Deformation Twinning in Metals and Ordered Intermetallics-Ti and Ti-Aluminides M

Deformation twinning in metals and ordered intermetallics-Ti and Ti-aluminides M. Yoo, C. Fu, J. Lee

To cite this version:

M. Yoo, C. Fu, J. Lee. Deformation twinning in metals and ordered intermetallics-Ti and Ti- aluminides. Journal de Physique III, EDP Sciences, 1991, 1 (6), pp.1065-1084. 10.1051/jp3:1991172. jpa-00248626

HAL Id: jpa-00248626 https://hal.archives-ouvertes.fr/jpa-00248626 Submitted on 1 Jan 1991

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(1991) Phys. 1065-1084

J. 1991, III1

1065 PAGE JuiN

Classification

Physics Abstracts

61.70N 62.20F 62.20D

twinning intermetallics-Ti ordered Deformation metals and in

Ti-aluminides and (1)

C. Fu K. Yoo, H. and J. M. L. Lee (2)

Ridge, 37831,6115, Ridge Laboratory, Division, Oak TN Oak National Metals Ceranlics and

U-S-A-

1990) (Received19 accepted September 1990, 4 June

cons6quences maclage ductilitd des la ddformation de fracture Rksumk.-Los la la

et par sur

cristallographie,

intermdtalliques fonction

alliages ordonnds dtudides de

de mdtaux la et sont en

systdmatique

l'dnergie cindtique maclage. analyse ddformations dtd faite

de des Une

et a par en

comparaison systdmes

Ti~Al, consid6rant Ti, TiAl moddles. En le A13Ti

quatre et avec comme

important maclages intrinsdque difficultd Ti, maclages dans observds T13Al des de nombre dans la

dragging

shuming interchange

mdcanisme de

de mdcanisme

rationalisde d'« Un

est tenure ».

l'origine physique faible mobilitd explique la des

fault» bask l'interaction de «torque» sur

(I Ii) qui macles 112. superdislocations dans TiAl conduire k nucldation des la vissdes peuvent

glissement conjugude le alliages AJ3Ti, la made relation TiAl Dans les tels la et entre et

compatibilitd la ddformation importante fagon contraintes (ordinaire) I lors des de contribue de la

d'addition tempdrature. bdndfiques potentiels dldments plastique efiets lids k des haute £ Des sur

dgalement discutds. maclage le de sont processus

ductility and ordered twinning strength of metals of deformation in the and The role Abstract.

kinetics crystallography, energetics and

of the of alloys examined basis interrnetallic is on

taking four TiAl, systematic analysis by and Ti, twinning. T13Al, A made A13Ti deformation is as

difficulty twinning Ti, of comparison twinning in intrinsic in profuse with the model In systems.

(SISF) dragging shuffling interchange fault A the mechanism. rationalized is of T13Al in terms

mobility of

physical for the

explains the low mechanism interaction based the

torque source on

[1Ii]

(1Ii) TiAI and

nucleation. TiAI, twin In superdislocations in which lead

to may screw

twin-slip relationship important contribution conjugate (ordinary)

makes alloys, A13Ti the to an

Potentially alloying high,temperature plasticity. beneficial additions compatibility for the strain to

twinning discussed. promote are

Sciences, (I) Energy of Office Basic U-S- Sciences, sponsored Division of Materials by Research the

Systems, Energy DE-ACo5-840R21400 with Martin Marietta Energy, under Department of contract

Inc.

Metallurgical Engineering, Michigan Department Materials of and address.- Permanent (2)

Houghton, 49931, Technological University, U-S-A- MI

PHYSIQUE M loss JOURNAL DE III 6

InUoducfion. 1.

plastic of twinning principal deformation

in Slip modes the low and temperature two are

published

monograph twinning deformation

than crystalline solids. The last

two on more was

Mahajan

[I], subject given and Williams

general by and last the decades review

ago on a was

effectively twinning experimentally strengthen

deformation observed that It is [2].

can a

clarify under circumstances others. weaken it under To material and this apparent some

twinning hexagonal dichotomy role of fracture of cubic metallic and the and in understand to

objectives twinning

symposium the deformation materials of [3]. the last More

were on

importance twinning recently, deformation of of and the behavior the in fracture of awareness

alloys particularly tetragonal interrnetallic the in and Llo ordered has D0~~ type type grown,

crystal [4]. structures

twinning

strength

The of this deformation the role of in the is and to purpose paper survey

ductility alloys, compounds point intermetallic metals, of ordered and from theoretical of a

adopted develop intended,

general approach

overview here is While is the view.

to a a

analysis twinning plays alloys interrnetallic in of the model metal and selected systematic role

approach

specific binary this Ti-Al. motivation for establish The is

from

system, to e-g- a one

unique physical properties analysis consisting

electronic basis for the and of the common

specific

bonding binary Experimental

characteristics of data mechanical the atomic system. on

properties description and deformation first brief Inicrostructure section reviewed in 2. A are

crystallography twinning given by energetic 3, the of section followed the in is of -and kinetic

analyses growth Finally, twinning in of nucleation and section the role of twin 4. in

toughness plastic generalized flow 5, and fracture is effect assessed in section and the of

alloying twinning

discussed section is in 6. on

hexagonal close-packed (hcp) alloys

metal, a-Ti, a~-Ti~Al, interrnetallic A and three of ~+

single-phase Al3Ti

TiAl, Figure four models for the chosen the and overview. I

present are as

crystal (A3, four D019, Llo and shows the and axial ratios the D0~~) types structure

(cla)

model superlattice

of four materials is The these temperature.

