Tensile Properties Study of E-Glass/Epoxy Laminate … The usage of composites has increased in...

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429Polymers & Polymer Composites, Vol. 24, No. 6, 2016

Tensile Properties Study of E-Glass/Epoxy Laminate and π/4 Quasi-Isotropic E-Glass/Epoxy Laminate

1. IntroductIon

1.1 udF Glass/Epoxy udF LaminatesGlass/epoxy UDF laminates are used in various industries like aerospace, automotive and marine due to their appealing factors such as strength-to-weight ratio, fatigue properties and corrosion resistance. The laminates that are used in the above mentioned industries undergo a variety of loadings and damage. When the fibre-reinforced composites undergo damage, two kinds of approaches

are followed depending upon the severity of damage: 1. Replacing the damaged structure. 2. Repairing the damaged structure. Of these two, the former is a costlier process, and the latter is an economical one and needs more theoretical knowledge on materials, understanding of magnitude of loads at the local damaged zone and suitable repair practices. As this study would be a preliminary contribution towards optimum usage of π/4 quasi-isotropic E-glass/epoxy laminate repair practices, it is important to understand the material properties. Therefore, the

tensile properties of UDF E-Glass/epoxy laminate have been studied experimentally.

In order to understand the tensile properties of E-glass/epoxy laminate, many similar studies have been carried out and reported. Moreover, ASTM (American Society for Testing and Materials) described the standard test method for tensile properties of polymer matrix composite materials in the specification of ASTM D 3039/D3039M-001.

Though many databases are available on glass/epoxy UDF laminates, a few, which are mentioned in the references2-9, are reviewed for the present work. The references2-9 are


M. Gopalakrishnan1**, S. Muthu2, r. Subramanian3, r. Santhanakrishnan4, and L.M. Karthigeyan5

1E, R&D (Unit-51), Brakes India Private Limited, Padi, 600050, Chennai, India2Department of Mechanical Engineering, Dr. N.G.P. Institute of Technology, 641048, Coimbatore, India3Department of Metallurgical Engineering, PSG College of Technology, 641004, Coimbatore, India4Department of Aeronautical Engineering, Hindustan University, 603103, Chennai, India5Department of Mechanical Engineering, Hindustan University, 603103, Chennai, India

Received: 12 October 2014, Accepted: 2 October 2015

SUMMARYThe usage of composites has increased in various fields, including automotive and aerospace, due to their high strength-to-weight ratio. The optimum use of composite material is also being studied to bring down the fuel costs and carbon emissions to atmosphere. The concept of optimum usage of composite material could be applied at the initial design stage or when repairing damaged composite structures. This paper describes preliminary work towards the optimum usage of π/4 quasi-isotropic E-glass/epoxy laminate repair practices, and it demonstrates the procedure followed to determine their tensile properties. This work used unidirectional fibre (UDF) laminae and UDF laminate specimens to understand the tensile properties of UDF E-glass/epoxy laminate. This paper provides a unique comparison between experimental results of UDF laminae and UDF laminate level. The tensile properties obtained from UDF laminae and UDF laminate were suitably used to derive [A][B][D] matrices of π/4 quasi-isotropic laminates, so as to understand whether the laminates were pertaining to the quasi-isotropic category. Finally, π/4 quasi-isotropic laminates with the above-mentioned codes were tested to understand the tensile properties. The derived properties could be suitably used for future work on quasi-isotropic E-glass/epoxy composite laminate repair practices.

Keywords: Glass/Epoxy; E-Glass; Quasi-isotropic; Tensile; Composite

**Corresponding author, email: [email protected]

430 Polymers & Polymer Composites, Vol. 24, No. 6, 2016

M. Gopalakrishnan, S. Muthu, R. Subramanian, R. Santhanakrishnan, and L.M. Karthigeya

intentionally not detailed as they discuss proverbial points such as the contribution of tab types to tensile strength, tensile strength behaviour at low service temperatures, strain rate contribution to tensile strength and fracture surface, specimen size effect on tensile strength, response of glass-fibre-reinforced epoxy specimens to high rates of tensile loading, consequence of transverse compressive stresses on tensile rupture and influence of glass fibre-epoxy resin interface on static mechanical properties. These papers provided adequacy background to understand the tensile properties of UDF E-Glass/Epoxy at laminar level and laminate level, which is one of the objectives of this work.

1.2 Quasi-isotropic LaminatesThe word “quasi-isotropic” is used frequently in the domain of composite materials and aerospace industries. In this work, a “quasi-isotropic laminate” will be defined as one in which the fibre orientation and lay-up order of different laminas are such that they offer in-plane isotropic material behaviour. Coming to the notation of π/4, the fibre orientation of each lamina would be in the order of 45o

to form the quasi-isotropic laminate. Though some advanced methods of testing are available like the ultrasonic non-destructive method, in this work the elastic properties of quasi-isotropic laminate were measured using universal mechanical testing (UTM).

