On the measurement of the activation energies for creep and stress relaxation

A theory is proposed which enables activation energies for creep (ΔHc), and stress relaxation (ΔHs,r) to be calculated when the limiting moduli vary with temperature. The theory explains the agreement obtained by Kê between ΔHc, ΔHs.r. and the activation energy for internal friction ΔHi, f. for the grain boundary relaxation in aluminium . The theory rectifies the existing discrepancy between ΔHc (or ΔHs.r.) for the β-relaxation in polymethyl methacrylate (PMMA) and ΔHi.f.. The discrepancy is shown to be due to the assumption that GU and GR, the unrelaxed and relaxed moduli, do not vary with temperature. It is eliminated by assuming that both limiting moduli have the same finite temperature dependence. This temperature dependence is obtained from measurements of the real component of the shear modulus G'(ω) at 3·3 x 104 c/s on the assumption that in the β-region ( — 50 to 20 °C) and at this frequency the temperature dependencies of G'(ω) and GUare the same. It is probable that the many previous determinations of ΔHc and ΔHs.r. for rigid polymers exceed the true values by amounts of the order of 70%, the discrepancy in PMMA . The theory is also used to determine ΔHs.r. for a Snoek relaxation for which GU decreases and GR increases with increasing temperature. The result obtained for oxygen in tantalum is ΔHs.r.= 27 kcal/mole in agreement with ΔHi.f..