The martensite transformation in steels with low stacking fault energy

THE

MARTENSITE LOW

TRANSFORMATION STACKING FAULT

IN STEELS ENERGY*

WITH

P. M. KELLY? The martensitic y to c( transformation in two high alloy steels with low stacking fault energy has been investigated using transmission electron microscopy. In a 12 y0 Mn-10 o/0Cr-4 o/oNi steel the cc-martensite formed as laths, which were always contained within { 11lJy bands of almost perfect hexagonal E. The long direction of these laths was parallel to (11O)r and the habit plane was close to a { 112}, plane, which was perpendicular to the a-bands. The orientation relationships between the three phases y, E and a were determined to within *2” using selected area electron diffraction and in suitable cases to within &p using Kikuchi line patterns. The transformation in a 17 % Cr-9 “/9Ni steel was also examined and found to be essentially similar to the transformation in the Mn-Cr-Ni steel. The Bowles-MacKenzie theory has been applied to this martensite transformation, assuming a (lll),[I2f], lattice invariant shear system, instead of the (11O)J 1101, system used to account for the more familiar transformation to internally twinned martensite, and the theoretical predictions were found to be in good agreement with the experimental results. LA

TRANSFORMATION MARTENSITIQUE ENERGIE DE FAUTE

DANS DES D’EMPILEMENT

ACIERS

A FAIBLE

A l’aide de la microscopic Blectronique par transmission l’auteur a Btudie la transformation martensitique y --f a dans deux aciers allies Q faible Bnergie de faute d’empilement. Dans l’acier a 12:/, Mn-10% Cr-4% Ni, la martensite a apparait sous forme de baguettes qui sont toujours contenues dans des bandes {l 1l}r de la phase 8 hexagonale quasi parfaite. Le grand axe de ces baguettes est parallele aux directions (1 lo), et le plan d’habitat est proche du plan {112},, lui-meme perpendiculaire aux bandes E. Les relations d’orientation entre les trois phases y, E, a ont Qte d&ermin&ss a & 2” en utilisant la diffraction Blectronique selective et dans oertains cas favorables a & p par interpretation des lignes de Kikuchi. La transformation martensitique d’un acier a 17y. Cr-9 y. Ni est similaire a celle de l’acier Mn-Cr-Ni. La theorie de Bowles-MacKenzie a Bti: appliquee & o$te transformation martensitique en faisant l’hypothese que le systeme de oisaillement est (lll)y[121], au lieu du systeme classique (llO),[liO], choisi pour interpreter la plupart des transformations prodmsant une martensite ma&e interieurement. Dans ces conditions, un bon accord est obtenu entre les previsions theoriques et les resultats experimentaux. DIE

MARTENSITUMWANDLUNG IN STAHLEN STAPELFEHLERENERGIE

MIT

NIEDRIGER

Mit Hilfe des Elektronenmikroskops wurde die Martensitumwandlung in zwei hochlegierten Stahlen mit niedriger Stapelfehlerenergie untersucht. In einem Stahl mit 12% Mn-10% Cr-4% Ni bildete sioh u-Martensit in Form von Nadeln, die stets in {lll}r-Blndern der fast idealen hexagonalen s-Phase enthalten waren. Die Langsrichtung dieser Nadeln war parallel zu (110)~ und die Habitusebene war nahe {112},, senkrecht zu den &-Bandren. Die Orientierungsbeziehungen zwischen den drei Phasen y, s und c( wurden mittels Elektronenbeugung in ausgewiihlten Gebieten auf f 2” genau bestimmt, sowie in Die Umwandlung in einem 17% Cr-9% geeigneten Fallen auf )” genau mittels Kikuchi-Linienmustern. Ni-Stahl wurde ebenfalls untersucht und erwies sich als iihnlich der Umwandlung in dem Mn-Cr-Ni-Stahl. Die Bowles-MacKenzie-Theorie wurde auf diese Martensitumwandlung angewandt unter der Annahme anstelle des zur Beschreibung der bekannteren eines gitterinvarianten (lll)y[121]y-Schubsystems, Umwandlung in innerlich verzwillingten Martensit benutzten (1 lO)r[liO],Systems. Die theoretische Vorhersagen und die experimentellen Resultate stimmten gut tiberein.

INTRODUCTION

an

In a number of highly alloyed steels, notably containing

appreciable

hexagonal

e-martensite

amounts is found

the b.c.c. a-martensite.‘l-g)

of

Cr or

in association

those Mn,

a

with

This type of a-martensite,

18-8

stainless

deformed

steel is quenched

at this temperature,

formed parallel to (1 lo),

to -196”C,

martensite

(i.e. (111 ),).

The dislocation

density in these needles was relatively was no sign of the internal

or

needles are

twinning

high, but there found

in high

which appears to form only in low stacking fault energy austenites, has been studied using X-ray diffraction on both optical and electron micros-

The needles often lay in sheets parallel to {ill}, (i.e. (lol},) and adjacent needles in the sheets were generally twin-related. No E was

c~py.(~-~~) Kelly and Nuttingos)

detected in this steel, but isolated stacking faults and fault bundles were observed. The orientation relationship between tc and y was determined using electron

reported that when

* Received September 11, 1964. t Department of Metallurgy, Yorkshire, England. ACTA METALLURGICA,

VOL.

Leeds University, 13, JUNE

1965

Leeds 2,

carbon

martensites.

diffraction 635

and within

the limited

accuracy

of this

ACTA

636

technique

appeared

jumov-Sachs

to be consistent

relationship.

was formed

E and b.c.c.

by stacking

with the Kurd-

After

similar steel in tension at -196’C, both hexagonal

METALLURGICA,

deforming

a

Venables(5) found

u. The hexagonal

faults over-lapping

phase

to form

sheets of more or less perfect E. The u-martensite always associated

was

with one or more of these c-sheets

and the intersection

of two such sheets on different

{ 11 l}? planes was a favoured tc. The orientation

site for the nucleation

relationships

between

of

the three

13,

consequence

1965

of the shears involved

found

that in an Fe-15.1 y0 Cr-11.7%

one transformation

temperature

three different techniques.

which

for

the

ii woi, and

a

relationship.

