Viscoelastic-plastic deformation behavior of polypropylene after cyclic preloadings

Stress-relaxation behavior is studied in polypropylene samples subjected to different cyclic preloadings and to simple tension. The relaxation tests are performed under different sets of strain amplitude, number of cycles, and strain rate, using a closed-loop, electrohydraulic, servocontrolled testing machine. The calculated stress-strain curves are determined from a constitutive equation based on an overstress theory in which an equilibrium stress and a viscosity function are treated. The calculated results agree well with the experimental ones. It is concluded that the overstress theory explains the nonlinear viscoelastic-plastic behavior of polypropylene.     

Effect of morphology on stress relaxation of polypropylene

Samples of isotactic polypropylene having different morphologies and crystallinities were prepared and subjected to stress-relaxation experiments at different levels of strain. The relaxation moduli were determined in the range of temperature between – 20 and 40°C over a period of time from 1 to 1000 seconds. Using the time-temperature superposition principle, the activation energy values of the shift factors a_T were determined and the master curves were obtained for the various structures. Increasing crystallinity and/or crystalline aggregate size increases the relaxation modulus of the material and changes both shape and location of the spectrum of relaxation times so that no simple method can be found to correlate the various master curves.     

Prediction of stress–relaxation and creep of linear aromatic polyesters related to poly(ethylene terephthalate) in the nonlinear range

A study of the nonlinear viscoelastic properties of polymers was made using the Halsey-Eyring model with one- and three-dimensional mathematical analyses. Various parameters to calculate stress–relaxation and creep could be calculated from a single stress–strain curve of the same polymer. The parameters so calculated reconstituted the stress-strain curves, the one-dimensional equations yielding the better fit. The same constants were applied to predict stress-relaxation and creep. The fit using the three-dimensional equations is much better for stress-relaxation and creep than the one-dimensional equations.     

Constitutive modeling for mechanical behavior of PMMA microcellular foams

Constitutive equations for nonlinear tensile behavior of PMMA foams were studied. Five viscoelastic models composed of elastic and viscous components were accounted for the modeling of the constitutive equations. The developed constitutive equations are expressed in terms of material properties and foam properties such as strain, strain rate, elastic modulus, relative density of foam, and relaxation time constant. It was found that the stress-strain behaviors by Generalized Maxwell model, Three Element model and Burgers model could be described by the constitutive equation obtained from the Maxwell model. For the verification of the constitutive model, poly(methyl methacrylate) (PMMA) microcellular foams were manufactured using batch process method, and then uniaxial tensile tests were performed. The stress-strain curves by experiment were compared with the theoretical results by the constitutive equation. It was demonstrated that nonlinear tensile stress-strain behaviors of PMMA foams were well described by the constitutive equation.     

Effect of hydrogenation on density and viscosity of sunflowerseed oil

The densities and viscosities of unhydrogenated and hydrogenated sunflowerseed oils have been determined at temperatures ranging from 25 to 50°C at 5°C intervals. The densities of these oils vary linearly with temperature. The values of the parameters for the density equation have been calculated. Smooth curves were obtained when the changes in viscosity with temperature were plotted in the form of ln η vs. 1/T. The energy of activation, the free energy of activation, and the entropy of activation have been calculated at 25°C, and they decreased with the degree of unsaturation in the fatty acid chains of the sunflowerseed oil.     

Strain‐rate and temperature effects on the deformation of polypropylene and its simulation under monotonic compression and bending

Monotonic compressive loading and bending tests are conducted for solid polypropylene (PP) under constant or time‐varying strain‐rates and temperatures of 10, 25, 40°C. The observed compressive stress‐strain responses under constant conditions have revealed that the inelastic deformation behavior is remarkably dependent on loading rates and temperatures of normal use. The examination of such inelastic behavior has indicated that the strain‐rate effects correspond with the temperature effects based on the concept of time‐temperature equivalence. The viscoplastic constitutive theory based on overstress (VBO) has successfully reproduced the experimental responses with stress‐jumping phenomena using the equivalent time. Four‐point bending tests are performed under monotonic loading and holding for PP beams at three different temperatures. The observed deformation behavior has shown that the Bernoulli‐Euler hypothesis is valid. The VBO model and beam bending theory has generated the basic equations for PP beams, showing an analogy with the uniaxial one. In the numerical analysis, the equations are transformed into nonlinear ordinary differential equations with use of Gaussian quadrature for the spatial integrals. The comparison of numerical and experimental results has suggested some modifications for actually loaded moment taking the effect of deflection and friction into consideration. Finally, the numerical calculation has simulated the experimental time‐histories of curvatures fairly well.     

