Stacking fault tetrahedra in fatigued stainless steel

STACKING

FAULT

TETRAHEDRA 0.

IN

FATIGUED

STAINLESS

STEEL*

VINGSBOt

Stacking fault tetrahedra have been found in fatigued l&l3 stainless steel. From the maximum edge length the stacking fault energy is estimated to about 8 ergs/cme. Two mechanisms for the nucleation of triangular Frank dislocation loops during cyclic load are discussed. One mechanism requires the diffusion of vacancies created during the fatigue test, while in the other only dislocation movements are involved. As a comparison quenched specimens were observed after different annealing treatments, and only prismatic loops were found. It is concluded that the stacking fault tetrahedra are more probably created by the dislocation mechanism than by the vacancy. mechanism. TETRAEDRES

DE FAUTES

D’EMPILEMENT DANS L’ACIER FATIGUE

INOXYDABLE

APRES

Des t&x&dres de fautes d’empilement ont Bte observes dans l’acier inoxydable apres essais de fatigue. L’estimation de l’energie de faute d’empilement a partir de l’ar&e la plus longue donne environ 8 ergs/cm%. On discute deux mecanismes de la nucleation, pendant l’application d’une charge cyclique, des boucles de dislocations de Franck triangulaires. L’un de ces mecanismes suppose la diffusion des lacunes c&es pendant l’essai de fatigue, alors que dans l’autre seuls sont impliques les mouvements des dislocations. A titre de comparaison, on a observe, apms differents recuits, des Bchantillonstrempes et on n’y a trouve que des boucles prismatiques. On en con&t que le mecanisme de creation des tetrddres de fautes d’empilement par les dislocations est plus probable que le mecanisme lacunaire. STAPELFEHLERTETRAEDER

IN ERMUDETEN

ROSTFREIEN

STAHLEN

In ermiidetem rostfreien 18-13 Stahl wurden Stapelfehlertetraeder beocachtet. Aus der maximalen Kantenlange wird die Stapelfehlerenergie zu etwa 8 erg/cm* abgeschiltzt. Es werden zwei Mechanismen fiir die Entstehung dreieckiger Frankscher Versetzungsringe wiihrendder zyklischen Belastung diskutiert. Der eine Mechanismus erforderte eine Diffusion von Leerstellen, die wahrend des Ermiidungsversuches entstanden sind, wiihrend bei dem anderen Mechanismus nur Versetzungen beteiligt sind. Zum Vergleich wurden abgeschreckte Proben nach verschiedenen AnlaDbehandlungen untersucht. Es wurden nur prismatische Ringe gefunden. Es wird gefolgert, da9 die Stapelfehlertetraeder mit grBBerer Wahrsoheinliohkeit duroh den Versetzungsmechanismus als duroh einen Leerstellenmechanismus gebildet werden.

1. INTRODUCTION Stacking fault tetrahedra

silver(s) and nickel-60 subsequent creation

A dislocation

collapsed

vacancy

model discs

for the

tetrahedra

Loretto

fault

equation

and

deformed

gold,

silver and

(1)

can

be approximated

derived

1%

in which they the

following

relation between the maximum tetrahedron length 1, and the stacking fault energy y - 4 lnl

=

edge

2Ga2 97T 1/Z (1 -

(1)

r)y

* Received April 6, 1966; revised June 30, 1966.

t Institute of Physics, University of Uppsala. Uppsale, Sweden. ACTA METALLURGICA.

6L0 where the assumption

=

VOL.

16, APRIL

1967

616

I’ = y/Gb, the

simple

I?

r,, = b/2 and v = 4 is made.

Relation (2), however, does not take into account the fact that forces act between the moving partial dislocations,

while the original Frank

transforming

into a stacking fault tetrahedron.

sessile loop is

Czjzek et a1.(s) have performed theoretical calculations of intermediate development stages. They plotted the misfit energy as a function of a tetrahedron development variable for different combinations

r0

to

expression

copper-aluminium

of the material Hirsch

b along the fsult energy

is expressed by the dimensionless parameter

alloys.

fault energy Silcox

edge length by L,

distances

et aZ.f4) have found stacking

Stacking fault tetrahedra are of special interest because they provide a means of calculating the stacking

atomic

edge, so that L, = 1,/b. If the stacking

copper and a number of gold-tin,

occur.

