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Effect of cyclic strains on electrical conductivity and work hardening of copper at 4.2K
Several decisions in the design of superconducting magnets depend upon the effects of strain cycling that will occur during the expected lifetime of the device. This report describes the effects of strain cycling in liquid helium on the electrical resistivity and the progressive work hardening in several grades of copper that may be used as the matrix in composite conductors or as the sole conductor in a normal magnet. I t was found that the resistivity increase with number of constant strain cycles is relatively large after a few hundred cycles at strain ampfitudes per cycle greater than O. 175%. The major parameters in determining the resistivity increase and the degree of work hardening in C101 grade copper are described. About one-half of the matrix copper resistivity induced by strain cycling can be annealed out by warming to ambient room temperatures, but work hardening is not reduced. Applications of the results to design considerations are discussed and the results are related to basic causes by comparing with other work where point defects are introduced in copper at cryogenic temperatures.
Effect of cyclic strains on electrical conductivity and work hardening of copper at 4.2K E.S. Fisher, S.H. Kim, R.J. Linz and A.P. Turner
This work was carried out as a direct application to the design of large superconducting magnets that are subject to several different modes of cyclic strain during assembly and normal operations. The specific purpose of this phase of the programme is to assist evaluation of the total increase in the bulk resistivity, Po, of copper at 4.2 K after well defined cyclic-strain modes, the most important of which will be the hoopstress variation created during energizing and de-energizing of the magnet. In order to relate the tension and compression components of strain to the change in Po, APo, an apparatus was built to produce push-pull (pure tension-compression) cycling of relatively large copper samples of different purity and fabrication history. The Po after a given number of cycles was measured in the most direct manner by the four-point probe, voltage-drop technique. The results of the measurements were highly gratifying in that the Apo measured for a given set of conditions was reproducible to within 5%. As a consequence, the data have permitted us to determine the relative importance of several factors that contribute to the rate of change of Po with the number of constant strain cycles and to make some reliable quantitative predictions of such rates of change as a function of the following parameters: 1. grade of copper, as defined by standard ASTM and CDA designations, 2. fabrication and annealing history of the material, 3. amplitude of strain per cycle and 4. frequency of strain cycle. For practical reasons we have limited the range of variation in each parameter to those areas most relevant to conditions The authors are at Argonne National Laboratory, Argonne, Illinois 60439, USA. R.J. Linz is at B.K. Dynamics, Inc, Rockville, Maryland 20850 USA. Work supported by the US Energy Research and Development Administration. Paper received 20 March 1978.
CRYOGENICS. JULY 1 9 7 8
0011-2275/78/1807-040552.00
expected in large superconducting magnets such as those proposed for fusion plasma confinement systems. The experiments were, however, designed to provide sufficient understanding of the source of the Apo so that extrapolation from the data to more extreme conditions would be based on reasonable models. It appears that the scope of the work accomplished under this programme was indeed sufficient to provide a reliable basis for specifyin~ the optimum purity and heat treatment of the copper to bepurchased, and to obtain estimates of the increase in Po during cyclic straining of any particular copper during magnet operation.
Experimental detail Tension-compression apparatus. The stress cycling was produced by an Instron mechanical testing machine, Model TTOCM-L with crosshead speeds from 0.03 cm min -1 and a load capability to 10 000 kg. Fig. 1 is a schematic representation of the assembly. Massive copper test samples were coupled to the load cell in the f'txed beam of the machine and the lower grip end was attached to an outer sleeve that moved up or down with the moving beam. Lateral movement of the sample was restricted by a flexible diaphragm through which the load cell coupling rod moved in the push-pull mode. The assembly was immersed in liquid helium contained in a cryostat fixed to a flange on the moving beam. Strain gauge and electrical resistivity measurements. Four strain-gauge resistors (SR-4 FNB-12-35) were glued to the closed end of the 'U' clamps, with one resistor on each face of both clamps. A resistance bridge constructed from the four strain-gauge resistors determined the strain amplitude. Fig. 2 is a block diagram of the instrumentation used to measure electrical resistivity and stress-strain characteristics of the specimen during cycling. The electrical resistivity of the specimen was obtained by means of the standard four-probe dc technique. With the 0.635 cm
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original billet, but metallographic examination indicated that the final reduction to 1 in (2.54 cm) diameter was a cold work operation. This group consisted of four samples. Another rod from the same vendor, also 1 in (2.54 cm) diameter, was further cold-rolled to 5/8 in (1.59 cm) diameter prior to machining,and yielded eight samples making up Group 3 of Table 1. The stock for Group 4 was similar in history to Group 3, but was obtained from a different source. It should be noted that the rrr for Groups 2, 3 and 4 samples were within a relatively narrow range extending from 212 to 233, reflecting the C 101 impurity composition and the fully annealed state. For Group 5, however, the rrr values in the annealed condition varied from 110 to 200, reflecting the non-uniform distribution of the second-phase impurities in the free-machining grades.
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Stress-strain cycling modes. Fig. 3 is a typical stress-strain diagram for a specimen subjected to 600 constant-strain cycles. When cyclic stresses in excess of the elastic limits are applied to a specimen, the stress-strain curve forms a 'hysteresis' loop. In this report the loop width at zero stress is defined as ep, the amount of plastic strain in the cycle. As cycling progresses, the interactions between dislocations and the point defect production during plastic straining cause work-hardening of the material with a progressive decrease in ep, ie, the stress-strain loop continually narrows during cycling. The specimen will quickly approach a completely elastic behaviour if the cycling continues for several periods at constant load. At constant
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sample gauge diameter and 2 cm gauge length a A#o of 0.2 nI2-cm could be readily detected.
E
=-
Description of copper samples. The primary UNS grade l that was considered in this study is that designated C101, with OFE (oxygen free electronic) designation. Some tests were also carried out with a free machining grade designated C147, containing between 0.20 and 0.5% sulfur, and also with a very high purity research grade containing 99.999% copper (designated in this report as 5N). One of the principal results of this study is that the fabrication history of the material, as it affects the preferred orientation of the grains, is a very important factor in determining ~o o with strain cycling. Consequently, the description of the different groups of samples listed in Table 1 contains the known history prior to machining of the samples from the raw stock. One group of C 10I (#2 of Table 1) samples were machined directly from the rod as received from the vendor as a 2.54 cm diameter rod. This rod was presumably 'hot rolled' from the
406
% Strain, ¢x102
0.20
Fig. 3 Stress-strain diagram for a Group 2 sample subjected to 600 constant-strain, push-pull cycles. Strain notations are • t and ~p, the total strain per cycle and the loop width or plastic strain per cycle at zero stress.
CRYOGENICS.
JULY 1978
T a b l e 1. H i s t o r y o f c o p p e r s a m p l e s f o r c y c l i c s t r a i n s t u d i e s
Anneal after machining Sample group
Source
Grade or UNS #
Fabrication before machining
Asarco
5N
Utility Brass Co.
Temp, °C
Time, h
rrr
Annealed as received,* 3/4" diameter
400
7
2200
C101
Received as cold rolled** 1" diameter
385
8
223
Utility Brass Co.
C101
Cold swaged from received* 1" to 5/8" diameter
385
8
212
Amax Corp.
C101
Cold swaged from received* 1" to 5/8" diameter Cold rolled to 5/8" diameter
400 385
6 8
233 229
Sample ~1
Cold rolled to 5/8" diameter
650
6
200
Sample
Cold rolled to 5/8" diameter
350
6
110
Sample
Cold rolled to 5/8" diameter
450
6
135
Sample
Cold rolled to 5/8" diameter
650
6
156
Sample
Cold rolled to 5/8" diameter
--
-
75
Sample #6
Cold rolled to 5/8" diameter
-
-
75
Stock, free machining C147
* as delivered from source ** approx. 10% reduction in area by vendor 1 in=2.54cm
strain, however, the work-hardening is reflected in the added stress per cycle to produce et, and ep decreases to a constant non-zero value. The intent of the present study was to primarily determine the Ap developed for constant et values between 0.10% and 0.30% strains. Before the constant strain studies with ofe samples, several exploratory runs were carried out with Ap and work hardening observations during constant load cycling of the very pure 5 N grade copper (Table 1). The actual mode and amplitudes of stress and strain are presented in the results.
of the initial load-strain loop at zero load was nearly a s large as the total strain in the first half cycle. The loop width at zero load, or total plastic strain, ep, decreased rapidly with work-hardening to less than 50% of the total strain after 220 cycles as shown in the dashed curve. The Po vs N curve reflects the rapidly decreasing ep per cycle as it approaches an apparent saturation value at N = 500. In this case, the Pd 2.5 Poi, wherepoi is the initial po. Seventyfive percent of the t~ial Pd is produced by N = 200, where dPo/dN decreased rapidly.
The recovery or loss of/Xp by wanning was not investigated by a systematic isochronal annealing study. The results reported here are due to observations made after overnight or over several, day, warming excursions, because of interruptions with the cycling experiments. These annealing observations are perhaps a reasonable approach to simulate the recovery that will take place during wanning of magnet coils during service by comparison with annealing spectra following irradiation damage or single crystal mechanical deformation. However, the observations are clearly insufficient to establish the mobility of the point defects.
The effect of wanning to 185 K during a 15-h interruption after constant-load cycling is shown by the vertical dashed line at N = 800. The anneal caused a recovery during wanning of about 1 n~2-cm in Po measured at 4.2 K after the annealing. This was about 20% of the total Pd- The anneal also evidently caused a strain-aging effect, in which the point defects migrate to the dislocations causing an increase in the yield stress by dislocation pinning. This appears to be the same effect observed by Blewitt et al2 and by Birnbaum 3 after unidirectional strains and by Hull 4 and by Johnson and Johnson s after cyclic strains. The subsequent increase in Po in Fig. 8 at N > 1000 is the result of increasing the load gradually withN, so as to increase et to 0.3%.
