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BULLETIN OF APPLIED MECHANICS 7(27), 46-49 (2011) 46
Comparison of the Young's Modulus of Lamina and
Textile Composite
Petr Janda, Tom Kroupa, VclavaLaov
1Abstract - The usage of composite material is not common inmachine tool design, because of conservatism in this branch and
insufficient knowledge of such materials. In the near future, theremight be a growth of composite materials application, thanks totheir inherently low weight and high tensile strength (inlongitudinal direction) in comparison with classical construction
material like cast iron or steel. There is a difference in mechanicalproperties of textile composites and lamina, caused by the fibreundulation. For designers, the valid mechanical properties with
desirable accuracy are very important. This paper deals withcomparison of Youngs modulus of lamina and textile composite.
The finite element method is used for the prediction of Youngs
modulus of both composite structures. The finite element meso-scale models are created in commercial software packages SiemensNX 7.5 and MSC Marc 2008r1.
Index Terms composite, mechanical properties, numericalanalyses
INTRODUCTION
Application of composite materials in machine tools design is
not as usual as in automotive, airplane or sporting goods
design. This is caused by conservative approach of machine
tools designers to selection of material and lack of knowledge.
One of the most important information about material is the
mechanical properties of material. Mechanical properties areusually determined using experimental approach, but the
experiments are expensive and time-consuming. Other
approaches of mechanical properties determination are
analytical and numerical approaches (Janda, 2009). These
approaches offer lower costs and sufficient agreement with
experimental data. In this paper, the numerical approach is
used for Youngs modulus determination.
PROBLEM FORMULATION
There is a wide variety of composite structures applicable in
technical practice. The composite structures are classified into
structures with fibre undulation and structures without fibre
1 Manuscript received October 9, 2011. This work was supported in part by
the Research Project 1M6840770003 and GA P101/11/0288.
P. Janda is with the University of West Bohemia, Faculty of Mechanical
Engineering, Department of Machine Design, Univerzitn 22, 306 14 Pilsen,
Czech Republic, phone: +420 377 638 272, email: [email protected]
T. Kroupa is with the University of West Bohemia, Faculty of AppliedSciences, Department of Mechanics, Univerzitn 22, 306 14 Pilsen, Czech
Republic, phone: +420 377 632 367, email: [email protected]
V. Laov is with University of West Bohemia, Faculty of MechanicalEngineering, Department of Machine Design, Univerzitn 22, 306 14 Pilsen,
Czech Republic, phone: +420 377 638 200, email: [email protected]
undulation (with straight fibres). Figure 1 demonstrates
composite structure formed by one layer of textile composite
with plain weave. Figure 2 shows a composite structure with
two layers formed by unidirectional laminae without fibre
undulation.
Fig. 1Composite structure with fibres undulation
Fig. 2Composite structure with straight fibres
It is clear that mechanical properties of composite with fibre
undulation will be different than mechanical properties of
composite without fibre undulation. The fibre undulation is
present at composite structures in many applications. The
main goal of this paper is to analyze the influence of fibreundulation on mechanical properties of composites, namely
the Youngs modulus. The modulus of textile composite and
of composite with two layers of straight fibres will be
compared.
The classical laminate theory (La, 2008) is usable for the
evaluation of mechanical properties without fibre undulation.
The prediction of mechanical properties of textile composites
(with fibre undulation) requires modified laminate theory
(Ishikawa, a dal, 1982). This analytical approach is very fast
but predicted data have lower accuracy.
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BULLETIN OF APPLIED MECHANICS 7(27), 46-49 (2011) 47
Numerical methods can provide accurate results in the
prediction of mechanical properties of textile composites. This
method is based on modelling of elementary unit cell (meso-
modelling). The elementary unit cell is the smallest repeatable
structure of composite (Fig. 3).
Fig. 3Elementary unit cell
The periodic boundary conditions must be applied on
elementary unit cell. The numerical approach for the
prediction of mechanical properties of textile composites is
used in this paper and was verified by previous work (Kroupa,
et al. 2010).
NUMERICAL SIMULATIONS
The numerical approach is based on elementary unit cell. Two
elementary unit cells were created in our case. Both
elementary models have the same volume fraction of fibres
and matrix and therefore they are comparable.
The first model of elementary unit cell consists of two
unidirectional composite layers which are placed at angles 0
and 90. The bundles of fibres are without fibre undulation
(Fig. 4).
Fig. 4Elementary unit cell with straight fibres
The second model of elementary unit cell consists of one
layer of textile with the plane weave. The weft and warp fibres
are angle-wise 90. The elementary unit cell of textile
composite with the plain weave is in Figure 5.
Fig. 5Elementary unit cell with fibres undulation
Dimensionless lengths of edges of the unit cells were
5 x 5 x 0.3. The geometry of unit cell and mesh was created in
commercial software Siemens NX. The mesh was exported to
FEM solver MSC.MARC and the periodic boundary
conditions were applied on both models. The periodic
boundary conditions principle can be described as (Kroupa, et
al. 2010).
