# Mathematical Model on Flexural Properties of Composite Laminates

DOI : 10.17577/IJERTV6IS060151

Text Only Version

#### Mathematical Model on Flexural Properties of Composite Laminates

Msc. Maja Mijajlovikj1, Ph D Svetlana Risteska2, Ph D Blagoja Samakoski2, math. eng. Natasha Stevanoska3

1Faculty of Technology, Goce Delcev University-Stip Macedonia 2Institute of Advanced Composites and Robotics-Prilep, Macedonia 3 SOU Riste Risteski-Ricko" Prilep, Macedonia

Abstract Aim of this study is to investigate the impact of number of layers, applied pressure and fiber direction on flexural properties of laminated composite materials. For that purpose, E-glass/epoxy resin prepreg has been fabricated and used in the production of laminated composite samples with help of press technology. Produced samples have been tested on three-point-bending test according to ASTM D790. In order to present the relationship between technological parameters of production and flexural behavior of manufactured samples, factorial design of experiment (DOE) 23 was used. With help of DOE influence of technological factors and their relationship on mechanical properties of manufactured samples was quantitative calculated. Received results shown that number of layers, applied pressure and fiber direction used to manufacture the samples significantly affect samples flexural strength. With help of scanning electron microscopy (SEM) analysis was used to analyze the gaps the interfacial behavior and breaking the fibers.

This study demonstrate technological parameters which lead to optimal flexural properties of laminated composite samples, where maximal flexural strength of 474,9 MPa was reached. According to them, fiber direction has direct influence on flexural behavior of manufactured samples, whereas number of layers and applied pressure performed similar effect.

Keywords: DOE, flexural strength, three point bending

1. INTRODUCTION

A composite laminate is a structural plate consisting of multiple layers of fiber reinforcement encased in cured resin. The number of layers, the type of fiber (carbon, glass, or other), the fabric configuration (e.g. woven, stitched mat, unidirectional), the type of resin, and other factors can be varied to design a structural element that is suitable for a particular need.

In [1] flexural tests on composite samples with two different thicknesses were conducted, where it was found that the increase in thickness decreases the flexural properties of manufactured samples, such as flexural strength and flexural modulus. Also, it was concluded that the load carry capacity of the specimen increases with increase of specimen thickness. Contrary to this, in [2] it is stated that slight increase in thickness is recommended in order to increase the flexural properties of composite samples. Similar results have been reported in [3-5], where it was reported that thickness can play a vital role in mechanical properties.

Lassila et al. [6] investigated the influence of position of fiber rich layer on flexural properties of fiber-reinforced

composite (FRC) construction. In [6] was found that specimens with FRC positioned on the compression side show flexural strength of approximately 250 MPa, while FRC positioned on the tension side show strength ranging from 500-600 MPa.

Influence of volume fraction on tensile and flexural strength of E-glass/epoxy laminated composites where studied in [7] were it is reported that volume fraction of 65:35 is optimal for composites tensile and flexural strength. The effect of different fiber volume fractions on flexural behavior at hybrid composites was reported in [8]. Flexural behavior of hybrid composites was investigated in [9-12].

Quasi-isotropic and unbalanced stacking sequences of carbon fiber/epoxy laminated structures were tested on three- point bending test, where it was stated that quasi-isotropic composite samples exhibit higher flexural stress and brittle behavior in comparison to unbalanced composite sample with flexural stress of around 780 MPa and progressive failure mode consisting of fiber failure, debonding and delamination [13].

Microstructure of voids and their influence on mechanical properties of composite samples have been studied in [14, 15]. In these studies it is reported that tensile strengths decrease with increase of void content and cracks emanate from voids when void content in manufactured samples is 8.0% – 9.0% after tensile strength test.

The aim of this research is to study the effects of fiber orientation, number of layers and applied pressure on flexural behavior on plain E-glass/epoxy composites. For that purpose three-point-bending test were performed on manufactured composite samples. With help of factorial design of experiment (DOE) the influence between technological parameters used in sample production was presented.

2. EASE OF USE

A. Specimen Preparation

In this study is used preimpregnated composite material (prepreg), which was produced on vertical impregnation machine manufactured by Mikrosam AD. For the production of prepreg material plain E-glass fabric EW300-2000mm by Sinoma Science and Technology Co., & Ltd was impregnated in a solution of brominated epoxy resin CHS-EPOXY B200 M80 by Spolchemie. In table 1 and table 2 are given the properties of used E-glass fabric and epoxy resin, whereas table 3 gives the properties of produced prepreg material.

Total of fifteen and twenty plies of manufactured E- glass/epoxy fabric prepreg with dimensions 700mm x 500mm were used in the production of composite laminates. The plies were stacked in press machine where final curing of the preforms was performed at constant temperature of 1450C and variable compressive pressure of 18 kg/cm2 and 14 kg/cm2. With help of machine five rectangular forms of MD direction and five rectangular forms of CD direction were cut from finished composite laminates according to ASTM D790 [16]. Dimensions and thickness of prepared specimens were measured with micrometer.

