Empirical nonlinear viscoelastic model for injection molded thermoplastic composite

Injection molded components made from fiber reinforced thermoplastics exhibit strong viscoelastic behavior. In the present study, the bending creep tests show that the 43-wt% glass fiber reinforced polyamide 66 is highly stress-dependent and requires a nonlinear viscoelastic representation. However, such representation is complex for isotropic materials and is even more arduous for composite materials. In order to overcome this complexity, an empirical approach is used herein to develop a viscoelastic model based on a simple power law with stress-dependent parameters. The proposed model demonstrates high stress sensitivity and agrees with experimental data over a wide range of applied stress.     

Application of a fractional model for simulation of the viscoelastic functions of polymers

In the present work the dynamic behavior of two representative polymeric materials, experimentally studied in previous works, has been analyzed by a fractional derivative model. It is shown that the well‐known fractional derivative Zener model, in its simplest form as a four‐parameter model is capable of capturing the main features of the dynamic moduli of the polymeric structures examined. Furthermore, the time dependent viscoelastic functions, namely the compliance and the relaxation modulus could be simulated with the same model parameter values, indicating this way that the fractional model can provide a method of interconversion between viscoelastic material functions. The model's inadequacy of describing the loss modulus peak asymmetry, exhibited by the materials, has been encountered by the five‐parameter version of the fractional Zener model. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43505.     

Extensive validation of a thermodynamically consistent, nonlinear viscoelastic model for glassy polymers

The nonlinear thermoviscoelastic formalism presented in the preceding paper is validated with four amorphous polymer systems. Validation is performed over a broad range of relaxation phenomena in the glass transition region, including the temperature and rate-dependence of the stress-strain behavior through yield, volume and enthalpy relaxation, and stress relaxation during multi-step loading histories. The objective is to obtain quantitative agreement between the constitutive theory and all experimental results using one set of model parameters for each material system. The nonlinear viscoelastic formalism is shown to predict the wide range of behavior observed experimentally, indicating that the formalism does capture the essential physics of glassy polymers. Moreover, the material parameters required in the constitutive formalism can be readily obtained from independent experiments and are relatively insensitive to how these parameters are determined experimentally from the various characterization techniques.     

Modeling nonlinear viscoelastic response

We present a model for calculating nonlinear viscoelastic response which we call the “phases model” (PHM). In terms of a mechanical model representation the PHM is a generalized Maxwell model with nonlinear elements where each Maxwell element is referred to as a phase. The viscous material properties are represented in the model in terms of flow curves of the individual phases. The collection of flow curves form the flow diagram. We show how to calibrate the flow diagram from a family of constant rate test curves by means of a simple straightforward procedure. We give an example of such a calibration for a certain rigid polyurethane. We applied our model to the calculation of nonlinear viscoelastic response to varius loading programs in uniaxial tension, and to the creep of a simply supported beam, and obtained good agreement with experimental data.     

Mechanical response of beams of a nonlinear viscoelastic material

A constitutive equation for nonlinear viscoelasticity is used to model the mechanical response of solid polymers such as polycarbonate. The nonlinearity arises from a reduced time which causes stress relaxation to accelerate with increasing strain. The constitutive equation can account for the occurrence of yield in a homogeneous uniaxial constant strain rate test. The constitutive equation is used in a study of the pure bending of beams. It is assumed that the classical assumption of beam theory is valid, i.e., plane sections remains plane. At each fixed time, the strains vary linearly through the depth of the beam. At a fixed material element the strain varies in time with the curvature. This spatial variation of the strains combined with the nonlinear dependence of the reduced time on strain leads to a significantly different response from that given by traditional beam theory. The implications of this for the bending moment history, stress distributions, and other factors that relate to beam design are discussed.     

