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Physics Procedia 58 (2014) 98 – 101

26th International Symposium on Superconductivity, ISS 2013

Mechanical properties of MgB2 bulks
A. Murakamia*, H. Teshimab, T. Naitoc, H. Fujishiroc, T. Kudoda

Department of Mechanical Engineering, Ichinoseki National College of Technology, Takanashi, Hagisho, Ichinoseki 021-8511, Japanb
Nippon Steel & Sumitomo Metal Corporation, 20-1 Shintomi, Futtsu 293-8511, Japanc
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, JapandAdvanced Course of Production Engineering, Ichinoseki National College of Technology, Takanashi, Hagisho, Ichinoseki 021-8511, JapanAbstract
MgB2 is one of promising bulk superconductors because grain boundaries are not weak-links in this material and thus the uniform
distribution of trapped magnetic fields is easy to obtain even for large samples. In the present study, mechanical properties of MgB2bulks with different packing ratio have been evaluated through bending tests for specimens cut from the bulks. The mechanicalproperties of MgB2 bulks are significantly influenced by their packing ratio or connectivity, and the fracture strength can be
improved by a factor of 5 by increasing the packing ratio to 90 % or over.

©
2014 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license© 2014 The Authors. Published by Elsevier B.V.
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Selection and peer-review under responsibility of the ISS 2013 Program Committee.
Peer-review under responsibility of the ISS 2013 Program Committee
Keywords: MgB2; Bulk superconductor; Bending test; Fracture strength

1. Introduction
MgB2 is one of promising bulk superconductors because grain boundaries are not weak-links in this material.
MgB2 bulk superconductors can be fabricated by sintering and thus the uniform distribution of trapped magnetic fields
is easy to obtain even for large bulk samples [1-3]. Since bulk superconductors are subjected to electromagnetic force
and thermal stress in the superconducting devices [4-6], understanding of mechanical properties, such as fracture
strength and Young’s modulus, of bulk superconductors is indispensable for the practical application. So far,evaluations of mechanical properties have been carried out for various RE-Ba-Cu-O (RE: Y or rare-earth elements)bulks [7] and MgB2 bulks [8]. However, mechanical properties of MgB2 bulks have not been understood extensively
in comparison with those of RE-Ba-Cu-O bulks. Further investigations are needed for the practical application ofMgB2 bulks. It is well-known that packing ratio of MgB2 bulks depends on fabrication process. In the present study,evaluations of mechanical properties of MgB2 bulks with different packing ratio have been carried out at room
temperature through bending tests for specimens cut from the bulks. Observations on the fracture surfaces are also
carried out.
2. Experimental
MgB2 bulk samples with different packing ratio, 50, 63 and 92 %, were prepared through ex-situ or in-situ process.
The packing ratios were measured by using the Archimedian method. Diameter of the bulk samples was 30-70 mm.
Samples with the packing ratio of 50 % were fabricated by using capsule method [1], which are denoted as Sample 50.
Samples with the packing ratio of 63 and 92 % were fabricated by using a HIP (Hot isostatic pressing) furnace, which*Corresponding author. Tel.:+81-191-24-4734; fax: +81-191-24-4734.
E-mail address: amura@ichinoseki.ac.jp

1875-3892 © 2014 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Peer-review under responsibility of the ISS 2013 Program Committee
doi:10.1016/j.phpro.2014.09.034

A. Murakami et al. / Physics Procedia 58 (2014) 98 – 101

are denoted as Samples 63 and 92, respectively. HIP pressure, temperature and time were 98-196 MPa, 1173 K and 3h, respectively. Mechanical properties of these bulk samples were evaluated through four-point bending tests. Bending
test specimens with the dimensions of 2.8 x 2.1 x 24 mm3 were cut from the bulk samples such that the longitudinal
direction of the specimens was almost perpendicular to the thickness direction of the bulk samples. In order to measure
the strain caused by loading, one strain gage was glued to the centre of the 2.8 x 24 mm2 surface of the specimens. Thegage length of the strain gage was 0.2 mm. Four-point bending load was applied at room temperature in the 2.1 mmdirection of the specimens under the crosshead speed of 0.2 mm/min. Stress ı caused by the loading was calculated by
the following equation.
V3P ( L  l )2 wt 2(1)

where P is the applied load, L is outer supporting span (21 mm), l is upper loading span (7 mm), w is width (2.8 mm)
and t is thickness (2.1 mm) of the specimens. After the bending tests, fracture surfaces were observed by using
scanning electron microscope.
3. Results and discussion
Fig. 1 shows stress-strain curves of specimens cut from the Samples 63 and 92. Non-linear stress-strain behavior
was observed for the Sample 63. Slope of the stress-strain curves of the Sample 63 decreases with increase of thestress. On the other hand, stress-strain curves of the Sample 92 are almost linear until the fracture. Non-linear stressstrain behavior of the Sample 63 is presumably attributable to the opening or slow speed propagation of cracks byloading.
㻌300

