Effect of Thickness on Interlaminar Stresses in Simply Supported FRP Angle-Ply Laminate with A Circular Cut Out

Effect of Thickness on Interlaminar Stresses in Simply Supported FRP Angle-Ply Laminate with A Circular Cut Out

Ch. Siva Sankara Babu, S. Srilakshmi

Dept. of Mech. Engg., P. V. P. Siddhartha Institute of Technology.

Vijayawada 520 007, A.P, India.

Abstract

The present research work deals with the prediction of interlaminar stresses in simply supported laminated FRP composite plate with a circular cut-out under transverse load using 3-D finite element analysis. The finite element analysis software ANSYS has been successfully executed and the finite element model is validated. The interlaminar stresses are evaluated by varying length-to-thickness ratio (s) and constraints. The effect of s and the boundary conditions on the interlaminar stresses is discussed. The present analysis will be useful in quantifying the effect of above said factors that helps in the safe and efficient design of the structural elements made of laminated FRP composites.

Keywords: FRP, Interlaminar stresses, Angle-ply laminate, cut-out

Nomenclature

E1 = Youngs modulus of the lamina in the fibre direction

E2 = E3= Youngs modulus of the lamina in the transverse direction of the fibre

G12= G13= Shear modulus in the longitudinal plane of the fibre

G23= Shear modulus in the transverse plane of the fibre

12 = 13 = Poissons ratio in the longitudinal plane of the fibre

23 = Poissons ratio in the transverse plane of the fibre

I-1 = First interface i.e. interface between 450 and – 450 laminae

I-2 = Second interface i.e. interface between

-450 and -450 laminae

I-3 = Third interface i.e. interface between

-450 and 450 laminae

l = Length of the Square plate d = Diameter of the cut-out

t = Thickness of laminate

s = l/t = thickness-to-length ratio d/l = diameter-to length ratio

SS-1 = plate simply supported along all the four edges

SS-2 = plate simply supported along edges parallel to Y-axis

SS-3 = plate simply supported along edges parallel to X-axis

1. Introduction

   The increasing use of fiber reinforced laminates in space vehicles, aircrafts, automobiles, ships and chemical vessels have necessitated the rational of structures for their mechanical response. In addition, the anisotropy and non homogeneity and larger ratio of longitudinal to transverse moduli of these new materials demand improvement in the existing analytical tools.

   FRP composites deliver more strength per unit of weight than most metals. In fact, FRP composites are generally 1/5th the weight of steel. The composite can also be shaped into one complex part, often times replacing assemblies of several parts and fasteners. The combination of these two benefits makes FRP composites powerful material system- structures can be partially or completely pre-fabricated at the manufacturer's facility, delivered on-site and installed in hours. The addition of the reinforcement to the polymer matrix increases the creep resistance of the properly designed FRP part.

   As a result, the analysis of laminated composite structures has attracted many research workers and has been considerably improved to achieve realistic results. Depending upon the nature of application, these structural elements are acted upon by mechanical thermal loads of varied nature. Usually, the anisotropy in laminated composite structures causes complicated responses under different loading conditions by creating complex couplings between extensions, bending and shear deformation modes, it must be described by three dimensional elasticity theories.

   In practical applications, composite plates with cut-outs are required for various purposes, such as joining of riveted and bolted joints. Till now there are number of approaches have been

   proposed to solve the three dimensional elasticity equations of rectangular plates. The interlaminar stresses in symmetric laminates under uniform axial extension were first evaluated by Pipes and Pagano [1] by applying a finite difference technique to solve the Navier equations of elasticity for off- axis plies. Srinivas and Rao [2] and Srinivas et al.

   [3] presented a set of complete analytical analyses on bending, bucling and free vibration of plates with both isotropic and orthotropic materials. Pagano et al. [4] has given exact solutions for the deflections and stresses of a cross ply laminated rectangular composites using elasticity theory. Following the approach used by Pipes and Pagano [ 1] the interlaminar stress distribution in a four layer composite laminate in bending was studied by salamon [ 5]. He predicted that the magnitudes of the interlaminar normal and shear stresses, although in general relatively small, rise sharply near the free-edges. Kong and cheung [6] proposed a displacement-based, three- dimensional finite element scheme for analyzing thick laminated plates by treating the plate as a 3-dimensional inhomogeneous anistropic elastic body.

   A.Srinivas et al [7] evaluated the displacements, in-plane, out-of-plane and interlaminar stresses in a four layered symmetric balanced angle-ply laminates subjected to longitudinal and in plane transverse loads. Using a double fourier series approach Kabir[8] presented the results of the variations of transeverse displacements and moments for various parametric effects for antisymmetric angle-ply (450/-450) and for symmetric angle-ply (450/-450) laminate plate[9] with simply supported boundary conditions at all edges. Chen and Kam [10] presented a two level optimization method for elastic constants identification of symmetric angle-ply laminates. To study the interlaminar stresses in cylindrical shells under static and dynamic transverse loads and to determine the dynamic magnification factors (DMF

   i.e. the ratio of the maximum dynamic response to the corresponding static response) Bhaskar and varadhan [11] used the combination of Naviers approach and a Laplace transform technique to solve the dynamic equations of equilibrium. Ravi kiran [12] presented the prediction of interlaminar stresses in simply supported laminated FRP cross- ply laminate with a circular cut-out under transverse load using 3-D finite element analysis. In the present analysis interlaminar stresses in simply supported laminated FRP angle-ply laminate with a circular cut-out under transverse load are analyzed using 3-D finite element analysis.

