A Comparison of Linear with Nonlinear Viscoelastic Solutions for Shear Stress Concentration in Double Lap Joints

The correspondence principle based on the Maxwell model and a nonlinear viscoelastic solution involving an iterative scheme are used to describe the time dependent variation of the adhesive maximum shear stress in adhesively bonded double lap joints. The results indicate that if the correspondence principle is applied, the use of Maxwell chain is necessary to approximate the continuous change in the relaxation time and to coincide with the results calculated using the nonlinear viscoelastic theory.     

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.     

Investigation and prediction on the nonlinear viscoelastic behaviors of nylon1212 toughened with elastomer

Studies on the nonlinear viscoelastic behaviors of nylon1212 toughened with styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The linear relaxation curves at relatively low shear strains show good overlap, the relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model. The nonlinear relaxation curves of nylon1212 blends at different shear strains have been obtained and their damping functions were evaluated. Meanwhile, it is found that most blends in the experimental windows follow the strain‐time separation principle and Laun double exponential model can predict damping curves well. The successive start‐up of shear behavior was investigated. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data of nylon 1212 blend with 10 wt % SEEPS well, but there exists some deviation for experiment data of nylon1212 blends with high SEEPS concentrations. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Semi-analytical solution for electro-thermo-mechanical non-stationary creep behaviour of rotating disk made of nonlinear piezoelectric polymer

Electro-thermo-mechanical non-stationary creep response of a rotating disk made of nonlinear polymeric piezoelectric material has been investigated. The viscoelastic properties of the material are time, stress and temperature dependent which vary along radius. The long-term creep constitutive equation is the Burgers viscoelastic model. A non-homogeneous differential equation with variable coefficients is derived using stress-displacement relations, equilibrium equation, charge equation of electrostatics and the Maxwell equation. Time-dependent creep strains are involved in the non-homogeneous term of the differential equation. A semi-analytical solution has been developed to obtain displacement, stresses, strains and electric potential in terms of creep strains. Then, Prandtl–Reuss relations and the creep constitutive model are employed in a novel numerical procedure based on the Mendelson method to obtain history of displacement, stresses, electric potential and strains. It has been concluded that the displacement is increasing with time while effective stresses are decreasing. The results are validated by finite element methods modelling using ABAQUS software. A very good agreements between the results can be observed.     

Effects of the molecular weight of poly(ether imide) on the viscoelastic phase separation of poly(ether imide)/epoxy blends

The phase separation of diglycidyl ether of bisphenol A/methyl tetrahydrophthalic anhydride blends modified with three poly(ether imide)s (PEIs) of different molecular weights was investigated with scanning electron microscopy (SEM) and time‐resolved light scattering (TRLS). The morphologies observed by SEM for the three blends were all close to a cocontinuous structure with different periodic distances. The results of TRLS indicated that the phase separation for the PEI‐modified epoxy blends took place according to the spinodal decomposition mechanism and the onset time of phase separation, with the periodicity of the phase structure depending on the PEI molecular weight and cure temperature. The time‐dependent peak scattering vector was simulated with a Maxwell‐type viscoelastic relaxation equation, indicating that the coarsening process of epoxy droplets was mainly controlled by the viscoelastic flow. Relaxation times obtained at different temperatures for the three blends could be described by the Williams–Landel–Ferry equation. The effects of the PEI molecular weight on the processes of viscoelastic phase separation were investigated, and the observed trends could be explained qualitatively through thermodynamic analysis. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Some new operational modes and parameters of stress relaxation for the viscoelastic characterization of solid polymers. III. The area ratio mode and the intrinsic “strain–clock” function

The introduced area ratio mode of operation with its corresponding parameters seems to have a fairly high sensitivity to the viscoelastic response of the solid polymer. This appeared from the fact that a good distinction among the linear viscoelastic, the nonlinear viscoelastic, and the viscoplastic ranges of behavior can be made. By using a relevant rheological modeling and its corresponding algorithmical approach, in the case of isotactic polypropylene, this material can be characterized as a morphological three‐phase material consisting of an intraspherulitic crystalline, an amorphous phase, and a interspherulitic para‐crystalline phase. In this sense, the material was simulated using two models: the Poynting–Thomson and the Maxwell–Wierchert, from where a good response of the material to the first model appeared. The so‐called intrinsic “strain–clock” function and its corresponding coefficient of strength of nonlinear viscoelastic behavior, which were relieved by the experimental data, seem to be some powerful and very practical “tools” that can give a proven suplementary characterization of the material. Finally, by this intrinsic function, the existence of permanent internal stresses, was confirmed, in an indirect way, which was mentioned in part II of this study. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 149–158, 2003     

周期载荷下的阻尼硅橡胶动态粘弹性研究

研究了阻尼硅橡胶的非线性粘弹行为及在周期载荷下的动态粘弹性能变化。结果表明,在周期性载荷作用下,阻尼硅橡胶表现出非线性粘弹行为,且在疲劳后此种非线性特征更为明显;阻尼硅橡胶的疲劳过程分为3个阶段,分别为模量稳定阶段、微观损伤阶段及宏观损伤阶段;达到第3阶段时,基本可以判定硅橡胶材料达到了疲劳损伤寿命。     

