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ICASE 2015 IST – Islamabad, Pakistan

1

Optimal Design of Laminated Composites

K. Hayat1,*, H. T. Ali2, X. Lei3, M.T. Hussain4, B. Batul4

1 Dept. of Mechanical Engineering, University of Lahore, 1-kM Raiwind Road Lahore, Pakistan

2 Dept. of Aerospace Eng., Queen's Building, University of Bristol, BS8 1TR, UK 3Dept. of Mechanical Engineering, Hanyang University, South Korea

4Satellite Research and Development Center, Lahore, Pakistan

Off-axis fiber angles of laminated composites of a wind turbine blade skin layup should be optimally selected so that a laminate can

exhibit adequate stiffness, strength, bend-twist coupling, buckling stability, and fatigue resistance. Keeping all above in view, a detailed

parametric study is conducted to determine the optimal ply-angles of a typical tri-axial (TX) skin laminate with conventional 45 degrees

off-axis fiber angle of the angled plies. Results show that lower angles (i.e. close to 0-degree) are more appropriate to achieve higher

stiffness, strength and fatigue resistance. The highest coupling magnitude can be achieved by generating ply-angle, ply-thickness and

ply-material based unbalances. Moreover, for enhanced buckling resistance, a higher off-axis fiber angle of plies close to 45 degrees is

more effective.

Index Terms— Laminated composites, In-plane loads, Parametric study

I. INTRODUCTION

Laminated fiber reinforced plastics (FRPs) composites are

widely used in advance engineering applications due to their

light weight and highly directional stiffness and strength

properties compared to the conventional metals counterparts.

One of typical applications is large-scale wind turbine blades

made of FRP composite used to achieve a lighter, stronger and

stiffer blade design.

The large-scale wind turbine blades capture more energy, and

offer a cost-effective and efficient solution. Traditional

composite design practices are restricted to use only symmetric

and balanced biaxial (BX:[±θ]S) and triaxial (TX:[02/±θ]s) composite laminates, with off-axis fiber angle θ of 45 degrees

in the skin layup of large-scale composite blades. For example,

the skin layup of a 5 MW wind turbine blade, of length 61.5 m,

mainly consists of TX:[02/±45]s laminate [1], hereafter

denoted as TX45. Since a wind turbine blade is a slender beam

structure, therefore, the off-axis fiber angle of 45 degrees of the

TX skin laminate is not an optimal selection.

Complicate blade geometry, huge number of plies in the

composite layup and the presence of a variety of loading

conditions, makes optimization of the laminated composites

laminates in the skin layup of the blade a daunting task. In

addition, it is difficult to simultaneously fulfill the design

requirements of adequate stiffness, strength, buckling stability

and fatigue resistance as specified by the wind turbine standards

[2, 3]. For this purpose, a preliminary parametric study of the

TX laminate of the blade skin layup is carried out in this paper.

The TX laminate is selected to perform the parametric study

because it is typically used in the skin layup of large-scale wind

turbine blades [1, 4].

A wind turbine blade can be considered as hollow beam

structure, consisting of thin skin layup that can be assumed to

be in plane-stress conditions. Thus, a TX:[02/±θ]s skin

laminate can be optimized using classical laminate theory

(CLT). This preliminary parametric study can provide a deep

insight to the optimization process of a complete skin layup of

the composite wind turbine blade structure. The results of

parametric study can also be extended to perform a multi-

objective optimization in which an optimal off-axis fiber angle

of TX:[02/±θ]s laminate can be found by simultaneously

evaluating the stiffness, strength, buckling stability and fatigue

design requirement.

II. THEORETICAL BACKGROUND

A wind turbine blade consists of two halves, represented by

pressure-side (PS) and suction-side (SS), which are connected

together with shear webs fitted between them, as shown in

Figure 1. The PS and SS layups are mainly made of TX external

and internal skin laminates. The BX skin laminate are used for

shear webs. There are unidirectional (UD) spar caps on both PS

and SS, to withstand the bending loads.

The outer aerodynamic shape of blade is maintained using TX

skin laminates and foam core construction. Foam core material

is used to enhance the buckling resistance. Traditional design

of a blade skin layup is to use TX laminate with 45 degrees

oriented off-axis angles. However, by finding an optimal off-

axis fiber angle of TX skin laminates, a lighter, stiffer and

stronger blade design can be achieved [1].