Results
Constant peak load. Most of the constant-peak-load experiments were carried out with the Grade 1 copper. Typical results are shown in Fig. 4 for a rrr of 700. As shown in the load vs strain curve in the inset of Fig. 4, the total strain during the first 1/4 cycle was about 0.14% and the sample was subsequently cycled between constant load limits of +175 kg. (The load may be converted to stress units ofMN m -2 or psi by multiplying by 0.309 MN m -2 and 43.8 lbs kg -1 in -2 respectively). The width
CRYOGENICS. JULY 1978
=
Load-unload cycling. Fig. 5 shows Po vs N with the loadunload cycling of a high purity copper sample. These data were obtained by introducing a total strain of 0.3% and then cycling between strain limits of +0.3% and +0.1%; the lower strain limit occurred at zero load. The cycling conditions of the first 1 1/4 cycles are similar to the loop shown in the insert. Most of the increase in Po occurs in the first 1/4 cycle with about O. 18% plastic strain. Subsequent
407
decreases from approximately O. 12% in the first full cycle to 0.055% a f t e r N = 500.
200 ,f 150 -
In Fig. 6, the peak stress, loop width at zero load and the increase in resistivity Pd are all plotted as a function of N at et = 0.20% for this Group 2 sample, q'ypical data have the following general properties:
100 After 40 cycles ----"J -50 -100
// ~
After 220 cycles
1. The increase in Pd has three different stages. For N < 30 (Stage I), Pd increases rather rapidly with an average value o f d p d / d N = 5.5 x 10 -2 nI2 2m cycle -1 . The region of 50 < N < 200 (Stage II) is a transition region from the rapid increase of Pal to a linear increase in Pd with an average slope dpd/dN = 2.8 x 10 -2 n ~ - c m cycle -I . For N > 200 (Stage III), the increase in Pd is linear (dPd/dN = 1.3 x 10 -2 n~2 cm cycle -1 is a sonstant).
I/ /
-150 -200 -0.16
J
t -0.08
I
J 0 Strain,%
I 0.08
I 0'16
10
2. Two days at 300 K after cycling to N = 500 is sufficient to anneal out the Pd produced in the Stage III o f the cycling process. After another 100 cycles, it is shown that one day at 300 K is not enough to remove the defect production of Stage III. In this particular sample the increase in Pd after each annealing was linear with the same value o f d p d / d N = 1.3 x 10 -2 n~2 cm cycle -1 as
9 8 7 uE
6
c4
5
A 2
'o
~o 3
I
I
I
i
I t t 500 N, Cycles
i
=
I 1000
t
I
Fig. 4 T o t a l resistivity and f r a c t i o n a l change with 1 - constantload cycling t o N = 800, as in load-strain diagram, 2 - warming t o 185 K a f t e r N = 800, 3 - c o n t i n u a t i o n o f cycling at 175 kg load and 4 -- gradual increase in load per cycle so as to achieve e t = 0.30%. Initial r r r = 7 0 0 0
O' 20 2 uE
°°°t
=, o
42
~o
_9 °
1
_2OOl
load-unload cycling involved ep < 0.10% and, thus very little increase in Po. It should be noted that the simple load-unload cycle for the copper matrix would apply to a magnet structure with no steel hoop structure and insignificant load bearing by the superconducting filaments. As the amount of steel reinforcement and/or superconductor is increased, the amount of compression in the copper will increase, assuming no plastic yield in the structural or superconductor materials. With sufficient structural material the compressive strain on unloading will be significant and give rise to wider loops and more increase in Po. In addition, the coldworking in the copper will no longer restrain et, since the total strain will approach that in steel subjected to a constant load in the elastic range, ie, a constant strain.
General characteristics of constant-peak strain cycling results. The stress-strain plot of Fig. 3 represents the constant peak strain mode for a C101 sample of Group 2 where the constant peak strain, et, is 0.20%. Although the stress-strain curve during the initial 1/.4 cycle is typical of easy glide behaviour, the character of the curve changes rapidly during the first few cycles. The stress to produce et = 0.20% increases from about 61.25 MN m -2 in the fully annealed state to about 102.9 MAr m -2 during the initial 100 cycles. The other rapidly changing parameter is the loop width at zero load, or the ep per cycle, which
408
t I 0"2 0.4 Strain . %
0.11
I 5
I 10
I 15 N, Cycles
I 20
I 0"6
I 25
I 30
Fig. 5 T y p i c a l Po versus N p l o t f o r load-unload cycling, as indicated in load-strain diagram
150
C101 Group 2,et =0"20% 11.C 10"C 9-0 8.0 7-0 E u 6'0 50 4.0 30 20 1.0
log
iO N ,
0
E
100
,
200
,
300
l,
400
, .... ,---, 5O0 6OO 70O
N, Cycles
Fig. 6 Defect resistivity (left scale), peak stress per cycle (right scale) and l o o p width at zero load, ep, as a f u n c t i o n o f n u m b e r o f constant-strain cycles at et = 0.20% f o r G r o u p 2 sample
CRYOGENICS. JULY 1978
Table 2. S u m m a r y of average Pd increase per cycle during constant-strain cycling, arranged in increasing total strain per cycle, et et, %
Sample group
rrr
~pd/~N (Units
of 10 ~ n ~ cm/cycle)
N = 0 + 30
N ~
30
0.05
5
75
0
0 (0 -
0.10
2
223
0
5
156
3
2.5 (300 0.5 (300 -
0.15
2
223
2.3
2.3 (0 -
600)
0.175
2
223
6.3
6.3 (0 -
350)
0.2
1
2200
29
2
223
55
3
212
39
4
233
34
4
236
40
4
237
5
200
42 36 45
2 3
150 223 206
23 80 70
4
229
70
4.1 (150 - 275) 6.8 (after 300 K anneal) 28 (50 - 190 13 (200 - 700 13 (100 - 200 10 (250 - 400 11 (150 - 300 5.5 (400 - 700 12 (150 - 300 6.5 (40O - 7O0 13 (150 - 300 20 (50 - 100 15 (70 - 250 1 2 ( 3 0 0 - 500 16 (80 - 280 26 (200 - 380 2 0 ( 1 5 0 - 200 14 (300 - 950 12 (500 - 700
5
110
370
100 (7O -
O.3O
0.42
before annealing. This behaviour indicates that the sample remains in Stage III during and following the anneal. 3. The peak stress and the loop width at zero load vs N show the work hardening during the cycling. As is the case with dpd/dN, the work hardening rate is very large in the first 30 cycles and decreases rapidly to a relatively constant rate above N = 200. In contrast to dpd/dN there is no clear separation of stages in the work-hardening rate before the first anneal. 4. The anneal-hardening, or strain-aging, effect after 2 days at 300 K is clearly observed by the increase in the peak stress for 0.20% et and the decrease in ep. The progression of work hardening after the initial anneal differs from that of Pd in that there are virtually no changes in peak stress and ep after the first annealing and that the subsequent anneals have no significant effect on work hardening.
Effects of impurities and fabrication history on results of constant-strain cycling. The results of constant-strain cycling at et = 0.20% for the different groups of samples listed in Table 1 are shown in Figs 7, 8, and 9. The values of dpa/dN at different stages of work hardening of all samples tested are given in Table 2. The increase in Pd with N is generally similar to the variation of Pd in Fig. 6. For a given N in Fig. 7, Pd for different samples can be divided into three different categories: Group 2 samples show the highest increase, the lowest increase is in Group 1,
C R Y O G E N I C S . J U L Y 1978
8200) 55O) 1600)
80)
and intermediate increases are found for Groups 3, 4, and 5. Although the relatively low rate of increase in Pd of the high purity copper (Group 1, Fig. 9) suggests that impurity content may be an important factor in explaining dpd/dN, the outstanding differences between the Group 2 samples and the Group 3 and 4 samples shows that other factors are of much greater importance among commercial grades. C101, Group o C147, a C147, £101
12
et= 0"20% Z days at 300 K
11 10
. cioi,
90
' C101, o C101,--
~
\
~ ~
\ \
2dm/satT?K
8'C
~ 7-C 6"C 4-C 3"£ 2'C 1.£] 0
. ¢ " ~
2 days at 300 K
~ '
9 months at 300K 1(~0
I 2(~0 I
3~0
I
4~)0 I
I 500
'
I 600
I 700 I
N, Cycles Fig. 7
D e f e c t resistivity, Pd, as a f u n c t i o n o f constant-strain
cycles at e t = 0.20% f o r 8 samples representing each o f the five groups listed in Table 1
409
unlikely that the small differences in grain size among the C 101 materials were at all influencing the final results. As testimony to the absence of grain size effects among the commercial samples, the average grain size in the annealed C147 samples (Group 5) was significantly larger (0.065 mm) than in the C101 samples. Nevertheless, the Pd values at N > 0 (Fig. 7) exceeded those for the samples of Groups 3 and 4.
140 120
q~ 100 ct = O' 20% i~
~
° C101 Group 2
!
