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Overflow is usually used to keep fluid continuously flowing to avoid the fluid from changing flow direction and subsequently inducing large stresses. To explore the mechanism of flow-induced stress evolution, a flow model was established in terms of compressible, non-isothermal, and viscoelastic flow. Based on the Leonov model and the mid-plane approach, a pseudo-Poisson type equation for pressure was derived to decouple the interdependence between velocity and pressure. To improve computational efficiency, a numerical approach involving double iterations was proposed to solve the flow problem. Two kinds of mold cavities, with and without overflow, were designed and manufactured. Molding experiments were conducted, and corresponding simulations based on the proposed model and algorithm were performed. The results show that the simulated contours of flow-induced stress are in good agreement with the photoelastic streaks. The use of overflow can significantly reduce flow-induced stresses. If the slot thickness is set to a proper value, the flow-induced stress can be reduced by more than 80%. On the other hand, a slot that is too thick does not have significant reducing effects. Therefore, using overflow to reduce flow-induced stresses during transparent part production is a promising approach if the material cost is worthy of the quality. Highlights * A double iteration method is proposed for viscoelastic flow problem. * Overflow can reduce the stress as much as 80% if the dimension is properly set. * The simulated stress streaks are in good agreement with photoelasticities. KEYWORDS finite element method, flow-induced stress, Leonov model, overflow, viscoelastic, 1 | INTRODUCTION Injection molding (IM) is the most efficient mass-production technology for manufacturing polymers in complex and detailed geometries with high precision. In view of these advantages, most transparent [...]

Polymerie materials are widely used in structural components and systems, and the accurate prediction of their complex time-dependent behavior is critical. Several constitutive models are available for different types of mechanical behaviors and loading conditions. However, selecting the model and the correct calibration of its parameters is often a challenge. This paper evaluates the applicability of the two-layer viscoplasticity (TLV) model to predict the viscoplastic behavior of polyvinylidene fluoride (PVDF) in a large range of strain rates and complex states of strain. The setting of parameters and model validation was made by performing experimentally and numerically uniaxial compression tests and relaxation tests. The model parameters were also analyzed in performing microindentation tests. The TLV model using the same set of parameters selected well predicted the PVDF behavior in a wide variety of compressive loading conditions. KEYWORDS elastoplastic-viscoelastic model, finite element analysis, instrumented indentation test, polyvinylidene fluoride, two-layer viscoplasticity model, 1 | INTRODUCTION Flexible pipelines are multilayered structures that transport fluids between wells and floating units in offshore oil fields. [1] They are composed of helical armoring layers and polymer [...]

Most industrial process lines involve mixing complex dispersions, which can include non-Newtonian liquids and viscoelastic particles. Knowledge of the parameters of these components may provide a key for understanding how dispersions are formed and how equipment should be designed. One parameter is the shear modulus, which describes the ability of particles to resist mechanical stresses. This parameter may play the main role in the mixing process, when a dispersion is formed by the mechanical influence of a rotor (slice or shear in a rotor-stator mixer). In this work, two methods were chosen for measuring the shear modulus: the evaluation method, based on the Warner-Bratzler cut test, and the oscillatory method. Both methods were used for measuring viscoelastic clusters of particles, and the results were adjusted for the purposes of the comparison. The comparison shows that the shear modulus values obtained from Warner-Bratzler are higher than the values obtained from the oscillatory test for the same conditions. This difference can be explained by differences in the mechanical processes during the experiments. KEYWORDS frequency sweep, shear modulus, viscoelasticity, Warner-Bratzler test, 1 | INTRODUCTION Viscoelastic materials are involved in many processes, for example, mixing, blending, and extrusion. Measurements of the viscoelastic characteristics of these materials are essential for the adjustment of [...]

