D.P. Hampshire, P. Foley, H.N. Niu and D.M.J. Taylor

Transcription

1 The effect of axial strain cycling on the critical current density and n-value of ITER niobium-tin VAC and EM-LMI strands and the detailed characterisation of the EM-LMI-TFMC strand at 0.7% intrinsic strand D.P. Hampshire, P. Foley, H.N. Niu and D.M.J. Taylor Superconductivity Group, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK Contract Nos.: FU05-CT (EFDA/02-626) August 2002 August 2003 The top end of the strain probe, with the computer-controlled stepper motor (on the left).

2 i The effect of axial strain cycling on the critical current density and n-value of ITER niobium-tin VAC and EM-LMI strands and the detailed characterisation of the EM-LMI-TFMC strand at 0.7% intrinsic strand D.P. Hampshire, P. Foley, H.N. Niu and D.M.J. Taylor Superconductivity Group, Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK Contract Nos.: FU05-CT (EFDA/02-626) August 2002 August 2003 Extended Abstract There are four experiments outlined in this report: Benchmarking (Task (i)): The role of spring material on the axial strain measurements is reported. It was found that independently of whether the springs were made of Ti-6Al-4V (standard ITER material), Cu-Be, brass or stainless-steel the intrinsic strain dependence of the critical current for the EM-LMI strand was the same. Strain Cycling (Tasks (ii) and (iii)): Measurements have been made of the effect of axial strain cycling on the critical current density and n-value of two ITER candidate niobium-tin strands (EM- LMI and VAC). The strands were subjected to ~1300 strain cycles to incrementally increasing applied tensile strains, with 100 cycles per 0.056% increment. For both strands, there were no changes in the critical current density or n-value for the ~500 cycles up to 0.282% applied strain (except for the first cycle of the EM-LMI strand). Cycling to higher applied strains ( %) caused the critical current density and n-value to incrementally increase at all applied strains, with the critical current density eventually increasing by 5% 7% at 12 T and zero intrinsic strain. Cycling to applied strains above 0.677% (~0.4% intrinsic strain) damaged the strands. Detailed measurements on an EM-LMI strand at 0.7% intrinsic strain (Task (iv)): The fourth task consists of two parts. In the first part, the electric field-temperature (E-T) and electric fieldengineering current density (E-J) characteristics of an EM-LMI Nb 3 Sn superconducting strand were measured at an intrinsic strain of 0.7% in magnetic fields up to 15 T. It was found that the E-T and E-J data were equivalent, with E(J,B,T,ε) data points from the two different measurements agreeing to within ~20 mk: hence the engineering critical current densities and n-values calculated from the E-T characteristics were consistent with the values calculated in the standard way from the E-J characteristics. In the second part of this task, the engineering critical current density was measured and parameterised at 0.7%. The scaling law used to parameterise the data was of the form: C(,, ) ( ) C( )( 1 ) C2(, ) n p q J B T ε = A ε T ε t B T ε b ( 1 b) and BC2 ( T, ε) = BC2 ( 0, ε)( 1 t ν ),

3 where t = T/T C (ε), b = B/B C2 (T,ε), A(ε) is a strain dependent variable, T C (ε) is the effective critical temperature and B C2 (T,ε) is the effective upper critical field. At 0.7% intrinsic strain, J C can be parameterised by p = 0.5, q = 2, n = and ν = 1.533, where the (strain-dependent) variables have the values B C2 (0, ε I = 0.7%) = T, T C (ε I = 0.7%) = K and A(ε I = 0.7%) = Am 2 K 2 T 0.63, and for which the only significant differences from the data occur close to B C2. The historical ITER-Summers scaling does not describe the strain dependence of these data accurately. ii

4 iii Contents Extended Abstract... i Contents...iii 1 General Report Introduction Strand specification and reaction Mounting strands on springs Measurement procedures used Results Discussion/Analysis Future work Conclusions Acknowledgements References Benchmarking tests for the spring material using the EM-LMI Nb 3 Sn Strand Figures: Cyclic data on the VAC Nb 3 Sn Strand and the EM-LMI strand Figures: Characterisation of the EM-LMI Nb 3 Sn strand at 0.7% at intrinsic strain

5 1 1 General Report 1.1 Introduction Benchmarking In the last ten years, the superconductivity group at Durham has developed a probe to make critical current measurements as a function of magnetic field, temperature and strain. Detailed measurements were performed for ITER under contract FU05-CT (EFDA/00-515). The reliability of data obtained and benchmarking of results obtained is absolutely critical. The first task reported considers the role of the spring material in making variable strain materials and outlines the evidence for good agreement in the literature for data obtained in Durham and that obtained by other specialist International group Strain cycling Strain has a very large effect on the superconducting properties of Nb 3 Sn. In superconducting magnets, strain arises from the differential thermal contraction that occurs on cooling to cryogenic temperatures, and the Lorentz-forces that occur during high-field operation. The international thermonuclear experimental reactor (ITER) will use magnets made from cable-in-conduit conductors (CICC s) with Nb 3 Sn strands [1]. For these large-scale high-field magnets, knowledge of the effects of strain is extremely important. In addition, the ITER magnets will undergo many charging cycles (up to ), and so the effects of cyclic strain and fatigue also need to be considered. The axial-strain dependence of the critical current density [2-4] (and n-value [5]) of technical Nb 3 Sn strands has been measured extensively. The effects are generally found to be reversible, to first order, for small numbers of cycles over quite large ranges of strain, while at higher strains damage occurs to the superconducting filaments. However, the effects of large numbers of strain cycles within the so-called reversible regime has not been widely investigated. A study of bronze-route Nb 3 Sn strands stress cycled at room-temperature did not observe fatigue effects [6], nor did a study of CICC s subject to axial strain cycles at cryogenic temperatures [7]. In contrast, investigations of transverse stress cycling of CICC s [8] and cyclic charging of ITER model coils [1] have found some evidence of fatigue effects and in order to understand these results, accurate data for the component strands are required. The second and third task presented in this report is the first reported investigation of the effects of axial strain cycling (involving >1000 cycles) at cryogenic temperatures on the critical current density and n-value of technical VAC and EM-LMI Nb 3 Sn strands.

