Williams Landel Ferry Research Articles

Implementation of nozzle motion for material extrusion additive manufacturing in Ansys Fluent

ABSTRACT Most computational fluid dynamics (CFD) modelling of material extrusion additive manufacturing (MEX-AM) mainly relies on a moving boundary condition applied to the print bed and not the direct modelling of the motion of the nozzle. This paper presents step-by-step and detailed implementation of the nozzle motion as well as non-isothermal non-Newtonian flow during MEX-AM in Ansys Fluent. For nozzle motion the overset approach is used for the meshing which allows for the nozzle and the rest of the domain to be meshes separately, streamlining meshing and motion. The method is initially used to simulate a single strand, which was validated against experimental and numerical data. It was then applied to demonstrate out-of-plane nozzle motion in two case studies: three-layer printing and printing on a ramp. The model is further developed to simulate a single strand deposition with the well-known Cross–William–Landel–Ferry (Cross-WLF) behaviour for a thermal and shear-dependent material flow.

Synthesis and Viscoelastic Properties of Polycaprolactone/Polyvinylidene Fluoride/Nanohydroxyapatite Composite Scaffolds

AbstractObtaining a polymer nanocomposite with optimum viscoelastic, thermal, and biocompatibility properties is the main objective when designing nanocomposite systems with potential applications in tissue engineering. For this purpose, a blend of Polycaprolactone (PCL) and Polyvinylidene fluoride (PVDF) in an 85/15 weight ratio, along with a nanocomposite reinforced by nanohydroxyapatite (nHA) particles, is fabricated using a solution casting method in a mold. The impact of nHA content on crystallinity, viscoelastic properties, thermal stability, and the properties–structure relationship of nanocomposites is evaluated using scanning electron microscopy (SEM). Dynamic mechanical thermal (DMTA) analysis is used to determine the William–Landel–Ferry (WLF) constants and the effect of nHA on the nanocomposite's viscoelastic behavior. The PCL/15PVDF/0.5 wt% nHA exhibits the maximum thermal stability (40% residual char value) and 95% increase in storage modulus at 90 °C (rubbery region) in comparison with PCL/15PVDF blend. Water contact angle (WCA) and biocompatibility tests are conducted on the PCL/15PVDF blend and nanocomposite scaffolds to design appropriate nanocomposite systems with potential applications in tissue engineering. The high hydrophilic properties are assigned to PCL/15PVDF/0.5 wt% nHA with a WCA of 67.5°. Finally, in vitro cell culture confirmed 0.5 wt% nHA significantly improves cell adhesion and cytotoxicity with MG‐63 cells.

Effect of thermal aging on the long‐term dynamic and stress relaxation behavior of glass‐fiber reinforced polypropylene composites

AbstractThe increasing use of glass‐fiber reinforced polypropylene (GFPP) composites in a wide range of applications requiring long‐term service in challenging environments underscores the importance of its long‐term durability. This study aimed to investigate the effect of thermal aging on the long‐term dynamic durability and stress relaxation of GFPP composites. The time–temperature equivalence principle (TTSP) was used to assess the dynamic modulus at various temperatures and frequencies, as well as the relaxation modulus at different temperatures and relaxation times. To better understand long‐term durability behavior, the study also examined the impact of molecular structure on the durability of GFPP. Changes in chemical composition, crystallinity, melting point, and melt flow index of GFPP due to thermal aging were measured and analyzed using Fourier transform infrared spectroscopy, and differential scanning calorimetry, respectively. The results revealed that oxidation led to a decrease in the crystallinity and molecular weight of GFPP. The destruction of GFPP's molecular structure due to oxidation resulted in reduced long‐term durability. While TTSP can predict the long‐term durability of GFPP for decades or even centuries, its application in predicting the long‐term durability of GFPP is more suitable for nonaging conditions.Highlights Thermal aging reduces glass‐fiber reinforced polypropylene (GFPP's) long‐term durability. Time–temperature equivalence principle predicts GFPP durability under aging. GFPP's activation energy drops with thermal aging. Long‐term GFPP behavior aligns with Williams–Landel–Ferry model. Predictive models refine understanding of GFPP longevity.