The

cooling.

y is the

In

same

y

to

E

steels

the

with

studied two and after

a-martensite In

one steel

in

(llO),

the martensite

directions

although

their

evidence

relationship

techniques,

and

plates

single

were elongated

surface

trace

analysis

was

using X-ray

a to y relationship

was

to the {ill},

that

but single some

of

the

a-martensite

pl ane of the band.

Lagenborgu’)

{ill),

bands,

rather

than

to

the

related

e-phase in the austenite,

and

proposed a nucleation mechanism for the a-martensite in terms

showed

planes inclined at 60”

this {225}, habit plane to the hexagonal

partials.

to {ill},,

appeared

The {225}, martensite showed

of slip on two {llO},

associated

with sheets parallel

with the (11 l}, plane of the band.

in the other steel, however,

to each other, one of these (1 lo}, planes being parallel

about 4” away from the exact Kurdjumov-Sachs relationship. The u-martensite in this case was again analysis

both

to have a {259}, habit.

Kurdjumov-Sachs

by Breedis and Robertson@)

trace

Lagneborg@‘)

formed on cooling lay in bands parallel to (11 l}y.

The martensite

IIWI,

determined

surface

Ni alloy only

was detected

18-8 stainless steels both after deformation sub-zero

a large angle (ri85”)

Wl), II(OOOl), IIW), m,

in forming a. This

proposal was later supported by Goldman et ~2.o~) who

showed that the habit plane was a {225}, plane making

:

phases were found to be

VOL.

of the atomic

configuration

at Shockley

The aim of the present investigation

was to deter-

plates could have a habit plane near to (2251,. Reed t7) showed that in 18-8 stainless steels the a-martensite was in the form of plates and not

two steels of low stacking fault energy and in partic-

needles,

as suggested

ular to establish

number

of

these

directions

and

by Kelly

plates

single

were

surface

and Nutting.(lO) elongated trace

consistent with a {225}, habit plane. were elongated

in a direction,

12” from (llo),,

by

analysis

was

Half of the plates

and the habit planes of these plates

a-martensite

bounded

A

(110),

which deviate by up to

were found not to be consistent The

in

plates

{ill},

with a (2251, habit.

always

planes

and

appeared the

in sheets

direction

of

elongation

was always parallel to or close to a (1 lo),

direction,

which

lay in the bounding

{ill},

plane.

mine, as accurately orientation

relationships

determined

Other features, such as the relationship E, the substructure the morphology experimental

an a-martensite plane (ill), would have

results

habit

plane.

Dash

Thus, by the

using transmission

in sheets of faulted

hexagonal

E.

They

disagreed, however, with the suggestion, made by several previous workers, that E nucleates u and instead

proposed

that

the

formation

of

E

was

a

laths and The

in terms

of the

of martensite

trans-

invariant

shear on (11 l)?

WI,. The variant relationship

of the Kurdjumov-Sachs

used by Bowles

orientation

and MacKenzie;05)

ii m,

electron microscopy to study the martensite in 18-12 stainless steel, confirmed a number of the results of earlier investigations and showed that the a-martensite is contained

theory

using a lattice

mi,

in the direction [liO],, plane and not a (225),

and Otte,(s)

are analysed

habit plane

plate lying in a sheet bounded

and elongated a (225), habit

within the a-martensite

IIWL

with the plane of the (11 l}? sheet.

relationship. between a and

of these laths, were also studied.

Bowles-Mackenzie(13-15) formations

laths in

the habit plane, which is associated

(ill),

was always the (225}, plane which made the greatest angle (~85”)

of the a-martensite

(1 lo),

with a particular

the habit plane and

with a specific variant of the orientation

Reed pointed out that, although there are two planes of the type {225}, associated direction, the experimentally

as possible,

i.e.

is taken as the standard variant in the present paper and whenever particular, as opposed to general, indices of planes and directions text

they

are mentioned

refer to this variant.

Jawson-Wheeler(16)

correspondence

The

in the

appropriate

matrices are given

in Table 3. EXPERIMENTAL

The compositions

METHODS

of the two steels investigated

given in Table 1. The steels were rolled into strips 200-300 annealed

are

,U thick,

at 1000°C in argon for one hour and then Partial transformation to quenched into water.

KELLY:

MARTENSITE

TRANSFORMATION

637

FIG. 1. Mn-Cr-Ni steel quenched to -196°C showing a number of large c-bands

(B) containing a-martensite laths. The positions of these laths are indicated by the large arrows and the projected width of the cc-martensitehabit plane interface is visible at A. x 12,000 TABLE 1. Composition Main alloying elements

Cast number

of the steels used

Compo~~;t. Cr

C

-

%) Yi

a-matrensite

17.2

0.04

9.0

-

-

x

and quenched by chemically

samples to - 196°C. electron

polishing

Thin foils suitable

microscopy

min in a 10: 1 acetic:perchloric finally electro-thinning The orientation

relationships

line pattern@) trace analysis

&2’)

for 1 to 2

solution

and

electrolyte,

or the Bollmann

dc, y and E were determined (accuracy

acid

in a chromic-acetic

using either the “window”

between

technique. the phases

using electron diffraction

and where possible Kikuchi

(accuracy

*_t”).

As single surface

does not give a unique

result for the

procedure mal.

(which

gives

to those of a two surface analysis)

was adopted to determine the habit plane of the x-martensite laths. From the traces and projected widths of the numerous stacking faults on (1 ll}, in the austenite, a value of the foil thickness in the area of interest was obtained.

it was found that only one solution was the

same in all cases. EXPERIMENTAL

Mn-Cr-Ni this

Using this value of the foil

thickness and the projected width of the a-martensite habit plane interface (see for example Fig. 1) the angle

RESULTS

steel. The most characteristic

steel,

after

quenching

presence of numerous

to

feature of

--196”C,

bands on {ill},

was

that these bands were hexagonal not

perfect

faults,

and

although

sufficient

to lead

displacement

contained the

to any

of

of

e-bands

and

stacking

faulting

appreciable

was

streaking

of the hexagonal reflections.

to these broad c-bands,

showed

E. The bands were

a number

degree

the

planes in the

austenite (see Fig. 1). Selected area diffraction

formed

procedure

gave two solutions for the habit plane nor-

however,

microscope,

following

trace

Once a number of habit planes had been analysed

narrow

the

by single surface

Since the sense of the tilt of the

habit plane with respect to the foil was not known, this

habit plane of a planar feature and true two surface analysis is not possible with a thin foil in the electron results equivalent

circle determined

analysis was found.

were prepared

the strips down to 50 p in a

mixed acid solution,(17) then electropolishing

patterns

0.010

was achieved by cooling the austenitised

for transmission

In this way the position of the habit plane normal on the great

RM 3827 Mn-Cr-Ni 0.028 10.50 4.10 12.15 0.37 0.016 RM 3897 Cr-Ni

between the habit plane and the foil was calculated.

not or

In addition

a number of fault bundles or single

austenite were observed.

stacking

faults

The a-martensite

in the

laths were

within these E-bands (see Figs. 1 and 2) and

were limited

in size by the width of the bands.

