A Study of Flat-Joggle-Flat Bonded Joints in Composite Laminates

A Study of Flat-Joggle-Flat Bonded Joints in Composite Laminates

Sambamurty Saravakota, A. Nanda Kishore

1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India.

   Abstract – Flat-Joggle-Flat (FJF) bonded joints are designed to eliminate eccentricity by the presence of joggle so that loads remain in- plane and bending effect is avoided thereby the strength of the joint is increased. Experimental study carried on FJF bonded joints showed a 90% increase in failure load over flat joints. Finite element analysis of FJF joint is carried out using Hashin failure criteria for adherend and maximum shear stress, Ye-delamination and cohesive stress failure criteria for adhesive. There is a good agreement between FEM and experimental values.

   Keywords: Composites; Finite element stress analysis; Joint design; Flat-Joggle-Flat bonded joints.

   1. INTRODUCTION

      Adhesive bonding is often preferred for joining composite laminates because adhesive itself is the same polymer as resin matrix. However, due to layered nature of composite adherends and relative weakness in through-the-thickness direction, failure mechanism of an adhesively bonded composite joint tends to become more complex. Thus, more factors have to be considered in predicting the strength of composite joints [1].

      Bonded joints are prepared by joining laminates with a suitable adhesive and curing them together. The common types of adhesively bonded joints are single lap, double lap, step and scarf joints as shown in Figure 1.

      Figure 1. Adhesive bonded Joints [13]

      Bonded lap joints are preferred as they do not require machining of the substrates. Advantages of bonded joints are lightweight, distribution of load over larger area and elimination of holes which is the main cause of failure in mechanically

      fastened joints. The drawbacks of bonded joints are (i) difficult to inspect for the bond integrity (ii) degrade in service due to temperature changes and (iii) disassembly is difficult without destruction of the joint. In addition, it also requires surface cleaning and preparation before joining in order to get a good joint. Different failure modes associated with bonded joints are adhesive, cohesive, thin-layer cohesive, fibre-tear, light-fibre-tear and stock-break failure. A combination of failures can also happen.

      The strength of adhesively bonded joints in fibre reinforced plastics was reviewed by Matthews et al. [2]. Analytical, finite element methods and experimental tests to study joint parameters and failure modes were discussed. Experiments and numerical studies on wavy-lap bonded joints were carried by Avila et al. [3]. Their results showed an increase of 41% on loading compared to single-lap joints. They accounted this due to the compressive stress field developed inside the wavy-lap joint. Taib et al. [4,5] conducted experiments and finite element analysis to study the effect of joint configuration, adhesive layer thickness, defects, humidity, spew fillet and adherend stiffness in glass fibre/vinylester composite laminates bonded with epoxy in joggle lap joint (JLJ), L-section joints (LSJ), single lap joint (SLJ) and double strap joints (DSJ). Their numerical results agreed well with the experimental values. They also showed that the effect of peel and shear stresses is negligible in JLJ.

      Yan et al. [6] studied the effect of the length and depth of a parallel slot as well as the elastic modulus of the adhesive on the stress distribution at the mid bondline and in the adherend using finite element method. They found that the peak stresses vary significantly when length and depth of the slot is varied and negligible for a low elastic modulus adhesive and decreased for adhesives with high elastic modulus. Elawadly [7] studied the effect of stacking sequence and thickness of the layers on the interlaminar shear response of laminated composite specimens by analytical and experimental methods.