6 E-T versus E-J measurements at 0.7% for the EM-LMI strand Traditionally the current carrying capacity of superconducting strands is obtained by measuring their electric field-current density (E-J) characteristics and then parameterising the onset and increase in dissipation using the engineering critical current density (J C ) and the exponent of transition (n-value) respectively [9]. For technological conductors, J C and n vary as a function of magnetic field, temperature and strain [3, 5, 10]. However for very large superconducting coils such as the International Thermonuclear Experimental Reactor (ITER) model coils [11, 12] and the Nb 3 Sn cable-in-conduit conductors (CICC s) from which they are made [8, 13], an alternative method of characterisation is used which involves measuring the electric field as a function of temperature (E-T) while keeping the current density fixed. These variable temperature measurements are often preferred because of the greater relative ease of varying temperature in forced-flow-helium conductors and the constraint that no part of these large systems should be tested outside of their operating stress range. The current-sharing temperature, which is defined analogously to the engineering critical current density, is the temperature at which dissipation begins and is used to assess the performance of the coils, particularly in relation to the properties of the component Nb 3 Sn strands and their strain-state [14]. There are some measurements of the E-T characteristics of superconducting strands at low current densities to determine the effective critical temperature but very few at higher current densities [15]. It is generally assumed that E-T and E-J data are equivalent, with the electric field being a single-valued function of current density, temperature, magnetic field and strain. Nevertheless there is no fundamental reason for this equivalence since the critical current density of superconductors is not a thermodynamic property although the results of measurements on cable-in-conduit conductors (CICC s) show that one can expect fairly good agreement [8, 13]. Current-sharing temperature measurements have been reported for the ITER Toroidal Field Model Coil (TFMC) at a maximum operating current of 80 ka (111 A per strand), in self magnetic field (5.5 T to 7.5 T) and in a (net) background field (9 T to 9.5 T) [12]. In the TFMC, the Nb 3 Sn strands experience a large compressive thermal strain (mainly due to the stainless-steel jacket of the CICC), which to date has been considered to correspond to an intrinsic strain of approximately 0.7% on the superconducting filaments [14]. However as will be shown in this report, this calculated value of strain must now be considered in question. Since only limited data for this particular strand (made by EM-LMI) are available at these values of strain [3], the critical current density has so far been estimated by fitting scaling laws to the data available [2, 16] and extrapolating to the operating strain conditions [17]. This fourth task consists of two parts: a comparison of the E-T and E-J characteristics for the EM-LMI superconducting strand and a characterisation of the engineering critical current density and n-value of the EM-LMI strand close to what were believed to be the operating conditions used in the TFMC coil (i.e. at 0.7% intrinsic strain) as a function of magnetic field and temperature. The report concludes with a brief discussion of future work and the breakdown of the Summers-ITER comparison. 1.2 Strand specification and reaction Measurements were made on two different 0.81 mm diameter ITER candidate Nb 3 Sn strands: an internal-tin strand made by Europa Metalli-LMI (EM-LMI) and a bronze-route strand made by Vacuumschmelze (VAC). The strands were heat-treated in an argon atmosphere on (oxidised)

7 3 stainless steel mandrels in a large bore furnace with the temperature also monitored using a second thermocouple positioned next to the samples. The heat-treatment for the VAC strand was: Heat up to 570 o C at a rate of 100 o C per hour, dwell at 570 o C for 220 h, up to 650 o C at 80 o C per hour, dwell at 650 o C for 175 h and then back to room temperature at 100 o C per hour A number of considerations were relevant in deciding the heat-treatment of the EM-LMI strand. The heat-treatment recommended by Europa Metalli is the following: 210 o C/175 h o C /96h +650 o C/200h. Most of the I C measurements on samples in the literature were taken from billets manufactured for the ITER Toroidal Field Model Coil (TFMC) conductor (more than 200 billets were required) and were carried out after a reaction using the recommended schedule. However a shorter reaction schedule was applied for all the double pancakes of TFMC. This was done after a check that transport properties (critical current, hysteresis loss) were unaffected by the change. After correspondence with Dr. M. Spadoni and EFDA staff, it was agreed that the schedule actually used for the TFMC double-pancakes would be used for the measurements in Durham. The heat-treatment for the EM-LMI strand was (as used for the TFMC): 210 o C for 100 h, 340 o C for 24 h, 450 o C for 18 h and 650 o C for 200 h. The temperature was varied at a rate of 50 o C per hour throughout the heat-treatment. The step at 450 o C was introduced to clean out the residual gases released inside the TFMC cablein-conduit conductors. I C data for the witness samples reacted with the TFMC are shown in Table 1.1.