o c1~7
5
II |
zx o • • v
5 4 4 4 3
'
4O 20 I
0
Fig. 8
I 100
I
I 200
I
I I I 300 400 N , Cycles
t
r
C147 C101 C101 C101 C 101 I 500
I
I 600
I
I 700
Stress per cycle to p r o d u c e c o n s t a n t strain a m p l i t u d e of
0.20% for samples representing G r o u p s 2, 3, 4, and 5 Ct = 0'20% o A o • • • v
0"3C
~ 0-20
CI01, Group 2 C147, C101, C1~, C101, C101, C101,
"
5 4 4 4 4 3
7~ 0.1C I
I 100
I
I 200
I
I I I 300 400 No Cycles
I
I 500
I
I 600
I
I 700
Fig. 9 Progressivedecrease in loop w i d t h at zero load, or ep, w i t h increase in N f o r e t = 0 . 2 0 % in samples representing Groups
2 , 3 , 4 , and 5
Unlike the sample from Group 2, the 5 samples from Groups 3 and 4 that were cycled at et = 0.20% all showed p d values of(6.5 -+ 0.5) nI2 - cm or about 60% of that in Group 2 samples at N = 500 cycles, even though the starting rrr values were essentially the same. The increase in the peak stress for et = 0.20%, with N, is also considerably higher for the Group 2 sample, as is expected for a correlation ofpd and work hardening. A similar effect of fabrication history is observed for the samples cycled with constant peak strains of 0.30% (Fig. 10). The first CIO1 sample cycled at this et was from Group 2, whereas the other 2 samples tested at et = 0.30% were from Groups 3 and 4, respectively. A t N = 380 the Pd for the former sample (Group 2) reached 14.5 nI2 - cm, whereas for the latter two samples Pd was between 10 and 10.5 nQ - cm. Unlike the case of et = 0.20%, the difference in work-hardening parameters between Group 2 and the other two groups shows up only above N = 200. The effort to understand the very significant differences between Group 2 samples and the other CIO1 samples involved grain size studies, spectrochemical analyses of vapours from oxidized samples and a cursory search for differences in texture caused by the differences in fabrication prior to machining. The recrystallized grain sizes in all the C101 rods (Groups 2,3,4) were all within the range of (0.040 -+ 0.005) mm, with the Group 2 samples at the lower end. The high purity samples (Group 1) on the other hand, had starting grain sizes varying from 2 mm to 3 mm. Thus the very large grain size could well account for the relatively low rates of work-hardening and dPd/dN values in the Group #1 high purity material. It is, however,
410
The spectrochemical analysis showed no significant differences in purity among the commercial grade materials that could account for the observed differences in the results. The largest quantities of the impurity elements were in the 10 to 15 ppm (by weight) range with total impurity content below 50 ppm. The texture differences among Group 2 and Groups 3 and 4 samples are inferred from a diffractometer scan of reflected x-ray intensities from transverse cross-sections of two machined samples in the recrystallized state. The results of this study are shown in Table 3 where the diffracted intensities relative to that of the (111) reflection in a powder sample are listed. For the Group 2 sample the most significant deviation from the random sample was in the (200) reflected intensity while the (111) and (222) reflections were about the same intensity as the random case. The Group 3 rod, in contrast, showed a significantly different intensity spectrum, with the (111) and (222) reflected intensities significantly greater than in the random case and with an integrated average deviation from random of 31% compared to 24% for the Group 2 rod.
Strain-amplitude ef[ects at constant strain per cycle. The effects of strain amplitude on the change in Pd per cycle and the work-hardening parameters were investigated to some degree over the range of 0.42% to .05%. The primary 20"0 . ~-.~.. ,..,....a-'~ N 950
15-0 ~
ct = 0"30% o C101group 2 A C101group3 a C1e group 4
2 days o~ 300 K
E 104 c~
~ 5-o 0
Fig. 10
1 0
200
0 400 N. Cycles
500
600
700
D e f e c t resistivity, Pd, as a f u n c t i o n o f constant-strain
cycles at e t = 0.30% for samples f r o m G r o u p s 2, 3, and 4
/ J
12°~/ u0F ~ l v^ '^v/ !
of
r/
9 C147,grot~5, Et =0.42%
~
o /
9"0 r ~ 8'0
7 `/
6"0}t
32.0
~
y
0
~
J
d
ct=0 30%
. ~ group 2
v/
tct=O 15%
'> J
¢t =0"175°/'
o / All C101 ct =0.20%
. . . . .
I
.
~
o1
~c~ ~ I .~,i
H dayat 300K
a
y
s
1 0 " D 0
¢ -0"10%
at 300K ,,-..ll---.-"~ r 100 Z00
I 300
I 400 N. Cycles
I 500
I 600
I 700
Fig. 11 C o m p a r i s o n o f Pd increase w i t h N f o r d i f f e r e n t constantstrain a m p l i t u d e s
CRYOGENICS . J U L Y 1978
Table 3. Reflected intensities from 20 scan of plane perpendicular to rod axes of recrystallized samples Group 2 Machined from As received /
Powder / R
C101 group 2
8 0-3
o e t = 0.30 %
o
v c t = 0-20 %
0.2
Group 3 Swayed to 75% Ra before machining /
= ~;t =0.10 % 2 days at 300 K
~ 0.1 t00
111
100
107
129
200
46
64
43
220
20
10
4
311
17
11
12
222
5
5
8
400
3
3
3
331
9
5
4
420
8
3
5
208
208
208
.240
.308
R - ~l/R - / I
objective was to determine whether the changes in dpdldN at higher amplitudes are continuous or catastrophic at N < 1000 cycles and to ultimately predict whether any significant effects will occur at high frequency low amplitude conditions. The curves for 0.20% and 0.30% amplitude differ in character from the 0.10% strain amplitude curve in that, in the latter case, the initially rapid increase in Pd and work-hardening parameters are not observed (Figs 11, 12, and 13). At e t = 0.10% the initial plastic strain per cycle is only about 0.02%, so that over 50 cycles are necessary before a significant change in Po is observed. Another unique aspect of the curves for e t <( 0.20% (Fig. 11) is that dpd/dN increases with N for the initial 730 cycles at 0.10% and for the continuation of cycling at 0.150% and 0.175%. The relatively small decrease in Pd during the 300 K anneal after both 0.10% and 0.17% strain amplitudes indicates that most of the resistivity is derived from dislocations rather than point defects. The experiment at e t = 0.42% was carried out with a sample from Group 5. The conclusions drawn from this one test indicate that defect production during the initial cycling 150
100
~
300K
E
C101 group 2 = ct =0-30% o c t =0,20 %
mm 5O
a ct =0, 10 %
,& N, cycles
Fig. 12 Comparison o f peak stress increases for Group 2 samples w i t h d i f f e r e n t et
CRYOGENICS. JULY 1978
2OO
3O0
400 5O0 N, Cycles
6OO
700
Fig. 13 Comparison of ep versus N plots for Group 2 samples w i t h d i f f e r e n t et
16 ~N= 400 14
E
8
c:
0?6
0'10
0.20
0"30
0.40
Constant strain amplitude, Et % Fig. 14 Defect resistivity as a f u n c t i o n o f et per cycle at N = 30, 200, and 400 cycles. All data f r o m Group 2 samples, except for point at e t = 0.42%
stage at this level of constant strain amplitude is catastrophically larger than at 0,30%. This is shown when #d is plotted as a function of strain amplitude. (Fig. 14). The data indicate that Pd is relatively unimportant at et < 0.15% and that the important contributions begin for e t > 0.175%. The data further indicate that the rate of increase in Pd with et becomes very large above 0.30%. This point should, however, be further investigated, especially for the larger N values. Since work-hardening and, therefore, closing of the stress-strain cycling loop should occur rapidly at higher et, it may be expected that saturation in Pd will occur at relatively low N values.
High frequency cycling at low amplitudes. An important objective of this study was to evaluate the possibility of degradation in the magnet conductor caused by high frequency low amplitude stresses that may arise during operation. Two experiments were carried out with N > 1000, but with et of 0.01% and 0.05%. The first was carried out with
411
the sample of Fig. 6 after N = 680 cycles at e t = 0.20% and a 2-day anneal at 300 K. After 3300 cycles with et = 0.01% no increase in Pd was observed. This is to be expected since no plastic strain was detectable in the already work hardened sample. The second test was carried out with a sample from Group 5. The results are summarized in Fig. 15. This annealed sample was first cycled to N = 50 cycles at et = 0.10%, with ap d of 0.48 n ~ - cm. This is a relatively large Pd compared to that observed for the same e t in the C 101 material (Fig. 11) and is an indication that Pd may be impurity-sensitive in the O. 10% strain region. A f t e r N = 50 cycles the et was reduced to 0.05% per cycle for 8200 cycles at a rate of 3 s cycle -1. The total Pd increase was 0.1 nI2 - cm. A f t e r N = 8200, et was increased to 0.10% for 5 cycles; the Pd increase was about the same as in the previous 8200 cycles at 0.05% strain. Constant-strain cycling o f cold worked copper. Two experiments were carried out with samples of Group 4 that were not given a recrystallization anneal after machining and had rrr values o f 53. No significant change in Po was observed after N = 300 cycles at et = 0.20% or 0.30%. For the 0.20% amplitudes the deformation was totally elastic with constant peak stress values of 285 M N m -2 . For et = 0.30% the first three cycles involved a small plastic strain.
This appears to be a reasonably safe assumption for at least the first 3000 cycles at e t = 0.10 and 0 . 2 0 % , but this rate may perhaps be decreasing at et = 0.30% to somewhat lower values than measured here. As an aid in estimating PO in C 101 grade copper, Table 4 lists estimated values of Pd for N = t 000 and n = 2000 cycles for et values of O. 10%, 0.20% and 0.30%, respectively. For C101 material with history similar to Group 2 of Table 1, Pd can reach ~ 5 0 n ~ cm after 2000 cycles at et ~ 0.3%. For the < 1 1 1 > texture, however, the same conditions should produce only 29 n ~ cm, which is a substantial reduction that can be achieved by careful specification of metallurgical history. The importance of the Pd values listed in Table 4 relative to the initial impurity resistivity, Pi, is quite large. For example, if et is limited to a maximum amplitude of 0.10%, the Pd afte~r 2000 cycles will exceed the starting Po and the ratio Pd/Po can reach a factor of 7 at et = 0.30% for 2000 cycles. Relative to transverse magnetoresistanceS, Pro, the indicated Pa values are not overwhelming but are still quite significant. Some examples of the effect of Pd on the total Po, based on Po = Pi + P d
are used to illustrate the relative importance during operation of 40 kG and 100 kG magnetic fields. For the former case, withPm ~ 15 n~2-'cm, and 1000 cycles at et 0.20%,
Discussion of results
Po = (7 + 17.8 + 15) n ~ - c m for < 1 0 0 > texture
Application of data to magnet design Prediction o f Pd in C101 grade copper. In this study we have attempted to at least qualitatively survey the increments in Pd, developed under several possible modes of deformation cycling, and to find those variables in the cycling parameters and in metallurgical history that are most effective in determining ad in copper. The basic parameter in determining Pd is ep, the plastic strain per cycle. It is quite clear from Figs 11 and 15, that even very small but consistent ep values of 0.01% (ep = 10 .4) will begin to produce a significant increase in Pd after several hundred cycles. If the magnet design is such that constant-strain cycling will indeed result from energizing -de-energizing cycles, the present data can be readily used to predict Pa accumulation at et levels of 0.10% to 0.30%, assuming that dpd/dN values remain relatively constant after N = 300.
w
f
c ._
~.