A constitutive model for the nonlinear viscoelastic viscoplastic behavior of glassy polymers

Two features of the glassy state of an amorphous polymer, which play a key role in determining its mechanical properties, are the distributed nature of the microstructural state and the thermally activated (temporal) evolution of this state. In this work, we have sought to capture these features in a mechanistically motivated constitutive model by considering a distribution in the activation energy barrier to deformation in a thermally activated model of the deformation process. We thus model what is traditionally termed the nonlinear viscoelastic behavior as an elastic-inelastic transition, where the energetically distributed nature of inelastic events and their evolution with straining is taken into account. The thermoreversible nature of inelastic deformation is modeled by invoking the notion of strain energy stored by localized inelastic shear transformations. The model results are compared to experimental data for constant true strain rate uniaxial compression tests (nonmonotonic) at different rates and temperatures; its predictive capabilities are further tested by comparison with compressive creep tests at different stress levels and temperatures.     

Isochrone based mastercurves of viscoelastic functions

Summary Composite curves of the viscoelastic functions may be obtained not only by the usual shift of isotherme data along the frequency axis, but also by a shift of the respective isochrones along the reciprocal temperature axis. This shift along the 1 / T axis is equivalent to that of the isochrones of dynamic viscosity, along the slope of zero shear apparent activation energy of flow. It is demonstrated that both types of shift are related to this zero shear activation energy of flow, so that an unique shift mechanism is effective in both cases.Isochrone based mastercurves are favourable for studies on polymer blends particularly, because the problematical choice of the reference temperatures of the components is circumvented.     

On the characterization of nonlinear viscoelastic materials

Starting with specific constitutive equations, methods of evaluating material properties from experimental data are outlined and then illustrated for some polymeric materials; these equations have been derived from thermodynamic principles, and are very similar to the Boltzmann superposition integral form of linear theory. The experimental basis for two equations under uniaxial loading and the influence of environmental factors on the properties are first examined. It is then shown that creep and recovery data can be conveiently used to evaluate properties in one equation, while two-step relaxation data serve the same purpose for the second equation. Methods of reducing data to accomplish this characterization and to determine the accuracy of the theory are illustrated using existing data on nitrocellulose film, fiber-reinforced phenolic resin, and polyisobutylene. Finally, a set of three-dimensional constitutive equations is proposed which is consistent with nonlinear behavior of some metals and plastics, and which enables all properties to be evaluated from uniaxial creep and recovery data.     

A model viscoelastic fluid

Shear stress and first normal stress difference data are presented for materials which exhibit a constant viscosity and yet at the same time exhibit elasticity levels of the same order as polymer melts. Flow pattern observations in circular die entry flows in conjunction with independent shear and normal stress measurement strongly suggest that these fluids would make excellent model fluids for melt studies. Studies in which the influence of elasticity in the absence of shear thinning and fluid inertia can easily be made. Furthermore it is clearly shown that a realistic solution to the die entry flow problem is not obtained using second order flow theory. In the second order region the secondary cell is observed to be almost identical in size to the cell observed for an inelastic Newtonian fluid in creeping flow. Marked growth in the secondary cell as a function of elasticity is not observed until the shear rates exceed the region of second order behavior. This growth in cell size as a result of elasticity is followed at higher shear rates by a spiraling flow instability like that observed for some polymer melts.     

Modification and evaluation of a FRF-based model updating method for identification of viscoelastic constitutive models for a nonlinear polyurethane adhesive in a bonded joint

In this study, a Frequency Response Function (FRF) -based model updating method, was modified for the purpose of the identification of viscoelastic constitutive models. A steel beam, bonded to a heavy rigid steel block by a layer of Sikaflex-252 polyurethane adhesive, was employed as the test setup. Using the concept of Optimum Equivalent Linear FRF (OELF), accelerance FRFs were measured at different random excitation levels which demonstrated the nonlinear behavior of the adhesive. Using a finite element model, the sensitivity analysis showed that the selected FRFs are more sensitive to the storage and loss moduli of the adhesive near the resonances. Therefore, firstly, both of the storage and loss moduli were identified near each resonance separately and the results have been compared with the results based on Inverse Eigen-sensitivity Method (IEM). In continuation, five viscoelastic constitutive models were utilized and identified to characterize the dynamic mechanical properties of the adhesive at different excitation levels. Applying the identified models, the correlation between the FRFs of the FE models and the experimental ones were tested. The results show that amongst the identified models, The Standard Linear Solid (SLS) model in parallel with a viscous or constant structural damper (stiffness proportional) results in better correlation with experiments. Increasing the excitation level, the storage modulus of the adhesive decreases, whereas the loss modulus increases, especially at high frequencies.     