8 4 Table 1.1 Critical current measurements at ENEA on EM-LMI Nb 3 Sn witness samples delivered by Ansaldo after the reaction heat treatments of TFMC double pancakes. SAMPLE 11 Tesla 12 Tesla 13 Tesla 14 Tesla 14.5 Tesla n n n n n Bc2 (T) By Kramer plot NET A NET B NET C NET D NET E NET F* NET G NET H* NET I* NET L NET M NET HEAT TREAT. DP1 TFMC DP1 TFMC DP1 TFMC DP2 TFMC DP2 TFMC DP3 TFMC DP3 TFMC DP4 TFMC DP4 TFMC DP5 TFMC DP5 TFMC Standard by ENEA STANDARD heat treatment: 210 C/175h+340 C/96h+650 C/200h TFMC heat treatment: 210 C/100h+340 C/24h+650 C/200h Note: Actual heat treatment for TFMC DP s: 210 C/100h+340 C/24h+450 C/18h+650 C/200h * Low I C and n indicate a sample damaged by handling after reaction heat treatment Witness billet for FZK and ENEA: NET (April 24, 1999)

9 5 1.3 Mounting strands on springs After the heat-treatment, the chromium plating was removed from the strands using hydrochloric acid, and the strands were transferred to spring sample-holders using a purpose-built jig. They were then attached to the spring by plating (at room temperature) and soldering. In the benchmarking tests, four different materials were used to fabricate the springs. The brass, Cu-Be and stainless steel springs were plated with copper. The Ti-6Al-4V spring was plated with tin and then copper. The springs used in tasks (ii) (iv) had tee-shaped cross-sections designed to minimise the strain gradient across the strand [18, 19]. 1.4 Measurement procedures used Benchmarking procedure The measurement procedure for obtaining standard critical current data as a function of field has been outlined by many authors and reviewed extensively [20, 21]. Broadly, data acquisition was carried out as follows: at fixed magnetic field, temperature and strain, the current through the sample was slowly increased and the voltage across the sample monitored using a standard fourterminal V-I configuration. When the V-I transition had been recorded, the I C was determined at a criterion of 10 µvm 1 and 100 µvm 1 and stored digitally. Generally the measurement was then repeated as a function of magnetic field. The experiment was carried out using our strain probe [10, 22] which can twist one end of the spring with respect to the other and hence apply an axial strain to the strand [18]. Full details of the design and construction of the probe have been published elsewhere. For the benchmarking task (i.e. task (i)), voltage-current (V-I) measurements were made at 4.2 K with the strand directly immersed in a liquid-helium bath. These measurements involved slowly increasing the current, and measuring the voltages across three different sections of the strand using nanovolt amplifiers and digital voltmeters Cycling procedure The experiments were carried out using our strain probe [22] with an added computer-controlled stepper motor (see Fig. 3.1). This enables strains (and strain cycles) to be applied automatically, with a resolution of ~10 6% strain per step. The cyclic measurements consisted of single straincycles during which V-I measurements were made (test cycles), alternated with sets of 100 strain cycles (see Fig. 3.2). The maximum applied strain for such sets of 100 cycles was successively increased in increments of 0.056% until the strand was damaged. The test cycles were first carried out to 0.282% applied strain and after the set of 100 cycles to 0.282% had been completed, they were then carried out to 0.565%. V-I measurements were made at magnetic fields between 9 T and 15 T at zero applied strain at the beginning of the test cycle, at 10 T and 12 T throughout the first half of the test cycle and then at 10 T and 12 T at 0% at the end of the test cycle. No test cycles were carried out after sets of cycles to applied strains above 0.565%, but measurements were made at 10 T and 12 T during the 100 th cycle, at the maximum applied strain and at zero applied strain. The strain was changed at a constant maximum speed of 0.008% s 1 (e.g. cycles to 0.282% had a

10 6 time-period of ~90 s). In addition, the temperature of the strand was kept below ~20 K for the entire experiment (the VAC strand was subjected to a thermal cycle to room temperature after strain cycling to 0.565%, but this had no significant effect) Procedure for making E-T versus E-J measurements at ε I = 0.7% and detailed I C (B,T,ε I = 0.7%) measurements on the EM-LMI strand For task (iv), variable temperature measurements were made using our probe. The strand was located in a vacuum chamber containing a small quantity of helium exchange gas and the temperature was controlled using three independent controllers with Cernox thermometers and constantan wire heaters. The three thermometers were situated in the centre and at both ends of the turns of the spring sample-holder, with the central thermometer placed directly on top of the strand and the other thermometers placed on the sample-holder next to the strand. All three thermometers were calibrated commercially in zero magnetic field, while the central thermometer was also calibrated in-house in magnetic fields up to 15 T [10] and the small (~50 mk) corrections obtained from this were used for all three thermometers. The heaters were situated, correspondingly, on both ends of the sample-holder (in-between the turns of the strand), and around the central turns of the spring on the outside of an OFHC copper tube. Preliminary voltage-current measurements were first made at 4.2 K (with the strand directly immersed in a liquid-helium bath) at applied strains from 0.45% tension to 0.44% compression. The applied strain was then set to 0% and the probe was warmed to room temperature so that thermometry, heaters and a vacuum can could be fitted. The probe was then cooled back to 4.2 K, the strain was changed to 0.44% ( 0.7% intrinsic strain) and the remainder of the experiment was carried out. In the first part of task (iv), the voltage (V) across a section of the strand (length: 20.2 mm) was measured using a nanovolt amplifier and a digital voltmeter, with the measurements being made in two different ways: at constant temperature (T) with a slowly-increasing current (I), and at constant current with a slowly-increasing temperature. In our experimental set-up, it is more demanding to ramp the temperature than the current (the temperature controller is not designed for ramping temperature) but reasonably smooth temperature sweeping was obtained during most E-T measurements by sweeping the temperature set-point via the software. For task (iv), this report will refer to values of total current (superconductor + normal shunt), where the shunt current has not been subtracted (the shunt resistance is 5 µω at 6 T, corresponding to a shunt current of 40 ma at 10 µvm 1 ) [21]. V-I measurements were made at 1 K increments of temperature from 5 K to 13 K and at half-integer values of magnetic field up to a maximum of 15 T. Additional V-I characteristics were also obtained at 0.1 K increments of temperature at various magnetic fields. V-T measurements were made with the current fixed at 111 A, 50 A and 25 A at half-integer values of magnetic field up to 7.5 T, 10.5 T and 12.5 T respectively, and also with a current of 0.5 A at 0 T, 3 T, 6 T, 9 T and 12 T. In the second part of task (iv) detailed I C (B,T,ε I = 0.7%) measurements were made as a function of field and temperature at 0.7% intrinsic strain on the EM-LMI strand.