E
+ Pm
= (7 + 9 + 15) n ~ - c m for < l l l > texture. For the <1003> texture, Pd/Po ~ 0.45, whereas for the < 1 1 1 > texture, Pd/Po ~ 0.31. At 100 kG, with Pm estimated at ~ 4 0 nQ cm, the Pd/Po ratios are still about 0.29 and 0.15, respectively. In terms of material (copper), cost and weight for a given conductor length and maximum allowable resistance heating (I 2 R), the volume of copper required is directly proportional to Pp. A Pd/Po ratio of 0.10 increases the required volume by roughly 10%, if the heat capacity and surface area increases are neglected. Application o f work-hardening data. The data on the increase in tensile stress to produce a given constant strain per cycle are the only quantitative data for copper at 4.2 K and are clearly needed in the evaluation of the stress-strain data for superconducting composites in
C group 5 tt 147. = 0-10% ~
G1 0-05 % for interval
t/3
"0 n 70 ~
Table 4. Defect resistivities, Pd, from constant strain cycling at 4.2 K, as calculated from measured dpd/dNvalues for C101 grade copper
a
1000 cycles E
3"
et I 100
I 200
I I 300 400 N, Cycles
i 500
i 600
I 700
Fig. 15 Test of low-amplitude, high-cycle fatigue conditions on one sample of Group 5. Cycling at Et = 0.10% was interrupted at N = 50 cycles by inserting 8200 cycles at et = 0.50%. Effects of interruption were removed by 300 K annealing
412
2000 cycles
8200' cycles ot ~1 = 0.05%
0.10% 0.20% 0.30% 0.10% 0.20% 0.30%
Pd (n~2 cm) < 1 0 0 > or random texture 4.1
17.8
23.6
8.56
9.0
~17.0 --
30.8
51.6
Pd (n~2 cm)
<111>texture
--
15.5
29.0
CRYOGENICS . J U L Y 1976
160~150I140~130r 120l% 110~-
/ // ,/
Group 2
,' ,' I
~
a~
-
Group 4,
- 90t / 80
"
f
J
I
,oi'/f =I"//
F:~]~~I~
0.05
I
I 0.10
I 0.15
I 0-20
I 0-25
I 0.30
I 0.35
I
0'40
Fig. 16 Plots of peak stress per cycle, ot, as a function of accumulated plastic strain, :~Ep, for the three different groups of C101 samples. Dashed curve is tensile stress-strain data. s
service. The work hardening at e t > 0.175 % strain/ cycle is very significant during the first 200 cycles and one can expect to observe a significant effect on the yield stress and perhaps the overall et of the composite for a given constant stress if the volume ratio of steel to copper is relatively small. The need for these data becomes most apparent in that the increase in work hardening cannot be predicted from literature data for unidirectional deformation at 4.2 K, as given in Refs 2 and 7, for example. Although the initial stress values do indeed correspond to the yield stress values for fully annealed copper, s the increases in work-hardening with the number of cycles are considerably smaller than expected from a comparison of stress vs total plastic strain, where total ep is obtained from the summation of ep over N for all of the data. The plots of peak stress per cycle vs ~ ep for the several cyclic constant-strain experiments carried out in this study are shown in Fig. 16. The data plotted represent experiments with samples of Groups 2, 3, and 4 and et values of 0.20% and 0.30%. The Group 2 samples clearly show higher rates of work hardening than are shown by the Groups 3 and 4 samples. Within each group, the data for the two e t experiments (0.20% and 0.30%) overlap, indicating that the total cyclic strain is indeed the prime factor in (1) determining Pd and (2) the stress to produce a given total cyclic strain. The curve plotted as a dashed line represents unidirectional tensile stress-tensile strain data for polycrystalline ofe copper s tested at 4.2 K. When compared with the cyclic strain curves the difference in work-hardening mechanisms and/ or magnitudes becomes clear. Small amplitude cyclic strains do not produce the hardening that results from continuous unidirectional straining. This is clear in the initial cycling regime but the most important difference is in the relatively rapid decrease in the cycling stressstrain slope near Y, ep = 0.10 and the indications of near ~aturation at ~. ep of 0.30. In contrast, the typical unidirectional stress strain curves for either polycrystal or single crystal deformation at cryogenic temperatures show stage 3 work-hardening beginning at ep > 0.30. This, design data for evaluating strains resulting from magnet stresses should be carefully evaluated with respect to the difference between cyclic and unidirectional deformation. Another important application of the present data is to the relatively unpredictable effect of 300 K annealing on the work hardening at 4.2 K. Although the increased
CRYOGENICS. JULY 1978
stress to produce a given strain is in line with previous observations of strain-aging, 2~ the saturation after annealing shown in Fig. 8 is unexpected and not consistent with Pd data. The latter data indicate that rate of point defect production deformation after annealing is similar to that before annealing. Further work hardening is, on the other hard, severly diminished. This is one important effect that shows that the Pd increase is not simply related to work hardening. Another effect that is of similar importance is the observation that there is an abrupt increase in work-hardening after 77 K annealing, whereas no significant effect on Pd is observed. It appears that periodic warming of a magnet to T > 240 K will have the effect of not only decreasing Pd, but also arresting the rate of work hardening. It also appears that further basic studies of work hardening in copper, and in other metals at 4.2 K are needed to enable reliable prediction of stressstrain response as affected by texture differences and periodic annealing during magnet operation.
Application to basic studies of deformation-induced point defects. The value of the present results, in relation to point-defect research, is that they provide a quantitative basis for modelling the point-defect production from the dislocation interactions during cyclic deformation. 9 The two observations of primary importance in this respect are: 1. the indications of a constant dpd/dN for a given et, after an initial rapid work-hardening, and 2. the 300 K annealing experiments, where the fraction of #d that is lost is that part accumulated during the constant dPd/dN stage. A third related factor is that dPd/dN, after workhardening and 300 K annealing, appears to be the same as during the pre-anneal cycling. There thus appears to be essentially two distinct stages of defect production in constant strain cycling where stage one is associated with dislocation production and work-hardening by dislocation interactions. This stage corresponds to the dislocation bundling or clustering stage described by Basinski et al. ~° At the levels of et at 0.2 and 0.30% the extent of this rapid work-hardening stage is dependent on texture. For the light texture (Group 2) Stage 1 appears to extend to N ~ 250 cycles, whereas the strong < 1 1 1 > texture provides several sub-stages a t N < 500 cycles. Stage two is, of course, characterized by the constant rate of point defect production per cycle. This again is consistent with the metallographic observations of Basinski 1° where the accumulation of mottled areas between dislocation bundles is described. The remarkable inference of the present data is that the rate of point defect produced per cycle seems to depend only on the strain ep and is not directly related to the increase in stress to produce et. The absence of dependence on stress is similar to what has been reported for some experiments with unidirectional tensile deformation, 9 where pdccen; it is clearly not consistent with the more widely accepted Saada relation, 11 where Pd foe ode. The latter presumes that the strain energy is the important factor and that the point defects are produced by a mobile dislocation cutting through a stationary forest of dislocations.
Defects per cycle. The basic information that is useful for analysis of the point defect production process is dpa/dN in the range above the initial work hardening stage, ie, N = 300 cycles at e t ~ 0.20 to 0.30%. Since ep per cycle is relatively constant, the value of Z~od for each cycle reflects the mechanism by which defects are
413
produced. A parameter of principal interest is the number of defects produced during each cycle. For the Group 2 material we have established that Z~oa for each cycle at et = 0.20% is about 0.013 n~2-cm. Assuming z2kod is from point defects only and that 1 a/o Frenkel defects produces 2.0 b6"~-cm12 , the concentration of defects per cycle with et = 0.20% and ep ~ 0.05% is 0.65 x 10 -7. For et = 0.30% and ep ~ 0.10%, ~ o d per cycle is 2.6 x 10 -s ~"Vcm or about 1.3 x 10 -7 defect concentration. For the < 1 1 1 > textured samples the defect concentrations per cycle are about one-half those of the Group 2 samples. These concentrations are consistent with the conclusions 9 from unidirectional deformation data where it is estimated that ep = 1% produces a point defect concentration of 10 -~ and ep = 10% gives 10 -s . This programme was initiated as part of the programme entitled 'Materials Research in Support of Superconducting Machinery', ARPA Order No 2469. All efforts on this phase of the programme beyond October 1, 1974 were supported by a contract with the Magnetics and Superconductivity Section, Fusion Energy Division, Oak Ridge National Laboratory, operated by Union Carbide Corporation under contract to the US Energy Research and Development Administratxon, and by the Division of Physical Research of ERDA. The authors are indebted to the following for their participation and interest: J.B. Darby and R.W. Siegel (ANL), A.P. Clark and R.P. Reed (NBS, Boulder), M.S. Lubell and W.A. Fietz (ORNL) and John Purcell (GGA).
getting asood canbevery rewarding And you can get a GOOD COLD (room temperature to 10 kelvin) in about half an hour, with an LTS-21 Series closed cycle refrigerator system. Depending on the system you choose, your cold can be stable to +_0.5 kelvin or to _+ 0.003 kelvin. You can even get t w o colds at the same time for a lot less money than ever before. The new universal compressor supplied with all LTS-21 systems can power t w o cold heads simultaneously without sacrificing performance.
References
1 2
10 11 12
A complete tabulation of UNS and CDA letter designations with chemical composition limits is in the Application Data, Copper Development Assoc, New York Blewitt, T.H., Coltman, R.R., Redman, J.K., Defects in crystalline solids, The Phys Soc London (1955) Birnbaum, H.K., JAppl Phys 34 (1963) 2175 Hull, D.,Phil Mag 3 (1958) 513 Johnson, E.W., Johnson, H.H., TransAIME 237 (1965) 1333 Banz, M.G, JApplPhys 40 (1969) 2003 Pearson, W.B., Phys Rev 97 (1955) 666 Warren, K.A. and Reed, ILP., NBS Monograph 63, US Government Printing Office, Washington (1963) Beukel, A. van den, Vacancies and Interstitials in Metals, Schilling, W. et al. eds North Holland Publishing Co (1969) 427 Basinski, S.J., Basinski, Z.S., Howie, A.Phi~ffag 19 (1969) 899 Saada, G.,Acta met 9 (1961) 166 Ehrhatt, P., Schlagheck, U. J. Phys F 4 (1"974) 1589
Features:
Fast cool down (300 K to 10K in about half an hour) Smaller size State-of-the-art instrumentation System flexibility Capability to operate two cold heads simultaneously from one compressor Long maintenance interval To l e a r n m o r e a b o u t a GOOD COLD write or call: In Europe: Cryophysics Berinsfield, England (856) 340257 Darmstadt, W. Germany (6151) 74081
Geneva, Switzerland {22) 329520 Versailles,France (1) 9506578
In North America:
O
LRRESHORE (RYOTROnI(|,Int.
