Rheological behavior of a semi-crystalline polymer during isothermal crystallization

The theological behavior of a molten semi-crystalline polymer, namely, a high density polyethylene (HDPE), was investigated during isothermal crystallization from the melt, using dynamic oscillatory experiments at 1 tad/s in a parallel plates rheometer. The theological results were compared with those obtained from differential scanning calorimetry in the same conditions. During the crystallization, the molten and crystallizing polymer provides a useful model for filled polymers, the crystalline phase being the filler and the liquid phase being the matrix. In most cases, the filler can be considered to be spherical shaped (spherulites). Owing to the amorphous phase linking liquid and crystallites, the adhesion between matrix and filler in this system is perfect. The filler content increases continuously during the crystallization. This model might be used to test laws relating the theological parameters to the volume fraction of filler. Problems related to the rheometry for such systems are discussed and the key parameters insuring reproducibility and accuracy in the measurements are pointed out. The relative sensitivity of the various theological parameters (storage and loss moduli, loss angle) to structural changes of the liquid has been out forward. Some preliminary equations relating the variation of these parameters to the volume fraction of filler, through the use of simple fractal exponents have been derived and discussed in comparison with laws provided by various authors.     

Heat transfer and crystallization kinetics during fast cooling of thin polymer films

In this work, the heat transfer phenomena taking place during the cooling of thin films of crystallizable polymers were analyzed. The thermal histories, as recorded during experimental cooling runs carried out at various cooling rates, were compared with the predictions of a general purpose numerical code, which was resulted able to capture all the main features of the process. Thus, the conditions which allow homogeneous cooling (negligible temperature gradient within the sample) or homogeneous cooling history (the same cooling history for all the positions within the sample) were predicted by the simulation code.     

Constitutive model for a semi-crystalline polymer under dynamic loading

This paper deals with a viscoelastic–viscoplastic model for semi-crystalline polymers in crash applications. A polymer behaviour model is implemented in the commercial PAM CRASH© code thanks to a user material card. Global variables (load, displacement) and local variables (strain) are validated on flat and notched tensile specimens by comparing the numerical responses with data obtained by digital image correlation.     

半结晶聚合物非等温结晶结构演化模拟

在半结晶聚合物加工中,材料的结晶决定了结构形态的形成,而形态对最终制品的性能起着重要的作用,因而对聚合物结晶形态演化进行模拟具有重要意义。本文基于非等温结晶的微分控制方程组,采用龙格-库塔法,在matlab上实现了聚合物非等温结晶过程的模拟。模拟不同结晶条件下整体结晶动力学、晶核生成和晶体长大过程,并在此基础上计算晶体尺寸演化及分布。将等温和非等温结晶模拟结果与解析解和实验结果对比,结果吻合很好,验证了模拟程序。数值分析了结晶温度和冷却速率对晶体尺寸分布的影响,获得等温和非等温结晶中晶体尺寸分布规律。     

Process validation of the normalized rheological function behavior during polymer crystallization

The film casting process of an isotactic polypropylene was adopted as the source of data to evaluate the behavior of a crystallizing polymer. The increase in viscosity due to the crystallization was quantified, and a model was proposed to estimate the normalized rheological function (NRF) during the process. The estimation was based also on the availability of rich sets of data, i.e., the polymer temperature and crystallinity, the film velocity and width distribution along the draw direction, gathered during the process. The quasi-experimental NRF evolutions were compared with just two of the very numerous hardening models proposed in literature, and the main result is that the process is coherent with the choice of an NRF model which predicts the increase in viscosity only for substantial crystallinity amount.     

