Jean-François Agassant

Stationary and stability analysis of the film casting process

Abstract Film casting process is widely used to produce polymer film: a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This study is devoted to the extensional flow between the die and the chill roll. The film shows a lateral neck-in as well as a inhomogeneous decrease of the thickness. Thickness as well as width instabilities may be observed above a critical draw ratio. An isothermal and time dependent two-dimensional (2D) membrane model is proposed and compared to a non-constant width 1D model. Newtonian and viscoelastic constitutive equations have been tested. The influence of the processing parameters (draw ratio and aspect ratio) and of the rheology of the polymer (Deborah number) on the film geometry is first determined. The onset of the draw resonance instability is finally studied by linear stability analysis and through the dynamic response to small perturbations. A critical curve splitting the processing conditions into a stable and an unstable zone is derived. It is shown that an increase of the air-gap between the die and the roll improves the stability of the process. Numerical results concerning periodic fluctuations of the flow in unstable conditions are compared with previous experimental results.

A finite element method for computing the flow of multi-mode viscoelastic fluids: comparison with experiments

Abstract The numerical computation of viscoelastic fluid flows with differential constitutive equations presents various difficulties. The first one lies in the numerical convergence of the complex numerical scheme solving the non-linear set of equations. Due to the hybrid type of these equations (elliptic and hyperbolic), geometrical singularities such as reentrant corner or die induce stress singularities and hence numerical problems. Another difficulty is the choice of an appropriate constitutive equation and the determination of rheological constants. In this paper, a quasi-Newton method is developed for a fluid obeying a multi-mode Phan-Thien and Tanner constitutive equation. A confined convergent geometry followed by the extrudate swell has been considered. Numerical results obtained for two-dimensional or axisymmetric flows are compared to experimental results (birefringence patterns or extrudate swell) for a linear low density polyethylene (LLDPE) and a low density polyethylene (LDPE).

RHEOLOGY OF SHORT GLASS-FIBER REINFORCED POLYPROPYLENE

An anisotropic rheological constitutive equation for short fiber reinforced polypropylene is presented. The bulk stress is the sum of a contribution of the Newtonian suspending fluid and of the fiber contribution. This contribution depends on the orientation which is described by an orientation tensor. The rate of change in orientation is calculated using semidilute suspension theories. After simplifications the model contains only one adjustable parameter and the transient relative viscosity depends only on the strain and not on the shear rate or time separately. Transient and steady‐shear viscosities were determined for two reinforced polypropylenes using a constant stress and a rotational parallel plate rheometer. An overshoot in the viscosity versus time curve was observed. It is attributed to changes in fiber orientation, and it depends on the fiber content but not on the shear rate. The model predictions for 20 and 30 wt. % glass fiber reinforced polypropylene are fairly good.

Experimental study of the sharkskin defect in linear low density polyethylene

Abstract The sharkskin defect in linear low density polyethylene has been studied using both flow birefringence and roughness measurements. Roughness measurements allow us to detect accurately the onset of the defect and to quantify its amplitude. With increasing flowrate, the sharkskin defect appears at a critical value of the flowrate and then grows. This critical value and the maximum amplitude of the defect increase with temperature. Birefringence patterns give information on the stress distribution at the die entrance. At the appearance of the sharkskin defect, all birefringence patterns are identical and independent of the flowrate and the temperature. The influence of die geometry and the addition of lubricant to the polymer were investigated.

Experimental study and modeling of oscillating flow of high density polyethylenes

The influence of flow rate and die geometry on the observable flow rate/pressure relationship of a linear high density polyethylene is investigated using a capillary rheometer. The experimental results are applied to an adapted version of the relaxation–oscillation model proposed by Molenaar and Koopmans for describing the oscillating flow regime. The current model allows for a quantitative description of the hysteresis cycle in the oscillating flow regime in terms of the main experimental variables, such as imposed flow rate, reservoir (barrel) volume, and material compressibility.