The Activation Energy Temperature Dependence for Viscous Flow of Chalcogenides

For some chalcogenide glasses, the temperature dependence of the activation energy E(T) of viscous flow in the glass transition region was calculated using the Williams–Landel–Ferry (WLF) equation. A method for determining the activation energy of viscous flow as a function of temperature is proposed using the Taylor expansion of the function E(T) using the example of chalcogenide glasses As-Se, Ge-Se, Sb-Ge-Se, P-Se, and AsSe-TlSe. The calculation results showed that the temperature dependence of the activation energy for the Ge-Se, As-Se, P-Se, AsSe-TlSe, and AsSe systems is satisfactorily described by a polynomial of the second degree, and for Sb-Ge-Se glass by a polynomial of the third degree. The purpose of this work is to compare the values of the coefficients obtained from the Taylor series expansion of E(T) with the characteristics of the E(T) versus (T − Tg) curves obtained directly from the experimental temperature dependence of viscosity. The nature of the dependence E(T) is briefly discussed.

Construction and examination of temperature master curve for asphalt with different aging extents

Master curve is widely applied to assess the rheological properties of asphalt. The traditional master curve describes the variation of asphalt rheological properties with frequency. However, compared to frequency, the influence of temperature on asphalt properties is of greater concern. This study attempted to establish a method to transform the traditional master curve into temperature master curve. To this end, asphalt binder with different aging extents were prepared using aging simulation tests, and traditional complex shear modulus master curves of asphalt binder were established based on frequency sweep test. These were then transformed into temperature master curves using the established temperature-frequency equation. Furthermore, the accuracy of the temperature master curve was assessed through temperature sweep tests. The results showed that the temperature-frequency equation obtained based on Williams Landel Ferry equation effectively described the relationship between temperature and reduced frequency. The temperature master curve demonstrated good applicability for asphalt at different aging levels, with the differences between complex shear modulus values calculated by temperature master curve and the experimental values generally within 20%. The temperature master curve accurately characterized the trend of complex shear modulus with temperature. However, this accuracy and applicability were primarily focused on the mid-temperature and high-temperature ranges. The temperature master curve had obvious deficiency in predicting the complex shear modulus at low temperature. The findings provide new methods and insights into the relationship between asphalt rheological properties and temperature.

Star poly(ionic liquid)s: Chain architecture‐property relationships

AbstractIn this study, we report the synthesis of 3‐, 4‐, and 6‐arm star poly(ionic liquid)s (PILs) (specifically, star poly(vinylbenzyl methylimidazolium bis(trifluoromethane)sulfonimide) (poly(VBMIm‐TFSI))) via reversible addition‐fragmentation chain transfer (RAFT) polymerization with a core‐first approach, followed by quaternization and anion exchange. The impact of star polymer architecture on properties was explored by measuring the thermal, mechanical, and ion transport properties of each star PIL compared to those of an analogous linear PIL. The star PILs exhibited up to 2‐fold higher ionic conductivity, 150% higher elastic modulus, and 465% higher ultimate tensile strength compared to the analogous linear PIL. The Williams‐Landel‐Ferry (WLF) equation was employed to explore the effect of increased free volume on the improved ion transport properties of the star PILs. These results highlight the impact of star polymer architecture on PILs and star PILs as promising materials for electrochemical energy devices.

Study on the characterization method of dynamic modulus for asphalt mixture under multi-factor coupling conditions

