A numerical time-frequency transform technique is described that can be used to determine the complex modulus of a material as a function of frequency from stress relaxation experiments. This technique uses analog-to-digital data acquisition techniques to obtain the time domain response over several decades of time. Numerical filtering techniques are then applied to reduce spurious noise. An exponential interpolating function is fit to the relaxation data and this function is then transformed into the frequency domain with the use of piece-wise integration of the Laplace transform. The error associated with the numerical transform technique is found to be very small (on the order of 10−4%) when analyzing ideal behavior.
An experimental apparatus is developed and used in conjunction with this technique and initial tests of poly(methyl methacrylate) (PMMA) and polyethylene (PE), and PMMA/GF composites reveal that relaxation peaks (maximums in the loss modulus) associated with molecular transitions in the polymers can be detected with this method. Modulus-temperature-frequency plots indicate that the methodology is able to detect changes in peaks with increasing or decreasing temperature and that some of these peaks appear to correlate with known molecular transitions.