Anomalous {110} slip and the role of co-planar double slip in BCC metals

Scripta METALLURGICA

ANOMALOUS

Vol. 9, pp. 971-978, 1975 Printed in thb United States

Pergamon

Press,

Inc.

{Ii0} SLIP AND THE ROLE OF CO-PLANAR DOUBLE SLIP IN BCC METALS

H. Matsui Research

Institute

and H. Kimura

for Iron, Steel and Other Metals

Tohoku University,

Sendai,

Japan

(Received June 25, 1975)

i. Introduction The slip system with sharp and straight observed

in bcc metals deformed

(101) slip" for their remarkable low-stressed

peculiarities

plane in preference

coarse and straight

slip lines along

at low temperatures

dislocations structure

of two slip directions

with two slip directions

in the anomalous

slip plane

We have already presented preference

to the primary slip

of screw dislocations (S-E) mechanism"

(7,8).

emergence. nucle@tion

in a

slip, and

It is also known that (2).

The

in a lamellar network

(3-6). for the anomalous

The mechanism surface.

(S01) slip in

is based oa the interaction

We shall call it "surface

The mechanism may be summarized

Kinks are supplied perpetually to the crystal

metals.

are arranged

(Fig. I)

(ii) the slip lines are

in a common slip plane

a mechanism

with the crystal

hereafter.

(i) this slip occurs

to fine and wavy ones of the "normal"

(iii) this slip occurs only in very high-purity this slip consists

(I);

to the primary plane,

in contrast

(101) plane

are known as "anomalous

to the screw dislocation

effect

as follows:emerging

obliquely

surface with the aid of the image force at the point of

Since most of the stress to move screw dislocations of kink pairs on the dislocation,

the perpetual

is due to

supply of kinks

may greatly reduce the stress needed to move screw dislocations. We have confirmed specimens

the active operation of the S-E mechanism

by in-situ deformation

favored for the operation

experiment

in a HVEM

of the S-E mechanism

(a) The slip direction shear stress

The conditions

are as follows:-

should be at a small angle to the crystal

(b) The slip plane should be nearly normal resolved

(9).

in thin foil tensile

to the surface.

surface.

(c) The

should be large enough to move kinks along screw

dislocations. The choice of the slip system is therefore 971

influenced

by the orientation

of the

972

ANOMALOUS ( i i 0 )

SLIP IN BCC METALS

Vol.

local crystal surface.

9, No. 9

Some questions were

raised on the choice of the slip plane in a

anomalous plane

cylindrical crystal

(10), and most of them

were answered by considering the necessary conditions for the multiplication of dislocations activated by the S-E mechanism

(8).

The following problems, however, have been left unsolved with the S-E mechanism:-

primary

plane

(i) The anomalous

(i01) slip occurs even

in the orientation region of the specimen

=Ti ~

Ill

axis where a slip system other than (101)

IO1

slip system is most favored by the S-E

FIG. 1

mechanism.

Orientation of the anomalous slip.

(ii) For a cylindrical crystal,

the most favored slip plane for the S-E mechanism is not (I01) in a certain region

of the surface far away from the top surfaces for the two constituent slip directions. The anomalous slip lines are, however, usually observed along the trace o f [[01) plane in this region, too (the shaded area in Fig. 1 of ref. 8). It is impossible to explain with the S-E mechanism alone why only one slip system is chosen as the anomalous slip.

It has been suggested that these difficulties

may be removed by considering the role of the co-planar double slip together with the S-E mechanism

[ii).

The purpose of the present paper is to offer the

details of the co-planar double slip mechanism and a more satisfactory explanation of the anomalous slip. 2. Proposal of the "co-planar double slip (C-D-S) mechanism" The C-D-S mechanism is based on a consideration that kink pairs can be formed at the intersection of screw dislocations

of different slip directions with the

aid of their mutual elastic interaction.

Such a process may be expected to occur

in the dislocation network structure of the anomalous slip.