Let us express the tetrahedron the number of shortest

been

in plastically

and nickel-cobalt

(3 = shear mod-

has

suggested by Silcox and Hirsch.(l) Recently

core radius,

ulus, a = unit cell size and v = Poisson’s ratio.

‘A cobaltc3) after quenching and

annealing.

from

where r, = dislocation

have been found in gold,“)

of the L and

I? parameters. Examples of the obtained curves are schematically shown in Fig. 1. These curves show that energy barriers exist, which

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METALLURGICA,

MISFIT ENERGY

VOL.

15,

1967

edge length limit L,,. If, however, growth by addition of vacancies

can take place, tetrahedra

metastable

C

sizes

corresponding

of

region

can reach the

b without

development

energy

b-c border represents L,. As a comparison function

passing

the

barrier,

and the

(2) is plotted

into the

same diagram. The curve lies in the metastable region, rather close to the b-c border. This can be expected,

because

(2) does

not

energy barriers into account,

b

take

intermediate

which is equivalent

to

assuming that growth is possible. The purpose of this paper is to report that stacking fault tetrahedra have been found in fatigued stainless steel.

The

stacking

possible mechanisms

fault

energy

is estimated

of the tetrahedron

and

nucleation are

discussed. 2.

The investigated

(I TRIANGLE

Fm. 1. Examples of the misfit energy as a function of the degree of development of a staclkingfault tetrahedron from a triangular Frank dislocation loop. After Czjzek

et cd’5 tetrahedra

the transformation,

can be energetically

steel contained

13% nickel and 0.02%

TETRAHEDRON

may prevent

EXPERIMENTAL

and that complete stable, metastable

or

annealed

carbon.

18%

cooled. A series of push-pull

fatigue tests with zero mean

stress was carried out with a stress amplitude of lo-19

kp/mms,

or to fracture.

The frequency

was 2000 c/min.

a, b and c in Fig. 2. If no growth of complete

studied

Thin foils were prepared by

transmission

Siemens Elmiskop Laboratory

lODO-

microscopy

I, an OPL IB microscope

for Electron

The

from the specimens electron

a few cases, in the 1 million

1

range

during 104, 105, 106 and 10’ cycles

test pieces had a section of 25 x 5 mm.

hedra is assumed, th a-b border represents the upper

were

at 1050°C during 30 min and very slowly

unstable. In an L versus F diagram the surface therefore can be divided into different stability regions, tetra-

chromium,

The specimens

V microscope

Optics in Toulouse,

and in a

and, in of the France.

In2L0_r 900-

:/

BLO

3.

1 I I

Figure

RESULT

3 shows the obtained

S-N

curve.

Certain

grains, but not all, in specimens representing the indicated region in Fig. 3 contained stacking fault

800-

c

Unstable

region

1- ,103

FIG 2. Tetrahedron stability regions in the L-r surface. After Czjzek et aZ.16) The dashed curve represents equation (2).

Fm. 3. The S-N curve of the fatigue experiment. Specimens representing the shaded region contained stacking fault tetrahedra.

VINGSBO:

STACKIKG

FIG. 4. Stacking

tetrahedra. obtained

Figure

4 is a typical

fanlt

example

FAULT

tetrahedra

of the

images.

In those grams where tetrahedra mean density

were found,

was of the order of 5 x 1012 cm-3.

was not possible,

however,

to identify

tetrahedra

the It of

617

TETRAHEDRA

in fatigued

tetrahedron

stainless

steel.

sizes are more probably

reached directly

than by growth of complete tetrahedra by the addition of vacancies. If thus no growth is assumed, the a-b border gives r = 0.6 or y = 8 ergs/cm2.