High-speed melt spinning of bicomponent fibers: Mechanism of fiber structure development in poly(ethylene terephthalate)/polypropylene system

High-speed bicomponent spinning of poly(ethylene terephthalate)(PET)(core) and poly-propylene (PP) (sheath) was carried out and the structure development in the individual components, PET and PP, was investigated. The orientation and crystallinity development in the PET component was enhanced as compared to that of the single-component spinning while the PP component remained in a low orientation state and had a pseudohexagonal crystal structure even at high take-up speeds. To clarify the mutual interaction between the two components in bicomponent spinning, a semiquantitative numerical simulation was performed. The simulation results obtained using the Newtonian fluid model showed that the solidification stress in the PET component was enhanced while that of the PP component was decreased in comparison with the corresponding single-component spinning. This is due to the difference in the temperature dependence of their elongational viscosity. Simulation with an upper-convected Maxwell model as the constitutive equation suggested that significant stress relaxation of the PP component can occur in the spinline if the PET component solidifies earlier than does PP. Based on the structural characterization results, and the simulation results, it was concluded that the difference in the activation energy of the elongational viscosity and solidification temperature between the two polymers are the main factors influencing the mutual interaction in the bicomponent spinning process. © 1996 John Wiley & Sons, Inc.     

A SIMPLIFIED APPROACH TO THE PREDICTION OF PRIMARY NORMAL STRESS DIFFERENCES IN POLYMER MELTS

A relationship between the unified primary normal stress difference function and the unified viscosity function curves proposed earlier by the authors is sought based on a strain dependent single integral constitutive equation of the BKZ-type. The predictions of the equation are checked for best fit of the unified primary normal stress difference curves of low density polyethylene, high density polyethylene, polypropylene and nylon. The approach is then extended to give theoretical predictions of the unified primary normal stress difference curves for a number of other polymers whose unified viscosity curves are known. The approach provides a method to estimate the normal stress difference versus shear rate curves at any temperature through the unified curves merely from the knowledge of the melt flow index.     

Temperature dependence of polyolefin melt rheology

The rheology of polymer melts depends strongly on temperature. Quantifying this temperature dependence is very important for fundamental, as well as practical, reasons. The purpose of this paper is to present a unified framework for handling the temperature dependence of rheological data. We considered the case (by far the most common in polymer melts) where all relaxation times (in the context of linear viscoelasticity) have the same temperature dependence (characterized by a “horizontal shift activation energy”) and all relaxation moduli have the same temperature dependence (characterized by a “vertical shift activation energy”). The horizontal and vertical activation energies were extracted from loss tangent vs. frequency and loss tangent vs. complex modulus data, respectively. This is the recommended method of calculation, as it allows independent estimation of the two activation energies (statistically uncorrelated). It was shown theoretically, and demonstrated experimentally, that neglect of the vertical shift leads to a stress (or modulus) dependent activation energy and necessitates different activation energies for the superposition of loss and storage modulus data. The long standing problem of a stress-dependent activation energy in long chain branched LDPE was identified as originating from the neglect of the vertical shift. The theory was applied successfully to many polyolefin melts, including HDPE, LLDPE, PP, EVOH, LDPE, and EVA. Linear polymers (HDPE, LLDPE, PP) and EVOH do not require a vertical shift, but long chain branched polymers do (LDPE, EVA). Steady-shear viscosity data can be superimposed using activation energies extracted from dynamic data.     

Prediction of the tensile impact behavior of injection molded samples from quasi-static data

A methodology for predicting the mechanical behavior of injection molded semi-crystalline thermoplastics, within a wide range of strain rates and temperatures, is proposed in this work. This method is based on data obtained at isothermal low velocity tensile tests and on a phenomenological constitutive equation that describes the stress as a function of independent and multiplicative terms of the strain, strain rate and temperature. The effect of the processing conditions on the coefficients of this equation is considered by evaluating their dependence on thermo-mechanical indices, calculated from melt flow simulations. Using a finite element code that has this equation built-in, it is possible to predict the mechanical behavior of samples injected with different molding conditions. The extrapolation of the impact properties requires the consideration of the dependence of the material consistency on the strain rate, which is affected by the sample skin-core structure. So, any constitutive equation used to describe the mechanical behavior of the injection molded samples must consider the distinct contributions of the main microstructural layers.     