D01~ structure at room a

~hcp) having long-range of only perpendicular derivative the order A3 direction in the type to

consisting

Llo tetragonal face-centered The is

layers atomic the axis. of the type structure c

perpendicular along is

Ll~ axis. stacked the The related unit cells D0~~ type type two to to c

antiphase (APB) 1/2[110](001)

boundary (001) with of plane. the axis

other

type at every an c

SUength ductility. 2. and

yield

strength

TEMPERATURE

2.I material The of STRENGTH. DEPENDENCE YIELD oF a

yielding parabolic behavior

which shows the usually by defined the of is normal type stress,

corresponding strain,

specific

off-set of the four each For model 2 10~

e-g- «~,

a x e =

yield dependence the of the by determined has been temperature stress, systems, «~,

crystals. along single Figure schematically

the axis of experimental compressing shows 2 the c

Al3Ti reported [6], [7], Ti

TiAl and applied [5], T13Al for where data the

[8] strain

rate was

~positive) dependence noIninally anomalous An of 10~ in temperature all d

«~ occurs =

plays

twinning important

and deformation Ti~Al. role in all Al~Ti, except except an

peak the deformation K, mode a)

below the 650 temperature, Ti-At

temperatures

(ll13)

(l122)

hand,

twinning On (above entirely by the other

[5]. 90 almost 9b) at was

(c )

(10-30 fb) mode

major slip the minor above the mode and

temperatures was T~, + was a

(10fl) (10f2) strength yield reported twinning Therefore, rise and fall of for Ti the the [5].

M DEFORMATION 6 TWINNING METALS IN lo67

(h.c.p.) A3

DO~~

=1.59) (cla O.80)

cla Ti Ti~Ai =

L'o .D°zz

o °o

~. .

i o

a-~

TiAi~(Cla=2.23) TiAi(Cib=1.02)

phases Ti-Al Crystal Fig. model in of the four 1. system. structures

slip

involving displacement twinning transition be related from the

apparent to to may an

(c ) along

directions.

vector + a

yield strength Ti~Al b) T13Al-The compressive higher is measured much in than that Ti in

(Fig. 2).

peak shear Ti, The about 9b of the 1130 is modulus which is of K 4 stress at

T~ a =

twinning strength. Ti~Al of theoretical observed has been in the [6, The No 9]. measure

(1ill)

yield (1122) mobility Ti~Al anomalous in behavior is attributed edge of the low (~) to

superdislocations, higher originating glide increasing resistance with temperatures most

probably pairs from climb

superpartial difficulty dissociation the of for [6]. of The reason

twinning Ti~Al later will be in in discussed section 3.3.

c) figure TiAI-The dashed

single from shown in crystals obtained 2 Ti4sAls4 [7].

curve was

proposed physical number A positive source(s) rationalize the of theories have the been of to

[10-14], dependence of

but in TiAl dislocation which model for temperature

accounts «~ no

experimental observations, dependence of orientation the details such the the and strain- as

sensitivity developed. Although

twinning importance (111) ill been of of the has rate «~,

twinning, plastic generally acknowledged so-called ordered

[4], deformation is in (~), no

specific twinning yield strength in anomaly been role of has elucidated. the

The Miller indices fundamental

referred h,c.p. the

(3) lattice. to are

The indices

referred the f.c.c. lattice. (~) to are

PHYSIQUE M JOURNAL DE 6 III lo68

z-o

COMPRESSION ALONG

THE C-AXIS

' l.5

600

k '

~ l.O

~~ ~"",

' ~

400

', '

', # '

O.5

ZOO

' j~

O 400 ZOO 600 800 lOCO120044OO

TEMPERATURE,

T K

strength yield single dependence compressive Ti Fig. 2.-Temperature of the of and Ti-a1ulninide

crystals.

yield Al~Ti-This compound strength d) shows weakest four the the systems among

dependence major considered, it of The deformation normal and shows

temperature. «~ a on

ill

along ( ii twinning slip ii augmented ii10] ordered the which 00] by mode is it is the and I

[8, directions 15].

shows Figure of TEMPERATURE the 2.2 3

FRACTURE DEPENDENCE STRAIN. OF summary a

dependence Ti~Al fracture,

[16], [17, for of TiAl 18], [9], and strain the Ti temperature at er,

Except Al3Ti,

elongation A13Ti experimental from for [8]. the data obtained tensile were

samples.

ductility, polycrystalline Ti

fb, excellent Pure exhibits

22 measurements

on er an m

clearly compounds exhibit

brittle-to-ductile whereas the transitions three the test as

sensitively depends raised. transition is The each in temperature temperature apparent case

applied

grain

figure Nevertheless, the strain the size. shown in and the 3

rate

mean curves on

for obtained in the strain 10~ 2 which 10~ be used 4

rate s~

range may were x a x =

ductility polycrystalline by twinning played the

in general discussion materials. role of on

specific regard question twinning inducing the the of role deformation in a) of Ti-With to

given polycrystals, [19].

have been earlier review in of Ti In ductility

answers some an

generalized

important (c which ) deformation activity slip,

the of

the addition

to to very + a

compression

reference polycrystals, tension and in profusely both

Ti in types twins

mode in each than axis type. and shows

the

to one more c

M 6 DEFORMATION TWINNING METALS IN 1069

16 40

30 42

lo ~"

j ~

iT15Al

IO 4

O O

400 800 4000

T(K) TEMPERATURE,

polycrystals. Ti-alunfinide dependence elongation of and Fig. the tensile Ti Temperature of 3.

