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

Abstract

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, η. 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.

Accounting for viscoelastic effects in a multiscale fatigue model for the degradation of the dynamic stiffness of short-fiber reinforced thermoplastics

“…For viscoelasticity, phenomenological models include power-law models developed for, e.g., glass-fiber reinforced polypropylene [19], poly-propylene-wood composites [20] and sheet molding compounds (SMC) [21], or the HRZ [22]model developed for, e.g., short-fiber reinforced materials and also applied to long-fiber composites [23], describe the creep behavior accurately. Dacol et al [24] recently discussed an approach to transfer the relaxation properties analyzed in creep experiments to the dynamic behavior, valid for pure and reinforced polymers. Phenomenological progressive damage or fracture models, directly formulated for the composite material [25][26][27][28][29][30][31][32], may be used to model and predict the material behavior or the material degradation.…”

Theoretical and Experimental Investigation of Warpage Evolution of Flip Chip Package on Packaging during Fabrication

“…Conversely, the viscoelastic part gradually increases the strain (creep) or reduces the stress (relaxation), and eventually reaches stability. Polymer materials typically show viscoelastic relaxation behavior [13][14][15][16]. The stress relaxation effect is usually dominated by chemical phenomena at high temperatures for a long period of time.…”

Viscoelasticity in Large Deformation Analysis of Hyperelastic Structures

“…More information about the nonlinear dynamics of hyperelastic structures can be found in the recent review article [ 30 ]. Additionally, many studies have been carried out on analyzing viscoelastic structures [ 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 ]. Li et al [ 46 ] presented a perturbation approach for the lateral vibration analysis of viscoelastic microstructures.…”