Fracture Behaviour of FRP Cross-Ply Laminate With Embedded Delamination Subjected To Transverse Load

Fracture Behaviour of FRP Cross-Ply Laminate With Embedded Delamination Subjected To Transverse Load

Sriram Chintapalli1, S.Srilakshmi1

1Dept. of Mech. Engg., P. V. P. Siddhartha Institute of Technology.

Vijayawada 520 007, A.P, India.

Abstract

One of the most important damage mechanisms in composite materials is the delamination between plies of the laminate. In industrial applications, composite plates are sensitive to impact and delamination occurs. Many composite components have curved shapes, tapered thickness and plies with different orientations, which make the delamination grow depending on the extent of the crack. It is therefore important to analyze the delamination characteristics of composite structures. The main objective of the present investigation is the characterization of the delamination growth in four layered cross ply (0/90/90/0) fibre reinforced composite laminates along all sides of the delamination. The analysis has been carried out using Virtual Crack Closure Technique (VCCT) in combination with Finite Element Methods (FEM) with the help of commercially available Finite Element Software, ANSYS.

Keywords: VCCT, FEM, Strain Energy Release Rate (SERR), ANSYS.

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

G = Strain energy release rate

1. Introduction

   Delamination represents a crack like discontinuity between the plies, interlaminar crack, which can propagate under the effect of mechanical, thermal and hygrometric loads. Therefore, fracture mechanics is a useful tool for

   approaching composite delaminations. In addition fracture mechanics is a suitable approach to deal with material selection and structural integrity when interlaminar cracks are involved. Fracture mechanics of composite materials is mostly based on the measure of the strain energy release rate G. The interlaminar stresses in symmetric laminates under uniform axial extension were first evaluated by Pipes and Pagano1 by applying a finite difference technique to solve the Navier equations of elasticity for off-axis plies. An experimental and analytical study was conducted by E. F. Rybicky,

   D. W. Schnussor and J. Fox2 to examine the free edge delamination mode of failure in a [±30°/±30°/90°/90°]s Boron/Epoxy laminate. Energy release rates were evaluated by a simple computational scheme that does not require special singular element or knowledge of the existence of a stress singularity in the solution. R. B. Pipes3 determined the boundary layer effects in composite laminates and presented the distribution of interlaminar normal and shear stresses along the width of cross-ply laminate. A. D. Crocombe and

   R. D. Adams4 have studied the effect of the interaction between a realistic spew fillet and other joint parameters on the adhesive stress distribution in a single lap joint for a wide range of geometric and material parameters using a linear elastic finite element program.

   An approximate semi-analytical method for determination of interlaminar shear stress distribution through the thickness of an arbitrarily laminated thick plate was presented by Reaz A. Chaudhuri and Paul Seide5. Erian A. Armanios and Jian Li6 predicted the interlaminar stresses in a symmetric laminate under extension, bending, torsion and their combined effect using a simple analytical formulation. I. S. Raju, R. Sistla and T. Krishnamurthy7 have performed fracture mechanics analyses on two debond configurations, flange-ski strip and skin-stiffener. Three-dimensional finite element analyses were performed. Two methods that use the virtual crack closure technique (VCCT) were used to evaluate the strain energy release rate distributions across the debond front. Debagrata Chakraborty and Dr. B. Pradhan8 have examined the delamination initiation at the interface of broken and continuous plies in case of [0/90/±/0]s Gr/E and Gl/E laminates with broken central plies.

   A full 3D FE analysis was performed with each layer of the laminate modeled as homogenous and orthotropic. Based on the results of 3D FE analysis, GI, GII & G were calculated at the delamination front using Irwin`s Crack Closer Integral. Dr. B. Pradhan and D. Chakraborty9 have dealt with the delamination initiation from an existing embedded elliptical delamination at the interface of the FRP composite laminates. A full 3D FE analysis was performed to calculate the inter-laminar stresses at the interface responsible for delamination. Concept of fracture mechanics was used to calculate the components of strain energy release rates at the interface. Effects of important factors like orientation of the adjacent layers, laminate thickness and the aspect ratio of the elliptical delamination on strain energy release rate components was studied. S. K. Panigrahi and Dr.

   B. Pradhan10 have performed a three-dimensional finite element analysis and computed the out-of- plane normal and shear stresses in an adhesively bonded single lap joint (SLJ) with laminated FRP

   Bottom

   Right

   Left Top

   composite plates which in comparison to other analytical methods for bonded joint analysis, is capable of handling more general situations related to initiation of damages and its growth. Damage propagation was analyzed by fracture mechanics based strain energy release rate (SERR) approach using virtual crack closure technique (VCCT). In the present analysis, fracture behavior of four layered cross-ply laminates under transverse load having interlaminar embedded delamination at mid span is studied using finite element method through VCCT.

2. Problem statement

   In the present analysis, fracture behavior of four layered cross-ply laminates under transverse load having interlaminar embedded delamination at mid span is studied using finite element method through VCCT.

3. Problem Modelling

   3.1 Geometric Model

   The in-plane dimensions of the laminate considered for the present analysis is as shown in Fig.1. The length and width of the plate are taken as 100 mm with a length/depth ratio of 10. Four layers of equal thickness (10/4=2.5mm) are considered. The delamination is located at the centre of the laminate. The delamination length is taken as 25mm. The virtual crack length is taken as 0.11mm on four sides of the delamination.

   Fig.1Geometric model for centre delamination at the middle interface.

