TECHNICAL PAPER

Fuzzy logic model for the prediction failure analysis of compositeplates under various cure temperatures

Tamer Ozben • Mesut Huseyinoglu •

Nurettin Arslan

Received: 20 October 2011 / Accepted: 23 January 2013 / Published online: 23 September 2013

� The Brazilian Society of Mechanical Sciences and Engineering 2013

Abstract In this study, stress values were examined in

pin/bolt connected composite plates which were applied

preload and non-preload moment. Composite plates were

produced with different curing cycles and geometric

dimensions. Failure analysis of composite plates was car-

ried out by applying different preload moments. The results

obtained from experimental study were processed using

fuzzy model. The results of experiments and fuzzy model

were presented as a comparative. As a result of the com-

parison, it can be said that the initial stress values of failure

were approximately determined using fuzzy model.

Keywords Fuzzy systems � Matrix composite �Failure � Curing

1 Introduction

Composites produced using different curing temperatures

and periods have different failure behaviors. Prediction of

failure behavior is very important to understand what kind of

failure will occur. Various numerical modeling techniques

are used to predict failure, but the numerical model applied

must be compatible with the experimental results. Many

studies regarding this subject have been performed and

published. Oh et al. [1] investigated the effects of fiber ori-

entation, layer orientation, fiber volume ratio, washer outer

diameter and linking pressure on the bearing damage bolted

connections of the glass–epoxy and carbon-epoxy hybrid

composite plates. Iarve [2] presented analytical solution

using spline approach and the Lagrangian multiplier method

for the three-dimensional contact problem describing the

interaction between a circular hole on the composite plate

having [-45�/90�/45�/0�]s layer orientation with titanium

pin. Persson et al. [3] used finite element method to deter-

mine three dimensional stress fields for the pin connected

composite plates and verified with experimental results.

They used acoustic emission technique to determine initial

failure load of the samples. Xu et al. [4] investigated stress

distribution of multi-linked composite plates using finite

element method based on classical plate theory. They

showed that the stress distribution around holes depends on

fiber orientation of composite plate and geometry of the

connection. Yan et al. [5] presented an experimental study

that investigates the effect of fiber orientation, geometry of

connection, size of washer, washer force and friction on

tensile damage of graphite-epoxy composite. Lie et al. [6]

developed finite element model for the connection strength,

failure loads and behaviors. They showed that the proposed

model is compatible with the experimental results. Karakuzu

et al. [7] showed that damage by tensile strength of com-

posite samples, links, and identified forms of damage in

plates and composite connection behavior are affected by the

geometrical parameters. Aktas and Dirikolu [8] investigated

experimental and numerical analysis of connection strength

of pin connected carbon-epoxy composite plates having [0�/

45�/-45�/90�]s and [90�/45�/-45�/0�]s layer orientation.

Technical Editor: Lavinia Borges.

T. Ozben (&) � M. Huseyinoglu

Mechanical Engineering Department, Dicle University,

21280 Diyarbakir, Turkey

e-mail: tamoz@dicle.edu.tr

M. Huseyinoglu

e-mail: mesuth@dicle.edu.tr

N. Arslan

Mechanical Engineering Department, Balikesir University,

10100 Balikesir, Turkey

e-mail: narslan@balikesir.edu.tr

123

J Braz. Soc. Mech. Sci. Eng. (2014) 36:443–448

DOI 10.1007/s40430-013-0096-9

They estimated the damage of composite samples using

ANSYS package software for the numerical analysis and

reported that numerical results are close to experimental

results. Kelly [9] estimated stress distribution around the

hole, behavior of the connection and connection load transfer

with the ABAQUS finite element package software. Ana-

lysis of the mechanical strength of engineering structures

using fuzzy logic method began in the 1980s [10]. Uy-

gunoglu and Unal [11] suggested that the internal structure of

complex materials such as fly ash is to develop a model for

the calculation of strength, and proposed that fuzzy logic

model will save time, reduce wastage of material and reduce

the design cost. Fuzzy logic and artificial neural networks are

used in high-performance engineering applications and

determining the damages of the connection elements [12–

14]. Modeling the behavior of materials, control of the pro-

duction process and optimization are accomplished by fuzzy

logic model [15–18].

Numerical modeling is very important for the product

quality and development of production in the designing

process. The main objective of this study is to demonstrate

the effectively used fuzzy logic model for the failure

analysis.