P.O. Box 29876 Columbus, Ohio 43229 (614) 846-1250Telex: 24-5415 Cryotron Col
414
CRYOGENICS. JULY !978
Effect of cyclic strains on electrical conductivity and work hardening of copper at 4.2K E.S. Fisher, S.H. Kim, R.J. Linz and A.P. Turner
This work was carried out as a direct application to the design of large superconducting magnets that are subject to several different modes of cyclic strain during assembly and normal operations. The specific purpose of this phase of the programme is to assist evaluation of the total increase in the bulk resistivity, Po, of copper at 4.2 K after well defined cyclic-strain modes, the most important of which will be the hoopstress variation created during energizing and de-energizing of the magnet. In order to relate the tension and compression components of strain to the change in Po, APo, an apparatus was built to produce push-pull (pure tension-compression) cycling of relatively large copper samples of different purity and fabrication history. The Po after a given number of cycles was measured in the most direct manner by the four-point probe, voltage-drop technique. The results of the measurements were highly gratifying in that the Apo measured for a given set of conditions was reproducible to within 5%. As a consequence, the data have permitted us to determine the relative importance of several factors that contribute to the rate of change of Po with the number of constant strain cycles and to make some reliable quantitative predictions of such rates of change as a function of the following parameters: 1. grade of copper, as defined by standard ASTM and CDA designations, 2. fabrication and annealing history of the material, 3. amplitude of strain per cycle and 4. frequency of strain cycle. For practical reasons we have limited the range of variation in each parameter to those areas most relevant to conditions The authors are at Argonne National Laboratory, Argonne, Illinois 60439, USA. R.J. Linz is at B.K. Dynamics, Inc, Rockville, Maryland 20850 USA. Work supported by the US Energy Research and Development Administration. Paper received 20 March 1978.
CRYOGENICS. JULY 1 9 7 8
0011-2275/78/1807-040552.00
expected in large superconducting magnets such as those proposed for fusion plasma confinement systems. The experiments were, however, designed to provide sufficient understanding of the source of the Apo so that extrapolation from the data to more extreme conditions would be based on reasonable models. It appears that the scope of the work accomplished under this programme was indeed sufficient to provide a reliable basis for specifyin~ the optimum purity and heat treatment of the copper to bepurchased, and to obtain estimates of the increase in Po during cyclic straining of any particular copper during magnet operation.
Experimental detail Tension-compression apparatus. The stress cycling was produced by an Instron mechanical testing machine, Model TTOCM-L with crosshead speeds from 0.03 cm min -1 and a load capability to 10 000 kg. Fig. 1 is a schematic representation of the assembly. Massive copper test samples were coupled to the load cell in the f'txed beam of the machine and the lower grip end was attached to an outer sleeve that moved up or down with the moving beam. Lateral movement of the sample was restricted by a flexible diaphragm through which the load cell coupling rod moved in the push-pull mode. The assembly was immersed in liquid helium contained in a cryostat fixed to a flange on the moving beam. Strain gauge and electrical resistivity measurements. Four strain-gauge resistors (SR-4 FNB-12-35) were glued to the closed end of the 'U' clamps, with one resistor on each face of both clamps. A resistance bridge constructed from the four strain-gauge resistors determined the strain amplitude. Fig. 2 is a block diagram of the instrumentation used to measure electrical resistivity and stress-strain characteristics of the specimen during cycling. The electrical resistivity of the specimen was obtained by means of the standard four-probe dc technique. With the 0.635 cm
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original billet, but metallographic examination indicated that the final reduction to 1 in (2.54 cm) diameter was a cold work operation. This group consisted of four samples. Another rod from the same vendor, also 1 in (2.54 cm) diameter, was further cold-rolled to 5/8 in (1.59 cm) diameter prior to machining,and yielded eight samples making up Group 3 of Table 1. The stock for Group 4 was similar in history to Group 3, but was obtained from a different source. It should be noted that the rrr for Groups 2, 3 and 4 samples were within a relatively narrow range extending from 212 to 233, reflecting the C 101 impurity composition and the fully annealed state. For Group 5, however, the rrr values in the annealed condition varied from 110 to 200, reflecting the non-uniform distribution of the second-phase impurities in the free-machining grades.
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Stress-strain cycling modes. Fig. 3 is a typical stress-strain diagram for a specimen subjected to 600 constant-strain cycles. When cyclic stresses in excess of the elastic limits are applied to a specimen, the stress-strain curve forms a 'hysteresis' loop. In this report the loop width at zero stress is defined as ep, the amount of plastic strain in the cycle. As cycling progresses, the interactions between dislocations and the point defect production during plastic straining cause work-hardening of the material with a progressive decrease in ep, ie, the stress-strain loop continually narrows during cycling. The specimen will quickly approach a completely elastic behaviour if the cycling continues for several periods at constant load. At constant
Current lead
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sample gauge diameter and 2 cm gauge length a A#o of 0.2 nI2-cm could be readily detected.
E
=-
Description of copper samples. The primary UNS grade l that was considered in this study is that designated C101, with OFE (oxygen free electronic) designation. Some tests were also carried out with a free machining grade designated C147, containing between 0.20 and 0.5% sulfur, and also with a very high purity research grade containing 99.999% copper (designated in this report as 5N). One of the principal results of this study is that the fabrication history of the material, as it affects the preferred orientation of the grains, is a very important factor in determining ~o o with strain cycling. Consequently, the description of the different groups of samples listed in Table 1 contains the known history prior to machining of the samples from the raw stock. One group of C 10I (#2 of Table 1) samples were machined directly from the rod as received from the vendor as a 2.54 cm diameter rod. This rod was presumably 'hot rolled' from the
406
% Strain, ¢x102
0.20
Fig. 3 Stress-strain diagram for a Group 2 sample subjected to 600 constant-strain, push-pull cycles. Strain notations are • t and ~p, the total strain per cycle and the loop width or plastic strain per cycle at zero stress.
CRYOGENICS.
JULY 1978
T a b l e 1. H i s t o r y o f c o p p e r s a m p l e s f o r c y c l i c s t r a i n s t u d i e s
Anneal after machining Sample group
Source
Grade or UNS #
Fabrication before machining
Asarco
5N
Utility Brass Co.
Temp, °C
Time, h
rrr
Annealed as received,* 3/4" diameter
400
7
2200
C101
Received as cold rolled** 1" diameter
385
8
223
Utility Brass Co.
C101
Cold swaged from received* 1" to 5/8" diameter
385
8
212
Amax Corp.
C101
Cold swaged from received* 1" to 5/8" diameter Cold rolled to 5/8" diameter
400 385
6 8
233 229
Sample ~1
Cold rolled to 5/8" diameter
650
6
200
Sample
Cold rolled to 5/8" diameter
350
6
110
Sample
Cold rolled to 5/8" diameter
450
6
135
Sample
Cold rolled to 5/8" diameter
650
6
156
Sample
Cold rolled to 5/8" diameter
--
-
75
Sample #6
Cold rolled to 5/8" diameter
-
-
75
Stock, free machining C147
* as delivered from source ** approx. 10% reduction in area by vendor 1 in=2.54cm
strain, however, the work-hardening is reflected in the added stress per cycle to produce et, and ep decreases to a constant non-zero value. The intent of the present study was to primarily determine the Ap developed for constant et values between 0.10% and 0.30% strains. Before the constant strain studies with ofe samples, several exploratory runs were carried out with Ap and work hardening observations during constant load cycling of the very pure 5 N grade copper (Table 1). The actual mode and amplitudes of stress and strain are presented in the results.
of the initial load-strain loop at zero load was nearly a s large as the total strain in the first half cycle. The loop width at zero load, or total plastic strain, ep, decreased rapidly with work-hardening to less than 50% of the total strain after 220 cycles as shown in the dashed curve. The Po vs N curve reflects the rapidly decreasing ep per cycle as it approaches an apparent saturation value at N = 500. In this case, the Pd 2.5 Poi, wherepoi is the initial po. Seventyfive percent of the t~ial Pd is produced by N = 200, where dPo/dN decreased rapidly.
The recovery or loss of/Xp by wanning was not investigated by a systematic isochronal annealing study. The results reported here are due to observations made after overnight or over several, day, warming excursions, because of interruptions with the cycling experiments. These annealing observations are perhaps a reasonable approach to simulate the recovery that will take place during wanning of magnet coils during service by comparison with annealing spectra following irradiation damage or single crystal mechanical deformation. However, the observations are clearly insufficient to establish the mobility of the point defects.
The effect of wanning to 185 K during a 15-h interruption after constant-load cycling is shown by the vertical dashed line at N = 800. The anneal caused a recovery during wanning of about 1 n~2-cm in Po measured at 4.2 K after the annealing. This was about 20% of the total Pd- The anneal also evidently caused a strain-aging effect, in which the point defects migrate to the dislocations causing an increase in the yield stress by dislocation pinning. This appears to be the same effect observed by Blewitt et al2 and by Birnbaum 3 after unidirectional strains and by Hull 4 and by Johnson and Johnson s after cyclic strains. The subsequent increase in Po in Fig. 8 at N > 1000 is the result of increasing the load gradually withN, so as to increase et to 0.3%.
Results
Constant peak load. Most of the constant-peak-load experiments were carried out with the Grade 1 copper. Typical results are shown in Fig. 4 for a rrr of 700. As shown in the load vs strain curve in the inset of Fig. 4, the total strain during the first 1/4 cycle was about 0.14% and the sample was subsequently cycled between constant load limits of +175 kg. (The load may be converted to stress units ofMN m -2 or psi by multiplying by 0.309 MN m -2 and 43.8 lbs kg -1 in -2 respectively). The width
CRYOGENICS. JULY 1978
=
Load-unload cycling. Fig. 5 shows Po vs N with the loadunload cycling of a high purity copper sample. These data were obtained by introducing a total strain of 0.3% and then cycling between strain limits of +0.3% and +0.1%; the lower strain limit occurred at zero load. The cycling conditions of the first 1 1/4 cycles are similar to the loop shown in the insert. Most of the increase in Po occurs in the first 1/4 cycle with about O. 18% plastic strain. Subsequent
407
decreases from approximately O. 12% in the first full cycle to 0.055% a f t e r N = 500.