Plastic instability studied experimentally on a semi-crystalline polymer through thermomechanical heat source identification: the flow stress concept revisited

Micromechanical deformation phenomena such as those leading to macroscopic viscoelastic and plastic behavior must be studied from a thermodynamic viewpoint, as they induce complex and partly irreversible heat effects. Calorimetric measurements of the intrinsic volumetric thermomechanical heat sources (THS) activated in the material bulk during mechanical loads can produce valuable information with respect to that aim. They can be based on infrared imaging if submitted to inverse algorithms that allow a correct reconstruction of THS to be produced. Here, an inverse method relying on a diffusion-advection heat transfer model is applied to experimental temperature maps recorded during tensile tests. These are made on a semi-crystalline polymer that shows a strong development of plastic instabilities. Along with simultaneous kinematic observables produced with a digital image correlation system, the competition between advection and diffusion phenomena may be clearly established. 1-D profiles of the reconstructed THS and measured strain rates illustrate clearly that thermomechanical effects associated with necking onset and propagation follow the kinematic variable in a rather direct manner. Finally, we show for tensile experiments that THS estimations lead to analyze plasticity as a rheological behavior controlled by the flow stress, responsible of necking development and propagation.     

A 3-phase model for the numerical analysis of semi-crystalline polymer films in finite elastoplastic strains

In this paper, the mechanical behavior of semi-crystalline polymer films in finite elastoplastic strains is investigated. A 3-phase constitutive model has been specially developed in a previous paper and validated for various materials in both uniaxial and biaxial uniform hot drawing. In the present study, the numerical implementation of this 3-phase model in a finite element software is outlined in the perspective of using this model in more general non-uniform cases of complex geometries and/or loadings. In the present case, only polyethylene films at room temperature are considered. First, uniaxial tensile experimental tests are performed so as to calibrate the model parameters. Then, for validation purposes, two series of experimental tests are conducted on tensile specimens with central holes and double edge notched tensile (DENT) specimens. During these tests, digital image correlation is used to analyze the strain (or displacement) field history during loading. Finally, numerical computations are performed with the help of the finite element software including the 3-phase model previously implemented (cohesive elements are also needed for the simulation of the crack propagation in DENT specimens). In both cases, the comparison between the experimental and numerical force–displacement curves, together with the comparisons between the experimental and numerical strain fields at different times, give very satisfactory results.     

Towards a rheological classification of flow induced crystallization experiments of polymer melts

Departing from molecular based rheology and rubber theory, four different flow regimes are identified associated to (1) the equilibrium configuration of the chains, (2) orientation of the contour path, (3) stretching of the contour path, and (4) rotational isomerization and a deviation from the Gaussian configuration of the polymer chain under strong stretching conditions. The influence of the ordering of the polymer chains on the enhanced point nucleation, from which spherulites grow, and on fibrous nucleation, from which the shish-kebab structure develops, is discussed in terms of kinetic and thermodynamic processes. The transitions between the different flow regimes, and the associated physical processes governing the flow induced crystallization process, are defined by Deborah numbers based on the reptation and stretching time of the chain, respectively, as well as a critical chain stretch. An evaluation of flow induced crystallization experiments reported in the literature performed in shear, uniaxial and planar elongational flows quantitatively illustrates that the transition from an enhanced nucleation rate of spherulites towards the development of the shish-kebab structure correlates with the transition from the orientation of the chain segments to the rotational isomerization of the high molecular weight chains in the melt. For one particular case this correlation is quantified by coupling the wide angle X-ray diffraction and birefringence measurements of the crystallization process to numerical simulations of the chain stretch of the high molecular weight chains using the extended Pom-Pom model in a cross-slot flow.     

Parametric study of macrosegregation in the horizontal strip casting process for different cooling rates and different casting speeds

The objective of this paper is to investigate sensitivity of the macrosegregation profiles in steel strips produced by the horizontal strip casting process to the major technological parameters controlling this process, such as the cooling rate and the casting speed. To perform this investigation, a mathematical model which accounts for fluid flow as well as for heat and solute transport is suggested. Extensive numerical simulations of the horizontal strip casting process for different cooling rates and different casting speeds are carried out. Received on 17 September 1998     

A 3D study on the effect of gate location on the cooling of polymer by injection molding

Injection molding is one of the most widely used plastic part processing. The quality of the injection molded part is a function of plastic material, part geometry, mold structure and process conditions. Gate location is among the most critical factors in achieving dimensionally accurate parts and high productivity of the molding process. To investigate the effect of the gate location on the cooling of polymer by injection molding, a full three dimensional time-dependent analysis is carried out for a mold with cuboids-shape cavity having two different thicknesses. The cooling of the polymer material is carried out by cooling water flowing inside six horizontal circular channels. Three gate locations are assumed, normal to the cavity surface, normal to the small thickness of the cavity, and normal to the large thickness of the cavity. A numerical model by finite volume is used for the solution of the physical model. A validation of the numerical model is presented. The results show that the gate location normal to the small thickness of the cavity achieves the minimum time required to completely solidify the product and minimum solidification of the product during the filling stage. They also indicate that the temperature distribution through the output product is greatly affected by the position of the injection gate location.     