In the actual service process of asphalt pavement, the dynamic response of the pavement structure layer is induced by vehicle loads. The dynamic modulus is a crucial parameter for analyzing the mechanical response of asphalt pavement. Due to significant influences from temperature and loading frequency on test measurements, along with its time-temperature equivalence, it becomes imperative to investigate the behavior of dynamic modulus under different temperature frequencies. Furthermore, laboratory loading modes also exert substantial effects on dynamic modulus. Employing different loading modes during measurement often leads to significantly varied stress states in specimens, yielding distinct values for dynamic modulus. Therefore, this study conducts dynamic modulus tests using direct tension, uniaxial compression, and indirect tension under five test temperatures and six loading frequencies while examining its variations under different stress states and temperature frequencies. The corresponding master curves and prediction models of dynamic modulus are derived, providing a valuable reference for predicting the dynamic modulus under wide-area test conditions. Through comparative analysis of dynamic modulus values at different stress levels, the stress level is incorporated into the master curve to establish corresponding master curves of dynamic modulus. By applying relevant theories and research on time-temperature equivalence, we obtained dynamic modulus master curves for three loading modes by fitting and analyzing dynamic modulus test data at various temperatures and loading frequencies. Combining the Sigmoid model and Williams-Landel-Ferry(WLF) equation, we derived prediction models for dynamic modulus under three loading modes. Comparative analysis of dynamic modulus values under these three loading modes allowed us to establish transformation equations for the prediction models in different loading scenarios. Finally, representative dynamic modulus values for permanent deformation in typical pavement structure layers were predicted based on laboratory test results and the derived models. The research findings presented in this paper have significant implications in eliminating the influence of loading modes on dynamic modulus predictions, establishing a unified prediction model, and providing essential parameters for predicting permanent deformation and fatigue life equivalent temperature.

Dynamic characteristics of bladder type attenuator for hydraulic systems

Flow ripples caused by the pump will lead to system failure or equipment damage. The bladder type attenuator is utilised to suppress flow ripples in piping systems, though its mathematic model has not been given out precisely. In this paper, the governing equations of the hollow cylindrical shell describing the bladder’s behaviour are studied. Considering the bladder’s viscoelastic materials, the constitutive function is obtained through DMA (Dynamic thermo-mechanical analysis) test and the WLF (Williams–Landel–Ferry) equation. Thus, the dynamic model of the attenuator can be written as an impedance expression, which consists of integral, fractional, constant, and differential components. Three experiments are carried out to validate the theoretical models. The static and dynamic models of the bladder are validated by experiments, indicating good agreement. The impedance model of the attenuator is validated by a hydraulic experiment assessed with the IL (insertion loss) index, showing high accuracy. All models proposed in this work are proven to be effective and accurate, and can be used to evaluate and optimise the bladder type attenuator theoretically.

INVESTIGATING THE DEPENDENCE OF ELASTOMERIC FRACTURE ON TEMPERATURE AND RATE

ABSTRACT Decades of elastomeric fracture phenomenology resulting from the work of Thomas and Smith demonstrated the remarkable fact that rubbers are stronger and tougher at lower temperatures. The prevailing explanation relates the fracture behavior to polymer viscoelasticity. Given the recent insight and evidence that toughness is influenced by material strength, we examine elastomeric fracture with a different perspective and conclude that chain scission dictates fracture characteristics, including its temperature dependence. Working within selected temperature ranges, stretching is shown to be entirely elastic at a stretching rate less than 0.17 s−1. We demonstrate that the same temperature and rate dependencies of strength and toughness, observed by Thomas and Smith, also occur in our crosslinked polybutadiene and styrene–butadiene rubber. The temperature effects on rate dependence of strength and toughness are found to be much stronger than that prescribed by the Williams–Landel–Ferry shift factor aT. Moreover, crack propagates, upon either stepwise stretching or during creep, at a much lower speed at lower temperature that cannot be rationalized with polymer relaxation dynamics. Our new interpretation is that a carbon–carbon bond is stronger at a lower temperature. Because backbone bonds are more stable, a higher degree of network stretching occurs before rupture at lower temperatures.

INVESTIGATING THE DEPENDENCE OF ELASTOMERIC FRACTURE ON TEMPERATURE AND RATE

ABSTRACT Decades of elastomeric fracture phenomenology resulting from the work of Thomas and Smith demonstrated the remarkable fact that rubbers are stronger and tougher at lower temperatures. The prevailing explanation relates the fracture behavior to polymer viscoelasticity. Given the recent insight and evidence that toughness is influenced by material strength, we examine elastomeric fracture with a different perspective and conclude that chain scission dictates fracture characteristics, including its temperature dependence. Working within selected temperature ranges, stretching is shown to be entirely elastic at a stretching rate less than 0.17 s−1. We demonstrate that the same temperature and rate dependencies of strength and toughness, observed by Thomas and Smith, also occur in our crosslinked polybutadiene and styrene–butadiene rubber. The temperature effects on rate dependence of strength and toughness are found to be much stronger than that prescribed by the Williams–Landel–Ferry shift factor aT. Moreover, crack propagates, upon either stepwise stretching or during creep, at a much lower speed at lower temperature that cannot be rationalized with polymer relaxation dynamics. Our new interpretation is that a carbon–carbon bond is stronger at a lower temperature. Because backbone bonds are more stable, a higher degree of network stretching occurs before rupture at lower temperatures.