      A study of adhesive joints using a 3D FEA was carried out by Goncalves et al. [8]. They considered geometric and material non-linearities and developed interface elements to calculate stresses at the adherend-adhesive interface. They considered linear elastic and elasto-plastic materials behavior. Their results showed the importance of 3D nature of stresses and stress concentrations at interface. Lee et al. [9] conducted a parametric study to characterize the strength of the joint, peel stresses and failure modes in adhesively bonded single and double strap joints. They showed that joint strength has no effect on type of adhesive, decreased with adhesive layer and increased with overlap length. Panigrahi and Pradhan [10] developed a three- dimensional finite element model to compute the peel stress and shear stresses in an adhesively bonded single lap joint (SLJ) with laminated FRP composite plates. They calculated the failure index for the adhesive layer using quadratic failure criterion and used the Tsai-Wus coupled stress quadratic failure criterion for the interface of adherend and adhesive. Damage propagation is analyzed by fracture mechanics based on strain energy release rate (SERR) approach using virtual crack closure technique (VCCT). Apalak and Apalak [11] investigated the initiation and propagation of the damage zones in unidirectional composite plates of an adhesively bonded single lap joint under flexural loads based on Tsai-Wu and Hashin failure criteria. From three- and four-point bending tests and the SEM plots they observed that the local failure initiated inside the adhesive fillet and propagated along the upper plateadhesive interface. Kim et al. [12] predicted failure in composite single lap bonded joints considering both composite adherend and bondline failure using FEA. For failure in adhesive, elastic-perfectly plastic model and for adherend delamination failure of composite adherend was considered. Tong [1] proposed failure criteria to characterize the effects of interlaminar delamination in adhesively bonded joints. These failure criteria are implemented in analytical and FEA and a good correlation was observed between the measured and FEA results. Nanda et al. [13] performed experimental studies on Flat-Joggle- Flat bonded joints in composite laminates and observed 90% increase in failure load over the flat joints. However, there is no analytical or FEA validation performed to substantiate the experimental observations. The scope of this present work is to add FEA correlation, which can be utilized at future research studies with different laminate configuration under Flat-Joggle-Flat bonded joints.

   2. PRESENT WORK

      The study of bonded joints should consider geometry, material, loading condition, failure modes and other factors. In flat joints, also known as single-lap joints, loads act eccentric with respect to the centre of the joint shown in Figure 2. The eccentricity causes stress concentrations at the ends of the overlap, which affects the strength of the joint. To reduce stress concentration many researchers have modified the geometry which include adding fillets at the ends to prevent early initiation of crack, tapering of adherend, chamfering etc. Due to eccentricity, bending will result which in turn develops stresses in the thickness direction. These stresses are known as peel stresses. At the lap ends of the adhesive layer, a combination of peel and shear stresses are developed which affect the strength of the joint. Peel stresses can be reduced by having an adequate length and thickness of the laminate.

      Figure 2. Bonded joints undr loading

      In bonded joints, in order to transmit the load smoothly various parameters viz., adherend tapering, adherend surface treatment, adhesive thickness, adhesive type and curing of the adhesive were considered by several researchers. Analytical, numerical and FEA were carried out to analyze the stresses in the joint. Material and geometric non-linearity are also considered and various failure criteria were used to predict the strength of the joint.

      From the literature, it is observed that the peel and shear stresses are the main cause to initiate failure in adhesively bonded joints. These develop at the ends of the joint due to eccentricity in loading which causes bending moment. The bending moment in addition to the axial load gives rise to in-plane and interlaminar stresses near the edges of bonding in composite bonded joints. In order to reduce these effects, a new Flat-Joggle-Flat (FJF) bonded joints shown in Figure 2 are developed from the existing single-lap-joint. Flat-Joggle-Flat (FJF) bonded joints have the ability to reduce the stresses thereby increasing the load carrying capacity considering the same lay-up and same overlap-length as Flat bonded joints as shown in Figure 2.

   3. EXPERIMENTAL STUDY

      Experiments are conducted to find the strength of the Flat bonded joints and FJF bonded joints. A mould is prepared with Plexi-glass material to get the joggle bend in the laminate. Laminates are prepared on this mould using uni-directional glass

      fibre/epoxy comprising eight layers with the fibre orientation of

      [0o/45o/-45o/90o ]s

      layup by hand lay-up process. The

      specimen is then cut into the required dimensions. The overlap-length of the joint is divided into three-sections viz, flat, joggle and flat as can be seen in Figure 2. Flat joints are tested for comparison with FJF joints considering same lay-up and overlap- length. The geometry of flat and FJF joints are shown in Figure 3.

