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 .     

开孔泡沫塑料率相关的拉伸力学性能及本构关系

以Ｌｅｄｅｒｍａｎ的工作为基础，通过假设基体材料服从Ｖｏｉｇｔ体描述的粘弹性本构关系，导出了开孔泡沫塑料受拉伸的率相关本构关系；在此基础上研究了泡沫塑料力学性质同应变、应变率和结构参数的关系．     

温度对磁流变胶复合材料动态力学性能的影响研究与分析

磁流变胶(MRG)是新一代磁流变材料,其有效克服了磁流变液易沉降等缺点。磁流变胶是由软磁颗粒悬浮在凝胶状基质中形成的,其流变特性主要受磁场和温度两个因素控制。本文制备了含有羰基铁粉质量分数为60%的聚氨酯基磁流变胶。系统研究了温度对磁流变胶流变特性的影响。结果表明,温度对磁流变胶的粘弹性有显著影响。测量了频率分别为0.1、5和15 Hz,振幅分别为10%和50%的谐波应变信号在5个温度水平下的迟滞响应,分析了磁流变胶的粘弹性特性,并采用粘弹塑性模型预测了磁流变胶的非线性迟滞特性。分析结果表明,粘弹塑性模型能够准确预测磁流变胶在不同温度下的迟滞特性。     

橡胶动态生热数值模拟与实验研究

为提高橡胶动态生热数值模拟的计算精度,基于时温等效原理给出了一种同时考虑温度和应变率来确定拉伸测试条件的方法,它可同时满足设备测试条件和制品使用工况.此外,为获得更准确的超弹性本构方程参数,采用了一种用应力松弛实验得到橡胶完全松弛状态下的一组应力来拟合黏弹性算法中超弹性部分的方法.采用上述测试方法并借助ABAQUS软件...     

振簧法测定动态粘弹性Ⅰ.——用电容拾振法观察振簧的振动

过去对高聚物静态粘弹性能研究得较多,如Scott Blair(1945)等所用的蠕变及应力松弛法,Dillon(1933)的压缩塑性计,以及Mooney(1936)所用的转筒式粘度计等都是用静态的方法来研究高聚物的粘弹性。对高聚物来说:对温度及频率的响应存在弹性弥散,在弹性弥散区域伴随弹性模量骤急的改变出现內耗的峯值,通过对內耗峯的研究可深入了解其內部结构,此外在高聚物作为材料的实际应用中往往是在动态的情况下使用的,因而对高聚物动态粘弹性的研究不论在理论上或实用上都有其重要的意义。     

填充橡胶本构模型研究进展

填充橡胶材料是由纳米粒子增强的复合多相材料。由于橡胶交联网络和填充粒子所形成的二级网络并存,填充橡胶呈现出复杂的力学行为,如大变形黏超弹性、动态应力软化效应,自生热效应等。如何构建合理的本构模型准确描述其力学行为一直是橡胶材料研究的热点和难点。而近年来数值仿真技术的发展对填充橡胶本构关系的可靠性,准确性和数值稳定性提出了更高的要求。本文综合前人工作,总结了填充橡胶超弹性、黏弹性、流变本构研究的进展。特别从本构关系与有限元分析相容性的角度,分析了各常用模型的精度、使用范围和参数化性能,为橡胶力学仿真提供指导,并指出了目前橡胶本构模型研究中所存在的问题,探讨了改进的方向。     

基于三维椭球模型的构象弹性理论

基于合理的旋转异构态模型得到二维链构象分布函数,通过假设构象态消失规则得到的构象弹性理论能很好地描述高分子材料的橡胶弹性．本研究利用三维椭球模型,考虑各向异性的形变过程,对构象弹性理论进行了进一步修正;并且利用修正后的理论计算全同立构聚丙烯（iPP）的应力应变关系．理论结果成功地描述了在形变过程中,由于结构变化对自由能、熵及内能变化的影响．此外,对高分子凝聚态多尺度衔接问题也作了初步探索．     

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.     