200
150

㻌

Stress [MPa]250Sample 92Sample 63100
5000.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Strain [%]Fig. 1. Stress-strain curves of Samples 63 and 92.
Fig. 2 shows mechanical properties evaluated through the four-point bending tests. It is notable that the fracture
strength is dramatically improved by a factor of 5 by increasing the packing ratio to 90 % or over as shown in Fig. 2(a). Owing to the increase of the packing ratio, Young’s modulus is also improved as shown in Fig. 2 (b). Suchimprovements of the mechanical properties are due to the increase of the net cross-sectional area and reduction ofdefects, where the stress concentration occurs, by increasing the packing ratio. Since it has been reported that
improvement of the fracture strength with decrease of the porosity of ceramic materials can be expressed by using anexponential equation [9], data points in Fig. 2 (a) are approximated exponentially. From the approximation of the datapoints, the fracture strength at the packing ratio of 100 % is estimated to be about 350 MPa.
Scatter of the fracture strength data of the high-strength Sample 92 was evaluated through the Weibull plots; larger
Weibull coefficient value means smaller scatter of the fracture strength data. The Weibull coefficient value is 6, whichis slightly smaller than the value of RE-Ba-Cu-O bulks 8-10 reported in Ref. [10].
Fig. 3 shows fracture surface of the bending test specimen which showed the maximum fracture strength of theSample 63. Fig. 4 (a) and (b) shows fracture surfaces of the bending test specimens which showed the maximum andminimum fracture strengths of the Sample 92, respectively. Bottom of the figures corresponds to the tensile side where
the fatal crack initiates by bending loading. It is difficult to identify the crack initiation site on the tensile side fracturesurfaces. The fracture surface of the Sample 63 is not smooth. On the other hand, the fracture surface of the specimen
which showed the maximum facture strength of the Sample 92 is relatively smooth and the tensile side is flat inparticular. Such a smooth fracture surface is commonly observed for fine ceramics. However, the fracture surface ofthe specimen which showed the minimum fracture strength of the Sample 92 is not smooth, which is similar to thefracture surface of the Sample 63. It is deduced that the rough fracture surfaces were formed by the crack propagations
through the sintering defects and that higher connectivity is another reason for the higher fracture strength value

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A. Murakami et al. / Physics Procedia 58 (2014) 98 – 101

observed for the Sample 92. Excluding the fracture strength data of exceptional specimens which have rough fracturesurfaces, the Weibull coefficient value of the fracture strength of the Sample 92 would be 16, which is comparable tothe Weibull coefficient values of conventional ceramics.
300

250
Ave.

200
150

Sf=0.772exp(0.0612pr)

100
50
04050

60

7080

Packing ratio pr [%]90250(b)
Ave.

200
150
100
50
040100㻌㻌(a)Young's modulus
[GPa]
㻌

300

㻌

㻌

Fracture strength
Sf [MPa]
㻌

350

50

60

70

80

90100

Packing ratio [%]Fig. 2. Mechanical properties evaluated through four-point bending test. (a) Fracture strength of Samples 50, 63 and92. (b) Young’s modulus evaluated from initial part of stress-strain curves of Samples 63 and 92.

Fig. 3. Fracture surface of bending test specimen which showed the maximum fracture strength of Sample 63. Bottomof figure corresponds to tensile side.

Fig. 4. Fracture surfaces of bending test specimens cut from Sample 92. (a) Specimen which showed the maximum
fracture strength. (b) Specimen which showed the minimum fracture strength.
Since MgB2 bulks have brittleness, understanding of fracture toughness as well as fracture strength is important forthe practical application. Fracture toughness evaluations are commonly carried out through fracture strength tests forspecimens with an artificial pre-crack or V-shaped notch. In the present study, fracture toughness of the Sample 92 isestimated from the fracture strength of specimens without the pre-crack and V-shaped notch. Fracture toughness KIC isrepresented by the following equation.
K IC

EVSa(2)where ı is the maximum applied stress, a is length of crack or notch, ʌ is the ratio of circumference of a circle to its
diameter and ȕ is shape factor, respectively. Eq. (2) can be rewritten as follows [11].

A. Murakami et al. / Physics Procedia 58 (2014) 98 – 101

K ICEV(3)S areawhere area is defect area projected to the plane perpendicular to the maximum principal stress. In order to obtain ȕ,
fracture strength, fracture toughness and defect size of RE-Ba-Cu-O bulks were substituted for ı, KIC, and area of Eq(3), respectively. Fracture strength of an RE-Ba-Cu-O bulk is 93 MPa [12], which has been evaluated through bending
tests under the same conditions as those in the present study. Fracture toughness of the same RE-Ba-Cu-O bulk is 0.8
MPa m1/2 [12]. Defect observed on the crack initiation site of an RE-Ba-Cu-O bulk had area of about 100 x 100 ȝm2[13]. As a result, 0.5 was obtained as ȕ. Thus, KIC is expressed as follows.
K IC

0 . 5V S(4)area

Since it is difficult to identify the fatal defect on the fracture surfaces as mentioned above, relationship between thefracture toughness and fatal defect area has been estimated by using Eq. (4) as shown in Fig. 5. If the fatal defect sizeof the Sample 92 is about 100 x 100 ȝm2 same as that of a RE-Ba-Cu-O bulk, the fracture toughness is estimated to beabout 2 MPa m1/2.
㻌43㻌

1/2

Estimated KIC [MPa m ]

5

2
10

4

5.0x105

1.0x105

1.5x105

2.0x1025

2.5x10Area of fatal defect [䃛m ]Fig. 5. Fracture toughness estimated from fracture strength of Sample 92.
4. Conclusion
In order to evaluate mechanical properties of MgB2 bulk samples with different packing ratio, four-point bending
tests for specimens cut from the bulk samples were carried out at room temperature. The mechanical properties of theMgB2 bulks are significantly influenced by their packing ratio or connectivity, and the fracture strength can beimproved by a factor of 5 by increasing the packing ratio to 90 % or over. Relationship between the fracture strengthand fracture surface morphology has been revealed. Fracture toughness has been estimated from the fracture strengthdata.
Acknowledgements
We appreciate experimental supports by students of Ichinoseki National College of Technology. This work wassupported in part by the NIFS Collaboration Research Program (NIFS13KECA019).
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