(erw b) polycrystalline Ti~Al ductility fb) Ti~Al-The primary for the of 3

poor reason

(c twinning

) ) slip activity. density (c

specimens lack of and is The dislocations of the

+ + a a

by and especially below low, 900K, found TEM be

temperatures to at very was some

Also,

[1?]. ductility

increase faults, the in

or1nicro-twins observed 900 K extended at at were

(a) higher

dislocations attributed and the

of the climb the increase in temperatures to to was

(c a) mobility [20]. dislocations of +

TiAl-Lipsitt c)

mobility interpreted [17] brittle-ductile transition of the in the of al. terms et

1/6[lll]

superdislocation partial

[011] dislocation which constituent of the well is the

as as a

twinning ) twinning dislocation. increasing ( the mode contribution K the of At 1100 it I it

plasticity [17].

however, [21] of evidenced al. found TiAl K, At the 950 Court

to et was no

twinning, they evidence of attributed brittle-ductile transition increase and the the in to

relationship mobility 1/2[l10] high conjugate Noting of dislocations the temperatures. at

ill i12[i10] twinning ordinary slip, complementary I)[I ( [22] and the between the Yoo it

suggested propensity twinning increasing ordinary slip the and that both ordered of is the

conjugate relationship slip-twin brittle-ductile the observed transition. main for The is cause

following explained the in section.

Al~Ti-Twins

specimen observed side often from of

the the

propagate to to were one

might accompanying [23]. other audible initiation intersections clicks Crack have occured at

Yamaguchi of approximate [23] al. obtained such twins. the resolved values of critical shear et

PHYSIQUE JOURNAL M DE III lo7o 6

(001)[110]

twinning MPa, (I ill slip 1100 be MPa and 60 K for the and the 74 I I at to stress

relationship conjugate play significant respectively. slip-twin

role in the Therefore,

may a

increasing Al~Ti ductility also. satisfying compatibility hence of the and strain

Twinning. Crystanography of 3.

Twinning given is figure shear

twinning

described in 4. crystallographic elements of The are

by interspacing intersected (with

of planes Ki number of the and is the

by 2 d~ 4,

g q cos

superlattice bcc-based twinning has been crystallography and fcc- of in The structures n1~,

deformation theory of Laughlin basis of the the recently Christian and

by discussed [24] on

concemed here

[26, 27]. and Crocker We by Bilby twinning and Crocker and Bevis [25] are

rational) give

all which (I.e., compound only Ki, twin and with

K~, systems

a are ah, n1~

/).

relatively twinning (viz. shear low

g «

_ ~~

fi~

'§

Crystallograpllic twinning- Fig. elements of 4.

stacking

Figure ORDERED the shows 5 3,I atom TWINNING ANI> ANTI-TWINNING-

(abc) compound (111) of of Ki plane Llo the AB the All the

structure.

sequence on an =

possible figure plane

I) layer. Burgers shown lie in the A of in 5 the I three vectors set c

trui-twinning

partials by only

twinning

distinct indicated for b's, There is

vectors one » are «

1/6[11 twinning,

which also is hence Llo with that does alter the

not structure b~ upon =

(lll)[lli]

twinning

twinning». the called «ordered This with because atomic occurs

displacements (Fig.

4) PQ of cell the in accordance the in unit homogeneous with shear a

ii,

(Fig. 5),

1/2[11 direction words, intermix with other do A B In

not atoms atoms.

ah or =

(Fig. (l10), plane 4), alternating

layers. of shear S of A and the consists

atom

1/6[lil

ill

partial 1/6 dislocations hand, bi other the'other with and lead On the

= =

W [211],

(Fig. 5),

instance,

pseudo-twinning

in direction the For the

~i ». or

disrupt Lio coordination the chemical for displacements the of homogeneous structure atoms

consisting planes (Fig. 5). (011) the Inixed of plane in this is AB the of shear S because

case =

gives which resulting transformation similar is the crystal L11 from this The type, to structure

TiAl. high internal the in of

energy case a

projected in

twinning Llo

the crystallography ordered of Figure shows 6 the structure on

with figure

primary twinning shown in 6a (l10).

shear, The plane of S

the occurs =

M 6 DEFORMATION TWINNING METALS IN 1071

[°i'j

[,2,j

[2<1)

a- o

O b-

Q T [142j

PHYSIQUE JOURNAL DE M 6 1072 III

crystallographically 2

shuttling. This cla, atomic has 1)/A and (2 where

g no

= =

(lll)1/2[l12]

(Fig.6c), and reciprocal) twin conjugate (or equivalent viz. system

f)1/2[112].