200 ,f 150 -
In Fig. 6, the peak stress, loop width at zero load and the increase in resistivity Pd are all plotted as a function of N at et = 0.20% for this Group 2 sample, q'ypical data have the following general properties:
100 After 40 cycles ----"J -50 -100
// ~
After 220 cycles
1. The increase in Pd has three different stages. For N < 30 (Stage I), Pd increases rather rapidly with an average value o f d p d / d N = 5.5 x 10 -2 nI2 2m cycle -1 . The region of 50 < N < 200 (Stage II) is a transition region from the rapid increase of Pal to a linear increase in Pd with an average slope dpd/dN = 2.8 x 10 -2 n ~ - c m cycle -I . For N > 200 (Stage III), the increase in Pd is linear (dPd/dN = 1.3 x 10 -2 n~2 cm cycle -1 is a sonstant).
I/ /
-150 -200 -0.16
J
t -0.08
I
J 0 Strain,%
I 0.08
I 0'16
10
2. Two days at 300 K after cycling to N = 500 is sufficient to anneal out the Pd produced in the Stage III o f the cycling process. After another 100 cycles, it is shown that one day at 300 K is not enough to remove the defect production of Stage III. In this particular sample the increase in Pd after each annealing was linear with the same value o f d p d / d N = 1.3 x 10 -2 n~2 cm cycle -1 as
9 8 7 uE
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Fig. 4 T o t a l resistivity and f r a c t i o n a l change with 1 - constantload cycling t o N = 800, as in load-strain diagram, 2 - warming t o 185 K a f t e r N = 800, 3 - c o n t i n u a t i o n o f cycling at 175 kg load and 4 -- gradual increase in load per cycle so as to achieve e t = 0.30%. Initial r r r = 7 0 0 0
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1
_2OOl
load-unload cycling involved ep < 0.10% and, thus very little increase in Po. It should be noted that the simple load-unload cycle for the copper matrix would apply to a magnet structure with no steel hoop structure and insignificant load bearing by the superconducting filaments. As the amount of steel reinforcement and/or superconductor is increased, the amount of compression in the copper will increase, assuming no plastic yield in the structural or superconductor materials. With sufficient structural material the compressive strain on unloading will be significant and give rise to wider loops and more increase in Po. In addition, the coldworking in the copper will no longer restrain et, since the total strain will approach that in steel subjected to a constant load in the elastic range, ie, a constant strain.
General characteristics of constant-peak strain cycling results. The stress-strain plot of Fig. 3 represents the constant peak strain mode for a C101 sample of Group 2 where the constant peak strain, et, is 0.20%. Although the stress-strain curve during the initial 1/.4 cycle is typical of easy glide behaviour, the character of the curve changes rapidly during the first few cycles. The stress to produce et = 0.20% increases from about 61.25 MN m -2 in the fully annealed state to about 102.9 MAr m -2 during the initial 100 cycles. The other rapidly changing parameter is the loop width at zero load, or the ep per cycle, which
408
t I 0"2 0.4 Strain . %
0.11
I 5
I 10
I 15 N, Cycles
I 20
I 0"6
I 25
I 30
Fig. 5 T y p i c a l Po versus N p l o t f o r load-unload cycling, as indicated in load-strain diagram
150
C101 Group 2,et =0"20% 11.C 10"C 9-0 8.0 7-0 E u 6'0 50 4.0 30 20 1.0
log
iO N ,
0
E
100
,
200
,
300
l,
400
, .... ,---, 5O0 6OO 70O
N, Cycles
Fig. 6 Defect resistivity (left scale), peak stress per cycle (right scale) and l o o p width at zero load, ep, as a f u n c t i o n o f n u m b e r o f constant-strain cycles at et = 0.20% f o r G r o u p 2 sample
CRYOGENICS. JULY 1978
Table 2. S u m m a r y of average Pd increase per cycle during constant-strain cycling, arranged in increasing total strain per cycle, et et, %
Sample group
rrr
~pd/~N (Units
of 10 ~ n ~ cm/cycle)
N = 0 + 30
N ~
30
0.05
5
75
0
0 (0 -
0.10
2
223
0
5
156
3
2.5 (300 0.5 (300 -
0.15
2
223
2.3
2.3 (0 -
600)
0.175
2
223
6.3
6.3 (0 -
350)
0.2
1
2200
29
2
223
55
3
212
39
4
233
34
4
236
40
4
237
5
200
42 36 45
2 3
150 223 206
23 80 70
4
229
70
4.1 (150 - 275) 6.8 (after 300 K anneal) 28 (50 - 190 13 (200 - 700 13 (100 - 200 10 (250 - 400 11 (150 - 300 5.5 (400 - 700 12 (150 - 300 6.5 (40O - 7O0 13 (150 - 300 20 (50 - 100 15 (70 - 250 1 2 ( 3 0 0 - 500 16 (80 - 280 26 (200 - 380 2 0 ( 1 5 0 - 200 14 (300 - 950 12 (500 - 700
5
110
370
100 (7O -
O.3O
0.42
before annealing. This behaviour indicates that the sample remains in Stage III during and following the anneal. 3. The peak stress and the loop width at zero load vs N show the work hardening during the cycling. As is the case with dpd/dN, the work hardening rate is very large in the first 30 cycles and decreases rapidly to a relatively constant rate above N = 200. In contrast to dpd/dN there is no clear separation of stages in the work-hardening rate before the first anneal. 4. The anneal-hardening, or strain-aging, effect after 2 days at 300 K is clearly observed by the increase in the peak stress for 0.20% et and the decrease in ep. The progression of work hardening after the initial anneal differs from that of Pd in that there are virtually no changes in peak stress and ep after the first annealing and that the subsequent anneals have no significant effect on work hardening.
Effects of impurities and fabrication history on results of constant-strain cycling. The results of constant-strain cycling at et = 0.20% for the different groups of samples listed in Table 1 are shown in Figs 7, 8, and 9. The values of dpa/dN at different stages of work hardening of all samples tested are given in Table 2. The increase in Pd with N is generally similar to the variation of Pd in Fig. 6. For a given N in Fig. 7, Pd for different samples can be divided into three different categories: Group 2 samples show the highest increase, the lowest increase is in Group 1,
C R Y O G E N I C S . J U L Y 1978
8200) 55O) 1600)
80)
and intermediate increases are found for Groups 3, 4, and 5. Although the relatively low rate of increase in Pd of the high purity copper (Group 1, Fig. 9) suggests that impurity content may be an important factor in explaining dpd/dN, the outstanding differences between the Group 2 samples and the Group 3 and 4 samples shows that other factors are of much greater importance among commercial grades. C101, Group o C147, a C147, £101
12
et= 0"20% Z days at 300 K
11 10
. cioi,
90
' C101, o C101,--
~
\
~ ~
\ \
2dm/satT?K
8'C
~ 7-C 6"C 4-C 3"£ 2'C 1.£] 0
. ¢ " ~
2 days at 300 K
~ '
9 months at 300K 1(~0
I 2(~0 I
3~0
I
4~)0 I
I 500
'
I 600
I 700 I
N, Cycles Fig. 7
D e f e c t resistivity, Pd, as a f u n c t i o n o f constant-strain
cycles at e t = 0.20% f o r 8 samples representing each o f the five groups listed in Table 1
409
unlikely that the small differences in grain size among the C 101 materials were at all influencing the final results. As testimony to the absence of grain size effects among the commercial samples, the average grain size in the annealed C147 samples (Group 5) was significantly larger (0.065 mm) than in the C101 samples. Nevertheless, the Pd values at N > 0 (Fig. 7) exceeded those for the samples of Groups 3 and 4.
140 120
q~ 100 ct = O' 20% i~
~
° C101 Group 2
!
o c1~7
5
II |
zx o • • v
5 4 4 4 3
'
4O 20 I
0
Fig. 8
I 100
I
I 200
I
I I I 300 400 N , Cycles
t
r
C147 C101 C101 C101 C 101 I 500
I
I 600
I
I 700
Stress per cycle to p r o d u c e c o n s t a n t strain a m p l i t u d e of
0.20% for samples representing G r o u p s 2, 3, 4, and 5 Ct = 0'20% o A o • • • v
0"3C
~ 0-20
CI01, Group 2 C147, C101, C1~, C101, C101, C101,
"
5 4 4 4 4 3
7~ 0.1C I
I 100
I
I 200
I
I I I 300 400 No Cycles
I
I 500
I
I 600
I
I 700
Fig. 9 Progressivedecrease in loop w i d t h at zero load, or ep, w i t h increase in N f o r e t = 0 . 2 0 % in samples representing Groups
2 , 3 , 4 , and 5
Unlike the sample from Group 2, the 5 samples from Groups 3 and 4 that were cycled at et = 0.20% all showed p d values of(6.5 -+ 0.5) nI2 - cm or about 60% of that in Group 2 samples at N = 500 cycles, even though the starting rrr values were essentially the same. The increase in the peak stress for et = 0.20%, with N, is also considerably higher for the Group 2 sample, as is expected for a correlation ofpd and work hardening. A similar effect of fabrication history is observed for the samples cycled with constant peak strains of 0.30% (Fig. 10). The first CIO1 sample cycled at this et was from Group 2, whereas the other 2 samples tested at et = 0.30% were from Groups 3 and 4, respectively. A t N = 380 the Pd for the former sample (Group 2) reached 14.5 nI2 - cm, whereas for the latter two samples Pd was between 10 and 10.5 nQ - cm. Unlike the case of et = 0.20%, the difference in work-hardening parameters between Group 2 and the other two groups shows up only above N = 200. The effort to understand the very significant differences between Group 2 samples and the other CIO1 samples involved grain size studies, spectrochemical analyses of vapours from oxidized samples and a cursory search for differences in texture caused by the differences in fabrication prior to machining. The recrystallized grain sizes in all the C101 rods (Groups 2,3,4) were all within the range of (0.040 -+ 0.005) mm, with the Group 2 samples at the lower end. The high purity samples (Group 1) on the other hand, had starting grain sizes varying from 2 mm to 3 mm. Thus the very large grain size could well account for the relatively low rates of work-hardening and dPd/dN values in the Group #1 high purity material. It is, however,
410
The spectrochemical analysis showed no significant differences in purity among the commercial grade materials that could account for the observed differences in the results. The largest quantities of the impurity elements were in the 10 to 15 ppm (by weight) range with total impurity content below 50 ppm. The texture differences among Group 2 and Groups 3 and 4 samples are inferred from a diffractometer scan of reflected x-ray intensities from transverse cross-sections of two machined samples in the recrystallized state. The results of this study are shown in Table 3 where the diffracted intensities relative to that of the (111) reflection in a powder sample are listed. For the Group 2 sample the most significant deviation from the random sample was in the (200) reflected intensity while the (111) and (222) reflections were about the same intensity as the random case. The Group 3 rod, in contrast, showed a significantly different intensity spectrum, with the (111) and (222) reflected intensities significantly greater than in the random case and with an integrated average deviation from random of 31% compared to 24% for the Group 2 rod.