Modeling morphology evolution and mechanical behavior during thermo-mechanical processing of semi-crystalline polymers

A new model is proposed that combines statistical mechanics and thermodynamic aspects to characterize orientation development, nucleation and growth of crystallites, and chain entanglement slippage with interdependent relationships necessary to accurately correlate and in some cases predict the morphology and mechanical behavior of semi-crystalline polymers during various thermo-mechanical processes in the rubbery state, close to the glass transition temperature. Internal state variables (ISVs) that directly represent the underlying microstructure state are used to characterize polymer morphology and the resulting properties throughout deformation. The model uses fundamental thermodynamic coefficients for polyethylene terephthalate (PET) and is correlated to experimental data at various strain rates and temperatures just above the glass transition temperature. Experimental data are used that measure the stress, amorphous orientation, and crystallinity during uniaxial deformation of PET. The model is found to correlate well to these experimental data.     

A comparison between spray cooling and film flow cooling during the rewetting of a hot surface

The paper is dealing with a research carried out at the Institute of Thermal-Fluid Dynamics to investigate the rewetting of a hot surface. The rewetting of the hot surface by spray cooling has been analyzed in previous works. After the droplet impingement, the liquid film falls along the surface, and rewetting by falling film takes place. The experiment was characterized by a 1-dimensional liquid spray, i.e., drops having a uniform, constant diameter, impinging on the heated surface. The cooling rate of the hot surface has been detected as a function of wall temperature, drop diameter and velocity, and impact point of the spray. The working feature of the spray is based on the varicose rupture of the liquid jet: imposing a periodic (symmetrical) perturbation with appropriate amplitude and frequency on the jet surface, the flow is “constrained” to break soon after leaving the nozzle, eventually obtaining constant diameter drops, depending on the nozzle diameter and liquid velocity. In this paper, previous results with spray cooling are compared with experimental runs in which the spray injection is replaced with a falling film all along the test section. The rewetting velocity has been calculated from the response of the thermocouples placed on the heated wall and using a digital image system based on the video image registered during the runs.     

Discontinuous solid solutions of anthracene-phenanthrene:Thermodynamics and crystallization kinetics

We explored such issues as the formation mechanism,structure and propriety of the solid solutions of anthracene(ANT)-phenanthrene(PHE).Solution crystallization ...     

Effects of solvent,supersaturation ratio and silica template on morphology and polymorph evolution of vanillin during swift cooling crystallization

Swift cooling crystallization of vanillin was investigated in water, ethanol, isopropanol and ethyl acetate. Morphology and polymorph evolution of vanillin were discussed in terms of solvent, supersaturation ratio and silica template. PXRD, DSC, FTIR and microscope were used to identify polymorphs of vanillin. Results showed that the nucleated polymorphs of vanillin depended largely on the solvent, supersaturation ratio and silica template. Low supersaturation ratios favor the nucleation of stable form I in water, and high supersaturation ratio exceeds 7 generating 100% metastable form II. However, if the supersaturation ratio is too high (S>8), liquid–liquid phase separation will occur, and no crystals could be obtained. In other solvents such as ethanol, isopropanol and ethyl acetate, only form I was obtained. However, it should be noted that the morphology of form I prepared in ethanol, isopropanol and ethyl acetate is distinct from that obtained in water, the former is flake-like and the latter is rod-like. The nucleation of vanillin from different solution was also studied with the presence of SiO₂, SiO₂–NH₂ and SiO₂−COOH templates, which did not change the nucleated polymorph of vanillin, but changed the nucleation and growth rate of stable form I.     

