On the pressure dependency of the viscosity of molten polymers

Approaches for Numerical Modeling and Simulation of the Filling Phase in Injection Molding: A Review

Injection molding is a multiphase process that requires accurate simulation of the filling phase. This is a key element in predicting the complete injection molding cycle. The filling phase presents a complex set of challenges, including migrating melt fronts, multi-phase flow, non-Newtonian fluid dynamics, and intertwined heat transfer. Evolving from 1D to 2D, 2.5D, and 3D techniques, filling simulation research has adapted to capture the intricacies of injection-molded parts. However, the need for accuracy in the characterization of the rheological properties of polymers during filling is still of paramount importance. In order to systematically categorize the numerical methods used to simulate the filling phase of injection molding, this review paper provides a comprehensive summary. Particular emphasis is given to the complex interaction of multiple geometric parameters that significantly influence the dynamic evolution of the filling process. In addition, a spectrum of rheological models is thoroughly and exhaustively explored in the manuscript. These models serve as basic mathematical constructs to help describe the complex viscous behavior of polymers during the filling phase. These models cover a spectrum of complexity and include widely recognized formulations such as the Power-Law, second-order, Herschel-Bulkley, Carreau, Bird-Carreau, and Cross models. The paper presents their implementation to include the temperature-dependent influence on viscosity. In this context, the extensions of these models are explained in detail. These extensions are designed to take into account the dynamic viscosity changes caused by the different thermal conditions during the filling process. An important contribution of this study is the systematic classification of these models. This categorization encompasses both academic research and practical integration into commercial software frameworks. In addition to the theoretical importance of these models, their practical value in overcoming challenges in the field of injection molding is emphasized. By systematically outlining these models within a structured framework, this classification promotes a comprehensive understanding of their intrinsic characteristics and relevance in different scenarios.

High-Precision Thin Wall Bipolar Plates for Fuel Cell Applications via Injection Compression Molding with Dynamic Mold Temperature Control

In recent years, the demand for polymer compound solutions for the application of bipolar plates in polymer electrolyte membrane fuel cells (PEMFC) has increased continuously due to significant cost and lifetime advantages compared to metallic solutions. The main challenge of the compounds is the high filler content required to ensure sufficient electrical conductivity of the bipolar plates. The associated increase in viscosity and simultaneously increased thermal conductivity limit the conventional injection molding process in terms of achievable flow path length to wall thickness ratios (plate aspect ratio). In order to evaluate the extent to which highly modified electrically conductive polymer material systems can be processed into thin-walled and highly dimensionally stable bipolar plates, an injection compression molding process with dynamic mold temperature control (ICM-DT) has been developed. For this purpose, a compound was prepared from polypropylene (PP) and graphite-flakes. The compound was characterized with respect to the achieved filler content, the electrical conductivity, as well as the pressure- and temperature-dependent solidification range. The ICM-DT experiments were carried out by varying the maximum mold temperature and the compression force. In addition, the process was designed with multiple compression and decompression steps to account for a possible pressure-dependent solidification of the compound. The plates were characterized with respect to the achieved plate aspect ratio and the flow-path-dependent dimensional thickness stability. It was shown that the plate aspect ratio could be increased by up to 125% with the maximum filler content compared to conventional injection molding processes provided in the literature. With the multi-stage ICM-DT process, it was also possible to optimize the thickness dimensional stability with a maximum deviation of 3% over the flow path.