      Figure 3. Geometry of bonded joints [13]

      Three samples of flat bonded joint and four samples of FJF bonded joint are tested and their average values are taken. Epoxy resin is used as adhesive as they are compatible with the resin used for preparing the laminates and also due to their better wetting ability, low cure shrinkage, superior mechanical properties and excellent chemical resistance. They possess the relatively high values of surface free energy and this makes them more receptive to adhesive bonding. The mechanical properties of the laminate and adhesive are tested as per ASTM standards and are given in Tables 1 and 2 respectively.

      Table 1 Mechanical properties for UD-750 gsm glass fibre/epoxy laminate (MPa)
      E11	E22	E33	G12	G23	G13	12	23	13
      26000	6000	6000	3120	2000	3120	0.3	0.5	0.3
      XT	XC	YT	YC	ZT	ZC	S12	S23	S13
      500	300	22.5	60	22.5	60	45	30	45

      Table 2 Mechanical properties for adhesive (MPa)
      E	12	YT
      3270	0.3	50

   4. FINITE ELEMENT ANALYSIS

      Finite element analysis (FEA) is considered to be a versatile and efficient method to provide the accurate numerical solutions to problems in mechanics of composites. The simulation model should have the similar boundary conditions and the same loading schemes so that it can serve as a physical prototype of the real system. The structural failure in the laminated composites cannot be decided globally based on the extreme stress locations of the structure; instead it has to be determined locally for each layer based on the failure criteria in layer local coordinates.

      A 3D finite element analysis is carried out using ANSYS [14] to find the stresses and estimate the strength and damage propagation in FJF bonded joint. The model is solved for the large displacements by considering the geometric nonlinear behavior. Lamina stresses are determined for a given load step and it is used with a failure criterion to check for any failures during this load step. If no failures are detected then the load is increased to the next load step and the analysis is continued.

      Figure 4. 3D FE model of FJF bonded [0/45o /-45o /90o ]s laminate joint with BCs

      A finite element mesh model with the loads and boundary conditions is shown in Figure 4. Only half of the model is considered due to symmetry. Symmetric boundary conditions are applied along the length of the laminate to reduce the computational time. Load is applied using displacements in increments at the end of the laminate. SOLID95 elements are used for modeling the joint. It has 20 nodes with three translational degrees of freedom at each node. This element is chosen as it has the option to include fibre orientations and initial stress (ISTRESS) that is required for progressive damage. Post failure material behavior is analyzed by progressive failure analysis. After solving for first load step, results are verified to check for any failures in laminate and/or adhesive. Once failure is detected, appropriate degradation rules are employed on the failed elements. The steps in progressive damage model are described by means of a flow chart as shown in Figure 5.

      Figure 5. Flow chart for progressive damage model simulation

   5. FAILURE CRITERION

      Failure theories are applied in the design of components to calculate margin of safety, and to determine the weak and strong directions. Various failure theories are proposed in the literature. They consist of a set of mathematical equations to predict possible failures. Since the criteria are for orthotropic materials, failure stress or strain values should be provided in all the directions. Based on the criteria, the stress ratio in each layer should be maintained less than or equal to 1 to avoid failure. A three- dimensional finite element model can address more complex modes of failure compared to a two-dimensional as it can accommodate all modes of failure such as matrix cracks, fibermatrix debond, fiber fracture, and delamination. Hashin

      polynomial failure criteria is used as they can distinguish different modes of failure. They are ideal for use in finite element models especially when adapted to progressive damage models. Hashin proposed a set of failure criteria for predicting the failure of uni-directional composites. Each mode of failure has its own degradation rules and the reduction in stiffness is strongly dependent on the failure mode. The seven failure criteria each representing a mode of failure is given in [15].

