单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .     

Mittag-Leffler函数及其在粘弹性应力松弛中的应用

Mittag-Leffler函数在分数阶粘弹理论中起着重要作用. 我们对该函数的计算及收敛性进行了分析; 利用遗传算法结合共轭梯度法, 提出了对广义函数进行非线性参数拟合的方法. 用分数Maxwell模型对强弱、硬柔具有显著差别的塑料、玻璃态合金及聚合物近熔体的应力松弛过程进行了研究.     

从静态应力松弛实验求材料准松弛时间谱的一种数值计算方法

避开繁琐困难的函数求解过程，采用数值计算方法，从常规的静态应力松弛实验，直接求被测材料的松弛单元的表现松弛强度．主松弛时间τ０由单－ＭＡＸＷＥＬＬ模型求得，其他松弛时间分别约取为１０（－２）·τ０，１０（－１）·τ０，１０１·τ０，１０３·τ０。应力松弛万程取５参数模型，记为谱的强度ａｉ（或Ａｉ）通过多元线性回归，由最小二乘法确定．对一种天然橡胶试样在不同温度下的松弛曲线进行处理，回归值与原始实验值吻合良好，不同温度下的松弛单元对总松弛的贡献，反映出温度对松弛过程的活化作用．     

基于广义Maxwell模型的轮胎橡胶动态压缩性能分析

为了定量分析轮胎胎面胶动态力学性能及能量损耗,建立了基于广义Maxwell模型的黏弹性本构关系,根据胎面胶在各个温度下恒温动态压缩时的储能模量与损耗模量的频率扫描实验数据并采用非线性回归法求解误差函数的极小值的方法,确定各个温度下的黏弹性广义Maxwell模型参数.利用ABAQUS/Standard有限元软件数值模拟胎面胶动态压缩过程,得到不同温度下胎面胶的损耗角正切随激振频率的变化规律,并与实验结果进行对比分析.结果表明,黏弹性广义Maxwell模型及其参数的获取方法可以准确地用于胎面胶动态力学性能分析.在此基础上,定量预测了在不同温度及频率下每一循环载荷周期中胎面胶的应力-应变迟滞回线以及单位体积胶料的能量损耗,分析显示随频率增大,单位体积胶料的能量损耗逐渐增大,并且随着温度降低,能量损耗增大的幅度加大.     

基于回归分析模型与随机过程模型的硅橡胶泡沫应力松弛预测对比

本文针对硅橡胶泡沫的应力松弛实验数据,基于二阶Prony级数,采用非线性回归分析方法(曲线拟合法)、基于Wiener过程的贝叶斯方法、基于Gamma过程的贝叶斯方法进行参数估计从而分别建立预测模型,通过对比三种建模方法的预测值与实验值的偏差,比较了三种建模方法的效果。结果发现,采用曲线拟合的方法进行参数估计,其预测偏差要大于基于Wiener、Gamma随机过程的贝叶斯方法,表明由于考虑了性能退化过程存在的不可避免的随机性,随机过程模型可以更好地预测硅橡胶泡沫的应力松弛趋势,同时由于应力松弛过程是单调增加的,基于非负的Gamma过程的随机过程模型的预测偏差要小于基于Wiener过程的模型。本文工作可为基于高分子材料性能退化数据的退化预测模型的建模提供一种较好的参数估计方法,有助于提高预测结果的准确性。     

尼龙1010应力松弛行为研究

尼龙1010样品在初始应变为1%、2.8%和5.1%的条件下,在不同的恒温环境中分别进行不少于10 h的应力松弛实验,得到20~80℃范围的应力松弛曲线.研究了不同应力、温度下的应力松弛速率、松弛过程的残余应力、活化体积以及相关参数的数学关系.结果表明,尼龙样品在松弛过程中存在一定的形变残余应力,体系存在恒定的长时模量.不同初始应变的尼龙样品松弛过程表现出相似的规律,当松弛速率-d(σ/σ0)/dlnt达到最大值后,在一段时间内聚合物内部活化单元发生松弛,-dσ/dt与作用于样品的有效应力σ*为指数关系.随着松弛过程的进行,应力减小到一定程度后,活化体积V逐渐增加,此时独立的活化单元运动受到限制,聚合物内部依靠多个活化单元的协同运动将内应力逐渐松弛,应力辅助功Vσ*为常数,-dσ/dt与σ*满足幂律关系,幂指数为σ*V/(k T).     