 Properties of E-glass fabric EW300-2000mm FAW (g/m2) 300 Width (mm) 2000 Thickness (mm) 0.3 Count warp (ends/cm) 8Â±1 Count fill (ends/cm) 7Â±1 Type plain

TABLE I. PROPERTIES OF E-GLASS FABRIC EW300-2000MM

Fig. 2. Three-point-bending test on universal testing machine.

C. Design Of Experiment (DOE)

To optimize the production process of laminated composite samples and quantitatively to determine the influence of production parameter: number of layers (X1), applied pressure (X2) and fiber orientation (X3), design of experiment (DOE) has been followed. DOE has been well known for its efficiency and allow gaining a maximum of information from a minimum amount of experiments.

TABLE II. PROPERTIES OF

EPOXY

RESIN

CHS-EPOXY B200 M80

For that aim factorial design of experiment with 23 permutations was used in the production of composite samples. Used technological parameters in two different levels with number of permutations 23 are presented in Table 4, whereas Table 5 represents manufacturing parameters of each laminated sample.

 Properties of epoxy resin CHS-EPOXY B200 M80 Colour gardner Epoxide equivalent weight (g/mol) 435-556 Epoxide index (mol/kg) 1,8-2,3 Hydrolizabe chlorine content (%) Max. 0,1 Non-volatile substances by 140oC for 2h (%) 78,5-81,5 Viscosity by 25oC (mPa.s) 1100-2300

 Symbol Parameters Parameter level 1 2 A (X1) Number of layers 15 20 B (X2) Pressure 14 kg/cm2 18 kg/cm2 C (X3) Direction of fiber CD MD

TABLE IV. LEVEL OF USED PARAMETERS

TABLE III. PROPERTIES OF MANUFACTURED PREPREG

 Properties of manufactured prepreg Volatile content (%) <2 Mass resin content (%) 30-35 PAW (g/m2) 428-455

B. Flexural Test

Flexural properties of manufactured samples were determined with help of three-point bending test in accordance with the procedure described in [16]. For that purpose computer controlled universal testing machine (UTM) Hydraulic press, SCHENCK- Hidrauls PSB with maximal load of 250 kN, constant crosshead speed of 5 mm/min and span-to-depth ratio of 16:1 was used. Load and displacement were recorded by an automatic data acquisition system for each sample. Minimum five reproducible tests were conducted for each sample at room temperature. Samples ready for testing are presented on Fig. 1, whereas three-point-bending test is given on Fig. 2

TABLE V. DESIGN OF EXPERIMENT (23) FOR LAMINATED SAMPLES

 Sample No X1 X2 X3 A B C 1 A1 B1 C1 15 14 CD 2 A2 B1 C1 20 14 CD 3 A1 B2 C1 15 18 CD 4 A2 B2 C1 20 18 CD 5 A1 B1 C2 15 14 MD 6 A2 B1 C2 20 14 MD 7 A1 B2 C2 15 18 MD 8 A2 B2 C2 20 18 MD

D. Fractographic Analysis

Fractured surfaces obtained from performed three-point- bending tests were examined at different magnification with help of scanning electron microscope (SEM) from Tescan type Vega3 in order to observe fracture behavior of laminated specimens.

Fig.1 Prepared composite samples ready for testing.

3. RESULTS AND DISSCUSSION

1. Flexural Strength

Manufactured composite samples were clamped and three-point-bending tests were performed. The tests were closely monitored and the load at which completed fracture of the specimen occurred has been accepted as breakage load.

Load-displacement curves were plotted for every sample and values for stress, strain and module of elasticity were calculated as average. The flexural stress (f) in the outer surface of the test specimens occurred at the midpoint. These stresses were determined from the relation [16]:

TABLE VI. RESULTS FROM FLEXURAL TESTING FOR EACH DESIGN

3FL

f 2bp

(1)

Where, f is the flexural stress (MPa), F is the load (N), L is the support span (mm), b is the width of the specimen (mm), and h is the thickness of the specimen (mm).

Flexural modulus of elasticity (Ef) and flexural strain (f) of the composite specimens were determinate using equations (2) and (3) [16]:

E f 3

L3m (2)

4bh

6sh

f L2

(3)

Where, m is the slope of the tangent to the initial straight- line portion of the load-deflection curve (N/mm) and s is maximum deflection of the center of the specimen (mm).

Received results from performed tests on laminated composite samples are given in table VI, where maximal flexural strength of 474,9 MPa for sample No8 and minimal flexural strength of 166,2 MPa for sample No3 can be observed. All technological parameters used in the production of sample No8 are at level 2. In comparison, specimen No3 had performed 65% lower flexural strength manufactured at highest pressure and level 1 of X1 and X3.

