Some aspects of cross-slip mechanisms in metals and alloys

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Submitted on 1 Jan 1989

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Daniel Caillard, J.L. Martin

To cite this version:

Some

_aspects

of

_cross-slip

mechanisms

in metals and

_alloys

D. Caillard

₍₁₎

and J. L. Martin

₍₂₎

(1)

Laboratoire

_{d’Optique Electronique}

du CNRS, B.P. 4347, F-31055 Toulouse Cedex, France

(2)

Institut de Génie

_Atomique,

Ecole

_{Polytechnique}

Fédérale de Lausanne, CH-1015 Lausanne,

Switzerland

(Reçu

le 6 mars _1989,

_accepté

sous

_{forme définitive}

le 24 mai

₁₉₈₉₎

Résumé. 2014 Des modèles ont été

proposés

pour décrire le

glissement

dévié des dislocations dans les métaux de structure CFC et HC. On montre comment ces modèles se sont

_développés

et comment des résultats

_{expérimentaux}

récents confirment leurs

_{prédictions. Quelques}

aspects

macroscopiques

de la

_plasticité

_{des cristaux tels que les}

_énergies

d’activation de

_fluage,

les anomalies de limite

_élastique

et les stades de durcissement sont discutés à la lumière de ces

modèles

_{microscopiques.}

Abstract. 2014 Dislocation _cross

slip

in FCC and HCP metals has been described in terms of various models. The

_development

of these models is reviewed and their

_predictions

are

_compared

with

recent

_experimental

observations. Some

macroscopic

features of

plastic

deformation

_(creep

activation

_{energies, strength}

anomalies and deformation

_stages)

are examined in the

_light

of these

microscopic

mechanisms. Classification

Physics

Abstracts 62.20H

1. Introduction.

Cross

_slip

occurs when the local stresses

_push

a dislocation into a

_plane

which is different from

the

_{original plane}

of

_splitting.

It has been evidenced

_long

_ago

_by

the observation of

_slip

traces at

_sample

surfaces. The outlines of the first realistic models were then derived

_by

_Friedel,

both for face-centered cubic

_(FCC)

metals

_[1]

in 1956 on the basis of calculations of Stroh

(1954) [2]

and for

_{hexagonal close-packed}

_(HCP)

metals

_[3]

in 1959. In the mean

_time,

another

_theory

for dislocation cross

_slip

was

_developed

(see

_{e.g. Refs.}

[4]

and

[5]).

Later on, similar

_slip

trace

_{observations,}

_{after creep} at intermediate

temperatures,

led some

authors to

_interpret

the

_{corresponding}

activation

_energies

in terms of

_cross-slip

_{(Lytton et}

_{al. ,}

1958

_{[6] ;}

Friedel,

1959

_[3]

and 1964

_[7]).

This mechanism has also been claimed to be the

_key

process at the transition stress _’iII1 between the

_{hardening stages}

II and III of FCC metals

(Schoeck

and

_Seeger,

1955

_{[4] ;}

Friedel,

1956

_[1]

and

_Haasen,

1967

_[8]).

More

_recently,

the

_importance

of cross

_slip

in the

_plasticity

of metals has however been

ignored

or underestimated.

In the

_present

_paper, we

_attempt

to describe how these first ideas

_developed

with time into detailed

_models,

and how these have been confirmed or

_{improved recently through}

FCC metals and then consider Peierls

_type

friction related to

_slip

in

_body

centred cubic

_(BCC)

metals and non

_compact

_slip

in metals with a close

_packed

structure. We then summarize the results

_concerning

a

_newly

observed

_type

of

friction,

the «

locking-unlocking

mechanism _»,

both for

_{prismatic slip}

of

_beryllium

and

_slip

in

_L12

ordered structures.

_Macroscopic

_aspects

of

plastic

deformation such as

_strength

_anomalies,

_{creep activation}

_energies,

deformation

stages

of the FCC metals are then discussed in terms of the above dislocation mechanisms.

2. Cross

_slip

in FCC metals.

The

_elementary

_{process of dislocation} cross

_slip

from a

_compact

_plane

onto another

_compact

plane although frequently

observed

_{experimentally,}

is a _very

_poorly

known _process.

The theoretical

_aspects

of cross

slip

have been studied

by Escaig

(1968 [10, 11]),

_following

Friedel’s view. In his

model,

cross

slip

occurs

_through

the mechanism sketched in

_figure

1. It starts from a

_primary

constriction on a screw dislocation. Under the influence of the

_applied

stress aided

_by

thermal

activation,

the two halves of the constriction are

_separated

_and,

as

suggested by

Friedel

_{(1956 [1],}

1957

_[12]),

the dislocation

_segment

between

_{them, splits}

at once on the cross

_{slip plane.}

This model seems to be more realistic than the former one of

Schoeck and

_Seeger

_{(1955) [4].}

In

_particular,

_Escaig

_{has shown that the process}

_depends

mainly

on the ratio of the width of

_splitting

under stress on the

_primary

and the cross

_slip

planes.

