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Numerical Investigation of Characteristic of Anisotropic Thermal Conductivity of Natural Fiber Bundle with Numbered Lumens


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Natural fiber bundle like hemp fiber bundle usually includes many small lumens embedded in solid region; thus, it can present lower thermal conduction than that of conventional fibers. In the paper, characteristic of anisotropic transverse thermal conductivity of unidirectional natural hemp fiber bundle was numerically studied to determine the dependence of overall thermal property of the fiber bundle on that of the solid region phase. In order to efficiently predict its thermal property, the fiber bundle was embedded into an imaginary matrix to form a unit composite cell consisting of the matrix and the fiber bundle. Equally, another unit composite cell including an equivalent solid fiber was established to present the homogenization of the fiber bundle. Next, finite element thermal analysis implemented by ABAQUS was conducted in the two established composite cells by applying proper thermal boundary conditions along the boundary of unit cell, and influences of the solid region phase and the equivalent solid fiber on the composites were investigated, respectively. Subsequently, an optional relationship of thermal conductivities of the natural fiber bundle and the solid region was obtained by curve fitting technique. Finally, numerical results from the obtained fitted curves were compared with the analytic Hasselman-Johnson’s results and others to verify the present numerical model.
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Research Article
Numerical Investigation of Characteristic of
Anisotropic Thermal Conductivity of Natural Fiber
Bundle with Numbered Lumens
Guan-Yu Zheng
Department of Building Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China
Correspondence should be addressed to Guan-Yu Zheng; zheng guanyu@.com
Received  July ; Accepted  July ; Published  August 
Academic Editor: Song Cen
Copyright ©  Guan-Yu Zheng. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Natural ber bundle like hemp ber bundle usually includes many small lumens embedded in solid region; thus, it can present lower
thermal conduction than that of conventional bers. In the paper, characteristic of anisotropic transverse thermal conductivity of
unidirectional natural hemp ber bundle was numerically studied to determine the dependence of overall thermal property of the
ber bundle on that of the solid region phase. In order to eciently predict its thermal property, the ber bundle was embedded into
an imaginary matrix to form a unit composite cell consisting of the matrix and the ber bundle. Equally, another unit composite cell
including an equivalent solid ber was established to present the homogenization of the ber bundle. Next, nite element thermal
analysis implemented by ABAQUS was conducted in the two established composite cells by applying proper thermal boundary
conditions along the boundary of unit cell, and inuences of the solid region phase and the equivalent solid ber on the composites
were investigated, respectively. Subsequently, an optional relationship of thermal conductivities of the natural ber bundle and the
solid region was obtained by curve tting technique. Finally, numerical results from the obtained tted curves were compared with
the analytic Hasselman-Johnson’s results and others to verify the present numerical model.
1. Introduction
Natural bers like kenaf ber [], hemp ber [], sisal ber
[], date palm ber [], wood ber [], and bamboo ber []
have unique advantages of low density, high specic prop-
erties, biodegradable nature, and low cost; thus, composites
lled with natural bers, such as natural ber reinforced
polymer/cement composites, are usually viewed as green
and environmentally friendly composites and have attracted
much attention of researchers for potential engineering
application. As one of inherent material properties of natural
bers, thermal property of natural bers is of great impor-
tance in natural ber reinforced composites, due to inherent
hollow microstructure of natural bers. Recent researches
have shown that natural bers consisting of cellulose or
lumens can present extremely lower thermal conduction than
conventional bers like glass bers and carbon bers [];
thus, natural bers reinforced composites can be considered
to be thermal insulator in such engineering as building and
furniture. In addition, it is viable to achieve the aim of light-
weight and proenvironment composite materials by consid-
ering natures of hollow microstructure and biodegradability
of natural bers.
