NEW EXPERIMENTS CONCERNING THE SLIP PROCESSES AT

PROPAGATING FATIGUE CRACKS-I*?

P. NEUMANN$§

Elrperiments are described, in which fatigue cracks with simple and well reproducible crack geo- metries are produced in copper single.crystals: The crack surfaces are maoroscopically plane and the crack front can be forced by appropriate ester& force distributions into any preselected direction. In suitably shaped crystals crack fronts can be obtained, which are straight all ohe way through the specimen. Due to this well defined crack geometry and the simple structure of the material (single- crystals) the crack propagation rate could be reproduced in different specimens under identical condi- t.ions with an accuracy of 1.1 per cent. Furthermore with this new experimental technique detsils of the course of pl8.stic deformation 8t the crack tip can be observed during one load cycle. of the coarse slip model of fatigue could be verified by direct evidence.

Xanypredictions

SO‘LlrELLES E-XPI?RIEXCES CO1C’CERN;LVT LES PROCESSUS DE GLISSESIEST _%CS CR.%QXjELURES EX PROPAGATIOS CAUStiES PAR L-4 F_ATIGUE-I

Des exp&iencee sent d&rites dans lesquelles des craquelures de fatigue avec des geom&ries de craquelure simples et reproduisiblea sont prod&es dans des cristaux simples de cuivre: Les surfaces crsquel&s sont macrosoopiquement planes et le front de craquement peut btre force par des distri. butions de forces errternes appropri&es dans tout sells ohoisi par avance. Dan.3 tout cristel de forme convenable des fronts de craquement peuvent &re obtenus et qui sont droits dans toute la masse du sp&cim&ne. Du fait de cette g&om&rie de eraquelure bien d#inie et de la structure simple du mat&au (cristaux simples) le taux de propagation des craquelures pourrait &re reproduit dam divers spbim+nes sow des conditions identiques avec une precision de 1,s pour cent. De plus, avec cette nouvelle tech- niclue exphrimentale, les d&ails du tours de la deformation plastique B la Crete de la craquelure peuvent Btre observks au tours d’un cycle de charge. De nombreuses previsions du modele de glissement grassier de fatigue pourrait itre v&if&s par Evidence directe.

XEUE E~PER~~~E ZU’R ~TERSU~HU~G DE GLEITPROZESSER _L\i FORTSCHREITEXDEX ER~IUD~GSRISSE~

Es werden Experimente beschriebn, bei denen in Kupfereinkristallen Ermiidungsrisse mit einfacher und gut reproduzierbarer RiDgeometrie erzeugt werden: Die RiOoberfl&ohen sind makroskopisch eben und die RiDfront kann durch entsprechende BuBere Kmftverteilung en in jede vorgewiehlte Lsge gezwungen xerden. In Kristallen mit geeigneter Form kann man so Rinfronten erzeugen, die durch die ganze Probe hidurch gerade sind. Aufgrund dieser wohldefinierten RiBgeometrie und der eix&achen Xaterialstruktur (E~~istalle) konnte die Ri~a~b~it~gsgeschw~djgkeit in verschiedenen Proben unter identischen Bedingungen mit einer Genauigkeit von 1,s Prozent reproduziert werden. Auaerdem kiinnen mit dieser neuen experiment&en Xethode Einzelheiten des Verlaufs der plastisehen Verformung an der RiDspitze wLhrend eines einzelnen Lrtstzyklus beobachtet werden. Viele Vorhemagen des Ermiidungsmodells (coarse slip model) konnten durch direkte Beobachtungen veri&iert werden.

INTRODUCTXON

Due to the vork of Laird and Smith(l) it is generally accepted that plastic deformation is responsible for the crack propagation in most ductile metals. Laird and Smith”) showed that under almost all con- ditions the crack tip is blunted in the tensile phase and is resharpened in the compression phase. To obtain such a ~han~g crack geometry out of a continuum mechanics calculation is an unsolved problem, because of the varying boundary conditions in connection with contained plastic flow. The

problem is greatly simplified, however, if the assump- tion is made that slip occurs only on slip planes emanating from the vertex of the crack tip.

Orowan proposed already in 1949(*) that the central void in the necked portion of a tensile specimen

could grow with the help of two pairs of slip planes passing through the vertices of this void. These ideas were extended and applied to explain the ductile fatigue crack formation and propagation by the author in 1967,(s) and independently by Pelloux in 1969.14) McClintock incorporated in his article in “Fract~e”(~) the concept of alternating slip on inter- secting slip planes into continue mechanics cal- culations concerned with unidirectional ductile frac- ture.

