Page 357 - Book Hosokawa Nanoparticle Technology Handbook

6.2 MECHANICAL PROPERTIES FUNDAMENTALS

10 -1
3Y-TZP

-2 1,673K
10

-3
10
Strain rate (s -1 ) 10 -4 1,373K

10 -5
Charit L=370nm
Figure 6.2.14 -6 Morita L=224nm
10 Owen L=410nm
Stress–strain curves in superplasticity of zirconia/alumina
Nanomaterial L=63nm
composite [7].
10 -7
1 10 100 1,000
A typical example of stress–strain curve is shown in Stress (MPa)
Fig. 6.2.14. Important properties for superplastic
forming are maximum elongation, flow stress and Figure 6.2.15
strain rate sensitivity index (m-value). Japanese Relationship between stress and strain rate in
Industrial Standards for testing superplasticity have nanocrystalline zirconia [8].
been established for metals.
JIS H 7007: Glossary of terms used in metallic cavity volume fraction C , it is necessary to evaluate
v
it for quality assurance
superplastic materials.
JIS H 7501: Method for evaluation of tensile
C 0 100[%] (6.2.14)
properties of metallic superplastic materials. v
JIS H 7502: Method for evaluation of compressive 0
properties of metallic superplastic materials. where is the density and the initial density.
0
JIS H 7503: Method for measurement of cavity 6.2.3.3 Creep and superplasticity in nanocrystalline
volume fraction of superplastically deformed materials
metallic materials. The strain rate is often expressed by the following
semi-empirical equation [9]
The superplastic elongation or elongation to fracture
[%] is defined by multiplying 100 to the nominal p n
⎛
strain of equation (6.2.9). Superplasticity is defined AGb b ⎞ ⎛ 0 ⎞ ⎟ D (6.2.15)
⎜ ⎟ ⎜
as an ability of polycrystalline material to exhibit kT ⎝ ⎠ ⎝ G ⎠
d
B
large elongations more than several hundreds percent

in the glossary (JIS H 7007). It is more than 300% for where is the strain rate, b the Burgers vector, G the
metals and about 100% for ceramics usually. shear modulus, the stress, the threshold stress, n
0
The relationship between strain rate and stress at the stress exponent, d the grain size, p the grain size
elongation of 10% is shown in Fig. 6.2.15 as an exam- exponent, D D exp ( Q/k T ) the diffusion coef-
0
B
ple. The slope of the curve is stress exponent n, and ficient, Q the activation energy, T the temperature and
the strain rate sensitivity index is the inverse of the k the Boltzmann’s constant.
stress exponent, m 1/n. The stability of tensile At high stresses, dislocation creep is controlled by
deformation, that is a uniform elongation of metals vacancy diffusion for dislocation climb. The stress
without necking, is dependent on strain rate sensitiv- exponent is n 3, and the grain size exponent is
ity index m 0.3. Generally the strain rate sensitivity p 0. At lower stress level, diffusional creep takes
index varies with stress. place. While atoms diffuse through the lattice in
Cavities or voids may be formed during superplas- Nabarro–Herring creep (n 1 and p 2), atoms diffuse
tic deformation. Since the mechanical performance of along grain boundaries in Coble creep (n 1 and p 3).
the superplastically formed products drops with The diffusional creep is enhanced with decrease in the
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