Mapping positron annihilation lifetime spectroscopy data of a polymer to classical molecular dynamics simulations without shifting the glass transition temperature.

Positron annihilation lifetime spectroscopy (PALS) enables the nondestructive measurement of nanoscale cavities in materials. In this study, a strategy was proposed for mapping PALS measurement data of isotactic polypropylene to classical molecular dynamics (CMD) simulations. The discrepancy between simulated and experimental glass transition temperatures was resolved by shortening the polymer chains, rather than adjusting for the temperature, using the Williams-Landel-Ferry (WLF) equation. The effective probe radii of ortho-positronium (o-Ps), determined by comparing PALS data with CMD simulations, were ∼0.8nm, which was consistent with the o-Ps size given by the solution of the Schrödinger equation. The free-volume fraction corresponding to the effective probe radius was 12.3% at the glass transition temperature, close to the value estimated using Simha-Boyer theory. The cavity number density was proportional to the effective probe radius and decreased with temperature. The o-Ps effective probe radius was proportional to both the critical probe radius and the -1/3 power of the monomer number density, and increased with increasing temperature. These findings suggest that combining PALS measurements with CMD simulations may provide insight into cavities in polymeric materials without relying on the WLF equation.

Temperature and Frequency Dependence of the Dynamic Viscoelastic Properties of Silicone Rubber.

Temperature-frequency sweep tests were performed on silicone rubber to investigate the dynamic viscoelastic properties. The test results show that the viscoelasticity of silicone rubber presents significant temperature dependence and frequency dependence. The dynamic viscoelastic test curves at different temperatures can be shifted along the logarithmic frequency coordinate axis to construct smooth master curves at the reference temperature of 20 °C, covering a frequency range of 10 decades, which indicates thermorheological simplicity on a macro level and frequency temperature equivalence of the silicone rubber material in the experimental temperature range. The van Gurp-Palmen plot and Cole-Cole plot for the test data at various temperatures merge into a common curve, which further validates thermorheological simplicity. The temperature dependent shift factors of silicone rubber material were well characterized by the Williams-Landel-Ferry equation. Moreover, the fractional-order differential Kelvin (FDK) model, the fractional-order differential Zener (FDZ) model, and the improved fractional-order differential Zener (iFDZ) model were used to model the asymmetric loss factor master curve. The result shows that the iFDZ model is in good agreement with the test results, indicating that this model is suitable for describing the asymmetry of dynamic viscoelastic properties of silicone rubber.

Effect of combining different factors on the rheological property of crude oil

ABSTRACT In this paper, a high-pressure rheometer (MARS 60) was used to conduct rheological experiments on crude oil under varying parameters, including temperature, static pressure, and methane (CH4) dissolution. Combining the Williams–Landel–Ferry equation (WLF equation), Barus equation, and Kishimoto – Fujita model (F-K model), a new model of combined shift factor was used to quantify the effects of different oil parameters on crude-oil viscosity. The results show that higher temperature, lower static pressure, and lower CH4 dissolution reduce crude-oil viscosity. Static pressure and CH4 dissolution have a more significant effect on viscosity in lower-temperature conditions when compared to higher-temperature conditions. Due to the combined effect of the saturation pressure, there is an optimal condition of CH4 dissolution for reducing the viscosity. The shift factor of CH4 concentration is defined as the ratio of the viscosity of crude oil under saturation pressure of CH4 and static pressure, and the results agree with the F-K model. A new model of the combined shift factor was developed with average deviations of the predicted shift factors for Shengli crude oil and Nanyang crude oil being 3.35% and 2.16%, respectively. Finally, the predicted and tested values are basically in agreement.