This is lower than the

edge lengths < 150 A, although a great deal of smaller

extended node value, referred to above.

dark contrasts were observed.

The calculated

it is an upper limit, when the tetrahedron

therefore must be considered

as a lower limit.

density

applied, for the following

The largest observed edge lengths were 1400 8. size distribution

of the identified tetrahedra

The

reason.

Nevertheless method

is

In order to be sure

that no larger tetrahedra exist. than those which have

is shown

in Fig. 5. No observable differences in density or size distribution between different specimens were found. No tetrahedra

were found

in specimens

fatigued

-

during lo4 cycles. 4.

ESTIMATION

OF

FAULT

The intersection

THE

STACKING

ENERGY

of the straight

line L = L, with

the curves of Fig. 2 gives the corresponding r values. In this experiment Lo was found to be 570. If growth of complete tetrahedra can take place, the b+ border gives r = 1.9, which in this material corresponds to y = 28 ergs/cm2 (the Silcox-Hirsch curve gives y = 22 ergs/cm2). This is considerably higher than the values published by other workers. Dulieu and Nutting(Q have performed extended node measurements on a similar steel, and obtained a value of

13 ergs/cm2. 3

This

indicates

that

the maximum

11

I

I

I

I

I_

x)o150200250300350400450500550600 FIG. 5. Size distribution

of the tetrahedra.

L

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618

METALLURGICA,

VOL.

15,

1967

(b)

FIG. 6(&-c). Dislocation mechanism for the formation of a triangular Frank dislocation loop. After Lo&to et ~1.‘~)

(0) been found, angular

it is necessary

Frank

loops,

to find undissocisted

representing

the

tri-

met&able

region of Fig. 2, that is of edge lengths L > L,,. No such loops were found. Referring to the discussion in Section 6 below, it is even doubted

atomic layer thick.

Frank sessile loops, created when

the cavities collapse, grow to equilateral

that Frank loops

of any size are stable and can be found in this material.

the addition

of vacancies.“)

triangles by

This is the mechanism

supposed to operate during quenching and subsequent annealing. In the present

experiment

the specimens

were in

Thus it is possible that L, > 570, and y < 8 ergs/cm2. The low y value obtained here indicates that the

thermal

calculations of Czjzek et al., which are based on a somewhat simplified geometric model, give too low

during the test.

values.

possible, however, that vacancies produced during the fatigue test can play an important role. Several

The same observation

has been made for silver

by Loretto et al(*) 5. NUCLEATION

If growth

of complete

left out of consideration,

stacking

fault tetrahedra

is

takes place in

two steps:

contribute

Therefore

to the nucleation

mechanisms

of a triangular

Frank

dislocation

loop of the loop into a stacking fault

tetrahedron. The last step is entirely a dislocation process, and shall not be further discussed here. The first step, however, the nucleation of a triangular Frank loop, can take place either by a vacancy mechanism or by mechanism.

The vacancy mechanism requires excess vacancies, which by diffusion cluster to disc-formed cavities, one

at room temperature of Frank

cannot

loops.

have been proposed

It is

for the

creation of vacancies by the oscillations of dislocations during cyclic load. The micrographs of this experiment indicate that screw dislocation jogs and edge dislocation The dislocation et al.,(*) describes

(ii) transformation

of the fatigue

thermal vacancies

dipoles might act as vacancy

(i) nucleation

a dislocation

at the beginning

test, and they were maintained

dislocation

MECHANISMS

the formation

equilibrium

loops

from

sources.

mechanism,

suggested

the nucleation

certain

dislocation

by Loretto

of triangular

Frank

jogs

plastic

during

deformation. With the notations of Fig. 6(a) a screw dislocation in the (lli) plane with the Burgers vector a/2 [liO] can get a pure edge multiple jog DA in the [llO] direction. “upper”

screw

If at a sufficient shear stress the

segment

cross slips downwards

(111) plane, and the “lower” the original (lli) jogs are formed

the

screw segment glides in

plane, Fig. 6(b), two new multiple along DB and AB.

