摘要
炭黑填充橡胶是一种黏超弹性复合材料，其力学行为与炭黑粒子的分布、粒径大小以及炭黑含量相关，并强烈依赖于温度、应变率、加载时间等。此外，由于橡胶材料具有黏弹特性，变形中的黏滞损耗导致材料温度上升，动态变形过程的温升尤为显著。本文研究炭黑填充橡胶材料的超弹性、黏弹性和黏超弹性本构模型，分析材料的热流变特性、考察动态力学性能与能量耗散的关系，探讨炭黑含量对填充橡胶力学性能的影响，并建立黏超弹性力学行为的细观力学分析方法。主要研究工作与结果概述如下。
1.对天然橡胶原材料性能、炭黑增强机理、炭黑填充橡胶主要力学性能、炭黑填充橡胶本构模型以及炭黑填充橡胶黏弹性的影响因素进行了简要概述。
2.概述了橡胶超弹性本构理论，对常用的超弹性本构模型进行了详细分析，探讨了各模型在单轴拉伸(ST)、等双轴拉伸(ET)和平面拉伸(PT)三类基本变形试验数据齐全时对试验数据的拟合能力，以及基本变形试验数据不齐全时各模型的预测能力，提出了超弹性本构模型的选取策略：(1)在ST、PT和ET试验数据齐全的情况下，最优先选用Ogden (N=3)模型，其次选用Yeoh模型和Arruda-Boyce模型；(2)通过两类基本变形试验来确定模型参数时，建议进行ET试验并选用Ogden (N=3)模型；(3)若仅有ST试验数据，小变形下可选用Neo-Hooke模型，大变形情况下，Arruda-Boyce模型为最佳选择。
3.通过试验研究了炭黑含量对填充橡胶材料Mullins效应、拉伸断裂强度、蠕变和松弛以及动态力学行为的影响，给出了炭黑粒子对橡胶材料增强效应的一般规律：(1)Mullins效应加剧；(2)显著提高材料的初始刚度和拉伸强度；(3)提高材料的蠕变抗力，降低松弛速率；(4)Payne效应和频率依赖性加剧；(5)玻璃化转变温度降低。
4.对炭黑填充橡胶进行不同频率下的动态力学温度扫描和不同温度下的频率扫描测试，研究材料的热流变特性。结果表明，填充橡胶不同温度下的动态模量和损耗因子曲线可沿着频率轴平移构建成一条光滑主曲线，说明材料为热流变简单材料，并由van Gurp-Palmen图和Cole-Cole图得到验证。此外，通过WLF方程和Arrhenius方程给出了温度移位因子。
5.对经典整数阶微分线黏弹性模型和分数阶微分线黏弹性模型进行了分析和对比，给出各模型的优缺点和适用范围。分数阶微分黏弹性模型具有参数少、适用性强的优势。分数阶微分Zener模型只需四个参数就可以描述填充橡胶的大部分力学行为，但不能描述其动态特性的非对称性。提出了一种修正的分数阶微分Zener模型来描述这种非对称性，模型与实验吻合良好。
6.研究了不同载荷频率，预应变和温度对炭黑填充橡胶Payne效应的影响。研究表明，动态模量随载荷频率的增高会增大；预应变在超过50%时才会对材料动态力学性能产生明显影响；Payne效应受温度影响很大，随着温度向玻璃化转变温度趋近，Payne效应越来越显著。此外，采用Kraus模型描述动态力学性能的频率与动态应变幅值相关性，给出了模型参数的新的确定方法。
7.对炭黑填充橡胶进行动态拉伸和压缩试验，研究了材料黏滞损耗的动态应变幅值和频率相关性。结果表明，动态加载过程中，黏滞损耗随动态应变幅值和频率的增大而增大。通过线黏弹性理论分析，给出了循环加载能量损耗密度的理论表达式，理论与实验吻合良好。黏滞损耗引起材料温度上升，通过红外热像仪测得圆柱橡胶试件动态压缩过程的表面温度场，试件表面温升显著。将黏弹性能量损耗视为材料内部热源，给出圆柱橡胶试件动态压缩的瞬态温度场控制方程,计算得到试件表面温度场的演化规律，计算与实验吻合良好。
8.采用随机序列吸附算法，发展了一种炭黑填充橡胶细观代表性体元(RVE)的建模方法，对材料的黏超弹性力学行为进行多尺度模拟。模拟结果表明，炭黑的加入提高了填充橡胶的模量和强度，这是由于随机分布的炭黑粒子引起了填充橡胶的细观应力集中，且应力集中程度随炭黑含量和加载应变率的提高而增大。此外，填充橡胶的刚度随应变率增大而增大，滞后损耗则随应变率增大先增后减。
Carbon black filled rubber is a typical visco-hyperelastic composite, its mechanicalbehaviors are affected by the dispersion, dimension and content of the filled particles, andremarkably influenced by temperature, strain rate and loading time. Furthermore, due tothe viscoelastic properties of the rubber material, hysteresis loss results in temperaturerise in rubber material during deformation, especially loaded with cyclic deformation. Inthis thesis, we studied the hyperelasticity, viscoelasticity and visco-hyperelasticalconsititutive models of the filled rubber, and the thermorheological characteristics andrelationship between hysteresis loss and dynamical properties were also investigated.Moreover, the effect of carbon black content on the mechanical behaviors of filled rubberwas explored, and a micro-mechanical analysis method was developed. The main worksand achievements are listed as follows.