This causes the process to be orientation

_dependent,

which will be discussed below.

Fig.

1. - Successive

stages of

_{cross-slip starting}

at a _{constriction,} in Friedel’s and

Escaig’s

model

_{[1, 10,}

11].

The activation energy

AGcs

has been derived for weak effective stresses :

with i = 1 or 2

_depending

on how many constrictions are _necessary to _{initiate the process ;}

bo

is the width of a recombined screw

dislocation ; 1£

the shear

modulus, a

(i )

an orientation

Do

the dissociation width at zero stress ; A is a

_slowly

variable function of IL,

b,

f.

The _{activation volume of the process is :}

A new

_{experimental technique}

has been

developed

to

_produce

a burst of cross

_slip

at the

yield point

[13] :

a _copper

single crystal

is deformed in

compression along

[110]

to the end of

stage

II to

_produce

a

_homogeneous

dislocation forest. New

_samples

are then cut out of this

crystal,

in a

_{single slip}

orientation. The new

_primary

dislocations are

_expected

to cross

_slip

at the

_{yield point}

because of the numerous forest dislocations

_acting

as obstacles. The tension

compression asymmetries predicted by

the

model,

as well as the orientation

_dependence

of

the critical stress for cross

_slip,

are in

_good

_agreement

with

_experimental

results obtained at room

_temperature.

As the

_temperature

is

_changed,

load relaxation

_experiments

are

performed along

the stress strain curves to obtain activation volumes. An

_example

is shown in

figure

2 for a

_{predeformation experiment}

at 473 K. The corrected activation volume exhibits a

minimum as a function of strain. This

_corresponds

to a value of about 300 atomic

_volumes,

in

fairly

good agreement

with

_{equation (2)}

and the width of

_splitting

_{of copper. The} stress

corresponding

to this minimum is then considered to be the critical stress for cross

_slip,

which is confirmed

_{by slip}

trace observations. The variation as a function of

_temperature

of this critical stress and of the

_{corresponding}

activation

volume,

is shown in

_figure

3

_[14].

The barrier energy for cross

_slip

in copper was estimated to be :

_AG§s

= 1.15 ± 0.37

eV,

which falls between the two values

_{predicted by equation}

₍₁₎

for i = 1 and 2

_{respectively.}

An

important

conclusion is that after the above measurements, it became obvious that the TIII stress and its variation as a function of

_temperature

are different from the critical stress for

cross

_slip

between

_compact

_planes.

The above

experimental

results,

especially

the orientation

dependance

of the critical stress for cross

_slip,

are

_clearly

in favor of Friedel’s and

_Escaig’s

views. The

_comparison

with the second

_type

of

_theory

for cross

_slip

_[4]

and

[5]

has

_already

been

_given

elsewhere

_[13].

Similar orientation effects have also been found in

_Ni3Al

and

interpreted successfully using

the

_{Friedel-Escaig}

cross

_{slip theory}

[15].

Fig.

2. - Resolved shear stress and corrected activation volume as a function of resolved shear strain.

Fig.

3. -

Critical stress for cross

_slip

and

_{corresponding}

activation volume as a function of _temperature in Cu. Cross

_slip

takes

_place

at the macro elastic limit T between 250 and 410 K. v is the atomic volume

[14].

3. Friction forces of the Peierls

_type.

The

_principle

_{of this kind of friction force is that the energy of}

_moving

dislocations

_necessarily

varies

_according

to the lattice

_periodicity.

_{Dislocations thus have their minimum energy in the}

so called « Peierls

_{valleys »,}

and their movement can be described as a series of

_jumps

between

_{adjacent valleys, through}

the nucleation and

_propagation

of kink

_pairs.

In the

_early

model of Peierls and

Nabarro,

the dislocations are assumed to

_{spread only}

in their

_{glide planes.}

_{This results in very low friction}

forces,

especially

for dislocations which are

largely split

(case

of

_glide

on the most

_compact

_planes).

More recent studies have shown that even

_larger

frictional forces can

_originate

when dislocations

_spread

out of their

_{glide plane.}

Under such

conditions,

the Peierls mechanism can

play

a _very

_important

role in the

_plasticity

of

_materials,

even at

_high

_{temperatures.}

This is for instance the case of

_L12

ordered

_alloys,

for which friction forces are

_present

_up to 0.7

_Tm

_{(Tm :}

_melting

_{temperature).}

These

_higher

friction forces are found to concern

mainly

screw

_{dislocations,}

which can

spread

more

easily

in different

planes,

because of their

higher symmetry

within the

_crystal

lattice. In order to move the

dislocation,

it is necessary to recombine its core, which involves the same fundamental mechanisms as for cross

_slip.

