CONVERSION OF OSCILLATORY SHEAR DATA FROM HIGHLY FILLED POLYMERS BY DIRECT NUMERICAL-INTEGRATION

A procedure was developed to enable the direct numerical integration o f the Fourier integral transform equation relating G(t) to G'(omega) b y considering integration limits that vary as a function of time and w hich define a range of discrete sub-intervals within the complete freq uency domain data set. The method provides results that are in very cl ose agreement to results determined from a relaxation spectrum. Howeve r, at low values of time the solution to the variable limit integral t ransform is sensitive to the absence of a contribution beyond the uppe r experimental limit of the frequency domain data. G(t) results determ ined from the conversion of shifted master G'(omega) experimental data using the variable limit integral transformation and the relaxation s pectrum compared favourably with actual shifted master G(t) experiment al data. The former curves were characterised by the same form and tre nd as the experimental results, confirming that the underlying viscoel astic behaviour is well represented. While the variable limit Fourier integral transform procedure provides a good approximation to relaxati on spectrum results, the latter is clearly the more robust method of c onverting data from the frequency to the time domain. It was observed that the time-temperature superposition procedure used in the construc tion of shifted master curves can magnify potential differences betwee n the shifted G(t) values determined from the conversion of G'(omega) data and the actual experimental G(t) results, when compared to data t hat has not been shifted to a master curve.