Remarks on properties of photoviscoelastic model materials

One of the basic problems of structural-model analysis, model photoelasticity and photoelastic coatings in the problem of mechanical and optical creep, relaxation and related phenomena. It is pointed out that, in spite of creep or relaxation, it is possible to achieve physical similarity between model and object if the model material behaves in a certain range as a linear viscoelastic material. Such a material is called a “momentarily linear material.” Several model materials behave in this way in a certain range of stress and time. Because of creep and relaxation, the common tensile tests are, in general, not quite adequate for evaluation of physical properties of plastics used for models. Also the bending test is not always adequate. It is shown how to obtain sufficiently accurate relations between stress, strain, birefringence and time, using tapered specimens. The problem of biaxial creep of model materials is discussed, and a simple method of evaluating the suitability of a given plastic as a model material is shown. Some conclusions concerning time-dependent factors are formulated, and some possible areas of investigation are shown.     

A review of the rheo-optical properties of linear high polymers

Some principles ans laws, expressing the mechanical and optical behavior of linear viscoelastic materials, are reviewed. The mechanical properties of the polymers in the transition region may be represented by a condensed general method containing Ferry's modulus or compliance-reduction scheme, the time-temperature superposition principle and the Gauss error integral representation. The optical behavior of high polymers is expressed by the stress- and strain-optical coefficients in creep or relaxation, which relate birefringence to stresses or strains. It was recently shown experimentally that, instead of a pair of independent linear differential operator relations, which characterize the mechanical properties of the viscoelastic materials, only one operator relation is needed and the initial value of another at the glassy or rubbery state. Then, a single test is sufficient for the complete determination of the mechanical and optical viscoelastic behavior, provided the value of another elastic constant at the glassy or rubbery state is also determined and the variation of birefringence with time is simultaneously measured with the mechanical-characteristic quantities of the material.     

Non-linear Viscoelastic Model for Behaviour Characterization of Temporomandibular Joint Discs

Generally, the complex behaviour of the disc of the temporomandibular joint (TMJ) cannot be adequately represented using linear elastic or linear viscoelastic models. Since the disc is regularly subjected to large strain and stress levels, the study of its non-linear response under compression is of practical interest, especially for analysis of medical dysfunctions. With this aim, relaxation and creep tests were carried out using round specimens of diameters ranging between 4 and 6 mm cut off from the central, anterior, posterior, lateral and medial zones of porcine discs to investigate the regional mechanical properties differences. The experimental data results are fitted using Prony series, based on generalized Maxwell and Kelvin models, allowing the relaxation and creep moduli to be represented, respectively, as a function of the strain and stress. The results show that the non-linear material behaviour of this biological tissue is properly described by the proposed models, to be considered subsequently in numerical calculations.     

Viscoelastic properties of epoxy resins derived from creep and relaxation tests at different temperatures

Summary Experimental data have been obtained on the creep compliance and the relaxation modulus of two epoxy resins in their transition regions. These tests were combined with birefringence measurements to follow the changes in bond orientation of the polymers as the strain or stress varies. Experimental data on the stress- and strain-optical coefficients are presented for both creep and relaxation experiments. It was proved that the validity of the time-temperature superposition principle can be extended to these two coefficients characterizing the optical viscoelastic properties of the two epoxy resins.Master curves ofF (t/k) versus log (t/k) were constructed, whereF (t/k) represents in turn one of the quantities studied namely creep compliance, relaxation modulus and stress- or strain-optical coefficients. The creep and relaxation time factorsk, corresponding to the creep and relaxation curves at the various temperatures, are plotted against the inverse of the absolute temperatureT. The approximate equality of the time factors for mechanical and separately for optical creep and relaxation was established from these plots. This equality proves that creepD-functions and relaxationE-functions are the reciprocals of one another at any time and that the variation of birefringence with time follows the same law in the respective creep and relaxation tests.

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Zusammenfassung Es wurden experimentelle Werte der Kriech-Compliance und der Relaxationsmoduln zweier Epoxydharze in ihren Transformationsbereichen festgestellt. Diese Prüfungen wurden mit Doppelbrechungsmessungen kombiniert, um die Änderung der Orientierung in den Polymeren bei Änderung von Spannung und Verformung zu ermitteln. Die experimentellen Ergebnisse für die optischen Koeffizienten sowohl bei verschiedenen Zug- wie Verformungswerten wurden sowohl für das Kriechen wie für die Relaxatíon untersucht. Damit ließ sich prüfen, inwieweit die Zeit-Temperatur-Superposition auf diese beiden Koeffizienten angewendet werden kann, die die optischen visko-elastischen Eigenschaften der zwei Epoxydharze charakterisieren.