   1. Finite Element Model

      Finite element mesh is generated using 8 node solid element SOLID45 in ANSYS software12 as shown in Fig. 2. This element is defined by 8 nodes having three degrees of freedom per node: translations in the nodal x, y and z directions. The element may have any spatial orientation. SOLID45 has plasticity, creep, stress stiffening, large deflection, and large strain capabilities. It has the capability to inherit orthotropic material properties and hence, best suited for analysing FRP composites.

      Fig. 2 Finite element model with boundary conditions

   2. Material Properties

      The material selected to carry out the present work is carbon epoxy11. The material

      properties used for the carbon epoxy material are given below:

      1. Youngs Modulus, E1 = 147GPa, E2 =9GPa,

         E3=9GPa

      2. Possons Ratio, 12= 13 = 0.27, 23=0.54

      3. Rigidity Modulus, G12=G13=7GPa, G23=3.7GPa

   3. Boundary Conditions and Loading

   Fixed boundary condition is imposed along the depth of the plate on four sides of the FE model. A transverse load of 1MPa is applied on the top surface of the laminate at y=10mm of the FE model.

   3.0 Analysis of Results

   The variation of strain energy release rate in opening mode GI with respect to the normalized length for a delamination length of 25mm along the four sides of an embedded delamination in a 4 layered laminate subjected to transverse load is shown in figs. 3 to 6. No constant trend is observed in the variation of GI along the top and bottom edges of the embedded delamination. A maximum value of 0.044871J/m2 is found at the 6th normalized location from left to right of the top and bottom edges. GI is found to be maximum 0.017734J/m2 at the 5th normalized location measured from bottom to top of the left and right edges of the embedded delamination.

   Fig. 3 Variation of GI with respect to normalized length along bottom edge of the delamination

   Fig. 4 Variation of GI with respect to normalized length along top edge of the delamination

   Fig. 5 Variation of GI with respect to normalized length along left edge of the delamination

   Fig. 6 Variation of GI with respect to normalized length along right edge of the delamination

   The variation of strain energy release rate in sliding mode GII with respect to the normalized length for a delamination length of 25mm along the

   four sides of an embedded delamination in a 4 layered laminate subjected to transverse load is shown in figs. 7 to 10. GII is found to be gradually increased up to the centre and then gradually decreased. A maximum value of 0.056957J/m2 is found at the 5th normalized location measured from left to right of the top and bottom edges. GII is found to be maximum 0.149215J/m2 at the 5th normalized location measured form bottom to top of the left and right edges of the embedded delamination.

   Fig. 7 Variation of GII with respect to normalized length along bottom edge of the delamination

   Fig. 8 Variation of GII with respect to normalized length along top edge of the delamination

   Fig. 9 Variation of GII with respect to normalized length along left edge of the delamination

   Fig. 10 Variation of GII with respect to normalized length along right edge of the delamination

   The variation of strain energy release rate in tearing mode GIII with respect to the normalized length for a delamination length of 25mm along the four sides of an embedded delamination in a 4 layered laminate subjected to transverse load is shown in figs. 11 to 14. GIII is found to be gradually decreased up to the centre and then gradually increased. A maximum value of 0.003844J/m2 is found at the 1st normalized location measured from left to right of the top and bottom edges. GIII is found to be maximum 0.016223J/m2 at the 1st normalized location measured form bottom to top of the left and right edges of the embedded delamination.

   Fig. 11 Variation of GIII with respect to normalized length along bottom edge of the delamination

   Fig. 12 Variation of GIII with respect to normalized length along top edge of the delamination

   Fig. 13 Variation of GIII with respect to normalized length along left edge of the delamination

   Fig. 14 Variation of GIII with respect to normalized length along right edge of the delamination

4. Conclusions

   Fracture analysis of a 4 layered FRP cross ply laminate with embedded delamination at the centre of the plate subjected to transverse load is carried out and the following conclusions are drawn:

   GI is maximum along the top and bottom edges of the embedded delamination.

   GII and GIII are maximum along the left and right edges of the embedded delamination.

   GII is found to be the dominating mode with a maximum value of 0.149215J/m2.

5. References

[1]. Byron Pipes R and Pagano N J, Journal of Composite Materials, 4 (1970) 538.

[2]. Rybicki E F, Schmueser D W and Fox J, Journal of Composite Materials, 11 (1977) 470.

[3]. Pipes R B, Fibre Science & Technology, 13 (1980) 49.

[4]. Crocombe A D and Adams R D, Journal of Adhesion, 13 (1981) 141.

[5]. Reaz A Chaudhuri and Paul Seide, Composites & Structures 25 (4) (1987) 627.

[6]. Erian A Armanios and Jian Li, Journal of Composites Engineering, 1(5) (1991) 277.

[7]. Raju I S, Sistla R and Krishnamurty T, Engineering Fracture Mechanics, 54(I) (1996) 371.

[8]. Pradhan B and Chakraborty D, Journal of Reinforced Plastics & Composites, 18(8) (1999)

735.

[9]. Pradhan B and Chakraborty D, Journal of Reinforced Plastics & Composites, 19(13) (2000)

1004.

[10]. Panigrahi S K and Pradhan B, Journal of Reinforced Plastics and Composites, 26(2) (2007) 183.

[11]. Isaac M. Daniel and Ori Ishai, A Text book titled Engineering Mechanics of Composite Materials, (2006).

[12]. ANSYS(12) reference manual.