,
,
,
AB
AB
AB
www
vvv
uuu
(4)
where u, v and w are the translation differences of pair of
opposing nodes in directions x, y and z, respectively. These
differences must remain constant for all pairs of corresponding
nodes on opposite sides. The principal is shown schematically
in Figure 6. Figure 7 describes the elementary unit cell with
periodical boundary conditions (using spring and link
elements).
Fig. 6Scheme of equivalently deformed opposite boundaries of unit cell.
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BULLETIN OF APPLIED MECHANICS 7(27), 46-49 (2011) 48
Fig. 7Boundary conditions of elementary unit cell
Fig. 8Unit cell of unidirectional bundle (hexagonal structure)
Two different materials of fibre bundles were considered
carbon fibres and Kevlar fibres. The mechanical properties of
both materials are listed in Table 1 and Table 2. The materialproperties of epoxy matrix are in Table 3. These properties
were used for computation of fibre bundles properties in all
cases.
Tab. 1Mechanical properties of Kevlar fibres
E1 [MPa] 104 000
E2 [MPa] 5 400
E3 [MPa] 5 400
12 [-] 0.4
23 [-] 0.4
13 [-] 0.021
G12 [MPa] 12 000
G13 [MPa] 12 000
G23 [MPa] 12 000
Tab. 2Mechanical properties of carbon fibres
E1 [MPa] 230 000
E2 [MPa] 15 000
E3 [MPa] 15 000
12 [-] 0.3
23 [-] 0.3
13 [-] 0.02
G12 [MPa] 50 000
G13 [MPa] 50 000
G23 [MPa] 50 000
Tab. 3Mechanical properties of epoxide matrixE[MPa] 3 000
[-] 0.3
The mechanical properties of fibre bundles were calculated
by numerical micro-model of fibre bundle (Figure 8). This
approach was described in previous work (Kroupa, et al.,
2010). The mechanical properties of Kevlar fibre bundles with
fibre volume ratios 60% and 70% are in Table 4. The
mechanical properties of carbon fibre bundles with fibre
volume ratios 60% and 70% are in Table 5.
Tab. 4Mechanical properties of Kevlar fibre bundles
Vf= 0.6 Vf= 0.7
E1 [MPa] 63 460 73 550
E2 [MPa] 4 360 4 600
E3 [MPa] 4 360 4 600
12 [-] 0.36 0.37
23 [-] 0.40 0.40
13 [-] 0.02 0.02
G12 [MPa] 3 420 4 340
G13 [MPa] 3 150 4 010
G23 [MPa] 3 420 4 340
Tab. 5Mechanical properties of carbon fibres bundles
Vf= 0.6 Vf= 0.7
E1 [MPa] 138 870 161 540
E2 [MPa] 7 050 8 330
E3 [MPa] 7 050 8 330
12 [-] 0.3 0.3
23 [-] 0.36 0.34
13 [-] 0.02 0.02
G12 [MPa] 4 260 5 900
G13 [MPa] 3 880 5 450
G23 [MPa] 3 260 5 900
The final mechanical properties obtained by numerical
analyses of elementary unit cell meso-models are summarized
in the following tables. The comparison of mechanical
properties of the Kevlar composite structures with fibre
undulation and the Kevlar composite structure without fibre
undulation is in Table 6. The comparison of mechanical
properties of the carbon composite structures with fibre
undulation and the carbon composite structure without fibre
undulation is in Table 7.
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Tab. 6Mechanical properties of Kevlar composite
with fibres undulationwithout fibres
undulation
Vf= 0.6 Vf= 0.7 Vf= 0.6 Vf= 0.7
E1 [MPa] 14 080 15 720 19 600 22 390
E2 [MPa] 14 080 15 720 19 600 22 390
G12 [MPa] 2 210 2 600 2 550 2 550
12 [-] 0.28 0.29 0.06 0.06
Tab. 7Mechanical properties of carbon composites
with fibres
undulation
without fibres
undulation
Vf= 0.6 Vf= 0.7 Vf= 0.6 Vf= 0.7
E1 [MPa] 27 750 31 890 40 320 46 650
E2 [MPa] 27 750 31 890 40 320 46 650
G12 [MPa] 2 600 3 300 2 600 3 270
12 [-] 0.33 0.33 0.04 0.04
CONCLUSION
The fibre undulations have significant influence on Youngs
modulus of investigated composite structures. The Youngs
modulus of composite structure with fibre undulation is
decreased by approximately 30% compared to composite
structure without fibre undulation. Particularly, the decrease of
Youngs modulus is 28.2% 29.8% in the case of Kevlar
fibres and 31.2%31.7% in the case of carbon fibres.
REFERENCES
Ishikawa, Takashi and Chou, Tsu-Wei. 1982. ElasticBehavior of Woven Hybrid Composites.Journal of Composite
Materials, 16, 1982.
Janda, Petr. 2009. Analytical, simulation, and experimental
modelling of properties of nonconventional materials and
structures. Report for state examinations, University of West
Bohemia,Pilsen, 2009.
Kroupa, Tom, Zemk, Robert and Janda, Petr. 2010. Linear two scale model for determination of mechanical
properties of textile composite material. 18th Conference on
Materials and Technology. 2010.
La, Vladislav. 2008. Mechanics of composite materials.
University of West Bohemia, Pilsen, 2008. ISBN 978-80-
7043-689-9. (in Czech)