11 7 1.5 Results Benchmarking Results This report will consider engineering critical current densities (J C(E) ) defined at an electric-field criterion of 10 µvm -1 and n-values calculated using E = αj n for the electric-field range µvm 1. Figures 2.1 and 2.2 provide historical data from a previous report on a Nb 3 Al strand: good agreement was found between variable-temperature data at fixed strain and variable strain data taken at 4.2 K obtained using the Durham probe and equivalent data from the Japanese Atomic Energy Research Institute [10]. Consider the data in Figs In Fig. 2.3, variable field data are shown at zero applied strain on the Ti-6Al-4V sample holders from Durham, Twente and CEA along with data on a Cu-Be spring in Durham. In Fig. 2.4, the I C data for the EM-LMI strand mounted on four springs of different materials are shown. It can be seen that to a first approximation, the intrinsic strain dependence on the different springs of different material is the same. Fig. 2.5 shows a detailed figure at 13 T and 15 T. It includes the comparison between the data obtained on the Ti-6Al-4V spring in Durham and equivalent data obtained from Twente and CEA on a Ti-ITER barrel at zero applied strain. Fig. 2.6 shows the electric field-engineering current density (E-J (E) ) characteristics for the three different sections of the EM-LMI strand (A, B and C) at zero applied strain before any cycling. E and J (E) were calculated from the voltage and current by dividing by the voltage-tap separation (typically ~20 mm) and the cross-sectional area of the strand ( m 2 ). The data are typical of both the VAC and EM-LMI strands, which were homogeneous in terms of their E-J (E) characteristics to within 5%. We conclude that there is strong support for the accuracy and reliability of data produced in this report. There are reports in the literature that are different from our results that have serious implications for the interpretation of the results from the TFMC coil. In some cases, this is simply because the more comprehensive data available in this report were not available so reasonable assumptions and extrapolations were made which have subsequently turned out to be incorrect. In others cases, differences occur because direct comparison is not possible because improved understanding indicates that the measurements were not equivalent: a) The well-known Specking samples : Variable strain I C data obtained at 4.2 K on EM-LMI strands in cable-in-conduit-conductors (CICC) [13] show a markedly weaker strain dependence to that found in Figs The complex strain state in the multi-component CICC s is different to the strand tests reported here. FEA is required to understand the CICC results. b) The U-bend brass spring Twente data on EM-LMI strands: It is well-understood that the precompression on brass is different to that on Ti- and Cu-Be. Nevertheless, the peak values (at zero intrinsic strain) of I C are significantly different to those shown in Fig. 2.3 to 2.5. Whether this is current transfer through the large brass U-bend spring, stress concentrations in the U-bend design, batch-to-batch variations in the EM-LMI wire or due to I C values being measured at 500 µvm 1 is not clear. c) There are a broad range of calculated and derived values in the literature for the intrinsic strain of the EM-LMI strand on the Ti- (ITER) barrel ( 0.21% to 0.16%). The experimental value measured directly is 0.12%.

12 8 Nevertheless, the benchmarking tests show clearly: a) The intrinsic precompression for the EM-LMI wire on a Ti-6Al-4V spring is 0.12%. b) The I C values obtained in Durham at zero applied strain are consistent with the CEA and Twente data at zero applied strain and the witness samples as shown in Table 1.1 c) Data on a Nb 3 Al strand show good agreement with data obtained by Koizumi et al for changes in magnetic field, temperature and strain. d) The strain dependence we have observed is reversible in strain to a few percent so the wire has not been damaged during the measurements Cyclic tests EM-LMI strand In Figs. 2.6/3.3, J C(E) and n clearly depend on the choice of criterion (e.g. n typically varies by 50% in the experimentally accessible electric-field range µvm 1, decreasing with increasing E), but the trends described below do not depend on this choice. Figs. 3.4 and 3.5 show the engineering critical current density and n-value for the EM-LMI strand as a function of applied strain (ε), measured after each set of 100 strain cycles. The intrinsic strain is, by convention, taken to be zero when J C(E) has its maximum value. Data are shown for one section of the strand (A) at a magnetic field of 12 T, but the same trends were observed for the other sections and at 10 T. In addition, Figs. 3.6 and 3.7 show the J C(E) and n data at zero applied strain and 12 T, measured after each set of 100 strain cycles before and after each test cycle. For cycles to applied strains up to and including 0.282% (~500 cycles in total), the data were reversible to within the experimental error. The only exception to this was the first test-cycle to ε = 0.282%, which caused a 1% decrease in J C(E) at ε = 0% for all three sections of the strand (for n, the experimental errors are too large to observe changes of this magnitude). In this reversible regime, J C(E) and n are a maximum at ε = ε M = 0.26% with values of Am -2 (152 A) and 24.5 respectively and are consistent with previous measurements [19]. However, for cycles to applied strains between 0.339% and 0.565% (another ~500 cycles) J C(E) and n increased after each successive set of cycles, resulting in a final increase in J C(E) at ε = ε M of 5% as well as a small increase in ε M itself to 0.29%. For lower applied strains ( 0.226%) the increases in J C(E) (and n) occurred mainly as a jump after the first test-cycle to ε = 0.565% (at ε = 0%, J C(E) increased by ~2% and was then unaffected by the following ~500 cycles, see Fig. 3.6). For higher strains the increases were proportionally larger (~14% at ε = 0.565%) and J C(E) and n increased approximately monotonically with the number of sets of cycles completed. Cycling to ε = 0.677% caused the change in J C(E) at zero applied strain to increase from 1% up to 3.5% (no test cycle was carried out). Finally, cycling to ε = 0.790% caused J C(E) and n at zero applied strain to reduce by 15% and 50% respectively, indicating damage to the strand. Further damage occurred after cycling to ε = 0.903%.