figure anti-twinning,

in involved complementary twinning, shown 6b is (I The I or

llA,

conjugate however,

shear, and this the larger twinning

I. In with

case, g

= =

slip (Ki, ~,), found anti-twinning mode, is be (K~,

mode, ~~), deformation the to to a

energetically anti-twinning

is figure Although (001)1/2[l10],

6d. the shown in system, as

approximately 4/(2 slip- primary twinning factor the

by )2, the of

from that of A reduced a

improved

compatibility for relationship the conjugate strain the twin meets necessary

high plasticity of TiAl temperatures. at

slip-twin relationships conjugate obtained

The 3.2 SLIP-TwiN RELATiONSHIPS. CONJUGATE

ordered (L12 type) (Llo, types) for those cubic non-cubic and and [22] Do22, D019 earlier

(82,

Do~, L21 cubic and crystal the based fcc ordered and structures structure structures on

alloys types)

all ordered which based the bcc suInmarized in table In the for I.

structure are on

slip available listed table [28], information deformation modes the in I the systems

on was

slip intermediate reported

secondary and but

low be the temperatures, systems to at to were

exception primary slip high only The above the become the temperatures. systems at to

anti-twinning high slip the modes the modes is the correlation between and temperature

(o0l) NiAl, alloys by slip along

CoTi, such directions, and 82-type that

of deform as group

[29]. AuZn

(Kj,

complementary ) and conjugate relationship the the between Table I. twin

system

~ j

~~) elevated slip (K~, temperatures. system at

Structure Complementary Active

Type

Slip Twin q

[f2f]

Ll~ (lll) [101] (010) 2

[lll] (l12) 82 (l10) [001] 2

2[fff]

D0~, (l12) (l10) L21 2[001] 4

1/2[ff2] Llo (lll) 1/2[101] (o01)

1/2[ff2]

(lll) D022 (001) [l10] 2

(11]1) 1/3[f126] 1/3[1llo] D0j~ (0001) 2

twinning

3.3 Figure TWiNNiNG shear, shows 7

AND SHEAR

ATomic SHUFFLiNG. g, a as

function ratio, of the cla, axial possible hcp

for six twin in the For A systems

structure.

a =

given hcp

intermetallic metal

compound the of D0j~ magnitude of the smaller the

type, or an

and/or twinning

the easier the Referring non-equivalent will become. conjugate the to q, g

(10fl)

(10f2) figure twin shown in prevalence and for the of 8, 6

systems 7

q q

= =

II)

(l122) twinning Mg in

and twinning Re, correctly predicted Zr, and Ti in in (11 was

anisotropy

of the figure shown [30]. Not in D019 compounds 7 terms

parameters many are

which axial Cd~mg, Co~mo, ratio Fe~mn, Ni~sn, have the

=1.60-1.63 of such A as

Ti~sn, Fe~Ge, Mn~sn. and predicted Among considered, all the it compounds from be can

(10T2)

twinning figure likely

that (1122) is 7 Pt~U twinning the and in is the most to occur

Al~ce Al~Th.

like in most or

M 6 DEFORMATION TWINNING IN METALS 1073

O.8

rmg~cd

rNi~Zr

Ni~ln~

~~ ~

j_p~ ~ O.7

O.6

(126),q=~

-3

O.5 ji

°'

O.4

(

O.3

O-Z

4.4 1.5 4.6 4.7 1.9 4.8

(cla) RATIO AXIAL

Fig. Dependence of

twinning (g) the the (cla) hcp in shear 7.- Doi~ and axial ratio metals on

compounds.

possible why

Ti~Al explained

twinning deformation observed A is be in

not may reason

figure

conceptually Any twinning with the aid of into

divided 8. be

stages, two process may a

homogeneous by pairs shuttling Figure atomic motif followed atomic shear of if 8a necessary.

(f011) (10f2)

twinning

of homogeneous the of shows the shear unit cell for in quarter one

possible shuttling Figures ideally the mechanisms for 8b and 8c show the D01~ structure.

respectively. fully

disordered and ordered of a-Ti, all the four the in In

atoms cases, case

layers displacements,

by (q 4) by shuttle additional indicated small the in

must

as arrows =

figure hand,

Ti~Al, the other of eight layers In all the the in 8.

atoms case on

shuttle,

(q ) important from but difference Ti fact that the the atoInic 8 is the motif

must

pairs 8a) positions (Fig. by face-centered shuwe much cell situated of the the four unit at must

larger interchange shuttling

suggested Laughlan displacements.

Christian

[24] the and

term » «

shuwing

order

this for

or process. » «

Inspecting displacements additional

figure 8b,

atoInic labelled the of in A those atoms one

altemating y-mechanisms of [31] notices coordinated combination which like and

appears a x-

ring synchronous the This

mechanism clock-wise direction. consistent with the shear in is

a « »

originally proposed

edge by of dislocation in the of twin [32] zonal which

atoms core an was

Kronberg [33]. Ti~Al, motion however, coordinated of is the of such In

atoms case a

iiterchange

disrupted required

of of relatively large the because the A and B atoms over

(Fig. 8c). twinning likely why This is intrinsically distances the deformation difficult is reason

compounds D0j~ intermetallic of in the type.