基于位形熵模型的山梨醇玻璃焓松弛的量热分析

利用DSC技术考察了无定形山梨醇体系的焓松弛行为, 在10 K•min^－1的升温速率下测定了经历不同降温速率(0.5～20 K•min^－1)的山梨醇在玻璃化转变(T_g)前后的比热容[c_p(T)]. 利用基于位形熵演变的焓松弛现象学模型(GR模型)模拟了实验数据. 不论是否假设松弛过程存在一个亚稳极限态, 模型参数均能很好地重现经历不同热历史体系的升温c_p(T)曲线. 在物理意义明确的模型参数组中, 除了非指数参数随降温速率的增加而增加外, 其余均不随热历史的变化而变化. 拟合较低降温速率下c_p(T)曲线获得的GR模型参数的预测力明显好于在较大降温速率下获得的结果. 由于松弛时间对拟合过程中选择的“固定参数”的取值很敏感, 因此模型能否预测体系的比热容不能看成确定松弛时间的唯一依据. 在利用GR模型分析无定形山梨醇体系的脆度时, 如果选择极限假想温度作为T_g, 会导致计算结果明显小于文献值.     

以时温等效方法研究尼龙1010应力松弛行为及使用寿命预测

以尼龙材料的应力松弛行为作为研究对象, 考察初始应变为1.0%, 2.8%和5.1%的尼龙1010样品在温度区间293353 K的松弛曲线, 采用时间-温度等效叠加方法得到了松弛模量主曲线, 计算出叠加过程中的表观活化能、 松弛过程中的活化体积和应力辅助功. 结果表明, 整个松弛过程中的表观活化能和应力辅助功表现出相同的变化趋势, 体现出松弛过程中克服运动单元位垒的过程. 当293323 K区间的松弛曲线叠加时, 随着初始应变的增加, 表观活化能和应力辅助功均逐渐降低, 有助于聚合物内部的运动单元越过能垒发生松弛, 与松弛过程中的应力辅助热活化理论相一致; 当333353 K区间的松弛曲线叠加时, 不同初始应变样品的表观活化能均为260 kJ/mol, 应力辅助功均为60 MPa·nm³, 说明松弛过程中克服运动单元的能垒与应力作用无关. 根据松弛主曲线, 计算出了尼龙1010在1.0%, 2.8%和5.1% 3种形变下, 长时间范围内应力衰减与时间的关系, 为预测实际使用过程中的应力松弛行为提供了依据.     

基于纳米压痕技术的炭黑/聚丙烯复合材料力学性能研究

利用纳米压痕技术对炭黑填充聚丙烯基(CB/PP)复合材料的弹性模量、硬度及蠕变行为等力学性能进行了实验研究。结果表明,炭黑颗粒对CB/PP复合材料具有强化作用,随着炭黑含量的增加,复合材料的弹性模量和硬度增加。实验得出了纯PP及CB/PP复合材料蠕变应力指数和蠕变特征松弛时间,结果表明炭黑含量的增加增大了复合材料的蠕变应力指数,并且提高了硬度和抗疲劳性能。同时炭黑含量增加,复合材料的蠕变特征松弛时间减小,表明炭黑颗粒有效阻碍了聚合物分子链的移动。     