2 Production of composite plates and experimental

study

Fiber-reinforced composite plates were manufactured at

the Mechanical Engineering Laboratory of the Balikesir

University Engineering and Architecture Faculty. Com-

posite plates using fiberglass as a reinforcement element

are obtained from Fibroteks Industry and Commerce, and

polyester resin using as a matrix element obtained from

Camelyaf Incorporated Company. Cobalt accelerator (1 %)

is used in the preparation of the matrix material. Hardener

MEK-peroxide (Methyl Ethyl Ketone peroxide), Poliya

Polivaks using rub on the mold and Poliya Polivaks EKO

PVA liquid mold release materials are provided from

Poliya Polyester and Auxiliaries. The mechanical proper-

ties of glass fiber-epoxy laminated composite material were

determined with the computer-controlled Instron 1114

tensile device and indicator at Mechanical Testing and

Research Laboratory of Dokuz Eylul University. The

mechanical properties of composite materials produced in

two different curing cycles are given in Table 1.

In addition, curing temperatures and geometrical

parameters of glass fiber-epoxy composite samples are

given in Table 2.

Laminated rectangular plates of glass fiber-epoxy com-

posite were produced under constant pressure 0.3 MPa and

Fig. 1 Geometry of pin-connected laminated composite plates

Table 1 Mechanical properties of composite materials

Material properties 90 �C 120 �C

Fiber volume fraction Vf % 57 55

Elasticity modulus of fiber direction E1 MPa 41,173 42,952

Elasticity modulus of transverse fiber direction E2 MPa 10,654 10,470

Shear modulus G12 MPa 6,785 6,882

Poisson rate m12 – 0.218 0.248

Tensile strength of fiber direction Xc MPa 760 763

Tensile strength of transverse fiber direction Yc MPa 110 108

Compressive strength of fiber direction Xb MPa 842 786

Compressive strength of transverse fiber direction Yb MPa 154 145

Shear strength S MPa 94 92

Table 2 Curing temperatures and geometrical parameters of the

glass fiber-epoxy composite samples

Curing temperature and time 90 �C/1.5 h 120 �C/1.5 h

Layer orientation [0�/90�]S [0�/90�]S

Thickness (mm) 1.00 1.00

The hole diameter, D (mm) 5.00 5.00

E/D 1, 3, 5 1, 3, 5

W/D 2, 3, 4, 5 2, 3, 4, 5

444 J Braz. Soc. Mech. Sci. Eng. (2014) 36:443–448

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two different curing cycles (90 �C–1.5 h, 120 �C–1.5 h).

Composite plates are symmetric with respect to mid-plane.

Figure 1 shows the geometry of the composite plate. Mold

plates are removed and cooled at room temperature after

curing. Hole diameter D = 5 mm, length L = 90 mm and

thickness t = 1 mm are kept constant, only the edge dis-

tance and width dimensions are varied.

Figures 2 and 3 show that the maximum failure loads of

the 90 and 120 �C curing temperatures for the (a) M = 0 Nm

and (b) M = 3 Nm preload moments of the pin connected

composite plates. As can be seen from the figures, lowest

maximum failure loads are obtained at W/D = 2 and highest

failure loads are obtained at W/D = 5. Therefore, maximum

failure loads increase with increasing (W/D) ratio. In addi-

tion, increasing preload moments increases maximum failure

loads. In this study, maximum failure load is obtained at

90 �C curing temperature, (E/D) = 5, (W/D) = 5 and 3 Nm

preload moment.

3 Prediction of the maximum failure loads using fuzzy

logic

People are different from computers because they have the

ability to think and process the information to decide if it

includes quite or inadequate, incomplete and uncertainty.

In general, various ways such as complexity and uncer-

tainty are not full and accurate sources of information are

called fuzzy resources [19].

Fuzzy logic is an artificial intelligence method that some or

all of input and output parameters are defined by fuzzy

membership functions. Fuzzy sets, logic, and system con-

cepts were proposed in 1965 by Lotfi Zadeh [20]. This idea is

emerged from efforts of many years in the field of control,

non-linear equations, complexity of the method and difficulty

of solution. In 1974, Mamdani [21] provided to connect from

fuzzy input sets to fuzzy output sets with a rule base using

Fig. 2 Maximum failure loads according to (W/D) and (E/D) for

90 �C curing temperatureFig. 3 Maximum failure loads according to (W/D) and (E/D) for

120 �C curing temperature

J Braz. Soc. Mech. Sci. Eng. (2014) 36:443–448 445

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Zadeh theories. Mamdani firstly used the inference method

for the operation of a steam engine and boiler.