In the past few years, many researchers investigated
thermal properties of natural bers and composites lled
with them. For example, El-Shekeil et al. experimentally
and thermal properties of kenaf ber reinforced thermo-
plastic polyurethane composites []. Liu et al. evaluated the
transverse thermal conductivity of Manila hemp ber in
solid region by the nite element method and analytical
Hasselman-Johnsons model [].Also,theystudiedtheeect
mal conductivity of unidirectional composite with abaca and
bamboo bers, by experiment and nite element simulation
[]. Behzad and Sain predicted the thermal conductivity for
hemp ber reinforced composites by experimental measure-
ment [], and subsequently they developed a nite element
Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2014, Article ID 506818, 8 pages
Mathematical Problems in Engineering
50 𝜇m
Solid region
F : (a) Cross-section morphology of the hemp ber bundle [] and (b) schematic version of the hemp ber bundle.
simulation procedure to predict the temperature prole and
the curing behavior of the hemp ber/thermoset composite
during the molding process []. Mangal experimentally
measured the thermal properties of pineapple leaf ber
reinforced composites []. Takagi and cooperators analyzed
ahot-wiremethod[]. All these works mentioned above
have been benecial in understanding of thermal transfer
mechanism in the natural ber and design of natural ber
lled composites with desirable thermal properties.
As important llers of green composites, it is necessary to
establish comprehensive understanding of thermal properties
of natural bers or ber bundles. In this paper, the emphasis
is put on the study of thermal properties of the natural hemp
hemp ber bundle can be viewed as composite material
with outstanding thermal properties, because, in the natural
ber bundle of interest, there are a large number of lumens
lled with air in transverse direction of it (see Figure (a)
for the cross-section morphology of the hemp ber bundle
[]). e thermal properties of the natural ber bundle vary
considerably depending on lumen volume and size and also
the thermal property of solid region phase, which encloses
thelumensinthenaturalberbundle.Figure (b) shows a
schematic illustration of the natural ber bundle consisting
of lumens and solid region. It is observed in Figure  that
the large-scale ber bundle is lled with many small-scale
lumens in the solid region; thus, thermal properties of the
lumen and the solid region are important parameters of the
natural ber bundle. In practice, the lumen ller is lled
with air; thus, its thermal conductivity is usually specied
with very small value, for example, .W/(mK), which is
normally the thermal conductivity of air measured at the
standard atmosphere. erefore, the thermal conductivity of
the ber solid region more signicantly aects the whole
thermal performance of the ber bundle than that of lumen.
Here, the main purpose of this study is to investigate the
eect of material thermal property of the solid region phase
on the equivalent anisotropic thermal property of the natural
ber bundle by nite element simulation [,]ofcomposite
microstructure [] and then establish an optional interrela-
tionship between them by curve tting technique []togive
a rapid and highly accurate prediction of material thermal
properties for both of them.
2. Finite Element Model for
Anisotropic Natural Fiber Bundle
Reinforced Composites
In this paper, the natural ber bundle is assumed to be
embedded into a polymer matrix with constant thermal
conductivity to form a square representative volume element
(RVE) (or unit cell) (see Figure ), as was done by many
researchers in the analysis of heterogeneous materials [
]. en, the nite element model of natural ber bundle
reinforced composites [,,]willbeestablishedto
investigate the inuence of solid region phase on the ber
bundle. e established unit cell consists of three dierent
regions, that is, matrix, solid region, and lumen. Each region
has isotropic thermal conductivity.
eoretically, the distribution of lumens in the natural
ber bundle will cause anisotropy of the composite under
consideration. erefore, in this study, the anisotropic ther-
mal conductivities of the composite will be investigated. In
steady-state heat conduction problem, the temperature eld
within the anisotropic representative volume element satises
the quasiharmonic dierential equation:
=0, ()
where the thermal conductivities 𝑥and 𝑦are piecewise
constant. Because the matrix, the solid region, and the lumen
are assumed to be locally isotropic and homogeneous, 𝑥=
𝑦=𝑚in the matrix, 𝑥=𝑦=𝑠in the solid region and
equal to 𝑙in the lumen, respectively.
Mathematical Problems in Engineering
F : Schematic illustration of a square cell embeded with the natural hemp ber bundle. (a) Boundary conditions for 𝑒
conditions for 𝑒
Besides, in the heat conduction system, the heat ux com-
ponents 𝑥and 𝑦are, respectively, dened by temperature
In the present composite computational model, the proper
thermal boundary conditions should be applied along the
boundary of the cell shown in Figure  to construct a com-
plete composite heat transfer system being solved by nite
element technique [,,], which has been successfully
employed by many researchers for the analysis of eective
thermal properties of unidirectional ber composites [
]. According to the work of Islam and Pramila [], the
prescribed temperature boundary conditions 1,0on the
vertical or horizontal boundaries of the cell can produce the
most accurate results up to a relatively high ber volume frac-
tion, and the remaining boundaries of the cell are assumed to
be insulating, as shown in Figure . It is assumed that 1>0;
thus, the average heat ux components 𝑥and 𝑦loaded on
the data collection face, for example, the le side face for the
case (a) and the bottom side face for the case (b), are positive.