The slip processes according to the fatigue model quoted above are shown in Fig. 1 for the case of large crack propagation rates. This model explains qual- itatively the general ~haracte~~ics of fatigue fracture and some specific consequences could be versed experimentally.(3*“*6) Verification of details was, however, hindered by a severe drawback in the ex- perimental technique : In polycrystais macroscopi- tally well defined and plane fracture surfaces can be produced with the help of “compact tension speci- mens”. The irregular grain boundaries interfere, however, with the slip processes near the crack tip in

* Received February 6, 1954 r Submitted as “Rabilitationsschrift” at the University of

Gattingen, Kest Germany. $ Argonne Sational Laboratory, ..%rgoMe, Illinois 60439,

T;.S.A. 5 Present address: 31PI f. Eisenforschung, 4 Diisseldorf,

Germany.

XCTA JIET,1LLURGIC_4, VOL. 22, SEPTEJIBER 1971 1135

llj6 dCT_1 MET_iLLURGICA, VOL. ‘9, 1974

I CRACK OPENlNG ~TENS~ONI

CRACK CLOSING IC OMPRESSIDV 2nd TENSION

J

PIG. 1. Slip processes during one loading cycle according to the coarse slip fatigue model’zi*6’ drawn for the ease of 1,arge crack propagation rates (more than one pair of activated slip pianes per cycle). d new sub- picture 1J drawn after every activation of a slip plane. The last motion of one of the crack sides is indicated by an arrow above the last activated slip plane. Corresponding points in the undeformed material

ahead of the crack tip are at the same height in all subpictures.

an unpredictable way and make detaiied observations

impossible. In single crystals on the other hand,

the strong anisotropy of plasticity usually makes the

crack profanation also very unpredictable even in

circumferentially notched crystals, so that up to

recently macroscopically plane fracture surfaces

could not be produced in single crystals. The dif-

ficulties both in poly- as well as in single-crystals

are reflected in the fact, that measurements of the

crack propagation rate were subject to a large scatter,

typically of t,he order of a factor two.

In this work experiments are described in -rvhich for

the first time well defined macroscopically plane

fracture surfaces with a controllable crack front direction are produced in fatigued single crystals.(3)

According to the n-e11 defined crack geometry as well as the simple structure of the material, crack propa-

gation rates could be reproduced from specimen

to specimen to within I.5 per cent. With these new

experimental techniques observations of consider-

able details of the slip processes at a crack tip were

carried out and +ll be described.

EXPERIMENTAL

easy crack nucleation. The notches xvere cut by a

wire in a spark erosion machine. The resulting

notches had parallel walls, were about 0.27 mm wide,

and had a circular root. In order to guarantee crack

initiation along a well defined straight line in the bottom of the notch, a razor blade rvas pressed

manually into the root of the notch, producing a

very sharp cut of about 0.1 mm dept,h.

Two types of tests xere performed : Fully reversed

four-point bending tests and push-pull tests u-ith

zero mean stress. Figure 2 shows schematically the

arrangement for the bending test: In one half cycle

forces are applied as indicated by the drawn out arrows, whereas the broken arrows indicate the applied

forces during the other half cycle. All of these forces

p-----A

.*Y +-J 1 :yF--: i 4 : ,P -----___, - mo, ,;,*- ----___ _ ! J i”i / /‘

I Oriented copper single crystals were grown from Orientation A : c = lC@1/ I

99.999 per cent pure copper by the Brid,man method Orieototion 8: c =lOlll

under purified hydrogen. The crystals had a square ’

cross section of 6 x 6 mm. FIG. 1. Geometry and orientation of the bending

All tests were performed with notched crystals for specimens. The cross section is 6 x 6 mm (l/4 by

l/i in.)

Frc. 3. Geometrv I and orientation of the push-pull specimpew. The cross section is 8 x 6 mm (1!4 by

li?, in.)

uwe nppliiecl with the help of knives, which were

kept in place by sheet metal strips allon-ing for

lateral motion of the 1iIlivW. Steel platelets between the knives and the specimen surface kept

the linires from cutting iuto the soft copper specimens, Figure 3 shows the specimen geometry for the push-

pull tests : cylindrical stainless steel pieces xere silrer-

soldered onto the encls of the crystal proriding hard

shoulders which could be clamped by the grips of the

testing machine without causing any plastic defor-

mation of the copper specimen. Single crystals are very soft initially and their

yield stress is increased by cyclic hardening by a factor

of t twenty-. Therefore cyclic deformation of notched

virgin single crystals would result in a very inhomoge-

neous hardening due to the stress concentrations

around the notch and the yield stress would be strongly

position dependent. In order to reduce this inhomoge-

neity the crystals used for push-pull tests nere

c_vclicall~- hardened up to 31 S/mm” shear stress

before the notch x-as cut,. The bending specimens

were not prehardened because the stresses in bending

are inhomogeneous also n-khout a notch.

