Correlation of Thermal Conductivities of Unidirectional Fibrous Composites Using Local Fractal Techniques

1991 ◽  
Vol 113 (4) ◽  
pp. 788-796 ◽  
Author(s):  
R. Pitchumani ◽  
S. C. Yao
Keyword(s):  
Cross Section ◽  
Volume Fraction ◽  
Fibrous Composite ◽  
Flow Direction ◽  
Fractal Dimensions ◽  
Unit Cell ◽  
Small Range ◽  
Fiber Volume ◽  
Unit Cells ◽  
Traditional Approaches

The arrangement of fibers strongly influences heat conduction in a composite. Traditional approaches using unit cells to describe the fiber arrangements work well in the case of ordered arrays, but are not useful in the context of disordered arrays, which have been analyzed in the literature by statistical means. This work presents a unified treatment using the tool of local fractal dimensions (although, strictly speaking, a composite cross section may not be an exact fractal) to reduce the geometric complexity of the relative fiber arrangement in the composite. The local fractal dimensions of a fibrous composite cross section are the fractal dimensions that it exhibits over a certain small range of length scales. A generalized unit cell is constructed based on the fiber volume fraction and local fractal dimensions along directions parallel and transverse to the heat flow direction. The thermal model resulting from a simplified analysis of this unit cell is shown to be very effective in predicting the conductivities of composites with both ordered as well as disordered arrangement of fibers. For the case of square packing arrays, the theoretical result of the present analysis is identical to that of Springer and Tsai (1967).

A New Unit Cell Concerned Realistic Geometry Structure of 3D Four Directional Braided Composite

2016 ◽  
Vol 860 ◽  
pp. 65-68
Author(s):  
Hai Jun Zhang ◽  
Chu Wei Zhou
Keyword(s):  
Volume Fraction ◽  
Unit Cell ◽  
Fiber Volume ◽  
The Real ◽  
Braided Composite ◽  
Packing Factor ◽  
Geometry Structure ◽  
Element Simulation ◽  
Unit Cells ◽  
Realistic Geometry

This paper represented a new unit cell of 3D four directional braided composite for mechanical properties calculation. There are three disadvantages of unit cells in most previous works such as the fiber volume fraction hard to touch the reality despite the packing factor is maximum 1, the yarns are curved subjectively which is far away from realistic geometry structure, a quantity of connected surfaces are neglected as the yarns are not match the real appearance. A new unit cell established based on the real manufacturing process and structure could improve these aspects in this work. The yarn in the unit cell was similar to the real one which was constructed by photos. The details at the conjoined position were also expressed thoroughly. The result of finite element simulation was in good agreement with the available experimental data.

3D layer-to-layer orthogonal interlock woven composites under monotonic loading: Multiscale modeling

2017 ◽  
Vol 36 (17) ◽  
pp. 1263-1285 ◽  
Author(s):  
M Muthukumar ◽  
J Prasath ◽  
S Sathish ◽  
G Ravikumar ◽  
YM Desai ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Multiscale Modeling ◽  
Cross Section ◽  
Composite Structure ◽  
Volume Fraction ◽  
Woven Composites ◽  
Woven Composite ◽  
Fiber Volume ◽  
Element Analysis ◽  
Unit Cells

Multiscale modeling of 3D layer-to-layer orthogonal interlock woven composite structure for elastic and strength behavior is presented. Due to the inherent nature of weaving, 3D woven composites can be represented by repetitive unit cells at the meso level. The present study focuses on identifying different types of repetitive unit cells considering both the geometry and the boundary conditions. For a typical 3D layer-to-layer orthogonal interlock woven composite, there are eight types of meso repetitive unit cells taking into account both the geometry and the boundary conditions. Additionally, for a practical situation, fiber volume fraction (Vf) in the impregnated strand is not uniform throughout the cross-section. In other words, Vf would be different for different micro repetitive unit cells. The properties of the macro structure, i.e. the 3D woven composite structure has been determined by applying periodic boundary conditions at micro and meso levels and iso-strain conditions at the macro level using finite element analysis. The continuity between the blocks is provided by merging the nodes in the intersection regions. The effect of different Vf at different locations in the transverse cross-section of the strand on the elastic and the strength properties of 3D layer-to-layer woven composite structure is presented.