the eective thermal conductivities of the composite can be
given as [,]
where is the side length of the square cell,
0𝑥0,>0 ()
for the case in Figure (a),and
0𝑦(,0)>0 ()
for the case in Figure (b). e integrals in ()and()canbe
evaluated by trapezoidal numerical integration.
In the practical computation, the side length of the square
cell is set to be , which is a normalized length. If the volume
fraction of the ber bundle to the cell is assumed to be a
moderate value of %, the normalized radius of the ber
bundle is .. Furthermore, if the volume fraction of
lumen to the ber bundle keeps constant, that is, .%,
which is the experimental result [], the normalized radius
the number of lumens in the ber bundle. For example, if
disperse of lumens in the ber bundle (see Figure ), then
the normalized radius of each lumen is .. Besides, the
specied temperature boundry conditions along the two ver-
tical edges of the unit cell are set to be  and , respectively.
Moreover, the thermal conductivities of matrix, solid region,
and lumen are, respectively, normalized with the reference
value . W/(mK), which is the thermal conductivity of
lumen, in the nite element procedure below. In the paper,
the symbols 𝑚,,and𝑙, respectively, indicate the thermal
condctivities of matrix, solid region, and lumen.
3. Numerical Results and Discussions
3.1. Convergence Investigation. Generally, the nite element
(FE) solution will be more accurate as the model is subdivided
into smaller elements. e only sure way to know if we
have suciently dense mesh is to make several models with
dierent grids of elements and check the convergence of the
solution. In order to investigate the convergence of the FE
Mathematical Problems in Engineering
T : Summary of the numerical test for the solution mesh size independence.
Approximated element
size Number of elements Number of nodes Ave rage he at ux
component 𝑥Deviation (%)
Size  .   . .
Size  .   . .
Size  .   . .
Size  .   . Reference
(a) (b)
F : Finite element model of the composite with natural ber bundle including  lumens. (a) Computational domain. (b)
Computational mesh.
solution, the composite model in Figure (a) is studied by
ABAQUS and the FE size is changed from very coarse to
very ne. e element type employed in ABAQUS is DCD.
In each of FE size levels, the average horizontal heat ux
component 𝑥at the le wall of the square unit cell is
calculated. Tab l e  gives a summary of the output of these
size levels indicating the number of elements and nodes used
in the computational domain corresponding to each element
size. In this table, Size  stands for very coarse elements and
Size  means very ne elements. e table also indicates
the deviation between the average heat ux component at
element sizes and that calculated using the nest element
size of . e summarized results in Table  indicate that the
maximum deviation between the solution using the nest
element of  that corresponds to  elements and the
coarsest element of  that corresponds to  elements is
.%. is reects clearly that the numerical solution
obtained via this FE simulation is mesh size independence.
Additionally, looking for high accuracy, the authors decided
to use a ne element size of  in the following computation.
3.2. Anisotropy Investigation. It is known that the distribution
mode of lumen may cause anisotropy of both ber bundle
and composite. To investigate this eect, let us consider the
composite model involving polymer matrix, solid region, and
lumens, as displayed in Figure (a),inwhichlumens
are regularly distributed in the ber bundle to approximate
the real distribution of lumens in the practical natural ber
T : Anisotropic thermal conductivities of the composite for
various thermal conductivities of the solid region phase.
. .
. .
. .
. .
bundle (see Figure ). Figure (b) presents the computational
mesh of element Size . Results in Tab l e  display the change
of anisotropic thermal conductivities of the composites for
various thermal conductivities of the solid region phase
in the natural ber bundle. It is obvious that the thermal
conductivities of the composite along two directions are
extremely similar, so it is concluded that the approximated
practical distribution of lumen in the ber bundle causes
clusion was drawn by Liu et al., who predicted that the
anisotropy of the composite became smaller with the number
of lumens increasing []. erefore, it is reasonable to assume
following analysis.