While designing aircraft structures, designers are very comfortable with isotropic materials like aluminium and titanium, because their strength and stiffness properties are similar in all directions. Moreover, the usage of UDF (Uni-Directional Fibre) reinforced laminates would offer better strength in the direction of the fibres than in the transverse direction. Hence, it is important to have composite laminate that offers isotropic properties at least in-plane.

It would enable the designer to have better control over delamination and crack propagation issues.

Prior to studying the tensile properties of quasi-isotropic E-Glass/Epoxy laminate, the following papers were reviewed. Douglas L et al.10 experimentally investigated how isotropic are quasi-isotropic laminates using basic ultrasonic equipment and recorded the observation of a variation up to 30% in the elastic modulus and Poisson’s ratio of the laminate. Fumiharu Namiki et al.11 studied the tensile behaviour of a quasi-isotropic carbon-carbon composite and recorded that the variation between the unloading and reloading modulus of elasticity was less than 3%. M. R. Wisnom et al.12 experimentally investigated the size effects in unnotched tensile strength of UDF and quasi-isotropic carbon/epoxy composites and deduced a noteworthy size effect, with a 14% fall in tensile strength. Sub-laminate level scaling augmented strength by 10% over a factor of 4 increase in size, whereas ply level scaled specimens showed a 62% fall in strength over a factor of 8 increase in size. J. Wang et al.13 made experimental and numerical investigation of the tension and compression strength of un-notched and notched quasi-isotropic laminates and summarised that for the quasi-isotropic laminates undergoing uniformly distributed tension or compression, rupture was visibly progressive. The progressive failure behaviour was simulated by accounting basic ply failure criteria and degraded material properties. Amar C. Garg14 experimentally investigated the fracture behaviour of quasi-isotropic graphite/epoxy laminate and inferred that the load related to the first pop-in and initial notch length may lead to a significant fracture toughness parameter. Alfredo Balaco de Morais15 revisited the open hole tensile strength of quasi-isotropic laminate code [0o/ 45o/90o]. In this work, the local strength-based

failure criterion was investigated to understand the failure of the above-mentioned laminate. This approach offers more significant correlation than the existing approaches that use characteristic distance, damage zone size, etc., and it does not correlate with experienced damage. Pengcheng Cheng et al . 16 experimentally investigated the tensile behaviour of patch-repaired quasi-isotropic CFRP laminates and showed that the failure progression in the parent base material depended on the arrangement of plies in the patch structure. Both in-plane stiffness and (to a lesser degree) ply stacking sequence influence the level of ultimate failure load and the damage mechanism.

With knowledge of the above-ment ioned papers and other references17-18, the experimental work of tensile testing on π/4 quasi-isotropic E-Glass/epoxy laminate was carried out, which was another objective of this paper.

1.3 Present Work1.3.1 Tensile Properties of UDF Laminae and LaminateTensile properties for this UDF laminae and laminate were determined using a conventional UTM. For this work, each five specimens of laminae and laminate were considered, with the size of 0.16x25x250 mm and 16x25x250 mm respectively. The observation of results variation was recorded.

Theoretically (Classical Lamination Theory), tensile properties at lamina or laminate level are similar. But they do not offer the same properties at lamina and laminate levels considering size effects5 and manufacturing variations. Hence an attempt was made to understand the results variation between them. The elastic moduli variation with different fibre orientations were also recorded, as this work dealt with two other different quasi-isotropic laminates with codes of [90/0/-45+45] and [0/45/90/-45 ]S.



1.3.2 [A][B][D] Matrix Calculation and VerificationAlthough the objective of this work was to understand the tensile properties of the quasi-isotropic laminates with the codes of [90/0/-45+45]and [0/45/90/-45]S, it was mandatory to understand whether the laminate codes met the quasi-isotropic laminate conditions theoretically. Hence firstly, transformed and reduced stiffness matrices for different fibre orientations were suitably derived for the above laminate codes, and finally, the [A][B][D] matrix was derived independently for those laminates.

1.3.3 Tensile Properties of Quasi-isotropic Laminates with Codes of [90/0/-45+45] and [0/45/90/-45]S

As was done for UDF lamina and laminate, the tensile properties for these π/4 quasi-isotropic laminates were also determined. It was planned that the laminate code of [0/45/90/-45]S would be used as parent material and laminate code of [90/0/-45+45] as patch (repair) material, in future work on π/4 quasi-isotropic E-glass/epoxy composite repair practices.

