Näherungsmethoden in der Theorie des Viscoelastischen Verhaltens I

Abstract

Linear viscoelastic behaviour is described by a system of complicate equations (chapter 2). As these equations contain integral transformations they cannot be applied to experimental curves which are defined graphically only. Using Alfrey's approximation method a complete system of approximate equations is obtained of a very simple character. By differentiation of the creep curve, resp. the relaxation curve the retardation spectrum resp. the relaxation spectrum can be found without using the elasticity modulus E (5.5). The creep curve and the relaxation curve are reciprocal and yield unity on multiplication (5.7). The relaxation curve is a continuation of the real part of the complex elasticity modulus so that these two curves can be considered as two branches of the “generalised relaxation curve”. In the same way the creep curve without flow yields together with the real part of the compliance, the “generalised creep curve” (5.11). The spectra can be obtained from the generalised curves by differentiation (5.15), a formalism which may be transferred into the logarithmic time scale (chapter 6). By introducing the approximation into the main equations one obtains very perspicuous expressions for the stress-strain-relations (7.1). The obtained results should make it possible, to control creep and relaxation measurements by one another, to change from one dynamical function to the other and to compare static and dynamic measurements by varying the timescale (time-temperature relation).