textiles composites

7/31/2019 Textiles Composites

1/4

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.
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


2/4


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.


3/4


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.


4/4


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)

textiles composites

Documents