Stochastic Generalized-Order Constitutive Modeling of Viscoelastic Spectra of Polyurea-Graphene Nanocomposites

Abstract

Polyurea (PUa) elastomers are extensively used in a wide range of applications spanning from biomedical to defense fields due to their enabling mechanical properties. These materials can be further reinforced through the incorporation of nanoparticles to form nanocomposites. This study focuses on an IPDI-based PUa matrix with exfoliated graphene nanoplatelet (xGnP) fillers. We propose a generalized constitutive model by integrating one Fractional Maxwell Model (FMM) and one Fractional Maxwell Gel (FMG) branch in a parallel configuration via introducing a new dimensionless number to bridge between these branches physically and mathematically. Through systematic local-to-global sensitivity analyses, we investigate the behavior of these nanocomposites to facilitate simulation, design, and performance prediction. Consistently, the constructed models share the same most/least influential model parameters. $α_1$ and $E_{c_1}$, the power exponent and the characteristic modulus of the first branch, are found to be the most influential model parameters, while $τ_{c_2}$ and $τ_{c_1}$, the characteristic time-scales of each branch, are recognized as the least influential model parameters. The proposed PU nanocomposite constitutive laws can now make an impact to the design and optimization of coating and shock-absorbing coatings in a range of applications.

Figures (14)

• Figure 1: Schematic illustration of a (b) Fractional Maxwell Model (FMM) and its two limiting cases: (a) Fractional Maxwell Gel (FMG) and (c) Fractional Maxwell Liquid (FML).
• Figure 2: Schematic of two constitutive models considered in the present study: (a) FMG-FMG model: The FMG1 branch corresponds to the filler soft phase, and the FMG2 branch corresponds to the percolated hard phase (both consist of a spring-pot and a spring in series). (b) FMM-FMG model: the FMM1 branch (consists of two spring-pots in series) corresponds to the filled soft phase, whereas the FMG2 branch corresponds to the percolated hard phase.
• Figure 3: Schematic representation of the polyurea-GnP nanocomposite morphology. Here, SP is soft phase, PHP is percolated hard phase, DHP is dispersed hard phase, and GNP is graphene nanoplatelet. The distance $L$ is the "characteristic size" (on the order of 15-20 nm) that usually is seen as a peak in small-angle X-ray scattering experiments.
• Figure 4: Master curves for the tensile storage and loss moduli. (a) 20% HSWF matrix with 0, 0.5, 1.0, and 1.5 wt.% xGnP. (b) Same as (a) for the 30% HSWF matrix. (c) Same as (a) for the 40% HSWF matrix.
• Figure 5: Experimental and FMM-FMG master curves fitted for 40% HSWF nanocomposite systems with (a) no added nanofillers; (b) 0.5 wt.% xGnP; (c) 1.0 wt.% xGnP; (d) 1.5 wt.% xGnP. Circles and triangles represent the storage and loss modulus, respectively; Blue and red solid lines are the storage and loss moduli model fits, respectively.