      Matrix tensile failure y 0

      y

      2

      2

      xy

      +

      2

      + yz

      1 (1)

      YT S12 S23

      Matrix compressive failure y 0

      2

      y

      2

      + xy

      2

      + yz

      1 (2)

      YC

      S12

      S23

      Fibre tensile failure x 0

      2 2 2

      x

      + xy

      + xz 1

      (3)

      XT S12 S13

      Fibre compressive failure x 0

      2

      x

      XC

      1 (4)

      Fibre-matrix shear-out x 0

      2 2 2

      x

      + xy

      + xz

      1 (5)

      XC

      S12

      S13

      Delamination in tension z 0

      2 2 2

      z

      + xz

      + yz

      1 (6)

      DZeTlaminaSti1o3 n in cSo2m3 pression z 0

      2 2 2

      z

      + xz

      + yz

      1 (7)

      ZC S13 S23

      where ij and ij are the layer-stresses in the ij direction and the denominators are their strengths in the corresponding directions.

      Three failure modes Ye-delamination, maximum shear stress and cohesive failure are considered for adhesive failure in FJF bonded joints. The adhesive failure is mainly attributed due to the interlaminar effects. 3D elements are better suited in estimating interlaminar stresses in the thickness direction. Delamination generally occurs at the interface of adhesive and adherend.

      Cohesive failure occurs within the adhesive. It is a parabolic yield criterion and reduces to von-Mises stress when YC = YT. In

      Eqs. (8-11), 1 , 2 and 3 are the principal stresses, z is normal stress, xz and yz are shear stresses in the adhesive.

      max is the shear strength (lap shear strength-[18]) of the adhesive, ZT is the normal strength and S13 , S23 are interlaminar

      shear strength of the adhesive and are considered to be equal. It is predicted from three-point bend test [19]. YC and YT are the tensile and compressive yield strengths of the adhesive material and are considered to be equal.

   6. Material property degradation

      The material property degradation rules determine the post failure material properties for regions that have been subjected to damage. The degradation rules are different for each failure mode, since each of them has different effect on the load carrying capability of the composite. Once failure is detected through any of the modes of failure, appropriate degradation of material properties are applied on the failed ply elements so that it carries no or less load. The properties of the failed ply are partly degraded according to the given material property degradation rules. Degradation is performed on an element basis. In case of FJF joint where Hashin failure theory is used the appropriate degradation factors used which are associated to their failure modes are

      Matrix tensile failure

      E22 0.2E22 ,

      G12 0.2G12 ,

      G23 0.2G23

      (12)

      Matrix compressive failure

      E22 0.4E22 ,

      G12 0.4G12 ,

      G23 0.4G23

      (13)

      Fibre tensile failure

      E11 0.07 E11

      Fibre compressive failure

      E11 0.14E11

      Fibre-matrix shear-out failure

      G12 0.1G12

      Delamination in tension and compression

      (14)

      (15)

      (16)

      E33 0.1E33 ,

      G13 0.1G13 ,

      G23 0.1G23

      (17)

      For the adhesive, which is isotropic, the degradation is carried by reducing the Youngs modulus close to

      zero but not exactly zero in order to avoid numerical problems.

   7. Results and discussion

      Figure 6 shows the load-displacement curves obtained from experiments for flat and FJF bonded

      joints.

      Figure 6. Load vs. displacement curves from experiments [13]

      Table 3 shows a comparison between flat and FJF composite bonded joints. It can be observed that there is a 90% increase in load in FJF bonded joints compared to flat joints. This shows that reduction in eccentricity has a major influence on the strength of the joint.

      Table 3 Experimental observations in flat and FJF bonded joint
      	Flat Joint (kN)	FJF Joint (kN)	%Increase in load
      Failure Load	10.8	20.5	90

      The failed specimens of FJF bonded joints are shown in Figure 7. It can be observed that failure is at the interface of the joint in light-fibre-tear mode which is an accepted mode of failure as per ASTM standards. It is also observed a delamination failure in the middle of the laminate due to matrix crack propagation. It might be due to the loading plane passing through the centre of the laminate, damage might have propagated and failed in this mode. As laminate can withstand much higher load than adhesive, the strength of the joint might have increased. The failure observed for flat joint is at the interface in light-fibre-tear mode. In this, damage has not propagated between the layers of the laminate as observed in FJF joint, since the loading plane passes through the interface of the joint. It is found that the FJF joint can take higher load compared to flat joint.