The first ideas about this mechanism were

_{suggested by}

Hirsch

_{(1960) [16]}

and

_Yoshinaga

and Horiuchi

_{(1963) [17]}

for BCC and HCP

_{metals, respectively.}

Detailed

models,

based on

the recombination of dislocations dissociated into several

_partials,

have been derived

_by

Kroupa

(1963) [8],

Schottky

et al.

_{(1965) [19],}

Vitek

_{(1966) [20]}

and

_Escaig

_{(1968) [21].}

Recent calculations

_{by Seeger}

_{(1984) [22]}

based on

_{sophisticated}

kink-kink

_{interactions,}

do not use _any

_description

of the recombination _{process of dislocations}

_spread

out of their

_glide

plane

(cross

slip

description).

The similitudes and differences between the

_early

« classical » model of Peierls and

Nabarro,

and the model

_including

the

_spreading

of dislocations out of their

_{glide plane}

(sometimes

called

_{« pseudo}

Peierls » or « kink

_pair

mechanism »)

have been discussed

_by

Friedel

_{(1968) [23].}

The differences between this and the classical Peierls case

_only

concern

details :

- the

- the

long

range interaction between kinks

depends

on _{the way the kinks}

_locally

affect the

splitting ;

- the active

applied

stresses are both in the

_{slip plane}

and in the

_{splitting planes}

(«

_Escaig

effect

_»).

Experimental

data on the Peierls mechanism are summarized below.

3.1 PEIERLS STRESSES IN BCC METALS. - The dislocation movement has been studied in situ

in a

_{high voltage}

electron

_{microscope by Furubayashi}

_{(1969) [24]}

and

Louchet,

Kubin and

Vesely

(1979) [25].

The Peierls mechanism was

_clearly

identified for the first time

_by

the

rectilinear

_shape

and the slow and smooth movement of the screws.

3.2 PEIERLS STRESSES IN HCP METALS _{(PRISMATIC SLIP).} - In the

case of

titanium,

which

glides

more

_easily

on the

_prismatic

than the basal

_plane,

the observations of Naka et al.

₍₁₉₈₈₎

[26]

also reveal

_strong

frictional forces on screw dislocations

_gliding

in

_{prismatic planes.}

This friction

_corresponds

to a non

_{planar spreading}

as in BCC metals.

The Peierls mechanism has also been

_clearly

identified

_{by in}

situ observations in

magnesium,

in which

_glide

is easier on the basal than on the

_{prismatic plane,}

above room

temperature

[27].

The tensile axis was chosen

_parallel

to the basal

_plane,

so that the latter was

unstressed and

_prismatic

_{glide only}

is activated. The dislocation

_behaviour,

observed in a

200 kV electron

_microscope

_corresponds

to a smooth movement of rectilinear screw

dislocations,

unlike non screw

_portions,

which

_glide

much faster

(see

_Fig.

4).

Fig.

4. -

Dislocation

glide

in the

_{prismatic plane}

of

_magnesium.

Evidence of friction forces on screw

dislocations a, f3 and _y. In situ

_experiment

120 _kV, 300 K

_[27].

The

_{corresponding}

mechanism is detailed in

_figure

5. Screw dislocations are

_spread

in the basal

_plane

and

_glide

in the

_{prismatic plane by nucleating}

and

_propagating

kink

_pairs.

More

_clearly

than in BCC

metals,

it appears in

magnesium

that the

_generalized

Peierls mechanism involves cross

_slip.

In the

_{configuration 5c,}

screw dislocations are

_glissile

in the

basal

_{plane. Large amplitude}

basal to and fro movements thus occur under internal stresses and add to

_prismatic

movements

_{(Fig. 6).}

This

_{experiment clearly}

shows that screw

dislocations

_really

cross

_slip

between basal and

_{prismatic planes during}

the process.

Quantitative

evaluations of the dislocation velocities as a function of stress and

_temperature

yield

an activation area of 9

b 2 at

room

_temperature

and an activation _energy at zero stress

Fig.

5. - Schematic

representation

of a sctew dislocation

_gliding

on the

_{prismatic plane}

P of an HCP

crystal following

the kink

_pair

mechanism. L = distance between

compact rows

_(L

=

c/2).

The

hatched

_portions

of the dislocation lie on the basal

_plane

_{(perpendicular}

to

_P).

Fig.

6. -

Wavy

movement of a screw dislocation

(S)

in

_Mg

(in

situ TEM

_experiment

120

_kV),

20 °C. Arrows underline oscillations of the two _{dislocation traces,}

_parallel

to the basal trace

_(B).

(b :

Burgers

vector).

From

_[27].