13 VAC strand Equivalent data for the VAC strand are shown in Figs. 3.8 to The scatter on the data is generally larger, but J C(E) and n are again reversible to within the experimental error for cycles to applied strains up to 0.282% (no irreversible effect due to the first cycle was observed in this case). In this case J C(E) = Am 2 (128 A) and n = 35 at ε = ε M = 0.26% and 12 T, which agree well with previous measurements [19]. J C(E) and n again increased after each successive set of cycles to applied strains between 0.339% and 0.565%, with J C(E) at ε = ε M and 12 T increasing by 7% in total, which was similar to the EM-LMI strand. In contrast, at low applied strains ( 0.113%) larger increases occurred (J C(E) increased by 6% in total at zero applied strain) and there was no evidence for any shift in ε M. Evidence for damage from J C(E) data was first observed after cycling to ε = 0.790%, although n decreased very significantly (by 25%) after cycling to ε = 0.734% E-T versus E-J results at 0.7% and detailed I C (B,T,ε I = 0.7%) data for the EM-LMI strand Fig. 4.1 shows the engineering critical current density (calculated by dividing the critical current by the cross-sectional area of the strand) defined at 10 µvm 1 as a function of applied strain (ε A ) at a temperature of 4.2 K. J C at zero applied strain is reversible to within 0.1% for the strain cycle to ε A = 0.45%, and to within 3% (J C increased) for the cycle to ε A = 0.44%. Intrinsic strain (ε I ) is defined by ε I = ε A ε M (equal to zero where J C is a maximum) so an applied strain of 0.44% corresponds to an intrinsic strain of 0.7%, which is the strain at which most of the experiment was carried out. At 12 T and 4.2 K, J C is a maximum at ε A = 0.26% (= ε M ) with a value of Am 2 (152 A) and is reduced to Am 2 (46.5 A) at ε A = 0.44%. The E-J data can be parameterised by the standard power-law expression: (,,, ε ) (,, ε ) E J B T = E J J B T. (1) C The exponent n (the n-value) was calculated using Equation (1) for electric fields between 10 µvm -1 and 100 µvm -1 and found to be 24 at 4.2 K and 12 T at zero intrinsic strain and 15 at 4.2 K and 12 T at ε I = 0.7%. C n Comparison of E-T and E-J characteristics Figures 4.2 and 4.3 show electric field-engineering current density (E-J) characteristics for the strand at 0.1 K increments of temperature and at magnetic fields of 6 T and 9 T respectively. The n- value is approximately constant over one order of magnitude of electric field (at constant B, T and ε), but decreases slowly with increasing electric field. Figures 4.4 and 4.5 show electric fieldtemperature (E-T) characteristics for, respectively, a current of 111 A and magnetic fields between 5.5 T and 7 T, and a current of 50 A and magnetic fields of 9 T and 9.5 T. In order to compare the data obtained from the two different types of measurement, E(J,B,T,ε) data points have been taken from the E-J characteristics at a particular value of current (dashed lines in Figures 4.2 and 4.3) and plotted together with the E-T characteristics: it can be seen that the data superimpose, with a typical uncertainty of ~20 mk.

14 10 Values of current-sharing temperature (T CS ) can be obtained from the E-T characteristics, where T CS is defined as the temperature at which the electric field reaches a particular electric field criterion value. Fig. 4.6 shows the engineering critical current density as a function of temperature, where J C has been calculated in the standard way from the E-J characteristics at an electric field criterion of 10 µvm -1, and T CS has been calculated from the E-T characteristics at the same E-field criterion. The J C data lie on a unique curve at a particular magnetic field whether obtained from E-J or E-T characteristics. Figures 4.4 and 4.5 show that the E-T characteristics can also be described by a power-law, where the exponent is again approximately constant over one order of magnitude of electric field (we note however that an exponential dependence gives a similarly accurate parameterisation). In this report, we will not explicitly discuss the values of this exponent (which varied from ~50 to ~200 for the measurements made) but will instead calculate equivalent n-values. The power-law exponent of the E-T characteristics (i.e. log E / logt) can be related to the n-value using the following expression (note that the partial derivatives mean that J, B and ε are constant): log E log E log J C TCS JC = = n logt log J logt J C T T= T T= T C CS T= TCS CS. (2) This expression has been used to calculate values of n from the exponents of the E-T characteristics (between 10 µvm -1 and 100 µvm -1 ), the values of and T CS and J C (at 10 µvm 1 ) and the partial temperature derivatives of J C (calculated at T CS using spline fits to the standard J C data). These calculated values of n are plotted as a function of temperature in Fig. 4.7 together with n-values calculated in the standard way from the E-J characteristics (also for electric fields between 10 µvm 1 and 100 µvm 1 ). The n-values obtained using the two different methods lie on a single curve at a particular magnetic field to within the accuracy of our measurements. The differences in n-value obtained from these different measurements are predominantly associated with the uncertainties in obtaining n-values from E-T and E-J characteristics that do not show strict power law behaviour although the differences, that equate to an uncertainty in temperature of ~100 mk, could also be attributed to a change in temperature during the transition (from 10 µvm 1 and 100 µvm 1 ) of ~10 mk Parameterisation of the engineering critical current density for the EM-LMI strand at -0.7% intrinsic strain The engineering critical current density data can be parameterised using a scaling law of the form [23]: 2 2 n 3 p 1 C( ε) ( ε) C( ε)( ) C2( ε) ( q J BT,, = A T 1 t B T, b 1 b, (3) where t = T/T C (ε), b = B/B C2 (T,ε), A(ε) is a strain dependent variable, T C (ε) is the effective critical temperature and B C2 (T,ε) is the effective upper critical field. As shown in the Kramer plot of Fig. 4.8 [24], an accurate fit to the data at 0.7% intrinsic strain can be obtained by setting p = 0.5 and q = 2, in which case the only significant deviations occur close to B C2, where the measured values )

