ESTIMATION OF A MECHANICAL CHARACTERIZATION FOR WOVEN FABRIC COMPOSITES BY FEM BASED ON DAMAGE MECHANICS

Tetsusei Kurashiki 1, Masaru Zako 1, Satoru Hirosawa 1, Stepan Lomov2,

and Ignaas Verpoest 2

1 Dept. of Manufacturing Science, Graduate School of Engineering, Osaka University,

2-1, Yamadaoka, Suita, Osaka, 565-0871, Japan 2 Dept. of Metallurgy and Materials Engineering, Katholieke Universiteit Lueven,

de Croylaan 2, B-3001 Heverlee, Belgium

ABSTRACT Woven fabric composites with spread tow may induce better resin impregnation, mechanical properties, etc.

than the conventional woven fabric composites. However, the mechanism of damage development of woven fabric composites with spread tow has not been investigated. To investigate the effect of spread tow on the damage development, the numerical simulation of the mechanical behavior is one of the effective procedures. We have developed a computer program based on damage mechanics. From the numerical results of mechanical behaviors under tensile loading for woven fabric composites with/without spread tow, it is revealed that the location of occurrence and the type of propagation of transverse cracks are quite different due to the effect of spread tow. Furthermore, we have prepared two numerical models with a distribution of volume fraction in a strand, and an effect of the volume fraction in a strand on the damage development has also been investigated. It has been recognized that the damage development inside lamina considering an effect of a spread tow, which has been never observed in experiments, can be predicted by the developed finite element analysis based on damage mechanics.

1. INTRODUCTION Woven fabric reinforced plastics have been applied widely to many structures, because

they have some advantages like easy handling, high lateral strength, etc. In addition, a woven architecture with spread tow has been developed to obtain superior properties. The architecture may produce the improvements of resin impregnation, high strength, etc by small undulation. The mechanical behavior of woven fabric composites with spread tow has to be investigated. However, the estimation of damage development is very difficult, because matrix cracks and delamination at the crossover parts of fiber bundle may occur leading to complicated fracture modes in comparison with uni-directional fiber reinforced composites. If damages can be estimated with numerical simulation, it will become very useful tool for the estimation of mechanical properties of woven fabric composites. We have developed a numerical simulation program on damage development of woven fabric composites based on damage mechanics [1,2]. A tensile test and a fatigue test for a lamina of woven fabric composites with In-site observation had been carried out [3]. Though the effect of a disorder of pile-up for woven fabric composites laminate on damage development had been investigated, the effect of a spread tow on the damage development had not been considered in a previous paper [4].

We have developed a numerical simulation program on damage development of woven fabric composites with spread tow based on damage mechanics. The failure behaviors for woven fabric composites with several types of spread tow under static tensile load have been analyzed by the developed program. In this paper, the numerical results of the damage states are described. 2. SIMULATION METHOD OF DAMAGE DEVELOPMENT

In the simulation, the modeling of anisotropic damage is very important. Woven fabric composites are treated as heterogeneous bodies with anisotropy for fiber bundles and with isotropy for matrix, respectively. The isotropic damage model is applied for matrix, and anisotropic damage model is applied for the fiber bundle, respectively. The damage in fiber

Z

TL

Mode L

Mode Z&ZL

Mode T&LT

Mode TZ

a b c d e f

bundle consists of four modes as shown in Fig.1 [1,2]. Mode L is dominated by fiber breaking, the others are matrix cracking caused by different stress components. The occurrence of damage can be predicted by Hoffman’s criterion. The damage mode is judged by the maximum value among the corresponding stress-to-strength ratios in Table 1. The constitutive equation can be obtained by the characterization of the damage mode. Table 1 Classification of damage mode

Fig.1 Anisotropic damage mode (σ, τ : stress, F : strength t : tension, c : compression, s: shear) 3. NUMERICAL RESULTS AND DISCUSSION 3.1 Distribution of volume fraction inside a fiber bundle

The volume fraction in a fiber bundle has been measured by the digital image processing and SEM. Figure 2(a) shows a cross section of the fiber bundle by SEM. From this figure, the volume fraction inside a fiber bundle can be evaluated with an image process. In case of a woven FRP, volume fraction is distributed in a fiber bundle. The center part in it has the highest volume fraction 65.3% and edge parts have lower value 58.3%. This tendency is same as the results of previous paper [4].