Viscoelastic properties of polyarylene ether nitriles/thermotropic liquid crystalline polymer blend

Polyarylene ether nitriles (PEN)/thermotropic liquid crystalline polymer (TLCP) blend was prepared via melt mixing. The immiscible phase morphologies, linear and nonlinear, as well as transient viscoelastic properties of the blend were studied using SEM, rheometer, and DMA. The linear dynamic viscoelastic behavior of the blend shows temperature dependence due to further evolution of the immiscible morphology and, as a result, the principle of time‐temperature superposition (TTS) is invalid. In the steady shear flow, the discrete TLCP phase is difficult to be broken up because of the high viscosity ratio of the blend systems, while is easy to be coarsened and followed by elongation, and finally, to form fibrous morphology at high TLCP content and high shear level. During this morphological evolution process, the transient stress response presents step increase and nonzero residual relaxation behavior, leading to increase of the dynamic viscoelastic responses after steady preshear. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Modeling the viscoelasticity of polyetherimide

Viscoelasticity is a mechanical phenomenon where the material modulus varies with time and temperature. Modern experimental methods can determine material properties within certain time and temperature ranges, but modeling the viscoelastic behavior remains challenging, mainly because the data processing is complex and different materials have distinct properties. Using polyetherimide as an example and based on the change in the secondary bonds of polyetherimide in different viscoelastic stages, we proposed a new shift factor model in Arrhenius format with alterable activation energy. We also used two methods based on nonlinear least squares to obtain the Maxwell model of the polyetherimide, and we then used a novel method integrated with Laplace transforms and partial fraction decomposition to convert the Maxwell model into the Voigt model. The results of our model are reliable and self‐consistent, showing its potential for modeling the viscoelasticity of other materials. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46102.     

Residual stress and viscoelastic deformation of film insert molded automotive parts

Complex automotive parts were produced by film insert molding and the ejected parts were annealed to investigate the viscoelastic deformation. Warpage of the part was predicted by numerical simulation of mold filling, packing, and cooling stages with non‐isothermal three‐dimensional flow analysis. The flow analysis results were transported to a finite element stress analysis program and the stress analysis was performed by using time‐temperature superposition principle to investigate viscoelastic deformation. Predicted residual stresses, viscoelastic deformation, and warpage showed good agreement with experimental results. Thermal shrinkage of the inserted film and relaxation of the residual stress affected the viscoelastic deformation of the part significantly during annealing. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

I. THEORY AND FINITE ELEMENT FORMULATION

A theoretical basis for a nonlinear thermo-hydro viscoelastic boundary value problem was developed. An incremental finite element formulation was derlved using the principle of virtual work. The effects of non-uniform temparature and moisture gradients and solution dependent material property functions are outlined. An appropriate     

Modeling nonlinear viscoelastic response

We present a model for calculating nonlinear viscoelastic response which we call the “phases model” (PHM). In terms of a mechanical model representation the PHM is a generalized Maxwell model with nonlinear elements where each Maxwell element is referred to as a phase. The viscous material properties are represented in the model in terms of flow curves of the individual phases. The collection of flow curves form the flow diagram. We show how to calibrate the flow diagram from a family of constant rate test curves by means of a simple straightforward procedure. We give an example of such a calibration for a certain rigid polyurethane. We applied our model to the calculation of nonlinear viscoelastic response to varius loading programs in uniaxial tension, and to the creep of a simply supported beam, and obtained good agreement with experimental data.     

Viscoelastic properties of lupin proteins produced by ultrafiltration-diafiltration

The linear and nonlinear rheological properties of defatted lupin proteins produced by ultrafiltration-diafiltration were investigated. Five concentrations ranging from 10 to 30% of the defatted ultrafiltered-diafiltered (DUD) lupin proteins were prepared. The viscoelastic properties strongly depended on concentrations. Below 12%, the DUD lupin proteins exhibited more fluid-like behavior. At 15%, lupin proteins became more viscoelastic, and above 20%, the viscoelastic solid-like properties became stronger. Below 12%, the high-frequency behaviors of moduli were proportional to ω^1/2, as expected for a semiflexible coil. Above 20%, the high-frequency behaviors of moduli were proportional to ω^1/2, indicating a flexible coil. The nonlinear steady shear rheological properties were also concentration-dependent and showed shear-thinning behavior, which could be described by a power law constitutive model. The trend of the power law exponent shift is very consistent with the linear viscoelastic behavior change with the lupin protein concentration. These results suggest DUD lupin proteins undergo a structural change between 12 and 20%.     