An Iterative Approach for the Parameter Estimation of Shear-Rate and Temperature-Dependent Rheological Models for Polymeric Liquids

Numerical flow simulations play an important role in polymer processing. One of the essential prerequisites for accurate and precise flow simulations is to obtain accurate materials functions. In the framework of the generalized Newtonian fluid model, one needs to obtain shear viscosity as a function of the rate-of-shear and temperature—as determined by rheometry—and then fitted to a mathematical model. Often, many subjectively perform the fitting without paying attention to the relative quality of the estimated parameters. This paper proposes a unique iterative algorithm for fitting the rate-of-shear and temperature-dependent viscosity model under the time–temperature superposition (TTS) principle. Proof-of-concept demonstrations are shown using the five-parameter Carreau–Yasuda model and experimental data from small-amplitude oscillatory shear (SAOS) measurements. It is shown that the newly proposed iterative algorithm leads to a more accurate representation of the experimental data compared to the traditional approach. We compare their performance in studies of the steady isothermal flow of a Carreau–Yasuda model fluid in a straight, circular tube. The two sets of parameters, one from the traditional approach and the other from the newly proposed iterative approach, show considerable differences in flow simulation. The percentage difference between the two predictions can be as large as 10% or more. Furthermore, even in cases where prior knowledge of the TTS shifting factors is not available, the newly proposed iterative approach can still yield a good fit to the experimental data, resulting in both the shifting factors and parameters for the non-Newtonian fluid model.

Development of a Rheology Die and Flow Characterization of Gas-Containing Polymer Melts

We present a novel measurement die for characterizing the flow behavior of gas-containing polymer melts. The die is mounted directly on the injection-molding cylinder in place of the mold cavity and thus enables near-process measurement of viscosity (i.e., under the conditions that would be present were a mold attached). This integration also resolves the issue of keeping gas-containing polymer melts under pressure during measurement to prevent desorption. After thermal characterization of the die, various correction approaches were compared against each other to identify the most suitable one for our case. We conducted measurements using polypropylene in combination with two different chemical blowing agents. Increasing the blowing-agent content to up to 6% revealed an interestingly low influence of gases on melt viscosity, which was confirmed by elongational viscosity measurements. For verification, we compared our results to corresponding measurements taken on a high-pressure capillary rheometer and found that they were in excellent agreement. Our die cannot only be used for rheological characterization. Combined with ultrasound sensors, it provides an innovative way of measuring the volumetric flow rate. This development represents an important step in improving the sustainability of gas-containing polymer processing.

Advances and challenges in the high-pressure rheology of complex fluids

Complex fluids and soft materials are ubiquitous in nature and industry. In industrial processes, these materials often get exposed to high hydrostatic pressures. Some examples include polymer melts, crude oils, gas hydrates, food systems, foams, motor oils, lubricants, etc. In spite of the relevance and utilization of hydrostatic pressure in many industrial applications, the role of pressure on the rheological properties has not been examined extensively in the literature. We review the high-pressure rheometric systems and present advantages and drawbacks of various kinds of rheometers such as capillary rheometer, sliding plate rheometer, falling ball viscometer, and rotational rheometer. By outlining the design complexities, precision, low-torque resolution limits and the inherent error sources of each type are critically evaluated. Furthermore, the high-pressure rheology data, chosen to cover a broad range of pressures and material class ranging from simple Newtonian fluids (incompressible), complex non-Newtonian fluids and compressible fluids featuring various key applications from different industries, are reviewed. The literature suggests, while effect of pressure on the rheological behavior is vital for many applications, compared to the effects of temperature on the rheological behavior, knowledge of the effect of pressure is still in its infancy.

Dynamic Compression Induced Solidification

This study presents a method for the determination of the dynamic pressure-dependent solidification of polycarbonate (PC) during flow using high pressure capillary rheometer (HPC) measurements. In addition, the pressure-dependent solidification was determined by isothermal pressure-volume-temperature (pvT) measurements under static conditions without shear. Independent of the compression velocity, a linear increase of the solidification pressure with temperature could be determined. Furthermore, the results indicate that the relaxation time at a constant temperature and compression rate can increase to such an extent that the material can no longer follow within the time scale specified by the compression rate. Consequently, the flow through the capillary stops at a specific pressure, with higher compression rates resulting in lower solidification pressures. Consequently, in regard to HPC measurements, it could be shown that the evaluation of the pressure via a pressure hole can lead to measurement errors in the limit range. Since the filling process in injection molding usually takes place under such transient conditions, the results are likely to be relevant for modelling the flow processes of thin-walled and microstructures with high aspect ratios.