To estimate the woven architecture with/without spread tow on the damage development, finite element model has been prepared as shown in Fig.2(b) and the mechanical properties at each divided part of a bundle was calculated. A fiber bundle is treated as uni-directional fiber reinforced composites, and the mechanical properties can be calculated by the rule of mixture based on the obtained volume fractions as shown in Table 2.

Table 2 Distribution of volume fraction

(a) Cross section of a fiber bundle by SEM

(b) Finite elements of a part of a fiber bundle Fig.2 Numerical model with a distribution of volume fraction inside a bundle

Volume fraction (%)

65.3f

64.5e

63.6d

62.1c

60.6b

58.3a

Volume fraction (%)

65.3f

64.5e

63.6d

62.1c

60.6b

58.3a

Damage modeMaximum value

Mode TZ

Mode Z & ZL

Mode T & TL

Mode L

Damage modeMaximum value

Mode TZ

Mode Z & ZL

Mode T & TL

Mode L

or

or

cX

tX

L

FF

2σ

cY

tY

T

FF

2σ2

s

TZ

LT

Fτ

cZ

tZ

Z

FF

2σ2

s

ZL

ZL

Fτ

2

s

TZ

TZ

Fτ

3.2 Comparison of damage development of woven FRP with/without spread tow The mechanical behaviors of woven fabric composites with/without spread tow under on-

axis tensile load have been analyzed by the developed computer program. Figures 3 and 4 show the finite element models. Two types of numerical model have been generated. One is the model with non-spread tow, which has 3.1mm width of a bundle and 0.73mm thickness. The other is the model with spread tow, which has 6.1mm width of a bundle and the thickness of the composites is 0.36mm. Numerical models of the damage states are also shown in Figs.3 and 4. To make clear the damage in the strand, the only strand parts are also indicated. The black parts represent the damaged elements judged by Hoffman’s criterion.

In case of the numerical model for non-spread tow, the initial damage of transverse cracks (Mode T&LT) appears at the center of a weft bundle. However, no cracks occur at the edge part as shown in Fig.3(a). After that, the damages propagate and the Mode ZL, which is the damage mode caused by shearing stress at the warp bundles, appears at the strain 1.25% in Fig.3(b).

On the other hand, numerical results for spread tow indicate that the initial failure appears at the center of a weft bundle as shown in Fig.4(a). The transverse cracks have developed in the edge parts of a weft bundle at the strain 1.25%, however, the Mode ZL doesn’t appear in the warp bundles. From these results, it is revealed that the location of occurrence and propagation of damages are quite different due to the effect of a spread tow.

Numerical results of relation between stress and strain are shown in Fig.5. The results show that a woven architecture for spread tow is high rigidity and strength as compared with the conventional one. It is difficult to detect the strain level of the initial failure by the experiments, the strain of initial damage can be also evaluated conveniently with the proposed numerical simulation.

Fig.3 Damaged states of woven FRP for non-spread tow

Tensile direction Mode T

Matrix crackMode T

Mode ZL

(a) ε = 0.66%

(b) ε = 1.25%

Tensile direction Mode T

Matrix crackMode T

Mode ZL

(a) ε = 0.66%

(b) ε = 1.25%

Fig.4 Damaged states of woven FRP for spread tow

Fig.5 Numerical results of stress-strain curves 3.3 An effect of fiber volume fraction in a spread tow on damage development

Numerical results of the damage development indicate what the initial damages (transverse cracks) have appeared at the center parts of a weft bundle with/without spread tow. We can guess that an effect of interfacial bonding force between a fiber and resin caused by the distribution of volume fraction inside a bundle is emerged. The center part of a weft bundle has high volume fraction, and the high volume fraction area induces the decrease of interfacial bonding force. Therefore, we propose a new woven architecture which has a low volume fraction in the center part of a fiber bundle. Figure 6 shows the distribution of the volume fraction for a fiber bundle as shown in Fig.2(b). Type (A) means the distribution of a specimen measured by the digital image processing and SEM as shown in Fig.2(a). Type (B)

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Strain (%)

Stre

ss (M

Pa)

Spread towNon-spread towOccurrence of initial damage

Tensile direction Mode T

Matrix crack Mode T

(a) ε = 0.58%

(b) ε = 1.25%

Tensile direction Mode T

Matrix crack Mode T

(a) ε = 0.58%

(b) ε = 1.25%

means the proposed distribution which the volume fraction for the center of a fiber bundle is low.