A series of statistical copolymers of 4-vinylbiphenyl and styrene were prepared via free radical polymerization to investigate the effect of the comonomer ratio on their microstructure and rheological properties. The glass transition temperature of the copolymers follows a nonlinear monotonic decreasing dependence with increasing styrene content which is well described by the GordonTaylor equation. WAXS measurements reveal that both the backbone to backbone and the inter-phenyl distances (dx and [d.sub.2], respectively) are decreasing functions of the styrene content in the copolymers. The apparent monomeric friction coefficient, calculated from dynamic frequency sweeps in the linear viscoelastic regime, decreases exponentially with the styrene content in the copolymer. We postulate that the strong effect of the copolymer composition on the friction coefficient is due to the larger overlapping distance between phenyl rings of adjacent polymer chains (d0Veriap)> giving rise to stronger aromatic n-n interactions, which in turn results in stronger friction between adjacent chains. The increase in doveriap and monomeric friction coefficient also leads to a significant increase in the extensional strain hardening measured during extensional startup flow measurements. KEYWORDS copolymerization, differential scanning calorimetry (DSC), glass transition, polystyrene, rheology, WAXS, 1 | INTRODUCTION The viscoelastic response of thermoplastics is intimately related to the polymer chain conformation as well as to the local structure (at the monomer level). From a practical [...]

In this work, a new constitutive equation for the description of the nonlinear viscoelastic response of polymeric materials is presented, by proposing modifications on a model developed in previous works. This time-dependent equation has been derived on the basis of transient model, and a new assumption regarding the kinetics of active molecular chains due to the imposed deformation. The present treatment was proved to be more flexible, given that it contains a relaxation function that has been derived by considering, instead of first-order kinetics, a fractional derivative that controls the rate of molecular chain detachment from their junctions. It has been further explored that the potential of this equation to be employed for the evaluation of the dynamic modulus master curve, once the experimental data of the compliance modulus of a polymeric structure have been matched., INTRODUCTION The extended application of polymers and polymer matrix composites as engineering materials in aerospace, automotive industry, and civil engineering structures demands for their correct characterization with regard to the [...]

HDPE pipes are frequently laid in buried or submerged conditions and are often subjected to considerable internal pressure. This context requires the consideration of HDPE as a structural material and demands constitutive models to predict failure possibilities in short and long terms. This article presents an approximate procedure to simulate the viscoelastoplastic nature of HDPE's material behavior under creep conditions. While a generalized Kelvin-Voigt model based on Prony series is used to model viscoelasticity, the power law of Zapas-Crissman is adopted to account for viscoplastic effects. The associated material parameters are obtained from experimental creep-recovery tests evaluated at different stress levels and constant temperature. As this type of test allows an uncoupled procedure for identifying the viscoelastic and viscoplastic material parameters, this task is divided into two stages: (i) a constrained nonsmooth optimization problem is defined and solved for the viscoelastic parameters, and (ii) the viscoplastic parameters are determined by linear regression. Thereafter, the viscoelastic and viscopiastic parameters obtained for each experimental stress level are interpolated linearly for intermediate stress conditions. Finally, a numerical-experimental example is presented, showing that the proposed procedure is able to reproduce adequately more complex loading conditions., INTRODUCTION Motivated by ever more challenging industrial requirements, technological advancements have thrusted the development of nontraditional structural materials, which frequently show improved multifunctional properties with respect to those of conventional [...]

A thermodynamically consistent rate-type viscoelastic-viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time-dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one-dimensional Theological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub-components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time-dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time-dependent stress-strain responses of the PC can be reasonably predicted by the proposed model., INTRODUCTION Nowadays, polymeric materials have been widely applied in many areas, such as aerospace, automotive industry, biomedicine, and civil engineering, etc., due to their low cost, high specific stiffness, capability [...]

In this article, visco-hyperelastic constitutive model is developed to describe the rate-dependent behavior of transversely isotropic functionally graded rubber-like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and rate-dependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neo-Hookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history-integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye-BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber-like materials in different deformation and wide ranges of strain rate., INTRODUCTION Elastomeric materials are frequently used to diminish damage caused by impulsive or impact loads because of their low modulus, high damping, and large extensibility. For instance, buildings and bridges [...]