2. ExPERiMEnTAL WORk

2.1 Specimen Fabrication2.1.1 Constituent MaterialsA commercially available E-glass UDF and LY556 epoxy resin have been used to fabricate the laminae and laminates for this study, along with hardener HY 951. The resin-to-hardener ratio was maintained at 100:10.

2.1.2 Lay UpThough different layup procedures were available, specimens for this work were prepared using the wet layup method. The table surface was cleaned and applied with the wax as releasing agent. Subsequently, one coat of mixture of resin and hardener was applied in the above-mentioned ratio. Then, UDF layers were wetted one by one. Afterwards, the red film

was applied over the final lamina. This red film carries many minute holes through with the excess resin escapes and also offers a smooth surface finish to laminate. Finally, a surface mat was applied so as to absorb the excess resin in course of vacuum bagging.

2.1.3 Vacuum Bagging and CuringThe above set up was completely covered with polythene sheet and sealed around the wet laid laminas. On this set up, atmospheric pressure was maintained as 14.7 psi and the envelope pressure was 6 psi. The difference in pressure (8.7 psi) was used for clamping purposes. This state of clamping extended for 2 hours and then brought to normal cure for 12 hours. Finally, post cure was made for 2 hours at the temperature of 80 oC.

2.1.4 Specimen CuttingAfter the curing process, the laminates were sized as specimens with the dimensions of 25 mmx250 mm. This size was derived based on ASTM specification D 3039/D3039 M-00 and by considering the strain gauging feasibility. The specimen sizing process was accomplished using water jet cutting.

2.1.5 Specimen Preparation and TestThe objective of the study was to understand the tensile properties of two types of π/4 quasi-isotropic E-glass/epoxy composite laminates. In order to achieve this, four categories of specimens were prepared as follows: 1. UD Lamina; thickness 0.16 mm (0 deg - 05 Nos, 45 deg - 05 Nos and

90 deg - 05 Nos), 2. UD Laminate; thickness 1.6mm (0 deg - 07 Nos, 45 deg - 05 Nos and 90 deg - 05 Nos), 3. π/4 quasi-isotropic E-glass/epoxy composite laminate; thickness 1.6 mm - 07 Nos 4. π/4 quasi-isotropic E-glass/epoxy composite laminate; thickness 0.8 mm - 07 Nos. in total, 46 specimens were considered for this whole exercise.

All the above mentioned specimens were prepared with the dimensions shown in Figure 1. These dimensions were based on ASTM D 3039/D3039 M-00. The gripping length of all the specimens was roughened using T460 silicon carbide abrasive paper (# 80). Following this, the gripping area was cleaned using acetone. Two types of gripping materials were used in the course of end tabbing. 1. The same silicon carbide abrasive paper was used for lamina level and 2. Scratched aluminium sheet (2 mm) was used for laminate level. The combination of Araldite AW 106 and hardener HV 953 IN was used to bond the specimen and end tab material. The bonding materials were mixed in the ratio of 50:50 as per manufacturer’s instruction.

Tensile testing was done according to ASTM D 3039/D3039 M-00 “Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials”. This test determines the in-plane tensile properties of polymer matrix composites reinforced by high-modulus fibre. Tensile tests were performed using two types of Universal Testing Machines with wedge-type mechanical grips. The 5 KN & 100 KN INSTRON UTM machines were used

Figure 1. GFrP tension coupon dimensions



for lamina and laminate level testing respectively, so as to understand the tensile properties. These tests were performed with the test machines at a constant crosshead speed of 2 mm/min.

Strain gauging was done on the six specimens (T1 & T2) to study the Poisson’s ratio of 0o fibre orientation laminate. For this work, 10 KN UTM was used. On each specimen, two strain gauges (longitudinal and lateral) that were perpendicular to each other were used. Considering the tensile testing machine limitation, testing was done up to 7.5 KN. Though the load-carrying capability of specimen (UD 0o FIBRE ORIENTATION -1.6 mm thickness) was in the range of 20-23 kN, for Poisson’s ratio measurement, loading was done only up to 7.5 kN. Similarly, Poisson’s ratio measurement was done on the specimens T3, T4 (thickness=0.8 mm) and T5, T6 (thickness=1.6 mm) with the laminate codes [90/0/-45/45] and [0/45/90/-45]S respectively with suitable UTMs.

The micro strains were measured using foil type strain gauges (FLA-5-11) made by TML, Japan.

The complete strain gauging exercise was done using 16 channel MGC PLUS data acquisition system installed with CATMAN EASY 4.3.2 software.