The kink pairs

propagate along screw dislocations under the action of the applied stress, so that the screw dislocations

lying.

proceed easily in the plane where kink pairs are

Since the kink pairs are supplied continuously,

the screw dislocations

continue their motion under a stress smaller than that to move screw dislocations in the normal manner,

i.e., nucleating kink pairs by thermal fluctuation.

Now, let us find the force components acting between two nearby dislocations with different Burgers vectors, and then examine the behavior of these interacting dislocations. In Fig. 2(a) are illustrated two infinitely long screw dislocations 1 and 2, with Burgers vectors ~i and b2, respectively, in a Cartesian co-ordinates xyz. The dislocation 1 is parallel to x-axis separated by z from the dislocation 2 lying in xy-plane and making an angle e with x-axis.

For bcc metals, screw

Vol.

9, No,

9

ANOMALOUS

(110)

SLIP

IN BCC METALS

Y

973

/2

2

r'~8 {= 71°)

\

x

X ,,

(a) PIG.

2

/

I I

(b)

(c)

Co-ordinates of the dislocations, in pure screw orientations (a), twisted about z-axis by an angle a (b). Schematic illustration of the distributed force components ~Fy and ~F z (c).

dislocations plane

al

~

i and 2 are along

and 8 is about

directions,

so that xy-plane

71 ° .

For large

z the mutual

hence the two dislocations

lie along

the screw orientations

As z is reduced,

these

screw orientations.

two dislocations

The calculation

force on the two dislocations are no longer

straight

three dimensional consistent) practical estimate cations

of the interaction are now deflected

make x-axis equation

force.

to the dislocation

411 of the dislocation (12) for isotropic

6Fy

In this figure,

=

P{b2 [-~-~. s sin20

crystals

as

+ bebs(l

-

+ ~-~/v~-{bebs(l

6F z = [ ~ { Z b e b s sin20

+ ~{beb

i.

- cos28)

cosZe)}

+ [b~ - be2)COSZO

2(b)

a complex

the exact

structure.

(self It is

in an approximate

system

screw dislotwo

is taken to

6~ felt by the differential

by utilizing

x x2sin28

- b 2 sin20} e

and assume

two original

The force

1 may be obtained

interaction

and the angle between

The co-ordinate

2(a).

since the dislocations

to determine

in Fig.

by an angle e in xy-plane

is 8, so that 8 + 2e = 71 ° parallel

intractable,

as shown

and

in Fig.

from their original

of mutual

field for such a dislocation

the configuration

is negligible

as shown

but are curved

It is impractical

shape and the stress

dislocations element

in the plane,

configuration.

to consider

may be deflected

of the components

then may become

or lying

interaction

is a {Ii0}

the Hirth and Lothe

+ z2

2 xz (x2sin2O + z2)2 ] dll'

-~I--~b2% i-~ e"

z x2sin28

+ z2

s sin20 - bee(1 + cos20)} z(x2sin2O - z2)1 d l l , (x2sin28 + z2) 2~

974

ANOMALOUS

(110) SLIP IN BCC METALS

Vol.

9, No. 9

with b e = b sine, b s = b cosa, and ~ = (71 ° - 0)/2, where ~ and v are the shear modulus and Poisson's ratio, respectively. These forces are calculated for the two original components

screw dislocations

per unit length of the dislocation

and the parameters

attatched

the force is ~b2/4~z.

and z < 0, respectively. the filled triangle the behaviors

6F

at 8 = 71 ° in Fig.

for x,z > 0 as functions

of 0,

for z = 0 is also shown in this figure,

3.

In the following,

under the above mentioned

(i) two dislocations

with like sign,

we will discuss interaction

(ii) dislocations

force with

sign.