3.3 PEIERLS STRESSES IN FCC METALS (NON COMPACT SLIP). -

Although

these metals deform

_{easily by glide}

on the octahedral

planes, slip

line observations

long

_{ago revealed that}

glide

can also take

_place

on non

_{compact planes}

(see

review

_by

Carrard

et al.,

1987

[28]).

In aluminium above

200 °C,

for

_example,

these non

_compact

_planes

were of the

{100}, { 110 } , {112} and {113}

type.

A detailed

quantitative study

of {110}

slip

was

electron

_microscopy

_(TEM)

and showed that

_{{ 110 }}

_slip

_{exists per} se and is not the net result of

_composite

_slip

_{on {111}.}

It was also

shown,

through

constant strain rate tests, that

{110}

slip

is

_thermally

activated. It starts

_operating

above a critical

_temperature.

For low

stacking

fault energy

metals,

this

_temperature

is a

_higher

fraction of the absolute

_melting

point.

This

suggests

that some kind of cross

_slip

_{process is involved in the}

_operation

of non

compact slip.

A detailed

_study

of the mechanism related to

₍₀₀₁₎

_slip

in 112 aluminium

_{single crystals}

has been undertaken more

_recently

[28] [30].

_Although

the

high symmetry

of the FCC

crystals

makes it

_impossible

to neutralize thé

_{four {111}}

_planes

at the same

_time,

the

_[112]

orientation allows extensive

_{[110] (001)}

_glide

to be activated

_(see

_{stereographic projection}

of

_Fig.

7 and

Fig.

8).

Stress strain curves of different

_shapes

are observed as a function of the active

slip system

(see

Fig.

9).

If

_compact

_{slip only}

is

_operating,

a monotonic increase of stress is observed as a

function of

_strain,

the curves

_exhibiting

an

approximately parabolic shape.

If

(001)

slip

operates,

the curves start with a

_steep

increase in stress and then exhibit a

_sharp

decrease in

hardening

rate. It could be established that the latter

_corresponds

to the critical stress

Tooi at which

(001)

slip

starts

operating

for a

_{given temperature}

and strain rate. The stress

Tooi was

plotted

as a function of

temperature

for different strain rates

_{(Fig. 10).}

It can be seen

that an athermal

plateau

is reached

slightly

above

400 °C,

that TOO1 is

strongly temperature

dependent

below 400 °C and that it cannot be measured below 270 °C where

_{compact slip}

takes over. It was

_possible

to measure an

_apparent

activation

_enthalpy

for

(001)

_glide,

AHOO,

= 1.74

eV,

from the _curves of

figure

10.

These conclusions where confirmed

_{by in}

situ

_experiments

_{[28, 32]}

and

_by

the observation of

_long

_straight

screw dislocations

_pinned

under load after creep of Al-Zn

single crystals

[31].

A

_microscopic

mechanism of the Peierls

_type

for

₍₀₀₁₎

_slip

was

_{proposed taking}

into account the above

_macroscopic

and microstructural observations. It

_presents

some similarities

with the

_preceding

mechanism in HCP

_metals,

and can

_easily

be extended to other

_types

of

Fig.

7. -

[112]

stereographic projection.

(Pl, bl)

and

_{(p2, b2)}

are the

_primary

octahedral _systems.

Fig.

8. - Two 90° views of a

[112]

aluminium

single crystal

after deformation at 314 °C with

y = 12 x

10- 4 s-1.

(001)

and { 111 }

slip

systems are activated in the two

_regions

1 and II,

respectively

[30].

Fig.

9. - Stress-strain curves at different temperatures in

[112]

aluminium

single crystals :

y = 12 _x

10- 4 S-I.

When

(001) glide

is activated, the critical stress is indicated

by

an arrow

[30].

non

_{compact systems.}

It considers the motion on

(001)

of screw

dislocations,

which are

normally

dissociated on

_compact

_planes,

as the rate

_controlling

_{process. Under the}

_applied

stress, the dislocation recombines over a

critical length

to

_glide

on

(001).

Under low stresses,

Fig.

10. - Variation in the CRSS

Twi for

(001)

glide

with temperature for three strain rates in

_[112]

aluminium

single crystals :

(+) y = 12 x 10’ s’ ;

(8)

= 12 x 10- 4 s-1;

(0)

=12 x 10- 3 s-1.

The curves

_correspond

to the

_kink-pair

model

_[30].

screws which was evidenced

_above,

indicates that the kink

_{pair propagation}

is easier than its

nucleation.

Analysis

of the curves of

_figure

10 in terms of the rate

_equation

of § 3.4 below

_yielded

a

value of the activation energy at zero stress of

_AGooi

= 1.40 eV.

It can also be seen in

_figure

10 that the

_agreement

betwen the rate

_equations

and the

experimental

data is

_{satisfactory,}

at least in the 150 °C

_temperature

interval over which

₍₀₀₁₎

glide

could be observed.