2.1.6 Specimen Photographs

Table 1. Specimen identificationSL. no

Specimen identification

numbers

no of Specimens

Laminate code

no. of Layers

Width(mm)

thickness (mm)

1 1 - 5 5 [0] 1 25 0.162 11 - 15 5 [90] 1 25 0.163 21 - 25 5 [45] 1 25 0.164 31 - 35 5 [0]8 8 25 1.65 41 - 45 5 [90]8 8 25 1.66 51 - 55 5 [45]8 8 25 1.67 61 - 65 5 [0/45/90/-45]S 8 25 1.68 71 - 75 5 [90/0/-45/45] 4 25 0.89 T1 & T2 2 [0]8 8 25 1.610 T3 & T4 2 [90/0/-45/45] 4 25 0.811 T5 & T6 2 [0/45/90/-45]S 8 25 1.6

Figure 6. udF laminate (1.6 mm thick) with 90o fibre orientation


Figure 4. UDF lamina (0.16 mm thick) with 45o fibre orientation

Figure 3. udF lamina (0.16 mm thick) with 90o fibre orientation




2.2 Experimental data

Figure 9. Quasi-isotropic laminate [90/0/-45/45]; 0.8 mm thick

Figure 8. Quasi-isotropic laminate [0/45/90/-45]S; 1.6 mm thick


Figure 10. udF laminate with 0o fibre orientation (1.6 mm thick) - Strain gauge setup for Poisson’s ratio measurement

Figure 11. udF laminate with 0o fibre orientation (1.6 mm thick) - Strain gauge setup in utM for Poisson’s ratio measurement

table 2. tensile properties of udF laminae (0o fibre orientation)Sl. no

Property Symbol units E-Glass/Epoxy (Specimen identification) Mean Sd cV1 2 3 4 5

1 Fibre volume fraction Vf - 55% - - -2 Longitudinal elastic

modulusE1 MPa 32988 34099 31502 33713 33644 33189 916 0.028

3 Major Poisson’s ratio γ12 - 0.26 0.26 - -4 Shear modulus G12 MPa 6313 6313 - -5 Ultimate longitudinal

tensile strength(σ1

T) Ult MPa 689 751 763 775 738 743 30 0.040

6 Failure load P0 N 2850 3066 2873 3254 2940 2997 149 0.050



table 3. tensile properties of udF laminae (90o fibre orientation)Sl. no


1 Fibre volume fraction Vf - 55% - - -2 Transverse elastic modulus E2 MPa 7252 7367 6769 7398 6874 7132 260 0.0363 Minor Poisson’s ratio γ21 - 0.056 - - -4 Ultimate lateral tensile strength (σ1

T) ult MPa 23 25 23 22 21 23 1.33 0.0585 Failure load P 90 N 96 101 99 88 93 95 4.59 0.048

Table 4. Tensile properties of UDF laminae (45o fibre orientation)Sl. no


1 Fibre volume fraction Vf - 55% - - -2 Elastic modulus Ex MPa 13590 12087 13476 12225 12500 12776 634 0.0493 Ultimate tensile strength (σ1

T) ult MPa 69 61 78 67 68 69 5.46 0.0794 Failure load P 45 N 267 249 316 258 284 275 24 0.086

table 5. tensile properties of udF laminate (0o fibre orientation)Sl. no


1 Fibre volume fraction Vf - 55% - - -2 Longitudinal elastic modulus E1 MPa 35297 34570 31022 32180 32042 33032 1627 0.0493 Major Poisson’s ratio γ12 - 0.26 - - -4 Shear modulus G12 MPa 4396 4396 - -5 Ultimate longitudinal tensile

strength(σ1

T) ult MPa 890 876 730 850 760 821 64 0.078

6 Failure load P 0 N 24279 23801 27355 27294 21636 24873 2191 0.088

table 6. tensile properties of udF laminate (90o fibre orientation)Sl. no

Property Symbol units E-Glass/Epoxy (Specimen identification)

Mean Sd cV

41 42 43 44 451 Fibre volume fraction Vf - 55% -2 Transverse elastic modulus E2 MPa 7367 6833 7622 7053 7762 7327 346 0.0473 Minor Poisson’s ratio γ12 - 0.056 - - -4 Ultimate longitudinal tensile

strength(σ1

T) ult MPa 28 30 25 29 24 27 2.32 0.085

5 Failure load P 90 N 1190 1191 1121 1165 907 1115 107 0.095

Table 7. Tensile properties of UDF laminate (45o fibre orientation)Sl. no Property Symbol units E-Glass/Epoxy (Specimen identification) Mean Sd cV

51 52 53 54 551 Fibre volume fraction Vf - 55% - - -2 Elastic modulus Ex MPa 10725 9602 10682 10730 11101 10568 506 0.0483 Ultimate tensile strength (σ1

