Applications of exact causality relationships to materials dynamic analysis

Using the DMA (dynamic mechanical analyzer), measurements of the viscoelastic properties of materials can be carried out: complex Young’s modulus or shear modulus. By applying the ‘WLF time–temperature equivalence principle’, one can obtain ‘master-curves’ from a sweeping in both frequency and temperature. The practical boundaries make the mechanically scanned frequency domain very limited, but the frequency–temperature equivalence allows to put together the different frequency sweepings that were made at different temperatures, and to synthesize them in one pair of master-curves (real and imaginary parts). With a linear viscoelastic assumption, these curves are linked by a causality relationship, as are the phase and log-amplitude. This relation is expressed in terms of Hilbert transform. We built an algorithm that is convenient for very large frequency intervals (30 powers of ten). Examples are shown of phase generating from the magnitude measurement, and of master curve quality assessment from a causality defect.