IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 26, NO. 4, JUNE 2016

6800205

Trapped Field Characteristics and Fracture
Behavior of REBaCuO Bulk Ring During
Pulsed Field Magnetization
Hidehiko Mochizuki, Hiroyuki Fujishiro, Tomoyuki Naito, Yoshitaka Itoh,
Yousuke Yanagi, and Takashi Nakamura

Abstract—We have performed pulsed field magnetization(PFM) for the GdBaCuO ring bulk (60 mm in outer diameter,
36 mm in inner diameter, and 17 mm in thickness) with an aluminum alloy bandage at 65 K. When a magnetic pulsed field over3 T was applied, a fracture was confirmed in the bulk by thetrapped field profile. Using a numerical simulation by a finiteelement method, the trapped field and the hoop (σθ ) and radial(σr ) stresses were analyzed. A huge compressive stress concentrated at the inner peripheral edge of the ring bulk mainly by
the thermal contraction. The additional compressive stress wasapplied by the flux-pinning-induced magnetostriction around the
maximum field during PFM. The mechanical reinforcement in the
inner periphery part of the ring bulk must be considered during
PFM using a cylinder.
Index Terms—Compressive stress, fracture behavior, pulsed
field magnetization (PFM), REBaCuO bulk ring.

I. I NTRODUCTIONNUCLEAR magnetic resonance (NMR) spectrometer withhigh resolution is a powerful apparatus to analyze complex molecular structure or to develop new drugs. Recently,
1020 MHz (24.0 T) NMR spectrometer using novel and complex superconducting coils has been developed [1]. A compact
and cryogen-free NMR spectrometer with a medium resolutionof 200 MHz (4.7 T)—270 MHz (6.3 T) is also desired, becausea large superconducting coil magnet system for NMR cooledby liquid helium is very expensive and occupies a wide space torealize the homogeneity of the magnetic field. REBaCuO superconducting bulk (RE: rare earth element and Y) has a promisingpotential as a quasi-permanent magnet, which can trap a highManuscript received October 16, 2015; accepted December 15, 2015. Dateof publication December 30, 2015; date of current version January 15, 2016.
This work was supported in part by the project “Development of System andTechnology for Advanced Measurement and Analysis” of the Japan Scienceand Technology Agency (JST) and by the Japan Society for the Promotion of
Science (JSPS) under KAKENHI Grant 15K04646.
H. Mochizuki, H. Fujishiro, and T. Naito are with the Faculty of Engineering,
Iwate University, Morioka 020-8551, Japan (e-mail: t2214035@iwate-u.ac.jp;
fujishiro@iwate-u.ac.jp; tnaito@iwate-u.ac.jp).
Y. Itoh and Y. Yanagi are with the IMRA Material R&D Company Ltd.,Kariya 448-0032, Japan (e-mail: y-itoh@ai-i.aisin.co.jp; yanagi@ai-i.aisin.co.
jp).
T. Nakamura is with RIKEN, Wako 351-0198, Japan (e-mail: takashi.
nakamura@riken.jp).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TASC.2015.2513415