T) ult MPa 60 65 60 61 67 63 3 0.0454 Failure load P 45 N 2540 2991 2700 2450 3130 2762 260 0.094



Table 8. Comparison between tensile properties of UDF laminae & laminateSl. no. Property Symbol units “0” Degree fibre orientation

Lamina Laminate1 Fibre Volume Fraction Vf - 55% 55%2 Elastic Modulus E1 MPa 33189 330323 Elastic Modulus E2 7132 73274 Poisson’s Ratio γ12 - 0.265 Poisson’s Ratio γ21 - 0.0566 Shear Modulus G12 MPa 6313 43967 Ultimate Tensile Strength (σ1

T) ult MPa 743 8218 Failure Load P N 2997 24873

Table 9. Tensile properties of π/4 quasi-isotropic laminate [0/45/90/-45 ]s ; 1.6 mm; 8 layersSl. no.


1 Fibre volume fraction Vf - 55% - - -2 Longitudinal elastic modulus E1 MPa 17697 18163 17906 18208 18024 18000 185 0.0103 Major Poisson’s ratio γ12 - 0.242 - - -4 Shear modulus G12 MPa 7124 7312 7209 7330 7256 7246 125 0.0105 Ultimate longitudinal tensile

strength(σ1

T) ult MPa 165 190 182 198 169 181 12.4 0.069

6 Failure load P N 7395 7775 7735 7952 7666 7706 181 0.023

Table 10. Tensile properties of π/4 quasi-isotropic laminate [90/0/-45+45]; 0.8 mm; 4 layersSl. no


1 Fibre volume fraction Vf - 55% - - -2 Longitudinal elastic modulus E1 MPa 17804 18140 17425 17865 18133 17873 262 0.0153 Major Poisson’s ratio γ12 - 0.242 0.242 - -4 Shear modulus G12 MPa 7167 7303 7015 7192 7300 7195 106 0.0155 Ultimate longitudinal tensile

strength(σ1

T) ult MPa 150 142 151 160 149 150 5.75 0.038

6 Failure load P N 2951 2817 3096 3253 3004 3024 146 0.048

Table 11. Comparison between tensile properties of quasi-isotropic laminates of [0/45/90/-45 ]s and [90/0/-45+45]Sl. no.

Property Symbol units Quasi-isotropic Laminates[0/45/90/-45 ]S [90/0/-45+45]

1 Fibre Volume Fraction Vf - 55% 55%2 Elastic Modulus E MPa 18000 178733 Poisson’s Ratio γ12 - 0.2424 Shear Modulus G12 MPa 7246 71955 Ultimate Tensile Strength (σ1

T) ult MPa 181 1506 Failure Load P N 7706 3024



2.2.1 Shear Modulus CalculationThe shear modulus values in the above tables were derived through the following modulus transformation relation. All the components in the following relation were determined through experimental work, except the shear modulus:

(1)

The only unknown in the above equation is G12, hence:

(2)

2.2.2 Poisson’s Ratio CalculationPoisson’s ratio in the fibre direction (on T1 and T2) was determined through the experimental work exhibited in Figures 10 and 11. But, Poisson’s ratio in the direction perpendicular to the fibre was determined using the following reciprocal relation:

(3)

Figures 20-25 show the Poisson’s ratio measurement on the specimens T1, T2, T3, T4, T5 & T6. This exercise was carried out on the UDF laminates and π/4 quasi-isotropic laminates with the codes of [90/0/-45/45] and [0/45/90/-45]S. The strain gauging exercise was not done on the laminae due to handling difficulties and strain gauge attachment complications on the laminae.

2.3 Stress-Strain diagrams of tested Specimens2.3.1 Elastic Constants Variation with Different Angle of LaminasAs the elastic constants of UDF laminae have been derived already, it is important to understand how they vary with different angles of fibre orientation. Following table 12 and Figures 26-31 throw clear picture of it.