To estimate an effect of volume fraction inside a fiber bundle on the damage development, four numerical models with different thicknesses have been analyzed. Figure 7 shows the numerical results of the strain level when the initial failure (Mode T) generates. In case of the numerical model for spread tow (0.36mm thickness) with the proposed distribution type (B), the initial transverse cracks appear at the edge parts of the weft bundles. The strain of initial failure of type (B) is larger than that of type (A). The results have revealed that an effect of volume fraction inside a bundle can not be neglected for the estimation of damage development of woven fabric composites, and the control of the distribution of volume fraction in the bundle has a possibility of high rigidity and strength.

Fig.6 Volume fraction inside Fig.7 Relation between strain level of a fiber bundle an initial damage and thickness 3.4 Damage development inside laminate with three layers considering an effect of fiber volume fraction in a spread tow

Woven fabric laminate consist of a pile of woven layers impregnated with a resin. To

estimate the mechanical behaviors of woven fabric laminates with three layers, two types of numerical model with distributions of micro volume fractions in fiber bundles have been

Fig.8 Damaged states of woven FRP laminate for spread tow with distribution type (A) of volume fraction (ε=0.90%)

Matrix crack

Transverse crack(Mode T)

Tensile direction

Matrix crack

Transverse crack(Mode T)

Tensile direction

50

55

60

65

70

Vol

ume

frac

tion

(%)

a b c d e f

Distribution type (A)Distribution type (B)

0.2

0.4

0.6

0.8

0.4 0.5 0.6 0.7 0.8Strain (%)

Thic

knes

s (m

m)

Type (A)Type (B)

Fig.9 Damaged states of woven FRP laminate for spread tow with distribution type (B) of volume fraction (ε=0.93%)

prepared, and an effect of volume fraction in spread tow on the damage development has been analyzed. Figures 8 and 9 show the numerical results of damaged states under on-axis tensile load. In case of the laminate model with distribution type (A), the initial transverse cracks appear at the center of every weft bundles, and the matrix cracks appear at the surface of the laminate. On the other hand, the numerical model with distribution type (B) in Fig.9, transverse cracks have propagated zigzag to thickness direction, and the matrix cracks does not appear at the surface of the laminate. The applied strain when the initial damage occurs is larger than that of numerical model with distribution type (A). From these results, it is recognized that the control of the distribution of micro volume fraction in fiber bundles is effective to the produce of high-functional materials. 4. CONCLUDING REMARKS

The failure behaviors for woven fabric composites with/without spread tow under static tensile loading have been simulated with the developed computer program. The location of occurrence of damages is quite different due to the effect of a woven architecture. It is recognized that the damage development inside a lamina considering an effect of a spread tow which had been never observed in experiments can be predicted, and the strain of initial damage can be also evaluated conveniently by the proposed simulation. Therefore, the proposed numerical method is very useful for the estimation of mechanical properties of woven fabric composites with spread tow.

The numerical results show that an effect of the distribution of volume fraction inside a bundle can not be neglected for the estimation of damage development of woven fabric composites. In this paper, we propose a new woven architecture which has a low volume fraction in the center part of a fiber bundle. The numerical results derive that a woven architecture with the proposed distribution has good mechanical properties as compared with the conventional architectures. ACKNOWLEDGEMENTS

The part of simulation was supported by "The 21st Century COE Program in Japan (Project: Center of Excellence for Advanced Structural and Functional Materials Design)".

Tensile direction

Transverse crack(Mode T)

Tensile direction

Transverse crack(Mode T)

And the part of experiment was supported by Ministry of Education, Culture, Sports, Science and Technology (Grants-in-Aid for Scientific Research (B) No. 14350057).

We would like to express our thanks to Mr. Yoshihiko Hayashi (Graduated student of Osaka univ., JAPAN) for their cooperation. References

1. Zako, M., Uetsuji, Y., and Kurashiki, T., “Finite Element Analysis of Damaged Woven Fabric Composite Materials”, Composites Science and Technology, Vol.63, (2003), 507-516.

2. Zako, M., Takano, N., and Uetsuji, Y., “Prediction of Strength for Fibrous Composites based on Damage Mechanics”, Proc. 3rd international symposium TEXCOMP, (1996), 7/1-7/9.

3. Zako, M., Takano, N., Kurashiki, T., and Moriki, H., “Characterization of Low Cycle Fatigue for Woven Fabric Composites (Below the Freezing Point)”, 2nd Asian-Australasian Conference on Composite Materials (ACCM-2), (2000), 111-117.

4. Kurashiki, T., Zako, M., and Verpoest, I., “Damage Development of Woven Fabric Composites Considering an Effect of Mismatch of Lay-up”, 10th European Conference on Composite Materials (ECCM-10), (2002), CD-ROM