No

cr-martensite laths, which were not associated with these e-bands were ever observed. The cc-martensite showed no evidence of internal twinning and contained very few dislocations. The electron diffraction containing reflections

patterns from the e-bands

a-martensite were complicated, since from all three phases--y, F and a-were

ACTA

638

METALLURGICA,

VOL.

13,

1965

FIG. 2. (a) Bright field micrograph of the Mn-Cr-Ni steel quenched to - 196°C. The E appears as dark bands running approximately horizontally and the cr.martensitelaths are contained within these bands. Retained au&mite between the E-bands is shown at A. x 22,000 (b) Dark field micrograph of the same area taken with a {loil}, reflection. The s-bands now appear light while both the cr.martensite and the austenite are dark. x 17.600

generally

present.

technique

of selecting a diffracted beam as an imaging

By

using the simple

beam, it was possible to determine

dark

which phase gave

rise to a particular

spot on the composite

(see Figs.

2(b)).

2(a)

produced

and

adjacent these

In addition,

by the double diffraction

was diffracted

pattern

reflections

and then in the

second phase could be distinguished. electron

orientation

relationship

determined

to within 12’.

were consistent

diffraction

From

patterns

the

between the three phases was All the patterns analysed

with the relationships

:

although

relationship

0.4”

from

(ill),

[lli],

0.5”

from

[iTo],

Unfortunately

would not

Despite

which

could

to be the plane, e-band.

which

addition,

The degree of

identify

the

particular

relationship

In two cases Kikuchi phases were obtained

was not obeyed in this

line patterns and from

of two of the

these patterns

the

Kikuchi

of the orientstion electron Kikuchi

was in every case found

was faulted

of u-martensite

approximately

diffraction lines, much

from these patterns.

This was true even when In

the Nishiyama steel.

i

plane, which is approximately

parallel to (OOOl), and (lOl),

e-band.

was, however, always sufficient to show that

show

be obtained

orientation

accuracy

from

did not

of

relationship.

and (OOl),

satisfactory

accuracy

determined

could not be distinguished the Greninger-Troiano

with

the limited

have been outside the range of accuracy. In these cases the Kurdjumov-Sachs orientation relationship from the same variant

i (ill),

lying between

pattern from all three phases in the same area.

For example the {ill},

of up to two or

(lOl),

patterns

another

austenite:

lines were rare and it was not possible to get such a

information

three degrees from these exact relationships

between

lath and the adjacent

(lOl),

patterns

IIU~101, II[lm,

in some cases deviations

orientation

u-martensite

relationships

(1111, II(OOOl),IIW), WI,

while the second set of Kikuchi line patterns gave the following

of a beam, which

first in one phase

composite

field

it

to produce

the

more

one

was present was

(llO),

always direction

parallel to a (11 l),

more that one a-martensite

than

in a single possible that

direction.

lath was observed

to was

When in a

single E-band their orientations were either the same or represented two of the six Kurdjumov-Sachs variants associated with the (11 l)y plane of the band (see Fig. 6).

orientation relationships were determined to an accuracy of **O. One set of Kikuchi line patterns

In the latter case the two variants distinguished.

‘came from an u-martensite lath and the surrounding e-band and gave the following orientation relationship :

The cc-martensite within the e-bands was in the form of laths, so possessing both a long direction, which is usually associated with a rod or needle-like

(lOI),

0.9”

from

(OOOl),

[lli],

1.0”

from

[1210],

structure, of a plate.

could always be

and a habit plane, which is characteristic The long direction

of the lath always lay

KELLY:

MARTENSITE

639

TRANSFORMATION

cases where no satisfactory

diffraction

patterns were

obtained from the cr-martensite, the habit plane could not of course be related to a particular

variant of the

However, orientation relationship. results indicated that an u-martensite with an e-band on say (III), relationship

as

the

other

lath associated

must have an orientation

which is one of the six variants associated

with the plane of the band (i.e. one of the six variants shown

in Fig.

relative

6), the position

of the habit

plane

to the plane of the band could be inferred.

In all these cases the habit plane was found

to be

close to a {112}, plane, which was perpendicular

to the

(11 l)y plane of the band. FIG. 3. Stereographic projection showing the poles of the habit plane normals of a-martensite laths in the Mn_cr-Ni steel. All the laths analysed were in the standard variant of the orientation relationship i.e. (ill),

II(OOOl)EII(1Ol)a

Although

the greater part of the work steel some observa-

tions were also made on a Cr-Ni steel to compare the transformation

behaviour in a material that is thought

to have a higher stacking fault energy.

[iioly 11 pie], 11liiild

crystallographic

and were contained within E-bands parallel to (11 l),.