Figure 1. Typical composite skin layup construction of a wind turbine blade

[1].

The incident wind and other kind of loads generate tensile and

compressive regions on the blade PS and SS, respectively. Due

to thin skin layup of a wind turbine blade, the TX laminates on

PS and SS, can be assumed to experience a plan-stress

conditions (i.e. the out-of-plane stresses are assumed to be

zero), as shown in Figure 2. The TX laminates on the PS and

SS are subjected to combined in-plane tensile and shear stresses Corresponding author: *K. Hayat (e-mail: [email protected])


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and combined in-plane compressive and shear stresses,

respectively. Since, a wind turbine blade is a slender beam

structure, therefore, the effect of in-plane transverse stresses

can be ignored, due to their small magnitude.

Figure 2. Pressure-side (PS) and suction-side (SS) skin laminates under plane-

stress conditions.

A. Stiffness and Strength

Under plane-stress conditions, the relation between in-plane

stresses and in-plane strains for a UD ply oriented along the off-

axes 12, shown in Figure 3, are [5]:

[

σ1

σ2

σ6

] = [

Q̅11 Q̅12 Q̅16

Q̅12 Q̅22 Q̅26

Q̅16 Q̅26 Q̅66

] [

ϵ1

ϵ2

τ6

] Eq. 1

where Q̅ij are the elements of the off-axis stiffness matrix in

coordinate system12, oriented to the ply on-axis coordinate

system 1′2′ through angle θ.

Figure 3. Off-axis stiffness of unidirectional (UD) ply along axes 12.

A composite laminate consists of UD plies oriented in

difference directions. Under plane-stress condition, the in-plane

strains and in-plane stresses of a composite laminate with

orthotropic axes xy, as shown in Figure 4a, are related to each

other through ABD stiffness matrix, as [5];

[ σx

σy

σzτyz

τxz

τxy]

=

[ A11 A12 A16

A12 A22 A26

A16 A26 A66

B11 B12 B16

B12 B22 B26

B16 B26 B66

B11 B12 B16

B12 B22 B26

B16 B26 B66

D11 D12 D16

D12 D22 D26

D16 D26 D66]

[ ϵx

ϵy

ϵzγyz

γxz

γxy]

Eq. 2

Where the elements of ABD matrix in Eq. 2 are computed as:

Aij = ∫ Q̅ijdz, Bij = ∫ Q̅ijzdz, and Dij = ∫ Q̅ijz2dz,

respectively.

Apart from the laminate stiffness, the strength properties also

play a pivotal role in defining the intended use of the structure.

A frequently, ply-stress-based Tsai-Wu failure criterion, also

called quadratic failure criterion, is widely accepted by the

composite designers. According to Tsai-Wu failure criterion

[5]:

Fxxσx2 + Fyyσy

2 + Fssσs2 + 2Fxyσxσy + Fxσx

+ Fyσy = 1 Eq. 3

Where Fxx = 1

XX′ , Fyy =

1

YY′ , Fss =

1

SS′ , Fx = (

1

X−

1

X′), Fy =

(1

Y−

1

Y′), with X, X′, Y and Y′ representing the UD ply

longitudinal tensile, longitudinal compressive, transverse

tensile and transverse compressive strengths, respectively. The

symbol Fxy is an interaction parameter and is computed

as Fxy =1

2√XX′YY′ .

B. Buckling Resistance

One of the design requirements for a composite layup of a wind

turbine blade is to demonstrate adequate buckling stability. The

TX skin laminates on the blade SS are subjected to either

compressive load or combined compressive and shear loads. In

order to compute the critical buckling load, the panel bucking

theory is used. The theory is restricted to orthotropic

rectangular composite laminate with dimensions Lx and Ly and

simply supported on the edges. The theory is based on elastic,

thin plate, small deflection, CLT in which the rectangular

composite plate is considered to behave as a homogeneous

orthotropic material whose orthotropic axes xy are aligned with

the plate edges. The theory takes into account the axial

compressive and shear loads, governed by the D matrix defined

by CLT [5].

Figure 4. (a) Orthotropic plate, (b) in-plane compression load, (c) in-plane

shear load, and (d) combined in-plane compression and shear loads.