Figure 12. Stress - Strain curves 1-5 udF lamina 0o; Thickness = 0.16 mm

Figure 13. Stress - Strain curves 11-15 udF lamina 90o ; Thickness = 0.16 mm

Figure 14. Stress - Strain curves 21-25 UDF lamina 45o; Thickness = 0.16 mm

Figure 15. Stress - Strain curves 31-35 udF laminate 0o; 1.6 mm



Figure 16. Stress - Strain curves 41-45 UDF laminate 90o; 1.6 mm

Figure 17. Stress - Strain curves 51-55 UDF laminate 45o; 1.6 mm

Figure 18. Stress - Strain curves 61-65 Qi laminate [0/45/90/-45]S; 1.6 mm

Figure 19. Stress - Strain curves 71-75 Qi laminate [90/0/-45/45]; 0.8 mm

Figure 20. Poisson’s ratio - Specimen t1 udF laminate 0o; 1.6 mm

Figure 21. Poisson’s ratio - Specimen t2 udF laminate 0o; 1.6 mm



Figure 22. Poisson’s ratio - Specimen T3 Qi laminate [90/0/-45/45]; 0.8 mm

Figure 23. Poisson’s ratio - Specimen T4 Qi laminate [90/0/-45/45]; 0.8 mm

Figure 24. Poisson’s ratio - Specimen T5 Qi laminate [0/45/90/-45]S; 1.6 mm

Figure 25. Poisson’s ratio - Specimen T6 Qi laminate [0/45/90/-45]S; 1.6 mm

Figure 26. Elastic modulus E1 as a function of angle of lamina for a glass/epoxy lamina

Figure 27. Elastic modulus E2 as a function of angle of lamina for a glass/epoxy lamina



table 12 and Figures 26-31 show how the elastic constants varied with different angles of lamina. From the above table and figures, one can understand that E1 & E2 are inversed to each other. The value of E1 reaches maximum and minimum at θ = 0o and θ = 90o respectively, and vice versa for E2. The observed shear modulus was a maximum at θ = 45o. The maximum values of shear coupling coefficients m1 and m2 were observed at θ = 35o and θ = 55o respectively. The concept of shear coupling is absent in isotropic materials and UDF laminas, whereas it cannot be avoided in angled laminas.

2.3.2 [A] [B] [D] MATRIX for Laminate Code [90/0/-45+45]; 0.8 mm; 4 LayersAs the tensile properties of UDF laminae was derived already, it is possible to derive the tensile properties of a quasi-isotropic laminate. Prior to

this, it is important to understand whether the above said laminate code meets the quasi-isotropic laminate condition. The following equation represents the physical significance of the isotropic stress-strain relations:

(4)

The square matrix in the following equation represents the [A][B][D] matrix of the laminate. A laminate is said to be quasi-isotropic if its extensional stiffness

table 12. Elastic constants response for different angles of laminaeSl. no Angle of

Lamina (deg)

Elastic constants Shear coupling coefficients

E1(MPa)

E2(MPa)

γ12 G12(MPa)

m1 m2

1 0 33032 7327 0.26 4396 0.00 0.002 15 24876 7566 0.27 4625 1.20 0.563 30 15323 8449 0.25 5161 1.84 1.204 45 10568 10568 0.20 5480 1.75 1.755 60 8449 15323 0.14 5161 1.20 1.846 75 7566 24876 0.08 4625 0.56 1.207 90 7327 33032 0.06 4396 0.00 0.00

Figure 28. Poisson’s ratio γ12 as a function of angle of lamina for a glass/epoxy lamina

Figure 29. In-plane Shear modulus G12 as a function of angle of lamina for a glass/epoxy lamina



matrix [A] acts like that of an isotropic material. So, A11=A22, A16=A26=0 and A66=(A11-A12)/2. The reason behind the terminology quasi-isotropic is that other stiffness matrices [B] and [D] may not behave as isotropic material:

(5)

Transformed reduced stiffness matrix for the laminate code [90/0/-45/45 ] for each of the four plies is:

The extensional stiffness matrix [A] is:

(6)

The coupling stiffness matrix [B] is:

(7)

The bending stiffness matrix [D] is:

(8)



The assembled [A][B][D] matrix for the laminate code [90/0/-45/45 ] is as follows:

From the above square matrix, one can understand that the assumed laminate code [90/0/-45/45]; 0.8 mm; 4 layers; is quasi-isotropic as it meets the required conditions (A11=A22, A16=A26=0 and A66 = (A11- A12)/2). As this laminate is quasi-isotropic, it will be used in future work as a patch material for repairing the damaged symmetric quasi-isotropic laminate (parent material). A thickness of 0.2 mm is assumed for each layer to perform the above [A][B][D] calculation.

2.3.3 [A] [B] [D] MATRIX for Laminate Code [0/45/90/-45]S; 1.6 mm; 8 LayersThe same transformed reduced stiffness matrix that was derived for the laminate code [90/0/-45/45 ]; 0.8 mm; 4 layers; could be used to derive the [A][B][D] matrix for this laminate code as well.

The extensional stiffness matrix [A] is:

The coupling stiffness matrix [B] is:

The bending stiffness matrix [D] is:

The assembled [A][B][D] matrix for the laminate code [0/45/90/-45 ]S is as follows:



From the above square matrix, one can understand that the assumed laminate code [0/45/90/-45 ]S is symmetric quasi-isotropic as it meets the required conditions (A11=A22, A16=A26=0, A66 = (A11- A12)/2 and [B] = 0). Hence it was decided to use it in the future work as a parent material to understand the composite repair practices.