Viscoelastic simulation of PET stretch/blow molding process

In the stretch/blow molding process of poly(ethylene terephthalate) (PET) bottles, various parameters such as displacement of the stretch rod, inflation pressure, and polymer temperature distribution, have to be adjusted in order to improve the process. An axisymmetric numerical simulation code has been developed using a volumic approach. The numerical model is based on an updated-Lagrangian finite element method together with a penalty treatment of mass conservation. An automatic remeshing technique has been used. In addition, a decoupled technique has been developed in order to compute the viscoelastic constitutive equation. Successful stretch/blow molding simulations have been performed and compared to experiments.

A study of stress distribution in contraction flows of anb LLDPE melt

Abstract Numerical simulations are carried out for a linear low-density polyethylene (LLDPE) flowing through an 8:1 planar contraction equipped with slit dies of different length (L/2H = 2 and 8) at two different temperatures (145 and 205°C). The emphasis is on determining the stress distribution and comparing it with birefringence experimental results that have previously appeared in the literature. The working constitutive equation is a realistic integral model of a K-BKZ type with a spectrum of relaxation times. The material parameters have been obtained by fitting experimental viscosity and normal stress data as measured in shear, and by using elongational viscosity data available in the literature. The numerical simulations are performed for a wide range of apparent shear rates (10 s−1

Fibre orientation calculation in injection moulding of reinforced thermoplastics

Abstract The orientation of short fibres during the filling with reinforced thermoplastics of a tube and a disk is computed. The flow kinematics is obtained using a finite element method with a moving mesh technique in two dimensions. The orientation is calculated with a decoupled method. Results show the evolution of the orientation of individually tracked fibers, especially in the material front region, for a Newtonian and a shear-thinning matrix behavior, and for different thermal conditions and fiber interactions.

Investigation of Bubble Instabilities in Film Blowing Process

Abstract This paper describes an original on-line video device developed in order to study bubble instabilities occurring in the film blowing process, taking into account their three-dimensional behavior. For a linear low-density polyethylene, two forms of instabilities and combination have been observed: draw resonance and helical instability. These instabilities could be quantitatively described and differences in behavior could be assessed using real objective measurements and criteria. The influence of key processing conditions was investigated and the results showed that the instabilities are enhanced by increasing the draw ratio, blow up ratio and frost line height. These first results are in agreement with the majority of the results reported in the literature, but allow for a more accurate analysis of the phenomena.

Numerical simulation of the film casting process

The film casting process is widely used to produce polymer film: a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This study is devoted to the extensional flow between the die and the chill roll. The film shows a lateral neck-in as well as an inhomogeneous decrease of the thickness. An isothermal and Newtonian membrane model, constituted of an elastic-like equation for velocity coupled to a transport equation for thickness and a free surface computation, is used. These equations are solved via the finite element method (continuous Galerkin for velocity and discontinuous Galerkin for thickness). Both tracking and capturing strategies are used to determine the position of the free surface (lateral neck-in). The influence of the processing parameters (Draw ratio and Aspect ratio) on the film geometry is first determined. The onset of the Draw Resonance instability is then studied through the dynamic response of the process to small perturbations. A critical curve splitting the processing conditions into a stable and an unstable zone is derived. It is shown, consistently, with results of a 1D model, that an increase of the air-gap between the die and the roll improves the stability of the process. Numerical results concerning periodic fluctuations of the flow in unstable conditions are compared with previous experimental results. The film casting process is widely used to produce polymer film: a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This study is devoted to the extensional flow between the die and the chill roll. The film shows a lateral neck-in as well as an inhomogeneous decrease of the thickness. An isothermal and Newtonian membrane model, constituted of an elastic-like equation for velocity coupled to a transport equation for thickness and a free surface computation, is used. These equations are solved via the finite element method (continuous Galerkin for velocity and discontinuous Galerkin for thickness). Both tracking and capturing strategies are used to determine the position of the free surface (lateral neck-in). The influence of the processing parameters (Draw ratio and Aspect ratio) on the film geometry is first determined. The onset of the Draw Resonance instability is then studied through the dynamic response of the process to small perturbations. A critical curve splitting the processing conditions into a stable and an unstable zone is derived. It is shown, consistently, with results of a 1D model, that an increase of the air-gap between the die and the roll improves the stability of the process. Numerical results concerning periodic fluctuations of the flow in unstable conditions are compared with previous experimental results.