Surface Damage Influences the JKR Contact Mechanics of Glassy Low-Molecular-Weight Polystyrene Films

Using a surface forces apparatus (SFA), we quantitatively study the influence of surface damage on the contact mechanics of self-mated glassy polystyrene (PS) films. We use the SFA to measure the contact radius, surface profile, and normal force between the films, including the adhesion force. The molecular weight (MW) of the polymer influences the repeatability of the adhesion measurements and the effective surface energy calculated using the Johnson-Kendall-Roberts (JKR) theory. For low-MW PS (MW = 2.33 kDa), the effective surface energy increases over repeated adhesion cycles as the films become progressively damaged. For high-MW PS (MW = 280 kDa), the effective surface energy is constant over repeated adhesion cycles, but hysteresis is still present, manifested in a smaller contact radius during compression of the surfaces than during separation. Our results demonstrate that while the JKR theory is appropriate for describing the contact mechanics of glassy polymer thin films on layered elastic substrates, the contact mechanics of low-MW polymer films can be complicated by surface damage to the films.

Full Characterization of Multiphase, Multimorphological Kinetics in Flow-Induced Crystallization of IPP at Elevated Pressure

Understanding the complex crystallization behavior of isotactic polypropylene (iPP) in conditions comparable to those found in polymer processing, where the polymer melt experiences a combination of high shear rates and elevated pressures, is key for modeling and therefore predicting the final structure and properties of iPP products. Coupling a unique experimental setup, capable to apply wall shear rates similar to those experienced during processing and carefully control the pressure before and after flow is imposed, with in situ X-ray scattering and diffraction techniques (SAXS and WAXD) at fast acquisition rates (up to 30 Hz), a well-defined series of short-term flow experiments are carried out using 16 different combinations of wall shear rates (ranging from 110 to 440 s-1) and pressures (100-400 bar). A complete overview on the kinetics of structure development during and after flow is presented. Information about shish formation and growth of α-phase parents lamellae from the shish backbones is extracted from SAXS; the overall apparent crystallinity evolution, amounts of different phases (α, β, and γ), and morphologies developing in the shear layer (parent and daughter lamellae both in α and γ phase) are fully quantified from the analysis of WAXD data. Both flow rate and pressure were found to have a significant influence on the nucleation and the growth process of oriented and isotropic structures. Flow affects shish formation and the growth of α-parents; pressure acts on relaxation times, enhancing the effect of flow, and (mainly) on the growth rate of γ-phase. The remarkably high amount of γ-lamellae found in the oriented layer strongly indicates the nucleation of γ directly from the shish backbone. All the observations were conceptually in agreement with the flow-induced crystallization model framework developed in our group and represent a unique and valuable data set that will be used to further validate and implement our numerical modeling, filling the gap for quantitatively modeling crystallization during complicated processing operations like injection molding.

Rheological Behavior of Mixtures of Polystyrene with HCFC 142b and HFC 134a

The processes for the production of thermoplastic foams, often in the shape of extruded sheets or boards, are largely dictated by the rheology of the mixture of a polymeric matrix with a blowing agent. This paper focuses on the theological behavior of mixtures of polystyrene (PS) and physical blowing agents (HCFC 142b and HFC 134a), examined using a commercial on-line rheometer mounted on an intermeshing co-rotating twin-screw extruder. The PS resin was extruded while the blowing agent was injected at high pressure and various compositions. The extent of plasticization was found to be dependent on the blowing agent concentration and its type. The effects of type of blowing agent, composition, pressure, shear rate and temperature on the theological response were measured. These variables were incorporated into a generalized mathematical model, which described the viscosity of the PS/blowing agent mixture over the studied range.

