Non-linear viscoelasticity for epoxy-based polymers: theoretical modeling and numerical implementation

Download

index.pdf

Date

2019

Author

Koral, Ateş

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

224
views

124
downloads

The present thesis aims at modeling creep behaviour under hydrostatic and uniaxial loadings of a certain silica filled epoxy compound at various temperatures with numerical implementation of algorithms into finite element method. Time dependent behaviour of polymers has been examined and many approaches have been proposed by researchers. Some of the models are inspired from micro-mechanical structure of polymers. These models generally take relaxation of a single entangled chain in a polymer gel matrix upon loading into account. In this thesis, a finite viscoelasticity model, which takes into account volumetric and isochoric creep/relaxation phenomena, is developed for epoxy-based compounds over glass transition temperature. Deformation gradient is multiplicatively split into elastic and inelastic parts and related with associated stretches of the single chain. In this thesis, the non-linear viscous evolution law proposed by Dal is adopted. As a novel aspect, apart from equilibrium bulk modulus parameter, in order to simulate time dependent volumetric creep behaviour of the epoxy compound, a viscous bulk modulus parameter is included in the proposed free energy function. Hence, volumetric effects in viscoelastic behavior is also taken into consideration without needing to split free energy function into volumetric and isochoric parts. Proposed model properly predicts behaviour of epoxy compound above 110 celsius degree in the rubbery state and also in the transition range. It has been demonstrated that the model prediction is quite satisfactory around and above the glass transition temperature, whereas the constitutive behaviour of the epoxy-moulding compounds at temperatures well below the glass transition temperature can not be captured as expected. The model parameters are identified from the experimental results. The algorithmic implementation of the model is carried out in the Eulerian setting in the sense of Dal and Kaliske and the computational performance is demonstrated through representative boundary value problem.

Subject Keywords

Polymers., Viscoelasticity, creep, stress relaxation, inelastic stretch, finite element method, non-linear viscoelasticity, epoxy, polymer, material modelling,continuum mechanics, computational mechanics, volumetric effects, time dependent, free energy function, uniaxial, hydrostatic.

URI

http://etd.lib.metu.edu.tr/upload/12624606/index.pdf
https://hdl.handle.net/11511/44469

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Finite viscoplasticity of amorphous glassy polymers in the logarithmic strain space Miehe, Christian; Göktepe, Serdar; Mendez Diez, Joel (Elsevier BV, 2009-01-01) The paper outlines a new constitutive model and experimental results of rate-dependent finite elastic-plastic behavior of amorphous glassy polymers. In contrast to existing kine-matical approaches to finite viscoplasticity of glassy polymers, the formulation proposed is constructed in the logarithmic strain space and related to a six-dimensional plastic metric. Therefore, it a priori avoids difficulties concerning with the uniqueness of a plastic rotation. The constitutive framework consists of three major ...
Coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory Miehe, Christian; Mendez Diez, Joel; Göktepe, Serdar; Schaenzel, Lisa Marie (Elsevier BV, 2011-06-15) The paper outlines a constitutive model for finite thermo-visco-plastic behavior of amorphous glassy polymers and considers details of its numerical implementation. In contrast to existing kinematical approaches to finite plasticity of glassy polymers, the formulation applies a plastic metric theory based on an additive split of Lagrangian Hencky-type strains into elastic and plastic parts. The analogy between the proposed formulation in the logarithmic strain space and the geometrically linear theory of pl...
Size dependent stability and surface energy of amorphous FePt nanoalloy Akdeniz, Mahmut Vedat; Mehrabov, Amdulla (Elsevier BV, 2019-06-05) The effects of particle size (2-6 nm) and temperature (300-2700 K) on the stability and local structural evolutions of amorphous equiatomic FePt bulk/nanoalloys have been investigated by combining Embedded Atom Model (EAM) with classical molecular dynamics (MD) simulation method. The three dimensional (3D) atomic configuration of amorphous FePt NPs by means of Voronoi analysis reveals that, deformed bcc (d-bcc) and icosahedron (d-ico) type structures are most probable local atomic configurations for 2-6 nm ...
The finite element method for MHD flow at high Hartmann numbers Nesliturk, AI; Tezer, Münevver (Elsevier BV, 2005-01-01) A stabilized finite element method using the residual-free bubble functions (RFB) is proposed for solving the governing equations of steady magnetohydrodynamic duct flow. A distinguished feature of the RFB method is the resolving capability of high gradients near the layer rep-ions without refining mesh. We show that the RFB method is stable by proving that the numerical method is coercive even not only at low values but also at moderate and high values of the Hartmann number. Numerical results confirming t...
A modular regularized variational multiscale proper orthogonal decomposition for incompressible flows Eroglu, Fatma G.; Kaya Merdan, Songül; Rebholz, Leo G. (Elsevier BV, 2017-10-01) In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The projection-based VMS stabilization is added as a separate post-processing step to the standard POD approximation, and since the stabilization step is completely decoupled, the method can easily be incorporated into existing codes, and stabilization parameters can be tuned independe...

Citation Formats

A. Koral, “Non-linear viscoelasticity for epoxy-based polymers: theoretical modeling and numerical implementation,” Thesis (M.S.) -- Graduate School of Natural and Applied Sciences. Mechanical Engineering., Middle East Technical University, 2019.