1. Properties of nature rubber, mechanism of carbon black enhancement, mainmechanical properties of filled rubber, and the recent advanced constitutive models forrubber material and the influence factors of the viscoelastic behaviors of filled rubberswere briefly reviewed.
2. Accurate material parameters of hyperelastic constitutive models are critical forstructural finite element calculation of rubber components. The prediction performancesof six often used hyperelastic models and the model selection strategies were explored inthe case of incompletion of the three basic types of mechanical tests, and finally a modelselection strategy was developed. That is, in the case of complete data under ST, PT andET tests, Ogden model (N=3) is the first choice, and the Yeoh and Arruda-Boyce modelare the substitutive ones. If there are only two types of basic tests available, ET test ispreferred, and the Ogden model (N=3) is the best model that can precisely predict thethird deformation mode. The Arruda-Boyce model provides most excellent prediction forPT and ET deformation based on the ST test data only.
3. The influence of carbon black content on the Mullins effect, break strength, creep,stress relaxation and dynamical behavior of filled rubbers were experimentally studied. Itis shown that adding carbon black into rubber material can effectively improve its initialmodulus, break strength and exacerbate its stress softening and viscoelastic property.
4. The thermorheological property of filled rubber was studied. Temperature sweep and frequency sweep DMA tests were performed to investigate the frequency dependentglass transition temperature and to identify the thermorheological nature of the material.The test data show that master curves of dynamical properties can be created byhorizontal shifts alone and cover a frequency range of21decades, verifying the material'sthermorheological simplicity. Such simplicity is also confirmed by the van Gurp-Palmenplot and the Cole-Cole plot. Moreover, the temperature dependence of the shift factors iswell modeled by both WLF equation and Arrhenius equation.
5. Three classic viscoelastic constitutive models and their corresponding fractionalderivative models were theoretically derived. The results show that, the classic models areinaccurate to describe the viscoelastic behaviors in a wide range of time and frequency,while the fractional derivative models overcome these shortages. However, the fractionalderivative Maxwell and Kelvin-Vogit model can only usable to describe dynamicbehaviors at high and low frequency range, down and up to the loss peak. For thefractional derivative Zener model, it is enough to fit experimental curves in a widefrequency range with four parameters, but the loss modulus, loss factor for the fractionalZener model are symmetric which is not observed for real polymers. A modifiedfractional derivative Zener model was developed to capture the unsymmetric behaviors ofreal viscoelastic materials, and its capability was vertified by experimental data.
6. The influence of loading frequency, pre-strain and temperature on the Payne effectof filled rubbers were experimentally studied. It is shown that the frequency has slightinfluence on the Payne effect of the filled rubbers, and the pre-strains over50%caninfluence the Payne effect, while the Payne effect is influenced remarkably bytemperature. Furthermore, the Kraus model was used to capture the Payne effect of thefilled rubbers, the model is in good agreement with experimental data.
7. Cyclic compressive loadings and cyclic extension loadings were applied to filledrubbers, the strain and frequency dependence of the stress-strain behavior and hysteresisloss of the filled rubbers were experimentally investigated. The results show that, thestress-strain curves of filled rubber subjected to cyclic loading were hysteresis loops, andthe area of the loop increased with increasing frequency and strain amplitude. Accordingto the linear viscoelasticity, a model was developed to calculate the energy dissipatedduring testing. Due to the hysteresis loss, obvious temperature rise on the surface of thespecimen was observed. Take the energy loss as an internal heat source, a controlequation to calculate the transient temperature field of rubber cylinder under dynamicalcompression was given. The calculated temperature rises agree with the teste data.
8. Three dimensional RVE models of filled rubber were developed based on therandom sequential absorption (RSA) algorithm, and the multiscale visco-hyperelasticmechanical behaviors of filled rubber were modeled. The simulation results show that thecarbon black improves the modulus and strength of the filled rubbers, which is due to themicromechanical stress concentration near the randomly distributed carbon blackparticles. The degree of stress concentration increases with the increase in carbon blackcontent and the strain rate. In addition, the stiffness of filled rubbers increases with strainrate, while the hysteresis loss increases first and then decreases with the increasing strainrate.
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