3.3. Eect of the ermal Conductivity of the Solid Region in
the Natural Fiber Bundle. To estimate the eect of the solid
region on the composite, it is assumed that the normalized
Mathematical Problems in Engineering
Quadratic polynomial
Cubic polynomial
F : Variation of the eective thermal conductivity of the
composite against the solid region.
thermal conductivity of the solid region changes in the inter-
val [,]. By nite element computation, the distribution of
horizontal heat ux component and the corresponding aver-
surface for each specic value of the normalized thermal
conductivity of the solid region. en, the normalized eec-
tive thermal property of the composite can be evaluated by
(). e variation of the eective thermal conductivity of the
composite is given in Figure ,fromwhichitisobservedthat
the simulated eective thermal conductivity of composite
increases with the increasing thermal conductivity of solid
region, as we expect. Simultaneously, it is found that the
variation shown in Figure  shows slight nonlinearity, instead
of linearity. us, to describe the nonlinear variation shown
in Figure , the following quadratic and cubic polynomial
expressions from curve tting technology are, respectively,
(i) Quadratic polynomial tting:
𝑙+5.673. ()
(ii) Cubic polynomial tting:
𝑙+5.604. ()
3.4. Eect of the ermal Conductivity of the Homogenized
Fiber Bundle. In this section, the composite model shown in
Figure (a) is taken into consideration to investigate the eect
of the homogenized ber bundle on the composite. In the
model, the homogenized ber bundle is represented by a solid
ber with the same size. Also, the same thermal boundary
applied along the outer boundaries of the cell. To conduct the
nite element analysis, a total of  quadratic quadrilateral
elements of type DCD with  nodes are generated
by ABAQUS to discretize the computational domain (see
Figure (b)).
It is assumed that the normalized thermal conductivity of
thesolidberchangesintheinterval[,]; thus, the eective
nite element simulation for any specic value of thermal
conductivity of the equivalent solid ber. e variation of the
eective thermal conductivity of the composite against the
equivalent solid ber is displayed in Figure , which clearly
the composite nonlinearly increases with the increasing value
of the thermal conductivity of the equivalent solid ber. To
accurately capture the nonlinear variation shown in Figure ,
the following quadratic and cubic polynomial curves are,
respectively, employed by means of curve tting technology.
(i) Quadratic polynomial tting:
𝑙+5.301. ()
(ii) Cubic polynomial tting:
𝑙+5.269. ()
3.5. Optional Interrelationship between the ermal Conduc-
tivity of the Solid Region and the Fiber Bundle. Finally, the
equivalence of the two composite models, respectively, shown
in Figures (a) and (a) requires that the two composite
models should have same eective thermal conductivities.
erefore, combining ()–(), we have an optional interrela-
tionship between the thermal conductivity of the solid region
and the ber bundle; that is,
𝑙+0.372 ()
Mathematical Problems in Engineering
(a) (b)
F : Unit square cell embeded with a solid ber to represent the homogenized ber bundle. (a) Computational domain. (b)
Computational mesh.
Quadratic polynomial
Cubic polynomial
F : Variation of the eective thermal conductivity of the
composite against the homogenized ber bundle.
from which the variation of 𝑠in terms of is plotted in
Figure .
To verify the obtained relation of thermal conductivity
Hasselman-Johnsons model derived from the interface inter-
action between the circular matrix and circular inclusions
embedded in the matrix [] is taken as reference for the pur-
pose of comparison. Here, an analytical expression from the
the thermal conductivity of the solid region 𝑠with respect
to that of the ber bundle ;thatis,
Hasselman-Johnson’s model
Results of cubic tting curve
Results of quadratic tting curve
F : Approximated relation of thermal conductivities of the
natural ber bundle against the ber solid region.
where V𝑙represents the volume fraction of lumen to the ber
Mathematical Problems in Engineering
According to the experiment data in [], the practical
volume content of the lumen to the ber bundle is about
.%; thus, the substitution of V𝑙=30.87%into() yields
from which one can get the variational curve of 𝑠in terms
of ,asshowninFigure  forthepurposeofcomparison.
Specially, if is taken to be . W/(mK) [,], the thermal
conductivity of the solid region 𝑠is calculated by ()as
. W/(mK).