15 11 of J C are greater than the fitted values. The resulting values of effective upper critical field can be parameterised by: C2 (, ε) C2 ( 0, ε)( 1 ) B T = B t ν, (4) with B C2 (0 K) = T, T C = K and ν = (see Fig. 10), and the best fit to the J C data is obtained with n = and A = Am 2 K 2 T At constant strain, Equation (3) is equivalent to the simplified Summers scaling law [16, 17] where n = 2.5, C(ε) = A(ε)T C (ε) 2 and the effective upper critical field is often taken to be of the form: C2 2 (, ε) = ( 0, ε)( 1 )( 1 3) B T B t t. (5) C2 In this case, the best fit at an intrinsic strain of 0.7% is obtained with: B C2 (0 K) = 21.4 T, T C = K and C = AT 0.5 m -2, and the root-mean-square deviation of the parameterisation from the measured data is 1.0 A The critical temperature at 0.7% intrinsic strain In large superconducting coils, measurements at low current densities (in zero-field) which provide a measurement of the critical temperature can be used to investigate the strain-state or possible damage to the component strands of the coil. Parameters obtained from the scaling laws (e.g. T C (ε)) cannot be reliably used because the scaling laws break-down at the lowest current densities in the tail of the J C -B characteristic close to T C or B C2 as shown in Fig This can be attributed to the distribution of T C and B C2 found in composite conductors [25, 26]. In Fig. 4.9, electric field-temperature data are shown that were obtained at a low fixed current of 0.5 Amps from which a direct measurement of T C and B C2 have been obtained at a criterion of 10 µvm 1. Fig shows a comparison between these direct measurements and values of B C2 obtained from the scaling law. Consistent with a tail in the J C -B characteristic, the direct measurements are about 0.35 K higher than the values obtained from fitting the scaling law. 1.6 Discussion/Analysis Cyclic Measurements For engineering purposes, it may be sufficient to know that there were no decreases in the critical current density or n-value for either strand during the >1000 strain cycles to applied strains up to 0.677%. Nevertheless, significant increases in J C(E) and n did occur as a result of strain cycling to applied strains between 0.339% and 0.677%. The brittle Nb 3 Sn filaments behave elastically until damage (cracking) occurs at an intrinsic strains (relative to ε M ) that for many conductors are generally in the range 0.3% 0.6% [27] (compared to ~0.4% in this work). The increases in J C(E) are associated with increases in the effective upper critical field (Kramer plots not shown) and are therefore likely to be caused by changes in the strain-state of the Nb 3 Sn filaments. The copper and bronze matrix materials have elastic limits of ~0.1% and ~0.2% respectively (and are in thermal

16 12 pretension at zero applied strain), and so will be plastically deformed during strain cycling [27]. In general, loading-unloading treatments on strands can be carried out to reduce the axial thermal prestrain on the filaments [6]. However in our experiment the axial strain is explicitly controlled, therefore the changes in J C(E) or n observed during cycling can only be explained by also considering the non-axial strains. Preliminary analysis suggests that deviatoric strain alone cannot explain the increase in J C(E) observed since for example at zero intrinsic strain, the deviatoric strain is zero. The effects of tensorial strains on Nb 3 Sn are not fully understood, although the consensus is that increases in either deviatoric or hydrostatic strain cause the superconducting parameters to decrease, with the deviatoric strain (related to the change in shape) having the larger effect [3, 28]. Such general considerations suggest that the increases in J C(E) and n are due to a decrease in one or both of these quantities. However detailed knowledge of the complex effects associated with plastic deformation and work hardening of the components of the matrix requires finite element analysis modelling which is in progress Comparison of E-T and E-J characteristics Figs demonstrate that there is superb agreement between the E-T and E-J characteristics. One can be confident that if large coil systems are properly understood (including the complex distributions of magnetic-field, temperature and strain), the E-T data from large coils should agree with E-J data on strands. It is well established that J C can be a hysteretic function of applied field and temperature [26]. Although this hysteresis is most probably associated with large inhomogeneities in the conductor, and hence is commonly observed in high temperature superconductors [29], a quantitative explanation for J C hysteresis or the length scale for these inhomogeneities is not yet available. We tentatively suggest that the equivalence between the E-T and E-J data reported here will be associated with conductors that show non-hysteretic J C and hence correlated with homogenous conductors showing uniform J C along their length Parameterisation of the engineering critical current density for the EM-LMI strand at 0.7% intrinsic strain The Summers scaling law is commonly used in the ITER community, although a lot of work is being carried out on developing more accurate scaling laws and improving our understanding of the underlying science [3, 10]. Here, it provides an accurate parameterisation of the temperaturedependence of J C at one particular strain namely 0.7% intrinsic strain, but the resulting values for the strain-dependent parameters obtained in this work at ε I = 0.7%. (i.e. C(ε), B C2 (ε,0) and T C (ε)) do not agree at all well with the values obtained by extrapolating the standard functional forms for these parameters that have been fit using data at other values of strain [2, 16, 17]. In particular the values of I C found at 0.7% are typically a factor different to those found from the historical data used in the literature. We note that obtaining a simple and accurate parameterisation of the n-value data is problematic and beyond the scope of this report: assuming, for example, that n is a function of J C alone leads to errors of typically 25% (n systematically decreases with increasing temperature at constant J C ).

