Time-temperature superposition principle on relaxational behavior of wood as a multi-phase material

The time-temperature superposition principle of wood is discussed by modeling the relaxation spectrum of wood and then the application is examined, considered a high order structure and a multi-phase system for wood. The relaxation spectrum of wood was theoretically derived on the several assumptions. After theoretical calculation on the assumptions, in the relaxation time region where wedge-type spectra overlap each other, which is probable for wood, the spectrum of wood is represented by $$lnH = - M_0 (ln\tau - lnA_T ) + M_1 $$ , whereM ₀ andM ₁ are constants related to volume fractions of wood components.A _T is represented by the following equation as a parameter which is the product of a slope (?b and ?c) of a wedge-type spectrum and a volume fraction (φ _B andφ _C) of a wood component related to the relaxation process: $$lnA_T = \phi _B b/ (\phi _B b + \phi _c c) \cdot lna_{Tb} + \phi _C c/ (\phi _B b + \phi _C c) \cdot lna_{Tc} $$ , wherea _Tb anda _Tc are shift factors of wedge-type spectra of wood components. This equation shows that the apparent shift factorA _T consists of shift factors of the relaxation processes of wood components. Consequently, the time-temperature superposition principle does not unconditionally apply for wood, since the temperature dependence of relaxation times is generally different from each other for relaxation processes of wood components. This can explain the experimental result for wood that relaxation curves at various temperatures do not superpose on a relaxation curve at a reference temperature, that is, the principle cannot be applied.