A New Viscoelasticity Dynamic Fitting Method Applied for Polymeric and Polymer-Based Composite Materials

The accurate analysis of the behaviour of a polymeric composite structure, including the determination of its deformation over time and also the evaluation of its dynamic behaviour under service conditions, demands the characterisation of the viscoelastic properties of the constituent materials. Linear viscoelastic materials should be experimentally characterised under (i) constant static load and/or (ii) harmonic load. In the first load case, the viscoelastic behaviour is characterised through the creep compliance or the relaxation modulus. In the second load case, the viscoelastic behaviour is characterised by the complex modulus, E*, and the loss factor, eta. In the present paper, a powerful and simple implementing technique is proposed for the processing and analysis of dynamic mechanical data. The idea is to obtain the dynamic moduli expressions from the Exponential-Power Law Method (EPL) of the creep compliance and the relaxation modulus functions, by applying the Carson and Laplace transform functions and their relationship to the Fourier transform, and the Theorem of Moivre. Reciprocally, once the complex moduli have been obtained from a dynamic test, it becomes advantageous to use mathematical interconversion techniques to obtain the time-domain function of the relaxation modulus, E(t), and the creep compliance, D(t). This paper demonstrates the advantages of the EPL method, namely its simplicity and straightforwardness in performing the desirable interconversion between quasi-static and dynamic behaviour of polymeric and polymer-composite materials. The EPL approximate interconversion scheme to convert the measured creep compliance to relaxation modulus is derived to obtain the complex moduli. Finally, the EPL Method is successfully assessed using experimental data from the literature.