Relaxation modulus
Er(
t, ε) of polyethylene films measured at various temperatures from -20°C to near melting point under strain of 1_??_5% are expressed by following equations:
(1) Time-strain factorized model;
(2) Time-strain reduced model; In the above equations, the nonlinearized functions
f(ε) and
aε (ε) are approximated by where ε
0 is the reduced strain. The α
f; and α
a represent the nonlinearity in the respective models. The nonlinearities of high density polyethylene are greater than those of low density polyethylene at any temperature. The α
f and α
a decrease with increasing temperature in the low temperature range, while they depend less on temperature in the high temperature range.
The α
f and α
a are analyzed by a composite model of crystalline and noncrystalline phase and a free volume theory, respectively. If the various assumptions are introduced in the analyses on the basis of molecular aspects, the above experimental results are interpreted qualitatively.
Master curves of the time-temperature superposition reduced to 20°C at each strain are obtained by the horizontal shift alone. The shift factor
aT(
T) is found to be independent on strain at each temperature. The evaluated apparent activation energies, however, are larger than those in references. Since this result can not be explained resonably, it would be still premature to conclude that the time-temperature superposition might hold in the nonlinear stress relaxation process.
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