Delamination effect on vibration for laminated composite structure

Asst. prof. Sandeep Bhoi

Department of Mechanical Engineering, Parala Maharaja Engineering College, Sitalapalli,

Ganjam Odisha

Mr. Hema Kalyana Sahu

M-Tech scholar, Department of Mechanical Engineering, PMEC, Berhampur

ABSTRACT

Composite materials are widely used in the industries such as marine, automobile, aerospace,

civil, aviation, etc. Because of their excellent mechanical properties also for light in weight and

easily mould in any shapes and size as per requirement. But one of the serious defect occur in the

laminated composite plate is delamination. However, composite laminates are prone to

delamination, which may not be visible externally, but can substantially affect the performance

of the composite structure. Free vibration analysis of a laminated plate with delaminations is

presented using a layerwise theory. Equations of motion are derived from the Hamilton's

principle, and a finite element method based on the first order shear deformation theory is

developed to formulate the problem. The validity of developed models has been established by

comparing the responses with those available published literature. The results of this research are

useful for detecting delamination in multi-layer composite materials. It was shown that the

different mode shapes of the frequency of the plate decreases if the delamination area increases.

Keywords: Delamination, Structure, Free Vibration, Laminated Structure

INTRODUCTION

Now days, the commonly used material in industries is composite material for their excellent

mechanical properties. They are known for their incredible lightweight, stiffness to weight and

strength to weight ratios. We can achieve difficult structures, complex shape or design with the

help of composite material. But the common mode of damage is occurring in composite material

called as delamination. Delamination is nothing but separation of two layers of composites.

Delamination occur in composite plate is invisible because it occur inside of the material.

Delamination also develops due to repeated cyclic stresses, manufacturing defects, low velocity

impact, unlike environment condition. Due to delamination in composite plates may reduce

mechanical properties such as loss in strength, toughness, stiffness, and material unbalance.

Therefore detecting such type of damage the nondestructive test are used for composite and to

solve such type of problem by using various approximate techniques in which finite element

method can be used by using software ANSYS 15.0 for damage monitoring of laminated

composite plates.

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Literature

Mechanical, aerospace, civil Engineering structures, sport equipment and mechanical prosthetics are

the broad areas where composite components are being used. This is well known that the composite

materials are very much flexible as compared to the conventional material and they suffer from large

delamination effect under combined loading. Hence, for designing of high performance components,

simulating the true material behaviour of delaminated composite beams and plates have been studied

since last two decades, in this regard some of the recent and earlier literatures are discussed in the

following paragraph.

Tenek et al . [1] obtain the vibration behavior of delaminated composite plates using the finite

element method based on the three-dimensional theory of linear elasticity. Buckling responses of

orthotropic beam-plates are analyzed with multiple central delaminations by the Huang and

Kardomateas [2] using analytical method and non-linear beam theory Kardomateas[3] Presented the

delaminated composites under pure bending can undergo snap buckling under pure bending and it is

demonstrated experimentally and investigated theoretically by an energy procedure.

Ju et al .[4] presented a two- dimensional finite element approach for the analysis of free vibration of

laminated composite plates with multiple delamination based on the Midline plate theory. Zheng and

sun [5] proposed a triple plate finite element model to analyze the delamination interaction in

laminated structures static behavior of delaminated composite beams are studied by Carrella-Payan

and Allegri [6] using a layer wise split- element technique.

Lee [7] proposed a layer wise model to formulate the equation of motion of a delaminated plate.

Numerical results are obtained and compared with those of other theories addressing the effects of the

lamination angles, location, size and number of delamination on vibrating frequencies of delaminated

beams. It is found that a layer wise approach is adequate for vibration analysis of delaminated

composites. Nguyen et al. [8] proposed an automatic numerical method requiring minimal user

intervention to simulate delamination in composite structures.

PROBLEM DEFINITION

Now- a -days, composite material are widely used in the industries but one of the type of damage

occur in composite plate called as delamination. These plates fails during the service orthotropic-

ally, sometimes cracks are observed and the structure becomes weak, also sometimes its fail due

to vibrations. Detect the delamination in the composite plate in the time to take remedial action

in advance and to reduce the effect of delamination.

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FINITE ELEMENT FORMULATION

Formulation:

In the present modal analysis we are using a finite element method (FEM) for free vibration

analysis of delaminated composite plates. We consider a rectangular laminated plate with

delamination.

Fig. 1: Rectangular plate with through width delamination

The model 100*100*5 mm plate delamination type of damage creating from 25 mm to35 mm

and from 60 mm to 70 mm. damage is 10% of x-axis which is 10 mm and damage is in thickness

at 2.5 mm of z-axis.

