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Characterization of the strain rate dependence of the shear stress for niobium single crystals
Scripta METALLURGICA
Vol. 1, pp. 83-88, 1967 Printed inthe United States.
Pergamon Press, Inc.
CHARACTERIZATION OF THE STRAIN RATE DEPENDENCE OF THE SHEAR STRESS FOR NIOBIUM S~NGLE CRYSTALS*
R. W. Armstrong
Division of Engineering, Brown University Providence, Rhode Island
R. E, Reed and H. D, Guberman
Solid State Division, Oak Ridge National Laboratory Oak Ridge, Tennessee
(Received July 21, 1967) There are two alternative descriptions which are widely used for characterizing the temperature and strain rate dependence of the resolved shear stress for single crystals.
One
involves the relation (1)
m'
~
(d in ~]
(l)
~d in T~ T and the other, (2)
v
_
~y=
(2) T
where T is the shear strain rate, T is the applied shear stress, Tth is the thermal component of the applied shear stress, v usual m e a n i n g .
is an activation "volume", and the other symbols have their
Normally ~ and Tth a r e r e l a t e d
by
= Tth + ~G
(3)
where TG is the athermal component of the applied stress, and, for a strain rate change test
This research was sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation.
83
84
STRAIN RATE DEPENDENCE
Vol. 1, No. 2
(41 Our purpose is to compare the two parameters defined by equations 1 and 2 for strain rate change tests performed on niobium single crystals producedunder various growth conditions. Niobium single crystals were grown from Wah Chang stock using electron beam floating zone techniques with the rod axis close to (491). elsewhere (3)-
Details of the growth procedure are described
For the experiments reported here the growth rate was the major variable.
had the effect principally of varying the substructure and purity (3).
This
Table I lists the
growth conditions and the resulting mechanical properties for the samples tested.
Compression
TABLE I Summary of Growth Conditions and Mechanical Properties
Sample
~c
Zoning Rate (cm/hr)
Number of Zone Passes
34
(1)
Nbc (2)
4.6
~LY (kg/mm2) *
Strain . Rate (Sec -~)
m'(7 = 9%)
One
3.22
6.7 x io -5
16.o
One
2.13
6.6 x lO -5
ll. 8
Nb-020-1
lO
One
2.23
1.7 x 10 -4
12.3
Nb-023-2
i0
Two
1.65
8.8 x 10 -5
i0.0
*Lower yield stress resolved on (iOl) (iii) slip system samples were cut from the as-grown rod either by a high speed abrasive wheel or by a spark erosion process.
The samples cut by the abrasive wheel were first heavily polished chemically~
then lapped by hand to produce flat and parallel ends, and, finally chemically polished lightly prior to compression testing. cut samples.
The intermediate polishing procedure was omitted for the spark-
The samples were approximately 1.3 cm long and about O. 4 cm in diameter.
The specimens were tested in various Instron tensile machines using a number of compression Jigs.
All the tests were done at room temperature.
Strain rate changes were made as a function
of strain by varying the cross-head speed an order of magnitude in the range of 0.013-0.13 and 0.050-0.00 cm/min.
Thin teflon sheets were used on the sample ends as a lubricant.
Figs. 1 and 2 show the m' and v*/kT values respectively, which were determined as a function of the compressive shear strain.
All compression tests showed a well defined yield drop
and the first strain rate change was made after the lower yield load had been reached.
The
tests were interrupted at least once in each case for either stress relaxation measurements (4) or for x-ray analyses.
Fig. 1 shows that the m' values are not easily extrapolated to zero
Vol. 1, No. 2
85
STRAIN RATE DEPENDENCE ORNL-DWG 67-7270 t8
l
•• ~
.• . . . . . . L
,r,/,;"
16
>..,# °-~
&
/,
III
"~ I0
-
NIOBIUM
o t PASS, I0 cm/hr A 2 PASS, I0 cm/hr _ _
2
L
A t PASS, 4 6 cm/hr •
| PASS, 54 cm/hr i
I
I0 '~2 t4 6 8 T. COMPRESSIVE SHEAR STRAIN (%)
4
t6
FIG. 1 m' versus compressive shear strain for niobium specimens prepared under various crystal growth conditions. The starting compression axis was near (491)o The data were obtained using the strain rate cycling technique at room temperature.