Hole Fraction Dependence on Linear Viscosity of PS, PP and ABS

A linear dependency of zero shear, constant shear-rate and constant shear-stress viscosities with temperature and hole fraction (“thermo-occupancy” function) was derived for polyacrylonitrile-butadiene-styrene (ABS), polypropylene (PP) and polystyrene (PS). The relation of viscosity parameters, such as transmission coefficient and a measure of activation energy coefficient, with shear-rate and shear-stress was also investigated and some conclusions on the differences for the studied polymers were discussed. In particular, it was found that, for all materials, the derivative of logarithm of viscosities at zero shear, constant shear-rate and constant shear-stress decreases with decreasing rate with the hole fraction.

On the Pressure Dependency of the Bagley Correction

The effect of pressure on the viscosity of polymer melts is an often forgotten parameter due to the inherent difficulty to measure this quantity. Different experimental approaches have already been undertaken in literature in the past. A popular methodology to measure the pressure dependence of the viscosity is to use a capillary rheometer equipped with a counter pressure chamber in which the exit pressure can be controlled. In order to process the data, one of the key elements is the Bagley correction that is required to determine the correct entrance pressure at a specific shear rate. In all analysis approaches presented in literature on data at controlled exit pressure, the Bagley correction was always determined at atmospheric exit pressure, disgarding possible effects of an enhanced exit pressure. In this paper, a new analytical approach is presented that for the first time allows for a direct assessment of the entrance pressures obtained when capillary measurements are performed with controlled counter pressures. It is demonstrated, using polycarbonate, that the entrance pressure correction needed to obtain correct viscosity values under pressure is significantly different than the one needed to correct measurements performed at atmospheric exit pressure.

On PVT and Rheological Measurements of Polymer Melts

The relation between PVT and rheological measurements of several polymer melts including polyethylenes, polypropylene, polystyrene, poly(methyl methacrylate), and polycarbonate has been taken into investigation. Pressure-temperature dependent viscosities, determined on rotational and backpressure-modified capillary rheometers, were fitted through the Carreau-Yasuda model. PVT data was analyzed by the help of the Simha-Somcynsky equation of state (SS EOS). The thermodynamical parameters of the SS EOS were connected to constant-stress viscosity (experimental) and zero-shear viscosity (extrapolated). The Doolittle relationship was modified into the form of η   =   exp ( C 1   ln ( h ′ h ) ) . The relation was employed and tested for the data evaluation. It proved to be a good tool for linearization of PVT and rheological data.

Pressure and Temperature Dependence of LDPE Viscosity and Free Volume: The Effect of Molecular Structure

Temperature and pressure dependencies of shear and elongational viscosities were examined using rotational and capillary rheometers. Two different batches of the same polymer grade have shown that the molecular structure diversion significantly influences the magnitudes of pressure coefficients, which vary more than the temperature coefficients. The pressure effect on viscosity notably depends on the amount of long-chain branching in polymer. Further, the paper shows that pVT data analysis via the Simha-Somcynsky equation of state can be employed to reveal differences in temperature and pressure viscosity dependencies through the free volume fraction.

Free Volume from Pressure and Temperature Dependent Viscosity and from PVT Measurements for Homo- and Copolymers

Pressure and temperature dependency of shear and elongation viscosity and the thermal expansivity and the compressibility determined from PVT data were investigated for propylene homo- and propylene-1-pentene, -1-hexene, 1-heptene and -nonene copolymers and ethylene homopolymer and ethylene-1-butene, 1-pentene and 1-hexene copolymers. The short branching degree dependence of thermal sensitivity and pressure coefficient and the thermal expansivity and the compressibility has been determined. The fractional free volumes were calculated from the viscosity and PVT curves and the thermal expansion coefficient and compressibility factor of fractional free volume were determined. The temperature, pressure and stress dependence of fractional free volume was investigated. The fractional free volume calculated from viscosity data were compared from values comes from PVT measurement. A conversion equation was suggested.