Numerical Simulation for Mechanical Behavior of Carbon Black Filler Particle Reinforced Rubber Matrix Composites

2011 ◽  
Vol 137 ◽  
pp. 1-6
Author(s):  
Qing Li ◽  
Xiao Xiang Yang
Keyword(s):  
Carbon Black ◽  
Mechanical Behavior ◽  
Plane Stress ◽  
Volume Fraction ◽  
Filler Particle ◽  
Three Dimensional ◽  
Rubber Matrix ◽  
Two Dimensional ◽  
Rubber Composites ◽  
Dimensional Plane

In this paper, the micromechanical finite element method based on Representative Volume Element has been applied to study and analyze the macro mechanical properties of the carbon black filled rubber composites by using two-dimensional plane stress simulations and three-dimensional axisymmetric simulations under uniaxial compression respectively. The dependence of the macroscopic stress-strain behavior and the effective elastic modulus of the composites, on particle shape, particle area/volume fraction and particle stiffness has been investigated and discussed. Additionally, the simulation results of the two-dimensional plane stress model and the three-dimensional axisymmetric model are evaluated and compared with the experimental data, which shows that the two-dimensional plane stress simulations generate poor predictions on the mechanical behavior of the carbon black particle reinforced rubber composites, while the three-dimensional axisymmetric simulations appear to give a better prediction.

Percolation Phenomenon in Thermal Conductivity of Carbon Black Filled Rubber and Morphology

2010 ◽  
Vol 146-147 ◽  
pp. 575-580
Author(s):  
Jun Ping Song
Keyword(s):  
Thermal Conductivity ◽  
Carbon Black ◽  
Natural Rubber ◽  
Percolation Threshold ◽  
Volume Fraction ◽  
Graphitized Carbon Black ◽  
Rubber Matrix ◽  
Rubber Composites ◽  
Percolation Behavior ◽  
Percolation Phenomenon

A kind of graphitized carbon black 40B2 was incorporated in natural rubber matrix and vulcanizates were prepared. The content of carbon black varied from 4 to 100phr for 100phr of natural rubber. Thermal conductivity of the CB/rubber composites was studied as a function of CB loadings and temperature. TEM and SEM were employed to explore the morphology of the carbon black and the composites. It was found that percolation phenomenon existed in thermal conductivity of CB/rubber composites at different filler loadings, which was much similar with percolation behavior in electrical conductivity properties of many composites, and the percolation threshold was about 13.63%. The influence of temperature on thermal conductivity was more obviously within the region from the percolation threshold to the volume fraction of 26.2%.However, no great effect could be found on the percolation behavior of the composites in thermal conductivity. The result of TEM indicated that the mean size of CB particles was about 25nm, the maximum size of CB aggregates was about 125nm, and the CB aggregates were multichain in shape. The results of SEM showed that the distribution of CB differed at different filler loadings. Before the percolation threshold, the CB aggregates existed isolatedly, nevertheless at the percolation threshold, some long chains made up of CB aggregates ran through the rubber matrix, which resulted in the rapid increase in thermal conductivity value, and then with the addition of CB loadings, the number of chains increased. When the volume fraction was up to 26.2%, some three dimensional networks formed.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

Modeling of a Beam and a Rotor with an Edge Crack Using Dissimilar Elements

2003 ◽  
Vol 9 (10) ◽  
pp. 1159-1187 ◽  
Author(s):  
A. Nandi ◽  
S. Neogy
Keyword(s):  
Finite Elements ◽  
Stress Field ◽  
Edge Crack ◽  
Three Dimensional ◽  
Transition Element ◽  
Two Dimensional ◽  
Cracked Beam ◽  
One Dimensional ◽  
Beam Elements ◽  
Dimensional Plane

Vibration-based diagnostic methods are used for the detection of the presence of cracks in beams and other structures. To simulate such a beam with an edge crack, it is necessary to model the beam using finite elements. Cracked beam finite elements, being one-dimensional, cannot model the stress field near the crack tip, which is not one-dimensional. The change in neutral axis is also not modeled properly by cracked beam elements. Modeling of such beams using two-dimensional plane elements is a better approximation. The best alternative would be to use three-dimensional solid finite elements. At a sufficient distance away from the crack, the stress field again becomes more or less one-dimensional. Therefore, two-dimensional plane elements or three-dimensional solid elements can be used near the crack and one-dimensional beam elements can be used away from the crack. This considerably reduces the required computational effort. In the present work, such a coupling of dissimilar elements is proposed and the required transition element is formulated. A guideline is proposed for selecting the proper dimensions of the transition element so that accurate results are obtained. Elastic deformation, natural frequency and dynamic response of beams are computed using dissimilar elements. The finite element analysis of cracked rotating shafts is complicated because of the fact that elastic deformations are superposed on the rigid-body motion (rotation about an axis). A combination of three-dimensional solid elements and beam elements in a rotating reference is proposed here to model such rotors.