The asial orientations of all crystals used Kere of

the type .~lOOj in order to obtain a {lOO}-fracture

surface, which is the only plane in f.c.c. metals along

which macroscopically stable .‘mode 2” crack propa- gation is possibIe (see “results and discussion”).

For the bending specimens two different, azimuthal

orientations A and B (see Fig. 2) were used. In

orientation _-i the root of the notch is a <OOl)-direction.

Orientation B is turned by 15’ about the specimen

axis as compared with orientation A, so that the root of the notch is now a (Ollj-direction. The depth of the notch in the bending specimens was 1.6 mm,

i.e. about one quarter of the specimen thickness. All push-pull specimens had a diagonal notch

going halfway through the specimen and the bottom of the notch was alvzt;vs parallel to a :@ll)-direction (see Fig. 3).

The tests were performed in air at room temperature

with the help of a sophisticated hyIraulic closed-loop

testing system. In the push-pull test.s the machine

Lras controlled to gke a constant plastic strain

amplitude. This resulted in a constant crack propa-

gation rate throughout the crystal. In the bending

tests it was necessary to increase the plastic bending

amplitude with decreasing stress amplitude (due to

the increasing crack length) in order to get a constant

crack propagation rate throughout the specimen.

RESC’LTS ASD DISCUSSION

Reprodmzibility of crack geonetry and cratkpropagation

rate

Due to the plastic anisotropy of single crystals it

is difficult to obtain a regular crack shape. There is

evidence that fatigue cracks in single crystals propa-

gate in a very irregular nlanner.(3~6.J.y’ The fracture

surface is far from being plane on a macroscopic

scale since the direction of crack growth changes frequently. In the course of our experiments we

found, however, one important exception: In bending as well as in push-pull tests a macrostopically plane

and regular fracture surface was obtained in single

crykald a-ith a {loo} cross section. Figs. 5(a, b) and S(a. b) give esamples of these (100) fracture

surfaces. The macroscopic appearance of the fracture

surfaces of differently oriented bending specimens

- /II

ii2 /

FIG. 4. Fracture surfaces of differently oriented bending specimens shoving that macroacopica$ plane fatigue crack propagation is only po&ble m $001; planes. I-pper black areas are the n-alla of the notches. Crack

propagation from the top to the bottom.

(b)

Fxas. 5(a, b). Optical micrographs of t,he total fracture surface of bending specimens of orientation d and B respectively (see Fig, 2). The upper border is the root of the notch. Crack propagation from top to bottom. The white lines are rest lines indicating the position of the crack front after every 400 cycles. Repro- ducibility of pattern (i.e. also crack propagation rate) is 1.5 per cent for different specimens under identical

conditions.

can be compared in Fig. 4, demonstrating the unique- ness of the (100) planes. This experimental result can be easil? understood in terms of the coarse slip model (Fig. 1) as will be shown in detail later on.

The choice of the axial orientation thus determines whether a nell defined plane fracture surface is obtained or not. But eren if this is achieved b>- using <lOO)-oriented cr>-stals, the direction of the crack front tithin the (100; fracture plane is not prescribecl

in a push-pull test. The situation is different in

bending tests. Since the tensile stress in a bent. bar

increases with the distance from the neutral plane,

there is obriousl~ a tendency to make the crack

front parallel to the bending axis: If we assume a. crack front n-hich is not parallel to the bending axis, those parts of the crack front which are ahead

are in regions of smaller applied stress and moTe more sloul~- than those lvhich are lagging behind and thus

are in areas of larger applied stresses. Therefore such a crack front, will soon become parallel to the bending axis and then all parts will propagate tith the same speed. If even in bending tests the crack front is not straight and parallel to the bending axis. this is an indication of differences in the clrix-ing forces. For example near the surface the driving force for the crack is smaller than in the interior (plane stress TS plane

strain) and therefore the crack front is lagging behind at the surface (see Figs. Qa. b). In summarizing it can be said, that in bending tests of ;lOO; crystals both the fracture plane as well as the direction of the crack front should be well defined and should be reproduc- ible with high accuracy in different specimens.