In this study, a fuzzy model is developed using data

from the experiments. MATLAB fuzzy logic toolbox is

used to develop the model. Generated fuzzy model is given

in Fig. 4. Four input parameters (W/D, E/D, Preload

moments, Curing temperatures) are provided to the fuzzy

model and one output parameter (Maximum Failure Loads)

is taken from the model. Considering the input parameters,

W/D has four membership functions and others have three

membership functions. Double-sided sigmoid function is

used for membership functions of all of the input param-

eters. In addition, triangular-shaped function is used for

output membership functions.

These membership functions are defined based on the

experimental data. Mamdani rule table is used to define the

relationship between input and output parameters. The

rules of the fuzzy model are formed for predicting maxi-

mum failure loads and are based on experimental data.

The relationship of conformity between fuzzy logic

model and experimental results of maximum failure loads

for all composite samples is given Fig. 5. It can be said that

experimental results are close to results obtained from the

fuzzy logic when the figure is examined.

Relative errors obtained from experimental results and

fuzzy logic results are given Tables 3 and 4. Results of

prediction obtained from fuzzy logic model for maximum

failure loads are close to experimental results.

Fig. 4 Fuzzy logic model

0 500 1000 1500 2000 2500 3000 35000

500

1000

1500

2000

2500

3000

3500

Experimental

Fuz

zy L

ogic

Fig. 5 Fuzzy logic and experimental results of maximum failure

loads

Table 3 Maximum failure loads of composite samples for 90 �C curing temperature

W/D E/D Maximum failure loads (N)

Preload moments

0 Nm 3 Nm

Experimental Fuzzy logic Relative error (%) Experimental Fuzzy logic Relative error (%)

2 1 654 621 5 1,847 1,836 0.6

3 864 892 3.2 2,105 2,100 0.2

5 870 847 2.6 2,165 2,193 1.3

3 1 651 680 4.4 1,964 1,932 1.6

3 932 904 3 2,480 2,512 1.3

5 949 928 2.2 3,113 3,135 0.7

4 1 488 503 3.07 1,985 2,000 0.8

3 959 922 3.9 2,660 2,654 0.2

5 903 900 0.3 2,828 2,807 0.8

5 1 533 511 4.1 1,798 1,805 0.4

3 769 790 2.7 2,460 2,506 1.9

5 900 892 0.9 3,265 3,224 1.3

Average error 3 0.9

446 J Braz. Soc. Mech. Sci. Eng. (2014) 36:443–448

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Relative errors for fuzzy logic model are ranged from

0.2 to 7.9 %. Average errors for curing temperature 90 �C

and 1.5 h for 0 and 3 Nm preload moments are 3 and

0.9 %. In addition, average errors are 4.6 and 1.2 % for

composite samples of curing temperature 120 �C, 1.5 h and

0 and 3 Nm preload moments.

4 Conclusions

In this study is presented an application of Fuzzy Logic for

the failure analysis of Fiber-reinforced composite plates.

Results of the study are given below.

Strength of composite plates is increasing resistance to

the implementation of the preload moments. The ratios of

composite plate width to the hole diameter (W/D) and edge

distance to hole diameter (E/D) reaches high values with

increasing strength. The unidirectional reinforced glass

fiber epoxy composite plate which is produced at high

temperature (120 �C) gives higher strength value than glass

fiber epoxy plate manufactured at lower temperature.

Fuzzy logic was used to determine the maximum failure

loads attained by various geometrical parameters and cur-

ing temperatures. Mamdani rule tables developed using

Fuzzy logic are reasonable, accurate and can be used for

prediction within the limits of the factors investigated.

As a result, this study showed that it is possible to use

fuzzy logic systems for failure analysis in the mechanical

applications. This study is taken further for optimum pro-

duction conditions and thereby optimum process

parameters can be determined using Genetic Algorithm

(GA), Taguchi, Ant Colony etc. optimization techniques.

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Table 4 Maximum failure loads of composite samples for 120 �C curing temperature

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Average error 4.6 1.2

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