Strain-amplitude ef[ects at constant strain per cycle. The effects of strain amplitude on the change in Pd per cycle and the work-hardening parameters were investigated to some degree over the range of 0.42% to .05%. The primary 20"0 . ~-.~.. ,..,....a-'~ N 950
15-0 ~
ct = 0"30% o C101group 2 A C101group3 a C1e group 4
2 days o~ 300 K
E 104 c~
~ 5-o 0
Fig. 10
1 0
200
0 400 N. Cycles
500
600
700
D e f e c t resistivity, Pd, as a f u n c t i o n o f constant-strain
cycles at e t = 0.30% for samples f r o m G r o u p s 2, 3, and 4
/ J
12°~/ u0F ~ l v^ '^v/ !
of
r/
9 C147,grot~5, Et =0.42%
~
o /
9"0 r ~ 8'0
7 `/
6"0}t
32.0
~
y
0
~
J
d
ct=0 30%
. ~ group 2
v/
tct=O 15%
'> J
¢t =0"175°/'
o / All C101 ct =0.20%
. . . . .
I
.
~
o1
~c~ ~ I .~,i
H dayat 300K
a
y
s
1 0 " D 0
¢ -0"10%
at 300K ,,-..ll---.-"~ r 100 Z00
I 300
I 400 N. Cycles
I 500
I 600
I 700
Fig. 11 C o m p a r i s o n o f Pd increase w i t h N f o r d i f f e r e n t constantstrain a m p l i t u d e s
CRYOGENICS . J U L Y 1978
Table 3. Reflected intensities from 20 scan of plane perpendicular to rod axes of recrystallized samples Group 2 Machined from As received /
Powder / R
C101 group 2
8 0-3
o e t = 0.30 %
o
v c t = 0-20 %
0.2
Group 3 Swayed to 75% Ra before machining /
= ~;t =0.10 % 2 days at 300 K
~ 0.1 t00
111
100
107
129
200
46
64
43
220
20
10
4
311
17
11
12
222
5
5
8
400
3
3
3
331
9
5
4
420
8
3
5
208
208
208
.240
.308
R - ~l/R - / I
objective was to determine whether the changes in dpdldN at higher amplitudes are continuous or catastrophic at N < 1000 cycles and to ultimately predict whether any significant effects will occur at high frequency low amplitude conditions. The curves for 0.20% and 0.30% amplitude differ in character from the 0.10% strain amplitude curve in that, in the latter case, the initially rapid increase in Pd and work-hardening parameters are not observed (Figs 11, 12, and 13). At e t = 0.10% the initial plastic strain per cycle is only about 0.02%, so that over 50 cycles are necessary before a significant change in Po is observed. Another unique aspect of the curves for e t <( 0.20% (Fig. 11) is that dpd/dN increases with N for the initial 730 cycles at 0.10% and for the continuation of cycling at 0.150% and 0.175%. The relatively small decrease in Pd during the 300 K anneal after both 0.10% and 0.17% strain amplitudes indicates that most of the resistivity is derived from dislocations rather than point defects. The experiment at e t = 0.42% was carried out with a sample from Group 5. The conclusions drawn from this one test indicate that defect production during the initial cycling 150
100
~
300K
E
C101 group 2 = ct =0-30% o c t =0,20 %
mm 5O
a ct =0, 10 %
,& N, cycles
Fig. 12 Comparison o f peak stress increases for Group 2 samples w i t h d i f f e r e n t et
CRYOGENICS. JULY 1978
2OO
3O0
400 5O0 N, Cycles
6OO
700
Fig. 13 Comparison of ep versus N plots for Group 2 samples w i t h d i f f e r e n t et
16 ~N= 400 14
E
8
c:
0?6
0'10
0.20
0"30
0.40
Constant strain amplitude, Et % Fig. 14 Defect resistivity as a f u n c t i o n o f et per cycle at N = 30, 200, and 400 cycles. All data f r o m Group 2 samples, except for point at e t = 0.42%
stage at this level of constant strain amplitude is catastrophically larger than at 0,30%. This is shown when #d is plotted as a function of strain amplitude. (Fig. 14). The data indicate that Pd is relatively unimportant at et < 0.15% and that the important contributions begin for e t > 0.175%. The data further indicate that the rate of increase in Pd with et becomes very large above 0.30%. This point should, however, be further investigated, especially for the larger N values. Since work-hardening and, therefore, closing of the stress-strain cycling loop should occur rapidly at higher et, it may be expected that saturation in Pd will occur at relatively low N values.
High frequency cycling at low amplitudes. An important objective of this study was to evaluate the possibility of degradation in the magnet conductor caused by high frequency low amplitude stresses that may arise during operation. Two experiments were carried out with N > 1000, but with et of 0.01% and 0.05%. The first was carried out with
411
the sample of Fig. 6 after N = 680 cycles at e t = 0.20% and a 2-day anneal at 300 K. After 3300 cycles with et = 0.01% no increase in Pd was observed. This is to be expected since no plastic strain was detectable in the already work hardened sample. The second test was carried out with a sample from Group 5. The results are summarized in Fig. 15. This annealed sample was first cycled to N = 50 cycles at et = 0.10%, with ap d of 0.48 n ~ - cm. This is a relatively large Pd compared to that observed for the same e t in the C 101 material (Fig. 11) and is an indication that Pd may be impurity-sensitive in the O. 10% strain region. A f t e r N = 50 cycles the et was reduced to 0.05% per cycle for 8200 cycles at a rate of 3 s cycle -1. The total Pd increase was 0.1 nI2 - cm. A f t e r N = 8200, et was increased to 0.10% for 5 cycles; the Pd increase was about the same as in the previous 8200 cycles at 0.05% strain. Constant-strain cycling o f cold worked copper. Two experiments were carried out with samples of Group 4 that were not given a recrystallization anneal after machining and had rrr values o f 53. No significant change in Po was observed after N = 300 cycles at et = 0.20% or 0.30%. For the 0.20% amplitudes the deformation was totally elastic with constant peak stress values of 285 M N m -2 . For et = 0.30% the first three cycles involved a small plastic strain.
This appears to be a reasonably safe assumption for at least the first 3000 cycles at e t = 0.10 and 0 . 2 0 % , but this rate may perhaps be decreasing at et = 0.30% to somewhat lower values than measured here. As an aid in estimating PO in C 101 grade copper, Table 4 lists estimated values of Pd for N = t 000 and n = 2000 cycles for et values of O. 10%, 0.20% and 0.30%, respectively. For C101 material with history similar to Group 2 of Table 1, Pd can reach ~ 5 0 n ~ cm after 2000 cycles at et ~ 0.3%. For the < 1 1 1 > texture, however, the same conditions should produce only 29 n ~ cm, which is a substantial reduction that can be achieved by careful specification of metallurgical history. The importance of the Pd values listed in Table 4 relative to the initial impurity resistivity, Pi, is quite large. For example, if et is limited to a maximum amplitude of 0.10%, the Pd afte~r 2000 cycles will exceed the starting Po and the ratio Pd/Po can reach a factor of 7 at et = 0.30% for 2000 cycles. Relative to transverse magnetoresistanceS, Pro, the indicated Pa values are not overwhelming but are still quite significant. Some examples of the effect of Pd on the total Po, based on Po = Pi + P d
are used to illustrate the relative importance during operation of 40 kG and 100 kG magnetic fields. For the former case, withPm ~ 15 n~2-'cm, and 1000 cycles at et 0.20%,
Discussion of results
Po = (7 + 17.8 + 15) n ~ - c m for < 1 0 0 > texture
Application of data to magnet design Prediction o f Pd in C101 grade copper. In this study we have attempted to at least qualitatively survey the increments in Pd, developed under several possible modes of deformation cycling, and to find those variables in the cycling parameters and in metallurgical history that are most effective in determining ad in copper. The basic parameter in determining Pd is ep, the plastic strain per cycle. It is quite clear from Figs 11 and 15, that even very small but consistent ep values of 0.01% (ep = 10 .4) will begin to produce a significant increase in Pd after several hundred cycles. If the magnet design is such that constant-strain cycling will indeed result from energizing -de-energizing cycles, the present data can be readily used to predict Pa accumulation at et levels of 0.10% to 0.30%, assuming that dpd/dN values remain relatively constant after N = 300.
w
f
c ._
~.