The plate subjected to in-plane compressive loads Nx and Ny

only, which do not vary with x and y directions, these internal

in-plane forces are related to loads λNx0 and λNy0, where λ is

the load parameter. For a buckled plate the load parameter is

denoted by λcr, and is determined by [5]:

(λcr)ij = π2 [D11 (i

Lx

)4

+ 2(D12 + 2D66) (i

Lx

)2

(j

Ly

)

2

+ D22 (j

Ly

)

4

]

/ [Nx0 (i

Lx

)2

+ Ny0 (j

Ly

)

2

]

Eq. 4

Where (λcr)ij must be computed for different set of i and j (i.e.

i, j = 1,2, … ). For simply supported orthotropic plates, the

lowest buckling load corresponds to a mode that has a half wave

in at least one direction.

On other hand, for an orthotropic plate subjected to pure shear

load, the critical buckling load Nxy0 ,cr can be estimated as [5]:

Nxy0 ,cr =

4β1

Lx2

√D11D2234

∶ 0 ≤ K ≤ 1 Eq. 5


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where β1 = 8.125 + 5.045K, K = (2D66 + D12) √D11D22⁄ .

Rx + Rxy1.9+0.1K = 1 Eq. 6

where Rx = Nx,cr Nx0,cr⁄ and Rxy = Nxy,cr Nxy

0 ,cr⁄ : with Nx,cr

representing critical compression when the in-plane

compression and shear are combined, Nx0,cr representing critical

compression when only in-plane compression is applied, Nxy,cr

representing critical shear load when in-plane compression and

shear loads are combined, and Nxy0 ,cr representing shear load

when only the in-plane shear load is applied.

C. Bend-twist Coupling

The life of wind turbine blades can be increased by reducing

the incident fluctuating loads with passive control that can be

realized by implanting bend-twist coupling (BTC) feature [6].

The BTC describes the dynamic interaction between the blade

bending and torsion deformations. Under the influence of

aerodynamic loads the blade twists as it bends, which causes a

change in the angle of attack, consequently, directly altering the

incident loads [7]. A desired BTC magnitude can be achieved

by effectively utilizing the anisotropic properties of the blade

composite skin layup, known as aero-elastic tailoring [8, 9].

The magnitude of BTC that can be achieved depends on the

amount of unbalance present in the skin layup of blade.

However, the conventional skin layup of a blade is made of

symmetric and balanced laminates. In order to achieve BTC of

the highest magnitude, there are three kinds of unbalances that

can be generated in a skin laminate. For example, the three

kinds of unbalances which are ply-angle, ply-material and ply-

thickness based unbalances, that can be developed in a BX

laminate are shown in Figure 5, where G and C represent glass

and carbon ply-materials, θ and ϕ represent ply-angles, and t1

and t2 represent ply-thicknesses.

Figure 5. Unbalance in a bi-axial laminate due to: (a) ply-angle, (b) ply-

material, and (c) ply-thickness based biasness, respectively, reproduced from [6].

The BTC magnitude due to unbalance in the TX laminate, can

be estimated in terms of a normalized parameter called BTC

interaction parameter α. For a laminate, the interaction

parameter can be computed as [10]:

α =D16

√D11 × D66

Eq. 7

where Dij is the term representing the laminate bending

stiffness matrix D that depends on the fiber orientation angle.

D. Fatigue Life

The fatigue life of a wind turbine blade is evaluated using the

SN-curves and the constant life diagram (CLD) [11-13]. The

SN-curves represent the fatigue life in terms of number of

fatigue cycles to failure Nf for an applied fatigue stress ratio R.

The stress ratio R is defined by Eq. 8, where σmin, σmax, σa and

σm represent minimum stress, maximum stress, mean stress and

stress amplitude, respectively. A CLD describes the

relationship between the mean and amplitude components of

fatigue stress ratio; and is made by combining the SN curves

measured or estimated at typical R ratios of 0.1 representing to

pure tension (T-T) loading, -1 representing for tension-

compression (T-C) for full-reversed loading and 10 for pure

compression (C-C) loading as recommend in [14]. The number

of cycles to failure is then extrapolated for other fatigue stress

ratios.