Prediction of internal geometry and tensile behavior of 3D woven solid structures by mathematical coding

2021 ◽  
pp. 152808372110013
Author(s):  
Vivek R Jayan ◽  
Lekhani Tripathi ◽  
Promoda Kumar Behera ◽  
Michal Petru ◽  
BK Behera
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Areal Density ◽  
Woven Fabrics ◽  
Tensile Behavior ◽  
Geometrical Parameters ◽  
Fiber Volume ◽  
Acceptable Error ◽  
Internal Geometry ◽  
Unit Cells

The internal geometry of composite material is one of the most important factors that influence its performance and service life. A new approach is proposed for the prediction of internal geometry and tensile behavior of the 3 D (three dimensional) woven fabrics by creating the unit cell using mathematical coding. In many technical applications, textile materials are subjected to rates of loading or straining that may be much greater in magnitude than the regular household applications of these materials. The main aim of this study is to provide a generalized method for all the structures. By mathematical coding, unit cells of 3 D woven orthogonal, warp interlock and angle interlock structures have been created. The study then focuses on developing code to analyze the geometrical parameters of the fabric like fabric thickness, areal density, and fiber volume fraction. Then, the tensile behavior of the coded 3 D structures is studied in Ansys platform and the results are compared with experimental values for authentication of geometrical parameters as well as for tensile behavior. The results show that the mathematical coding approach is a more efficient modeling technique with an acceptable error percentage.

The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

scholarly journals Thermal conductivity of unidirectional composites consisting of randomly dispersed glass fibers and temperature-dependent polyethylene matrix

2019 ◽  
Vol 26 (1) ◽  
pp. 412-422 ◽  
Author(s):  
Wan-Qing Lin ◽  
Yu-Xuan Zhang ◽  
Hui Wang
Keyword(s):  
Thermal Conductivity ◽  
Finite Element ◽  
Test Temperature ◽  
Volume Fraction ◽  
Glass Fibers ◽  
Simple Algorithm ◽  
Extensive Study ◽  
Unit Cell ◽  
Fiber Volume ◽  
Polyethylene Matrix

AbstractThis extensive study investigated the influence of microstructure on the effective transverse thermal conductivity of unidirectional glass fiber reinforced composites, in which the fibers are randomly dispersed and the thermal conductivity of polyethylene matrix is a function of test temperature. The microstructure is characterized by parameters such as the number of fibers, fiber volume fraction, fiber size, fiber arrangement and thermal property contrast. Firstly, a simple algorithm is developed to automatically generate closest-to-real random array of fibers in unit cell to reconstruct the composite microstructure. Then, the established two-dimensional random two-component composite unit cell is solved using finite element simulation and the obtained effective thermal conductivities are compared with the theoretical predictions and the experimental results. Subsequently, the effects of microstructure parameters and test temperature are investigated, respectively. It is found that the finite element predicted properties are in very good agreement with the experimental predictions, while they are always lower than the analytically predicted properties. These results can find applications in the design of composite materials taking into account the fiber distribution morphology.

scholarly journals Efficiently, accurately, intelligently dissecting bamboo: characteristic of vascular bundle in Phyllostachys

2021 ◽  
Author(s):  
Haocheng Xu ◽  
Ying Zhang ◽  
Jiajun Wang ◽  
Tuhua Zhong ◽  
Xinxin Ma ◽  
...  
Keyword(s):  
Cross Section ◽  
Radial Distribution ◽  
Vascular Bundle ◽  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Width Ratio ◽  
Vascular Bundles ◽  
Fiber Volume ◽  
Detection Model ◽  
Gradient Change

AbstractA comprehensive understanding of vascular bundles is the key to elucidate the excellent intrinsic mechanical properties of bamboo. This research aims to investigate the gradient distribution of fiber volume fraction and the gradient changes in the shape of vascular bundles along the radial axis in Phyllostachys. We constructed a universal transfer-learning-based vascular bundle detection model with high precision of up to 96.97%, which can help to acquire the characteristics of vascular bundles quickly and accurately. The total number of vascular bundles, total fiber sheath area, the length, width and area of fiber sheath of individual vascular bundles within the entire cross-section were counted, and the results showed that these parameters had a strongly positive linear correlation with the outer circumference and wall thickness of bamboo culms, but the fiber volume fraction (around 25.5 %) and the length-to-width ratio of the vascular bundles (around 1.226) were relatively constant. Furthermore, we layered the cross section of bamboo according to the wall thickness finely and counted the characteristics of vascular bundle in each layer. The results showed that the radial distribution of fiber volume fraction decreased exponentially, the radial distribution of the length-to-width ratio of vascular bundle decreased quadratically, the radial distribution of the width of vascular bundle increased linearly. The trends of the gradient change in vascular bundle’s characteristics were found highly consistent among 29 bamboo species in Phyllostachys.One sentence summaryA universal vascular bundle detection model can efficiently dissect vascular bundles in Phyllostachys, and the radial gradient change of vascular bundles in cross-section are found highly consistent.