magnetic field over 17 T by the reinforcement against theelectromagnetic force [2], [3]. One of the practical applications
using the bulk magnet is a compact cryogen-free NMR magnet.
Nakamura et al. developed REBaCuO superconducting bulk
magnet for the 2.89 T (123 MHz) NMR spectrometer using
six annular REBaCuO bulk rings, which were magnetized byfield cooled magnetization (FCM) using a superconducting coilmagnet [4]. The NMR spectra of ethanol with a full widthat half of the maximum (FWHM) of 0.1 ppm (21 Hz) wereobserved with a 1.3 mm diameter and 4 mm length using a
multichannel shim coil [5]. The magnetic resonance imaging(MRI) was also investigated using annular EuBaCuO bulks[5], [6]. A new technique to realize the field homogeneity inthe cylindrical bulk has been proposed and confirmed by theinsertion of the cylinder wrapped by high-Jc superconducting
tapes [7]. We confirmed the insertion effect using a numericalsimulation [8].
Pulsed field magnetization (PFM) is a promising techniqueto magnetize the superconducting bulk, because of the compact
and inexpensive experimental setup with no use of superconducting coil magnet. However, the trapped field Bz by PFM
is lower than that by FCM because of a large temperaturerise caused by the dynamical motion of the magnetic flux. We
have studied the PFM technique mainly for the disk shapedbulk experimentally and numerically to enhance the trappedfield Bz [9], [10]. If the trapped field strength and the field
homogeneity are fairly enhanced in the REBaCuO cylindricalbulk magnetized by PFM, the magnetizing technique to realize
the NMR bulk magnet might be replaced from FCM to PFM.
During the magnetizing process for superconducting bulks,
the mechanical strength must be considered to avoid theirfracture, because a huge flux pinning induced magnetostriction
is exerted on the bulk. For the FCM process, both hoop andradial stresses are experienced in the bulk. The disk bulk is
usually reinforced by fitted metal ring or a glass fiber to preventthe fracture from expansive stress [2], [3]. For the PFM process,a compressive stress is also applied at the ascending stage of
PFM. REBaCuO bulk is a brittle ceramic material, and has a
low mechanical strength of 30–100 MPa [11], [12]. Ren et al.
reported that cracking is more likely during activation and mostprobable at the center of the disk bulk with the cracks running
outward for FCM [13]. Johansen et al. calculated the hoop andradial stresses during FCM and zero-field cooled magnetization(ZFCM) [14], [15]. These papers were based on the Bean’s1051-8223 © 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
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model for the c-axis oriented long superconducting cylinder.
The increase in the mechanical strength of the bulk by adding
Ag and the mechanical reinforcement is the most important
issue.
In this paper, we performed PFM experiments for the
GdBaCuO ring bulk to apply to NMR spectrometer. Unfortunately, the ring bulk was broken during PFM process. We
analyzed the time dependence of the hoop and radial stresses
in the ring bulk using a finite element method (FEM) anddiscussed the reason of the fracture occurrence and the method
to prevent it.

TABLE IM ECHANICAL PARAMETERS U SED IN THE N UMERICAL S IMULATION

II. E XPERIMENTAL P ROCEDURE
Ag-doped GdBaCuO ring bulk (60 mm in outer diameter,
36 mm in inner diameter and 17 mm in height) was used, which
was fabricated by the modified quench and melt growth (QMG)
method. The ring bulk was glued in aluminum alloy ring(60.1 mm in inner diameter and 5 mm in thickness) using epoxy
resin to prevent the mechanical fracture against the expansive
hoop strain. The ring bulk was mounted on the cold stage ofthe Gifford McMahon (GM) cycle helium refrigerator and theinitial temperature Ts was set to 65 K. Magnetizing solenoid
copper coil dipped in the liquid nitrogen was placed outside
the vacuum chamber. The magnetic pulse Bex (= 2.5 ∼ 3.1 T)with a rise time of 13 ms was applied to the ring bulk. A
local magnetic field BLC (t) was monitored by axial-type hallsensor (BHA 921; F. W. Bell) at the center of the hole using
digital oscilloscope. Two-dimensional trapped field profile Bz
was mapped 1 mm above the bulk surface using the samehall sensor. The detailed experimental procedure is described
elsewhere [9], [10].
III. M ODELING OF N UMERICAL S IMULATION
Based on the experimental setup of PFM, we proposed thefollowing framework of numerical simulation. An infinite long
cylindrical superconducting bulk (60 mm in outer diameter and
36 mm in inner diameter) was mounted in aluminum alloy
cylinder (60.1 mm in inner diameter and 5 mm in thickness) using epoxy resin. The critical current density Jc of the bulk was
supposed to be 2.25 × 108 A/m2 , which was a typical Jc value
at 65 K for the present bulk and was supposed to be independentof temperature and magnetic field according to the Bean’s
critical state model. In this case, a disk bulk with r = 30 mm
in radius is fully magnetized with B ∗ = μ0 Jc r = 8.48 T by
FCM. In the simulation, the imaginary magnetic pulse wasapplied from 0 to Bex by 10 steps at the ascending stage andthen from Bex to 0 by 10 steps at the descending stage using apulse coil (100 mm in inner diameter). The compressive stressgenerated by the thermal contraction cooled from 300 K to 65 K
was also calculated. The mechanical parameters (Young’s modulus E, Poisson ratio γ, bulk modulus B and thermal expansion
coefficient α) used in the elastic simulation are summarizedin Table I. Commercial software, Photo-Eddy, combined with
Photo-ELAS (Photon Ltd., Japan), was used for the analysis of
the distributions of magnetic field, current density and elastic
stress in the cylindrical bulk during PFM.