In this paper, a modified viscoelastic-plastic constitutive model has been proposed on the framework of Anand's work to describe the uniaxial ratcheting behavior of polycarbonate (PC) under tension-tension cyclic loading. The experimental observation illustrates that the previously accumulated deformation has an assignable influence on the subsequent material response during the ratcheting process of PC. Thus, the deformation resistance in the viscoelastic micromechanism is assumed to be evolving with the local accumulated inelastic strain rather than keeping unchanged in the original Anand's model. The proposed model is validated firstly by the monotonic tension and creep experiment results of PC. Then, its capability to describe the uniaxial ratcheting behaviors is compared with Anand model. Finally, the modified model is adopted to study the effect of mean stress, stress amplitude, loading rate, and peak holding time on the ratcheting behaviors of PC. It is shown that the proposed model can predict reasonably the uniaxial tension-tension ratcheting behavior of polymer., INTRODUCTION Polycarbonate (PC) has been extensively utilized in automatic vehicle, civil engineering and aerospace industry due to its excellent mechanical properties [1, 2], The structural components made by PC are [...]

A constitutive model is derived for the viscoelastic behavior of physically aged amorphous polymers under non-isothermal loading. The model is based on the concept of transient reversible networks, where a polymeric material is treated as a network of active chains (adaptive links) that break and reform because of micro-Brownian motion. The breakage and reformation rates for active chains in an aged medium are assumed to depend on the current temperature and the time after cooling below the glass transition temperature. To validate the model, the long-term viscoelastic response is predicted on the basis of data obtained in the standard short-term creep tests and compared with data from long-term experiments. Fair agreement is demonstrated between numerical results and observations. The model is used to calculate residual stresses in a polymeric spherical pressure vessel cooled down (after curing) to the room temperature. It is shown that physical aging of the polymer significantly affects stresses and displacements in the vessel., 1 INTRODUCTION The paper is concerned with the non-isothermal viscoelastic behavior of physically aged polymers. Our objective is twofold: (i) to derive a constitutive model for the long-term viscoelastic response [...]

A new constitutive model is derived for the viscoelastic behavior of polymers under non-isothermal loading. The model extends the Tobolsky concept of adaptive links (entanglements) between polymeric molecules to thermoviscoelastic media. Employing this model, we calculate residual stresses built up in an epoxy resin plate under cooling from the rubber-glass transition temperature, analyze the effect of material parameters on residual stresses, and compare results of numerical simulation with experimental data., 1. INTRODUCTION This paper is concerned with constitutive relations for non-isothermal loading of viscoelastic media in the vicinity of the rubber-glass transition temperature. The subject is of essential interest because [...]

The poor solutions of numerical simulations at a contraction has often been attributed to the numerical scheme used. However, the solution of a numerical simulation is also highly dependent on the constitutive equation. A study of various constitutive equations on the simulation of the 4:1 contraction flow is made in this paper, and their effects on the results analyzed. The constitutive models considered include the Upper Convected Maxwell model, the Oldroyd-B model, the White-Metzner model, the Phan-Thien-Tanner model and the Giesekus-Leonov model. It was found that although the Phan-Thien-Tanner model gave the best results, the solution at higher shear rates were still not satisfactory., INTRODUCTION With the increasing use of computers, research in the simulation of molding processes gained importance in the 1970s. Initial simulations were done using analytical solutions or the Hele-Shaw equations, [...]

Recently, Friedrich proposed an empirical model for linear viscoelastic fluids corresponding to a constitutive equation with fractional derivatives [Phil. Mag. Lett., 66, 287 (1992)]. For this model, the relaxation modulus, the dynamic moduli, the relaxation time spectrum, and other material functions have been explicitly calculated as a function of the few parameters that characterize a viscoelastic fluid within this model. By fitting this model to experimental data, the model parameters can be determined and other material functions, in particular the relaxation time spectrum, can be calculated immediately. This paper reports to what extent this method, which may be called analytical inversion, is appropriate for the determination of relaxation time spectra. For that purpose, the spectra of a number of very different polymeric materials are determined with this method. The spectra calculated in this way are compared with the spectra obtained by nonlinear regularization. It turns out that the empirical model describes the linear viscoelastic properties of a variety of different materials with high accuracy. Keeping in mind that the determination of the relaxation time spectrum requires the solution of an ill-posed problem, the agreement between the relaxation time spectra obtained by analytical inversion and by regularization is satisfactory for these materials., INTRODUCTION The determination of the relaxation time spectrum from experimental data for a material function is one of the oldest tasks in rheology. It is, however, not an easy task, [...]