Creep performance of PVC aged at temperature relatively close to glass transition temperature

In order to predict the mechanical performance of the polyvinyl chloride(PVC) at a high operating temperature,a series of short-term tensile creep tests(onetenth of the physical aging time) of the PVC are carried out at 63 C with a small constant stress by a dynamic mechanical analyzer(DMA).The Struik-Kohlrausch(SK) formula and Struik shifting methods are used to describe these creep data for various physical aging time.A new phenomenological model based on the multiple relaxation mechanisms of an amorphous polymer is developed to quantitatively characterize the SK parameters(the initial creep compliance,the characteristic retardation time,and the shape factor) determined by the aging time.It is shown that the momentary creep compliance curve of the PVC at 63 C can be very well fitted by the SK formula for each aging time.However,the SK parameters for the creep curves are not constant during the aging process at the elevated temperatures,and the evolution of these parameters and the creep rate versus aging time curves at the double logarithmic coordinates have shown a nonlinear phenomenon.Moreover,the creep master curves obtained by the superposition with the Struik shifting methods are unsatisfactory in such a case.Finally,the predicted results calculated from the present model incorporating with the SK formula are in excellent agreement with the creep experimental data for the PVC isothermally aged at the temperature relatively close to the glass transition temperature.     

Measurements of Two Independent Viscoelastic Functions by Nanoindentation

Current nanoindentation measurement techniques normally assume that one material function (such as the Poisson's function) is a constant, and measures just one material function, such as the creep compliance in shear. For materials with significant viscoelastic effects and unknown viscoelastic functions, assuming a constant for one material function is not satisfactory. Accurate measurements require simultaneously determining two independent material functions. This paper provides a method to use nanoindentation to measure both bulk and shear relaxation functions. Two different nanoindenter tips, namely Berkovich and spherical indenters, are used for nanoindentation on polymers. Any two independent viscoelastic functions, such as bulk relaxation modulus and shear relaxation modulus, have different representations in the load–displacement curves obtained with these two indenters so that the two independent viscoelastic functions can be separated and determined. Two polymers, poly(vinyl acetate) (PVAc) and poly(methyl methacrylate) (PMMA) were used in nanoindentation. Nanoindentation measurements were conducted on PVAc above glass transition temperature (Tg) and on PMMA below Tg. Both shear and bulk relaxation functions determined from nanoindentation were found in a reasonably good agreement with data obtained from conventional tests, providing validation of the method presented. The new method can be applied in measurements of two independent viscoelastic functions at sub-micron scale of very small amounts of materials such as polymeric films on a substrate, heterogeneous materials such as bones, tissues, and nanocomposites.     

Thermodynamics of relaxation processes in the glass transition region

Relaxation processes in the glass transition region, especially the recovery of the volume and the physical ageing of polymers, do not follow the common (linear) theory of relaxation. On the contrary, they show a development which depends on the previous history, may be non-monotonous and requires a relaxation time that may have negative values and a pole. These phenomena can be explained if the single relaxation time is replaced by a spectrum of relaxation times and the relaxation times are supposed to be subjected to a feedback via certain structure- and temperature-parameters (as, for instance, in the KAHR-theory).However, the feedback and a pole of the relaxation time arise already for a single internal degree of freedom by themselves, if, in the non-equilibrium thermodynamics, a dynamic and a static temperature are strictly differentiated. In the case of the relaxation of the diffusive translational motion of the molecules in the glass transition region the dynamic temperature is identical with the socalled fictive temperature introduced by Tool.With regard to the relaxation of the volume three different temperature regions must be distinguished: A fluid region at high temperatures where the relaxation is controlled by the free volume and complies with the linear theory at least approximately; a glass-like region at low temperatures where the relaxation is controlled by the thermal expansivity of the free volume and where, under certain conditions, the statements set up by Davies and Jones are valid; an intermediate region (the glass transition region) where the free volume as well as its coefficient of expansivity are decisive. In that region the effective relaxation time of the volume may have a pole and the dynamic temperature may approach its equilibrium value by discontinuous jumps or in a chaotic manner.Dedicated to Professor Dr. J. Meissner (ETH Zürich) on the occasion of his 60th birthday     