All the jogs are

VINGSBO

: STACKING

FAULT

619

TETRAHEDRA

Fra. 7. Prismatic dislocation loops in quenched and annealed stctinlesssteel.

supposed

to dissociate

according

to the reaction

If the tetrahedra vacancy

whereby a trapezoidal

Frank dislocation

loop is formed

in the (ill) plane. When the screw segments meet in B, the loop is an equilateral triangle, ADB, Fig. 6(c). 6. DISCUSSION

The density of stacking fault tetrahedra was found to be of the order of 5 x 1012 cmM3. From Fig. 5 it can be seen that the mean edge length was about 150 6.

are supposed to be created by the

mechanism,

the above values correspond

to

a vacancy concentration of 10P5. At a dislocation density of lo9 cmm2 during 105 cycles, a production of 250 vacancies/halfcycle

and cm dislocation

necessary to obtain this concentration. On the other hand, for the dislocation

then is

mechanism

to be possible, the same values require one favourably operating jog of mean length 150 b/50 halfcycles and cm dislocation. Each of these

alternatives

seems

quantitatively

620

ACTA

METALLURGICA,

possible with respect to the described ever, it is known

that Frank

models.

dislocation

How-

loops

rare in stainless steel after any mechanical

are

or heat

VOL.

15,

This can be seen in Fig. 7 from the zig-zag dislocation contrast

near the foil surfaces.

the stacking fraction

of a stacking fault fringe couple.

on the depth

are quite common.

appears

of vacancies

do

not

form

Frank

loops,

and

then

If a loop is sessile,

fault inside it can give rise to only a

treatment, though other stacking fault configurations, such as dissociated dislocations or extended nodes, So it is possible that aggregates

1967

under the foil surface

Depending

the loop

darker than, equal to or brighter

background.

Because of the relatively

important

foil

cannot be the origin of stacking fault tetrahedra. In order to decide whether the vacancy mechanism

thickness,

can operate

the central regions of the foils, while loops near the

experiment quenched

or not was

in stainless

performed.

steel,

Thin

a quenching

specimens

were

from

1170°C into iced brine and annealed

at temperatures

between room temperature and 700°C.

eventual

anomalous

then

than the

absorption

effects decrease the

stacking fault contrast

of loops, situated in

surfaces might exhibit a detectable No deviation be detected

contrast,.

from the background

in any loop.

could

The quenching temperature was chosen to give the vacancy concentration calculated above as corre-

however,

that

would

be

restricted

to only the central region in all foils.

If

sponding

thus the depth distribution

to the tetrahedron

density

of the fatigued

specimens. time at lower temperatures

contained small dislocation

Frank

sessile dislocation

favourable,

quenching

Shockley

rates at the surface and in the interior of

the specimens. density

In regions where loops were found, was

about

3 x 10s cmP3,

300 8.

well to a vacancy

and

As these values

concentration

the

average

correspond

of 10e5, it may be

assumed that the loops have been created from vacancy discs. The loop size is considerably jection

of

loops

is assumed to be random

not sessile, but prismatic. It is concluded that in austenitic

loops. Figure 7 is a typical example. Not all polished foils contained loops, possibly due to the different

diameter

occurrence

and all loops of the same type, the loops are probably

Specimens annealed for 1 hr at 350°C or for a longer

the

the

intensity

It does not seem probable,

of the extinction

smaller than the pro-

(a)

but turn prismatic partial dislocation,

stainless

by being swept by a

in spite of the fact that

this reason it seems more probable fault tetrahedra mechanism Only

For

that the stacking

have been formed by the dislocation

than by the vacancy

occasionally

found

steel

are not energetically

the alloy has a very low stacking fault energy.

been

distance on the glide planes.

loops

stacking

in unidirectionally

mechanism.

fault

tetrahedra

deformed

have

stainless

steel. Further, it seems probable that the suggested dislocation mechanism applies better to the case of

(b)

Fm. 8(a). Formation of a pure edge jog in a pure somw dislocation. The Thompson tetrahedron notations are used. 8(b). Dissociation of a jog on the p and y planes. 8(c). Development of a stacking fault tetrahedron from a dissociated jog.