ORNL- DWG 6 ? ' - 7 2 6 9
4~\~-
-
°
°
"
±"
"_i
T.E. MITCHELL. R.A. FOXALL AND PB. H
I-
PHIL.
M.zlG..8. t895 (t965).
FROM TO MEASUREMENTS ill
2
• t PASS (10cm/hr)
0
o 2 PASS (10 cm/hr) • t P A S S (54cm/hr) a t PASS (4.6cm/hr)
.
I
2
4
i
I
[
6 t0 t2 t4 ),,COMPRESSIVE SHEAR STRAIN (%)
t6
t8
FIG. 2 v*/kT versus compressive shear strain for the same niobium specimens as in Fig. 1.
86
STRAIN RATE DEPENDENCE
Vol. I, No. 9
strain and that appreciably different m' values are found for the various crystals. scatter of about 25% was found in m' for a given crystal. data of Fig. 2 for
A maximum
This same scatter is found in the
v ~-~; however, for this method of characterization the data for all samples
fall within the same scatter band, including the data of Mitchell et.al.
(9). The latter data
were determined from measurements of the critical resolved shear stress for crystals tested individually at different strain rates.
The value v
be about 79 b 3 (9). The average value for v
calculated from this data was reported to
calculated from Fig. 2 is (80 + 9 b3).
This fur-
ther compares with values for v * of 70 to 80 b 3 for similarly oriented niobium single crystals tested at comparable strain rates by Gregory (6).
Conrad and Stone (7) found v
to lie in the
range of 40 to 80 b 3 for the same stress levels.
The agreement of all these data is very en, couraging because they apply near to room temperature where v seems to be a very sensitive
function of ~th (7)The data shows that m' increases as the flow stress increases while v stant for all of our samples. equation 2, v
is essentially con-
According to the thermal activation rate analysis underlying
is solely a function of ~th"
The near constancy of v
in Fig. 2 implies that
~th is similarly constant, independent of strain and growth history for the crystals.
Taking
into account the postulates of the thermal activation rate analysis, expressed in equations 3 and 43 the left hand sides of equations 1 and 2 are related by: rdln
~
v T
Since v
is essentially constant, m' must vary directly as ~.
seen by comparing m' in Fig. 1 with the values of ~ in Table I.
That this is indeed so may be The results imply that the
variation in T with strain and crystal growth history is only in the athermal component of the applied stress. In addition, it may be that equation 9 will prove useful for determining the values of m' at small strains but further experiments are required on this point. References 1.
R. W. Guard, Acta Met. ~ 163 (1961)~ W. G. Johnston and D. F. Stein, Acta Met. ll, 317 (1963); S. Floreen and E. Scott, Acta Met. 12, 798 (1964); J. C. M. L-[k~-dJ.'~. Michala~k; Acta Met. 12, 1497 (1964)~ S. Floreen and T. E. Scott, Acta Met. 12, 1499 (1964).
2.
H. Conrad, J. Iron and Steel Inst. 198, 364 (1961); H. Conrad and W. Hayes, Trans. ASM 56, 249 (1963)~ H. L. Prekel and H. Conrad, Acta Met. 15, 9~9 (1967)-
3-
R. E. Reed, Proceedings of the Second International Conference on Electron and Ion Beam
Vol. I, No. 9.
STRAIN R A T E D E P E N D E N C E
87
Science and Technology, April 17-20, 1966, New York, N. Y., Gordon and Breach, Publishers, to be published 1967. 4.
H. D. Guberman, to be published.
5-
T. E. Mitchell, R. A. Foxall, and P. B. Hirsch, Phil. Mag. 8, 1895 (1963).
6.
