ELSEVIER
Materials
Science
and Engineering
A234-236
(1997)
695-698
On the role of incomplete Kear-Wilsdorf
locks in the yield stress
anomaly of N&Al
D. Caillard a,*, G. Moknat
a CEMESICNRS,
b Institute of Physics,
a, V. Paidar b
29 rue Jeanne Marvig,
BP 4347, 31055 Toulouse Cedex 4, France
Academy
of Sciences, Na Slovance 2, 180 40 Praha 8, Czech Republic
Received
5 February
1997
Abstract
In situ straining
experiments
in an Ni-25.9at.X
Al alloy at room temperature
indicate that the density of incomplete
Kear-Wilsdorf
locks is high during deformation. The model of mechanical properties which is based on their unlocking by an
intrinsic cross-slip process is described, and compared with the alternative kink model. The results indicate that the alloy
investigated has a higher complex stacking fault energy than stoichiometric
N&Al. 0 1997 Elsevier Science S.A.
KeyMaords:
In situ experiments;
N&Al;
Yield-stress
anomaly
1. Introduction
The models of yield stress anomaly in N&Al are all
based on the thermally activated locking of screw superdislocations by cross-slip onto the cube plane,
namely by formation of Kear-Wilsdorf
(KW) locks
[1,2]. The most recent models differ only in the unlocking processeswhich can release dislocations and allow
for further plastic strain. In the so-called kink model
[3], unlocking is assumedto take place at the non-screw
parts (the kinks) because intrinsic unlocking by crossslip onto the primary octahedral plane is considered to
be a too difficult process. In the double cross-slip
model, on the contrary [4,5], intrinsic unlocking is
considered to be possible. This second model is supported by experimental observations of so-called APB
jumps and double long-range cross-slip, by means of in
situ experiments and post-mortem observations [6&9].
In reality, unlocking may be either possible or impossible, depending on the stress level and the amplitude of
cross-slip onto the cube plane: cross-slip leading to
dislocation locking may indeed take place over various
distances, leading to either complete or incomplete
KW
locks. Incomplete KW locks have been sometimes re-
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ported in post-mortem observations [lo]. APB jumps
also provide abundant indirect evidence of incomplete
KW locks formed by short range cross slip onto the
cube plane. This article reports additional evidence
of the high density of incomplete KW locks which
are formed during deformation in an Al rich Ni,Al
alloy. The model based on the locking and unlocking of
these incomplete locks is then briefly described and
discussed.
2. Results and interpretation
In situ straining experiments have been conducted at
room temperature, in a Ni 25.9 at.% Al alloy provided,
and also studied, by D. Dimiduk (Wright Lab.) [II].
Microsamples have been cut in the (i33) plane, along
the [Oli] direction. The whole procedure of in situ
experiments has been described elsewhere [12].
Deformation started by the planar glide of a group of
[TO11superdislocations in the (111) primary octahedral
plane. As seen in Fig. l(a), after they stopped, the
superdislocations involved were straight in their screw
orientation. Some of these superdislocations subsequently glided further in the same plane. A few other
dislocations, however, immediately started gliding in
the intersecting (010) cube cross-slip plane. One of these
dislocations can be seen in Fig. l(b) and l(c): it is still
696
D. Caillard
et al. /Materials
Science
and Engineering
A234&236
straight and screw, and it glides steadily at a constant
speed of 0.1 urn s-‘.
We emphasize here on the very different behaviours
of two types of straight screw dislocations: those which
remain immobile or glide further in the octahedral
plane, and those which are highly mobile in the cube
cross-slip plane. Similar behaviour has been observed in
the 11’ phase of a superalloy at the same temperature
(Fig. 1 of [13]) and in Ni,(Al, 0.25 at.% Hf) at 573 K
(Figs. 6 and 7 of [7]).
These results can be interpreted as follows. Complete
KW locks have the right configuration
to glide in the
cube plane, which they do quite easily. The cube slip is
then probably controlled by a Peierls mechanism resulting from the non planar superpartial
cores involved
[14]. Straight screw dislocations which under the same
conditions are sessile in both octahedral and cube cross-
(1997)
695-698
+ movement
gk---+~
Fig. 2. Behaviour
of an incomplete
KearrWilsdorf
lock under stress:
(a) definition
of the total forces for cube slip on the leading (L) and
the trailing (r) superpartials.
11’is the width of the APB in the (loo]
plane. (b) Calculated
values of 5r (the applied shear stress in the
primary
{ 111) plane). as a function
of w.Q,
and r; [4]. see text.
slip plane are considered to have a different core structure, namely to be incomplete KW locks. This indicates
that during straining, a large density of screw superdislocations may form incomplete KW locks, at least at
the temperatures
investigated in the different alloys.
This must be taken into account in the models.
3. Incomplete
Fig. 1. In situ straining
experiment
in Ni-25.9at.%
Al at room
temperature:
(a) screw superdislocations
after glide in the (111)
primary
plane. The Burgers vector direction,
b, is seen in projection.
(b. c) Dynamic
sequence showing one of the superdislocations
seen in
(a), gliding in the (010) plane after cross-slip. The star is a fixed point.
Kear-Wilsdorf
locks
under
stress
We consider a superdislocation dissociated partly in
the cube plane, partly in the octahedral plane (Fig.