The [A][B][D] matrix calculations performed on laminate codes [90/0/-45/45] and [0/45/90/-45]S were to understand whether the considered layup sequence would meet the quasi-isotropic laminate conditions.



Figure 34. UDF lamina (0.16 mm thick) with 45o fibre orientation



Figure 37. udF laminate (1.6 mm thick) with 45o fibre orientation3. RESULTS AnD DiSCUSSiOn

3.1 Failure Photographs

Figure 38. Quasi-isotropic laminate (1.6 mm thick - "A" side)



3.1.1 Stress-Strain Curves (UDF Laminae and Laminate)Most of the stress-strain curves (Figures 12-17) on the laminae and laminates exhibit perfectly linear behaviour in the initial portion and show slightly non-linear behaviour in the later portion (near ultimate tensile strength). Based on the above observations, one could understand this. All the tensile testing was carried out in the room temperature of 25 oC. All the elastic constants that were calculated from the stress-strain curves were taken in the micro strain range of 1000-3000.

3.1.2 Stress-Strain Curves of π/4 Quasi-Isotropic Laminates [0/45/90/-45]S and [90/0/-45/45 ]Stress-strain curves (Figures 18 and 19) on these laminates also exhibited perfectly linear behaviour in the initial portion and show slighly non-linear behaviour in the later portion (near ultimate tensile strength). As the above-said laminate codes are quasi-isotropic, the impact of progressive failure was expected in the stress-strain curves, but it was not present in Figures 18 and 19. This pattern of stress-strain curves is in line with the points that recorded in the technical paper12. That is to say load drop behaviours were not observed due to weaker ply failure and delamination prior to ultimate failure.

3.1.3 Poisson’s Ratio CurvesMicro strain variation in the longitudinal and lateral directions with tensile load is recorded in these curves (Figures 20-25). As the objective is to understand only the Poisson’s ratio (elastic constant) tests were not extended till failure. All the tests were stopped in the range of 40-50% of its tensile load carrying capacity. The initial portions of the curves exhibit the marginal non-linear behaviour, and the later portion shows the perfectly linear behaviour.

3.1.4 Elastic Constants Variation With Different Angle of LaminaElastic constants variation with different angle of laminae is plotted for better understanding. All the elastic constants exhibit non-linear variation with different angles of lamina. The Poisson’s ratio and shear modulus exhibit the bell curve pattern of variation with different angles of laminae (refer to Figures 28 and 29). Shear coupling coefficients show the parabolic variation with different angles of laminae (refer to Figures 30 and 31).

3.1.5 0o UDF Laminae and Laminate Failure (Fibre Direction is Parallel to Loading Direction)From the naked eye inspection, according to Figures 32 and 35, the failure zone carries fibre rupture and longitudinal matrix cracking. These two failure behaviours were observed all along the gauge length. End tab failures like tab slippage due to improper adhesion between tab and specimen and specimen failure within end tab were not observed. Fibre and fibre-matrix interface offers resistance to this type of failure. This failure has both longitudinal and lateral fractured surfaces.

3.1.6 90o UDF Lamina and Laminate Failure (Fibre Direction is Perpendicular to Loading Direction)According to Figures 33 and 36, the failure zone has perfect matrix failure. This failure behaviour is observed within the whole gauge length. Matrix only offers resistance to this type of failure. The complete fractured surface is perpendicular to the loading direction.

3.1.7 45o UDF Lamina and Laminate Failure (Fibre Direction is at 45o to Loading Direction)According to Figure 34 (lamina level test), the failure zone appears to have perfect matrix failure, but that is not so.

Figure 40. Quasi-isotropic laminate (0.8 mm thick – “A” side)

Figure 41. Quasi-isotropic laminate (0.8 mm thick – “B” side)

Figure 39. Quasi-isotropic laminate (1.6 mm thick - "B" side)



In fact it is fibre-matrix interface failure, as can be understood from Figure 37 (laminate level test). The failure observed in Figure 37 is different from that observed in Figure 34. The partial connection between fibre and matrix can be seen in Figure 37 unlike the situation in Figure 34. This means that Fibre-Matrix interface offers resistance to this type of failure. Such failure behaviour is well observed within the gauge length. Here, the complete fractured surface is parallel to the fibre direction. i.e. at 45o. Hence, specimen preparation with more than one ply helps to understand the type of failure better.