R =σmin

σmax

=σm − σa

σm + σa

Eq. 8

The wind turbine standard Germanischer-Lloyd (GL)

recommends a simplified approach to evaluate the fatigue life

using a linear CLD, shown in Eq. 9 and plotted in Figure 6. The

number of fatigue cycles to failure Nf for a combination of mean

and amplitude components of the fatigue stress ratio (σ1,m, σ1,a)

can be estimated as [15]:

Nf = [X + X′ − |2γMaσ1,m − X + X′|

2(γMb C1b⁄ )σ1,a

]

m

Eq. 9

where X and X’ represent tensile and compressive strengths of

the laminate, and γMa and γMb represent the partial safety

factors of strength and fatigue based analyses. The C1b

parameter (i.e. C1b = N1/m) defines the fatigue curve for

applied number of cycles N and slope parameter m. If no SN-

curve data is available, then, the value of m can be assumed to

be 9 and 10 for glass fiber reinforce plastics (GRP) with

polyester resin matrix and epoxy resin matrix, and 14 for carbon

fiber reinforced plastics (CRP) [15].

Figure 6. Linear constant life diagram (CLD) as per GL guidelines [15].

E. Material Properties

Table 1 lists the stiffness properties of Glass/Epoxy and

Carbon/Epoxy materials used. For the parametric study of

stiffness, buckling stability, BTC of the TX skin laminate, the

stiffness properties of Glass/Epoxy were used. The stiffness

properties of Carbon/Epoxy material were also used to generate

BTC, based on the ply-material based unbalanced, by replacing

the Glass fibers material with Carbon fibers material, as

discussed previously in Section II.C.

In order to perform the parametric study from the strength and

fatigue life of the TX skin laminate, the strength properties of

Glass/Epoxy UD ply are listed in

Table 2. It should be noted that the strengths of TX: [02/±θ] skin laminate at various off-axis fiber angle θ were derived

using Tsai-Wu failure criterion, represented by Eq. 3.


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Table 1. UD ply stiffness properties, reproduced from [6].

Type tPly

(mm)

Stiffness (GPa) Poisson

ratio Ex Ey Exy

Glass (E-glass) / Epoxy 1 43.2 12.6 4.2 0.28

Carbon (T300) / Epoxy 1 155 9 3.5 0.30

Table 2. Strength properties of UD Eglass/Epoxy ply, reproduced from [1].

Strength (MPa)

X X’ Y Y’ S

972 702 40 140 30

III. RESULTS AND DISCUSSION

Figure 7 shows the polar plot of the normalized stiffness

variation of TX:[02/±θ] skin laminate. The highest

longitudinal stiffness E1 occurs at 0 degree off-axis fiber

angle θ. The highest transverse and shear stiffnesses,

represented by E2 and G, occur at 90 degrees and 45 degrees

off-axis fiber angles, respectively. The conventional TX:[02/±45] laminate, although, it demonstrates the highest shear

stiffness, but the longitudinal and transverse stiffnesses are not

optimal for the 45 degrees off-axis fiber angle θ. Considering,

the beam-type structure of the wind turbine blade, the

longitudinal stiffness plays a key role in limiting the blade

bending deflection. Therefore, use of lower off-axis fiber angle

less than that of conventional 45 degrees off-axis fiber angle, is

more appropriate. For example, the use of 25 degrees off-axis

fiber angle increases the longitudinal stiffnesses by

approximately 30%, however, reduces the transverse and shear

stiffnesses by approximately 23% and 20%, respectively. For

slender blade, the transverse stiffness is of relatively less

significance. In addition, even though the reduction in the shear

stiffness occurs, but still, in many cases, is adequate for torsion

and buckling stability.

Figure 7. Polar plot representing normalized stiffness variation.

Figure 8 shows the variation in the normalized strengths of the

TX:[02/±θ] skin laminate. When the conventional off-axis

fiber angle θ of 45 degrees is reduced, there is a significant

increase in the tensile longitudinal and compressive

longitudinal strengths, represented by X and X′, respectively.

On the other hand, the tensile transverse, compressive

transverse and shear strengths, represented by Y, Y′ and S, are

least affected. For a decrease in the off-axis fiber angle from 45

degrees to 25 degrees, the increase in the tensile longitudinal

and compressive longitudinal strengths is approximately 104%

and 36%, respectively.