In Figs. 5(a, 1,) the fracture surfaces of bending specimens of orientations A and B (see Fig. 2) are shown at a low magnification. In the upper part of the figures the notch is visible from which the crack started. The Tvhite lines indicate the position of the crack front after every 400 cycles. They were pro- duced by a tetnporary reduction of the loading amplitude, u-hi& reduced the crack propagation rate by about two orders of magnitude. These “rest lines” show- the well controlled crack propagation through-

out the specimen. The reproducibility of the pattern

of the rest lines and therefore of the crack propa-

gation rate was found to be 1.5 per cent for different

specimens uncler otherwise identical conditions.

Crystallographic constraints for the crack front clnd

the fracture plane

According to the model (see Fig. 1) two slip planes-

i.e. (111: planes in f.c.c. metals-pass through the

crack t,ip. Therefore the crack front should always

be paralIe1 to the intersecting line of txo {Ill)

planes which is a (011) direction. The simple pre-

diction of the model therefore is, that. the crack

front should be parallel to ~:Oll:- directions.‘3*4’

Due to possible multi-slip at the crack tip deriations

from these ideal directions of the order of 103 are to

be espected.

It is difscdt to rheck this prediction unambigu- ously in experiments with uncontrolled crack propa- gation and for u&now-n local orientation of the fracture plane. For example if the fracture plane is obarrved along a viewing direction, which is parallel to a 1111) directionl all sis different {Oil> directions would appear to form angles of 303, 6O”, 90”, MO”, lSO’, with each other. The reader can verify this by looking perpendicular on one face of the Thompson tetrahedron and by watching the edges. Thus in this l%eorst case the projection of nny direction is at most 13” away from the projection of a loll> direction. The situation is improred considerably if the local orientation of the fracture plane is known, because this limits the number of possible <Oil) directions.

In onr case of {lOO} fracture planes there are two (011) directions available. In orientation d (see Fig. 2) they form an angle of 15” with the bending axis. Therefore the crack front isforced by the bexdiltg to lie along the ~t~~o.st mfCtcor&Ee direction according b the ntodel, namely the bisector between the two available :OllJ directions in the fracture plane. Figure S(a) shalt-s that this can be achieved indeed in the center of the specimen. Figure 6(a) sholvs a representative area out of the center of Fig, 5(a) at a higher magnification. It is obrious that striations indicating the direction of the crack front on a mic- roscopic scale are indeed parallel to one of the tlTo (011) directions in spite of the different arerage direction of t,he crack front. The same is true for much larger crack propagation rates. Figure T(a) gives one examplefor~O~~m~cycle shoting convincin&- the zig-zag nature of the crack front. We believe tha$ these results are strong evidence for the validity of the coarse slip model, since the predicted striation direction is observed even when the external con- ditions do strongly favor a different one.

If on the other hand the crack front is forced by the external conditions into an allowed direction, long and straight striations are found. Figure B(b) sho\vs the macroscopic appearance of the fracture surface of a crystal with orientation B, where the bending axis is parallel to (01 1) . The crack front, is much straighter in the center of the specimen, since any det-iation from the ho~~ontal would require segments of the crack front being perpendicular to the bending axis. Due to the possibility of lateral relaxation of the stress concentrations at the surface (plane stress vs plane strain) the crack front. lags behind in the surface influenced areas (see Fig. 5b). This requires, as discussed above, crack front segments perpendicular to the bending axis if the requirements of the model we to be fuElled. Figure 8(b) shows a

ia)

(bf

FIGS. @a, b). SEX micrographs of flvpieal parts of Figs. @a. b) (center of Fig. 5[af axtd rtghc hand border between cent.rai anti surfwe influenced area of Fig. 5(b). Striations indicate local direction of the crack front, rhich i atways paratiel to <till:\ direczions, even if these are not perpendicular to the average direction of crack propagation {top to bottom at, a rate of OJ,um/

cycle).

representative area containing the well debed boun- dary between the center area and the right hand sur- face influenced area of Fig. 5(b). On the left hand side of the boundary in Fig. G(b) there are horizontal striations risible x-hi& are represenzatire for the s-hole center area. On the right hand side of the boundar)- there is a mixture of differently oriented striations with the tendency to lie either horizontal or -vert,ical. Qualitatively the same is true for crack propagation rates as large as 16 ,um#.cycle as shown in Fig. Y(b). Thus also under these rery adverse conditions there is a well recognizable tendency for the crack front. to lie parallel to a “11) direction. This indicates, that the major pars of the plastic

(b)

FIGS. ;(a, b). The same RJ Figs. 6(a, b) but for larger crack propagation rates of 4O,um/cycle and 16/cm/c~cle

respectively.

deformation at the crack tip still happens on t\ro slip systems with only minor activities on others.