用化学应力松弛法快速估算橡皮材料的贮存保险期

提出了一种用化学应力松弛法快速估算橡胶材料贮存保险期的方法。这种方法撇开动力学的复杂关系,用相对应力f/f_0来表征化学松弛过程所达到的阶段,进一步假设处在不同温度下达到某阶段时的松弛时间与温度间存在着 Arrhenius关系。因此以不同温度下达到某给定相对应力时的松弛时间对1/T作图应得到直线关系,由此外推即可求出室温下的松弛时间。 研究了松弛过程极不相同的丁基和丁腈橡胶。所有的实验结果支持了上述假设。     

Relaxation modulus in the fitting of polycarbonate and poly(vinyl chloride) viscoelastic polymers by a fractional Maxwell model

 The stress relaxation of two different polymers under a constant strain has been studied and approached by using a fractional Maxwell model in which the stress appears as a noninteger-order derivative of the strain. To obtain an accurate approximation of the experimental data for the model, two noninteger values for the derivative order are required. These values are related to two relaxation types. For short times, the derivative order is smaller and near zero, which indicates behavior close to the ideal elastic solid. For long times the derivative order is higher, showing more plastic behavior. In this work some classic models are revised and the fractional Maxwell model is used to fit the experimental data. Finally, the complex fractional modulus, the two derivative orders, and the relaxation times for samples of polycarbonate and poly(vinyl chloride) are obtained. Received: 16 June 2001 Accepted: 19 October 2001     

Relaxation Spectra and Viscoelastic Behavior of a Model Hydrophobically Modified Alkali-Soluble Emulsion (HASE) Polymer in Salt/SDS Solutions

The viscoelastic behavior of a semidilute hydrophobically modified alkali-soluble emulsion (HASE)-C20 polymer in NaCl and NaCl/SDS (sodium dodecyl sulfate) solutions was determined using a Rheometric fluids rheometer and the data were converted to relaxation spectra. The dynamic moduli can be fitted with a multiple modes Maxwell model. In the presence of increasing amounts of NaCl, the moduli decrease, where G', decreases more rapidly than G". However, in the presence of SDS and 0.4 M NaCl, the dynamic moduli increase to a maximum at a critical concentration and decrease thereafter. The relaxation spectra suggest that the structure of the polymer network is complex and it contains two to six relaxation times, depending on the NaCl or SDS/0.4 M NaCl concentrations. With increasing NaCl concentrations, the fastest peak shifts to longer times while the slowest peak decreases. This corresponds to the destruction of the network as the polymer backbone collapses to form clusters with a larger aggregation number. For HASE in SDS/0.4 M NaCl solutions, the lifetime of both the hydrophobic junction (fastest peak) and network relaxation (slowest peak) shift to longer times, which suggests the strengthening of active junctions by bound SDS molecules. However, beyond a critical SDS concentration, the relaxation time of the polymer and hydrophobic junction decreases to an asymptotic value. Copyright 2000 Academic Press.     

十二烷基聚氧乙烯硫酸钠胶束体系的流变性质研究

用流变学方法研究了无机电解质KBr存在时,阴离子表面活性剂十二烷基聚氧乙烯(3)硫酸钠(SDES)水溶液中胶束的生长和结构。通过测量体系的稳态剪切粘度(η)和应力(σ)关系,得到零剪切粘度(η0)、复合粘度(|η^*|)、动态模量[储能模量(G')和损耗模量(G")、平台模量(G0)、结构松驰时间(τ)等流变学参数,并应用Cox-Merz规则和Cole-Cole图,发现在SDES/KBr体系中可以形成蠕虫状胶束网络结构,体系为假塑性流体,偏离Maxwell模型,具有非线性粘弹性,没有单一的结构松驰时间。     

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.     

