a b s t r a c tA comprehensive approach is proposed for studying the microstructure of filled rubbers by optical and atomic force microscopy (AFM). The optical results are found to be dependent on the illumination angle. Algorithms based on the mathematical morphology are developed for the processing of optical images (removing scratches, identifying agglomerates). AFM-images are treated by a segmentation method which separates a continuous surface into segments that match filler. Parameters of secondary filler structures and the size of an area of homogeneous filler dispersion are obtained from the analysis of the segmented images. Seven carbon black filled rubbers with different mixing times are investigated. The combination of AFM with optical imaging techniques makes it possible to perform a quantitative structural analysis at scales from tens of nanometers to tens of microns, and to establish the relationship between the mixing time and the filler microstructure over the whole range of filler peculiarities.
В работе рассматривается численная реализация определяющих соотношений вязкоупругой модели сплошной среды. Модель описывает поведение наполненных вулканизатов в случае конечных деформаций. Используются аддитивное разложение тензора скоростей деформации, а также понятия макро-и структурного уровней деформирования. Гиперупругость связующего полимерного композита вводится соотношениями, построенными на базе обобщённой модели полимерной цепи в трубке. Реологические свойства представляются в виде дифференциальных соотношений. Опробованы различные виды слагаемого в потенциале свободной энергии, отвечающего за релаксационные свойства. Предложена зависимость коэффициента вязкого течения от параметров среды и внутренних тензорных переменных. Оценено соответствие результатов численного моделирования данным экспериментов на одноосное циклическое нагружение наполненных вулканизатов.Ключевые слова: вязкоупругость, конечные деформации, двухуровневая структурно-феноменологическая модель, эластомер, наполнитель, наполненные вулканизаты The paper focuses on the numerical implementation of constitutive relations of a continuum viscoelastic model, which describes the behavior of filled rubber vulcanizates under finite deformations. In the model, the additive decomposition of the strain rate tensor and the concept of macro and structural levels of deformation are used. The equilibrium hyperelastic behavior of a polymer binder is represented by relations that are based on the generalized tube model. Rheological properties are represented as differential relations. Various types of a term in the expression for free energy potential responsible for relaxation properties are tested. The viscous flow coefficient is analyzed as a function of continuum parameters and internal tensor variables. Simulation results are compared with the experimental data for filled rubber vulcanizates under uniaxial cyclic loading.
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