Calculation of discrete retardation spectra from creep data — I. Method

Abstract

A new method is proposed for the calculation of discrete retardation spectra from creep and recovery data. The calculation of the spectrum is not restricted to a special region of consistency, e.g., the terminal region. In a retardation time window which has to correspond to the time window of the original data set a spectrum can always be calculated. A linear regression technique is applied to the measured data in the iterative calculation of a spectrum with a logarithmically equidistant spacing of retardation times. In this way the number of retardation times is limited and problems with ill-posedness are avoided. In order to obtain only positive retardation strengths it is necessary to shift the set of prescribed logarithmically equidistant retardation times on the logarithmic time scale. It can be shown that there is a retardation time interval for this shift, in which the retardation times may be varied without obtaining negative retardation strengths. While varying the retardation times in this interval the relative error of description of the data passes through a distinct minimum. In this way a spectrum is obtained which best describes the input data. Generally, one retardation time per decade will be sufficient to describe the data within the limits of experimental error. In the case of noisy data, the method is shown to work just as well and leads to a smoothing of the original data set. The method may be used for the conversion of creep and recovery data to storage and loss compliance. The error connected with this procedure is discussed.