C and the applied pulsed field B
Fig. 1. Time dependence of the local field BL
exat the center of the hole for (a) Bex = 2.53 T and (b) 3.10 T at 65 K. The thickarrow shows the estimated position, at which the ring bulk was broken.

IV. E XPERIMENTAL R ESULTS
Fig. 1 shows the time dependence of the local field BLC (t) andthe applied pulsed field Bex (t) for Bex = 2.53 T and 3.10 T
at 65 K. For Bex = 2.53 T, the magnetic flux can hardly
penetrate into the ring bulk because of a pulsed field too low to
overcome the magnetic shielding. The inset shows the trappedfield profile, in which a small amount of magnetic flux wastrapped concentrically at the bulk periphery. On the other hand,for Bex = 3.10T , magnetic flux intruded abruptly at the central
position from t = 15 ms. BLC reaches a maximum at t = 24 ms
and decreased with increasing time. However, the trapped fieldBz was hardly generated and showed a slightly negative value

MOCHIZUKI et al.: TRAPPED FIELD CHARACTERISTICS AND FRACTURE BEHAVIOR OF REBaCuO BULK RING

Fig. 2. Magnetization curve for each applied field Bex , which was calculated
C (t) − B (t) using Fig. 1. The thick arrow shows the estimatedby M = BL
exposition, at which the ring bulk was broken.

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Fig. 3. Time step dependence of the profile of the local field By after applying
the magnetic pulsed field of Bex = 3.0 T.

at the center of the hole. The trapped field profile shown in
Fig. 1(b) suggested a crack creation at the lower left position inring bulk. We conceived that the bulk was broken during PFM
and the superconducting current circumvented by the crack,
although we were not able to confirm any cracks on the bulk
surface using an optical microscope. For the descending stageof PFM, an expansive stress is applied to the ring bulk withan aluminum alloy bandage, which is the same situation for
the FCM process. The aluminum alloy bandage is effective
to prevent the mechanical fracture from the expansive force.
However, for the ascending stage of PFM, a compressive force
was applied to the ring bulk without any reinforcement inside
the ring bulk and, as a result, the ring bulk might be broken.
Fig. 2 presents the magnetization curve for each Bex , which
was calculated by M = BLC (t) − Bex (t) using Fig. 1. In theascending stage of Bex (t), the magnetic flux can hardly penetrate into the bulk center and the M value is nearly equal to thenegative applied field, (M = −Bex ). A wide hysteresis loop
in the M vs. Bex curve and a slightly negative final M value
with increasing time can be seen. We cannot precisely conclude
when the crack was created from Figs. 1 and 2, but the time totake place the fracture is predicted to be just after the peak ofBex (t) (t = 15 ms) as shown by the thick arrow in the figures.
V. R ESULTS OF N UMERICALS IMULATION AND D ISCUSSION
A. Hoop and Radial Stresses by the Electromagnetic Force
Fig. 3 shows the time step dependence of the profile of thelocal field By for Bex = 3.0 T. The inset shows the time stepof Bex . The magnetic flux intruded and was trapped only atthe bulk periphery because of lower Bex than B ∗ , which fairly
represents the Bean’s critical state model.
Fig. 4(a) and (b) present the time step dependence of the
profile of the hoop stress (σθ ) and the radial stress (σr ) for
Bex = 3.0 T. In Fig. 4(a), the compressive hoop stress (σθ )increases with increasing strength of the pulsed field and takes
a maximum of −7.21 MPa at the maximum Bex = 3 T andthen decreases. After the 14 steps, which is lower than 1.8 T,