E
+ Pm
= (7 + 9 + 15) n ~ - c m for < l l l > texture. For the <1003> texture, Pd/Po ~ 0.45, whereas for the < 1 1 1 > texture, Pd/Po ~ 0.31. At 100 kG, with Pm estimated at ~ 4 0 nQ cm, the Pd/Po ratios are still about 0.29 and 0.15, respectively. In terms of material (copper), cost and weight for a given conductor length and maximum allowable resistance heating (I 2 R), the volume of copper required is directly proportional to Pp. A Pd/Po ratio of 0.10 increases the required volume by roughly 10%, if the heat capacity and surface area increases are neglected. Application o f work-hardening data. The data on the increase in tensile stress to produce a given constant strain per cycle are the only quantitative data for copper at 4.2 K and are clearly needed in the evaluation of the stress-strain data for superconducting composites in
C group 5 tt 147. = 0-10% ~
G1 0-05 % for interval
t/3
"0 n 70 ~
Table 4. Defect resistivities, Pd, from constant strain cycling at 4.2 K, as calculated from measured dpd/dNvalues for C101 grade copper
a
1000 cycles E
3"
et I 100
I 200
I I 300 400 N, Cycles
i 500
i 600
I 700
Fig. 15 Test of low-amplitude, high-cycle fatigue conditions on one sample of Group 5. Cycling at Et = 0.10% was interrupted at N = 50 cycles by inserting 8200 cycles at et = 0.50%. Effects of interruption were removed by 300 K annealing
412
2000 cycles
8200' cycles ot ~1 = 0.05%
0.10% 0.20% 0.30% 0.10% 0.20% 0.30%
Pd (n~2 cm) < 1 0 0 > or random texture 4.1
17.8
23.6
8.56
9.0
~17.0 --
30.8
51.6
Pd (n~2 cm)
<111>texture
--
15.5
29.0
CRYOGENICS . J U L Y 1976
160~150I140~130r 120l% 110~-
/ // ,/
Group 2
,' ,' I
~
a~
-
Group 4,
- 90t / 80
"
f
J
I
,oi'/f =I"//
F:~]~~I~
0.05
I
I 0.10
I 0.15
I 0-20
I 0-25
I 0.30
I 0.35
I
0'40
Fig. 16 Plots of peak stress per cycle, ot, as a function of accumulated plastic strain, :~Ep, for the three different groups of C101 samples. Dashed curve is tensile stress-strain data. s
service. The work hardening at e t > 0.175 % strain/ cycle is very significant during the first 200 cycles and one can expect to observe a significant effect on the yield stress and perhaps the overall et of the composite for a given constant stress if the volume ratio of steel to copper is relatively small. The need for these data becomes most apparent in that the increase in work hardening cannot be predicted from literature data for unidirectional deformation at 4.2 K, as given in Refs 2 and 7, for example. Although the initial stress values do indeed correspond to the yield stress values for fully annealed copper, s the increases in work-hardening with the number of cycles are considerably smaller than expected from a comparison of stress vs total plastic strain, where total ep is obtained from the summation of ep over N for all of the data. The plots of peak stress per cycle vs ~ ep for the several cyclic constant-strain experiments carried out in this study are shown in Fig. 16. The data plotted represent experiments with samples of Groups 2, 3, and 4 and et values of 0.20% and 0.30%. The Group 2 samples clearly show higher rates of work hardening than are shown by the Groups 3 and 4 samples. Within each group, the data for the two e t experiments (0.20% and 0.30%) overlap, indicating that the total cyclic strain is indeed the prime factor in (1) determining Pd and (2) the stress to produce a given total cyclic strain. The curve plotted as a dashed line represents unidirectional tensile stress-tensile strain data for polycrystalline ofe copper s tested at 4.2 K. When compared with the cyclic strain curves the difference in work-hardening mechanisms and/ or magnitudes becomes clear. Small amplitude cyclic strains do not produce the hardening that results from continuous unidirectional straining. This is clear in the initial cycling regime but the most important difference is in the relatively rapid decrease in the cycling stressstrain slope near Y, ep = 0.10 and the indications of near ~aturation at ~. ep of 0.30. In contrast, the typical unidirectional stress strain curves for either polycrystal or single crystal deformation at cryogenic temperatures show stage 3 work-hardening beginning at ep > 0.30. This, design data for evaluating strains resulting from magnet stresses should be carefully evaluated with respect to the difference between cyclic and unidirectional deformation. Another important application of the present data is to the relatively unpredictable effect of 300 K annealing on the work hardening at 4.2 K. Although the increased
CRYOGENICS. JULY 1978
stress to produce a given strain is in line with previous observations of strain-aging, 2~ the saturation after annealing shown in Fig. 8 is unexpected and not consistent with Pd data. The latter data indicate that rate of point defect production deformation after annealing is similar to that before annealing. Further work hardening is, on the other hard, severly diminished. This is one important effect that shows that the Pd increase is not simply related to work hardening. Another effect that is of similar importance is the observation that there is an abrupt increase in work-hardening after 77 K annealing, whereas no significant effect on Pd is observed. It appears that periodic warming of a magnet to T > 240 K will have the effect of not only decreasing Pd, but also arresting the rate of work hardening. It also appears that further basic studies of work hardening in copper, and in other metals at 4.2 K are needed to enable reliable prediction of stressstrain response as affected by texture differences and periodic annealing during magnet operation.
Application to basic studies of deformation-induced point defects. The value of the present results, in relation to point-defect research, is that they provide a quantitative basis for modelling the point-defect production from the dislocation interactions during cyclic deformation. 9 The two observations of primary importance in this respect are: 1. the indications of a constant dpd/dN for a given et, after an initial rapid work-hardening, and 2. the 300 K annealing experiments, where the fraction of #d that is lost is that part accumulated during the constant dPd/dN stage. A third related factor is that dPd/dN, after workhardening and 300 K annealing, appears to be the same as during the pre-anneal cycling. There thus appears to be essentially two distinct stages of defect production in constant strain cycling where stage one is associated with dislocation production and work-hardening by dislocation interactions. This stage corresponds to the dislocation bundling or clustering stage described by Basinski et al. ~° At the levels of et at 0.2 and 0.30% the extent of this rapid work-hardening stage is dependent on texture. For the light texture (Group 2) Stage 1 appears to extend to N ~ 250 cycles, whereas the strong < 1 1 1 > texture provides several sub-stages a t N < 500 cycles. Stage two is, of course, characterized by the constant rate of point defect production per cycle. This again is consistent with the metallographic observations of Basinski 1° where the accumulation of mottled areas between dislocation bundles is described. The remarkable inference of the present data is that the rate of point defect produced per cycle seems to depend only on the strain ep and is not directly related to the increase in stress to produce et. The absence of dependence on stress is similar to what has been reported for some experiments with unidirectional tensile deformation, 9 where pdccen; it is clearly not consistent with the more widely accepted Saada relation, 11 where Pd foe ode. The latter presumes that the strain energy is the important factor and that the point defects are produced by a mobile dislocation cutting through a stationary forest of dislocations.
Defects per cycle. The basic information that is useful for analysis of the point defect production process is dpa/dN in the range above the initial work hardening stage, ie, N = 300 cycles at e t ~ 0.20 to 0.30%. Since ep per cycle is relatively constant, the value of Z~od for each cycle reflects the mechanism by which defects are
413
produced. A parameter of principal interest is the number of defects produced during each cycle. For the Group 2 material we have established that Z~oa for each cycle at et = 0.20% is about 0.013 n~2-cm. Assuming z2kod is from point defects only and that 1 a/o Frenkel defects produces 2.0 b6"~-cm12 , the concentration of defects per cycle with et = 0.20% and ep ~ 0.05% is 0.65 x 10 -7. For et = 0.30% and ep ~ 0.10%, ~ o d per cycle is 2.6 x 10 -s ~"Vcm or about 1.3 x 10 -7 defect concentration. For the < 1 1 1 > textured samples the defect concentrations per cycle are about one-half those of the Group 2 samples. These concentrations are consistent with the conclusions 9 from unidirectional deformation data where it is estimated that ep = 1% produces a point defect concentration of 10 -~ and ep = 10% gives 10 -s . This programme was initiated as part of the programme entitled 'Materials Research in Support of Superconducting Machinery', ARPA Order No 2469. All efforts on this phase of the programme beyond October 1, 1974 were supported by a contract with the Magnetics and Superconductivity Section, Fusion Energy Division, Oak Ridge National Laboratory, operated by Union Carbide Corporation under contract to the US Energy Research and Development Administratxon, and by the Division of Physical Research of ERDA. The authors are indebted to the following for their participation and interest: J.B. Darby and R.W. Siegel (ANL), A.P. Clark and R.P. Reed (NBS, Boulder), M.S. Lubell and W.A. Fietz (ORNL) and John Purcell (GGA).
getting asood canbevery rewarding And you can get a GOOD COLD (room temperature to 10 kelvin) in about half an hour, with an LTS-21 Series closed cycle refrigerator system. Depending on the system you choose, your cold can be stable to +_0.5 kelvin or to _+ 0.003 kelvin. You can even get t w o colds at the same time for a lot less money than ever before. The new universal compressor supplied with all LTS-21 systems can power t w o cold heads simultaneously without sacrificing performance.
References
1 2
10 11 12
A complete tabulation of UNS and CDA letter designations with chemical composition limits is in the Application Data, Copper Development Assoc, New York Blewitt, T.H., Coltman, R.R., Redman, J.K., Defects in crystalline solids, The Phys Soc London (1955) Birnbaum, H.K., JAppl Phys 34 (1963) 2175 Hull, D.,Phil Mag 3 (1958) 513 Johnson, E.W., Johnson, H.H., TransAIME 237 (1965) 1333 Banz, M.G, JApplPhys 40 (1969) 2003 Pearson, W.B., Phys Rev 97 (1955) 666 Warren, K.A. and Reed, ILP., NBS Monograph 63, US Government Printing Office, Washington (1963) Beukel, A. van den, Vacancies and Interstitials in Metals, Schilling, W. et al. eds North Holland Publishing Co (1969) 427 Basinski, S.J., Basinski, Z.S., Howie, A.Phi~ffag 19 (1969) 899 Saada, G.,Acta met 9 (1961) 166 Ehrhatt, P., Schlagheck, U. J. Phys F 4 (1"974) 1589
Features:
Fast cool down (300 K to 10K in about half an hour) Smaller size State-of-the-art instrumentation System flexibility Capability to operate two cold heads simultaneously from one compressor Long maintenance interval To l e a r n m o r e a b o u t a GOOD COLD write or call: In Europe: Cryophysics Berinsfield, England (856) 340257 Darmstadt, W. Germany (6151) 74081
Geneva, Switzerland {22) 329520 Versailles,France (1) 9506578
In North America:
O
LRRESHORE (RYOTROnI(|,Int.
P.O. Box 29876 Columbus, Ohio 43229 (614) 846-1250Telex: 24-5415 Cryotron Col
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CRYOGENICS. JULY !978