The creep behavior of ideally atactic and commercial polymethylmethacrylate

Summary The shear creep behavior of polymethylmethacrylate, PMMA, samples has been studied in the neighborhood of and above their glass temperatures. One of the materials studied was ideally atactic with equal numbers of random isotactic and syndiotactic placements, while the other was a commercial or conventional PMMA which was about 76% syndiotactic. The glass temperatures,T _g , were found to be 106 and 117 °C respectively. Evacuation above the glass temperature for several weeks was necessary before reproducible creep compliance,J (t), curves could be obtained. It is believed that absorbed water plasticized the polar materials and its removal led to the shifting of theJ (t) curves to longer times. For both materials apparently successful temperature reduction was found to be possible within the temperature range of our investigations, i.e. up to 200 °C. Retardation spectra were calculated from the reduced curves and are compared. The temperature dependences, as described by the time scale shift factors,a _T , were similar when allowance is made for the different glass temperature. Botha _T curves could not be fitted to theWilliams, Landel, andFerry, WLF, free volume expression. These are the first examples of such a deviation for amorphous high polymers. It is proposed that the primary softening dispersion has two distinctly different groups of viscoelastic mechanisms contributing to it. On this basis the primary dispersion was decomposed into the two contributions. Both of the resulting temperature dependences were satisfactorily fitted to the WLF equation. Differences in the retardation spectra are noted. The glassy compliance of the commercial PMMA appears to be about twice that of the atactic PMMA.Data on commercial PMMA is incorporated in a thesis which has been submitted in partial fulfillment of the requirements for the degree of Master of Science in Materials Engineering, University of Pittsburgh, 1970.With 12 figures and 1 table     

Network-structure of plasticized epoxy resins by dynamic measurements

Viscoelastic parameters are strongly connected with the glass transition temperature and the degree of cross-linking of polymers. In this paper an attempt was undertaken to analyse the storage modulus in the rubbery plateau and the transition region of a series of plasticized epoxy polymers, in terms of their network structure, by means of dynamic measurements.A series of dynamic tests was carried out at frequencies between 0.1 and 100 Hz and temperatures from 50 °C to 140 °C. By applying the time-temperature superposition principle, composite curves for the storage modulusE () were derived over a wide frequency range.The crosslink density, or the molecular weight, between crosslinks could be changed by adding different amounts of plasticizer in the epoxy polymer, and it was calculated by applying the theory of rubber elasticity. The glass transition temperatureT _g for each substance was found to be influenced by the amount of plasticizer and the molecular weight between crosslinks. This behaviour of the highly crosslinked epoxies was different from that of rubbers or analogous materials.Finally, an estimation of the free volume of the materials tested was attempted by using the WLF-equation.     

An effective temperature theory for the nonequilibrium behavior of amorphous polymers

Amorphous polymers lack an organized microstructure, yet they exhibit structural evolution, where physical properties change with time, temperature, and inelastic deformation. To describe the influence of structural evolution on the mechanical behavior of amorphous polymers, we developed a thermomechanical theory that introduces the effective temperature as a thermodynamic state variable representing the nonequilibrium configurational structure. The theory couples the evolution of the effective temperature and internal state variables to describe the temperature-dependent and rate-dependent inelastic response through the glass transition. We applied the theory to model the effect of temperature, strain rate, aging time, and plastic pre-deformation on the uniaxial compression response and enthalpy change with temperature of an acrylate network. The results showed excellent agreement with experiments and demonstrate the ability of the effective temperature theory to explain the complex thermomechanical behavior of amorphous polymers.     

Generalized Maxwell model for the viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading

The linear viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading is investigated in the glass transition range. Using the time-temperature superposition technique, the master curves of the shear dynamic relaxation moduli are obtained at a reference temperature of 566°C. A method to determine the viscoelastic constants from dynamic relaxation moduli is proposed. However, some viscoelastic constants cannot be directly measured from the experimental curves and others cannot be precisely obtained due to non-linearity effects at very low frequencies. The generalized Maxwell model is investigated from the experimental dynamic moduli without fixing the viscoelastic constants. A set of parameters is shown to be in good agreement with the experimental dynamic relaxation moduli, but does not give the correct values of the viscoelastic constants of the investigated glass. The soda-lime-silica glass exhibits a non-linear viscoelastic behavior at very low stress level which is usually observed for organic glasses. This non-linear behavior is questioned.     