The maximum scatter in the results is about four times greater than the experimental error. The variation of habit plane with Ba for a (1 ll), [121]~ lattice invariant shear is shown as a dotted line. in the E-bands and could

Cr-iVi steel.

was carried out on the Mn-Cr-Ni

be considered

as the inter-

Cr-Ni

In general the

features of the transformation

steel and confirmed stainless steels. in which

the

previous

observations

There was however Cr-Ni

martensite

cr-martensite in the Mn-Cr-Ni

differed

were very imperfect and should probably as irregular

direction

reflections

fault

in the electron

results on martensite in Cr-Ni steels. Since a particular

not as common

variant

observed

of

the

distinguished

orientation

whenever

relationship

satisfactory

could

diffraction

terns from the u and y or E were obtained, direction

be pat-

the long

of the lath could be related to this variant.

bundles

reflections, disorder.

again

diffraction

they were streaked

the stacking always

the

be described

(see Fig. 4).

as in the Mn-Cr-Ni

the austenite

from

steel. First, the e-bands

Single surface

that this long with previous

on 18-8

several respects

section of the habit plane with the plane of the band. trace analysis showed was (1 lo), in agreement

in the

steel were similar to those of the Mn-Cr-Ni

Hexagonal

patterns

were

steel and when

and displaced

towards

as would be expected

from

The cr-matrensite laths were

associated

with

these imperfect

e or

In every case analysed the (1 lo), long direction proved

fault bundles, but in some cases the width of the lath

to be the same (llO),

was greater than the width of its fault bundle

direction

mately parallel to (111 ),-i.e. used

in the present

which was approxi-

in terms of the variant

paper

the long

always [ilo],. The habit plane of the martensite mined

to

described those

within

about

above.

where the habit

martensite

lath

52”

The most

direction

4).

number with

laths was deter-

using

the procedure

significant

results were

plane was determined

of known

was

Fig.

orientation

for a

relationship.

The of

fault

cr-martensite

previous

twin-related. twinning

work,

but

the

agreement

The

results

of

shown in Fig. 3.

fourteen

orientation such

relationship.

determinations

For the variant

are

of the orientation

relationship used in the present paper, the habit plane was always found to be near to (ii2),. These results are in agreement with those of Reed(‘) and Lagneborg’s) to the extent that the habit plane makes an angle of approximately

90” to the (ill),

plane of the e-band,

but differ from them in that the habit plane results are significantly closer to (112), than to (‘225),. In the

and,

adjacent

a

in agreement

laths

were

often

dislocation

density

within

the

higher

The results of the present analysis of the cr-marten-

particular

the

laths,

(see

contained

u-martensite was on the whole considerably than in the Mn-Cr-Ni martensite. site in the Mn-Cr-Ni

of

generally

Again there was no evidence of internal

In these cases the habit plane could be related to a variant

bundles

steels.

with

and the Cr-Ni steels are in good

previous

The results

work

on

18-8

on the transformation

steels, whose common

feature appears to be that the

austenite has a low stacking summarised as follows :

(1) The a-martensite

stainless in these

fault

energy,

is not internally

can be

twinned

and

the only form of internal substructure is dislocations. The dislocation density is not the same in the two steels and in some cases regular arrangements of dislocations are observed.

640

ACTA

METALLURGICA,

VOL.

13,

1965

FIG. 4. Cr-Hi steel quenched to -196°C showing three E-bands containing cc-martensitelaths. The orientation is such that the long direction of the laths is perpendicular to the foil. The z-bands are very imperfect, particularly at A. Note the high dislocation density in the rx-martensiteand that the twinrelated laths at B are somewhat wider than their associated E-bands. X 28,000.

The u-martens&e is always associated with bands of hexagonal E or faulted sustenite and the width of the lath is restricted to a considerable extent by the width of the band. (3)The orientation relationships between the three phases is spproximately :

(1111, II(OOO~L IIW),

(4)The habit plane of the a-martensite laths is near to a (112) plane which is perpendicular to the {Ill), plane of the faulted bundle or e-band. For the variant of the orient&tion relationship given above the habit plane is (1124. (5)The long direction of the a-martensite laths is [liO], in terms of the standard variant of the orientation relationship. (6)When more than one m&r~nsite lath is formed in a given band, adjacent laths are often twin Twin-related laths have identical related. habit planes and the same long direction. (7)In it given s-band, six variants of the orientation relationship are possible. These consist of three twin-pairs. In terms of the standard variant (112),. (121), and (2ii),, are the habit planes for the three pairs of twin-related laths in a (11 l)y band, while the relevant long directions are [ITO],, [iOl], and [Oli], respectively.

DISCUSSION

When the features of the martensite tr&nsform&tion in Mn-Cr-Ni and Cr-Ni steels are compared with those of the more familiar transformation in Fe-C, Fe-Cr-C, Fe-Ni, and Fe-Ni-C, which generally leads to internally twinned plates, certain fundamental differences, which distinguish this u-martensite from the inte~ally twinned variety, become apparent . The absence of internal twinning is not unduly significant, since the complementary strain could be accommodated by slip as well as by twinning, and portions of such martensite plates, which are free of twins, have been observed. The association with E or faulted y is a more ~h~r~~teristi~ distinguishing feature, while the most important difference between the cc-martensite in these Mn-Cr-Ni and Cr-Ni steels and internally twinned martensite is the habit plane. Admittedly the habit plane is close to a plane of the type (225), and the Bowles-MacKenzie theory of the m~rtensite transformation, as applied to internally twinned martensite,06) predicts a (225), habit at maximum dilatation. In terms of the variant of the orientation relationship used in the present paper, however, the internally twinned martensite should have s (2251, habit, while for the same variftnt of the orientation relationship the a-martensite laths in the Mn-Cr-Ni steel have it (ifa), habit plane, which is a few degrees from (2%5), not (225), (see Fig. 3). Hence, although the Bowles-MacKenzie theory, when applied to the y to OLtransformation with a lattice invariant

KELLY: TABLE

2.

MARTENSITE

Values of the magnitude of the lattice invariant shear 9 and the shear component of the shape strains for the three (11 l}Y( 112)Y lattice invariant shear systems?)

Case no.

Lattice invariant shear svstem in anntenite

1

(111),[121lY

(lol),[roll,

2

(111M1121,

(101),[13i1,

3

(111):~[2rr],

(101),[1371,

* Negative

shear on (llO), martensite, Cr-Ni

Magnitude of lattice invariant shear o(at S = 1.000)

Corresponding shear svstem in mnrtensite

(a) (b) (a) (b)

Magnitude of the shape strain s(at zi = 1.000)

+0.284 +0.423 -0.279* +1.548

0.219 0.219 0.398 1.861

Crystallographically

equivalent

to Case 2 above

values for 9 indicate that the shear is in the opposite direction to that given in the table.