Finally,

the rate

_equations

have been used to estimate the athermal

temperature

for

{ 110 }

slip

in various FCC metals

_[30].

_{This agrees}

_reasonably

well with

_experimental

values

[33].

3.4 COMMON FEATURES OF THE GENERALIZED PEIERLS MECHANISM. - These can be summarized as follows :

- mechanical

properties

are

_closely

related to individual dislocation mobilities and core

geometries

(see Fig. 11) ;

- the

corresponding

screw dislocations are

_straight

as

_they

move

_smoothly

and

continu-ously ;

- there

are intensive

_{multiplication}

_processes,

_through

the formation and

_development

of closed

_loops

_(see

Ref.

_[27]

for

_{magnesium) ;}

- the

velocity

of screw

_{dislocations,}

as derived

_{by Escaig}

_[11]

under low effective stresses,

2

_AGp

is

_{given by : v}

= a v

(

b

L

exp -

20132013 ,

where the critical distance between two kinks is

lc-

kit

1/2

lc

=

(

R 1l2

,Lb/2

7TT*; v

is the

_{Debye frequency,}

_âge

is the activation _energy for

Î

J-Lb2

Peierls

_glide,

R the _{recombination energy per unit}

_length

of

dislocation,

T * the effective stress

and g

is the shear modulus. The

_velocity

of dislocations is

_proportional

to their

_length

L,

which has been

_directly

verified in the case of

_magnesium

_{[27] ;}

-

the activation energy can be

_expressed

as :

_AGp

=

AGp -

T *

V,

where

AG’

equals

twice

the _{kink energy, i.e.}

_{G; ’" 2 L’ (J-Lb2 R)1/2 + 2 U}

_(U

= constriction energy, L = distance

Fig.

11. -

Comparison

between the

_{Friedel-Escaig}

mechanism in BCC and HCP metals. The screw

dislocation is seen end-on.

- the activation

area A is of the order of b .

fc

and is small. This

_implies

a

_strong

increase

of the elastic limit at low

_{temperatures,}

which

_{explains why}

non

_{compact slip}

cannot be observed in FCC metals at low

_{temperature ;}

- because of the

complex

core

_splitting

and the

_Escaig

effect,

Schmid law is often

violated,

as in the case of

_simple

cross

_slip

of § 2. Some

_aspects

of this

_problem

have been discussed for

non

_{compact slip}

in aluminium

_[30].

4. The

locking-unlocking

mechanism.

This new mechanism has been

_{experimentally}

detected on the basis of in situ

_experiments

on

prismatic slip

of

_beryllium

for the first time

_{[34, 35].}

_{It appears} to be

_operative

_{in many} different structures.

As in the case of the

_generalized

Peierls

_mechanism,

a screw core

_splitting

occurs out of the

glide plane.

However,

a metastable

_glissile

core

_{configuration}

_exists,

which allows free

_glide

over several interatomic distances before the dislocation is locked

_again.

The fundamental

idea at the

_origin

of the Peierls

mechanism,

i.e. the

_necessity

of a

_periodic

variation of the

dislocation _energy

_according

to the lattice

_periodicity,

is then lost.

4.1 BERYLLIUM. - The mechanism was first

_{suggested by Régnier}

and

_Dupouy

_{(1970) [36]}

and then

_{experimentally}

studied and

_fully

_described,

in the case of the

_{prismatic glide}

of

beryllium

[34, 35].

The screws exhibit a

_jerky

movement

_{(Fig. 12),}

at variance with the Peierls mechanism. It is sketched in

_figure

12. It can be shown that the

_{glissile configuration}

in the

prismatic plane

is metastable and of

_higher

energy than the sessile

configuration spread

in the basal

_plane.

_{It thus appears that dislocations have} a « fundamental state » which is the

only

one observed under static conditions and « excited states » of short

lifetime,

which can be

observed under

_dynamic

conditions

_only.

Unlocking

and

_{locking correspond}

to two

_elementary

cross

_slip

_{processes. The first is} cross

slip

to a

_plane

of

_higher

_{energy. The}

_description

of Friedel

[1,

3,

7]

leads to lower activation

Fig.

12. -

Locking-unlocking

on screw dislocations in

_{prismatic glide}

of

_beryllium

at 300 K.

_a)

to

_{e) :}

in situ _sequence

_illustrating

the

_jerky

movement of the screws. Schematic

_{representation}

of the

unlocking

process

f)

to

_h)

and of the

_locking

_process

_i)

to

_k).

