘. T.E.M. of the bands
A detailed (100 kV) T.E.M. study of the {OOl} (110) bands was performed on a [il2] Fe-Cr crystal after 250 cycles at &r = l.2.1O-2 (epcumz 4.5) and a, = 2.10-3 s-l. Figure 7 shows the dislocation microstructures at the matrix-band interface. Within the matrix a relatively open vein structure typical of
Fig. 6. Optic&l micrograph of a (001) [ilO] shear band and matrix in a [ll l] Fe-Cr crystal (after electropolishing and retesting).
MAGNIN
et al.:
FATIGUE-INDUCED
SHEAR BANDS
277
interface. Fe-26 Cr-1 MO (I 12) crystal cycled at kO.69; to eIEv,,,= 4.5.
Fig. 7. T.E.M. montage of a (001) (110) shear band-matrix
bee materials fatigued at moderately ‘high’ strain rates [ 133 is observed, Fig. 8. The band has a completely different cellular structure with a relatively high density of dislodations arranged in both the cell walls and within the cells. In Fig. 7 the matrix plane is parallel to (102) and the band plane -parallel to (i13) corresponding to a rotation of 520” about the [l lo] axis in confirmation of the X-ray results. Electron diffraction revealed that this rotation occurred at the matrix-band interface (or within less than 2 m of the interface), i.e. the interface can be considered almost as a high angle tilt boundary of thickness l-2 m made up of well-developed dislocation cells. This cellular structure at the interface is shown in greater detail in Fig. 9. The band in Figs 7 and 9 had a thickness of 4Opm but several other bands, running parallel to the band, were detected in the thin foil indicating that the macroscopic shear bands (width 300-SOOpm) are in fact made up of a number of micro-bands of width 40 jfm. 4. DISCUSSION The lo01 ) (110) shear bands observed in fatigued (111) crystals appear to be significantly different from either classical P.S.B.s. or deformation bands previously reported in cyclically or monotonically deformed metals. Although kink bands have been observed in fatigued Al [14], Nb [S-7] and Fe 163 crystals, the shear bands differ substantially from kink bands which, according to [lSJ, occur in single slip
Fig. 8. T.E.M. of typical matrix vein structure: same specimen as Fig. 7.
orientations and lie perpendicular to the primary slip plane. Saletore and Taggart [16] have described deformation bands in fatigued (122) Cu crystals oriented for double slip but these bands formed at 245’ to the stress a,xis. From the many detailed studies of deformation banding in tensile deformation the results of Reid et a/. [S] and Asaro [17.18] appear at first sight quite similar, but in fact do not account for the :OOlj (110) shear band orientation. Both authors propose geometrical softening type models to explain the [ 110; (001) bands in pure Nb at 77°K [4] and the shear bands in double-slip oriented Al-Cu crystals [18]. The latter model, based on bifurcation theory, predicts for similar (112) orientations, shear bands inclined at only = 4 or 5” to the slip planes. Moreover both Reid and Asaro observe substantial yield drops at the onset of shear banding in contrast to our fatigue results. In conclusion, to the authors’ knowledge, [OOli (110) bands have neither been experimentally observed nor theoretically predicted. They may, however, be explained quite simply in the following manner. A volume element of a bee crystal can be sheared by an amount d; on (001) [ilO] by slip on a (ilO) plane in 2 directions [l 1 l] and [iil], accompanied by a lattice rotation w = &c clockwise about the [l lo]
Fig. 9. T.E.M. of matrix-band Fig. 7.
interface:
specimen
of
278
MAGNIN et ai.:
FATIGUE-INDUCED
axis. This is easily demonstrated by a Bishop and Hill type analysis for constrained shear assuming either slip on I 110: ( 111) or, more appropriately, slip along (111) on the planes of maximum resolved shear stress [19, 20-J. Whether shear occurs on (001) depends upon the relative plastic work terms for (001) shear and matrix slip. The Schmid factors for slip on the (ilo) [Ill] systems for both the [ill] and [il2J crystals are 0.27 compared with values of 0.31 and 0.41 for matrix slip in the [ill] and [i12] orientations respectively (Table 1). Assuming no latent hardening of the systems in the shear band, shear on (001) could then become energetically favourable if the axial stress rises by t 150,” for [ill] and ~50% for [i12]. These values correspond closely to the experimental values of cyclic hardening before the onset of shear band formation, e.g. Fig. 3(d). On this basis, very high rates of cyclic hardening are required for shear band formation in o~entations further than ~30” from [ill], e.g. 8Vd for [i49]; neither shear bands nor substantial cyclic hardening were in fact observed for these orientations. The shear stress criterion based on the absence of latent hardening is also in very good agreement with the bicrystal results. This criterion does not however explain why slip is concentrated in bands rather than distributed homogeneously throughout the matrix. The reason for discrete band formation probably lies in the interactions of the [ill] and [iil] dislocations active on the (ilO) plane. Frank’s expression .for the long range stressfree subboundaries formed by dislocation intersections: ;i 3 (2(? x Qsin6/2 where d is the sum of the Burgers vectors of the dislocations cut by a vector i in the boundary plane, fi the rotation axis and 0 the angle of rotation, can be used to calculate the boundary plane, normal g, created by the intersection of 2 sets of Burgers vectors 6, and -&:iV = H x (6, x 5,) with B = [llOJ. & = [ill] and & = [iil], H = [OOl] which is in fact the experimentally observed interface plane. In other words the interaction of the [ill] and [iii] slip dislocations in the shear band leads to the formation of (001) dislocation subboundaries, which, as shown by optical and electron microscopy, do in fact make up a welldefined interface with the matrix. The above analysis treats the initial stages of band formation but is probably valid for the later stages. The z 30” lattice rotation within the bands rotates the stress axis in the band towards [i13] which tends to reduce the resolved shear stress on the (ilO) slip plane. However if slip is transferred from (ilo) towards the (211) [ill] and (i21) [El] systems the Schmid factor is increased (geometrical softening) while (001) boundaries would still be formed by the interactions of the same dislocation Burgers vectors. In conclusion, a simple model for (001; (110)
SHEAR BANDS
shear band formation in cyclically stressed crystals oriented near (111) is presented and shown to be in good agreement with the experimental observations. The model also implies an absence of latent hardening in cyclically deformed crystals. Shear band formation leads in general to premature failure; the fatigue lives of crystals in which shear band formation occurred were significantly lower (by a factor of = 3) than those of crystals which failed by other mechanisms. Shear bands may be an important feature of fatigue failure in other materials which exhibit very high rates of cyclic hardjening. This is particularly true in the case of high purity b.c.c. metals where classical P.S.B. formation has been shown by Mughrabi [8] to be rather difficult in the low temperature regime (high strain rates or low temperatures). Shear banding may then supersede P.S.B. formation as a fatigue failure mechanism in certain crystal orientations. Rcknowtedgemmfs-The authors are grateful to Professors De Fouquet, Escaig and Goux for helpful discussions and to Dr. H. Mughrabi for access to results prior to publioation
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