Modeling of nonlinear hyper‐viscoelastic and stress softening behaviors of acrylonitrile butadiene rubber/polyvinyl chloride nanocomposites reinforced by nanoclay and graphene

Abstract

This research work is devoted to the development of multiple material models as constitutive equations for the description of the complex mechanical behavior of a series of nanocomposites based on the acrylonitrile butadiene rubber (NBR)/polyvinyl chloride (PVC) reinforced by nanoclay graphene. The preparation method and the mechanical with other properties of these nanocomposites were already investigated and reported in our previous work. The developed model consists of the Marlow hyperelastic integral equation, strain hardening power‐law equation for the nonlinear viscoelastic behavior as well as Ogden and Roxburgh equation to simulate the stress softening behavior. Stress relaxation tests were first carried out to show the nonlinear viscoelastic behavior of the samples. Simple tensile and volumetric tests were performed for Marlow model. The parameters of the nonlinear viscoelastic and stress softening equations in the model were determined by solving an inverse problem using a novel numerical algorithm, which was based on the combination of an optimization loop using Down Hill simplex method and finite element simulation of a dumbbell test specimen under load. To achieve this task, quasi‐static tests under cyclic loading with different final extensions and three extensional rates were also performed. Then, their corresponding finite element models were developed and the associated inverse problems were solved. Comparing the force‐displacement data obtained via simulation using the mentioned model with their corresponding experimental data confirms of the model correctness and its applicability. Moreover, the mechanical behaviors of both neat and reinforced polymer blend (NBR/PVC) with nanofillers are shown to be supportive of the computed parameters.

Effects of nonlinear hyper-viscoelasticity and matrix/fiber debonding on mechanical properties of short carbon fiber/SBR composites under cyclic uniaxial loads using an RVE-based multiscale finite element model

“…The details of the above-mentioned model can be found in our previous works. See for examples [26,27]. In order to nd the parameters of the material model, the MCalibration software [28] was used.…”

Analysis and modeling of modified styrene–acrylonitrile/carboxylated acrylonitrile butadiene rubber nanocomposites filled with graphene and graphene oxide: Interfacial interaction and nonlinear elastoplastic behavior

“…In recent years, the Bergstrom-Boyce model has been used in many studies to predict stressstrain behavior of nanocomposites. [20] Based on this model, stress-strain behavior of nanocomposites could be divided into two parallel components including A and B networks, the hyperelastic equilibrium response or spring, the time-dependent viscoplastic response, respectively. Network B could be divided into two series components including hyperelastic and time-dependent elements (Figure 1).…”

Experimental and modeling studies of IPDI‐based polyurea elastomers – The role of hard segment fraction

“…The phase‐separated structure of the polymer plays a significant role in determining its mechanical properties. In particular, concentrating on linear elasticity as measured by Dynamical Mechanical Analysis (DMA)—also referred to as Dynamical Mechanical Spectroscopy (DMS) or Dynamical Thermal Mechanical Analysis (DMTA)—and tensile stress–strain behavior, it is possible to utilize micromechanical models typically used for two‐phase composites, with the soft phase playing the role of the matrix and hard phase playing the role of the filler 26–32 . In these micromechanical models, the modulus of the overall composite material is determined by the filler volume‐fraction and the modulus ratio of the filler and the matrix; in particular, the rigidity of the composite increases rapidly once the filler volume fraction exceeds the percolation threshold.…”

“…In particular, concentrating on linear elasticity as measured by Dynamical Mechanical Analysis (DMA)-also referred to as Dynamical Mechanical Spectroscopy (DMS) or Dynamical Thermal Mechanical Analysis (DMTA)-and tensile stress-strain behavior, it is possible to utilize micromechanical models typically used for two-phase composites, with the soft phase playing the role of the matrix and hard phase playing the role of the filler. [26][27][28][29][30][31][32] In these micromechanical models, the modulus of the overall composite material is determined by the filler volume-fraction and the modulus ratio of the filler and the matrix; in particular, the rigidity of the composite increases rapidly once the filler volume fraction exceeds the percolation threshold. Ginzburg et al 30 proposed that the percolation threshold in segmented polyurethanes is roughly equal to the spherical-to-cylindrical order-order transition for the corresponding multiblock copolymer; based on this assumption, they calculated Young's modulus at room temperature as a function of the hard segment weight-fraction (HSWF) for several model PU elastomers, and found a good semi-quantitative agreement between model and experiment.…”