2(a)). The width of the APB in the cube plane is called
IV. The trailing superpartial, T, is considered to be fixed
in the cube plane, whereas the leading one, L, can reach
easily its equilibrium position because it is considered
to be glissile in the octahedral plane. When a stress is
applied, both superpartials are subjected to a shear
stressrr, in the primary octahedral plane, and Nz, in the
cube cross-slip plane.
All the stressesacting on superpartials (including
their elastic interaction in the anisotropic media and the
surface tension of the APB) have been calculated in [4].
The total stressacting on the trailing partial in the cube
plane, namely the driving stressfor unlocking, is called
D. Caillard
et al. /Materials
Science
and Engineering
~22. Fig. Z(b) shows the values of zp which permit to
reach iuen ua1ue.sof $2, ‘hs a function of w, fox
N= J 312.
Before unlocking takes place, the leading superpartial
can also move in the cube plane under the stress ~$2,
which tends to lock again the superdislocation and
inhibit further movement. Unlocking by cube slip of the
trza&g SU~ERX~D~&~~
mu& &en be a fa&er ,~rtic
&i~
locking by cube slip of fhe leading one, in order IO
ot taia srtbstaatial dislocation maVemeuts. T&is implies
that ~2: 2 ~22.This condition has been shown in [4] to
be satisfied when zp is higher than a critical stress 2;
(Fig. 2b) and thus z”, is considered to be the effective
unlocking stress.
t; increaseswith increasing M?,from
f
I--- yc 1 + 2/A
y() 31j2 1
[
(the stress which corresponds to repeated APB jump,
according to [4]) to
$1
-;&I
(the critical stress for cube-octahedral cross-slip, acccrding ta (40, where yc arid y0 are the APB energies in
the cube and octahedral planes, respectively, and A is
the elastic anistropy factor. Since repeated APB jumps
and cube-octahedral cross-slip have been identified in
near-stoichiometric Ni,Al and Ni,Ga [6&9], the correspan&g applied shear stressesare respectively equal ta
the minimum and maximum values of z& from which
we could deduce that the ratio yc/yO must be close to
0.9. Similar order-of-magnitude estimates indicate that
z’p is also close to experimental values of zp in many
other alloys, which shows that unlocking of incomplete
KW locks must be considered as a possible controlling
mechanism.
4. Models of yield stress anomaly
In the most simple model [4], the distribution of
incomplete KW locks which are formed during the
glide process is assumed to be centered around an
average value $ which increaseswith increasing temperature. Then, the yield stress versus temperature curve
can be identified with the z; versus w curve in Fig. 2(b),
with fairly good order of magnitude of the stress.
A more realistic distribution of M?as a function of
temperature can be deduced from the crass-slip mechanisms which lead to the formation of incomplete KW
leeks (51. Zt can be taken as: P(ct; TT)= Poexp W’
G
- exp - 2,
where G,, is an activation energy of cross@
kT
slip. With this hypothesis, weak locks (small w) are the
most frequently formed at all temperatures; they are
A234-236
(1997)
695-698
697
releasedunder a moderate applied stress. A few strong
\ocks (large w) ase also formed, howevex, which cannot
unlock under the same conditions. The mobile dislocation density is thus progressively exhausted, which must
be compensated by an increase of zp (activation of new
sources). The corresponding strain-hardening coefficient is coasdered to be proportional to tie exhaustion
I&C Yi I%%KYEA%
t&l3 lLYCS?C&tig
?X@iiJZZW~ X33XPj%$
T), and jr decreaseswith increasing stressbecausemore
lacks are able ta uda3k. As a resdt, tfke strain &arching coefficient goes through a maximum when the rate
of exhaustion is the highest, in the middle of the
temperature range of yield stressanomaly. The quantitative estimations are shown to be consistent with experimental values in [5], and the yield-stress versus
temperature curve still follows the z’p versus w curve
with fairly good orders of magnitude of the stress.
5. Discussion
Microscopic observations indicate that a high density
of incomplete Kear-Wilsdorf locks are formed during
straining, and anisotropic elasticity calculations show
that tkeir inQinsic untocking exp<ains satisfactori<y tke
anomalous mechanical properties (yield-stress anomaly
and strain-hardening) of nickel-base alloys.
The kink model is an alternative way of unlocking
complete or incomplete KW lock. As these two competing mechanisms axe acting in paxaiel, however, the
stressis expected to increase till the easiestis activated,
and thus only the easiest should be observed in experiments. Now, as double cross-slip has been identified
unambiguously at different temperatures and stresslevels (see Section I), and as there is no evidence of the
same kind that the kink model should operate, double
cross slip should be the rate controlling mechanism.
This conclusion is corroborated by the recent results of
simulations which indicate that the intrinsic unlocking
process may be the dominant process in the temperature range of yield-stress anomaly [15].
As intensive cube slip has been observed at room
temperature in Ni 25.9 at.% Al and in the y phase of
superalloys, whereas it could be observed only above
573 K in Ni,Al, the CSF energy in thought to be higher
in the two former alloys. These experimental results
also explain why the temperature of the outset of the
yield stressanomaly is lower in Ni 25.9 at.% Al than in
stoichiometric N&Al, in agreement with the earlier conclusions of Dimiduk et al. [l 13.
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