Discussion on the method for the measurement of the flexural modulus of coupled materials and reasons of the shifts of theQ −1 maxima caused by coupling

Summary When measuringQ^–1 and the flexural resonance frequency of bars clamped at one end, constituted by a viscoelastic polymeric material glued to a rigid support of modulusE₁, it is possible to calculate the componentsE₂ andE₂ of the complex elastic modulus of the polymeric material examined. In this work the minimum (critical) value of the ratioa=E₂/E₁=a_c and the values of the ratioQ₂^–1/Q^–1=F₁ are evaluated beyond which no exact calculation ofE₂ and ofQ₂^–1 is possible.Within the confidence limits of the linear viscoelasticity theory, these values depend on the accuracy of measurement of both frequency and resonance curve, as well as on the instrument employed, on the operating temperature and on the ratio between the thicknesses of the two coupled materials.In order to keep outside the critical conditions, the most convenient method involves the use of measurements of coupled test-pieces having different ratiosz between their thicknesses and of supports having different modulusE₁, depending on the field of temperature of the analysis ofE₂ and tg ₂ concerning and E.P.R. elastomer and a vulcanized cis-1,4 polyisoprene in very wide ranges of temperature comprising the glass transition. Moreover, it is demonstrated by analysis the shift on the temperature axis of the tg maximum of the composite test-piece with respect to the position of the tg maximum of the polymeric material alone.With 11 figures and 1 table