2. Problem Modelling

   Three-dimensional finite element analysis of a four layered symmetric balanced angleply laminate has been taken up in the present work. The finite element model created in ANSYS

   software is validated and extended to evaluate the interlaminar stresses by varying the length-to- thickness ratio (s).

   1. Geometric Model

      A square plate of length 100 units is considered for the present analysis. Four layers of equal thickness with the fiber angle 450/-450/- 450/450 are arranged to observe the balance as well as symmetry across the thickness of the laminate. The thickness of the plate is selected from length- to-thickness ratio (s) which is varied as 10, 20, 30, 40 and 50. A circular cut out is considered at the centre of the plate with diameter-to-length ratio (d/l) = 0.2.

   2. Finite Element Model

      The finite element mesh is generated using Solid 45 [13] element as shown in figs. 1 and 2. Solid 45 is a second order brick element. It can tolerate irregular shapes without much loss of accuracy. Solid 45 elements have compatible displacement shapes and are well suited to model curved boundaries. This element is defined by 8 nodeshaving three degrees of freedom per node: translations in the nodal x, y and z direction. The element may have any spatial orientation and is suitable to model isotropic as well as orthotropic materials.

   3. Material Properties

      The following material properties are considered for the present analysis.

      1. Youngs Modulus E1=127.5GPa, E2=9.0GPa,

         E3= 4.8GPa.

      2. Poissons Ratio 12 = 13 = 0.28, 23 = 0.41

      3. Rigidity Modulus G12= G13=4.8GPa,

      G23 = 2.55GPa.

   4. Boundary Conditions and Loading

      Simply supported boundary conditions are applied along all the four edges of the plate in

      SS-1, along edges parallel to Y-axis in SS-2, and along edges parallel to X-axis in SS-3. A uniform load of 1 MPa is applied on the top surface of the FE model.

   5. Validation of FE model

      The present finite element model is validated by computing the out of plane stresses at the free surface i.e. at the bottom surface of the plate (z=0). The computed stresses are found to be close to zero (Table 1).

      interlaminar normal and shear stresses z, yz and zx at the bottom ,middle and top interfaces of the laminate under consideration.

      From Figs. 3-5 it is observed at all the interfaces, the interlaminar normal stress z is rapidly incresing with s. It is observed that the interlaminar normal stress z is maximum and same for SS-2 and SS-3 at all interfaces. z is minimum for SS-1 at all interfaces for all values of s

      Variation of the interlaminar shear stress yz with respect to s is shown in Figs. 6-8. It is observed that the interlaminar shear stress yz is rapidly increasing with s at all the interfaces. The shear stress yz in SS-3 is maximum for all s at all interfaces. And yz is minimum in SS-1 at all interfaces for the values of s.

      Variation of the interlaminar shear stress zx with respect to s is shown in Figs. 9-11. It is observed that the interlaminar shear sress zx is rapidly increasing with s at all the interfaces. The shear stress zx in SS-2 is maximum for all s at all interfaces. zx is minimum in SS-1 at all interfaces for the values of s.

      Fig 3: Variation of z with s in I-1

      Fig 4: Variation of z with s in I-2

      Bottom center	z	yz	zx
      SS-1	0.00010931	0.0030434	0.0023665
      SS-2	0.0010606	0.0069009	0.00079798
      SS-3	0.00076937	0.0010608	0.0022889

3. Discussion of Results

   Variation of the interlaminar stresses with respect to length-to-thickness ratio (s) is shown in Figs. 3-11. These figures shows the variation of

   Fig 5: Variation of z

   with s in I-3

   Fig 6: Variation of yz with s in I-1

   Fig 7: Variation of yz with s in I-2

   Fig 8: Variation of yz with s in I-3

   Fig 9: Variation of zx with s in I-1

   Fig 10: Variation of zx with s in I-2

   Fig 11: Variation of zx with s in I-3

4. Conclusions

Three dimensional finite element analysis is carried out for the pridiction of interlaminar stresses in a 4-layered angle-ply laminate subjected to out-of-plane transverse loads. The following conclusions are drawn.

z is maximum at bottom interface. yz is maximum at middle interface. zx is minimumm at middle interface.

Dominating stresses are interlaminar shear stresses yz and zx.

References

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2. Srinivas S. and Rao, A.K., 1970, Bending, vibration and bucling of simply supported thick orthograpic rectangular plates and laminates, Int. j. Solids Struct, 6, pp.1463-81.

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12. K. Ravi Kiran, S.Srilakshmi, V. Bala Krishna Murthy, G. Smambasiva Rao, Effect of thickness on interlaminar stresses in simply supported FRP cross-ply laminates with a circular cut-out, Inter.Jour. of Appl. Engg. Research ISSN 0973-4562 Volume 6, Number 20(2011) pp. 2391-2397

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