(i) Dislocations

with like sign

The force components for the original Dislocation

1 in Fig.

to be appreciable, dislocation

6Fy and ~F z on the dislocation

screw orientations

When z becomes

torque

in formation

in Fig.

in xy-plane

2)

2(c).

and an attractive

small enough for the interaction

the part of the dislocation

2, since ~F

element dl I (Fig.

are shown schematically

2(a) feels a clockwise

force along the z-axis.

results

3 are shown the force

The sign of 6F y and 6F z should be reversed for x < 0 Y The case of pure screw dislocations is indicated by

of the dislocations

in two cases:-

In Fig.

to the curves are values of x/z and the unit of

The component

in the unit of Bb2/4~x.

unlike

with like sign.

force

1 near x = 0 is pulled to the

is much larger than 6F

for x/z << I. This interaction y according to the following

a/2[lil]

a[OfO].

z of a junction dislocation

reaction,

The resultant

dislocation

+

a/2[iii]

÷

is of screw character.

in crystals with the anisotropy

This reaction

factor A less than 2.41

is possible

(13), where

A = 2c44/(Cli - c12 ). Then, at their neighboring parts to the node, the reactant screw dislocations tend to align themselves in the plane containing the junction dislocation,

since s'crew dislocations

they had a high "stiffness"

at low temperatures.

in bcc metals behave as if The behaviors

of screw dis-

locations with a high "stiffness" are often observed by in-situ deformation experiment in a HVEM; screw dislocations behave as if they were stiff and straight wires under stress

(14).

After the planar alignment

is established

z is 0 (x ~ 0), so that 6F z is 0, i.e., the interaction in xy~plane.

Then the only non-zero

very large near the node. stress corresponding dislocations high stress

force component

For example,

to 6Fy exceeds

for x smaller

the critical

force near the node is

is 6Fy and this can become than about 70A, the

stress T~ to move screw

in Mo, i.e., 30Kg/mm 2 (resolved yield stress at 77K). is enough to nucleate

reaction node as illustrated

kinks on the screw dislocation

in Fig.

4(a).

near the node,

Such a

near the

Note that the plane in which kinks

Vol.

9, No.

9

are n u c l e a t e d

ANOMALOUS

(110) SLIP IN BCC METALS

is the xy-plane which contains

Let us consider xy-Dlane larger

a crystal

subjected

975

the two slip directions.

to a stress

with magnitude

in the

than the critical

stress T k to propagate kinks along screw fi dislocations. The value T k may be a p p r o x i m a t e d by the critical stress T e to move c c edge dislocations, which is much less than T s at low temperatures (e.g. 15) c ' " Hence, She stress in the m a x i m u m resolved shear stress plane (MRSSP) can be still less than T s while that in the secondary slip plane, i.e. in xy-plane, exceeds c e Under these circumstances, screw dislocations cannot move in the "normal" TC • manner in any slip systems, while the kinks nucleated near the attractive junction nodes can move along the screw dislocations. as a whole

in the xy-plane

as shown in Fig.

is confined

to the xy-plane

dislocation

out of the xy-plane

4(b).

screw dislocations displacement

gives rise to a large restoring

interaction

stress

and the applied

other side of the node, to each other,

can move,

Az of the

force ~F z near

at one of the both ends

side A in Fig.

4(b), where

stress act in the same direction.

B, where the two stresses

the On the

act in the opposite direction

the kink cannot move and the d i s l o c a t i o n

of the kinks nucleated

as a whole,

i.e.,

can proceed

The m o t i o n of the dislocation

since some infinitesimal

It is likely that only those kinks nucleated

the node.

of the junction d i s l o c a t i o n

passage

Thus,

at the neighboring

can only move by t~e

node.

The network may move

since the Burgers vector of the junction d i s l o c a t i o n

is also

in

the

xy-plane. (~i) Dislocations

with unlike

sign

The sign of the force components

in Fig.

interaction between unlike dislocations. -25 ° ~ 8 ~ 25 ° since 6F z is positive dislocation

1 is pushed against

dislocation

2 being

location

1 in Fig.

with the repulsive dislocation

supposed

as shown in Fig.

the d i s l o c a t i o n

6F z (see Fig.

I near x = 0 may be bent until to each other

torque 5).

screw dislocations,

in xy-plane

is formed by climbing,

similar

an applied

climbing

is improbable.

The cross

to the bent part

ble that the torque separated

Thus,

in xy-plane

dislocation

of the kink pairs.

(i) is

however*

the

of the screw

since the screw parts

to be formed.

feel

It is still possi-

to form kink pairs on the d i s l o c a t i o n

2 with a small distance

1 may move along the d i s l o c a t i o n

the p r o p a g a t i o n

If such a

to that in the case

instead of the climbing,

is unlikely

assists

4(c).