\Ve shall no\r discuss the crystallography of frac- ture planes: Any segment of a fracture plane con- tains by definition at, some instant of time the crack

front which is, as shown above, parallel to a -,011> direction. Therefore any segment of a fracture plane must belong to a {Oil) zone. This is the necessary and sufiicient condition for the orientation of micro- facets of fracture planes. Xore detailed arguments are necessary to decide about preferences within this general class of possible orientations: As Ttill be shonn in,““’ following this paper, there is a criterion derirable from the coarse slip model in terms of the arern,ge strains 6,, ~~ on both slip systems inrolred

s-here c is a dimensionless material constant larger than ‘7, characterizing the coarseness of slip and x is the angle between the txo actiw slip planes (cos x =

--a for f.c.c. metals). Obviousl~~ it will be adrantag- eous to keep both E, and p2 as small as possible. According to (1) the largest ralue of E, and F, is minimal if .?I = P,. It is obvious from Fig. 1 that, 5, = P, x-ill result in a fracture plane bisecting the two slip planes. J1-ith the help of a Thompson tetra- hedron it cm be easilv seen. that there are only tn-o tJ-pes of planes which are bisecting planes of the 111 I>

slip planes: (100) and {Ollj. Therefore the facets of a fatigue crack will fa\*Orably be {l(:‘cb) Or {ol 11. as

pointed out by PellowP) and othetxiZZ! One ha6 to have in mind? however, that other planes in the (011) zones can come into play as n-e11 if Ed = E?. This situ- ation differs considerably from the constraints for the direction of the crack front di~cussect above: They cannot be violated easilv because this ~vould require at least the help of a third slip svmem.

Up to non- 9x2 discussed only the constraints for microscopic facets of the fracture plane in which the crack front is straight. Macroscopic crack fronts are

usually bent (see Figs. 5a, b). Therefore a plane \I-hich macroscopically is suitable for crack propagation must, at least contain two difireut {Oil’. dimtiom along which the two kinds of segments can Lie which are necessary to make up a macroscopicallr bent crack front,. With the h 1 e p of a Thompson tetrahedron the reader will easily verify, that onl- (100) and {I 11) planes hare this property. The (111) planes cannot

possibly become the fracture plane since this would require 8, = 53 and g2 = W (see Fig. 1 and equation (1)). Thus vith very simple arguments we hare derived from the coarse slip model. that the (100) planes are the only ones suitable for macroscopic

crack propagation. All other planes (excluding {ill) planes as discussed abore) uhich contain a :‘(ill) direction, contain only one. Thus they can contain only straight crack fronts, so that the crack has to leave this plane as soon as its front gets bent. This esplains the bump_x- appearance of fracture surfaces \vhich are not (100) planes as demonstrated in Fig. 4.

i This indicates, by the ray, that stage I crwk propagarion whenever it proceeds along a jlll: plane, re,q;Sres something else but slip on 8 second slip system. e.g. oxma:ion.

From Figs. 5(a, b) it is evident, that the change in streK<es between interior and surface of the specimen has a drastic effect on the shape of the crack front. Erenifthereisa (011: direction parallel to thebending axis, as in Fig. 5(b) the crack front deviates consid- erably from this direction near the surface. X look at the comples striation pattern in this surface in- fluenced area (Figs. 6b, ‘ib) shows convincingly that there is no hope to find a simple slip line pattern on the surface.

With a minor modification of the geometry one can, however, achieve straight and undisturbed crack

FIG. 9. Optical dark field micrograph of the slip line pattern accompanying the propagating crack on the side face of a push-pull specimen. The crack extends from the bottom of the round notch (at the top) down to the very tip of the undeformed dark triangular area

at, the bottom.

(b)

FIGS. dla, b). Optical micrographs of the cotal fracture surfaces of push-pull specimens (see Fig. 3). Crack propagation from top to bottom at a rate of 130;~m/cycle and 43Oym!cycle respectively. Khite line5 are r!ot rejt lines but true striations indicating the position of the crack front after every qele. Masimal undis-

turbed striation length 7.5 mm (0.3 in.).

fronts throughout the whole crystal from surface to surface: In Fig. 5(b) the undisturbed crack front would hit the surface under an angle of 90”. It is, however, bent back such that it hits the surface under about 4.5’. If the geometry is chosen in such a “-a,~~ that the undisturbed crack front hits the surface tmder 45’ to begin with: there might be no bending baclr at the surface at, all. The geometry of the push- pull specimens do fulfill these requirements (see. Fig. 3). Figures 6(a, b) show the resulting fracture surfaces. Obviously this purely empirical approach xorks very xvell, because straight and undisturbed crack fronts as long as 7.5 mm can be produced tith- out any evidence of a perturbation due to the surfaces. Sote: the white lines on the fracture surfaces in Figs. S(a, b) are real striation (though being 7.5 mm long!) representing the position of the crack front after every cvcle; they are not rest lines as in Figs. .?i(a, b). For smaller crack advance rates one can, of course, produce any striation spacing and the crack fronts till stay straight LIP to the surface.