The nonlinear viscoelastic characterization of graphite/epoxy composites

Fiber reinforced plastics offer many structural advantages for a variety of designs. Before these material systems can achieve more widespread usage, however, some of the unanswered questions regarding the long-term behavior and durability of these materials must be answered. Nonlinear compliance data is presented for T300/934 and T300/5208 graphite/epoxy composites. Several nonlinear viscoelastic techniques are compared for modeling the response. Comments for applying nonlinear models to orthotropic materials are given. A procedure for predicting long term laminate response from short term unidirectional data is reviewed.     

Time-dependent viscoelastic functions for cis-1,4-polybutadiene melts

Summary Relevant recent advances in slit die rheometry are discussed, and an error in the cited publication is corrected.     

Time-dependent viscoelastic functions for cis-1,4-polybutadiene melts

Summary Transient linear and nonlinear viscoelastic functions were measured on cis-1,4-polybutadiene melts and compared to the ROUSE theory and a nonlinear modification of the network theory. The latter was found to overestimate material nonlinearity, especially of the first normal stress coefficient at cessation of steady shear flow. Steady-state functions were recovered from the time dependent measurements. Single step strain experiments in the linear region were recorded by computer, up to 7 milliseconds after the sudden shear jump; a paradox arised in the interpretation of shear versus normal stress after a sudden shear strain.Financial support from DEUTSCHE FORSCHUNGSGEMEINSCHAFT and FONDS DER CHEMISCHEN INDUSTRIE is gratefully acknowledged. We thank CHEMISCHE WERKE HÜLS AG for providing the cis-1,4-polybutadienes. Finally, we are especially indebted to Dr. Michael KOWALSKI for intensive cooperation with ELECTRONICS.     

Modeling the response of monofilament nylon cords with the nonlinear viscoelastic, simplified potential energy clock model

The Simplified Potential Energy Clock Model has been previously shown to predict accurately glassy polymer responses such as yield, creep, enthalpy relaxation, and physical aging. It was now used to predict the behavior of monofilament Nylon fiber. Even though the fibers showed process-induced anisotropy, the simpler isotropic model could be used to describe uniaxial tests. The model predictions again accurately predicted a wide range of Nylon experimental data.     

Predicting the behavior of nonlinear viscoelastic materials under spring loading

Structural parts made of plastics are usually tested under creep loading conditions, i.e., the stress is applied almost suddenly and then kept constant, while defomation is measured. In practice, however it happens that such a structural part is loaded by an elastic member (for example, by a spring). In this case, the acting force is no longer constant; it decreases in the course of time, while the deformation of the specimen increases (and, obviously, that of the spring decreases). The present paper describes a numerical approach for the solution of this problem, based on the assumption that the creep behavior of the material is known. An example is presented.     

Quantitative analogies between the linear and non-linear viscoelastic functions

A method of determination of linear and non-linear viscoelastic functions is proposed. Through this method it is possible to calculate the non-linear functions P₁₁ - P₂₂ and η(γ) assuming that linear viscoelastic function (ω) is known. Alternatively from the function P₁₁ - P₂₂ we are able to calculate η(γ) and y'(ω) etc. The method is based on the assumption that the change from linear to non-linear functions is proportional to a molecular deformation for shear stress components P₁₂, and is dependent on the square of the deformation for the first normal stress difference, P₁₁ - P₂₂. The obtained results suggest straightforward modification of equations of state, this being demonstrated with the White-Metzner model of the convected Maxwell element. Consideration of available experimental data shows that this theory is capable of predicting the various functions, at least as well as currently available constitutive equations, while requiring less experimental information.