D. Gregory, Trans. AIME 227, 678 (1963).
7-
G. A. Stone and H. Conrad, Acta Met. 12, ll25 (1964).
Vol. 1, pp. 83-88, 1967 Printed inthe United States.
Pergamon Press, Inc.
CHARACTERIZATION OF THE STRAIN RATE DEPENDENCE OF THE SHEAR STRESS FOR NIOBIUM S~NGLE CRYSTALS*
R. W. Armstrong
Division of Engineering, Brown University Providence, Rhode Island
R. E, Reed and H. D, Guberman
Solid State Division, Oak Ridge National Laboratory Oak Ridge, Tennessee
(Received July 21, 1967) There are two alternative descriptions which are widely used for characterizing the temperature and strain rate dependence of the resolved shear stress for single crystals.
One
involves the relation (1)
m'
~
(d in ~]
(l)
~d in T~ T and the other, (2)
v
_
~y=
(2) T
where T is the shear strain rate, T is the applied shear stress, Tth is the thermal component of the applied shear stress, v usual m e a n i n g .
is an activation "volume", and the other symbols have their
Normally ~ and Tth a r e r e l a t e d
by
= Tth + ~G
(3)
where TG is the athermal component of the applied stress, and, for a strain rate change test
This research was sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation.
83
84
STRAIN RATE DEPENDENCE
Vol. 1, No. 2
(41 Our purpose is to compare the two parameters defined by equations 1 and 2 for strain rate change tests performed on niobium single crystals producedunder various growth conditions. Niobium single crystals were grown from Wah Chang stock using electron beam floating zone techniques with the rod axis close to (491). elsewhere (3)-
Details of the growth procedure are described
For the experiments reported here the growth rate was the major variable.
had the effect principally of varying the substructure and purity (3).
This
Table I lists the
growth conditions and the resulting mechanical properties for the samples tested.
Compression
TABLE I Summary of Growth Conditions and Mechanical Properties
Sample
~c
Zoning Rate (cm/hr)
Number of Zone Passes
34
(1)
Nbc (2)
4.6
~LY (kg/mm2) *
Strain . Rate (Sec -~)
m'(7 = 9%)
One
3.22
6.7 x io -5
16.o
One
2.13
6.6 x lO -5
ll. 8
Nb-020-1
lO
One
2.23
1.7 x 10 -4
12.3
Nb-023-2
i0
Two
1.65
8.8 x 10 -5
i0.0
*Lower yield stress resolved on (iOl) (iii) slip system samples were cut from the as-grown rod either by a high speed abrasive wheel or by a spark erosion process.
The samples cut by the abrasive wheel were first heavily polished chemically~
then lapped by hand to produce flat and parallel ends, and, finally chemically polished lightly prior to compression testing. cut samples.
The intermediate polishing procedure was omitted for the spark-
The samples were approximately 1.3 cm long and about O. 4 cm in diameter.
The specimens were tested in various Instron tensile machines using a number of compression Jigs.
All the tests were done at room temperature.
Strain rate changes were made as a function
of strain by varying the cross-head speed an order of magnitude in the range of 0.013-0.13 and 0.050-0.00 cm/min.
Thin teflon sheets were used on the sample ends as a lubricant.
Figs. 1 and 2 show the m' and v*/kT values respectively, which were determined as a function of the compressive shear strain.
All compression tests showed a well defined yield drop
and the first strain rate change was made after the lower yield load had been reached.
The
tests were interrupted at least once in each case for either stress relaxation measurements (4) or for x-ray analyses.
Fig. 1 shows that the m' values are not easily extrapolated to zero
Vol. 1, No. 2
85
STRAIN RATE DEPENDENCE ORNL-DWG 67-7270 t8
l
•• ~
.• . . . . . . L
,r,/,;"
16
>..,# °-~
&
/,
III
"~ I0
-
NIOBIUM
o t PASS, I0 cm/hr A 2 PASS, I0 cm/hr _ _
2
L
A t PASS, 4 6 cm/hr •
| PASS, 54 cm/hr i
I
I0 '~2 t4 6 8 T. COMPRESSIVE SHEAR STRAIN (%)
4
t6
FIG. 1 m' versus compressive shear strain for niobium specimens prepared under various crystal growth conditions. The starting compression axis was near (491)o The data were obtained using the strain rate cycling technique at room temperature.