M PHYSIQUE JOURNAL DE III 6 lo74

~~~©t~

O~'

/~)

'lz

iaJ

~=---~~-~

~ ~q

+ ~A

°°'? ~~

fcJ fbJ

(1012)[lot

a) configuration hcp homogeneous shear lattice, twinning ii of in the Fig. -Atomic 8.

shuming interchange shuming hcp alloy, c) the in b) disordered transformation, and in the atomic

alloy. ordered D01~

Energefics kinetics. and 4.

commonly twinning prevalent has believed deformation been that the It becomes mode

and/or non-cubic and only high metals ordered strain low In temperatures. rates at

alloy§, twinning important contributions however, deformation makes intermetallic to many

section,2.

reviewed

properties in all mechanical their temperatures,

at as was

Ti,

available elastic Table the of II fists

constants 4.I ELASTiC PROPERTiES. FAULT AND

experimental by listed for Ti the

from data 4 Al~Ti. elastic K The TiAl, and at constants are

6 M DEFORMATION TWINNING METALS IN lo75

of105 of Table Elastic Ti-aluminides, Ti II. and c,y, MPa. units in constants

Cjj Cm Cj~

Cj~ Ref. C~~ C~~

Ti (34) 0.87 1.76 0.68 1.90 0.51 0.45

TiAl 0.90 1.05 (14) 1,.90 0.50 1.85 1.20

(36) TiA13 2.02 0.88 0.60 2.43 1.45 0.20

Fisher

Renken and Ti~Al [34]. The elastic

of dynamic known, but the constants not are

Young's

Ti~Al polycrystals and shear moduli by of

Schafrik measured [35] GPa 146 E

are =

GPa. These and

compared Hill's be G 57 with elastic values obtained from the

may average =

~Tab. Ti II), of 131 GPa E'

for and G' 51 GPa. The elastic [14] TiAl constants

constants

Al~Ti by

and [36] determined using full-potential total calculations linearized the

energy were

augmented plane-wave (FLAPW) method.

stacking Available energies boundary data the fault

Introducing twin

and

on sparse. are

planar periodic

stacking using supercell calculjtion faults approach total the and

to energy a

TiAl, for boundary (I I) [I

determined stacking superlattice the intrinsic I twin I

energy, we

(SISF) superlattice fault energies stacking and (SESF) extrinsic be 60, 90, fault and to

mJ/m2,

respectively-[14].

80 Yamaguchi

[37] calculated al. the SISF of TiAl be to et energy

ml/m2

approximately using atomistic simulation method with different 60 several central- an

(l121)

ml/m2 potentials. force

boundary

hcp

The twin estimated be of metal 181

to an was

by potential [38], Minonishi al. by proposed Martin used the Lennard-Jones who truncated et

Using [39]. and potential the Bacon atomistic simulations, interatomic for Serra and same

), (1l12),

(I (10f2) [40] boundary obtained the Bacon energies 270, and twin be 211, I to

(10fl)

291ml/m2,

respectively. and boundary The is available. twin not energy

applying Eshelby's theory (41j inclusion

By 4,2 and TWIN NUCLEATION GROWTH, AND

shape analyzed Cahn's

[42], theory recently and bifurcation have effects of Johnson the we

applied

ellipsoidal the the elastic strain of and the twin around

stress stress state energy on an

tip [43]. Figure schematically change twin describes twin the 9 free in formation

energy as a

functio6 activation size, the twin. ratio, for twin and the of the V, of The p, aspect energy

(10fl)[10fi] (l122)[ ((III

ratio, *, formation, AG*, the critical for the and p and aspect

applied compressive

twin in Ti evaluated wide of The the

systems at

stress. range were a

by using figure10

calculated elastic of shown in Ti the results

constants at room were

(10fl

boundary [34] ) assuming equal that of and the of is that twin temperature to energy

(I112).

region According homogeneous twinning of

nucleation the of of in concept to stress a

ovir

conientration (10fl) (l122)

twinning [44], twinning predicted the is thus in Ti the at

(Fig. 10).

experimental findings This result consistent with the of is Paton temperature room

[5]. and Backofen

growth dislocation fcc, heterogeneous Many models the nucleation and of twins bcc, for in

hcp proposed, principle analogous and lattices have in Frank's

of which been to most are

crystal growth theory Mahajan Williams [45], by of and these reviewed and In the [2]. were

difficulty envisaging lattice, mechanism twin hcp there is dislocation of for nucleation the a

displacement factor, twinning (Fig. 4)

for is irrational number because the numerical

an e,

difficulty, cla. which is ratio,

47] [46, function the order avoid this Mendelson of axial In to a

possibilities embryonic suggested

of non-planar

twin result of the formation

as a

PHYSIQUE JOURNAL III M lo76 DE 6

' '

' ~

i '

' '

.~f

i i

' '

i i

I Aspect Ratio -

Fig.

9. description A schematic for

the free change (AG

) formation function of twin in

energy as a

size twin (V) and (p). ratio aspect

6G*

# ~

~ . ll122)

O O.03 O-Of O.02

I«/~l

MPRESSIVE PPLIED

Fig.

DEFORMATION M TWINNING METALS 6 IN 1077

slip dissociations dislocations. The atomistic simulation the of of studies of structure acre

1/3[l123](ll12) by feasibility 49] dislocations [48, eta?. showed the of Minonishi

non-jlanar

(l( (I

emanating edge twin nucleation from of dislocation. the substructure an

superdislocation

[011] three-fold lattice, Llo of dissociation of the the the the In

on a case

+1/6[f12], it

