576 Chapter 13: Mechanical Properties
Uemura and Takayanagi (1966) developed expressions for the shear
modulus and Poisson's ratio in an elastic two-phase system; Reddy
et al.
(1995), taking the inclusions to be voids, applied those expressions and found
G (7 - 5Vo) (1 - p)
= (24)
G O 15(1 -
Vo) p +
(7 - 5Vo)(1 - p)
B 4G0(1 -p)
9 (25)
Bo 4Go + 3Bop
Ledbetter
et al.
(Ledbetter and Datta, 1986; Ledbetter
et al.,
1994) applied
scattering theory to a homogeneous composite material consisting of a random
distribution of spheroidal particles in a continuum matrix. By considering the
inclusions to be massless voids with zero elastic resistance to shear and dilatation,
the shear and bulk moduli were expressed as
1
Go - 2--~1 [-A2
+ (A 2 - 4A1A3) '/2]
(26)
4G~
(27)
B~ -- 4(1 -
p)G o - 3pB
A 1 -8(1 -p),
A 2 - (3 -
2p)B - (8 + 4p)G,A 3 _
-3(1
+p)BG.
(28)
d. Property Data
Data for elastic properties are given in Tables 13.2 to 13.5. The elastic modulus
did not exceed 200 GPa for any material in Table 13.2, and the typical value was
on the order of only 100 GPa. The Bi : 2212 and Bi(Pb) : 2223 materials tended to
have an elastic modulus of less than 50 GPa, with the exception of one study
(Chang
et al.,
1993) that found highly anisotropic results for highly textured
Bi:2212 (nearly 120GPa in the ab-plane and about 45GPa along the c-axis).
Values of Poisson's ratio, Tablel3.5, were in the range from 0.1 to 0.3.
C
Strength
High-T c superconductors are predominantly brittle materials; that is, in a plot of
tensile stress vs strain, as illustrated schematically in Fig. 13.1, there is a critical
strain at which the material fractures. This situation is distinct from the behavior
of metals that deform plastically prior to the occurrence of material failure.
Conceptually, brittle fracture is the catastrophic propagation of a crack through
continguous regions of a material body resulting in the rupture of that body into