不同分子量可德胶水悬浮液的粘弹性研究

采用动态粘弹性测量研究了不同分子量的生物大分子可德胶 (Curdlan)水悬浮液 (ASC)的流变学特性 .室温下观察到ASC具有弹性 (Solid like)行为 ,储能模量G′在测量范围内轻微依赖频率 ,而损耗模量G″和损耗角正切tanδ存在最小值 .ASC粘弹性随可德胶分子量和浓度的增加而增强 .ASC的流动特性符合Herschel Bulkley模型 ;其弹性行为可以通过渗流理论的标度弹性模型来描述 .网络结构是由于可德胶颗粒聚集或絮凝而形成的 ,当可德胶含量超过临界浓度cs=0 3 %时 ,弹性模量G′与可德胶浓度存在标度关系G′=Goεt,其中标度指数t=2 5 4.     

从Maxwell串联模型定义的弛豫时间τ理解聚合物粘弹性的本质

在Maxwell串联模型所定义的参数里,反映弹性和粘性相结合的是弛豫时间τ=η／E,它不但表明粘弹性是材料同时具有粘性和弹性的结果,并且是仅取决于材料粘性系数和弹性系数的相对大小,而不是它们各自的大小。τ是表征材料弛豫现象的内部时间尺度,只有在外力作用时间与这个内部时间尺度同一数量级时,材料才会产生极大的弛豫,它的粘弹性本质才有最充分的显示。本文即以Maxwell串联模型为例对聚合物粘弹性的本质进行了讨论。     

Strain-hardening modulus of cross-linked glassy poly(methyl methacrylate)

The strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well-known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010     

Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields

The limits of linear viscoelastic behavior of polystyrene solutions have been investigated by subjecting them to large-amplitude oscillatory strains, γ₀. At strains less than one we find that the dynamic storage modulus G′(ω,γ₀) and the dynamic loss modulus G″(ω,γ₀) decrease quadratically with increasing strain. As a measure of the size of the linear viscoelastic region, we have determined the strain at which the moduli have fallen 5% below their zero-strain values. This strain, γNL, is found to be independent of frequency ω at high frequencies but to increase with decreasing frequency at low frequencies. Behavior of this type is in qualitative agreement with the recent constitutive equation developed by Doi and Edwards. More specifically, we find that the rate of decrease of the storage modulus with increasing strain is quite similar to that predicted by their theory, but that the rate of decrease of the loss modulus is much slower. Some possible approaches for improving the agreement with experimental results are suggested. In the course of our work an interesting hydrodynamic instability was observed. The nature of this instability and methods to avoid it are discussed.     

Dynamic property and constitutive model of polyvinyl butaral material at high strain rates

The polyvinyl butaral (PVB) interlayer of automotive windshield plays an important role in the protection of both pedestrian and passenger, the mechanical property of PVB material should be in‐depth studied. In this article, the systematical uniaxial tensile experiments of PVB material under high strain rates are conducted, the strain rates range from 125.6 to 3768 s^?1. The results of experiments show that there exists a phenomenon of stress spurt caused by the stress hardening in the final stage of tension, and the strain rate exerts great influence on mechanical property of PVB material. Further, the data fitting basing on Mooney–Rivlin model is carried out, it is found that the fitting results are consistent with the experiment data, which means that the Mooney–Rivlin constitution model can describe the large deformation behavior of PVB material. At last, the rate‐dependent mechanical behavior of the PVB material is further investigated in this article. On the basis of the experiment results and Johnson–Cook model, a rate‐dependent constitutive model is proposed to describe the tensile mechanical property of PVB material under high strain rates. This work will be beneficial to the simulation and analysis of automotive collision safety and pedestrian safety protection, which are related to damage of automotive windshield. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonlinear stress relaxation of a styrene–butadiene random copolymer