(I plane, ) -1/2[011] depicted [01ii +1/6[121] figure11

lead in

to may as

(Tab. II), appropriate Using nucleation under conditions. calculated elastic twin the constants

energies TiAl, equilibrium widths SISF for obtained APB and the

[14] be to we

mJ/m~),

high (510

0.8 and 5.0 of dissociation Because the APB the dA

d~ energy nm. nm

" =

essentially two-fold ribbon, considered be [011]- with the SISF

I.e. type may a

1/6[f12].

despite

1/6[154] Yet, ribbon,

offers the APB the of the existence APB

+ narrow an

important strengthening the thermal TiAl. clue for the of mechanism to source

tangential pair-wise partial forces [50] The of for each interaction component net

ml/m~.

88, figure11, in and While these F~ F~ Fj dislocation l12, also shown 24 is

= = =

(I,e. torque) dislocation finite. is As forces add the each

to moment at net zero, core up a

(iii

(Fig.

plane ii), the

superdislocation result, left the the when

to moves on a screw

(100) kink-pair plane,

formation thus by and

the the Fi exerted assist F~ torque onto can

hand, facilitating cross-slip-pinning the dislocation the

mechanism other When, [28]. the on

mobility trailing I), (I 2)

would be right (Fig.

dislocations and reduced of the the I

to as moves

[011] Therefore, leading (3).

all compared owing the the interaction

torque, to to

screw one

piining

SISF-dragging depending

superdislocations cross-slip capable [28] of TiAl in

on are or

pinning responsible

cross-slip for the resolved shear While the be the of the

stress. may sense

multiplication mechanism anomaly, dragging yield appropriate strength the with

SISF may an

nucleation lead of twin. to a

at i

( ([44zj [oil)

ds dA

F~ F~

liTi)

SISF APB

superdislocation plane o~l of [ol (1 TiAl. dissociation of Fig. Three,fold I 11.

a screw

M PHYSIQUE 6 JOURNAL DE III 1078

for edge compliance

cubic

Elastic 300 K dislocation

Table III. in twin constants at an

alloys. ordered

~2/~ lo-11 Twin Structure

System Alloy Type

~i6 ~66 S16

(lll)[l12] Ni~Al 0.06 1.65 0.24 Ll~

2.64 0.29 0.13

NiAl 0.07 0.24 (1 1.79

82 1] [1

0.67 3.62 0.18 CuZn

aid

.Veyssikre recently

nucleation of micro-twins proposed have mechanism Hug [51]

a « »

1/2[llll'superdislocations

their TiAl. mechanism based TEM from in This

was on

observatiIns

important Mn,doped samples. of in The the dislocation substructures T14~A1~4

preceded

apparently

by fact that each pr6posed mechanism is the twin of the

aspect one was

1/2[1ill

single Burgers dislocation with vector.

growth fully

of twin be origin the nucleus embryo, of of the the Regardless the

a can or

slip incorporation explained resulting

the dislocations into the twin. A from of

process as a

[52],

geometric analysis incorporation given by and Sax( number formal of the

processes was a

performed, example, for specific been for bcc analyses the for have of detailed types structure

Recently, experimental analysis

hcp [56] and [53],

fcc and TEM [54] [55]

structures. an a

superdislo- [57] performed interaction between of study simulation been the atomistic have

bouidary

crystallographically I special Ll~ alloys, which cations tilt of the in is and 3 type

a =

equivalent boundary. twin coherent the to

crystallographic theory The interracial dislocations 4.3 TWIN of DISLOCATION MOBILITY,

formally

by hcp dislocations outlined the [58], twin and of Pond in metals

structure was core

investigated

by using potentials different two-body forms found that the of [59]. It

was was

potential extremely and wide, widths sensitive the used be interatoInic

to very were core can

(10f2) (11]1)

especially boundaries, suggesting high mobility the for of twin and

dislocation,

planar dislocations. Peierls-Nabarro twin model For the of the

structure core a

anisotropic elasticity by [60] modified used estimate twin be relative dislocation the to may

riobility.

edge dislocation,

Peierls-Nabarro twin the is For stress an

(- ), anisotropic art16 factor, where is the

is the of ( 2 2

exp r~ energy measure a core =

width, Burgers magnitude exponential dislocation. is the of

of zonal twin The and b vector a

gliding is (16 factor which where modified is of the Su of the is

K~ S~~/2

g, a measure ease =

compliance frequently) only

(or [61]. mentioned section 3.3, in the shear As earlier

was more

conjugate crystallographically pair

non-equivalent correctly observed between mode the was

predicted crystals (16 in of for [30]. non-cubic terms many

Any

slip twinning predict viable dislocation model orientation should be able

for the to or

pointed dependence yield

the of recently that We have [29] low stress, temperatures out at «~.

dependence

using qualitatively predicted the orientation of Peierls-Nabarro be the

«~ can

anisotropic non-glide by coupling modified (Fig,12). effect model the of The stress

multiplied by factor, factor (16, exponential is of numerical I

(Si~/6~~)(«~/r~~)

a + + a =

Using the data for CuZn

0.19) in fully III, table

(S~~/6~~)(«~/r~~).

(S~~/6~~

can one

(l12)

(lll)

slip normal in alloys p-(CuNi)Zn the effect of the rationalize stress on