Three-dimensional braided composites with zero, negative and isotropic thermal expansion behavior

2020 ◽  
Vol 54 (13) ◽  
pp. 1761-1781
Author(s):  
SA Pottigar ◽  
B Santhosh ◽  
RG Nair ◽  
P Punith ◽  
PJ Guruprasad ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Three Dimensional ◽  
Braided Composites ◽  
Fiber Volume ◽  
Braided Composite ◽  
Expansion Behavior ◽  
Unit Cells ◽  
Composite Configuration

Three-dimensional braided composites with zero, negative and isotropic coefficient of thermal expansion are presented based on an analytical homogenization technique. The configuration of the braided composites is worked out considering the exact jamming condition leading to higher fiber volume fraction. A total of four configurations of three-dimensional-braided composite representative unit cells were analyzed. Among these, two arrangements are 4-axes and the other two are 5-axes. Special emphasis is given on the detailed description of the representative unit cells. Analysis reveals that a three-dimensional-braided composite configuration with thermoelastic isotropic properties having same coefficient of thermal expansion along x-, y-, and z-axes is achievable. As a special case, the homogenization model is used to predict, for the first time, a configuration of braided architecture and material leading to zero coefficient of thermal expansion along x-, y- and z-directions.

Parametric Generation of Random Distribution of Fibers in Long-Fiber Reinforced Composites and Micromechanical FE Analysis

2010 ◽  
Vol 452-453 ◽  
pp. 117-120
Author(s):  
Zhen Qing Wang ◽  
Xiao Qiang Wang ◽  
Ji Feng Zhang ◽  
Song Zhou
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Fiber Volume Fraction ◽  
Random Distribution ◽  
Volume Fraction ◽  
Fiber Reinforced ◽  
Fiber Volume ◽  
Parametric Generation ◽  
High Fiber ◽  
Damage Initiation

A method for the parametric generation of the transversal cross-section microstructure model of unidirectional long-fiber reinforced composite (LFRC) is presented in this paper. Meanwhile, both the random distribution of the fibers and high fiber volume fraction are considered in the algorithm. The fiber distribution in the cross-section is generated through random movements of the fibers from their initial regular square arrangement. Furthermore, cohesive zone element is introduced into modeling the interphase between the fiber and the matrix. All these processes are carried out by the secondary development of the finite element codes (ABAQUS) via Python language programming. Based on the model generated, micromechanical finite element analysis (FEA) is performed to predict the damage initiation and subsequent evolution of the composites. The results show that this technique is capable of capturing the random distribution nature of these composites even for high fiber volume fraction. Moreover, the results prove that a good agreement with the experimental results is found.

Effect of layer shift on the out-of-plane permeability of 0°/90° noncrimp fabrics

2014 ◽  
Vol 33 (22) ◽  
pp. 2073-2094 ◽  
Author(s):  
Liangchao Fang ◽  
Jianjun Jiang ◽  
Junbiao Wang ◽  
Chao Deng ◽  
Dejia Li ◽  
...  
Keyword(s):  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Dominant Role ◽  
Fiber Volume ◽  
Transfer Molding ◽  
Local Permeability ◽  
Out Of Plane ◽  
Unit Cells ◽  
Flow Through ◽  
Key Parameter

Layer shift has a great effect on the permeability which is a key parameter in resin transfer molding. In this paper, nine different unit cells were modeled based on the range of layer shift and decomposed into zones of characteristic yarn arrangement, respectively. For each unit cell, a set of equations was derived allowing description of the local permeability of each zone as a function of geometrical yarn parameters. The overall permeability was then modeled as a mixture of permeabilities of different zones with the electrical resistance analogy. Excellent agreement was found between predictions and experiment. Both results indicated that the channel flow had a dominant role in the whole flow through the fabrics. And the permeability values reached maximum when the empty regions were interconnected between upper and lower layers. In addition, the effect of fiber volume fraction on the differences of two extreme cases was also investigated.

Accuracy of the generalized self-consistent method in modelling the elastic behaviour of periodic composites

1993 ◽  
Vol 345 (1677) ◽  
pp. 545-576 ◽  
Keyword(s):  
Integral Equation ◽  
Volume Fraction ◽  
Fibrous Composite ◽  
Local Stress ◽  
Unit Cell ◽  
Elastic Behaviour ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Self Consistent ◽  
Consistent Method

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young’s modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

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