     

Photovisco-elastoplastic behavior of polycarbonate material under creep and tension tests

Polymers are widely used as photomechanical models of a prototype material (often a metal). Photoplasticity is one of the methods used in order to show the behavior of plastic materials stressed beyond the linear elastic limit. To illustrate this process we have analyzed the photovisco-elastoplastic behavior of polycarbonate as a photoplastic material. In this paper a technique for local and simultaneous measurement of birefringence and principal strains is presented. The mechanical and optical properties, at room temperature, have been evaluated by means of uniaxial tension tests. A series of creep tests has been carried out in order to study the photovisco-elastoplastic behavior of polycarbonate. In two different experiments we analyzed nonlinear birefringence and the amplitude of the corresponding strains. We could thus evaluate the distribution of strains and the distribution of uniaxial stress for each birefringence state and vice versa.     

Predictions of nonlinear viscoelastic behavior using a hybrid approach

An approach for nonlinear viscoelastic characterization is presented which uses the combined measurements from creep and dynamic mechanical tests. Although the methodology should extend to several materials and geometries, this research concentrates on thin film polymers used in the manufacture of high altitude scientific balloons. Typically, the constitutive behavior of these materials is characterized through the use of linear viscoelastic techniques. Although this linear approach provides an accurate model for small strains or loads, these materials have been shown to be highly stress dependent and, consequently, it is necessary to identify this nonlinear behavior. Traditional creep measurements require extensive laboratory test times, yet the results obtained from dynamic mechanical analysis provide the capability to predict long term material performance without a lengthy experimentation program. However, dynamic mechanical methods are currently limited to linear response; thus, an approach is presented in which the stress-dependent behavior is derived from short-term creep measurements in a manner analogous to time-temperature superposition. Predictions of material response using linear and nonlinear approaches are compared with experimental results obtained from traditional long-term creep tests. Although linear pre-dictions deteriorate for large stresses, excellent agreement is shown for the nonlinear model.     

Waterhammer modelling of viscoelastic pipes with a time-dependent Poisson's ratio

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.     

A non-linear uniaxial integral constitutive equation incorporating rate effects,creep and relaxation

A previously proposed first order non-linear differential equation for uniaxial viscoplasticity, which is non-linear in stress and strain but linear in stress and strain rates, is transformed into an equivalent integral equation. The proposed equation employs total strain only and is symmetric with respect to the origin and applies for tension and compression. The limiting behavior for large strains and large times for monotonic, creep and relaxation loading is investigated and appropriate limits are obtained. When the equation is specialized to an overstress model it is qualitatively shown to reproduce key features of viscoplastic behavior. These include: initial linear elastic or linear viscoelastic response: immediate elastic slope for a large instantaneous change in strain rate normal strain rate sensitivity and non-linear spacing of the stress-strain curves obtained at various strain rates; and primary and secondary creep and relaxation such that the creep (relaxation) curves do not cross. Isochronous creep curves are also considered. Other specializations yield wavy stress-strain curves and inverse strain rate sensitivity. For cyclic loading the model must be modified to account for history dependence in the sense of plasticity.     

Mechanical-optical properties of polycarbonate resin and some relations with material structure

Polycarbonate resin possesses optical and mechanical properties which make it particularly suitable for certain experimental investigations, including two-and three-dimensional photoelastic analysis. The ductility and transparency of this material might be usefully employed in photomechanical investigations of plastic and viscoelastic response. The similarity of the stress-strain law of polycarbonate to that of mild steel could simplify the similitude problem. In addition, its spectral transmittance in visible and infrared makes polycarbonate useful for studies of material properties and structure. The optical creep of polycarbonate is respresented by a normalized creep coefficient. The relationship of this factor to the theory of viscoelasticity is discussed, and the conditions for a valid calibration of birefringent materials are reviewed. The wavelength dependence of relative retardation is represented by the normalized retardation, from which the dispersion of birefringence can be deduced. The stress-birefringence-time-wavelength characteristics of two brands of polycarbonate resin were determined. Because of residual birefringence, it was necessary to heat treat the resin at about 146°C, and properties of both annealed and unannealed resins are presented. Retardation was measured over the visible and near-infrared portions of the electromagnetic spectrum (407 nm to 1900 nm). There exists a definite relationship between dispersion of birefringence, which amounts to 14 percent in visible, and the infrared spectral transmittance, which is indicative of material structure.     