Yamaguchi [62]. and Table by compliance Umakoshi the elastic IV lists determined constants

M 6 TWINNING DEFORMATION IN METALS 1079

compliance for edge Elastic

dislocation Table IV. hexagonal

0 K twin in constants at an

alloys. tetragonal metal ordered and

~2j~q lo-11 Twin Structure

Type System

~i6 ~66 S16

121] A3 Ti 0.07 -0.02 1.78

('11 ) [112] L10 TiAl 0.24 0.19

[112] TiAl~ D02i (111) 0.75 0.81 1,71

j~Y _~rxy

j~-

-'1

, ~ l

/ I -~ ~--

~x j j

Sj6~x

Sz6

Sssrxy

~ ~

~Y ~xy "

twinning

Anisotropic Fig, coupling

shear the for effect of the normal 12. strain components stress on

plane under strain condition. the

and given A13Ti, in the of 0.44 evaluated elastic table from the II. In

Sj~/l~A constants

case =

mobility of

the effect of the 0.47, normal and much 6~J2~~ stronger

stresses

on a =

1ii

) predicted. dislocations twin is (1

TM4nning fracture. S. and

morphology experimentally exhibit twin observed deformation rnicrostructures The in

a can

leading designation macrotwins, twins,, thickness of of wide ratio hence of and aspect to range

stacking microtwins, overlapping and macrotwin

The demarcation thickness faults. between a

quite ~perhaps, spacings), arbitrary microtwin

and is the order often lattice but that

a on

overlapping

stacking between aInicrotwin and faults is of of The thickness

set not. a a

periodicity qd, plane only stacking given Inicrotwin should

exceed but also the of Ki not a

interplanar spacing plane. example, crystal Ki md, is of where d the For structure,

respectively.

fcc bcc 6 3 and for and structures,

m m

= =

polycrys- importance twinning of deforrnation for The

GENERALizED S.I PLASTiC FLow.

by [63] ductility originally discussed and recently by talline Kocks and Westlake

was more

PHYSIQUE M I, JOURNAL JUIN 1991 6, DE iii -T 42

PHYSIQUE M JOURNAL DE III 1080 6

conditions, satisfying compatibility the liInited strain [64]. the of and Park Goo For purpose

significantly

twinning homogeneous shear small contribute

be strain from due to to to too may

measurable macrotwins formed into generalbed large However, when deformation.

are a a

sizable slip twinning primary twins make secondary fraction, within the and volume

can a

energetically provided slip-twin and twin-twin intersections

that the strain contribution are

feasible.

hop commonly observed twin in analyses of three combinational the systems In most

[11ill

(1122)

important satisfying twinning

for the metals, found be the

most to one von was

non-cubic

and Ti-aluminides Ti of all model of [64]. criterion The four Mises systems are

slip, associated with by

the of strain crystal deformation and unlike structure, sense

anti-twinning by Therefore, twinning the deformation unidirectional. is deformation or

slip-twin conjugate relationships particularly

twinning complementary associated the and are

alloys. important generalized plastic of ordered intermetallic for the flow non-cubic

twinning crack-tip plasticity importance of for fracture FRACTURE The in S.2 TOUGHNESS.

toughness [65] studied brittle crack by demonstrated Kohllloff has and Schmauder who been

growth coupled by modeling method. carried in the elasto-atoInistic We have a-Fe out an

slip analysis dependence crack-tip plasticity by twinning in TiAl of the orientation of and the

fior

activity twinning tip

crack,

potential of of Mode-I the the In order [4].

to at assess a

intensity

introduced,

is factor. arrKi,

Ki numerical factor where the

stress

was e,e a e =

crack-tip by

[66] strain, is field elastic related the The shear to stress e,e,

according figure

polar

shown in 13. Whereas coordinate

the

Si~

to S~~ S~~

+ as + e,e «, r,s =

anisotropic Si~/$~ S~~/6j coupling the for is effect of and 0.10 normal 0.12

stresses

= =

(001)1/2[110] ) twinning slip. larger TiAl, numerical (I [I in does exist for the The I it I I not

given parenthesis figure likely value which within the 13, of is the of

the

more occurrence e,

twinning

slip. or

for collectively (l10) figure13, magnitude The larger much shown the

overall of in is e,

(001) crack than for the supercell Using crack. approach

the mentioned section 4.I, in we

recently calculated have cleavage (two energy), the ideal strength times the surface

4.6J/m2

in TiAl be (l10), (010) 5.3, 5.6, (o0l), planes, the and for and

E~, E~

to =

respectively [67]. difference The plane, (110) in between the of Ti Al the

E~ types two pure or

I«ol

lOO

~j~~

T~(O.23) S(O.29)

r ,

(O.50)

MODE~I 6~

al joojj ii

~ ~~~ ~

', ,/ S (O)

,/ '

~~'~~~ ~

j (a lO.54) jo z~) s Tz

plasticity slip twinning by crack-tip and 13.-Potential Mode-I TiAl. crack in Fig. at

M DEFORMATION TWINNING METALS 6 1081 IN

figure

Therefore, (001) only concluded from is planes,

small, 9b. 5 it be 13 that and may very

higher twinning (110) stopping slip for the crack than the effectiveness localized and in is in

experimental (001) prediction by consistent with result the

crack. This is the of the case

[68]. al. Kawabata et

faulting

analysis (Fig. 13)

crack-tip twinning based factor of the shear shear strain The

or on

applicable alloy relatively

crystal Ll~ other instance, also. For in with low is

