Relaxation behavior of neat and particulate filled polypropylene in uniaxial and multiaxial compression

The recently developed confined compression test was used to measure the viscoelastic bulk and shear relaxation moduli of neat, glass bead and talc filled polypropylene. In this paper further modifications of the test are introduced and a criterion for the assessment of the quality of experimental data is suggested. As expected, shear as well as the bulk relaxation moduli were found to increase with the addition of particles. In order to determine the pressure sensitivity of the material, unconfined compression tests were also performed and compared with the confined tests through interconversion of the measured moduli. In agreement with earlier results on other polymers, it turned out that the relaxation response is significantly retarded at higher confinement levels. It is shown that the effect of filler particles on the long-term behavior depends on the specific uniaxial or multiaxial stress state. Poisson’s ratio was calculated by interconversion from the bulk and shear relaxation modulus; these results show that with a single test in the confined configuration, a complete viscoelastic characterization of the material can be obtained.     

基于细观力学的纤维沥青混凝土有效松弛模量

为了研究纤维沥青混凝土的本构模型,将其视为以沥青混合料为粘弹性基体,纤维为弹性夹杂的两相复合材料。对基于复合材料细观力学理论建立的有效模量表达式进行了修正,提出了纤维沥青混凝土的割线有效松弛模量。以聚酯纤维沥青混凝土为例进行了有效松弛模量的解析分析和模拟蠕变实验的有限元分析,分析结果与试验数据的比较表明,该文提出的割线有效松弛模量模型对于纤维沥青混凝土粘弹性力学行为具有很好的预测能力。应用该模型对路面弯沉变形进行了有限元分析,结果表明:纤维的加入有效的改善了沥青混凝土路面的粘弹性性能。     

The Temperature and Frequency Dependence of the Bulk Compliance of Poly(Vinyl Acetate). A Re-Examination

Measurements are described and analyzed for the determination of thedynamic bulk compliance for Poly(vinyl acetate) [PVAc] as a function offrequency and temperature at atmospheric pressure to generate a mastercompliance curve over a total frequency range of about 12 decades.Measurements are based on the compressibility of a specimen confined to anoil-filled cavity resulting from pressurization by a piezoelectricdriver and response of a like receiver. Experimental problems addressinglimitations in resolution capability are discussed. The results arecompared with the classical measurements obtained by McKinney andBelcher over thirty years ago. Further comparison of the bulk with shearcompliance data shows that the extent of the transition ranges for thetwo material functions are comparable, but the two transitions belong todifferent time scales, that of the bulk response falling mostly into theglassy domain of the shear behavior. One concludes thus that forlinearly viscoelastic response the molecular mechanisms contributing toshear and bulk deformations have different conformational sources.     

On the use of a spectrum-based model for linear viscoelastic materials

A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.     

Viscoelastic properties of architected foams based on the Schoen IWP triply periodic minimal surface

Abstract

In this article, we studied the viscoelastic properties of an architected foam based on the mathematically-known Schoen IWP triply periodic minimal surface (TPMS) under both time and frequency domains. IWP-based architectures possess unique multifunctional attributes when used as a three-dimensional (3D) reinforcement in composites. The 3?D representative volume elements (RVEs) of different relative densities (i.e., the ratio of the foam’s density to the density of its solid counterpart) were generated and studied using the finite element method in order to predict the effective uniaxial, shear, and bulk viscoelastic responses of IWP-foams as a function of relative density and/or frequency. The principle of time-temperature superposition principle was used to create the master curve of the observed relative-density dependent mechanical responses (loss tangent, storage and loss moduli) in frequency domains. Reduced uniaxial, bulk, and shear stiffness-loss map results suggested that the IWP-foam possesses strongest uniaxial viscoelastic response while highest damping can be achieved under shear responses. Relaxation behavior of IWP-foam was compared with other six different types of open-cell periodic foams. It was found that IWP-foam uniaxial response is similar to simple cubic foam, bulk relaxation response is similar to primitive-foam while shear response follows the behavior of body centered cubic foam. Among these foams, we found that IWP-foam is the best candidate to use as a damper under uniaxial and hydrostatic loading conditions.     