低密度开孔泡沫蠕变松弛特性分析

利用三维Voronoi模型和有限元方法分析了胞壁材料具有粘弹特性的低密度开孔泡沫的蠕变和应力松弛行为.采用了三参量标准线性固体模型来描述胞壁材料的粘弹特性.所得结果表明.低密度开孔泡沫具有与其胞壁材料相同的松弛时间,当相对密度较低时(低于1%)开孔泡沫的松弛模量与胞壁材料的松弛模量和泡沫相对密度平方成正比.此外,计算结果还表明,低密度开孔泡沫在较小的初始应力条件下具有与其胞壁材料相同的延迟时间.其蠕变柔度与胞壁材料的蠕变柔度和泡沫相对密度平方倒数基本成正比.但随着初始应力值的增大,泡沫的延迟时间将会显著增加.     

An intermediate model method for obtaining a discrete relaxation spectrum from creep data

A convenient method is described for obtaining a discrete stress relaxation spectrum from linear viscoelastic creep data by means of a three-stage process. In stage one, a discrete retardation spectrum is fitted to the creep data using a least squares procedure, subject to the constraint that the discrete spectrum must be a specified order of polynomial function of the retardation time. In stage two, the resulting generalised Voigt model is solved numerically for an imposed step in strain, to determine the stress relaxation modulus function of time. In stage three, a discrete relaxation spectrum is fitted to the calculated stress relaxation modulus function. Although three stages are involved instead of the usual two, the procedure has been found to have certain practical advantages. These advantages make it suitable for the generation of relaxation spectra needed in viscoelastic stress analyses of solids, for example by the finite element method. In order to illustrate the proposed procedure it is applied to both artificial data and experimental creep data for poly(methyl methacrylate) at 70°C and at the glass transition.     

Interrelation of creep and relaxation for nonlinearly viscoelastic materials: application to ligament and metal

Creep and stress relaxation are known to be interrelated in linearly viscoelastic materials by an exact analytical expression. In this article, analytical interrelations are derived for nonlinearly viscoelastic materials which obey a single integral nonlinear superposition constitutive equation. The kernel is not assumed to be separable as a product of strain and time dependent parts. Superposition is fully taken into account within the single integral formulation used. Specific formulations based on power law time dependence and truncated expansions are developed. These are appropriate for weak stress and strain dependence. The interrelated constitutive formulation is applied to ligaments, in which stiffness increases with strain, stress relaxation proceeds faster than creep, and rate of creep is a function of stress and rate of relaxation is a function of strain. An interrelation was also constructed for a commercial die-cast aluminum alloy currently used in small engine applications.     

Photomechanical behavior of cellulose acetate under viscoelastoplastic deformation

To confirm the possibilities of cellulose acetate as a material for a model analysis during viscoelastoplastic deformation, the time-dependent photomechanical properties of the material were examined by means of creep tests under constant stress and recovery tests after removal of stress. Consequently, though the strain and the fringe order of cellulose acetate during creep and recovery are greatly influenced by stress and room temperature, both of them can be described simply by a power function of time, and the coefficient of each of these formulas can be represented by a function of the ratio of active stress to yield stress only. The effect of temperature is included in the formulation of the yield stress. In addition, the strain and the fringe order can be represented by the viscous-viscoelastic model proposed by Findleyet al.,^1,2 in which both of them are divided into four components: elastic, plastic, time-dependent irrecoverable viscous and time-dependent recoverable viscoelastic. The relation between viscoelastic strain and viscoelastic fringe order, and the relation between viscous strain and viscous fringe order were verified to be equivalent to that between plastic strain and plastic fringe order, all of which do not depend on stress, temperature or time. Therefore, the strain distribution of cellulose acetate under viscoelastoplastic deformation can be determined directly from the value of the fringe order measured.     