From

_{[34, 35].}

study

of the

_waiting

times of locked dislocations has been

_made,

which leads to a

_single

value for the

_probability

of

_unlocking

_{per unit}

_time,

at a

_given

stress and

_temperature

_{(Fig. 13).}

In the same _{way, the statistics of the}

_{jump lengths}

leads to a constant

_probability

of

_locking

_per unit time. These

_{probabilities}

are observed to _vary

_according

to the stress and the

temperature,

in

_agreement

with the cross

_slip

models.

When the

_temperature

increases,

the

_probability

of

_locking

increases and the

_length

of the

jump

thus

_decreases,

until it becomes

_equal

to one interatomic distance

(Peierls mechanism).

Reciprocally,

a Peierls mechanism can be

_{replaced by}

the

_{locking-unlocking}

mechanism at lower

_{temperatures,}

_provided

a metastable

_glissile

_{configuration}

exists. This has been demonstrated

_recently

in the case of

_magnesium

below 200 K

_[37].

The Peierls mechanism

thus appears,

surprisingly

as a

_{« high temperature »}

_mechanism,

with

_respect

to

locking-unlocking.

Locking-unlocking

being really

a cross

_slip

_mechanism,

this

_{continuity again emphasizes}

the

importance

of the cross

_{slip description}

of the Peierls mechanism.

4.2

_Ni3Al.

- In

Fig.

13. - Data about _screw dislocations in the

locking-unlocking glide

process in Be.

a)

and

_b),

waiting

time measurements in the locked

_{configuration.}

AN is the number of screw

dislocations

waiting during

time _{t, to tB} +

_AtB.

_(a)

linear scale

_illustrating

an

_exponential

_{decrease ;} and

(b)

semilogarithmic

scale.

_Slope

=

PUL

= 3.5 s-1.

c)

and

_d),

_{jump length}

measurements

_{(proportional}

to the

_flight

_time)

in the unlocked

_{configuration.}

AN is the number of screw dislocations

_jumping

over a distance À to À + AÀ.

_(c)

linear scale

_illustrating

an

_exponential

decrease ; and

_(d)

_{semilogarithmic}

scale, the

_reciprocal

of the

_slope

is À = 0.068 _>m.

From

_[35].

Fig.

14. -

In the case of

_glide

_{in {100}}

_planes,

core structure

_computations

_[40]

lead to a

configuration

of minimum energy with the APB

in {100}

and each

_{superpartial spread}

in one

of the two

_possible

_{intersecting {111}}

_planes

_{(Fig. 15).}

Weak beam and

_high

resolution observations of dislocation cores

[41]

confirm this

_splitting

_geometry.

To

interpret

the

observed

_jerky

movements,

by analogy

with the case of

_beryllium,

_{it is thus necessary} to assume that a second

_{configuration}

of

_higher

_energy,

_glissile

and

_spread

in the

_{{ 100 }}

_plane,

exists

_during

_{very short times}

_{(Fig. 15).}

The movement is thus

_interpreted

as a series of cross

slip

events between these two

_{configurations,}

as in HCP metals. This

_hypothesis

is confirmed

by

the

_waiting

times and

_jump

_lengths

measurements, which

_obey

the same law as in

beryllium

[38].

In the case of

_glide

in

_{{ 111 }}

_planes,

the

_{locking-unlocking}

movement is

_interpreted

in a

similar way, with a stable sessile

_{configuration spread}

into

_{thé {111}}

cross

_{slip plane}

and a

metastable

_glissile

_{configuration spread}

in

_{thé {111}}

_{glide plane}

_[39].

Fig.

15. -

Schematic

configuration

of the core dissociation of a screw

_{in {100}}

_planes

of the

Ll2

structure. 1 = metastable

configuration

(planar

=

glissile).

2 and 2’ = stable

configuration

(non

planar

=

sessile).

4.3 COMMON FEATURES OF THE LOCKING-UNLOCKING MECHANISM. - The

common features

of the

_generalized

Peierls mechanism also

_apply

to

_{locking-unlocking, except}

for the

_following

points :

- the movement of dislocations is

no

_longer

smooth and

_continuous,

but

_{jerky ;}

- their

_velocity

is v = v V

PUL

_where

_{v is}

the instantaneous

_velocity

in the

_glissile

0 PL

0

configuration

and

_PuL

and

_PL

are the

_{probabilities}

of

_unlocking

and

_{locking, respectively.}

P uL

and

_{P L}

can be

_expressed

as :

and thus :

independent

of the dislocation

_length

L.

-

The activation energy is the difference between the activation

_energies

of the two cross

(except

for very

high

stresses)

which leads to a smaller elastic limit increase at

_decreasing

temperatures.

5. The

origin

of

strength

anomalies.

Several

_materials,

_{including beryllium}

in

_{prismatic glide}

and

_L12

ordered

_alloys,

exhibit an

anomalous flow stress increase at

_{increasing temperature.}

The most current models for this behaviour are based on the

_thermally

activated and irreversible

_locking

of dislocations

_by

cross

_slip

[36, 42].