Simplified Bulk Experiments and Hygrothermal Nonlinear Viscoelasticity

Bulk and shear linear viscoelastic functions were simultaneously determined using confined compression experiments on an epoxy primer, one component of a concrete/fiber-reinforced polymer composite bond line. The results were validated with data from separately conducted bulk creep compliance experiments. The transition region of the bulk modulus was as wide as those of the tensile and shear relaxation moduli. Thermal and hygral expansions were measured and used to calibrate a hybrid nonlinear viscoelastic constitutive model which represented the hygrothermal nonlinear viscoelastic response of the material. This model was a combination of Schaperys (Further Development of a Thermodynamic Constitutive Theory: Stress Formulation, AA {&} ES Report (69–2), 1969a, Purdue University, West Lafayette; Schapery, R.A., On the characterization of nolinear viscoelastic materials, Polym. Eng. Sci. 9 1969b, 295–310.) and Popelars (K., Multiaxial nonlinear viscoelastic characterization and modeling of a structural adhesive, J. Eng. Mater. Technol. Trans. ASME 119, 1997, 205–210.) shear modified free volume model, which was calibrated ramp using torsion and tension experiments at various temperature and humidity levels. Using free volume concepts to accomplish time shifting as a function of strain, temperature and humidity levels did not create the extent of the softening behavior that was observed in the experiments, particularly at high humidity levels. The vertical shifting concepts of Schapery were required to capture the extraordinarily strong hygral effect.     

Dynamic steady-state crack propagation in a transversely isotropic viscoelastic body

The problem considered herein is the dynamic, subsonic, steady-state propagation of a semi-infinite, generalized plane strain crack in an infinite, transversely isotropic, linear viscoelastic body. The corresponding boundary value problem is considered initially for a general anisotropic, linear viscoelastic body and reduced via transform methods to a matrix Riemann–Hilbert problem. The general problem does not readily yield explicit closed form solutions, so attention is addressed to the special case of a transversely isotropic viscoelastic body whose principal axis of material symmetry is parallel to the crack edge. For this special case, the out-of-plane shear (Mode III), in-plane shear (Mode II) and in-plane opening (Mode I) modes uncouple. Explicit expressions are then constructed for all three Stress Intensity Factors (SIF). The analysis is valid for quite general forms for the relevant viscoelastic relaxation functions subject only to the thermodynamic restriction that work done in closed cycles be non-negative. As a special case, an analytical solution of the Mode I problem for a general isotropic linear viscoelastic material is obtained without the usual assumption of a constant Poissons ratio or exponential decay of the bulk and shear relaxation functions. The Mode I SIF is then calculated for a generalized standard linear solid with unequal mean relaxation times in bulk and shear leading to a non-constant Poissons ratio. Numerical simulations are performed for both point loading on the crack faces and for a uniform traction applied to a compact portion of the crack faces. In both cases, it is observed that the SIF can vanish for crack speeds well below the glassy Rayleigh wave speed. This phenomenon is not seen for Mode I cracks in elastic material or for Mode III cracks in viscoelastic material.     

Fitting stress relaxation experiments with fractional Zener model to predict high frequency moduli of polymeric acoustic foams

This paper presents a time domain method to determine viscoelastic properties of open-cell foams on a wide frequency range. This method is based on the adjustment of the stress–time relationship, obtained from relaxation tests on polymeric foams’ samples under static compression, with the four fractional derivatives Zener model. The experimental relaxation function, well described by the Mittag–Leffler function, allows for straightforward prediction of the frequency-dependence of complex modulus of polyurethane foams. To show the feasibility of this approach, complex shear moduli of the same foams were measured in the frequency range between 0.1 and 16 Hz and at different temperatures between ?20 °C and 20 °C. A curve was reconstructed on the reduced frequency range (0.1 Hz–1 MHz) using the time–temperature superposition principle. Very good agreement was obtained between experimental complex moduli values and the fractional Zener model predictions. The proposed time domain method may constitute an improved alternative to resonant and non-resonant techniques often used for dynamic characterization of polymers for the determination of viscoelastic moduli on a broad frequency range.     

粘性弹耗能器恢复力模型的参数影响

首先在Kelvin-Voigt本构模型基础上,修正了振动频率对粘弹性材料剪切模量,损失模量的影响函数,其次,将环境温度 和剪切应变对上述模量的影响统一归为振动频率的转化系统;最后,由热力学第一定律导出了粘弹性耗能器疲劳温升模型。     

Modeling the nonlinear viscoelastic behavior of polyurea using a distortion modified free volume approach

The pressure-dependent behavior of polyurea was examined under monotonic loading in the confined compression configuration. Additional data from Arcan shear and uniaxial compression was used to respectively complete parameter selection for the linear and nonlinear behavior and then validate it. The bulk and shear relaxation behavior were both pressure dependent. Under ramp loadings, the shear and tensile responses were quite nonlinearly viscoelastic.     

Modeling short- and long-term time-dependent nonlinear behavior of polyethylene

A new methodology for developing macromechanical constitutive formulations for time-dependent materials is presented in this article. In particular, two phenomenological constitutive models for polymer materials are illustrated, describing time-dependent and nonlinear mechanical behavior. In this new approach, short-term creep test data are used for modeling both short-term and long-term responses. The differential form of a model is used to simulate typical nonlinear viscoelastic polymeric behavior using a combination of springs and dashpots. Unified plasticity theory is then used to develop the second model, which is a nonlinear viscoplastic one. Least squares fitting is applied for the determination of material parameters for both models, based on experimental results. Due to practical constraints, experimental data are usually available for short-term time-frames. In the presented proposed formulation, the material parameters determined from short-term testing are used to obtain material parameter relationships for predicting the long-term material response. This is done by extending short-term information for longer time frames. Finally, theoretical and experimental results of tensile tests on polyethylene subjected to various load levels and test times are compared and discussed. Very good agreement of the modeling results with experimental data shows that the developed formulation provides a flexible and reliable framework for predicting load responses of polymers.     

