Constitutive Modelling of Thermoplastics: Parameters Identification Procedure (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
A Constitutive Model for Thermoplastics with Some Applications
A constitutive model for thermoplastics is outlined in this paper. The model consists of two parts: A hyperelastic-viscoplastic response due to in ermolecular resistance denoted Part A, and an entropic hyperelastic response due to re-ori ntation of molecular chains called Part B. Both parts are developed within a framework for finite strains. The main constituents are the Neo-Hookean model describing large elastic deformations, the pressure-sensitive Raghava yield function, a non-associated visco-plas tic flow potential and Anand’s stressstretch relation representing the intramolecular st iffness. The 11 non-zero coefficients of the model are identified from uniaxial tension and comp ression tests on two materials, HDPE and PVC, which are respectively semi-crystalline an d amorphous thermoplastics. Subsequently, it is employed in numerical simulatio ns f three-point bending tests on the same materials. The model gives satisfactory predictions when compared to experimental behaviour.
International Journal of Engineering Science, 2013
Solids usually show complex material behavior. If deformation is finite, the description of the kinematics makes the mechanical model complicated. In fact, one of the basic questions in the formulation and analysis procedures of finite deformation thermoelasticity is: ''How can the finite deformation thermoelasticity response be best accounted for in the kinematic formulation?'' A rather attractive way to proceed is to use the approach of small strain analysis, and decompose the total strain into a mechanical part and a thermal part. In this paper, based on the multiplicative decomposition of the deformation gradient, the mechanical and thermal strains are defined in the power and exponential forms. Also, the decomposition of the total strain into the mechanical and thermal strains is investigated for extension of various constitutive models at small deformation to the finite deformation thermoelasticity. In order to model the mechanical behavior of thermoelastic continua in the stress-producing process of nonisothermal deformation, an isothermal effective stress-strain equation based on the proposed strains is considered. Regards to this constitutive equation and assuming a linear dependence of the specific heat on temperature, the state functions including the internal energy, free energy, entropy and stress tensor are derived in the case of finite deformation thermoelasticity. Based on this decomposition and the proposed strains, it can be seen that these state functions are an extension from small deformation to finite deformation thermoelasticity. In addition, the mechanical and thermal material parameters are determined using the mechanical tests done at constant and the free thermal expansion test data, respectively. Ó 2012 Published by Elsevier Ltd. dx ¼ FdX ð1Þ where F is called deformation gradient tensor. Consider two material elements dX (1) and dX (2) at the reference configuration. Due to the motion characterized by the deformation gradient F, the material elements are transformed into dx (1) and dx (2) at time t:
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.
Thermomechanical constraints and constitutive formulations in thermoelasticity
Mathematical Problems in Engineering, 2003
We investigate three classes of constraints in a thermoelastic body: (i) a deformationtemperature constraint, (ii) a deformation-entropy constraint, and (iii) a deformationenergy constraint. These constraints are obtained as limits of unconstrained thermoelastic materials and we show that constraints (ii) and (iii) are equivalent. By using a limiting procedure, we show that for the constraint (i), the entropy plays the role of a Lagrange multiplier while for (ii) and (iii), the absolute temperature plays the role of Lagrange multiplier. We further demonstrate that the governing equations for materials subject to constraint (i) are identical to those of an unconstrained material whose internal energy is an affine function of the entropy, while those for materials subject to constraints (ii) and (iii) are identical to those of an unstrained material whose Helmholtz potential is affine in the absolute temperature. Finally, we model the thermoelastic response of a peroxidecured vulcanizate of natural rubber and show that imposing the constraint in which the volume change depends only on the internal energy leads to very good predictions (compared to experimental results) of the stress and temperature response under isothermal and isentropic conditions.
MRS Proceedings, 2008
Les résultats présentés dans ce travail concernent la mise en place d'une base de données matériau pour trois différents thermoplastiques: le polycarbonate, le polypropylene et l'acrylonitrile-butadiene-styrene. Des essais mécaniques de compression et traction ont été menés à différentes vitesses de déformation afin de caractériser leur comportement mécanique. Une loi de comportement viscoelastique-viscoplastique basée sur les modèles existants [2; 7-13] a été développée et implémentée dans le code éléments finis ABAQUS afin de prédire le comportement mécanique de ces polymères.
ON THE THERMOPLASTICITY CONSTITUTIVE RELATIONS FOR ISOPTOPIC AND TRANSVERSELY ISOTROPIC MATERIALS
Transstellar Journals, 2019
The widely used engineering construction materials such as fiber and laminated composite materials are usually under the thermomechanical forces and undergoes thermoplastic deformations. These composites may be considered as a transversely isotropic or orthotropic materials. In this paper, the plasticity constitutive relations for isotropic and transversely isotropy materials proposed in [33]are developed taking into account the temperature and written up the strain and stress space thermoplasticity constitutive relations for aforementioned materials. For simplicity, thermoplasticity theories are restricted to a small deformations. The usefulness and privileges of the strain space thermoplasticity constitutive relations for the formulation the coupled thermomechanical boundary value problems are discussed. It is found that the strain space thermoplasticity constitutive relations are more convenient for numerical solution of the coupled thermoplasticity boundary value problems as compared to stress space theory.
International Journal of Plasticity, 2006
A phenomenological one-dimensional constitutive model, characterizing the complex and highly nonlinear finite thermo-mechanical behavior of viscoelastic polymers, is developed in this investigation. This simple differential form model is based on a combination of linear and nonlinear springs with dashpots, incorporating typical polymeric behavior such as shear thinning, thermal softening at higher temperatures and nonlinear dependence on deformation and loading rate. Another model, of integral form, namely the modified superposition principle (MSP), is also modified further and used to show the advantage of the newly developed model over MSP. The material parameters for both models are determined for Adiprene-L100, a polyurethane based rubber. The constants once determined are then utilized to predict the behavior under strain rate jump compression, multiple step stress relaxation loading experiment and free end torsion experiments. The new constitutive model shows very good agreement with the experimental data for Adiprene-L100 for the various finite loading paths considered here and provides a flexible framework for a three-dimensional generalization.