17 Future work Preliminary work beyond the scope of this report has been completed and is being analysed. In Fig. 4.11, data are shown at 12 T as a function of field and temperature. Also shown is a Summers fit to the data for applied strain above 0% and the historical ITER-Summers scaling. There are very significant differences between the historical parameterisation of the strand and the data presented in this report. Equally a Summers fit to our preliminary data does not provide an accurate parameterisation. 1.8 Conclusions Important results in this report include: Cyclic measurements on two ITER candidate Nb 3 Sn strands (EM-LMI and VAC) can be summarised as follows: Both strands were unaffected by the ~500 strain cycles to applied strains up to 0.282% (apart from a 1% decrease in the critical current density caused by the first test-cycle for the EM-LMI strand). The first test-cycle to 0.565% caused a 1% 2% increase in the critical current density at zero applied strain (for the EM-LMI strand, this was the only change in the zero applied strain data during the first ~1000 cycles). The ~500 strain cycles to applied strains between 0.339% and 0.565% caused the critical current density and n-value to incrementally increase at all applied strains; the final increases were proportionally larger at higher strains and varied from 2% to 14% (EM-LMI strand) and 6% to 11% (VAC strand). Cycling to applied strains above 0.677% (~0.4% intrinsic strain) caused large irreversible decreases in the critical current density and n-value. Detailed measurements on the EM-LMI strand at an intrinsic strain of 0.7%: The E-T and E-J data were shown to be equivalent: E(J,B,T,ε) data points from the two different measurements agree to within an uncertainty in temperature of ~20 mk. These results confirm that, within the limits of our measurement procedure, electric-field is a single-valued function of current density, magnetic field, temperature and strain in this EM-LMI conductor. There are significant differences between the calculated values for the intrinsic strain of an EM- LMI strand on an ITER barrel and those found experimentally. The experimental value is 0.12%. A Summers scaling was provided that parameterises the magnetic field and temperature dependence of the engineering critical current density data at 0.7% intrinsic strain however

18 14 the scaling function does not describe data at other values of strain. Direct measurements of the critical temperature were also presented. The Summers parameterisation in the historical ITER-Summers form does not parameterise the I C data accurately: typically a factor wrong at 0.7% intrinsic strain. The basic inconsistency with ITER-Summers strain dependence occurs at all temperatures (including 4.2 K). For a complete tabulation of the results described in this report, the reader is referred to Acknowledgements The authors acknowledge support from the EFDA/ITER program and EPSRC.

19 15 References [1] N. Mitchell, SOFT 2002, Helsinki, 2002). [2] J. W. Ekin, Cryogenics 20, 611 (1980). [3] B. ten Haken, A. Godeke, and H. H. J. ten Kate, J. Appl. Phys. 85, 3247 (1999). [4] N. Cheggour and D. P. Hampshire, J. Appl. Phys. 86, 552 (1999). [5] D. M. J. Taylor, S. A. Keys, and D. P. Hampshire, Physica C 372, 1291 (2002). [6] S. Ochiai, K. Osamura, and K. Watanabe, J. Appl. Phys. 74, 440 (1993). [7] W. Specking, J. L. Duchateau, and P. Decool, Proc 15th Conf Magn techn, 1210 (1998). [8] P. Bruzzone, A. M. Fuchs, B. Stepanov, et al., IEEE Transactions on Applied Superconductivity 12, 516 (2002). [9] M. Dhallé, in Handbook of Superconducting Materials, edited by D. A. Cardwell and D. S. Ginley (IOP Publishing, Bristol, 2003), Vol. II, p [10] S. A. Keys, N. Koizumi, and D. P. Hampshire, Supercond. Sci. Tech. 15, 991 (2002). [11] R. Zanino, N. Mitchell, and L. Savoldi-Richard, Cryogenics 43, 179 (2003). [12] R. Zanino and L. Savoldi-Richard, Cryogenics 43, 79 (2003). [13] J. L. Duchateau, M. Spadoni, E. Salpietro, et al., Supercond. Sci. Tech. 15, R17 (2002). [14] R. Zanino and L. Savoldi-Richard, Cryogenics 43, 91 (2003). [15] K. Hense, Submitted to Physica C (2003). [16] L. T. Summers, M. W. Guinan, J. R. Miller, et al., IEEE T. Magn. 27, 2041 (1991). [17] A. Martínez and J. L. Duchateau, Cryogenics 37, 865 (1997). [18] C. R. Walters, I. M. Davidson, and G. E. Tuck, Cryogenics 26, 406 (1986). [19] D. M. J. Taylor and D. P. Hampshire, (to be published) (2003). [20] L. F. Goodrich, D. F. Vecchia, E. S. Pittman, et al., (N.B.S. special publication, Boulder, 1984). [21] S. Keys and D. P. Hampshire, in Handbook of Superconducting Materials, edited by D. Cardwell and D. Ginley (IOP Publishing, Bristol, 2003), Vol. II, p [22] N. Cheggour and D. P. Hampshire, Review of Scientific Instruments 71, 4521 (2000). [23] S. A. Keys and D. P. Hampshire, Supercond. Sci. Tech. 16, 1097 (2003). [24] E. J. Kramer, J. Appl. Phys. 44, 1360 (1973). [25] D. C. Larbalestier, A. Gurevitch, D. M. Feldmann, et al., Nature 414, 368 (2001). [26] H. Kupfer and W. Gey, Philos. Mag. 36, 859 (1977). [27] G. Rupp, in Filamentary A15 Superconductors, edited by M. Suenaga and A. F. Clark (Plenum Press, New York, 1980). [28] D. O. Welch, Adv. Cryo. Eng. 26, 48 (1980). [29] A. B. Sneary, C. M. Friend, J. C. Vallier, et al., IEEE T. Appl. Supercon. 9, 2585 (1999).