Composite viscoelasticity in glassy,transitional and molten states

As part of a study of viscous and elastic behaviors, over a range of temperatures from below the glass transition up to the hot melt, we here report steady-shear viscosities at 0.007 to 13 s^?1 and at 160 to 220 °C of polystyrene containing 0 to 60% by mass of 0.18-micron diameter titanium dioxide particles. The materials were shearthinning without a yield stress, with a constant activation energy at constant stress, but having a shear-dependent activation energy at constant shear rate — proportional to the volume fraction of the polymer matrix. Superposition of the flow curves at different temperatures for the unfilled and filled systems was possible. All the data were represented by one equation with four parameters: 1) a shear stress coefficient (units Pa · s²); 2) a characteristic stress level for non-Newtonian behavior, independent of temperature and composition; 3) an activation energy at constant stress; and 4) an Einstein coefficient (or intrinsic viscosity of the filler). Other equations also fitted the data, but the others diverged widely when extrapolated.     

A linear viscoelastic model for solid polyethylene

Stress relaxation tests have been carried out on a blue, pipe grade PE 80 medium density polyethylene (BP Chemicals), to provide thermo-viscoelastic rheology for use in calculating thermal stresses in pipe production. Stresses up to 4 MPa were used, with strains up to about 2%, in tests at temperatures from 23° to 90°C. Within this range a linear viscoelastic model was applicable, provided the initial ramp strain rate was less than 7×10^–5 s^–1. The stress relaxation data was fitted directly by a model incorporating an elastic response to volumetric strains, and a generalised linear solid model, consisting of two Maxwell elements and a purely elastic element in parallel, for deviatoric strains. Arrhenius type temperature dependence of relaxation times and shear moduli is found, and within experimental accuracy the temperature dependence of all these model parameters is the same. As a consequence, and provided that the duration of the strain ramp is sufficiently short relative to relaxation times, the model leads to time-temperature superposition of the relaxation moduli, using the same shift factor on both the response magnitude and time axes.     

A new constitutive equation for the long-term creep of polymers based on physical aging

Based on the observation that during long-term creep the viscosity of polymers will continue to increase due to physical aging, a new constitutive equation is derived to describe the long-term creep behavior of polymers that are chrono-rheologically simple. The theory is developed using the concept of effective time for such materials whose long-term creep compliances with various aging times are characterized by a horizontal shift on the log(t)-scale. The derivation makes use of the basic mathematical structure for such a horizontal shift, with a result that is both sufficient and necessary. A linear viscosity function is found to be required for such a material, and the corresponding shift rate for both the long-term creep and the short-time creep is found to increase with aging time t_e, reaching an asymptotic value of unity. This theory improves Struik's (1978) classic theory for the special class of chrono-rheologically simple materials, in that, when the aging time is sufficiently long, both theories are identical, but when it is short, the present one can account for the transition to the asymptotic state. The developed effective-time theory is then extended to a polymer–matrix composite to predict the effect of physical aging on the long-term creep of a fiber-reinforced composite material.     

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.     

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.     