The isothermal uniaxial stress relaxation response in the vicinity of the glass-to-rubber transition has been measured for a lightly crosslinked poly(styrene–butadiene) random copolymer, 85% styrene by weight. The volume change during stress relaxation was determined by measuring the time-dependent lateral contraction of the specimen with a Hall-effect proximity detector. The specimen exhibited an instantaneous dilation upon application of the strain and a subsequent time-dependent volume decrease. The stress relaxation behavior and the associated volume relaxation were determined for a variety of strains and temperatures in both the linear and nonlinear viscoelastic regime. As the applied strain was increased the isothermal tensile modulus decreased and the shape of the log(modulus) vs. log(time) curve was altered. At equal levels of strain the tensile modulus exhibited increasing deviations from the linear viscoelastic response as the temperature was decreased. The maximum difference between the nonlinear tensile modulus and the linear viscoelastic response was observed at short times. Subsequently, the nonlinear tensile modulus began to approach the linear viscoelastic modulus with increasing time. Both the instantaneous dilation and the magnitude of the time-dependent part of the volume change increased as the level of applied strain was increased and/or as the temperature was decreased. The observed nonlinearity in the tensile stress relaxation response has been quantitively related to the experimentally measured volume relaxation with a free-volume model.     

Loaded rubber-like materials subjected to small-amplitude vibrations

This paper proposes a constitutive law and a method for characterizing highly preloaded viscoelastic materials subjected to linear （small-amplitude） vibrations. A multiplicative non-separable variables law has been suggested to model the behavior that depends on both stretch and time/frequency. This approach allows splitting the intricate combined test performed simultaneously on both stretch and frequency, generally in a limited experimental domain up to 100 Hz, into two independent tests. Thus, on one hand, the dynamic complex modulus dependent on frequency alone is evaluated on the basis of vibration tests in a large experimental domain up to 100 kHz. On the other hand, energetic parameters are determined from a quasi-static hyperelastic tensile test. The complex modulus, dependent on both stretch and frequency, is then deduced from the results acquired from uncoupled investigations. This work shows that, in extension, the elastic modulus increases with increasing stretch, and the loss factor decreases with increasing stretch; while, in compression, around the material undeformed state, the modulus increases as the stretch increases till a certain value of compression stretch （upturn point depending on material characteristics）, and then the modulus decreases as the stretch increases. Globally, preload rigidifies materials but reduces their damping property. These results closely match a well-known observation in solid mechanics.     

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     

Stress relaxation of PVC below the yield point

Stress relaxation of commercial poly(vinyl chloride) (PVC) is measured at strains below 3% and at different temperatures below the glass transition temperature. First it is shown that below the yield point the material follows a linear viscoelastic behavior. Then the data at a fixed deformation level (0.03) are fitted by considering a lognormal distribution function of relaxation times. Furthermore, from the measured stress-strain curves, the temperature dependence of the elastic tensile modulus is determined. The temperature dependence of the elastic modulus, the relaxation strength, and the parameters of the distribution: mean relaxation time, τ_m, and half-width, β, are given. Moreover, the distribution function and the temperature dependence of its characteristic parameters are discussed in terms of a cooperative model of the mechanisms involved in the mechanical relaxation of glassy polymers. Finally, the relationship proposed between the tensile modulus and the free volume helps explain the temperature dependence of the relaxation strength. © 1996 John Wiley & Sons, Inc.     

高分子熔体和浓溶液流变性能的研究

基于多重缠结网络结构模型和高分子链上缠结点在流动中可进行动态解缠和再缠结的多重蠕动机理,用统计力学和动力学相结合的方法,分别计算出了缠结链组的末端距分布函数;处于缠结状态下高分子链构象统计分布函数;受力下聚合物熔体粘弹性形变自由能和解除外力下高分子挤出体可回复性粘弹性形变自由能,提出了高分子挤出体可回复形变的粘弹性分子理论。推导出的高分子熔体的回忆函数、简单剪切流下的本构方程和物料函数,并采用一种新的方法测定出物料的四种参数： η0、 GN0、 n′和 a。对于高分子挤出体,可回复性粘弹性形变由快速弹性形变和慢速粘弹性形变两者组成,当把两种形变量的复合结构参数－分子链的反式构象分数引入两种形变自由能表达式后,就从理论上得到了可回复形变量同挤出胀大比间的定量表达式,从而建立起一个具有分子链结构参数的新的挤出胀大比方程,可回复形变量同挤出条件（温度、挤出速率和量以及口模长径比不同的挤出机）和树脂结构特征（分子量及分布）的关系式以及在特殊情形下的简化表达式,并用几种高分子熔融体系的挤出胀大比和可回复性形变量的实验数据对理论进行验证,理论方程同实验数据较好的符合。