20 16 2 Benchmarking tests for the spring material using the EM-LMI Nb 3 Sn Strand 200 Durham JAERI Critical Current, I C (A) K 10 K 8 K 6 K 4.2 K ε = 0% (b) 14 K Applied Field,B (T) Fig 2.1 Historical data: A comparison between variable temperature data measured in Durham on the Nb 3 Al strand and those on the same strand from Koizumi et al (Private communication).

21 Fig 2.2 Historical data: A comparison between the variable strain data measured in Durham and that obtained on the same Nb 3 Al strand from Koizumi et al (Private communication). 17

22 18 Engineering Critical Current Density (10 8 Am 2 ) T = 4.2 K 0% Applied Strain ENEA witness data CEA data Twente data Durham Ti-6Al-4V ( 0.12%) Durham Cu-Be ( 0.26%) Critical Current (A) Magnetic Field (T) Fig 2.3 Engineering critical current density (and critical current) as a function of magnetic field at zero applied strain and at a temperature of 4.2 K. Data obtained at Durham on a Cu-Be and on a Ti- 6Al-4V spring are shown (bracketed values show the intrinsic strain at zero applied strain), as well as additional data for the ENEA witness samples (mean ± standard deviation for samples D, E, G, L and M) and data from Twente and CEA (also on Ti-6Al-4V sample holders).

23 19 Engineering Critical Current Density (10 8 Am -2 ) Spring Material Cu Be Brass Ti 6Al 4V S. S. 316L Magnetic Field: 15 T Applied Strain (%) Critical Current (A) Fig. 2.4 Critical current measurements of the EM-LMI Nb 3 Sn strand on springs made of Cu-Be, Brass, Ti-alloy and s/s.

24 20 Engineering Critical Current Density (10 8 Am 2 ) T = 4.2 K B = 13 T Cu-Be Spring Ti-6Al-4V Spring Twente data CEA data Applied Strain (%) 15 T Critical Current (A) Fig. 2.4 Engineering critical current density (and critical current) at 10 µvm 1 as a function of applied strain at a temperature of 4.2 K and magnetic fields of 13 T and 15 T. Data are shown for EM-LMI wires mounted on a Cu-Be spring and on a Ti-6Al-4V spring. Data obtained on a Ti-6Al-4V sample holder at Twente and CEA are also shown.

25 21 Electric Field (µvm 1 ) EM-LMI Wire Section A B C ε = 0% B = 15 T Current (A) 10 T Voltage (Section A) (µv) Engineering Current Density (10 8 Am 2 ) Fig. 2.6 Electric field versus engineering current density (and voltage versus current) on a log-log scale for three different sections of the EM-LMI wire at zero applied strain (before any cycling) and integer magnetic fields between 10 T and 15 T.

26 22 3 Figures: Cyclic data on the VAC Nb 3 Sn Strand and the EM- LMI strand Fig. 3.1 The top end of the strain probe, with the computer-controlled stepper motor (on the left).

27 test cycle 100 cycles 0.6 Applied Strain (%) mm I II Time Fig. 3.2 The strain cycling procedure. The labels I and II refer to the measurements at zero applied strain at the beginning and the end of each test cycle respectively. Inset: spring sample holder with tee-shaped cross-section.

28 24 Electric Field (µvm 1 ) EM-LMI Wire Section A B C ε = 0% B = 15 T Current (A) 10 T Voltage (Section A) (µv) Engineering Current Density (10 8 Am 2 ) Fig. 3.3 Electric field versus engineering current density (and voltage versus current) on a log-log scale for three different sections of the EM-LMI wire at zero applied strain (before any cycling) and integer magnetic fields between 10 T and 15 T.

29 25 Engineering Critical Current Density (10 8 Am 2 ) EM-LMI Wire (Section A) B = 12 T Maximum applied strain for sets of 100 cycles (%) No cycles Applied Strain (%) Critical Current (A) Fig. 3.4 Engineering critical current density (and critical current) defined at 10 µvm 1 as a function of applied strain for section A of the EM-LMI wire at a magnetic field of 12 T, measured after each set of 100 strain cycles.

30 26 n-value (dimensionless) EM-LMI Wire (Section A) B = 12 T Maximum applied strain for sets of 100 cycles (%) No cycles Applied Strain (%) Fig. 3.5 n-value as a function of applied strain for section A of the EM-LMI wire at a magnetic field of 12 T, measured after each set of 100 strain cycles. The n-value was calculated for the electric field range µvm 1.