Stereographic Visual Displays and the Three-Dimensional Communication of Findings in Marketing Research

1997 ◽  
Vol 34 (4) ◽  
pp. 526-536 ◽  
Author(s):  
Morris B. Holbrook
Keyword(s):  
Three Dimensional ◽  
Marketing Research ◽  
Two Dimensional ◽  
Visual Displays ◽  
Structural Patterns ◽  
Dimensional Plane ◽  
Present Complex ◽  
Key Concepts

In their attempts to communicate with managers and other interested readers, marketing researchers frequently present complex findings in various sorts of visual displays. These diagrams, charts, maps, pictures, and other figures help elucidate the nature of the relationships and structural patterns involved. However, their ability to communicate is partially limited by their typical restriction to the two-dimensional plane of the printed page. As an aid to overcoming such problems, stereographic techniques permit the construction of three-dimensional representations whose vividness and depth provide greater clarity and enhance interpretability to strengthen the reader's grasp of key concepts. The author illustrates the stereographic approach to three-dimensional communication using general examples closely analogous to relevant applications in marketing research.

Study on Thermal Conductivity of Composites of Rubber/CB with Good Electrical Properties

2011 ◽  
Vol 221 ◽  
pp. 466-471 ◽  
Author(s):  
Jun Ping Song ◽  
Yan He ◽  
Lian Xiang Ma
Keyword(s):  
Thermal Conductivity ◽  
Carbon Black ◽  
Filler Loading ◽  
Graphitized Carbon Black ◽  
Acetylene Black ◽  
Rubber Matrix ◽  
Rubber Composites ◽  
Graphitized Carbon ◽  
The Difference ◽  
Better Than

Graphitized carbon black 40b2 and acetylene black were filled separately in natural rubber matrix for preparing vulcanized rubber. The thermal conductivity of both kinds of composites was studied considering filler loading and temperature. SEM and TEM were applied to observe morphology of the filler and composites. The experimental results show that thermal conductivity of acetylene black/rubber composites is much better than that of graphitized carbon black 40b2/rubber composites, which is opposite to the electric conduction properties. As filler loading increased, the difference increased, and when the filler loading is up to 40phr, the thermal conductivity value of acetylene black/rubber composite is 53% larger than the other one. TEM shows that acetylene black has more botryoidal structure, larger carbon black aggregates in size, and much looser surface than 40b2.Moreover, for acetylene black, particles contact by surface mainly, and for 40b2, particles contact by point mainly. SEM shows that the distribution of carbon black 40b2 in rubber matrix is much better than acetylene black. The better thermal conductivity for acetylene black is attributed to the higher structure, nonuniform distribution in rubber matrix and surface contact between particles.

scholarly journals Investigation of microvascular morphological measures for skeletal muscle tissue oxygenation by image-based modelling in three dimensions

2017 ◽  
Vol 14 (135) ◽  
pp. 20170635 ◽  
Author(s):  
B. Zeller-Plumhoff ◽  
K. R. Daly ◽  
G. F. Clough ◽  
P. Schneider ◽  
T. Roose
Keyword(s):  
Skeletal Muscle ◽  
Muscle Tissue ◽  
Cross Sections ◽  
Tissue Oxygenation ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Capillary Density ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Contrast Imaging

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, especially for skeletal muscle during exercise. Traditionally, microvascular oxygen supply capability is assessed by the analysis of morphological measures on transverse cross-sections of muscle, e.g. capillary density or capillary-to-fibre ratio. In this work, we investigate the relationship between microvascular structure and muscle tissue oxygenation in mice. Phase contrast imaging was performed using synchrotron radiation computed tomography (SR CT) to visualize red blood cells (RBCs) within the microvasculature in mouse soleus muscle. Image-based mathematical modelling of the oxygen diffusion from the RBCs into the muscle tissue was subsequently performed, as well as a morphometric analysis of the microvasculature. The mean tissue oxygenation was then compared with the morphological measures of the microvasculature. RBC volume fraction and spacing (mean distance of any point in tissue to the closest RBC) emerged as the best predictors for muscle tissue oxygenation, followed by length density (summed RBC length over muscle volume). The two-dimensional measures of capillary density and capillary-to-fibre ratio ranked last. We, therefore, conclude that, in order to assess the states of health of muscle tissue, it is advisable to rely on three-dimensional morphological measures rather than on the traditional two-dimensional measures.

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