A Constitutive Model for Thermoplastics with Some Applications (original) (raw)
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Constitutive model for thermoplastics with structural applications
International Journal of Impact Engineering, 2010
A constitutive model for thermoplastics is described, which allows for hyperelastic-viscoplastic response due to intermolecular resistance and entropic hyperelastic response due to re-orientation of molecular chains. The Raghava yield function is introduced to capture the pressure-dependent behaviour, and a non-associative viscoplastic flow potential is assumed for volumetric plastic strain control. The strainrate effects are formulated in a format suitable for structural applications. Assuming isothermal conditions, the material model requires 10 parameters which are easy to identify with uniaxial tensile and compressive tests. The constitutive model developed herein captures important features observed in polymers' behaviour, e.g. pressure dependency, volumetric plastic strain and strain-rate sensitivity. A detailed description of the constitutive model with numerical verification and parameter identification procedures is provided. Numerical simulations of three-point bending of beams and centrally loaded plates, all made of a polypropylene material, indicate that the constitutive model is able to predict reasonably well the load-carrying capacity observed in the tests.
A constitutive model for thermoplastics intended for structural applications
A constitutive model for thermoplastics is described, which allows for hyperelasticviscoplastic response due to intermolecular resistance and entropic hyperelastic response due to re-orientation of molecular chains. The Raghava yield function is introduced to capture the pressure sensitivity behaviour, and a non-associative viscoplastic flow potential is assumed for volumetric plastic strain control. The strain rate effects are formulated in a format suitable for structural applications. Assuming isothermal conditions, the material model requires 10 parameters which are easy to identify with uniaxial tensile and compressive tests. The constitutive model developed herein captures important features observed in polymers' behaviour, e.g. pressure dependency, volumetric plastic strain, strain rate sensitivity, and induced strain anisotropy. A detailed description of the constitutive model with numerical verification and parameter identification procedures is provided. Numerical simulations of * Corresponding author: mario.polanco@sintef.no 2 three-point bending of beams and centrally loaded plates, all made of a PP material, indicate that the constitutive model is able to predict reasonably well the load carrying capacity observed in the tests. A A A A J J J J
Behaviour of semi-crystalline thermoplastic polymers: Experimental studies and simulations
Computational Materials Science, 2012
The use of numerical simulations based on finite element analysis has become essential in designing new products, bridging basic material properties (obtained in various tests performed on material's specimens) and a product behaviour. Such simulations can account for a real geometry of designed components that can cause stress concentration as well as for in-service loading and/or environmental conditions. A challenging aspect for numerical simulations is anticipating the behaviour of advanced materials such as polymers and composites, demonstrating, i. a., anisotropy, heterogeneity and timedependent properties as well as non-trivial damage and fracture scenarios. The first step in achieving a valid product simulation is to perform simulations that can accurately reproduce the experimental results. The present work analyzes a possibility to simulate a response of a hyperelastic material (a semi-crystalline thermoplastic polymer) to monotonous uniaxial tensile loadings considering different strain-energy density functions as well as uniaxial cyclic loading using the commercial software ABAQUS/ CAE. The former case focuses on a stress-strain curve while the latter one deals with energy hysteresis, strain softening and strain hardening. The performed simulations produce good results for monotonous loading, but simulations of cyclic loading can only partially reproduce the material's behaviour.
A thermo-elasto-viscoplastic constitutive model for polymers
Journal of the Mechanics and Physics of Solids, 2018
In this study, a thermo-elasto-viscoplastic model is developed for a low density cross-linked polyethylene (XLPE) in an attempt to describe the combined effects of temperature and strain rate on the stress-strain response and the self-heating of the material at elevated strain rates. The proposed model consists of two parts. On the one side, Part A models the thermo-elastic and thermo-viscoplastic response, and incorporates an elastic Hencky spring in series with two Ree-Eyring dashpots. The two Ree-Eyring dashpots represent the effects of the main α relaxation and the secondary β relaxation processes on the plastic flow. Part B, on the other side, consists of an eight chain spring capturing the entropic strain hardening due to alignment of the polymer chains during deformation. The constitutive model was implemented in a nonlinear finite element (FE) code using a semi-implicit stress update algorithm combined with sub-stepping and a numerical scheme to calculate the consistent tangent operator. After calibration to available experimental data, FE simulations with the constitutive model are shown to successfully describe the stress-strain curves, the volumetric strain, the local strain rate and the self-heating observed in the tensile tests. In addition, the FE simulations adequately predict the global response of the tensile tests, such as the force-displacement curves and the deformed shape of the tensile specimen.