Analysis of Shear Stress Growth Experiments for Linear Constitutive Equations

Shear stress growth curves for viscoelastic fluids at low shear rates are analyzed using two linear rheological constitutive equations, an integral constitutive equation and a mixed type constitutive equation. It is shown that some published solutions do not satisfy all of the pertinent boundary conditions. For the low shear rate region, available experimental shear stress curves show a monotonic increase with decreasing slope in the shear stress. Shear stress curves calculated using a mixed type constitutive equation are found to exhibit this type of behavior while curves calculated using an integral constitutive equation do not. For the mixed type constitutive equation, the calculated developing velocity distribution is used to examine its effect on the developing shear stress distribution. For low values of E (the elasticity number), there is a moderate effect, but, for sufficiently large values of E, the developing velocity distribution has a negligible effect. It is also shown that results consistent with experimental data obtained at low shear rates can be attained using a single relaxation time. Additionally, incompressible Newtonian fluids are considered, and it is found that there can be single maxima in some shear stress curves with no maxima occurring in the velocity curves. Multiple maxima were not obtained in the Newtonian shear stress results unlike some published results.     

Rheological Properties of Thermoplastic Polyvinyl Alcohol and Polypropylene Blend Melts in Capillary Extrusions

A single screw extruder with a static mixer was used to prepare molten blends of thermoplastic polyvinyl alcohol (TPVA) and polypropylene (PP). The effects of shear rate, blending ratio and temperature on rheological properties for the blends in capillary extrusions were investigated, and ends correction was also carried out. Rheological parameters such as non-Newtonian index and activation energy were also calculated and evaluated. It was found that the viscosities of the blends were lower than those of TPVA and PP; moreover, the non-Newtonian indices and the activation energies of the blend melts were higher than those of the homopolymers. In particular, the blend with 60 wt% TPVA had the highest non-Newtonian indices and activation energies among blend melts. These results indicate that TPVA and PP blends are negative deviation blends. Furthermore, at a blending ratio of 60 wt% of TPVA, the shear-sensitivity of the viscosity was the lowest and the temperature dependence of the viscosity was the highest. In addition, an increase in temperature led to an increase in non-Newtonian index, therefore the shear-rate dependence of the blend viscosities decreased with a rise in temperature. As the shear rate was increased, the variation of the viscosity over blending ratios decreased while the activation energy of the blends decreased. Thus the effects of temperature and blending proportion on flow behavior were diminished by increasing shear rate.     

Dynamic Mechanical Behavior of PBX

The dynamic mechanical properties of PBX1314 and its binder are systematically investigated. Based on split‐Hopkinson pressure bar technique, the experimental results of PBX1314 and its binder are obtained under high strain rate. A constitutive theory is developed for modeling the mechanical response of dynamically loaded PBX1314 binder. To accomplish this aim, the PBX1314 binder is assayed by relaxation tests at different temperatures, in order to apply the time‐temperature superposition principle (TTSP) and raise the master curves, based on WLF equation. The rate dependence of mechanical response of the polymer binder is accounted for by a generalized Maxwell viscoelasticity model. The basis for this work is Mori and Tanaka's effective medium theory. The grains in this analysis are assumed to be spherical and uniformly distributed in the binder. The relaxation constitutive relations of particulate reinforced composites are investigated by Laplace transformation and the corresponding principle. The theoretical prediction coincides with experimental results.     

Light scattering by boron oxide in a nonuniform temperature field and upon varying temperature

It is established that the time dependence of the intensity of the polarized component of visible light scattering by boron oxide under the influence of a constant temperature gradient is characterized by the same features as in the case of temperature variation. Based on this analogy, the relaxation times of the process of increasing the intensity in a nonuniform temperature field for different temperature intervals are determined. The activation energy of the process of increasing the intensity for different experimental conditions is calculated using the Arrhenius equation, and it is found that the calculated activation energy values are in satisfactory agreement with each other and with the data of other studies. The uniform behavior of the time dependence of the intensity of visible light scattering and close activation energy values point to common physical reasons for the structural changes occurring on the boron oxide structure approaching the equilibrium and stationary states.     