In Figure , it is observed that there is good agreement
between the numerical results from either quadratic or cubic
curves and the theoretical result of Hasselman-Johnson’s
model for the case of moderate change of . For example,
for the case of = 0.115W/(mK), the thermal conduc-
tivity of the solid region 𝑠is calculated as . W/(mK)
for the quadratic approximation and . W/(mK) for
the cubic approximation, which has relative derivation of
.% and .% of the theoretical solution .W/(mK),
respectively. erefore, both quadratic and cubic relations of
thermal conductivity of the solid region and the ber bundle
can be used to evaluate thermal properties of the natural ber
bundle or the solid region in the bundle. Also, in contrast to
the analytical expression (), it can be seen from ()and()
that either 𝑠or is given, and one can easily determine
conveniently by a specied material thermal conductivity of
the solid region. is is an advantage of the optional relation
presented in the paper over the analytical solution.
Besides, it is obvious in Figure  that the existence of
lumen signicantly weakens the capacity of heat transmission
in the ber bundle. As a result, the thermal conductivity of the
ber bundle is greatly less than that of 𝑠.
4. Conclusion
In this paper, D computational composite model of the nat-
ural ber bundle including numbers of lumens is developed.
Due to the geometrical limitation of the ber bundle, it is not
convenient to directly apply thermal boundary conditions to
it to perform nite element analysis of composite. To treat
matrix with known thermal conductivity to construct unit
composite cell, which is numerically analyzed by applying
proper thermal boundary conditions along the cell boundary.
By means of the developed nite element computational
composite model, the eect of the solid region in the
bundle on the overall thermal property of the composite is
studied. Simultaneously, a homogenized composite model
is constructed, in which the ber bundle is replaced by
an equivalent solid ber to investigate the inuence of the
homogenized ber bundle. By comparing the two composite
models developed in this study, an optional interrelationship
between thermal conductivities of the solid region and the
homogenized ber bundle was obtained by curve tting
technique. Finally, the present computational composite
model is veried and numerical experiments show that either
quadratic or cubic predictions can produce almost similar
results for the solid region in the ber bundle, in contrast
to the theoretical Hasselman-Johnson’s model and other
numerical results. Moreover, the direct or inverse predictions
can be easily performed to evaluate the thermal conductivity
them is given. More importantly, the present computational
method can be easily extended for the prediction of thermal
property of other natural ber bundles with various lumen
Conflict of Interests
e authors declare no conict of interests regarding the
publication of this paper.
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... Since lumen of the natural fiber bundle is hollow over its length, thermal conductivity of the lumen region is equivalent to the air. Thus for the lumen region, thermal conductivity of 0.026 W/mK was substituted in the micromechanical models during the computation [16]. Therefore with the boundary conditions shown in Fig. 2.1A and B and the thermal conductivity of the polymer and lumen, longitudinal (k cII ) and transverse thermal conductivity (k c ⟘ ) of the natural fiber can be estimated. ...
... As the number of lumens increased in the fiber bundle, characteristics of the biocomposite changed from anisotropy to isotropy [19]. In his study, Zheng also found that k cII and k c ⟘ along the longitudinal and transverse directions were identical for the hemp fiber bundle with 106 number of lumens (taken based on the count in the microstructure of the hemp fiber bundle) [16]. Thus it is clear ...
... Schematic of 2D square-shaped RVE with single fiber bundle embedded in the polymer matrix: (A) boundary condition for kcII and (B) boundary condition for kc ⟘[16].Rule of mixture modelsVoigt model (upper bound)-longitudinal thermal conductivity parallel to the fiber cell/axis (k cII )k cII = k fII v f + k m v m + k v + v vReuss model (lower bound)-transverse thermal conductivity perpendicular to the fiber cell/axis (k c ⟘ Arithmetic mean for mixed orientation k c = k cII ε + k c ⟘ (1 − ε) ε is the fitting factor used as weightage for relative contribution from the longitudinal and perpendicular cells to the fiber axis.v f , v m and v v are volume fractions of fiber, matrix and void in the composite.Halpin-Tsai model (for longitudinal and transverse thermal conductivity) , k f = k fII or k f ⟘ ε is a geometric fitting factor-usually two times the longitudinal aspect ratio for k c = k cII and k f = k fII and two times the transverse aspect ratio for k c = k c ⟘ and k f = k f ⟘ . ...
