42 Ë 2 Superconducting materials
1 × 10 −^6 to 1× 10 −^5 K.−^1 in temperatures of 40–300 K ina-bplane. The coefficient is
in the range 3× 10 −^6 to 1.5× 10 −^5 K−^1 in temperatures of 40–300 K along thec-axis
and rises approximately linearly up to 150 K, then more slowly rising [132]. Some
measurement methods and data of thermal expansion can be found elsewhere [133].
The thermal expansion associated with trapped flux will be discussed in Section 2.7.
2.6 Mechanical properties of HTS bulk
In addition to the thermal properties above, the mechanical properties of the HTS
bulks are also extremely important for industrial applications. HTS bulks are brittle
materials with poor mechanical properties. This is because a number of voids are
produced by oxygen formation or gas trapped in the MTG YBCO process. In addition,
material fractures are caused by the existence and propagation of microcracks in the
superconductor. In particular, thermal stress and fatigue are produced with repeated
and rapid changes between room and low operation temperatures and hence cause
failure of YBCO superconductors. When the highest trapped fields are generated by
the external magnetic fields, large stress/strains will be induced and cause more
serious rupture, which can be very dangerous. A number of researches have been
carried out to improve the mechanical properties of melt-textured YBCO. The Vickers
hardness test is one of the convenient methods to estimate the mechanical properties
of materials. The mechanical properties of HTS bulk associated with the application
are briefly discussed in this section. Detailed data of the mechanical properties for
YBCO bulks can be found elsewhere [63, 134].
The mechanical properties of YBCO samples can be determined using the na-
noindentation technique. Stress-strain curves (휎-휀) and mechanical properties such
as hardness (H), elastic modulus (E), fracture toughness (KIC), fracture strength (휎f),
and yield stress (휎ys) can be obtained from the applied load (P) vs. indentation depth
(h) data and with the corresponding tip indenter.
The density of the HTS materials depends strongly on the preparation and proces-
sing technique. The density of the HTS bulk materials prepared by MTG is larger than
that by the sintering process. The density of HTS films and single crystals is the largest.
For either MTG or the sintering process, some porosity problems in the interior of bulk
materials are inevitable. The density of the HTS bulk ceramic materials휌depends
strongly on their porosity. The magnitude of the elastic modulus of ceramic samples
depends strongly on their density휌, which is less than the theoretical maximum
density휌max=6.383 g/cm^3. The ratio휌/휌maxdenotes the relative density.
The hardness (H) correlates with yield strength and Young’s modulus of the
material. Vickers hardness is the preferred method since the indentation traces are
small, typically 10–100μm.
The elastic modulusEof an object is defined as the slope of its stress-strain curve
in the elastic deformation region. The elastic modulus (Young’s or elastic modulus)