to structures an a

of symmetric

of SISF be formed in the wake SISF faults

pattern energy, may a an

experimental stacking along

intermittently advancing evidence faults of crack. The

a some

Ni)~Ti by explained

single crystals (Co, by observed could be siInilar [69] in Liu al.

crack et a

analysis.

alloying 6. EWem of additions.

Alloying general, (e.g. O), addition substitional interstitial and of both elements Al and in

alloying twinning twinning

[70, 71]. Ti~Al in in been effect Ti No has

to suppress cause

reported.

alloying activity Al~Ti twinning

conditions of ordered Effects of TiAl have in the and on

by Huang 73]. [72] Yamaguchi [23, reviewed Hall and al. Ti-rich exhibits been and TiAl et

ductility primarily due the lamellar which consist

structure, temperature at to may room some

a~-Ti~Al

(I ill ~+TiAl plates with thin without ) the transformation of twins of and I the I or

relationship ~+TiAl is Ti-rich in TiAl [74]. the the matrix that It twin between either sides

alloying the

[76] Zr, elements and and Nb, V, increase such Cr Mn [75] room-temperature as

ductility. alloying ductility the transition elements affect of Al-rich However, these do not

single-phase ~~-TiAl.

twinning two-phase propensity enhanced of in TiAl

effect addition of Mn the has The on

twinning

reported investigators by [51, for this 75, been several The enhancement 77]. reasons

pinning trailing by

following I) dislocations twin Mn

effect attributed the of the the

to were :

lowering segregation boundary [77], 2) [51], of transformation SISF the twin the to energy

weakening by boundary [77], 3) covalency twin and of Ti-Al bonds and the the hence energy

replacing charge density calculations supported by Al-sites is the electronic which the [75] Mn

reported solid [78]. additions into Also, and TiAl have been

[79] [80] of Ga Er promote to a

it softening mobility dislocations. increased twin In the latter and solution the of

case, was

responsible

matrix interstitial the TiAl gettering concluded the of elements from that Er was

twinning [80]. for enhanced the

ductility Al3Ti effect of improve [73]. of Hf, Li, the The Alloying additions and Zr, of B

compressive giving twinning, the rise best activity ordered

increase the of 0.5 atfb B to to was

ductility 9b. 3 temperature

at at

er room =

alloying potentially guidelines for beneficial elements search the Some for promote to

crystallography, energetics and kinetics

of twinning the basis of established be

can on

twinning Ideally, alloying seek element this overview. should deformation discussed in

one an

twinning through (g) change

boundary of reduces both twin and the shear which the

energy a

hop D0j~ (cla). alloys, specific however, ratios of of and the axial the axial ratio the In

case

=/, /

(l122), (12f2)

(10fl), twinning, cla avoided 3/2, should be and and for

Cd-Mg alloy respectively example, experimentally (Fig. [81] confirmed in it that For

7~.

a was

composition cla eliminating

alloy the became brittle when varied thus its make

was =

ill (10f2)

twinning. I)[I twinning in the axial ratio the ( Llo For D022 it structures, or

twinning alloys cla in alloy cla lower should order 2. be than In I D01~ promote

or or

= =

alloys and possibility pseudo-twinning converting Llo in of the enhance D022 to true to

shuffling alloying interchange which twinning, is will element also the

processes ease an

1082 PHYSIQUE JOURNAL III M 6 DE

preferred. interchange high instance, TiAl, the estimated the for be due

is In to to energy very

layers layer.

directional d-bonds well in the Ti Al between and cohesion Ti the strong

as as

dynaInics modeling using studies molecular simulation Further theoretical and Carlo Monte

energetics

understand kinetics techniques

needed better the and of deformation to are

twinning.

Summary. 7.

strength ductility by twinning deformation of in played overview role the and An of the

presented

alloys, compounds theoretical from metals, and ordered intermetallic has been a

twinning. highlights viewpoint crystallography, energetics,

kinetics and of The of the

a on

systematic using alloy follows analysis model Ti-Al the four

systems are as

(1012)(1011)

twinning

Ti~Al of and absence The in Ti the in I.

occurrence are

interchange shuwing shuwing rationalized mechanisms. of atomic in and terms

appropriate applied superpartial dislocation(s). TiAl,

trailing Under of in the 2. stress,

an a

superdislocation SISF-dragging )[11 [101] (I which nucleation lead twin I I

to may causes

suitable

multiplication with

process. a

componint

anisotropic coupling (compressive)

3. The effect of the normal stress on

(111)[l12]

twinning Al~Ti 0.47). in be is calculated (S~J2~~

strong

very =

Al~Ti slip-twin conjugate relationship (001) 1/2[110] alloys, and TiAl and the I-e- 4. In

1/2[ff2]

significantly compatibility intrinsic (I contribute the strain for the I I to necessary

high-temperature ductility.

Acknowledgments.

G. authors thank The Painter and S. manuscript. for their

M. Hazzledine P. the

comments on

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