TTS package: Computational tools for the application of the Time Temperature Superposition principle

The TTS package has been developed in R software to predict the mechanical properties of viscoelastic materials, at short and long observation times/frequencies by applying the Time Temperature Superposition (TTS) principle. TTS is a physical principle used in material science to estimate mechanical properties beyond the experimental range of observed times/frequencies by shifting data curves obtained at other temperatures relative to a reference temperature in the dataset. It is a methodology related to accelerated life-tests and reliability, whereas the TTS library is one of the first open source computational tool to apply the TTS principle. This R package provides free computational tools to obtain master curves that characterize materials from a thermal-mechanical approach. The TTS package also proposes, implements and explains our own method to obtain the shift factors and the master curve in a TTS analysis, based on horizontal shifting of the first derivative function of viscoelastic properties. This procedure provides shift factors estimates and smooth master curve estimates using B-spline fitting, in a fully automatic way, without assuming any parametric expression. Williams-Landel-Ferry (WLF) and Arrhenius TTS parametric models are also implemented in the TTS package. They can be fitted from shifts obtained by the our first derivative based method.

The roles of polymer relaxation phenomena, aqueous dye solubility and the physical properties of water in the mechanism of adsorption of a disperse dye on poly(ethylene terephthalate) fibres: part 5 analysis of polymer relaxation phenomena for different polymers

AbstractThe temperature dependent uptake of a commercial disperse dye on cotton and polyamide 66 fabrics at dyeing temperatures between 30°C and 130°C adhered to the Williams–Landel–Ferry equation, insofar as, very good correspondence was observed between plots of experimentally determined colour strength data points (log1/fk) and the respective structural relaxation times of the cellulose and nylon 66 polymers (logaT data points), as a function of the parameter (T − Tg). Adsorption of the dye on both types of fibre therefore concurs with the fundamental precept of the free volume model of dye diffusion. Comparison of the adherence of the uptake of the commercial dye on cotton and polyamide 66 fabrics with that secured on polyester fabric revealed that despite the major chemical and physical differences between the three types of fibre, the same dyeing mechanism likely applies to each fibre type. The marked temperature dependent uptake of the commercial grade disperse dye each of the three types of substrate is the consequence of two, different, but inherently interconnected, thermally activated phenomena, namely the relaxation times of the molecular rearrangements occurring within the respective cellulose, nylon 66 or poly(ethylene terephthalate) macromolecule, in which polymer glass transition assumes the principal role, and the aqueous solubility of the commercial grade disperse dye.

Rheological and Mechanical Study of Comb-Branched Polyolefin Elastomers Containing Macromer Residues

Comb-polyolefin elastomers (CPOEs) with crystalline long-chain branches (LCBes) demonstrate superior mechanical properties and processability. However, fully understanding the effect of LCBes on their material performance remains a huge challenge due to the residue of unreacted polyethylene macromers (PE-Ms). Here, we report a method of blending CPOEs with PE-Ms to study the structure–activity relationship of CPOEs via extrapolation. CPOE samples with different numbers of LCBes (q) between 0.0 and 9.9 and PE-Ms with an Mw value similar to the LCBes were prepared and studied. Blending CPOEs with 20–40 wt % of PE-Ms increased the melt fluidity and reduced the zero-shear viscosity (η0) value from 4590 Pa·s to 980 Pa·s without causing phase separation. These CPOEs exhibit dynamic responses with a similar temperature dependence where the time shift factors could be fitted by the same Williams–Landel–Ferry parameters with C1 at 4.88 and C2 at 443 K. For CPOEs with LCBes, as q increased from 1.1 to 9.9, the number of entanglements between the graft points (Zg) decreased from 11.78 to 0.93, and the chain conformation changed from sparse comb (SC) to dense comb (DC), respectively. The maximum η0 value of CPOEs occurs at the turning point of SC and DC, where Zg is equal to the entanglement number of the branched chain −Zbc of 4.72. Our study distinguished the different effects between the grafted and free PE-Ms on the CPOEs, enabling an in-depth understanding of macromolecular engineering in polymer and facilitating the future development of higher-performance CPOEs or other grafted polymers.