Mechanical and thermal properties of biocomposite reinforced with natural fibers have been determined traditionally from the experimental testing methods. This process is labor intensive, expensive and time-consuming. Hence, with the advancement of computational tools, modeling and analysis of the composites have become feasible. Finite element method (FEM) is a common tool used for the prediction of mechanical and thermal properties of the biocomposite. FEM-based computational analysis is relatively new and has great scope for research. Micromechanical, macromechanical and mesoscale analyses of finite-element models were used for the prediction of strength and stiffness of biocomposites. For thermal analysis, studies involve determining the thermal conductivity and analyzing the cure kinetics of the biocomposite. Hence, this chapter focuses on the various computational models used for predicting the mechanical and thermal properties of the biocomposite.
... Hemp fiber has a multi-celled structure, which can be seen as a composite material with numerous lumens side by side ( Figure 1b) [18,28,37]. A typical elementary fiber structure of hemp fiber is shown in Figure 1c. ...
... The retting processing for up to three weeks did not affect the tensile strength of the hemp fibers. [42]), (b) cross-section morphology of the hemp fiber bundle [37], and (c) schematic depiction of hemp elementary fiber (adapted from [38]). ...
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Industrial hemp (Cannabis sativa) is one of the most available and widely produced bast fibers with high cellulose content. Interest in these fibers is warranted due to environmental protection challenges as well as their inherent properties such as low density, high specific strength, and stiffness. In addition, advanced research and progress have gone into increasing their mechanical performance through surface treatments and in the development of new materials. The most promising application for hemp fibers is as reinforcement in polymeric composites or through hybridization. Nonetheless, more research is needed to improve their properties and expand their range of applications. The biodegradability issue is one problem that must be addressed when considering long life-cycle applications as the reproducibility of these composites’ final properties. This review is a comprehensive literature review on hemp fibers. It includes hemp fibers’ chemical and mechanical properties, surface modifications, hybrid composites, as well as current and future applications.
... Chemical composition and properties of single hemp fibreFig. 3. HF structure: (a) a section through the middle of the HF stem[44], (b) the morphology of the HF bundle[45], and (c) a simplified representation of the fundamental HF[6] ...
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Fibres have long been used as an additive in the fabrication of building elements and materials. A combination of natural and synthetic fibres has shown promise in preliminary research and testing, with the added benefit of greatly improved strengths of the composites. Compared to traditional reinforcement bars, natural fibre reinforcement's ratio of fibre required is significantly lower, making it more beneficial in terms of energy and economic values. Recent research has focused on the feasibility of using both natural and synthetic fibres as reinforcement in concrete and other construction materials. Thus, the purpose of this research is to investigate the feasibility of using hemp fibre at various percentages (0%, 0.2%, 0.4%, 0.6%, and 0.8%) as an additive in lightweight foamed concrete to enhance mechanical properties. Three LFC densities namely 500, 900 and 1300 kg/m3 were fabricated and tested. Axial compressive strength, flexural strength, splitting tensile strength, and ultrasonic pulse velocity were the four mechanical parameters that were assessed. The findings demonstrated that adding 0.4-0.6% of HF to LFC produced the best results for ultrasonic pulse velocity, compressive strength, flexural strength, and splitting tensile strength. The HF is essential in assisting to stop the spread of cracks in the plastic state of the cement matrix after the load was applied.
... Yaygın olarak keten kumaş olarak bilinen yaklaşık 4500 yıl önce keten kumaş bulunduğu Taş Devrinden beri dikkat çekmiştir (11). Keten lifi dünyanın birçok ılıman ve subtropikal bölgesinde doğal olarak yetişen Linum usitatissimum'un sapından gelir (33,34). Fransa, Rusya, Kanada, Belçika ve Çin'de lif ve yağ için keten yetiştirilmektedir. ...
