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Multiple slip in bicrystals
ACTA
216
not appear to be necessary
METALLURGICA,
for the ensuing analysis.
One may proceed further, then, and ask: matching answer
is not a suitable appears
at the
criterion,
moment
expression only in thermodynamic
to
if strain
what is?
The
be capable
terms.
of
When one of
several adjacent grain boundary
crystals deforms, the energy of the momentarily is raised. The atoms
comprising
transition
the
zone
must
relieve this energy by slip or actual gliding,
or
increase
the
then
(configurational)
enough to offset the gain in energy.
either
grain-boundary entropy
Thus new slip
VOL.
6,
single crystal strained
as
1958
and more like that of a crystal in
equation
in the immediate “additional”
(3).
vicinity
con-
It is usually
of the boundary
only
that the
slip markings are seen.
It is, of course, true that the slip systems actually utilized may vary from place to place along the boundary. Macroscopic continuity conditions alone can
only
lead
to
requirements
number of systems.
on
Our experimental
that the choice of systems is dictated conditions,
the
minimum
results indicate by microscopic
and these could vary along the boundary.
systems are activated in adjacent crystals and/or the disordered region increases its extent, i.e. the
As Frankel points out, the use of macroscopic continuity arguments was in no way essential to the
effective
analysis of our results.
“thickness”
of
the
grain boundary
must
increase. University of California
J. P. FRANKEL
Reference 1. B. CHALMERS Metal Interfaces p. 158. Amer. Sot. Metals (1952) for a discussion of strain inhomogeneity. * Received 1957.
September
3, 1957;
are helpful in understanding
conditions
multiple
defines conditions,
Los Angeles, Calif.
in revised form October 7,
We feel, however,
arguments
slip is necessary.
that such
under what Equation
satisfied by symmetric
special bicrystals, under which macroscopic itself requires no “additional” slip.
(4)
and other continuity
J. D. LIVINQ.STON General Electric Research Laboratory Schenectady, New York B. CHALMERS
Multiple
Harvard University, Cambridge
Slip in Bicrystals*
Massachusetts
Inasmuch as our macroscopic treatment of deformation neglected microscopic inhomogeneities such as slip bands,
it is clear that its conclusions
limited to strains observed
must be
on a scale large compared
to slip-line displacements and spacings. scale, macroscopic discontinuities in
On such a the
strain
References 1. S. K. TUNG and R. MADIIIN Trans.Amer. Inst. Min. (Metall.) Engrs. 209, 905 (1957). 2. F. E. HAUSER, C. D. STARR, L. TIETZ and J. E. DORN Trans.AmeT. Sot. Met&. 47, 102 (1955). * Received
October 24, 1957.
components of equation (3) of our paper would be observable as “grain boundary shearing”. Reference marks drawn
across
boundaries
before
would be displaced macroscopically
deformation
after deformation.
Sur l’oxydation
Such behavior is indeed observed at elevated temperatures and low strain rates,(l) but is not believed to be important
under
f.c.c. meta1s.t an important
non-creep
conditions,
Where grain boundary mode
of deformation,
at least
in
shearing is not the “transition
zone” of Fig. 1 of the above note as applied to the strain components of equation (3) must be macroscopic in extent. That is to say, macroscopic will be observed.
continuity
L’oxydation fait
l’objet
lesquelles celles
du cuivre de
il
t&s
dans l’air ou l’oxygkne
nombreuses
faudrait
de Pilling
de Wagner
du Cuivre dans 1’Intervalle 600-lOOO”C* t
titer
et Griinewald,c3)
de Valensi,c5) de Tylecote,(6) ses collaborateurs.(‘) Cependant,
tout
et Bedworth,
recherches
a
parmi
particuli&rement de Feitknecht,c2)
de BBnard et Talbot,t4) et de Fassell, Jr. et de
s’il a Bt6 reconnu que la loi parabolique
Macroscopic continuity was assumed in our treatment, but macroscopic homogeneity of strain over the
classique r6git en g&&al
entire bicrystal was not. As one moves progressively nearer the bicrystal boundary, the deformation presumably becomes less like that of an unconstrained
infhrieures & 1000°C est constitu6e par deux couches superpos6es de Cu,O et de CuO, de nombreux points restaient B pr&iser, et tout particulibrement la loi
t Grain boundary shearing has been reported in polycrystalline magnesium at room temperature,@ although it was suggested that it was possibly always preceded by local fracture.
t Cette recherche r&alis&e en liaison avec M. le Professeur J. BQnard a fait l’objet du contrat no 43 entre l’auteur et le “Consejo de Investigaci6n Cientifica” de l’Universit6 de ConcepcZn (Chili).
que la pellicule
l’ensemble
d’oxydation
pour
du ph&omi?ne
et
les temperatures
216
not appear to be necessary
METALLURGICA,
for the ensuing analysis.