The time-dependent stress-optical behavior of polycarbonate in the glass transition region

The mechanical and stress-optical behavior of Bisphenol-A polycarbonate was investigated in the glass-transition region. For this purpose, optical creep experiments were carried out in shear and elongation on a tensile tester specially designed for use on a microscope state. A Kohlrausch Williams Watts equation (KWW) with a temperature-independent parameter could successfully be applied to the curves describing the time-dependent values of the stress-optical coefficient for several temperatures. The temperature dependence of the corresponding retardation time could be established and described by the WLF equation. For variable stresses the time-dependent birefringence is obtained from a generalized linear stress-optical rule as modeled according to linear superposition. The time-temperature superposition principle was applied to all measurements. With the dynamic moduli some deviations were observed at the transition from the rubbery plateau to the relaxation. The strain-optical coefficient was found to decrease with increasing time and strain. The strain dependence was found to be independent of temperature at constant stress.     

Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network

Creep tests at constant stress are performed for the carbon-fiber reinforced epoxy composite at various temperatures and initial stresses. A nonlinear viscoelastic constitutive model is developed, and its material parameters are determined by fitting it to creep test data. Model results are found to agree very well with the experimental data at low temperature and low stress conditions. However, the agreement deteriorates at high temperatures, particularly in the vicinity of the glass transition temperature.An alternative model based on an artificial neural network (ANN) is developed to predict the stress relaxation of the polymer matrix composite. The ANN model is trained and validated with 9000 experimental data sets obtained from stress relaxation tests performed at various constant strain (initial stress) and constant temperature conditions. Training of the ANN employs a scaled conjugate gradient method. The optimal brain surgeon algorithm is employed to optimize the topology. The optimal ANN configuration has 88 processing elements (3 in the input layer, 45 in the first hidden layer, 39 in the second hidden layer, and 1 in the output layer) and 410 links. The predictions of the ANN model are found to be more accurate over a wider range of stress and temperature conditions than those of the explicit nonlinear viscoelastic model, in particular near the glass transition temperature.     

热环境中黏弹性功能梯度材料及其结构的蠕变

基于经典的对应原理, 将 Mori-Tanaka 方法等细观力学结果推广于定常温度环境下的黏弹性情形. 根据泊松比与时间呈弱相关的特点, 给出 Laplace 象空间中功能梯度材料的松弛模量和热膨胀系数, 并直接建立耦合热应变的多维黏弹性本构关系. 在此基础上, 求解黏弹性功能梯度圆柱薄壳在热环境中的轴对称弯曲蠕变变形问题. 考虑材料热物参数的温度相关性, 首先确定稳态温度场, 导出相空间中轴对称弯曲变形的解析解, 采用数值反演得到蠕变变形. 算例表明, 蠕变初期, 热环境的影响明显, 随着时间增加, 热应力松弛, 影响逐渐消失. 当圆柱薄壳受轴压时, 相比于两端固支, 两端简支的端部变形更加明显. 通过圆柱薄壳的轴对称弯曲求解, 给出体积含量呈任意分布的黏弹性功能梯度结构在热机载荷下的蠕变分析途径.      

A MICROMECHANICAL FRAMEWORK WITH AGGREGATE-MASTIC INTERFACE EFFECT FOR PREDICTING UNIAXIAL COMPRESSION CREEP OF ASPHALT MIXTURE

According to the elastic-viscoelastic correspondence principle, an elastic microme- chanical framework taking the inclusion-matrix interface effect into account is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded in a viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different temperature and stress conditions in order to determine the matrix constitutive parameters, the framework presented is validated by comparison with the experiment, and then some predictions of uniaxial compression creep behavior of asphalt mixture in different temperature and stress conditions are given.     

橡胶粘结颗粒材料粘弹性性能的试验研究与离散元模拟

制备了颗粒规则四方排列和六方排列的橡胶粘接颗粒材料试样,实验测试了所制备试样在单向拉伸载荷下的应力松弛曲线和不同应变率时的应力应变曲线。基于所测试的应力松弛曲线,采用曲线拟合方法得到了所测试材料的宏观Burger’s粘弹性本构模型参数。采用离散元模型中单元间连结模型代表颗粒间橡胶粘接剂的作用,并基于试样的宏观Burger’s模型参数与离散元模型中细观Burger’s连结模型参数间的关系,建立了橡胶粘接颗粒材料的无厚度胶结离散元分析模型。最后采用所建立的离散元模型计算了所测试试样的松弛和拉伸力学性能。离散元预测结果与实验结果的对比表明,采用无厚度胶结离散元模型能较好的计算颗粒规则排列的橡胶粘接颗粒材料松弛和拉伸力学性能,但基于应力松弛实验拟合而来参数不能准确反应橡胶粘接剂在高应变率条件下其力学性能的应变率相关性。