Numerical study of the natural convective cooling of a vertical plate

We study numerically in this paper the natural convective cooling of a vertical plate. The full transient heat conduction equation for the plate, coupled with the natural convection boundary layer equations are solved numerically for a wide range of the parametric space. Assuming a large Rayleigh number for the natural convection flow, the balance equations are reduced to a system of three differential equations with three parameters: the Prandtl number of the fluid, Pr, a non-dimensional plate thermal conductivity α and the aspect ratio of the plate ?. The nondimensional cooling time depends mainly on α/?², obtaining a minimum of this time for values of 1?α??².     

Structure development during crystallization of polycaprolactone

In this paper, the quiescent crystallization of polycaprolactone (PCL) melts is studied by rheological measurements coupled to calorimetry and optical microscopy. Based on a comparison between the different techniques, we find that the increase in viscoelastic properties during crystallization starts only when a relatively high degree of crystallinity is reached, which corresponds to a much developed crystalline microstructure. Like other semicrystalline thermoplastic polymers, the crystallization of PCL can be seen as a gelation process. In this case, however, we find a peculiar critical gel behavior, as the liquid-to-solid transition takes place at a very high (~20%) relative crystallinity, and this value is independent of temperature. These facts, and the comparison with optical microscopy observations, suggest that the microstructure at the gel point is controlled by the interactions between the growing crystallites. The gel time (from rheometry) and the half-crystallization time [from differential scanning calorimetry (DSC)] both show an Arrhenius-like behavior and have the same pseudoactivation energy. A practical implication of this parallel behavior of t _gel and t _0.5 is that the rheological measurements can be used to extend to higher temperatures the study of crystallization kinetics where DSC is not sufficiently sensitive.This paper was presented at the second Annual European Rheology Conference (AERC) held in Grenoble, France, 21–23 April 2005.     

Parametric study of the Hartmann–Sprenger tube

Experiments were conducted with a Hartmann–Sprenger tube (H–S) to study the effect of different parameters on the frequency and amplitude of acoustic fluctuations excited when the H–S underexpanded jet impinges on an in-line cavity. Time averaged shadowgraphs were acquired to study the flow field between the underexpanded jet and the cavity for varying parameters of the H–S tube. It was observed that the H–S tube primarily excited two different modes. The first mode corresponds to the jet regurgitant mode (JRG) where the frequency of oscillations scales as a function of the cavity depth. The other mode is screech where an oscillating shock is formed in front of the cavity. The screech mode excites a higher acoustic frequency than the JRG and it is observed to be a strong function of the pressure ratio R, and distance between the jet and the cavity X. At a fixed cavity length, varying standoff distance X could excite either the JRG or screech. At very low standoff distances (X/D_j<0.8), the current study indicates that there is a mode switch from screech to JRG. A cavity to jet diameter, D_c/D_j>1 was found to sustain JRG over a wide range of X. Diameter ratios D_c/D_j<1 sustained high frequency screech modes in a wide range of H–S tube parameters.     

Parametric study of the cyclic behaviour of a hygroscopic matrix in a desiccant airflow system

The study of the transport phenomena in desiccant airflow systems has been addressed in numerous research works, some of them concerning combined processes of cooling, dehumidification and energy recovery. In this paper a detailed numerical model is used to simulate the behaviour of a parallel-plate channel, cyclically exposed to two airflows with different inlet conditions, the plate being composed by a substrate and a desiccant porous layer. The modelled channel is considered to be representative of a real channel of a hygroscopic matrix that is operating at steady state regime, like it occurs in desiccant or enthalpy rotors. The numerical results are treated in order to represent the global behaviour of the hygroscopic rotor under steady state conditions. Results of a parametric study are presented as maps of isovalues of the heat and mass transfer rates and of the outlet states of both airflows, considering channels of distinct wall thickness, of different thickness of the desiccant and the subtract layers, together with wide ranges of the rotation speed and of the wheel partition. The mapped results presented provide an overview of the operation characteristics of hygroscopic rotors, allowing a quick determination of the optimum range of values for relevant parameters, such as the rotation speed and the wheel partition. The model is thus an interesting tool for design and manufacture purposes of enthalpy and desiccant wheels.