A Combined Exponential-Power-Law Method for Interconversion between Viscoelastic Functions of Polymers and Polymer-Based Materials.

Vitor Dacol,João R. Correia,Elsa Caetano

doi:10.3390/polym12123001

Abstract

Understanding and modeling the viscoelastic behavior of polymers and polymer-based materials for a wide range of quasistatic and high strain rates is of great interest for applications in which they are subjected to mechanical loads over a long time of operation, such as the self-weight or other static loads. The creep compliance and relaxation functions used in the characterization of the mechanical response of linear viscoelastic solids are traditionally determined by conducting two separate experiments—creep tests and relaxation tests. This paper first reviews the steps involved in conducting the interconversion between creep compliance and relaxation modulus in the time domain, illustrating that the relaxation modulus can be obtained from the creep compliance. This enables the determination of the relaxation modulus from the results of creep tests, which can be easily performed in pneumatic equipment or simple compression devices and are less costly than direct relaxation tests. Some existing methods of interconversion between the creep compliance and the relaxation modulus for linear viscoelastic materials are also presented. Then, a new approximate interconversion scheme is introduced using a convenient Laplace transform and an approximated Gamma function to convert the measured creep compliance to the relaxation modulus. To demonstrate the accuracy of the fittings obtained with the method proposed, as well as its ease of implementation and general applicability, different experimental data from the literature are used.

Highlights

The linear viscoelastic functions that describe the creep and relaxation behavior of polymers and polymer-based materials are mathematically equivalent, and each function contains essentially the same information on the creep and relaxation properties of those materials
Through an appropriate mathematical operation, a linear viscoelastic material function can be converted into another material function
In the second part, based on the works of Crevecoeur [13,14] and the study conducted in [15], this paper proposes a new interconversion procedure, which involves the combination of Laplace transform theory with an approximated Gamma function to convert the measured creep compliance to the relaxation modulus

Summary

Introduction

The linear viscoelastic functions that describe the creep and relaxation behavior of polymers and polymer-based materials are mathematically equivalent, and each function contains essentially the same information on the creep and relaxation properties of those materials. Through an appropriate mathematical operation, a linear viscoelastic material function can be converted into another material function. Despite the conceptual simplicity of the viscoelastic properties of polymeric materials, there are operational difficulties in obtaining them from experiments. In this context, interconversion procedures are especially useful due to the difficulty in running constant-strain relaxation tests on stiff materials and Polymers 2020, 12, 3001; doi:10.3390/polym12123001 www.mdpi.com/journal/polymers

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