Creep Viscosity and Stress Relaxation of Gel-Derived Silicon Oxycarbide Glasses

The temperature dependence of the viscosity and stress-relaxation kinetics of sol–gel-derived SiOC glasses that contain up to 14 at.% carbon have been characterized in the temperature range of 1000°–1400°C. The viscosity, as determined from relaxation experiments, is in good agreement with the creep viscosity and is typically two orders of magnitude higher than the viscosity of vitreous silica. However, materials suffer from partial crystallization at >1150°C, and the precipitation of β-SiC nanocrystals induces a flow-hardening behavior and results in a dynamic increase in viscosity, especially at >1200°C and for glasses with a high carbon content.     

纳米SiO2/环氧树脂/空心微珠反应动力学研究

研究了纳米SiO2／环氧树脂／空心微珠体系的粘度特性，说明填料的加入对体系有一定的增粘作用。同时，采用示差扫描量热法（DSC）研究了纳米SiO2／环氧树脂／空心微珠体系的固化过程，利用不同升温速率下的DSC曲线求出三元体系的表观活化能、反应级数和频率因子等参数，得出了固化体系的反应动力学方程。     

环氧树脂和环氧/环硫树脂与胺的固化反应动力学

采用非等温DSC法对低黏度体系CY184/IPDA环氧树脂体系及对CY184/ES184/IPDA环氧/环硫树脂体系的固化反应动力学进行了研究。用高级等转化率Vyazovkin积分法求取活化能E_a,通过Málek法确定了固化反应机理函数和动力学参数,得到固化反应动力学方程。结果表明:CY184/IPDA环氧树脂体系的平均活化能为47.04 kJ·mol^-1;CY184/ES184/IPDA环氧/环硫树脂体系的活化能为48.97 kJ·mol^-1。两种体系的模型拟合曲线与实验得到的DSC曲线吻合得较好,均符合esták-Berggren(m,n)模型。     

Influence of Residual Water in a Glass on Its Rheological and Relaxation Properties (by the Example of a 5Na2O · 95B2O3Glass)

Glasses of the 5Na₂O · 95B₂O₃(mol %) composition synthesized at a temperature of 1100°C for 180 and 20 min are studied. The temperature dependences of the viscosity and the thermal expansion of glasses are obtained. The thermal expansion coefficients and glass transition temperatures of the studied glasses are determined, and the parameters of structural relaxation (the constant characterizing the width of the spectrum of relaxation times, the relaxation modulus equal to the ratio of the viscosity to the relaxation time, and the relaxation time at zero reciprocal temperature) are calculated from the dilatometric curves measured at temperatures close to the glass transition range. The water content in the studied glasses is estimated by comparing the obtained dependence of the viscosity on the water content with the data available in the literature for glasses of a similar composition. The assumption is made that the structural relaxation time in sodium borate glass decreases with an increase in the water content.     

Temperature dependence of viscosity of polyurethane polyol solutions: Application of rheological models

Polyurethane polyols were synthesized by reacting the diols with polyisocyanates. Viscosity of their 50% (w/w) solutions in various solvents has been determined at different temperatures by using Haake Roto Visco RV12 Rotational Viscometer. The temperature dependence of viscosity data was solved by Levenberg Marquardt's algorithm by using nonlinear regression models based on WLF, Vogel, and Arrhenius equations. The T_g values obtained from WLF and Vogel equation are comparable to each other and these equations can be satisfactorily used for the analysis of temperature dependence of viscosity data of oligomer solutions. The residuals are random and the absolute average percentage error in analyzing the viscosity data by these equations is minimum. The values of constants in WLF equation are found to be system dependent and adjustable parameters. The predicted In η values obtained from WLF and Vogel equations fit well with the plots of experimental In η values as a function of temperature. © 1996 John Wiley & Sons, Inc.     

Viscous Relaxation and Non-Arrhenius Behavior in B2O3

Ultrasonic shear and longitudinal measurements were made in Bz03 from 650° to 1000° C. From these data both the shear and volume relaxation time spectra were determined. The spectra had the same temperature dependence, although the volume spectrum was always broader than the shear spectrum. The shear relaxation process can be represented by a single relaxation time above 800° C in the region where the shear viscosity is Arrhenius. Both processes exhibit an increasingly broad distribution of relaxation times in the non-Arrhenius region. The temperature dependence of the shear spectrum was analyzed in terms of a distribution of activation energies. A surprising conclusion of this study is that activation energies at low temperatures are smaller than the activation energy in the Arrhenius region.