Prediction Formula Describing Viscoelasticity of Unvulcanized Rubber Compound Based on Time-Temperature Equivalent Superposition Principle

Fitting unvulcanized rubber compound’s (URC) dynamic viscoelasticity prediction formula and then constructing its mechanical constitutive model are of great significance for studying defect mechanisms in rubber products. However, it is difficult to measure the dynamic viscoelasticity of unvulcanized rubber at high and low frequencies due to its rapid relaxation property. This paper presents a convenient method to measure the dynamic viscoelasticity of unvulcanized rubber. The data of different temperatures at a fixed frequency are measured by dynamic thermomechanical analysis, and the master curve of unvulcanized rubber is obtained by using the time-temperature equivalent superposition principle, which is used to predict the modulus and stress at different temperatures as a function of frequency. The predicted moduli are in good agreement with experimental data when the strain is less than 10% and the applicable temperature range of the Williams–Landel–Ferry (WLF) equation, which indicates that the proposed method is a feasible way to study the dynamic viscoelasticity of unvulcanized rubber at different temperatures.

The Temperature Interval of the Liquid–Glass Transition of Amorphous Polymers and Low Molecular Weight Amorphous Substances

We present calculation results of the temperature interval δTg characterizing the liquid–glass transition in amorphous materials obtained on the basis of available data of the empirical parameters C1 and C2 in the Williams–Landel–Ferry (WLF) viscosity equation. We consider the unambiguous dependence of the relative transition temperature interval δTg/Tg on the fraction of the fluctuation volume fg frozen at the glass transition temperature Tg utilizing Sanditov’s model of delocalized atoms. The parameter f = ΔVe/V, which determines the molecular mobility characteristic of delocalized atoms in the liquid–glass transition region, is weakly dependent on the nature of most vitreous substances and can be found as fg = 1/C1. We show that the temperature interval δTg is less than 1% of the Tg for most amorphous substances. This result conforms with Simon’s classical idea of a small temperature range in which the structure freezes. The structural relaxation time τg at Tg of polymers and chalcogenide glasses is also calculated.

A Systematical Rheological Study of Maize Kernel.

In this study, the rheological behavior of maize kernel was systematically investigated using a dynamic mechanical analyzer. The loss in toughness caused by drying resulted in a downward shift in the relaxation curve and an upward shift in the creep curve. The long relaxation behavior became obvious when the temperature was above 45 °C, resulting from the weakening of hydrogen bonds with temperature. The maize kernel relaxed more rapidly at high temperatures, caused by a reduction in the cell wall viscosity and polysaccharide tangles. The Deborah numbers were all much smaller than one, suggesting that the Maxwell elements showed viscous behavior. Maize kernel, as a viscoelastic material, showed a dominant viscous property at high temperatures. The decline in β with increasing drying temperature indicated an increase in the width of the relaxation spectrum. A Hookean spring elastic portion made up the majority of the maize kernel creep strain. The order-disorder transformation zone of maize kernel was about 50-60 °C. Due to the complexity of maize kernel, the William-Landel-Ferry constants differed from the universal values; these constants should be ascertained through experiments. Time-temperature superposition was successfully used to describe the rheological behavior. The results show that maize kernel is a thermorheologically simple material. The data acquired in this study can be used for maize processing and storage.

Study of the Thermomechanics of the Additive Manufacturing Process of Biocompatible Products Subject to the Viscoelastic Behavior of the Functional Material Polyetheretherketone

This study considers the problem of numerical modeling of the PEEK product’s 3D printing using the FDM technology. The aim of the study is to verify the adequacy of the use of a thermoviscoelastic model for numerical computations of the PEEK deposition process and to develop an algorithm for calculating this process. The Prony model is used to describe the thermoviscoelastic behavior of the material under study; the temperature-time shift is described by the Williams–Landel–Ferry function (WLF). To obtain the values of the material constants of the relaxation function, first, we used data from other authors; however, after their substitution into the numerical simulation, it was not possible to obtain results close to the full-scale experiment. Therefore, realized our own DMA experiment. The algorithm was developed and implemented in the ANSYS package to calculate non-stationary temperature fields and the stress–strain state of the structure during its layer-by-layer deposition. To solve these problems, the technology of “killing” and subsequent “aliving” of the PEEK material, implemented in the ANSYS package, is used. The numerical algorithm is verified with the results of an experiment on printing samples from PEEK. A good consistency of the calculated data with the experiment is shown.