ORNL- DWG 6 ? ' - 7 2 6 9
4~\~-
-
°
°
"
±"
"_i
T.E. MITCHELL. R.A. FOXALL AND PB. H
I-
PHIL.
M.zlG..8. t895 (t965).
FROM TO MEASUREMENTS ill
2
• t PASS (10cm/hr)
0
o 2 PASS (10 cm/hr) • t P A S S (54cm/hr) a t PASS (4.6cm/hr)
.
I
2
4
i
I
[
6 t0 t2 t4 ),,COMPRESSIVE SHEAR STRAIN (%)
t6
t8
FIG. 2 v*/kT versus compressive shear strain for the same niobium specimens as in Fig. 1.
86
STRAIN RATE DEPENDENCE
Vol. I, No. 9
strain and that appreciably different m' values are found for the various crystals. scatter of about 25% was found in m' for a given crystal. data of Fig. 2 for
A maximum
This same scatter is found in the
v ~-~; however, for this method of characterization the data for all samples
fall within the same scatter band, including the data of Mitchell et.al.
(9). The latter data
were determined from measurements of the critical resolved shear stress for crystals tested individually at different strain rates.
The value v
be about 79 b 3 (9). The average value for v
calculated from this data was reported to
calculated from Fig. 2 is (80 + 9 b3).
This fur-
ther compares with values for v * of 70 to 80 b 3 for similarly oriented niobium single crystals tested at comparable strain rates by Gregory (6).
Conrad and Stone (7) found v
to lie in the
range of 40 to 80 b 3 for the same stress levels.
The agreement of all these data is very en, couraging because they apply near to room temperature where v seems to be a very sensitive
function of ~th (7)The data shows that m' increases as the flow stress increases while v stant for all of our samples. equation 2, v
is essentially con-
According to the thermal activation rate analysis underlying
is solely a function of ~th"
The near constancy of v
in Fig. 2 implies that
~th is similarly constant, independent of strain and growth history for the crystals.
Taking
into account the postulates of the thermal activation rate analysis, expressed in equations 3 and 43 the left hand sides of equations 1 and 2 are related by: rdln
~
v T
Since v
is essentially constant, m' must vary directly as ~.
seen by comparing m' in Fig. 1 with the values of ~ in Table I.
That this is indeed so may be The results imply that the
variation in T with strain and crystal growth history is only in the athermal component of the applied stress. In addition, it may be that equation 9 will prove useful for determining the values of m' at small strains but further experiments are required on this point. References 1.
R. W. Guard, Acta Met. ~ 163 (1961)~ W. G. Johnston and D. F. Stein, Acta Met. ll, 317 (1963); S. Floreen and E. Scott, Acta Met. 12, 798 (1964); J. C. M. L-[k~-dJ.'~. Michala~k; Acta Met. 12, 1497 (1964)~ S. Floreen and T. E. Scott, Acta Met. 12, 1499 (1964).
2.
H. Conrad, J. Iron and Steel Inst. 198, 364 (1961); H. Conrad and W. Hayes, Trans. ASM 56, 249 (1963)~ H. L. Prekel and H. Conrad, Acta Met. 15, 9~9 (1967)-
3-
R. E. Reed, Proceedings of the Second International Conference on Electron and Ion Beam
Vol. I, No. 9.
STRAIN R A T E D E P E N D E N C E
87
Science and Technology, April 17-20, 1966, New York, N. Y., Gordon and Breach, Publishers, to be published 1967. 4.
H. D. Guberman, to be published.
5-
T. E. Mitchell, R. A. Foxall, and P. B. Hirsch, Phil. Mag. 8, 1895 (1963).
6.
D. Gregory, Trans. AIME 227, 678 (1963).
7-
G. A. Stone and H. Conrad, Acta Met. 12, ll25 (1964).