TTith such a geometry it can be expected, that the slip lines visible on the specimen surface are represen- tative of the real processes taking place during crack advance tithout being unduly disturbed bp the surface. Figure 9 shons on the specimen surface the slip accompanying the crack. The crack advance rate is small enough so that rre get contained plastic flow-. The slip line len.gth is independent of the crack length since the machine was controlled to give a constant crack propagation rate. The perturbations in the upper half of the picture are

due to the Vera blunt notch geometry which deter- mined the slip distribution in the be,$nning of the test. Again due to the well defined conditions the slip line pattern shonn in Fig. 9 is highly reproducible from specimen to specimen.

Figure 9 shows a striking resemblance to the schenmtic Fig. 1 as far as the following features are concerned :

(1) The slip near the crack tip is almost perfectly confined to txvo slip systems.

(2) The slip traces are emanating from the sides of the crack such that on each side of the crack there is mainly one slip system active.

(3) There is an almost slip-free triangular area in front of the crack tip.

By a more detailed inspection of the crack hip x-e will substantiate also the follo~vinmg features of the

W FIGS. lO(a, b). SEM micrograph showing the slip, which is necessary to open up the crack b- the amounts shown (5 I’m and 40 ,urn respectively). Oid slip lines n-hich formed prior to this last crack opening were clectro. polished away when the crack was complerely closed.

FIG. 11. SEX micrograph shorring the typical V-shaped crack tip after opening it up by 170 [irn. So previous

polishing.

model (Fig. 1) : (4) At any instant only the slip planes emanating

from the crack tip are active. (5) The open crack tip is a T--groove with a constant,

angle at the tip. The process of ‘-blunting” the tip by plastic deformation is a widening of the “Y” at constant crack tip angle.

(6) The crack closes in compression by slip re- versal at the current tip of the open part of the crack, leaving the angle at the tip of the open part of the crack unchanged.

In order to facilitate the comparison between the microyraphs and the schematic Fig. 1 it should be noted, that the slip line spacing was chosen in Fig. 1 to be very large in order to show the element.ary slip processes as clearly as possible. In reality this spacing is usually below the resolution of the scanning microscope and thus it cannot be clearly resolved in Figs. 9-12.

In order to test point 4 experimentally, the course of deformation x-as interrupted after the compressive phase in order to remove the slip lines by elect.ro- polishing. Then the deformation was continued by a small amount,. The newly formed slip lines are shown in Fig. 10(a). The crack is opened by about 5 ,um and the ne\v slip lines do in fact emanate from the current crack tip only. From all results we esti- mate the uncertainty to be about 5000 x. Fi,we 10(b) shows the same crack after 40 pm opening and it shows again, that the nerr slip lines al\vays start from the current crack tip.

Point 5 is easily verified by continuing the tensile deformation, which opens the crack more and more. Figure 11 shows another crack tip lvhich was opened in this manner up to 170 ,um. Sote the well defined

FIGS. lZ(a-ff. Sequence of succe&ve shapes of the crack tip durinr one loading cycle. There is a striliing resem. blame to Fig. 1 if the t-so folio-sing differences are taken into account: The slip Iin? spacing in Fig, 1 we,s chosen much tarper than in Fig. 12. The residual stresses do partly close the crack in Fig. 1‘3 during

every unloading before taking the SEX pictures.

F-shape. The arms of the V are straight to a good

approximation. Since slip occurs at the crack tip

only (point 4) this prot-es already that, the angle at

the crack tip was constant. during the process of

crack opening. A quantitative determination of the crack tip angle from Fig. 11 is not, possible since the

undeformed specimen surface was inclined to the

tiewing direction in the scanning electron microscope.