[liO],,

is very successful in accounting

of the lattice invariant. shear g and the shear compo-

features of internally twinned

nent of the shape strains in f.c.c. to b.c.c. transforma-

for the crystallographic features

641

TRANSFORMATION

it is not

of

the

steels.

consistent

with

transformation

The success

the observed

in Mn-Cr-Ni

and

show internally

twinned

(225), or (259), plates, leads to the conclusion

that any

alterations

steels, which

required

to account

these (11 l}y (112), shear systems have

been calculated

by Wechsler et &(20)

These values of

g and s are shown in Table 2.

of the phenomenological

theories in dealing with the martensite transformation in the other

tions involving

for (112), martensite

Although

there

is very

little

difference

in the

smaller values of g for the two distinct cases 1 and 2, the values of the shape strain s differ considerably. The lattice invariant

shear system

(111),[121],

gives

laths should not be made to the theories themselves,

the smallest, value of s and hence on the grounds

but to one of the assumptions

minimum

theories to this particular The current

(a) the

transformation

product

of

are based on

between

the parent, and

parameters

of

the

two

phases,

shear system.

can only be altered slightly,

whether this alteration is acheived directly by alloying or indirectly

invariant

by the introduction

of a small uniform

as is done in the Bowles-MacKenzie

theory.

In any event a small change in these parameters

will

can

be

produced

by

System I: and System II:

only

that the (11 l}y (112),

stacking

fault shear

might be an appropriate

invariant shear system for the transformation steels.

In terms of the standard variant,

mental results show that the faulted

lattice in these

the experi-

plane is (ill),

and so the three shear systems involving a (112), dire&ion lying in (11 l)? must be considered. One of these

systems,

[iOl],

in the martensite

(ill),

[121],

corresponds

to

(lOl),

while the other two, (ill),

namely:

(112),[11T],

(111),[121],

i.e.

(lOl),[iOl],

Since no other shear system gives a lower value s, then, if the criterion of minimum ing the transformation shear system, should

strain energy accompany-

governs

martensite transformation.

system in austenite

systems, i.e.

shear system as the only alternative.

suggests

two

(llO),[liO],

lattice invariant

E or faulted y

plane or

shows that the smallest possible value of s

systems

steels the association

system in either

of two such systems with either a common

This leaves the choice of a different

and hexagonal

survey(21)

or to a simple shear composed

(259), to (112),.

and Cr-Ni

of

lattice

to either a simple

slip or twinning

invariant

between the u-martensite

likely

in the y to u marten-

is restricted

not shift the habit plane from the region of (225), and

In the Mn-Cr-Ni

more

A more extensive

shear system involved

shear on a normal

suggests that this cannot be altered.

The lattice parameters

dilatation,

shear system.

direction,

The first of these is well established and the agreement

is the

of the values of g and s, which result when the lattice

austenite or martensite

(c) the lattice invariant with experiment

energy

site transformation

phases,

lattice

strain

invariant

theories,(l3JV9)

input data :

correspondence

(b) the

the

transformation.

phenomenological

the au&en&e-martensite the following

used in applying

operate

in any

martensite

application

y to

M.

shear system used in

of theories to the familiar

transformation

and Fe-Ni-C

of these two

particular

The first of these systems

is of course the lattice invariant the successful

the choice of lattice

one or other

in Fe-C

Fe-Cr-C,

Fe-Ni

and System II will now be used as the

lattice invariant shear system in applying the BowlesMacKenzie

theory to the transformation

and Cr-Ni steels.

The notation

will be used in this application in Table 3. Figure 5 is a stereogram variation

of the habit

plane

in Mn-Cr-Ni

and input data which of the theory are given

showing with

the calculated 6J2 obtained

by

[112], and (ll!), [211],, correspond to (IOl), 11311, and (101), [131], respectively and so are crystallo-

applying the Bowles-MacKenzie theory to the transformation with a lattice invariant shear on (111 )Y

graphically

[121],.

equivalent

to each other.

The magnitude

For comparison

the variation

of habit plane

ACTA

642

METALLURGICA,

TABLE 3. Notation and input data used in the application of Bowles-MacKenzie theory Jaswon-Wheeler

correspondence matrices for the chosen standard variant : to a (directions)

VOL.

13,

1965

habit plane is exactly solutions

(112), and the two habit plane

reduce to one, since gi = g,.

of the habit plane normal

ship

P,

for the

formation

more

with a (llO),

familiar [liO],

case of the trans-

lattice invariant

is also plotted on the same stereogram.

shear,

the Kurdjumov-Sachs

relation-

: (ill), IIWL ml,

II[1lQ,

which is only 8” away from the orientation ship determined

from

Kikuchi

be the plane

(ill),

and so this must be the plane

which is faulted to produce predicted

relation-

line patterns.

The shear has been taken to

plane of the lattice invariant

The with

at 8 = 6 is in very good

agreement with the experimental results (compare Fig. 3 and Fig. 5). The orientation relationship at this value of O2 is exactly

Lattice invariant shear system: (lllh, [1211y c’]a’ = tetragonality of martensite = 1 (cubic martensite) C&= lattice parameter of austenite = 3.58 A a’ = lattice parameter of martensite = 2.87 A 6 = the dilatation parameter, which represents a small isotropic volume change. 19= 6(a’/a) (the maximum value of 19~for cubic martensite is 8). 8 = the shear component of the shape strain. g = the magnitude of the lattice invariant shear. In general there are two values of g. These will be represented as g, and g2 where g1 is less than g,.

The position

(ii2),

the band of hexagonal

habit

plane

is exactly

E.

per-

pendicular to this band, in agreement with the experimental results. As

The direction

e2 varies

calculated

the

curve

habit

either

plane

moves

towards

along

(ill),

for

the small

which is perpendicular to the shear plane [iOl],, normal (ill), and the shear direction [121],, is an axis

values of the lattice invariant shear g or towards (OOl),

of two fold symmetry

for large values of g. The variation of the orientation relationship with e2 is closely similar to the variation

unique

or contraction

tortion

[OIO],.

lattice

invariant

‘K-degenerate’(22) solutions

and is also perpendicular

to the

axis of the pure lattice

dis-

The

case of transformation with a _shear on (111),[121] is therefore and

is reduced

sponding to eachvalue

the number

from ofg.

four

of habit

to two,

one

with e2 when the lattice invariant [liO],.

shear is on (llO),

For example when 19~= 0.643 (6 = 1.000) the

plane

habit plane for g, (the smaller of the two values of g)

corre-

is near (334), and the orientation

At e2 = $(6 = 1.018) the

to the Greninger-Troiano

relationship

relationship.

is close

The values

of the shape strain s vary with e2 in exactly the same way as they do when the lattice invariant (llO,)[liO],.