      (i) Front view

      Light-fibre-tear mode Damage propagation in adherend

      (ii) Top view

      1. Test sample 1

         Light-fibre-tear mode Damage propagation in adherend

         1. Front view

            Light-fibre-tear mode

         2. Top view

      2. Test sample 2

         Figure 7: Failed specimens of FJF bonded joint [13]

         From FEA at a load of 11.5 kN, the failure modes observed in adherend are matrix failure in +45o, -45o and 90o layers as can be seen from degraded mesh in Figure 8. In +45o and -45o layers matrix failure was observed in the non-overlap length of the joint. Failure at the interface of the joint is mainly due to maximum shear stress.

         Figure 8. Finite element model of FJF laminate and adhesive

         Figure 9 shows the stresses in the adherend along and perpendicular to the fibre direction. At the ultimate failure load, a combination of fibre and matrix modes is observed in layers +45o and -45o in the non-overlap length and a combination of matrix and delamination failure propagated upto joggle portion of the joint. A similar kind of failure is observed from experiments (Figure 7) which show that matrix and delamination mode of failure at the centre of the adherend in the thickness direction where 90o fibre layers are present.

         J\NSY

         ELEMENT SOLUTION STEP=l

         –

         SUB =1 TIME=l

         NMIS72 (NOAVG) DMX =.0127

         SMN =-29.417

         SMX =202.672

         -29.417

         -3.629

         D 22.158

         –

         D

         47.946

         73.734

         1. Stress along the fibre direction

            J\N

            D 99.521

            D 125.309

            D 151.096

            D 176.884

            202.672

            ELEMENT SOLUTION STEP=l

            –

            SUB =1 TIME=l

            NMIS73 (NOAVG) DMX =.0127 SMN=-4.452

            SMX =30.732

            -4.452

            -.542928

            3.366

            D 7.276

            –

         2. Stress perpendicular to the fibre direction

            1. Load of 11.5 kN

               J\N

               D 11.185

               D 15.095

               D 19.004

               D 22.913

               D 26.823

               30.732

               ELEMENT SOLUTION STEP=l

               SUB =1

               –

               TIME=l

               NMIS72 (NOAVG) DMX =.012317 SMN=-45.536 SMX =436.102

               -45.536

               7.98

               61.495

               D 115.01

               –

               (i) Stress along the fibre direction

               J\N

               D 168.526

               D 222.041

               D 275.556

               D 329.071

               D 382.587

               436.102

               ELEMENT SOLUTION STEP=l

               (ii) Stress perpendicular to the fibre direction

               SUB =1 TIME=l

               NMIS73 (NOAVG) DMX =.012317 SMN=-7.942

               SMX =42.676

               -7.942

               -2.318

               -D 3.306

               8.93

               D 14.555

               D 20.179

            2. Load of23.1 kN

         25.803

         31.427

         0 37.051

         42.676

         –

         Figure 9. Stress plots in the adherend of FJF bonded joint

         It is observed that matrix crack and delamination is not propagated upto end of the adherend. This may be due to shifting of adherend plane where joggle is present from its plane of loading. From experiments two samples failed in this mode and in the other two, damage has propagated upto the end of the adherend. The maximum shear and von-Mises stress deveoped at interface of the joint are shown in Figure 10 at ultimate failure load of 23.1 kN.

         Figure 10. Stresses developed in adhesive at the interface (at 23.1 kN)

         Table 4 shows a comparison between experimental and FEA failure loads in FJF joint. The error between the two is around 13 %.

         Table 4 Comparison of failure load in FJF bonded joint
         	Expt. (avg) (kN)	FEA (kN)	% Error
         Failure Load	20.5	23.1	13

   8. CONCLUSIONS

In the present work experiments and FEA are carried out for FJF bonded joints. To predict failure in adherend, Hashin failure criterion is used for laminate and maximum shear stress, Ye-delamination and cohesive stress failure criteria are used for adhesive.

• The design of FJF joints helps to eliminate eccentricity by the presence of joggle so that loading is in-plane avoiding any bending effects thereby increasing the strength of the joint.

• In FJF bonded joints, an increase in strength of 90 % is observed over flat joints.

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