Figure 8. Normalized strength variation.

Figure 9 shows the buckling load factor variation for

TX:[02/±θ] laminate. In case of pure in-plane compressive

load, the 0 degree off-axis fiber angle shows better buckling

resistance; and it decreases with the decrease in off-axis fiber

angle. However, with the addition of a foam core material (i.e.

with thickness: 6% of total thickness) between the plies of TX

laminate the bucking resistance increases by 27% on average.

Figure 9. Buckling load factor variation for compression load.

Figure 10. Buckling load factor variation for combined compression and

shear load.

In case of combined in-plane compressive and shear loads, the

45 degrees off-axis fiber angle demonstrates the highest

buckling resistance, as shown in Figure 10. The buckling

resistance decreases with an increase in the contribution of in-

plane shear load. For an increase in the in-plane shear load of

10% and 20%, there is an average decrease in the buckling

resistance of approximately 0.17% and 0.30%, respectively.


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It has been pointed previously, in Section II.C, that the highest

magnitude of BTC that can be generated, depends on the

amount of unbalance present in the TX laminate. There can be

three kinds of unbalances, i.e. ply-angle, ply-thickness and ply-

material based, that can be implanted in a skin laminate. In

order to generate the unbalance types, the parameter θ

representing ply-angle unbalance, t representing ply-thickness

unbalance, and m representing ply-material unbalance, were

defined for the TX skin laminate, as shown in Figure 11. Based

on ply-angle unbalance only, it can be clearly seen that the off-

axis angle of approximately 27 degrees provided the highest

BTC value of 0.07. In addition, ply-thickness unbalance

achieved by increasing the thickness of – θ ply of TX laminate

from 0.25% to 0.375%, increases the value of BTC to

approximately 0.09. The ply-material unbalance was then

further added to TX laminate by replacing the Eglass/Epoxy

material with Carbon/Epoxy material. When all three kinds of

unbalances coexisted, then, the highest value BTC achieved

was 0.15. It should be noted that the highest value BTC means

that the higher load reductions are possible, as demonstrated in

[6].

Figure 11. Estimation of bend-twist coupling.

Figure 12. Estimation of fatigue SN-curve.

Figure 12 shows the fatigue SN curves plotted for TX: [02/±θ] laminate for typical fatigue stress ratios of: 0.1 representing

tension-tension fatigue load, -1 representing tension-

compression fatigue load, and 10 representing compression-

compression fatigue load. For all stress ratios, the number of

cycles to failure Nf increase with a decrease in the off-axis fiber

angle θ. For a decrease in the off-axis fiber angle from 45

degrees to 25 degrees, the number of cycles to failure increased

from 2.67×1012 to 1.90×1015 for stress ratio 0.1, from 3.16×1018

to 1.15×1021 for stress ratio -1, and from 1.05×1012 to 1.99×1014

for stress ratio 10. Consequently, increase in the fatigue life

occurred at lower off-axis fiber angle.

IV. CONCLUSIONS

The parametric study of TX skin laminate, typically used in the

skin layup of composite blade, demonstrates that the lower off-

axis fiber angles close to 0 degree are appropriate in achieving

higher stiffness, strength and fatigue life. From buckling

stability point of view, the presence of in-plane shear load

makes the 45 degrees off-axis fiber angle more favorable. For

implantation of special features like BTC, the use of 27 degrees

off-axis fiber angle, in addition to ply-thickness and ply-

material based unbalances, can be used to materialize the

highest BTC magnitude. In a similar manner, the parametric

study can also be extended to the conventional BX:[±45] skin

laminate, and optimal off-axis fiber angle 𝜃 can be selected

accordingly. Finally, it is suggested that the optimal angle for

off-axis plies of TX and BX skin laminates should be selected

by performing multi-objective optimization in order to achieve

a stiffer, stronger blade design, demonstrating higher buckling

stability and fatigue life, as well as possessing bend-twist

coupling.

V. ACKNOWLEDGMENT

The authors are thankful to the their colleagues Professor Dr.

Iqbal Hussain and Associate Professor Dr. Aamir Khan of

Mechanical Department at the University of Lahore, Main

campus, 1-kM Raiwind Road, Lahore, Pakistan, for their timely

help and support.

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