At low temperatures,

is also improbable

a junction

from the d i s l o c a t i o n

stress.

1

to be bent

they must climb to combine with

to occur under

repulsion.

together

Since the bent parts attracting

expected

parts adjacent

(the

z, a part of

2 is considered

junction

mutual

stress

The screw dis-

For small

as shown in Fig.

slip,

e~cept for

Suppose that the

each other to form a junction d i s l o c a t i o n a process

for the

nearby parts of the dislocations

(dislocation

6F z become attractive.

each other are no longer

5.

2 by an applied

2(a) feels a counter-clockwise

where

is repulsive

to be locked by some obstacleS).

force component

and 2 become parallel simultaneously),

5 should be reversed

Interaction

as in Pig.

2 in the xy-plane

4(d).

The

as a result of

1

976

(110)

ANOMALOUS

SLIP IN BCC METALS

Vol, 9, No. 9

!oo. I¢1

L

{, °

'

i -2.

-I~

~

"

i

i

0

~

i

leo

ZTO

FIG. 3 Interaction f o r c e c o m p b n e n t s 6F v a n d 6F z f o r x , z > 0 a s f u n c t i o n s o f t h e a n g l e e b e t w e e n t h e two l i k ~ d i s l o c a t i o n s in Fig. Z(b). 6F V f o r z = 0 i s a l s o shown. Parameters attached to the curves are x/~. T ~ u n i t o f t h e f o r c e i s ~ b 2 / 4 ~ z , e x c e p t f o r t h e c u r v e o f 6Fy f o r z 0 where the unit of force is ~bZ/4~x. The i n t e r a c t i o n between pure screw dislocations corresponds to the point marked with a filled triangle at 0 = 71".

L

rb x

.-.g_

FIG. 4 Kink nucleation near the nodes with the aid of the interaction force and the kink propagation (b). J u n c t i o n f o r m a t i o n b e t w e e n two u n l i k e d i s l o c a t i o n s a s shown i n (c) i s i m p r o b a b l e . Double kink formation in the vicinity of an unlike screw dislocation (d).

(a),

Vol. 9, No. 9

ANOMALOUS

(110) SLIP IN BCC METALS

977

FIG. S Convergence of the slip due to the S-E mechanism into (i01) slip. From the above considerations, it is evident that screw dislocations canmove more easily in the co-planar slip plane than in the MRSSP provided that the resolved shear stress ratio T co-planar slip plane/TMRSSP is larger than Te/T c- s c" 3. Combination of the Surface-Effect and the Co-planar Double Slip Mechanisms The lamellar network structure may be introduced into the crystal as follows. The dislocations are very likely to be activated into motion by the S-E mechanism since this needs only Tec in the secondary slip plane favored by the S-E mechanism, and the axial stress can be smaller than the usual yield stress which is considered to be determined by the normal motion of.the screw dislocations in the primary slip system (as expected by the Schmid factor). As mentioned in the previous papers (7-9), the S-E mechanism is greatly influenced by the angle 8 between the slip direction and the crystal surface at the top surface of cylindrical specimens, and this angle is equal to the angle I between the slip direction and the specimen axis. The angle 8, and hence X should be small for the operation of the S-E mechanism. Consequently, the order of the preference for the S-E mechanism is usually [iIi],[iii],[iIi] and [[Ii] among the slip directions for mid-oriented specimens. Thus double.slip is most probable for [Iii] and [iII], so that the co-planar slip plane is (S01). Asimilar argument holds fob reGtangular sectioned specimens. The slip plane favored by the S-E mechanism does not always coincide with ([01) plane. It can be shown in the following how the slip introduced by the S-E mechanism in the arbitrary slip plane converge to the ([01) plane. In Fig. 5,

one

slip with ~ = [iIi] by the S-E mechanism is taken in the (101) plane

for simplicity, and the second slip with ~ = [iii] is introduced also by the S-E mechanism in the oZher slip plane. These slips must intersect in the crystal, and at ~he intersection, the co-planar double slip mechanism presented above operates. Kinks are nucleated in (101) plane, because (I01) plane contains both slip directions. Hence the slip alter the intersection is confined to the (I01) plane. This conclusion holds for the case where neither slip is in the (i01)