3.1.8 π/4 Quasi-Isotropic Laminates [0/45/90/-45]S and [90/0/-45/45 ] FailureAs per Figures 38, 39, 40 and 41, the failure zone shows fibre rupture and delamination. Progressive damage that occurred in the above mentioned laminate codes has resulted in this kind of failure. Lamina level failure criterion helps to understand the damage and failure of this kind of quasi-isotropic laminate. For uniaxial tensile loading, the individual lamina failure patterns in these laminate codes were as follows, Firstly, 90o lamina matrix failure, then,

45o lamina matrix failure and then finally, 0o lamina fibre rupture. But in this work, the failure was observed catastrophically. This kind of failure pattern was reported in another paper12. In that particular paper, the impact of progressive failure was noticeable in the stress-strain curves, only after scaling the specimens at ply level.

4. COnCLUSiOnS

In this work, the tensile properties of E-Glass/epoxy UD laminae, UD laminates, π/4 quasi-isotropic laminates and π/4 quasi-isotropic symmetric laminates at room temperature (25 oC) were studied. The consolidated results were recorded and compared. The UD lamina is a simple model to fabricate the composite structures, which are

built using several plies arranged at different angles. So the results of the present study can be used as input data for future work on E-Glass/epoxy composite repair practice.

The stress-strain curves in this study show perfect linear behaviour in the initial portion and significantly nonlinear behaviour in the later portion (near ultimate tensile strength).

Insignificant variations were observed in the determined tensile properties between UD laminae (single layer) and UD laminate (8 layers) except for the failure load. But, in order to understand the failure type, specimens that were prepared with more than one ply would offer better clarity. Hence, while studying the tensile properties of UD laminae, it is recommended to use more than 2 layers as the single layer lamina specimens demand vigilant fabrication, careful handling and better experience to infer something from the results.

Also, the elastic constant variations with different angles of the laminae were studied, based on theoretical calculations. E1 and E2 variation with angle of lamina oppose each other. The value of E1 is observed as maximum and minimum at θ = 0o and θ = 90o respectively, and vice versa for E2. The shear modulus was observed to be a maximum at θ = 45o. The maximum values of shear coupling coefficients m1 and m2 were observed at θ = 35o and θ = 55o respectively. The values of m1 and m2 were observed as zero at θ = 0o and θ = 90o.

The concept of quasi-isotropy is proved for laminate codes [90/0/-45/45] and [0/45/90/-45]S through [A][B][D] matrix.

The impact of progressive failure was not observed in either the π/4 quasi-isotropic laminate codes [90/0/-45/45 ] or [0/45/90/-45 ]S . It is in line with the technical paper14. These laminate

codes might need ply level scaling to observe the same in the stress strain curves.

The concept of “quasi-isotropic” laminate offers the advantage of in-plane isotropy and the drawback of reduced tensile strength when comparing to UDF laminate.

Insignificant variations were observed on the tensile properties that were arrived at between π/4 quasi-isotropic laminate (4 layers) and π/4 quasi-isotropic symmetric laminate (8 layers) except the failure load. According to the present work, the quasi-isotropic laminate has approximately 1/5th of the strength of UDF laminate.

FuturE ScoPE oF WorK

The tensile properties of E-glass/Epoxy at laminar level, laminate level, π/4 quasi-isotropic laminate, π/4 quasi-isotropic symmetric laminates can be suitably used in the future work of FEA simulation of π/4 quasi-isotropic E-glass-epoxy composite repair practices.

rEFErEncES1. ASTM D 3039/D3039M-00.

Standard test method for tensile properties of polymer matrix composite materials.

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8. Michael R. Wisnom, Composite Structures, 32 (1995), 621.

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11. Fumiharu Namiki and Tsu-Wei Chou, Journal of the American Ceramic Society, 81 (1998), 113.

12. M. R. Wisnom, B. Khan, S. R. Hallet, Composite Structures, 84 (2008), 21.

13. J. Wang, P. J. Callus, M. K. Bannister, Composite Structures, 64 (2004), 297.

14. Amar C. Garg, Engineering Fracture Mechanics, 23 (1986), 929.

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nOMEnCLATURE

UDF Uni-Directional FibreASTM American Society for Testing and MaterialsUTM Universal Testing Machine[A] Extensional stiffness matrixAij Extensional stiffness coefficient[B] Coupling stiffness matrixBij Coupling stiffness coefficient[D] Bending stiffness matrixDij Bending stiffness coefficient[] Transformed reduced stiffness matrixSij Compliance coefficienthk Height of lamina surface from reference mid planeσ Normal stressτ Shear stress𝝴 Normal strainγ Shear Straink Mid-plane curvatureN Newton (unit), Normal force, Shear forceM Bending moment, Twisting momentX MeanSD Standard DeviationCV Coefficient of variationmm Millimetre (unit)GPa Giga Pascal (unit)MPa Mega Pascal (unit)

Tensile Properties Study of E-Glass/Epoxy Laminate … The usage of composites has increased in...

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