At e2 = # the magnitude

strain

is 0.212

and

[-0.81,

0.47,

0.351,.

equivalent

its direction This

is approximately

shape

strain

is in fact

to a shear of 0.192 in the direction

plus an expansion

because

the

steel was associated give hexagonal tion between

[ilO],

of 0.089 normal to the habit plane

(112),. The lattice invariant chosen

shear is on

of the shape

shear system (1 ll),

cr-martensite

-[121], was

in the Mn-Cr-Ni

with faulting of the austenite to

8. In pursuing this apparent cc-martensite and faulting

connec-

of E forma-

tion great care must be exercised, since it is important to

distinguish

between

the

complementary

direction and the lattice invariant also between (loo)r

FIG. 5. Stereographic projection showing the theoretical variation of the habit plane with tP for the standard variant of the orientation relationship and a lattice invariant shear on (111)~ [121]r. The projection is plotted in the standard (001)~ orientation for austenite and the positions of the {lOO}a poles of the a-marten&e are indicated. For comparison, the habit plane variation with Befor the more familiar case of a (110)~ [ liO!y lattice invariant shear is shown as a dotted line.

opposite.

a stacking

shear

shear direction and

fault shear direction

and its

Stacking faults are formed in austenite by

displacing a {ill}, plane by 6(121), in relation to an adjacent {ill}, plane. If faulting occurs on every other {ill}, plane then hexagonal close packed E will be formed. If the E formation is homogeneous, the magnitude plane [lgl],,

of the shear involved

(ill), the possible [211], and [112],.

in 195’.

In the

faulting directions are The opposite direction

KELLY:

[T2T],,

[2ii],

directions

and

[ii2],

are not

since the displacement

over another in these directions

MARTENSITE

possible

643

TRANSFORMATION

forms within the band.

faulting

of one (11 l)? layer results in the atoms

In effect this means that, if

the E forms inhomogeneously,

as appears

to be the

case, then the e-band really represents a region of y

on adjacent layers being “pushed against one another”.

which has been subjected

The complementary

trans-

and the lattice

shear,

invariant plane strain (plus a slight “shuffle”

formation since

is the inverse of the lattice invariant

the

complementary

homogeneous lattice

strain

is regarded

as a

strain which distorts the lattice, and the

invariant

which

strain in the martensite

exactly

shear

cancels

is an inhomogeneous any shape displacement

that

It

is

therefore

important

to

of the complementary

invariant

shear direction

know

strain.

whether

is along a possible

direction in the transformation

faulting

being considered.

analysis is in fact based on the complementary being in a faulting

the

strain or the lattice

direction,

The strain

(OOOl),

planes)

Only

would

The

only

difference

interpretations

as an effect produced second case tively

This is

of atoms

therefore E to

these

by the formation

be

a.

two

possible

of c( and in the

is the cause of u formation.

E

the difference

time sequence, possibility

between

one further

is that in the first case the E is regarded

can be expressed

i.e. which

Alterna-

in terms of a

comes first u or

has its supporters.

Each

E.

Dash and Otte@) and

Goldman et a1.(12)take the view that E is a consequence and not a cause of tc formation

i.e. the complementary

strain is in the sense (1211, and not [121],.

adjacent

shears.

necessary to convert a portion of this

shear

would have been caused by the complementary direction

on

to both the complementary

invariant

and others+‘)

while Lagneborg@)

support the view that E forms before u.

borne out by the positive values of g when the lattice

There is no evidence in the present work to distinguish

invariant shear is chosen to be in the sense [121],.

between

leads to two possible interpretations between

cc-martensite

hexagonal

or E formation other

and

words

complementary

u-martensite

of M formation. forms

first and

of faulting.

complementary

into the austenite in the

If the value

(i.e. the a-martensite

of 02 is exactly

that, since the complementary

to the surroundThis implies

shear leading to E

then there is no need for the compensating

invariant

crystallographic

shear. theories

If this were so, then of

martensite

is inhomogeneous. formation would

the

formation

invariant plane.

have

an

If, on the other hand, the a-marten-

site and the surrounding

austenite

are subjected

to

applied.

possibility

macroscopic tion

between

distortion. a-bands

and would not lead to any

or faulting

it is unlikely that the

that of

in every case.

E

lath was formed

it is

laths could now form in

form

can form

form as a consequence

interpretation

the second

and cc-martensite would e-bands.

Irrespective

of the association

is correct, the theoretical

of

between

tc

analysis predicts that

at e2 = f the following relationships E

c-band

of u formation,

in the transformation

in these pre-existing E

in a given

even in a material where the

would be obeyed

between X, y and

should be observed: (ill),

II (OOOl), II (lOl),

PW, IIPm,

The austenite would still be faulted too, the

would be inhomogeneous

E

at a later stage

theories could still be

only difference being that in this case the e-formation

laths

Therefore,

first bands of

both the complementary strain and the lattice invariant shear the total strain would not be homogeneous and the crystallographic

of the lead to

if the first possibility

More u-martensite

of u-martensite

and

not

an e-band,

is

this c-band and it is well established that large numbers

homogeneous

would

the E formation

if an u-martensite

produce

correct.

both possibilities

In addition

of CI can precede

For example

which

as a result

of u is concerned,

the same results provided

would not longer apply as the total strain would be and

The controversy

one as it appears at

first sight, and as far as the crystallography formation

(see Fig. 4).

shear is accommodated

by the austenite as a homogeneous lattice

$

has a (112), habit) and all of the

strain is transmitted

ing y, a band of E should be produced.

formation,

In the

strain, instead of being confined to the

cr-martensite, is transmitted form

or

is that the faulting

is a consequence the

austenite

these two possibilities.

not, however, such a fundamental

of the association

faulted

The first possibility

E.

This

The

association

hexagonal

E

between

II[IlU, the

cc-martensite

and

may have an effect on the position of the

Examination

of the interac-

martensite

and

scratches

experimental results, the habit planes in the Mn-Cr-Ni steel cluster round (112), and not round the (22~5)~

surface

and

between e-bands on different planes shows that the F formation is apparently inhomogeneous. The second possible explanation of the association between ct-martensite and E or faulted austenite is that the e-band forms first and the cc-martensite then

habit

plane.