Fig. 2: Different layer of composite plate in ANSYS

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Fig. 3: 1st mode shape of composite plate in ANSYS with maximum deformation in x-axis

Fig. 4: 1st mode shape of composite plate in ANSYS with maximum deformation in y-axis

Fig. 5: 1st mode shape of composite plate in ANSYS with maximum deformation in z-axis

The fig 3 describes 1st mode of composite plate with maximum deformation

0.393559 in x-axis and maximum stress 0.006608 and minimum stress -0.006608.

The fig 4 describes 1st mode of composite plate with maximum deformation

0.393559 in y-axis and maximum stress 0.006607 and minimum stress -0.006607.

The fig 5 describes 1st mode of composite plate with maximum deformation

0.393559 in z-axis and maximum stress 0.173 and minimum stress -0.393514.

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Fig. 6:2nd mode shape of composite plate in ANSYS with maximum deformation in x-axis

Fig. 7: 2nd mode shape of composite plate in ANSYS with maximum deformation in y-axis

Fig. 8: 2nd mode shape of composite plate in ANSYS with maximum deformation in z-axis

The fig 6 describes 2nd mode of composite plate with maximum deformation 0.341049 in

x-axis and maximum stress 0.005767 and minimum stress -0.005767.

The fig 7 describes 2nd mode of composite plate with maximum deformation 0.341049 in

y-axis and maximum stress 0.007395 and minimum stress -0.007395.

The fig 8 describes 2nd mode of composite plate with maximum deformation 0.341049 in

z-axis and maximum stress 0.340968and minimum stress -0.340968.

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Fig. 9:3rd mode shape of composite plate in ANSYS with maximum deformation in x-axis

Fig. 10: 3rd mode shape of composite plate in ANSYS with maximum deformation in y-axis

Fig. 11:3rd mode shape of composite plate in ANSYS with maximum deformation in z-axis

The fig 9 describes 3rd mode of composite plate with maximum deformation 0.337614 in

x-axis and maximum stress 0.007393 and minimum stress -0.007393.

The fig 10 describes 3rd mode of composite plate with maximum deformation 0.337614

in y-axis and maximum stress 0.005694 and minimum stress -0.005694.

The fig 11 describes 3rd mode of composite plate with maximum deformation 0.337614

in z-axis and maximum stress 0.337531 and minimum stress -0.337531.

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RESULTS

Results analysis for four layers laminated composite plates:

Table – 1

Natural frequencies for laminated composite plate

No. of Layers Mode

Number

NATURAL

FREQUENCY

DMX

SMN SMX

8

1ST 94.7362 0.393559 -0.393514 0.173

2ND 185.698 0.341049 -0.340968 0.340

3RD 211.149 0.337614 -0.337531 0.337

CONCLUSION

Using finite element analysis and Ansys15.0 is used for the vibration analysis of the

laminated plates. Laminated variables are defined and values of frequencies are obtained

using Ansys15.0 for different set of variables. Using that data we have concluded that

-Free vibration behaviour of the laminated composite plates greatly depends on the

geometrical and material parameters..

-Frequency increases with increase in mode of vibration .For higher mode of vibration

the frequency will be higher. Effect of this variable is dominant at higher modes of

vibration.

References 1) L. H. Tenek, E. G. Henneke ll and Max D. Gunzburger, “Vibration of delaminated

composite plates and some applications to non-destructive testing” Composite

Structures, vol.23,no. 25, pp. 253-262;1993.

2) H. Huang and G. A. Kardomateas, “buckling of orthtropic beam plate with multiple

central delaminations” International journal of solid structure, vol.35.no. 13, pp 1355-

1362;1998.

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3) G. A. Kardomateas, “Snap Buckling of Delaminated Composites under Pure

Bending” Composite science and Technology, vol. 39, no. 32,pp. -63-74;1990.

4) F. JU, H. P. Lee and K. H. Lee, “finite element analysis of free vibration of

delaminated composite plates” Composites Engineering, Vol. 5, No. 2, pp. 195-209,

1995.

5) S. Zheng and c. T. Sun. “Delamination interaction in laminated structures”

Engineering Fracture Mechanics Vol. 59, No. 2, pp. 225-240, 1998.

6) H. P. Chen and p. j. Goggin, “Vibration of a delaminated beam plate relative to post

buckling states with shear deformation theory” Jornal of sound and vibration, vol.

176, no. 2. pp. 163-178; 1994.

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