VINGSBO:

fatigue,

STACKING

than to the case of unidirectional

the following

load, for

reason.

Using the Thompson

can only

dislocations

TETRAHEDRA

The question from vacancy

tetrahedron

notations,

Fig.

S(a), it is evident, that the BC screw dislocation on 6 can cross slip only in a. Thus elementary jogs along DA

FAULT

be formed

from

the intersection

by

of Burgers vector DA on #I or y. Multiple

antly behave

621

also arises, why Frank loops formed discs and from dislocat8ion jogs appar-

differently

in stainless steel.

be due to the difference in initial shape. always

so oriented

that

they

can

stacking faults on two octahedron by a stair rod dislocation,

This may

The jogs are

dissociate

into

surfaces, connected

Fig. 8(b).

This configuration

jogs can then be formed either by repeated intersection

has a very low misfit energy and may lock the stacking

in the same slip plane or by the addition of elementary

fault from the moment

jogs of the same sign moving

to cross slip.

Thr probability

along the dislocation.

of repeated intersection

to an average

place directly,

according

jog length of 150 b is about the same in the unidirec-

the formation

tional as in the cyclic case (if the frequency

A Frank dislocation,

high).

The possibility

of elementary

along the dislocation

is not very

jogs to oscillate

and add to jogs of the same

disc, however, the beginning.

plane, which is not close packed accepted

as a slip plane.

elementary

jogs

could

The

and BC is a (001) and generally

Yet it seems possible move

in the

close

not that

packed

direction BCeitherdirectly by slip, or by the successive, alternating vacancy and interstitial climb in the y and [j planes.

Certainly such an alternating

would be facilitated which

are created,

load. According the length

when

the

elementary

to this mechanism of multiple

jogs

the fact that no tetrahedra in tetrahedron

are

the density as well as with

an

This might explain

were observed

On the contrary,

jogs

during the cyclic

will increase

increasing number of load cycles. lo4 cycles.

climb motion

by the vacancies and interstitials

dragged along by their dislocations

no appreciable

after only increase

density and size was found for different

numbers of cycles above

105.

thus a possibility it has developed

a collapsed vacancy

Only small fractions

partial dislocation,

DA

to Fig. S(c), rather than via

surrounding

Burgers vector

the vectors

begins

then takes

has a more or less circular form from

along [IlO] directions

BC is a pure edge dislocation.

formation

of a triangular fault on y as in Fig. 6(c).

sign or annihilate jogs of opposite sign is, however, greater during cyclic load. The jog along DA of plane containing

the screw dislocation

The tetrahedron

of it are oriented

and able to split up.

There is

that it may be swept) by a Shockley removing the stacking fault, before into a triangle.

ACKNOWLEDGMENT

The author is indebted to Sandvikens Jernverk AB, Sandviken,

Sweden, for supplying

the steel and per-

forming the fatigue tests, and to the Swedish Technical Research Council for partial financial support. Part of the electron microscopical out at the Laboratory

work was carried

for Electron Optics in Toulouse,

France. REFERENCES 1. J. SILCOX and P. B. HIRSCH, Phil. Msg. 4, 72 (1959). 2. R. E. SMALLMAN, C. H. WESTMACOTT and J. H. COILEY, J. Inst.Metab 88, 127 (1959). 3. S. MADER, A. SEEQER and E. SIMSCH, 2. Metallk. 53, 785 (1961). 4. M. H. LORETTO, L.M. CLAREBROUGH and R. L. SEQALL, Phil. Mug. 11,459 (1965). 5. G. CZJZEK,A.SEEGER~~~ S.MADER, Phys.StatusSolidi 2, 558 f1962). 6. D. I&JLI&I and J. NUTTING, RISRA Conference paper MG/Conf/20/64.