锆基非晶合金的动态弛豫机制和高温流变行为

非晶合金的动态弛豫机制对于理解其塑性变形, 玻璃转变行为, 扩散机制以及晶化行为都至关重要. 非晶合金的力学性能与动态弛豫机制的本征关联是该领域当前重要科学问题之一. 本文借助于动态力学分析(DMA), 探索了Zramorphous alloy,dynamic mechanical analysis,high temperature deformation,structural relaxation,quasi-points defects,1)国家自然科学基金(51971178);陕西省自然科学基金(2019JM-344);中央高校基本科研业务费专项资金(3102019ghxm007);中央高校基本科研业务费专项资金(3102017JC01003)2020-01-062020-04-10非晶合金的动态弛豫机制对于理解其塑性变形, 玻璃转变行为, 扩散机制以及晶化行为都至关重要. 非晶合金的力学性能与动态弛豫机制的本征关联是该领域当前重要科学问题之一. 本文借助于动态力学分析(DMA), 探索了Zr$_{50}$Cu$_{40}$Al$_{10}$块体非晶合金从室温到过冷液相区宽温度范围内的动态力学行为. 通过单轴拉伸实验, 研究了玻璃转变温度附近的高温流变行为. 基于准点缺陷理论(quasi-point defects theory), 对两种力学行为的适用性以及宏观力学行为变化过程中微观结构的演化规律进行描述. 研究结果表明, 准点缺陷理论可以很好地描述非晶合金损耗模量$\alpha$弛豫的主曲线. 基于非晶合金的内耗行为, 玻璃转变温度以下原子运动的激活能$U_\beta$为0.63 eV. 与准点缺陷浓度对应的关联因子$\chi $在玻璃转变温度以下约为0.38,而在玻璃转变温度以上则线性增大. Zr$_{50}$Cu$_{40}$Al$_{10}$块体非晶合金在玻璃转变温度附近, 随温度和应变速率的不同而在拉伸实验中显示出均匀的或不均匀的流变行为. 非晶合金的高温流变行为不仅可以通过扩展指数函数和自由体积理论来描述, 还可以通过基于微剪切畴(shear micro-domains, SMDs)的准点缺陷理论来描述.     

物理老化对玻璃态高聚物非线性蠕变行为的影响

在不同应力水平下对经历不同老化时间的有机玻璃(PMMA)进行常温蠕变测试,分析物理老化和应力对材料蠕变柔量函数的影响.分析表明,老化时间对PMMA蠕变行为的影响满足流变简单性规律,即不同老化时间的蠕变柔量曲线可以沿对数时间轴平移而叠加到参考曲线上.取最长的老化时间为参考状态,依时间-老化时间等效原理,得到了各应力水平下的蠕变柔量主曲线.老化移位因子与老化时间在双对数坐标图上呈现线性关系,其负斜率就是老化移位率.结果表明,老化移位率随应力的增高而减小.     

Evaluation and comparison of routes to obtain pressure coefficients from high-pressure capillary rheometry data

A capillary rheometer equipped with a pressure chamber is used to measure the pressure-dependent viscosity of polymethylmethacrylate (PMMA), poly-α-methylstyrene-co-acrylonitrile (PαMSAN), and low-density polyethylene (LDPE). Data analysis schemes are discussed to obtain pressure coefficients at constant shear rate and at constant shear stress. It is shown that the constant shear stress pressure coefficients have the advantage of being shear stress independent for the three polymers. The constant shear rate pressure coefficients, on the other hand, turn out to depend on shear rate, which makes them less suitable for use, e.g., in process simulations. In addition to the commonly used superposition method, a direct calculation method for the pressure coefficients is tested. Values obtained from both methods are equivalent. However, the latter requires less experimental and calculational efforts. From the obtained pressure coefficients, it is clear that PMMA and PαMSAN have a very similar pressure dependence, while LDPE is less sensitive to pressure.     

A finite deformation fractional viscoplastic model for the glass transition behavior of amorphous polymers

The stress response of amorphous polymers exhibits tremendous change during the glass transition region, from soft viscoelastic response to stiff viscoplastic response. In order to describe the temperature-dependent and rate-dependent stress response of amorphous polymers, we extend the one-dimensional small strain fractional Zener model to the three-dimensional finite deformation model. The Eyring model is adopted to represent the stress-activated viscous flow. A phenomenological evolution equation of yield strength is used to describe the strain softening behaviors. We demonstrate that the stress response predicted by the three-dimensional model is consistent with that of one-dimensional model under uniaxial deformation, which confirms the validity of the extension. The model is then applied to describe the stress response of an amorphous thermoset at various temperatures and strain rates, which shows good agreement between experiments and simulation. We further perform a parameter study to investigate the influence of the model parameters on the stress response. The results show that a smaller fractional order results in a larger yield strain while has little effect on the yield stress when the temperature is below the glass transition temperature. For the stress relaxation tests, a smaller fractional order leads to a slower relaxation rate.