Superplasticity by internal frictional heat under biased cyclic loading

Abstract

A new damping method was developed not only as a testing tool to investigate in situ deformation under stress, but also as a processing method to superplastically deform ceramics. The specific damping capacity (SDC) at low frequencies (<0.2 Hz) decreased with increasing frequencies, which matched previous internal friction results. However, at higher frequencies (0.2–5 Hz) SDC increased with frequencies, which was explained by a new internal frictional heat mechanism. Three different ceramics: a non-superplastic one and two superplastic ones with different activation energies, showed the same behavior at the high frequency damping tests (1–5 Hz). From these results, it was deduced that a cyclic load at high frequencies, superimposed on a static one, has a great potential to enhance superplasticity by specifically heating up grain boundaries from internal frictional heat.

Appendix I Estimation of temperature increase at grain boundaries under biased cyclic loading

Temperature increase by internal friction heat can be estimated from tribology theories. Suppose the tribology theory remains valid in the microscopic scale (sub micrometer), and the temperature increase ΔT [19] is:

$$ \Delta T = \frac{{2\mu Pvl}} {{k\sqrt {\pi (1.011 + \frac{{vl\rho C_p }} {{2k}})} }} $$

in which, the heating rate μ is the friction coefficient, P is the normal stress, ν is the relative velocity, l is width of the sliding band, k is thermal conductivity, ρ is the density, and C _p is the specific heat capacity. In our tests,

$$ \mu {\hbox{ = }}0.2,P{\hbox{ = }}20\;{\hbox{MPa, }}\rho {\hbox{ = 6050}}\;{\hbox{kgm}}^{ - {\hbox{3}}} {\hbox{, }}C_p {\hbox{ = 400}}\;{\hbox{Jkg}}^{ - {\hbox{1}}} \;{\hbox{K}}^{ - {\hbox{1}}} {\hbox{, }}k{\hbox{ = 2}}\;{\hbox{Wm}}^{ - {\hbox{1}}} \;{\hbox{K}}^{ - {\hbox{1}}} $$

For TZ3Y specimens in our test, the average grain size is about 300 nm, the sample size is 3 × 3 × 5 mm, $l{\hbox{ = 300}}\;{\hbox{nm $ \times $ }}\frac{{{\hbox{3}}\,{\hbox{mm $ \times $ 3}}\;{\hbox{mm}}}} {{{\hbox{300}}\,{\hbox{nm $ \times $ 300}}\,{\hbox{nm}}}}{\hbox{ = 30}}\,{\hbox{m}}$ Supposing the displacement is caused by uniform grain boundary sliding, for a 10 MPa as stress amplitude and 20 MPa as static stress, the relative velocity was determined to be ν = 1.0 × 10⁻⁵ ms⁻¹ from the actual displacement amplitude at f = 1 Hz and ν = 2.0 × 10⁻⁵ ms⁻¹ at f = 2 Hz, we have ΔT = 50 °C for f = 1 Hz and similarly, we have ΔT = 71 °C for f = 2 Hz.