Nonlinear viscoelastic properties of molten thermoplastic vulcanisates: An insight on their morphology

A series of thermoplastic vulcanisates (TPVs) in the molten state were submitted to large amplitude oscillating strain tests at different frequencies, to investigate their nonlinear viscoelastic properties. A purposely modified torsional harmonic tester with a closed cavity was used to run such experiments, whose results were treated with a Fourier transform (FT) algorithm to extract main torque and strain components, and harmonics if any. Quarter cycle integrations of (averaged) torque signal were also performed, to supplement FT analysis, namely to distinguish extrinsic and intrinsic nonlinear viscoelasticity. The nonlinear viscoelastic character of TPVs was found substantially differing from the one of a molten polypropylene (PP) used for comparison. Within the strain window investigated, no linear behavior is observed with TPVs, in contrast with the pure PP. However, extrapolated “linear” complex modulus G*₀ tends to decrease with increasing hardness of TPVs, but subtle differences between the various grades are clearly detected, when using simple models to fit experimental data. While the (room temperature) hardness is somewhat related with the viscoelastic behavior in the molten state, the strain sensitivity of TPVs appears essentially affected by the extractible content (mainly oil). TPVs nonlinear viscoelastic character appears to depend on the strain amplitude: mainly intrinsic, i.e., due to their morphology, at low strain, and essentially extrinsic, i.e., due to the large strain amplitude, at high strain, and in this respect, qualitatively similar to pure PP. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 4193–4205, 2006     

I. THEORY AND FINITE ELEMENT FORMULATION

ABSTRACT

A theoretical basis for a nonlinear thermo-hydro viscoelastic boundary value problem was developed. An incremental finite element formulation was derlved using the principle of virtual work. The effects of non-uniform temparature and moisture gradients and solution dependent material property functions are outlined. An appropriate     

A new method of characterizing material viscoelastic property by using vector fitting

A numerical algorithm is first established to characterize viscoelastic properties of materials by using vector fitting which is used more commonly for system identification in the field of electronic and automatic control. Combining with correspondence principle, the present numerical algorithm is employed to predict the viscoelastic properties of no‐flow underfill material. The predicted results are compared with the experiment data. Very good agreement between numerical algorithm and experiment results is illustrated for the materials. As the form is simple, the relaxation modulus can be easily switched from frequency domain to time domain by using inverse Laplace transformation. The present algorithm can also be used to characterize viscoelastic properties of other materials. POLYM. COMPOS., 37:1848–1853, 2016. © 2015 Society of Plastics Engineers     

A thorough study on the relationships between dispersion quality and viscoelastic properties in carbon black filled SBR compounds

A series of carbon black filled SBR 1500 compounds (without curatives) were prepared in carefully controlled lab‐mixing conditions so that filler content ranged from 0 to 50 phr, with the usual compounding ingredients. Carbon Black agglomeration and dispersion quality were assessed through an advanced microscopic technique with automated data treatment. Linear and nonlinear viscoelastic properties were evaluated using a closed cavity torsional rheometer, equipped for Fourier Transform rheometry experiments. In the linear viscoelastic regime, dynamic moduli mastercurves were derived from experiments in the 60−160°C temperature range. In the nonlinear viscoelastic regime, complex modulus and torque harmonics variation with strain amplitude were investigated at 100°C and frequency 0.5 and 1.0 Hz. Relationships between dispersion quality, carbon black loading and mixing parameters were investigated so that dispersion appears better when the filler loading is above a critical level that to some extent (but not exactly) corresponds to the theoretical percolation threshold (around 13%). Linear and nonlinear viscoelastic measurements demonstrate and quantify the role played by plasticizing compounding ingredients, that is, processing oil, stearic acid and other chemicals, with nearly no significant effect of mixing energy. At least 10−15 phr carbon black are necessary to recover the modulus loss associated with this plasticizing effect. Nonlinear results and particularly the torque harmonics reveal a number of details as to how the compounding ingredients do affect the viscoelastic behavior, with expectedly the carbon black playing the major role. By fitting results with mathematically simple models, all of the observed effects can be summarized in a rather limited number of parameters so that the effects of compounding ingredients can be studied in details. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Rheological properties of aqueous α A12O3 suspensions: Influence of dispersant concentration

The effects of concentration of polyacrylic acid as a dispersant on rheological properties of aqueous alumina suspensions have been investigated under steady and oscillatory shear conditions. At solid volume fractions between 0.45 and 0.6, a high degree of particle stabilization is achieved when 0.2 wt% of polyacrylic acid is added. At lower dispersant concentrations, suspensions exhibit pronounced irreversible thixotropic behaviour, whereas at higher dispersant concentrations, time dependent effects on the flow properties are not detectable. When the saturation adsorption limit of the polyelectrolyte on Al₂O₃ is reached, further addition of the dispersant appreciably changes the flow behaviour, as well as the viscoelastic response of investigated suspensions. The data under steady shear are described by application of the generalized Casson model, and for the analysis of viscoelastic data the generalized Maxwell model is used.     

牛奶纤维拉伸性能建模的研究

对牛奶纤维的力学性能进行了测试,利用四元件非线性粘弹模型对其应力应变关系进行了分析和模拟计算。结果表明:理论和实测结果符合得很好,该模型可用于预测牛奶纤维的拉伸性能。