If comparison is made between three-point-bending results of samples manufactured with different number of layers and same technological parameters can be noticed an increase of up to 51% of flexural properties only by samples manufactured at X2 at leevl 2. Main cause for this result is the high percent of voids, up to 4,6% by samples manufactured with smaller pressure (table VII). Same effect can be concluded for the influence of pressure as technological parameter on flexural properties on laminated composite samples. In this case, the influence of voids can be neglected.

(Pressure at level 2 used in the production of laminated composite sample together with bigger number of layers leads to an increase in flexural properties of tested samples. In this case, the influence of voids can be neglected.)

Comparison between results of specimens manufactured at same technological parameters, but different fiber orientation can give a notice that all samples tested at MD direction had performed better flexural properties in comparison to the samples tested at CD direction. This means that fiber direction directly affects flexural properties of laminated composite samples up to 30%.

/tr>

 No Break force mean (N) Flex. (yexp.) (MPa) Flex. Mean (MPa) No Break force mean (N) Flex. (yexp.) (MPa) Flex. Mean (MPa) 1-1 325,97 5-1 427,15 1-2 296,29 5-2 470,72 1-3 704,24 330,99 317,74 5-3 970,2 477,51 454,65 1-4 326,27 5-4 450,34 1-5 309,23 5-5 447,55 2-1 317,23 6-1 323,77 2-2 215,31 6-2 256,93 2-3 960,4 254,08 272,62 6-3 1070 334,76 296,36 2-4 267,23 6-4 254,57 2-5 309,21 6-5 311,77 3-1 142,54 7-1 261,30 3-2 178,89 7-2 259,33 3-3 568,03 177,21 166,2 7-3 658,7 228,60 249,74 3-4 169,34 7-4 243,43 3-5 163,07 7-5 256,06 4-1 341,58 8-1 499,51 4-2 322,36 8-2 464,32 4-3 967,82 369,38 344,44 8-3 1404 460,86 474,90 4-4 340,11 8-4 469,93 4-4 348,78 8-5 479,87

Finally, average flexural strain at maximal stress has been estimated for each laminated sample (table VII). Calculated values are between 2,26% and 3,80%, whereas average module of elasticity had reached values between 4,41 GPa and 16.91 GPa for sample No 3 and sample No 8, respectively (table VII).

TABLE VII. DIMENSIONS OF THREE POUINT BENDING SPECIMENS

 No f average (MPa) f average (%) Ef Average (GPa) Void (%) No 1 317,74 2,87 11,40 1,6 No 2 272,62 2,85 9,74 / No 3 166,20 3,80 4,41 0,7 No 4 344,44 2,72 12,75 0,1 No 5 454,65 3,10 14,82 1,5 No 6 296,36 2,26 13,34 4,6 No 7 249,74 3,61 6,69 0,8 No 8 474,90 2,81 16,91 0,2

Fig. 3. Average flexural strength with number of layers, direction and pressure.

2. Design Of Experiment (DOE)

The results for flexural strength, dispersion and minimal value of parameters final coefficients for factorial design 23 in this research are shown in table 8. According to table 8, minimal calculated value of parameters final coefficients is 10,13. Parameters function and their interaction with 5% mistake are represented with (4).

Y=322,08+25X1-13,26 X2+46,83X3+75,85X1X2+20,01X1X2X3

(4)

From design 23 were calculated Cochran criteria (Gcal) with value 0.391 and Fisher criteria (Fcal) with value 0.4, which fulfill the rule Gcal < Gtab and Fcal < Ftab [17, 18]. According to this, the hypothesis for model 23 is acceptable with 5% mistake.

TABLE VIII. RESULTS FROM DESIGN OF EXPERIMENT (DOE)

 No yexp ycal Sy2 Sy2sum Sy2mid S2bi bi 1 317,75 319,35 212,14 4734,5 591,8 4,96 10,13 2 272,62 257,67 1746,46 3 166,21 181,15 215,42 4 344,45 342,83 288,76 5 454,65 453,03 401,54 6 296,36 311,31 1441,07 7 249,75 234,79 188,07 8 474,90 476,51 241,03
3. Scanning Electron Microscopy (SEM) Analysis

Scanning electron microscopy (SEM) analysis were performed in order impregnation quality of glass fibers into the epoxy resin during press process to be determined. In figure 4 are presented SEM analysis from already tested composite samples. However, voids with smaller dimensions can be observed on some places at samples manufactured with X2 at level 1, which can lead to reduction of mechanical properties of laminated samples.

Also, optical analysys were obtaied to characterize da fracture surface of laminated sample, where dominant faliure mode was compressing failure.