Furthermore t,he Burgers rectors of the active slip

systems do not lie in the undeformed specimen surface which makes the surface in the slipped

regions inclined to the unslipped specimen surface as

well. By careful inspection of Fig. 11 the reader will

realize that the crack is closed at the very tip for

about. G jtrn. Therefore the geometry corresponds to

that of Fig. 1 in the beginning of the compression phase, if we hare in mind again that Fig. 11 has much

more slip lines wit,h a much smalier mutual distance

than in Fig. 1 (making the short closed portion of the

crack a smooth vertical line in Fig. 11 but not in

Fig. 1). If the specimen is not unloaded before it is

examined in the scanning electron microscope and

if it is examined under stress, no such crack closure is

risible at all. From this it can be deduced, that the crack closure is due to compressire residual stresses

around the crack tip lx-hi& were produced by the tensile deformation and lead to reverse deformation

during unloading. An examination under stress,

however, imposes such serious limitations on the

precision of the control of the deformation, that it was preferred to tolerate the partial crack closure before et-cry examination tith the scanning electron

microscope. In order to test point, 6, a series of pictures was

taken during one cycle of deformation (Fig. 1’1). The crack closure due to unloading in the tension

phase is risible as small vertical segments in the arms

of the otherwise L.-shaped crack t,ip. In detail the

erents during the course of the deformation are as follows : In the first. subpicture the closed crack is

tisible with the slip lines emanating from both sides

of the closed crack and the almost undeformed tri- angular aren in front of the crack tip. After opening

the crack by 70 !trn, the Fig. 12(b) shoit-s the typical

Y-shaped crack tip with about 10 ,‘cm of closed crack

due to unloading for the esaminat.ion. On the right

hand arm of the T- there is a flaw which is untypical

and should be disregarded. If the crack opening is

continued by i0 llrnl Fig. 19(c) is obtained. The

borders of the crack which existed in Fig. l>(b) already, were moved apart b>- 70 ‘Urn but othewise

stayed total17 unchanged (including the flaw and the

vertical segment due to unloading) since the new slip

occurred always at. the current crack tip, i.e. below

the old track borders. The nexv slip formed the new

lower T’ in Fig. 12(c). again with about 10 !trn of

closed crack due to unloading. Sow a compressire stress was applied, which closed the crack by about

40 ‘urn (Fig. Ed) so that the open part looks almost

like that of Fig. 12(b) again. Further compression

closes the crack completely (Fig. Eel. Sote that

during compression no slip occurred in front of the

crack tip. Instead only the old tensile slip was re-

persed in such a manner that the ac-Gre slip planes

are emanating from the tip of the open part of the

crack (point 4). The latter can be concluded from

Fig. 11 in the following xx-av: BeloT the tip of the

open part, e.g. in Fig. 12(d) no considerable amount

of slip can occur since the crack is closed already and

abore no slip can have occurred since the profile of

the borders of the open part of the crack are in

Fig. l_‘(d) exactly those of Fig. lZ(c; including flaw

and rex-tical segments. The nest ten& deformation

opens the crack at its new crack tip &ich had prop-

.gated from Figs. E(a-e) (one cycle) bv about

1715 {m.

The sequence shown in Fig. 12 gives a rather

detailed picture of the slip processes during one cyele.

It is. however, impossible to obtain angles or exact diztanfes from pictures l&e those of Figs. 10-2,

sirwe the>- are projections of an inclined surface

(kawe of maximal secondary electron emission}

which is not plane (the rwultant slip rectors of the &p processes is not contained in the specimen SW-

face).

If the slip reversal in the compression plxwe were

perfect, i.e. if esactly the same amount of slip occurred

in the opposite direction on exactly the saute slip

planes is esactlf the same sequence as compared to

the tension phase, then the closed crack should not

contain any periodicity corresponding to the c,vcles of loading. However, any imperfect slip reversal

will produce such a periodicitJ- on the fracture surface. Figures 12 (e, f) shows an example: At the

end of the crack closure reverse slip on the right

hand side exceeded that on the left hand side. This

procluccd a kink in the closed crack (Fig. lie; and in both fracture surfaces (Fig. l?f), which v,ill show

up as striations. Since striations in our pictures are the result of

imperfect slip rerersal, it is easy to understand. that

the profile of striations can have almost any &ape

depending on the specific circumstances pre-centing

perfect slip reversal. This agrees well with the

results of experimental investigations xhicb rerealed

many different and hardly reproducible striation

profiles.(l,xL-l*’ There is a rarietp of reasons for

imperfect slip reversal : Csually the length of a

fatigue crack is 1000-10000 times larger than its

maximal width. Furthermore the fracture surfaces

are extremely bumpy. The irregular crack propa-

gation producing this bumpy fracture surfaces also

produces residual stresses which can laterally displace

the fracture surfaces with respect to each other by small amounts so that it is almost unaroidable that

