Constitutive modeling of polymer materials at impact loading rates (original) (raw)
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International Journal of Solids and Structures, 2007
A robust physically consistent three-dimensional constitutive model is developed to describe the finite mechanical response of amorphous polymers over a wide range of temperatures and strain rates, including the rubbery region and for impact loading rates. This thermomechanical model is based on an elastic-viscoplastic rheological approach, wherein the effects of temperature, strain rate, and hydrostatic pressure are accounted for. Intramolecular, as well as intermolecular, interactions under large elastic-inelastic behavior are considered for the mechanisms of deformation and hardening. For a wide range of temperatures and strain rates, our simulated results for poly(methyl methacrylate) (PMMA) and polycarbonate (PC) are in good agreement with experimental observations.
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.
EPJ Web of Conferences, 2015
During the last decades, the part of polymeric materials considerably increased in automotive and packaging applications. However, their mechanical behaviour is difficult to predict due to a strong sensitivity to the strain rate and the temperature. Numerous theories and models were developed in order to understand and model their complex mechanical behaviour. The one proposed by Richeton et al. [Int. J. Solids Struct. 44, 7938 (2007)] seems particularly suitable since several material parameters possess a strain rate and temperature sensitivity. The aim of this study is to implement the proposed constitutive model in a commercial finite element software by writing a user material subroutine. The implementation of the model was verified on a compressive test. Next a normal impact test was simulated in order to validate the predictive capabilities of the model. A good agreement is found between the FE predictions and the experimental results taken from the literature.
Simulation of impact tests on polycarbonate at different strain rates and temperatures
2011
The use of lighter and impact resistant materials, such as polymers, in vehicular systems is an important motivation for the automotive industry as these materials would make vehicles more fuel-efficient without compromising safety standards. In general, polymers exhibit a rich variety of material behavior originating from their particular microstructural (long molecular chains) behavior that is strongly temperature, pressure, and time dependent. To capture such intricate behavior, a number of polymer constitutive models have been proposed and implemented into finite element codes in an effort to solve complex engineering problems (see for a review of these models). However, developing improved constitutive models for polymers that are physically-based is always a challenging area that has important implications for the design of polymeric structural components.
2012
This paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress state dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation , developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by in which physically-based internal state variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for (i) the material strain softening induced by the polymer chain slippage; (ii) the material strain hardening at large strains induced by chain stretching between entanglement points; (iii) the time, temperature, and stress state dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress states. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions.
A general inelastic internal state variable model for amorphous glassy polymers
Acta Mechanica, 2010
This paper presents the formulation of a constitutive model for amorphous thermoplastics using a thermodynamic approach with physically motivated internal state variables. The formulation follows current internal state variable methodologies used for metals and departs from the spring-dashpot representation generally used to characterize the mechanical behavior of polymers like those used by Ames et al. in Int J Plast, 25, 1495–1539 (2009) and Anand and Gurtin in Int J Solids Struct, 40, 1465–1487 (2003), Anand and Ames in Int J Plast, 22, 1123–1170 (2006), Anand et al. in Int J Plast, 25, 1474–1494 (2009). The selection of internal state variables was guided by a hierarchical multiscale modeling approach that bridged deformation mechanisms from the molecular dynamics scale (coarse grain model) to the continuum level. The model equations were developed within a large deformation kinematics and thermodynamics framework where the hardening behavior at large strains was captured using a kinematic-type hardening variable with two possible evolution laws: a current method based on hyperelasticity theory and an alternate method whereby kinematic hardening depends on chain stretching and material plastic flow. The three-dimensional equations were then reduced to the one-dimensional case to quantify the material parameters from monotonic compression test data at different applied strain rates. To illustrate the generalized nature of the constitutive model, material parameters were determined for four different amorphous polymers: polycarbonate, poly(methylmethacrylate), polystyrene, and poly(2,6-dimethyl-1,4-phenylene oxide). This model captures the complex character of the stress–strain behavior of these amorphous polymers for a range of strain rates.
Strength and deformation of rigid polymers: the stress–strain curve in amorphous PMMA
Polymer, 2003
Poly(methyl methacrylate) (PMMA) is used to model the relaxation and plastic flow mechanisms of deformation, and the characteristic stress -strain response, relating it to its structure as much as it is known. The scope of this work is to identify and quantify the micromechanisms and the corresponding stress-strain relationships, and to assemble these into a coherent and self-consistent model for the observed mechanical behaviour. Detailed relationship between relaxation strength and time constants has been derived for some of the secondary motions. It is proposed that plastic events occur when the tension in chain segments pulls the chains out of/through constriction points. The scheme for simulating the isothermal true stress -strain curve is carried out under the following limitations: (i) geometrical effects, such as elastic instability and necking, (ii) thermodynamic adiabatic effects, and (iii) structural and kinetic effects, such as may arise from quenching or annealing, are neglected. Qualitative agreement achieved here is considered satisfactory in view of the simplicity of the model and only a few adjustable parameters. q
An analysis of impact-induced deformation and fracture modes in amorphous glassy polymers
Engineering Fracture Mechanics, 2008
The finite deformation response of a planar block of polymer material subject to impact loading is analyzed using two constitutive models for glassy polymers, a reference Drucker-Prager type model and a physics-based macromolecular model, supplemented by a phenomenological model for craze initiation and widening. Full transient finite element analyses are carried out using a Lagrangian formulation of the field equations. The analyses allow an assessment of possible failure mechanisms under dynamic loading and the ability of the different models to predict such behavior. The results highlight the effect of the stress-strain behavior of polymers, notably the post-yield softening and large strain hardening, on localization of plastic flow. This behavior is adequately captured only by the macromolecular model.
A generalized mechanical model using stress–strain duality at large strain for amorphous polymers
Mathematics and Mechanics of Solids, 2020
Numerous models have been developed in the literature to simulate the thermomechanical behavior of amorphous polymers at large strain. These models generally show a good agreement with experimental results when the material is submitted to uniaxial loadings (tension or compression) or in the case of shear loadings. However, this agreement is highly degraded when they are used in the case of combined load cases. A generalization of these models to more complex loads is scarce. In particular, models that are identified in tension or compression often overestimate the response in shear. One difficulty lies in the fact that 3D models must aggregate different physical modeling, described with different kinematics. This requires the use of transport operators complex to manipulate. In this paper, we propose a mechanical model for large strains, generalized in 3D, and precisely introducing the adequate transport operators in order to obtain an exact kinematic. The stress–strain duality is ...
Uniaxial compression stress–strain tests were carried out on three commercial amorphous polymers: polycarbonate (PC), polymethylmethacrylate (PMMA), and polyamideimide (PAI). The experiments were conducted under a wide range of temperatures (À40 °C to 180 °C) and strain rates (0.0001 s À1 up to 5000 s À1). A modified split-Hopkinson pressure bar was used for high strain rate tests. Temperature and strain rate greatly influence the mechanical response of the three polymers. In particular, the yield stress is found to increase with decreasing temperature and with increasing strain rate. The experimental data for the compressive yield stress were modeled for a wide range of strain rates and temperatures according to a new formulation of the cooperative model based on a strain rate/temperature superposition principle. The modeling results of the cooperative model provide evidence on the secondary transition by linking the yield behavior to the energy associated to the b mechanical loss peak. The effect of hydrostatic pressure is also addressed from a modeling perspective.