This

_corresponds

to the first

_step

_only

of the

_{locking, unlocking}

mechanism. A

_study

of the

_glide

of dislocations in

_{prismatic planes}

of

_beryllium

reveals a behaviour

which is at variance with this

_prediction,

since

_{locking-unlocking}

is observed over the whole

,

temperature

range,

including

the domain of the anomalous flow stress increase

_{[34, 35].}

The

origin

of the

_{strength anomaly}

is thus an increase in the

_difficulty

of cross

_slipping

as the

temperature

rises due to an increase of the recombination energy R. In the elastic

approximation,

this would

_correspond

to a decrease of the

stacking

fault energy as the

temperature

is increased. Similar behaviour has also been observed in a nickel based

_alloy

[38],

in the case of

_glide

_{in {100}}

_planes,

and the same mechanism could also be at the

_origin

of the

_{strength anomaly}

of

_Ni3Al,

in the case

_{of {111 }}

_glide

[39].

It can also account for the

thermally

activated dislocation motion evidenced at the

_{strength anomaly}

_[43].

It is clear that since all cross

_slip

mechanisms are _{very sensitive} to _{the recombination energy}

_R,

i.e. the

stacking

fault energy, the

possible

temperature

variation of these

_parameters

should be included in the models.

6.

_Creep

at intermediate and

_high

temperature.

The variation of the creep activation

energies

with

_temperature,

as reviewed

_by

Poirier in pure FCC and HCP metals

[44],

suggests

that different mechanisms are rate

_controlling

in different

temperature

domains

_{(see Fig. 16).}

In the case of aluminium and FCC

_metals,

the

Fig.

16. -

Creep

activation

_enthalpies

measured

by Sherby et

al.

₍₁₉₅₇₎

in aluminium

_polycrystals

_[50].

The results obtained in

_[112]

_{single crystals}

between 200 and 320 °C are also

_reported

for 001

_glide

plateau

of activation energy at intermediate

_temperature

has been attributed to cross

_slip

(Friedel [3],

Lytton

et al.

_[6]),

while the

_{high temperature}

_{range has been considered} to be climb controlled

_through

self diffusion.

_Conversely,

for HCP

_metals,

the intermediate

temperature regime

was attributed to self

diffusion,

while the

_higher

_{activation energy in the}

high temperature

domain was

_thought

to

_correspond

to dislocation cross

_slip

from the basal to the

_{prism plane}

_[44].

More recent detailed models have been

_proposed

for

_{cross-slip-controlled}

_creep mechan-isms. Friedel

_{(1977) [45]}

_suggests

_{that creep is controlled}

_by

the dissociation of dislocations

along

the

_plane

of the

network,

their escape

necessarily

involving

cross-slip

to the more

_highly

stressed

_glide

_plane.

Poirier

_[46]

_{considers that the creep} rate is controlled

_by

a _recovery

mechanism inside the

_{subgrains :}

this can occur either

_by

the annihilation

_through

cross

_slip

of

the screw

_portions

of the

_loops

at intermediate

_temperature,

or

_through

climb of the

_edge

portions

at

_{higher temperatures.}

These

_suggestions

can now be

_pursued

in more detail thanks to

_newly

available transition electron

_microscope

observations.

6.1 ALUMINIUM (AND THE Al-Zn SOLID SOLUTION) AT INTERMEDIATE TEMPERATURES. -Strain is associated with the

_glide

of dislocations

_escaping

from subboundaries

_[47],

which necessitates

_high

local internal stresses.

_They

have been measured

_directly

_[48]

and

_they

originate

in the

_{subboundary migration}

process

[49].

The creep rate is thus controlled

_by

the

_glide

of some of the

_{subboundary segments}

on

{001}

planes

and the activation energy

corresponds

to _{the energy of} one kink in

{001} (see

Fig.

17)

with a value at zero stress

_{AGO -}

0.7 eV. This is in reasonable

_agreement

with the

_enthalpies

of

_figure

16,

after the

entropy

correction has been made

_[50].

Fig.

17. - Schematic

representation

of the

_{subboundary migration}

_process.

_a)

_xi

_(i

= 1, 2,

3)

_are the 3

dislocation families of the

_subboundary

mesh.

_b,

are their

_{respective burgers}

vectors,

Pi

there

_respective

glide planes.

b)

Onset of

_migration

while the screw _{segment xi}

_glides

on

_(100).

From

_[49].

6.2 ALUMINIUM AT HIGH

TEMPERATÙRE. -

_{The creep} rate is controlled

_by

non

_compact

_slip

of screw dislocations across the

_subgrains

at least at the onset of the

_high

_temperature

domain. This is

_{supported experimentally by}

the observation of

_long

rectilinear screw

_{dislocations,}

which were

_pinned

under load at _{the end of the creep} test in an Al-Zn solid solution

_(see

Fig.