Despite

the scatter

in the

habit determined by Reed(‘) and by Lagneborg,t9) who both used single surface trace analysis. More important,

the experimental

habit plane results lie some

15” from the habit plane predicted

for zero dilatation

ACTA

644

(02 = 0.643, 6 =

between

1965

the theoretical

(e2 = Q, 6 = 1.018).

interest to note that the maximum is also required

of this 1.8% dilatation

It is of

value of the dilata-

to produce

habit found in plain carbon steels. the Mr-Cr-Ni

13,

habit planes occurs at the maximum

value of the dilatation tion parameter

VOL.

1.000). Consequently in the Mn-Cr-

Ni steel the best agreement and experimental

METALLURGICA,

the (225),

The introduction

to explain the

(ii2), habit in

steel seems to be supported

by the fact

that at this value of ti2 the complementary

shear is

exactly that required to produce E from y and at some other value of e2 the complementary give rise to perfect for example,

E. When

the complementary

strain should result

in imperfect E containing approximately ten

(OOOl), planes.

perfect

the

stable

to expect

than imperfect

E, the

at S = 1.018 (e2 = $), which

be associated to

one fault every

As it is reasonable

E to be more

transformation

shear will not

6 = 1.000 (e2 = 0.643)

would

with perfect E, may occur in preference

transformation

at

which would be associated

6 = 1.000

Pm. 6. Stereoeraohic oroiection showine the theoretical variation of the habit *plaAe with Oafor?he six variants of the orientation relationship that have (111 by 11(101)~. The lattice invariant shear is on (111)~ in every case and the uositions of the C-axis of the cc-martensitefor each variant are shown bv the black souare8. The variants with the same subscript (e.g. XI a;d Ys) comprise a twinrelated Kurdjumov-Sachs pair when Be = #. YB is the standard variant used in the paper.

(es = 0.643),

with imperfect

E.

In addition to the effect on the position of the habit plane,

the

association

hexagonal site

between

E also determines

grains.

This

type

u-martensite

of

cr-martensite

has

described by previous workers both as needlea plates.’ the

and

the shape of the martenbeen and as

Neither of these terms give a true picture of

shape

described

of

the

martensite,

as a lath.

morphology

which

The reason

can

best

be

for this lath-like

is that the growth of the martensite is to a

large extent

restricted

by the width

The habit plane of the martensite the band and growth

is perpendicular

to

along the normal to the band

would require further faulting of the band.

of the E-band.

to increase the width

This restriction does not apply to growth

in the direction

[lie],, which lies in the plane of

line.

These six habit lines are in fact three pairs, each

pair touching at a pole of the type {112}, when e2 = Q. The

two

orientation

Sachs variants. comprise

corresponding touch habit so

habit

at (112)

that

two

lattice invariant orientation plane.

shear.

relationship

There are six variants of the associated with a given

The position of the martensite

six variants in each case.

j] [lOl),

The standard variant considered

when

e2 = #.

to X,

workers.@@))

(lgi),.

pair

these

two

This

These

therefore and

the

variants

common

(112)

in the martensite,

laths

with

would

related laths with their common plane

twin

to (12i),

and Y,

Kurdjumov-

and Y,

orientations

appear as twin-

habit plane being the

twin-related

laths

have

in the present work and by previous The shape strain for the lath in orienta-

tion Y, can be regarded as a shear on the habit plane (ii2) in the direction [ilO], plus an expansion

(11l)y normal to the habit, while for the lath in the X,

c axis for these

is shown in Fig. 6 where (ill),

8,

for

a-martensite

corresponding

been observed using a (111),[121],

lines

plane is parallel

plane. point emerges from the theoret-

The variants

a Kurdjumov-Sachs

twin

Another important

at this common

point of each pair consist of twin-related

the band and, as a result, the u-martensite forms as a lath with a [liO], long direction and a (112), habit

ical analysis of this transformation

relationships

so far

orientation

the shear component

is in the direction therefore

[liO],.

of the shape strain

These twin-related

have shear components

laths will

of their respective

has been that denoted by Y, in Fig. 6, where the lattice invariant shear direction was taken to be [i2i],. By selecting the appropriate (112), direction lying in (ill), for each variant of the six orientation

shape strains that are exactly opposite. This should lead to a pair of these twin-related laths forming next

relationships

theoretical

associated

with

(ill),,

the

six habit

plane lines shown in Fig. 6 are obtained. The variant corresponding to each habit line is marked next to the

to one another, so that the shear components of their shape strains could cancel each other. Finally the analysis

predicts

that three such sets of

twin related laths with habit planes (ii2),, (2iijy and (121)could occur in a given (ill), sheet of faulted y

KELLY:

of hexagonal

MARTENSITE

TRANSFORMATION

E. Cases of more than one set of twin-

related laths occurring

in the same (11 l)? sheet have

645

should

form

energy

is low enough

in austenites

where the stacking

to make

been reported.(8y10)

&(110) dislocations

Dash and Otte’s) and Lagneborg@) observed that in the a-martensite formed in stainless steels there was

occurrence.

evidence

will be difficult and transformation

state

of slip on {llO),

that

planes.

Dash and Otte(s)

three

sets of dislocations are observed w found only two. Examination of while Lagneborg the published indicates

that

predominate. is parallel (liO),,

to

photographs

while alloys

and

the other

appears

to be

There is little evidence

shear is

This would

bands on (lol),.

lead to

This suggestion

that in the Mn-Cr-Ni

is

steel

the E formation

is

nearly perfect and few dislocations

are observed in the

a-martensite,

steel the e is less

while in the Cr-Ni

and the dislocation

density

in the u-marten-

site is high. The presence of dislocations on (liO), cannot be explained in this way. This may be evidence of the operation of a second lattice invariant shear system as suggested by Lagneborg.@)

Another

is that the apparent slip on (liO), represents

accommodation

fortunately,

of

the

shape

strain.