before complete crack closure at the rer>- crack tip, the fracture surfaces touch at some far remote point. This can stop or at Ieast reduce the closing motion of the two crack faces or force this motion into a

different direction (if the touching occurs on in-

clined surface elements). In the first case (incomplete crack closure at the

crack tip) the pro& of the expected striations can

be easil? deduced from Fig. 1 as ~~83 done by Brwk

and B~n-les.~~~~ This t_qe of striation is of the

mirror type uhere the opposing fractnre surfaces

are approximate mirror images of each other with a

mirror-plane in the middle of the crack. Khenerer there is enough compressire stress to

oVercome all possible obstacles againS complete

era& c&we then the fracture swfaces till jbv dei’-

i&ion of complete crwk closure) fit onto each other

and not be mirror images. In this case a large variety of striation profiles is possible depending on the

detailed conditions under \vhich complete crack

closure i3 posAhle,

There are. of course all kinds of misrures of these

two types of striation profiies possible. because there will aln-a!-s be partial closure of the crack tip, Jo that

part of one and the same striation protile can be of the fittinp and part of the mirror type.

CONCLUSIONS

1. There is a ;itrong tendency to make the crack

front of a fatigue crack parallel to a 110 direction:

If the crack front ia forced into a differenr direction by

suitable macroscopic force distri~~~~tio~ 1 bendiq), it

forms a zig-zag line on a microscopic x3Ie with the

segmenta parallel to YllO: direction:. This agrees

with the coarse slip model of fatigue.

2. Macrv~copically plane fracture aurkes can be

obtained in f.c.c. metals only along It)ijl) planes

(see Fig. 11, since these are the onI>- planes which

contain r\vo non-parallel crack front directions which

are allowed according to the model.

;3. The crack propagation rate can be reproduced

in different single crystalline specimens with an ac-

curacy of 1.3 per cent if the fracture surface is plane

and the direction of the crack front is uniquely- pre-

scribed, e.g. by bending.

4. Crack fronts \\llich are straight all the way

through the specimen can be obtained in suitahiy

shaped cr+als. Straight striations a3 long as

i.5 mm (0.3 in.) at a spacing of up to 3CW unl can be

produced in this way.

5. The plastic zone of cracks nith xeh straight

fronts is representative for the slip processes res-

ponsible for the crack propagation. By observation

of these plastic zones the follo~kg derails predicted

by the coarse slip model of fatigue could be rerified:

(a) -It. an- instaut only those slip planes are

activated, which pass through the immediate

neighborhood of the rertcs of the currently open

part of the crack tip. (The maximal distance

SEUY_kSS : SLIP _iT PROPAGATISG F_%TIGUE CR_iCKS-I 1163

between active slip plane and crack tip vertex

is estimated to be less than 5000 -1.) (b) Only two different sets of parallel slip planes, intersecting each other along the crack tip, are activated in such a way that on each side of the crack one set of slip lines is dominant and an almost slip-free triangular area is immediately in front of the crack tip. (c) Tensile strains produce a V-shaped crack tip which becomes deeper and wider whereas the angle at the vertex of the crack tip stays constant. (d) Crack closure starts at the vertex of the crack tip and proceeds backwards by activating slip reversal on slip planes which pass through the immediate neighborhood of the vertex of the currently open part of the crack tip. (e) The angle at the vertex of this not yet closed part of the crack t.ip stays constant also during crack closure.

ACKNOWLEDGEMENTS

The author wishes to express his thanks for many

Scattergood, and D. Bacon. It is also a pleasure to acknowledge the helpful assistance of E. Kay, L. Johnson and J. Sanecki in carrying out t.he experi- ments. The author is grateful to S. L. Peterson and P. G. Shewmon for their continuous support and to P. Haasen for helpful comments and for reading the manuscript. This work was performed under the auspices of the U.S. ,4tomic Energy Commission.

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Vol. 3, 47. Academic Press (1971). p. 6. P. NE~XIXX, A&z Jfet. 17, 1219 (1969). 7. P. lu’~.r;l\ra>~, fnt. Conf. f+act. Xinchen, m, 833 (1973). S. K-H. SCHWALBE, 2. .MelaZZb. 62, 59 (1971). 9. J. DGXCH and P. HAASEF, 2. Netdk. 62, 580 (1971).

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75 (197”). 12. P. J. E. FORSYTH, A& 3fet. 11, 703 (1963). 13. A. J. MCEVILY, JR. and T. L. JOHSSTOS, Int. Conf.

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stimulat,ing discussions with U. F. Kocks, R. 0.