One may proceed further, then, and ask: matching answer
is not a suitable appears
at the
criterion,
moment
expression only in thermodynamic
to
if strain
what is?
The
be capable
terms.
of
When one of
several adjacent grain boundary
crystals deforms, the energy of the momentarily is raised. The atoms
comprising
transition
the
zone
must
relieve this energy by slip or actual gliding,
or
increase
the
then
(configurational)
enough to offset the gain in energy.
either
grain-boundary entropy
Thus new slip
VOL.
6,
single crystal strained
as
1958
and more like that of a crystal in
equation
in the immediate “additional”
(3).
vicinity
con-
It is usually
of the boundary
only
that the
slip markings are seen.
It is, of course, true that the slip systems actually utilized may vary from place to place along the boundary. Macroscopic continuity conditions alone can
only
lead
to
requirements
number of systems.
on
Our experimental
that the choice of systems is dictated conditions,
the
minimum
results indicate by microscopic
and these could vary along the boundary.
systems are activated in adjacent crystals and/or the disordered region increases its extent, i.e. the
As Frankel points out, the use of macroscopic continuity arguments was in no way essential to the
effective
analysis of our results.
“thickness”
of
the
grain boundary
must
increase. University of California
J. P. FRANKEL
Reference 1. B. CHALMERS Metal Interfaces p. 158. Amer. Sot. Metals (1952) for a discussion of strain inhomogeneity. * Received 1957.
September
3, 1957;
are helpful in understanding
conditions
multiple
defines conditions,
Los Angeles, Calif.
in revised form October 7,
We feel, however,
arguments
slip is necessary.
that such
under what Equation
satisfied by symmetric
special bicrystals, under which macroscopic itself requires no “additional” slip.
(4)
and other continuity
J. D. LIVINQ.STON General Electric Research Laboratory Schenectady, New York B. CHALMERS
Multiple
Harvard University, Cambridge
Slip in Bicrystals*
Massachusetts
Inasmuch as our macroscopic treatment of deformation neglected microscopic inhomogeneities such as slip bands,
it is clear that its conclusions
limited to strains observed
must be
on a scale large compared
to slip-line displacements and spacings. scale, macroscopic discontinuities in
On such a the
strain
References 1. S. K. TUNG and R. MADIIIN Trans.Amer. Inst. Min. (Metall.) Engrs. 209, 905 (1957). 2. F. E. HAUSER, C. D. STARR, L. TIETZ and J. E. DORN Trans.AmeT. Sot. Met&. 47, 102 (1955). * Received
October 24, 1957.
components of equation (3) of our paper would be observable as “grain boundary shearing”. Reference marks drawn
across
boundaries
before
would be displaced macroscopically
deformation
after deformation.
Sur l’oxydation
Such behavior is indeed observed at elevated temperatures and low strain rates,(l) but is not believed to be important
under
f.c.c. meta1s.t an important
non-creep
conditions,
Where grain boundary mode
of deformation,
at least
in
shearing is not the “transition
zone” of Fig. 1 of the above note as applied to the strain components of equation (3) must be macroscopic in extent. That is to say, macroscopic will be observed.
continuity
L’oxydation fait
l’objet
lesquelles celles
du cuivre de
il
t&s
dans l’air ou l’oxygkne
nombreuses
faudrait
de Pilling
de Wagner
du Cuivre dans 1’Intervalle 600-lOOO”C* t
titer
et Griinewald,c3)
de Valensi,c5) de Tylecote,(6) ses collaborateurs.(‘) Cependant,
tout
et Bedworth,
recherches
a
parmi
particuli&rement de Feitknecht,c2)
de BBnard et Talbot,t4) et de Fassell, Jr. et de
s’il a Bt6 reconnu que la loi parabolique
Macroscopic continuity was assumed in our treatment, but macroscopic homogeneity of strain over the
classique r6git en g&&al
entire bicrystal was not. As one moves progressively nearer the bicrystal boundary, the deformation presumably becomes less like that of an unconstrained
infhrieures & 1000°C est constitu6e par deux couches superpos6es de Cu,O et de CuO, de nombreux points restaient B pr&iser, et tout particulibrement la loi
t Grain boundary shearing has been reported in polycrystalline magnesium at room temperature,@ although it was suggested that it was possibly always preceded by local fracture.
t Cette recherche r&alis&e en liaison avec M. le Professeur J. BQnard a fait l’objet du contrat no 43 entre l’auteur et le “Consejo de Investigaci6n Cientifica” de l’Universit6 de ConcepcZn (Chili).
que la pellicule
l’ensemble
d’oxydation
pour
du ph&omi?ne
et
les temperatures