Elastoviscous properties of polyisobutylene. IV. Relaxation time spectrum and calculation of bulk viscosity

The elastoviscous behavior of polyisobutylene may be interpreted in terms of a mechanical model consisting of a distribution of Maxwell elements connected in parallel. The structure of this “generalized Maxwell model” is specified by the distribution of relaxation times of the component elements. The relaxation of stress curve of the material is directly related to the distribution of relaxation times, and general expressions for the bulk viscosities (tensile and shear) of such a system in terms of the distribution of relaxation times are readily obtained. A simple “box distribution” of relaxation times is described which can be used to approximate the relaxation behavior of polyisobutylene at the long-time end of the relaxation time spectrum, and in terms of which the expressions for bulk viscosity reduce to very simple form. The parameters specifying this distribution may be determined from experimental relaxation curves by a simple graphical method. Values of these parameters as a functions of molecular weight and temperature are computed, by use of these data. It is shown that bulk viscosity values calculated from relaxation data by this method are in good agreement with experimental values for both tensile and shear deformations, and for both unfractionated and fractionated polymers. Measurements of viscosity and of relaxation of stress can thus be directly correlated, and could be used in combination to characterize elastoviscous properties over wide ranges of molecular weight and temperature.     

Prediction of stress‐relaxation behavior in high density polyethylene solids

The stress‐relaxation behavior of a high density polyethylene solid was investigated using a nonlinear viscoelastic model in which two nonlinear parameters such as the anharmonicity in elastic response and the plastic deformation are introduced into a generalized Maxwell model. The determination of the nonlinear parameters demands the transient modulus data under a constant rate of deformation. The nonlinear viscoelastic model developed from the tensile behavior was found to predict the stress‐relaxation behavior in the nonlinear region.     

Effects of concentration and temperature on viscoelastic properties of aqueous potassium oleate solutions

The rheological properties of semidilute aqueous solutions containing long cylindrical micelles of an anionic surfactant, potassium oleate, are studied. It is shown that, at surfactant concentrations above 1 wt %, the rheological properties of the solutions are adequately described in terms of the simple Maxwell model of a viscoelastic liquid characterized by a single relaxation time. Based on the analysis of normalized dependences of the loss modulus on the storage modulus, the characteristic times of the processes governing the rheological properties of the above systems, i.e., the average breaking time and reptation time of micelles, are estimated. It is found that the breaking time of micelles decreases and relaxation time increases with increasing surfactant concentration due to lengthening of micellar chains.     

Convective flow of a Maxwell hybrid nanofluid due to pressure gradient in a channel

In this work, analytical solution of hybrid Maxwell nanofluid of the vertical channel due to pressure gradient is discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions is converted into dimensionless form. Fractional model for Maxwell fluid is developed by Caputo time fractional differential operator by using the constitutive relation. The dimensionless expression for temperature and velocity are found using Laplace transform. Draw graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters. As a result, we have found by increasing the volumetric fraction of copper and alumina temperature increases and velocity decreases. Also, fluid flow properties showed dual behavior for small and large time, respectively, by increasing fractional parameters values.

     

Nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer

Studies on the nonlinear viscoelastic behavior of styrene‐[ethylene‐(ethylene‐propylene)]‐styrene block copolymer (SEEPS) were carried out. The nonlinear viscoelastic region was determined through dynamic strain sweep test, and the critical shear strain (γ_c) of transition from linear viscoelastic region to nonlinear viscoealstic region was obtained. The relaxation time and modulus corresponding to the characteristic relaxation modes were also acquired through simulating the linear relaxation modulus curves using Maxwell model, and the damping functions were evaluated. Meanwhile, it is found that the nonlinear relaxation modulus obtained at relatively low shear strains follows the strain–time separation principle, and the damping function of SEEPS can be fit to Laun double exponential model well. Moreover, the successive start‐up of shear behavior, the steady shear behavior, and the relaxation behavior after steady shear were investigated, respectively. The results showed that Wagner model, derived from the K‐BKZ (Kearsley‐Bernstein, Kearsley, Zapas) constitutive equation, could simulate the experiment data well, and in addition, experiment data under the lower shear rates are almost identical with the fitting data, but there exists some deviation for data under considerable high shear rates. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1309–1319, 2006