978

ANOMALOUS (110) SLIP IN BCC METALS

Vol. 9, No. 9

p l a n e , s i n c e ( i 0 1 ) p l a n e i s t h e o n l y p l a n e c o n t a i n i n g b o t h o f t h e two s l i p directions [111] and [ 1 i l ] . D e t a i l s of the network f o r m a t i o n in t h i s g e n e r a l case will

be d i s c u s s e d

elsewhere

(6,14).

I n c o n c l u s i o n , t h e anomalous ( i 0 1 ) s l i p i s a s l i p i n t r o d u c e d by t h e S-E mechanism and c o n v e r g e d t o t h e ( i 0 1 ) p l a n e by t h e C-D-S mechanism f o r ~ u r t h e r development. A l t h o u g h i n some o r i e n t a t i o n r a n g e o f t h e s p e c i m e n a x i s , t h e r e may be s e v e r a l s l i p s y s t e m s f a v o r e d by t h e S-E mechanism, t h e C-D-S mechanism can f a v o r o n l y t h e s l i p on ( i 0 1 ) p l a n e , s i n c e t h i s i s t h e o n l y s l i p p l a n e c o n t a i n i n g two s l i p d i r e c t i o n s [111] and [ 1 i l ] ; t h e s e s l i p d i r e c t i o n s a r e t h e most f a v o r e d ones by t h e S-E mechanism. Very r e c e n t l y ,

the active

motion of the network in the

( i 0 1 ) p l a n e has been

o b s e r v e d i n Mo i n a HVEM ( 1 6 ) . The component s c r e w d i s l o c a t i o n s and a l s o t h e j u n c t i o n d i s l o c a t i o n s move i n t h e ( i 0 1 ) p l a n e . This seems t o be a s t r o n g s u p p o r t f o r t h e p r e s e n t c o n s i d e r a t i o n a b o u t co-planar double slip. Detailed presentation of the observation i s now i n p r e p a r a t i o n .

of the network observation the role of.the and t h e a n a l y s i s

Acknowledgement The a u t h o r s a r e v e r y g r a t e f u l

t o Dr. M. Suezawa who k i n d l y r e - e x a m i m e d t h e

formulae. References 1. J . W. C h r i s t i a h , Second I n t . p. 31, ASM., (1970) 2. C. J .

B o l t o n and G. T a y l o r ,

Conf. on t h e S t r e n g t h o f M e t a l s and A l l o y s , Phil.

3. A. L u f t and L. Kaun, P h y s . S t a t . 4. L. P. Kubin and B. J o u f f r e y ,

Mag., Sol.,

Phil.

26, 1359 (1972) 37, 781 (1970)

Mag.,

27, 1369 (1973)

5. R. J. Wasilewski, R. Hutchings and H. H. Loretto, Phil. Mag., 29, 521 (1974) 6. H. Matsui and H. Kimura, to be published. 7. H. Matsui and H. Kimura, Scripts Met., 7, 905 (1973) 8. H. Matsui and H. Kimura, Scripta Met., 8, 463 (1974) 9. H. Matsui, H. Saka, K. Noda, H. Ki~ura and T. Imura, Scripts Met., 8, 467

(1974)

i0. G. Taylor, Scripta Met., 8, 459 (1974) ii. H. Matsui and H. Kimura, Scripta Met., 8, 1205 (1974) 12. J. P. Hirth and J. Lothe, Theory of Dislocations, p. 116, McGraw-Hill; (1968) 15. Y. T. Chou, Mater. Sci. Eng., i0, 81 (1972) 14, H. Matsui, H. Saka, K. Noda, T. Imura and H. Kimura~ to be published. 15. H. Saka, K. Noda and T. Imura, Crystal Lattice Defects, 4, 45 (1973) 16. H. Saka, H. Matsui, K. Nods, H. Kimura and T. Imura, to be published.