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Comment on the critical resolved shear stress (CRSS) of CuCo alloys containing coherent particles
Scripta
METALLURGICA
Vol. 3, pp. 3 7 5 - 3 7 6 , 1969 P r i n t e d in t h e U n i t e d S t a t e s
Pergamon
Press,
COMMENT ON THE CRITICAL RESOLVED SHEAR STRESS (CRSS) OF Cu-Co ALLOYS CONTAINING COHERENT PARTICLES
Herbert Glelter
Gordon McKay Laboratory, Harvard University Cambridge, Mass., U.S.A.
(Received
April
7,
1969)
The measurements of the increase of the CRSS on single crystals of various Cu-Co alloys reported by Wltt and Gerold I) are very useful since most experimental data which are available in this fleld are based on measurements on polycrystals.
In order to cal-
culate the CRSS of alloys containing dlstoEted particles two papers 2)3) have been published in recent years.
Both calculations are based on the assumption that the strength-
enln E of the alloys is due to the interaction between the dislocations and the strain fleld of the partlcles 4). locations.
Gerold et. al~ ) have used the approximation of rigid dis-
The particle distance along the dislocations was determined in their cal-
culation from the equation derived by Flelscher.
They found that the CRSS should be
proportional to fl/2 (f is the volume fraction of the particles).
In the other estl-
mate 3) the flexlbillty of the dislocations was taken approximately into account.
In
order to calculate the distance of the particles along the dislocation the equation derived by Frledel was used. to f51DfO.8.°--
According to this calculatlon 3) the CRSS is proportional
Recently, Kocks 5) has considered the distance between obstacles (e.g.
particles) along a flexlble dislocation.
According to his results the .equation of
Frledel seems to be the more accurate approximation to calculate the CRSS in a precipitation hardened alloy.
The assumption of rigid dislocations was discussed recently 6).
In order to compare the results of the calculations with experimental observations, the precipitation hardening of Cu-Co alloys may be used.
However, one has to keep in
mind that in both calculatlons 2)3) assumptions are made which are, in general, not fulfilled in precipitation hardened alloys (e.g. it is assumed that all partlcles are of the same size, that the interface between the particles and the matrix is sharp and that the crystal is Isotroplc.)
Due to these assumptions there may be an appreciable
discrepancy between the experimental observations and the calculated results. Furthermore, the experimental data which are presently available do not seem to be consistent.
According to the measurements of Livlngston 7) the CRSS of Cu-Co alloys
is proportional to fO.8. of the form fl/2.
The results by Witt and Gerold I) indicate a proportionality
Therefore it may be necessary to obtain more experimental data and
375
Inc
376
COMMENT
ON CRSS
OF C U - C O
ALLOYS
Vol.
3, No. 6
t o i m p r o v e t h e t h e o r y by r e m o v i n g some o f t h e a s s u m p t i o n s w h i c h a r e m e n t i o n e d a b o v e i n order to get a quantitative
a g r e e m e n t b e t w e e n t h e t h e o r y and t h e e x p e r i m e n t a l
observations.
REFERENCES 1)
M. Witt~ V. G e r o l d ,
Scripta Met., in press.
2)
V. Gerold, H. llaberborn, Phys. Star. Sol. 16, 675 (1966).
3)
H. Glelter, Z. Angew, Phys. 23, 108 (1967).
4)
N.F. Mott~ F.R.No Nabarro, Proc. Phys. Soc. (London) 52, 86 (1940).
5)
U. Kocks, Sch~nwaldtagung, Germany, 10-11 October (1967).
6)
H. Glelter, Acta Met. 16p 829 (1968).
7)
J.D. Livlngston~ Trans. AIME 215, 566 (1959).
METALLURGICA
Vol. 3, pp. 3 7 5 - 3 7 6 , 1969 P r i n t e d in t h e U n i t e d S t a t e s
Pergamon
Press,
COMMENT ON THE CRITICAL RESOLVED SHEAR STRESS (CRSS) OF Cu-Co ALLOYS CONTAINING COHERENT PARTICLES
Herbert Glelter
Gordon McKay Laboratory, Harvard University Cambridge, Mass., U.S.A.
(Received
April
7,
1969)
The measurements of the increase of the CRSS on single crystals of various Cu-Co alloys reported by Wltt and Gerold I) are very useful since most experimental data which are available in this fleld are based on measurements on polycrystals.
In order to cal-
culate the CRSS of alloys containing dlstoEted particles two papers 2)3) have been published in recent years.
Both calculations are based on the assumption that the strength-
enln E of the alloys is due to the interaction between the dislocations and the strain fleld of the partlcles 4). locations.
Gerold et. al~ ) have used the approximation of rigid dis-
The particle distance along the dislocations was determined in their cal-
culation from the equation derived by Flelscher.
They found that the CRSS should be
proportional to fl/2 (f is the volume fraction of the particles).
In the other estl-
mate 3) the flexlbillty of the dislocations was taken approximately into account.
In
order to calculate the distance of the particles along the dislocation the equation derived by Frledel was used. to f51DfO.8.°--
According to this calculatlon 3) the CRSS is proportional
Recently, Kocks 5) has considered the distance between obstacles (e.g.
particles) along a flexlble dislocation.
According to his results the .equation of
Frledel seems to be the more accurate approximation to calculate the CRSS in a precipitation hardened alloy.
The assumption of rigid dislocations was discussed recently 6).
In order to compare the results of the calculations with experimental observations, the precipitation hardening of Cu-Co alloys may be used.
However, one has to keep in
mind that in both calculatlons 2)3) assumptions are made which are, in general, not fulfilled in precipitation hardened alloys (e.g. it is assumed that all partlcles are of the same size, that the interface between the particles and the matrix is sharp and that the crystal is Isotroplc.)
Due to these assumptions there may be an appreciable
discrepancy between the experimental observations and the calculated results. Furthermore, the experimental data which are presently available do not seem to be consistent.
According to the measurements of Livlngston 7) the CRSS of Cu-Co alloys
is proportional to fO.8. of the form fl/2.
The results by Witt and Gerold I) indicate a proportionality
Therefore it may be necessary to obtain more experimental data and
375
Inc
376
COMMENT
ON CRSS
OF C U - C O
ALLOYS
Vol.
3, No. 6
t o i m p r o v e t h e t h e o r y by r e m o v i n g some o f t h e a s s u m p t i o n s w h i c h a r e m e n t i o n e d a b o v e i n order to get a quantitative
a g r e e m e n t b e t w e e n t h e t h e o r y and t h e e x p e r i m e n t a l
observations.
REFERENCES 1)
M. Witt~ V. G e r o l d ,
Scripta Met., in press.
2)
V. Gerold, H. llaberborn, Phys. Star. Sol. 16, 675 (1966).
3)
H. Glelter, Z. Angew, Phys. 23, 108 (1967).
4)
N.F. Mott~ F.R.No Nabarro, Proc. Phys. Soc. (London) 52, 86 (1940).
5)
U. Kocks, Sch~nwaldtagung, Germany, 10-11 October (1967).
6)
H. Glelter, Acta Met. 16p 829 (1968).
7)
J.D. Livlngston~ Trans. AIME 215, 566 (1959).