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Uzay, Havacılık ve Otomotiv Endüstrileri yakıt tasarrufunu arttırmak amaçlı hafif bileşenlerin geliştirilmesi yönünde sürekli çalışmalar yürütmektedir. Termoplastik matrisli kompozitler ağırlık azaltma, geri dönüşebilirlik, özgül mukavemet, korozyon direnci artırma, maliyet düşürücü ve tasarımın çok yönlü açısını belirgin hale getirmek için araştırmalar yürütülmektedir (1). Doğal Lifler biyolojik olarak parçalanabilmeleri, doğada bol olmaları ve düşük maliyetleri sayesinde bu malzemelerin kapsamını genişletmekle kalmaz aynı zamanda petrol bazlı ürünlere olan bağımlılığı da azaltır. Bu yazımızda doğal liflerin özellikleri konusunda kapsamlı bir son teknolojiden bahsedeceğiz. Ağırlıklı olarak bitki lifleri ve bunların kompozit takviye olarak kullanımı, ardından mühendislik mimari ürün üretmek için kullanılan tekstil teknolojilerinden bahsedeceğiz (1). Ayrıca herhangi bir spesifik ürün geliştirme için kesin malzeme ve sürecin seçimini sağlamak için yaygın olarak bulunan termoplastik matrislerin özelliklerini ve kompozit üretim tekniklerini de kapsar. Son olarak doğal elyaf takviyeli termoplastik kompozitlerin mekanik özellikleri gözden geçirilmiş ve ele alınması gereken temel zorluklar vurgulanmıştır.
... Cross-section of hemp fibre, reprinted from Hindawi[36] under the Creative Commons Attribution License. ...
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The automotive and aerospace industries are in continuous struggle towards the development of lightweight components to improve fuel efficiency. Thermoplastic matrix composites offer distinct advantages in terms of weight reduction, recyclability, specific strength, corrosion resistance, cost-efficiency, and design versatility. Natural fibres owing to their biodegradability, abundance in nature, and low cost not only expand the scope of these materials but also curtail the dependency on petroleum-based products. This review presents a comprehensive state of the art in natural fibres properties; mainly plant fibres, and their use as composite reinforcement followed by the textile technologies used to fabricate the engineered architectures. The review also covers the properties of commonly available thermoplastic matrices and the composite fabrication techniques to enable the selection of the precise material and process for any specific product development. Finally, the mechanical properties of natural fibre reinforced thermoplastic composites are reviewed and the key challenges that need to be dealt with are highlighted.
... These properties are used in this paper as an input for the FE model constituted for determining the stresses and strains for the specific failure load and life as determined by experiments. The behavior of the natural fiber composites was predicted frequently in the literature using FE modeling [35][36][37][38][39][40] for determining micromechanical properties (strength, failure, deformation, and damage) [41][42][43], macro shape deformation (fracture and stress-strain) [44][45][46][47] and thermal conductivity [48,49]. The representative volume element model was considerably reported in the literature along with the multi-scale homogenization-based constitutive method. ...
The objectives of present work include finding the low-cost alternative of environmentally-unsafe carbon fiber composites and disposing of the waste cow-dung productively. An inexpensive way to treat cow-dung fibers using the waste glass powder and Poly Vinyl Alcohol (PVA) adhesive is reported. The treatment has increased the bending cyclic fatigue strength (CFS) of cow-dung fiber reinforced epoxy composite (CDFRC). It was found that CFS of CDFRC was comparable to carbon fiber reinforced epoxy composite (CFREC). A finite element (FE) model using the numerical homogenization technique was constituted to predict the elastic properties of treated/untreated CDFRC. Further, the predicted elastic properties were used as an input for the macro-mechanical FE model constituted using transient analysis module of ANSYS. The macro model was used to calculate the stresses and deformations at different load ratios (R) for the corresponding lives of the CDFRC. The stress-strain-life relations for treated/ untreated CDFRC were established. The reasons for increased CFS were identified collectively with the help of scanning electron microscopy (SEM) micrographs, FE results, and statistical analysis. Finally, the effect of natural weathering on untreated and treated CDFRCs was evaluated. The treated CDFRCs have shown higher resistance to natural weathering.
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This paper focuses on the morphology evolution in the forming process of unidirectional flax reinforced polypropylene composite laminates. The link between the morphology evolution and thermal conductivity during consolidation stages is investigated. Hot press forming allows to manufacture several composite laminates at different consolidation stages as a function of the compaction thickness. Microscopic evolution of the laminates in terms of morphology and porosity fractions are evaluated by scanning electron microscopy and X-ray microtomography (µ-CT). Hot disk technique is applied to measure the thermal conductivity of the laminates in in-plane and transverse directions. It is found that the in-plane thermal conductivity almost linearly increases with the reduction of porosity fraction. However, the transverse thermal conductivity remained constant. Beside the proposed relations, a theoretical model, based on a two-level Mori-Tanaka homogenization method is proposed. Considering the three-phases material (i.e., porosity, fiber, and polymer matrix), there is a good agreement between the experiment data and model predictions, but limited predictivity for porosity level above 15% certainly due to simplifying assumptions used in the predictive model.