until the surface tilts associated

transformation

in these steels have

and

with

compared

the

values

Unwith the

been measured

predicted

by

the

theory, this latter suggestion cannot be tested experimentally. The found

differences

between

in the Mn-Cr-Ni

found in Fe-C,

Fe-Ni-C

the

a-martensite

steel and in 18-8

steels and the internally

appreciable fault

twinned and Fe-Ni

laths

energies

and form

lath martensite

associated

CONCLUSIONS

The

results

formation

of the investigation

in the

Mn-Cr-Ni

using

transmission

electron

listed

at the end

of

The

results. MacKenzie lattice

theory

invariant

lattice

twinning

for

of u-martensite

and

the

Cr-Ni

steel

microscopy

have

been

section

on

made

the

by

case

experimental the

Bowles-a (111),[121],

of

shear are entirely

these experimental follows : (1) The

the

predictions

consistent

invariant

shear

system

internal twinning

should be observed.

the transformation

to a-martensite

(2) The martensite

habit

plane, for the standard at

82 = i.

to

This habit

plane is perpendicular

the (ill), band of the E or faulted y associated with the a-martensite. (3) The orientation

relationships

between the three

phrases at e2 = # are: (Ill),

II (OOOlL II W),

[1W, IIWOI, IIWlQ (4) When

6 = 1.018

(e2 = #),

the

cc-martensite

MacKenzie

the

be associated

with imperfect

further

may explain

why the transformation

features

of these

emphasises magnitude

the

two

types

distinction

predict

of martensite between

of the shape strains involved

them.

The

are exactly

the same in both cases so that, on strain energy considerations alone, one transformation is just as likely to occur as the other. The difference between the lattice invariant shear systems does, however, provide a possible means of deciding which transformation will occur in a given alloy. The lath martensite, which -has a lattice invariant shear on (ill), in [121],, 5

be

variant used in the present paper, is (ii2),

alloys are suffi-

to

Instead

with faulting or E formation.

should be associated

treatment

a

and no should

of martensite formation. The fact that different lattice invariant shears must be used in the Bowlestheoretical

as

is not

in the a-martensite

associated

with

results and can be summarised

system

plates

cient to show that these represent two distinct modes

containing

of Cr or Mn have low stacking

with faulting or E formation.

stainless

martensite

energy,

amounts

which is 10” from

to be non-uniform. by the fact

possibility

The

evidence available to date supports this, alloys have a relatively

studied in the present investigation

some

should occur via shear system.

fault

dense dislocation

perfect

experimental

lattice invariant and Fe-Ni-C

and as a result the lattice invariant

supported

the (llO),[liO], as the Fe-Ni

The slip on (101), can easily be explained in these alloys the faulting is by no means

also likely

high stacking fault energy this dissociation

high stacking

for slip on the third plane (Oil),

uniform

On the other hand in a material with a

relatively

these references

which is 5’ from (OOl),.

(Ill),. since

of

into &( 112) partials a fairly common

two slip planes, rather than three, One of these is the plane (101), at which (ill),

in both

fault

the dissociation

with perfect E while, when

6 = 1.000 (e2 = 0.643), the a-martens&

mum dilatation formation (5) The

should

or faulted E. This

occurs in preference

at maxito trans-

at zero dilatation.

a-martensite

is in the

form

of

a lath

because its growth into a true plate is restricted by the width of the e-band. In terms of the standard variant the long direction of the lath is [lie],. (6) At e2 = $ twin-related a-martensite laths with the same habit plane may be formed next to one

ACTA

646

METALLURGICA,

another. In fact, in a given (ill>, band three such sets of twin-related laths are possible, each lath following a variant of the KurdjumovSachs orientation relationship associated with the particular (11 l}, plane. ACKNOWLEDGMENTS

The author would like to thank Professor J. S. Bowles for a number of valuable comments and constructive criticisms and for the many stimulating discussions during the preparation of the manuscript. The author is also indebted to the United Steel Companies for supplying samples of the two steels investigated. REFERENCES 1. B. CINA, J. Iron. St. Inst. 177, 406 (1954). 2. B. CINA, J. Iron. St. Inet. 179,230 (1955). 3. B. CINA, Acta Met. 8, 748 (1958). 4. G. P. SANDERSON and R. W. K. HONEYCOMBE, J. Iron et. Inst. Q0Q, 934 (1962). 5. J. A. VENABLES, Phil. Msg. 7,35 (1962). 6. J. F. BREEDIS and W. D. ROBERTSON,Acta Met. lo,1077

(1962).

VOL.

13, 1965

7. R. P. REED, Acta Met. 10,865 (1962). 8. J. DASH 8nd H. M. OTTE, Actcc Met. 11, 1169 (1963). 9. R. LAQNEBORQ,Acta. Met. 12,823 (1964). 10. P. M. KELLY and J. NUTTINQ, J. Iron St. Inst. 197,199

(1961).

Institute of Metals 11. B. A. BILBY and J. W. CHRIST-, Monograph No. 18 Mechanism of Phase Tramformatione in Metals p. 121 (1955). 12. A. J. GOLD-, W. D. ROBERTSON and D. A. Koss Trans. Amer. In&. Min. (Met&?.) Engw 280, 240 (1964). 13. J. S. BOWLES and J. K. MACKENZIE, Actu Met. 2, 129 (1954). 14. J. K. MACKENZIE and J. S. BOWLES, Acta Met. 2, 138 (1954). 15. J. S. BOWLES and J. K. MACKENZIE, Acta Met. 2, 224 (1954). 16. M. A. JASWON and J. A. WHEELER, Acta Cyst. 1, 216 119481. 17. S. R. KEOWN and F. B. PICKERINQ, J. Iron St. Inst. QQQ, 757 (1962). 18. H. ik OT~E, J. DASH and H. F. SCHAAKE,Phys. Stat. Sol. 5, 527 (1964). 19. M. S. WECHSLER, D. S. LIEBERMAN and T. A. READ, T~ans. Amer. Iat. Min. (Metall.) Engrs 197, 1503 (1963). 20. M. S. WECHSLER, T. A. READ and D. S. LIEBERMAN, Trans. Amer. Inst. Min. (Metall.) Engr8 218,202 (1960). 21. P. M. KELLY, MetallurgicaZ DeveZopmente in High Alloy ~Y~e~~S.I./B.I.S.R.A. Conference Scarborough (1964). \----I

22. M. S.

W~CHSLER,

Acta Met. 7,793 (1959).