A viscoplastic constitutive model for polymeric materials
International Journal of Plasticity, 2008
Classical models based on the thermodynamics of irreversible process with internal variables dedicated to the inelastic analysis of metallic structures are modified and then used for modeling the mechanical behavior of polymers. The major difference comes from the expression of the yield criterion. Indeed, a generalized yield criterion, based on the parabolic Drucker and Prager criterion, is proposed including the first invariant of the stress tensor as well as the second invariant and the third invariant of the deviatoric part of the stress tensor. Close agreement between experimental data and yielding predictions is obtained for various polymers loaded under different states of stress. It has been established that the temperature T, the strain rate _ s, the critical molecular mass M c and the degree of crystallinity X c do not affect the parameter m of the proposed yield function. Furthermore, viscoplastic constitutive equations are developed in the framework of the general principles of thermodynamics with internal variables for generalized materials considering only the kinematic hardening rule. Experimental data obtained under different loading conditions are well reproduced by the proposed model. An accurate identification of the model parameters and the introduction of the isotropic hardening variable into the yield function and the drag stress will improve the predictions of the overall mechanical behavior of polymers especially the unloading path.
A constitutive model for finite deformation of amorphous polymers
International Journal of Mechanical Sciences, 2012
The paper introduces a three-dimensional constitutive model for the mechanical behavior of amorphous polymers, thermosets and thermoplastics. The approach is formulated in terms of finite deformations, appropriate for glassy polymers. The rheology of the model consists of a Langevin-type free energy function for the energy storage due to molecular alignment connected in parallel to a Maxwell element with a viscoplastic dashpot. The model proves successful for the constitutive description of glassy polymers over a large range of strain rates. To capture the smooth softening behavior upon yielding is the main purpose of this research. It is reached under consideration of absolute temperature and current strain rate with the proposed evolution law for the viscoplastic dashpot deformation. The rate-dependence of amorphous polymers is reproduced as well as the pressure dependence during different loading scenarios. A fully implicit numerical scheme appropriate for the finite element implementation is presented. The modeling capability of the proposed approach is demonstrated for epoxy, PC and PMMA. The efficiency of the proposed numerical scheme is demonstrated via a necking simulation of a flat PC coupon.
Response of semi-crystalline thermoplastic polymers to dynamic loading: A finite element study
Computational Materials Science, 2012
Mechanical behaviours and properties of polymers under dynamic loading conditions differ significantly from those under quasi-static loads. Consequently, for dynamic numerical analysis, a linear elastic/hyperelastic material model has its limitations and can produce inaccurate results. In order to obtain an adequate response to high-speed loading in simulations, a viscoelastic material model has been developed.
International Journal of Plasticity, 2018
In this paper, a new constitutive model is proposed for the behavior of thermoplastic polymers under non-isothermal conditions. The model couples linear viscoelasticity and viscoplasticity and thermal eects. It is formulated within the framework of irreversible thermodynamics. The total strain is the sum of viscoelastic, viscoplastic and thermal strains. General hereditary integrals describe the thermo-viscoelastic response. The viscoplastic part accounts for both isotropic and kinematic hardenings. The stress-strain response and the material self-heating are predicted and compared to experimental data on Polyamide 66 (PA66) and Polypropylene (PP). Good agreement between the numerical simulations and experimental data was obtained for the two materials.
Modelling the mechanical behaviour of polymers is a nontrivial task. Usual macroscopic approaches that decompose global deformation into three elementary components in a "a priori" manner often results in complex and "of limited efficiency" models. This study deals at promoting another concept of visco-hyper-elasticity for polymers close to Tg without arbitrary decomposition into "viscous" and "elastic" stresses or strains. To achieve that point, a hyper elastic model is extended to account for inelastic processes. Those latter are assumed to result in a kinetics of variation of internal variables that have to be accounted for in the energy balance at any time and that induce time effects in the writing. Variables of interest are related to de entanglement and/or strain induced crystallisation through specific kinetics laws. This version uses Edward-Vilgis' network theory that depends on four physical parameters: the density of fixed network nodes, the density of sliding nodes or entanglements, a parameter ultimately related to chain extensibility and a parameter ultimately representative for level of freedom of entanglements. The stress is written in the framework of Irreversible Processes Thermodynamics (IPT) and in the frame of large strain approximations. Mechanical problem is coupled to thermal problem using Taylor-Quinney coefficient β. Equations are included in a finite difference code (using a θ-method) to calculate temperature and stress through the central section of a sample. Parameters identification is based on the minimisation of a two objectives cost function that accounted for average axial stress in the section and for surface temperature at this section. This latter was written in a mean-square approach. .