Fig. 4. SEM analysis of tested samples. a) Sample 6. 20c/14B-MD with void b ) Sample 8. 20c/18A-MD without void

Fig. 5. Optical analysis of tested samples.

4. CONCLUSION

From present study on flexural properties of laminated E- glass/epoxy resin composite samples can be concluded, that flexural strength and flexural modulus of elasticity increase in MD direction in comparison to CD direction. From these results, is concluded that fiber direction as production parameter influence directly on the flexural properties of laminated composite samples. Contrary, number of layers or more specific, thickness and applied pressure as technological parameters perform similar effect on flexural behaviour on laminated samples. Flexural properties of tested samples are increased when level 2 of parameters X1 and X2 are used, regardless fiber direction.

Performed factorial design of experiment quantitatively determined the influence of technological parameters and their interactions on flexural properties of laminated E- glass/epoxy resin composite samples. Calculated mistake in DOE is 5%.

Finally, sample manufactured with level 2 of all production parameters has shown best flexural properties with flexural strength of 474.90 MPa.

REFERENCES

1. B. V. Babukiran and Dr. G. Harish, Influence of resin and thickness of laminate on flexural properties of laminated composites, International Journal of Engineering Science and Innovative Technology (IJESIT) Vol. 3, Issue 1, January 2014.

2. G. Rathnakar and H. K. Shivanand, Effect of thickness on flexural properties of epoxy based glass fiber reinforced laminate, International Journal of Science and Technology, Vol. 2 No.6, June 2012.

3. G. Rathnakar and H. K. Shivanan, Experimental evaluation of strength and stiffness of fiber reinforced composites under flexural load, International Journal of Engineering and Innovative Technology (IJEIT), Vol. 2, Issue 7, January 2013.

4. S. Aarthy, R. Vadivambal, C. Sharmila, K. Gowri and J. Mathew, Experimental determination of flexural strength of glass fiber, Reinforced Composite Laminates, Vol. 3, Issue 02, May 2015.

5. M. Davallo, H. Pasdar and M. Mohseni, Effects of laminate thickness and ply-stacking sequence on the mechanical properties and failure mechanism of unidirectional glass-polyester composites, International Journal of ChemTech Research, Vol. 2, No.4, pp. 2118-2124, October- December 2010.

6. L. J. Lassila and P. K. Vallittu, The effect of fiber position and polymerization condition on the flexural properties of fiberreinforced composite, Journal of Contemp. Dent., Vol. 5, No. 2, May 2004.

7. Y. Basavaraj and H. Raghavendra, Experimental and numerical study of the influence of volume fraction ontensile and flexural strength of e- glass epoxy cross ply laminates, International Journal of Mechanical and Industrial Technology Vol. 2, Issue 1, pp. 39-44, April 2014 – September 2014.

8. C. Dong and I. J. Davies, Flexural strength of bidirectional hybrid epoxy composites reinforced by E glass and T700S carbon bres, Composites Part B: Engineering, Vol. 72, pp. 65-71, April 2015.

9. S. R. J. Bumpus, Experimental setup and testing of fiber reinforce composite structures, Master Thesis, Department of Mechanical Engineering, University of Victoria, 2005.

10. C. Dong and I. J. Davies, Flexural properties of hybrid composites reinforced by S-2 glass abd T700S carbon fibres, Composites Part B: Engineering, Vol. 43, Issue 2, pp. 573-581, 2012.

11. I. D. G. A. Subagia, L. D. Tijing, H. R. Pant and H. K. Shon, Effect of stacking sequence on the flexural properties of hibrid composites reinforced with carbon and basalt fibers, Composites Part B: Engineering, Vol. 58, pp. 251-258, 2014.

12. C. Dong and I. J. Davies, Flexural properties of glass and carbon fiber reinforced epoxy hybrid composites, J. Materials: Design and Applications, Vol. 227, Issue 4, pp. 308-317, 2013.

13. A. Azzam and W. Li, An experimental investigation on the three-point bending behavior of composite laminate, 2014 Global Conference on Polymer and Composite Materials (PCM 2014), 2014.

14. H. Zhu, B. Wu, D. Li, D. Zhang and Y. Chen, Influence of voids on the tensile performance of carbon/epoxy fabric laminates, J. Mater. Sci. Technol., Vol. 27, Issue 1, pp. 69-73, January 2011.

15. S. Risteska, B. Samakoski and M. Stefanovska, Properties of composite trapezoidal parts manufactured with help of filament winding technology using taguchi method, International Journal of Engineering Research & Technology (IJERT), Vol. 3 Issue 7, July 2014.

16. ASTM D790-15e2, Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials, ASTM International, West Conshohocken, PA, 2015, www.astm.org

17. . . and . . , , , 1980.

18. A. Dean and D. Voss, Design and analysis of experiments, Springer- Verlag New York, 1999.