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Kenevir ve endüstri
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to the hybrid-Trefftz (HT) FEM that covers basic concepts and general element formulations of the method. It then concentrates on both the essentials and subroutines of MATLAB and C programming. The next few chapters present applications of T-elements to potential problems and linear plane elasticity, discuss how to solve body force in elasticity through radial basis functions, and examine how special purpose functions can be constructed. The final chapter explores advanced topics, such as the construction of Trefftz p-elements, dimensionless transformation, and an alternative formulation to HT FEM. Unifying the computer programming aspects of the Trefftz FEM, this book will stimulate the development and application of this novel method in many facets of practical engineering.
Macro-Micro Theory on Multifield Coupling Behavior of Heterogeneous Materials discusses high performance structures using macro-micro theories and a micromechanics approach. The monograph is intended for specialists in materials science and applied mechanics. Qing-Hua Qin is a professor at The Australian National University, Canberra, and has been in the area of applied mechanics for more than two decades. Professor Qing-Sheng Yang at Beijing University of Technology focuses his research interests at composites micromechanics, structural analysis and multifield coupling behavior of polymers and biomaterials.
Commercial wood flour, the most common wood-derived filler for thermoplastics, is produced in a mixture of particle sizes and generally has a lower aspect ratio than wood and other natural fibers. To understand how wood flour and fiber characteristics influence the mechanical properties of polypropylene composites, we first investigated the effect of different sizes of wood flour particles on the mechanical properties of wood-flour-filled polypropylene composites. We then compared the properties of wood-flour-filled composites to those of composites reinforced with refined wood fiber. We also studied the effect of a maleated polypropylene coupling agent on composite properties. Wood flour particles (35, 70, 120, and 235 mesh) were compounded at 40% by weight with polypropylene. Increases in tensile and flexural strength and modulus of the wood flour composites were found to correspond with increases in aspect ratio. Notched impact energy increased with increasing particle size, whereas unnotched impact energy decreased with increasing particle size. Refined wood fiber and 40-mesh wood flour was compounded at 20% and 40% by weight with polypropylene. Wood fiber resulted in higher strengths at both filler levels and higher moduli at the 40% level compared to the strength properties of wood flour composites. The higher aspect ratio of the wood fiber had little effect on impact energy. The maleated polypropylene coupling agent caused greater strength increases in wood fiber composites than in wood flour composites. The coupling agent did not significantly affect tensile or flexural moduli. Our results clearly support the use of higher aspect ratio wood fibers and coupling agents for increasing the strength of wood/plastic composites.
Applicability of the finite element method (FEM) in predicting the effective transverse thermal conductivity of fiber reinforced composites is systematically studied. Four different boundary condition combinations representing the periodicity of the temperature field are employed for ideal composites having perfect bond between fiber and matrix. Both circular and square cross-section fibers are studied. Comparisons of present FEM results with available analytical and experimental results reveal that periodicity realized by prescribed temperatures yields most accurate results up to high fiber volume fractions. In composites with interfacial thermal barrier resistance the effective conductivity varies in a wide range depending on the interfacial conductance between fiber and matrix. Best fit with available experimental results is obtained for both circular and square fibers when the dimensionless interfacial conductance is about 30. By employing the modeling practice found successful in the cases for which analytical and/or experimental results exist, some typical combined effects of partial debonding and matrix cracking, for which no such results exist, are finally considered.
Numerical Methods in Engineering with MATLAB® is a text for engineering students and a reference for practising engineers. The choice of numerical methods was based on their relevance to engineering problems. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB M-files accompany each method and are available on the book website. This code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method. MATLAB was chosen as the example language because of its ubiquitous use in engineering studies and practice. This new edition includes the new MATLAB anonymous functions, which allow the programmer to embed functions into the program rather than storing them as separate files.
Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements-for instance, the Generalized Conforming Element method, to name one-and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements. © 2009 Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg. All rights are reserved.