Fig. 4. Profile of the (a) hoop stress (σθ ) and (b) radial stress (σr ) in the bulk
during PFM, as a function of time step of Bex = 3.0 T.

the hoop stress changes to the positive value. It should be
noted that the maximum compressive hoop stress takes placeat the inner periphery edge and at the maximum applied field.
The dip of the hoop stress at r = 30 mm results from theexistence of the epoxy resin with low Young’s modulus. In
Fig. 4(b), the compressive radial stress (σr ) increases withincreasing strength of the pulsed field and takes a maximum
at the maximum Bex = 3 T and then decreases. At the descending stage, the radial stress changes to the positive value.

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Fig. 5. Time step dependence of the maximum σθ and σr values for the ringbulk and the disk bulk during PFM of 3 T.

Fig. 6. Profile of the hoop stress (σθ ) for the disk bulk and the cylindricalbulks with various inner diameters only by the cooling to 65 K.

The maximum σr value is smaller than σθ and the maximum position of the σr value is not situated at the inner periphery edge,
but in the bulk.
Fig. 5 summarizes the time step dependence of the maximumσθ and σr values shown in Fig. 4. The similar values for the
disk bulk with the same outer diameter (OD = 60 mm) arealso shown. The maximum compressive σθ and σr values foreach bulk attain at the maximum pulsed field. The maximum
compressive σθ of the cylindrical bulk is about twice as large asthat of the disk bulk.

Fig. 7. Applied pulsed field dependence of the maximum hoop stress (σθ ) at
65 K for the (a) cylindrical bulk (OD = 60 mm, ID = 36 mm) and (b) disk
bulk (OD = 60 mm).

that of the disk bulk. The compressive hoop stress by thethermal contraction is about ten times larger than that by theelectromagnetic force shown in Fig. 4(a).
In the actual PFM experiments, the stress by the flux pinninginduced magnetostriction is applied to the bulk cooled down
to 65 K. In this sense, the stress by the flux pinning induced
magnetostriction was added to that by the thermal contraction.
Fig. 7(a) shows the applied pulsed field dependence of the maximum hoop stress (σθ ) of the cylindrical bulk (ID = 36 mm)
at 65 K. The σθ values only by the cooling and only by theelectromagnetic force are also shown. The hoop stress without
cooling increases with increasing Bex . The maximum compressive hoop stress at 65 K, which is the sum of both contributions,exceeds −95 MPa for Bex = 3.0 T, which suggests that thevalue may be larger than that of the mechanical strength of
the REBaCuO bulk ranging 30–100 MPa [11], [12]. Fig. 7(b)shows the same relation for the disk bulk for comparison. The
hoop stresses for the disk bulk by both thermal contraction andelectromagnetic force is small, compared to those for the ringbulk (ID = 36 mm). In order to avoid the mechanical fractureof the cylindrical bulk during PFM, the reinforcement of theinner periphery part must be considered using, for example, aring material with negative thermal expansion coefficient andwith higher mechanical strength.

VI. C ONCLUSION
B. Thermal Contraction Down to 65 K
Fig. 6 shows the profile of the hoop stress (σθ ) for the disk
bulk and the cylindrical bulks with various inner diameters by
the only cooling to 65 K. For the disk bulk, the compressive
hoop stress is −35.4 MPa, which is independent of the distancefrom the center. For the cylindrical bulk, the compressive
hoop stress is enhanced at the inner periphery edge of thecylinder, which increases with increasing inner diameter. The
maximum compressive hoop stress of the cylinder 36 mm in
inner diameter is −89.1 MPa, which is about twice larger than

Pulsed field magnetization (PFM) for the GdBaCuO bulk
ring with an aluminum alloy bandage has been performed
at 65 K. A mechanical fracture was confirmed just after themagnetic pulse takes a maximum of 3 T. Using the numericalsimulation, it was confirmed that a huge compressive stress wasconcentrated at the inner peripheral edge of the ring bulk justafter the maximum magnetic pulse in PFM, together with thethermal contraction cooling down to 65 K. The reinforcementof the inner periphery part of the cylindrical bulk must be
considered.

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