18. -

Straight

screw dislocation substructure after creep. Al-11 wt. % Zn

_polycrystal.

T =

250 ’C, o,

= 17 MPa, e = 22 %. Dislocations _are

pinned

under load

[48].

6.3 MAGNESIUM AT INTERMEDIATE TEMPERATURE. - The results of the in situ

_experiments

described in § 3 lead to _{activation energy values for}

_{prismatic glide,}

that are not

_compatible

with those measured in creep at

_high

_{temperatures.}

_{The creep mechanism} at

_high

temperatures

is therefore not

_{yet fully}

understood.

_However,

at intermediate

_{temperatures,}

figure

19 shows that the activation energy values for

prismatic glide

as a function of

temperature

are

_compatible

with those measured in creep

[27].

Prismatic

slip

can therefore be

an _{alternate mechanism for creep} at intermediate

temperatures.

Fig.

19. -

Comparison

of activation

_enthalpies

in

magnesium,

for creep of

polycrystals

and for

_prismatic

7. Déformation

_stages.

In face centred cubic metal

_{single crystals,}

three deformation

_stages

on the stress strain curves

have been evidenced at

_temperatures

below or

_equal

to room

_temperature

_{(Friedel, 1956 [1]}

and 1959

_[3]).

As

_already

discussed in §

2,

recent

_experimental

information about cross

_slip

in copper shows that the critical stress for this mechanism is

_clearly

different from Tjjj, as well as its variation with the

temperature

[14].

Cross

_slip

is

_probably

active

_during

stage III,

but mixed

together

with other mechanisms such as the destruction of some

_types

of

junction

reactions

_[51].

However,

at

_large

strains and room

_temperature,

a

_stage

IV is

observed,

which is

characterized

_by

a new linear

_{hardening [52].}

At

_higher

_{temperatures, stage}

IV has also been

observed in covalent materials

_[53].

The same authors have detected a similar behavior in face

centered cubic

_metals,

_{by analysing previously published}

stress strain curves on Al

[54]

and on

Au

_[55].

In a recent

_study

of

_[112]

_copper

_{single crystals}

above 200

°C,

it has been shown that

stage

IV is also

_present,

and followed

_by

additional

_stages

_[56].

A careful examination of the

slip

traces has shown that the onset of

_stage

IV

_corresponds

to the activation of non

_compact

slip

which itself involves cross

_slip

_{(§ 3.3).}

8. Conclusions.

In this

review,

we have

_attempted

to show how realistic ideas about basic cross

_slip

mechanisms,

which were formulated about

_thirty

_{years ago,} are still

_{enlightening.}

This is

_quite

remarkable

_nowadays,

as the

_general

_tendency

is to

_ignore

the literature which is more than ten _{years old.}

These ideas stimulated the

_complete

derivation of the cross

_slip

mechanism when the

dislocation is dissociated in the

_{glide plane}

or out of it.

Later,

experimental

data were

produced, mostly

based on in situ observations in the electron

_microscope

and accurate mechanical tests.

_They

have confirmed the cross

_slip

_{model both in copper and in}

_magnesium

oriented for

_{prismatic glide.}

In these two cases, realistic values of activation

energies

and volume values have been obtained. The kink

_pair

mechanism for

_{prismatic glide}

could also be extended with success to non

_compact

_slip

in aluminium. Intermediate and

_{high temperature}

domains have been determined for which the cross

_slip

mechanisms seem to

_impose

well established creep activation energy values. A new mechanism of

_{locking-unlocking}

of the screws has been evidenced

_{experimentally.}

The latter seems to be rather common, the kink

pair

mechanism

_being

a

_special

case. It accounts for

_yield

stress anomalies in a

_variety

of

situations such as

_{prismatic slip}

in

_beryllium,

titanium,

etc... and in the

_Ni3Al

_compound

oriented for 111 or 001

_slip.

The amount of work needed to

_complete

the above results is

_{quite large.}

In the FCC

structure, cross

_slip

should be

_{experimentally}

studied in

_crystals

with various

_stacking

fault

energies ;

the same remark holds for non

_{compact slip}

on various

_planes.

This will allow a

better check of the models. In

_prismatic

_glide

of HCP

_crystals

and in the

_L12

structures,

accurate mechanical tests should be

_performed

to detect

_macroscopic

evidence of the

locking-unlocking

versus kink

_pair

mechanism. The connection between the former mechanism and

yield

stress anomalies should be better established in

_crystals

other than

_beryllium.

Acknowledgements.

The authors

_{acknowledge stimulating}

_{discussions with Dr. P. W. Hawks about this paper.}

They

thank Fonds National Suisse de la Recherche

_Scientifique

for the financial

_support

of

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