High-Frequency Shear Modulus and Relaxation Time of Soft-Sphere and Lennard–Jones Fluids

The high-frequency shear modulus, G, and shear relaxation time, _shear, are obtained using the Zwanzig–Mountain equation for soft-sphere and Lennard-Jones potentials. The Hansen and Weis soft-sphere radial distribution function and the Matteoli–Mansoori Lennard-Jones radial distribution function are used in the equation. The shear relaxation times of different isotherms for both of these fluids pass through a minimum at a reduced density of about 0.7, which indicates a change from fluid-like behavior to viscoelastic behavior. The origins of this common density point are discussed. It is also shown that for the Lennard-Jones fluid, if the ratio of the reduced relaxation time to a power of the reduced temperature is plotted as a function of the reduced density, all isotherms become superimposed on a single curve.     

An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule

Predicting the unloading and/or cyclic deformation behavior of polymers is a challenge for most nonlinear viscoelastic constitutive models. Experimental data of an epoxy polymer under uniaxial loading/unloading and two other types of cyclic loadings are used to assess the predictive capabilities of three types of nonlinear viscoelastic models. A general loading/unloading criterion and a switching rule, proposed recently by the authors, are further modified and incorporated into each of the three models. For each model, predictions by both the original formulations and that incorporating the proposed loading/unloading rule are compared with the test data. It is clearly shown that such a rule is essential to correctly simulate the unloading and cyclic loading behavior of polymers. By introducing such a rule to constitutive models, the quantitative predictions can be improved, to various degrees of success, with respect to cyclic deformation features such as ratcheting under cyclic loading with a mean stress and stress relaxation under cyclic straining with a mean strain.     

Analysis of viscoelastic laminated composite plates

A micromechanics analysis is performed for the determination of the five independent elastic moduli of unidirectional fiber composites. By considering viscoelastic phases and by using the correspondence principle and the inversion of the Laplace transform, the five time-dependent functions which characterize the effective behavior of viscoelastic composites are established. The predicted time-dependent behavior is applied for the analysis of viscoelastic laminated plates. The resulting viscoelastic effects are shown, and comparison between the results obtained within the classical laminated plate theory and the first-order shear deformation theory is discussed.     

粘弹性材料本构模型的研究

介绍了近年来建立粘弹性材料本构模型的方法。目前主要有两种方法:利用现有本构模型;对粘弹性材料进行试验研究,拟合实验曲线。     

The effect of particle shape on the mechanical properties of filled polymers

The existing models for predicting the elastic moduli of polymers dispersed with particles of shape other than spheres and continuous fibres are reviewed. The applicability and limitation of these equations are discussed. The emphasis of the review is to seek a unified understanding and approach to the effect of particle shape at finite concentration on the elastic moduli, thermal expansion coefficient, stress concentration factor, viscoelastic relaxation modulus and creep compliance of filled polymers. The effects of anisotropic particle shape on mechanical properties of polymeric composites are clearly illustrated. Attention is also drawn to the relationship between elastic moduli, thermal expansion, creep elongation and stress relaxation moduli.     

Measurement of Young’s relaxation modulus using nanoindentation

In a previous paper (Lu et al., Mechanics of Time-Dependent Materials, 7, 2003, 189–207), we described methods to measure the creep compliance of polymers using Berkovich and spherical indenters by nanoindentation. However, the relaxation modulus is often needed in stress and deformation analysis. It has been well known that the interconversion between creep compliance and relaxation function presents an ill-posed problem, so that converting the creep compliance function to the relaxation function cannot always give accurate results, especially considering that the creep data at short times in nanoindentation are often not reliable, and the overall nanoindentation time is short, typically a few hundred seconds. In this paper, we present methods to measure Young’s relaxation functions directly using nanoindentation. A constant-rate displacement loading history is usually used in nanoindentations. Using viscoelastic contact mechanics, Young’s relaxation modulus is extracted using nanoindentation load-displacement data. Three bulk polymers, Polymethyl Methacrylate (PMMA), Polycarbonate (PC) and Polyurethane (PU), are used in this study. The Young’s relaxation functions measured from the nanoindentation are compared with data measured from conventional tensile and shear tests to evaluate the precision of the methods. A reasonably good agreement has been reached for all these materials for indentation depth higher than a certain value, providing reassurance for these methods for measuring relaxation functions.