# Failure Analysis Of Bonded Joints English Language Essay

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## Objective and Scope

To determine the difference between cfrp and aluminium single-lap joints in terms of their failure strength with the aid of Finite element method, these results are then compared with results from experimental analysis

## Adhesively Bonded Joints

An adhesive is a material used to bond two other materials together ,In recent years the use of polymeric adhesives to join components for various applications has increased greatly, this is mainly due to the introduction of new more robust adhesives that can be used for complex geometries.

The adhesive joint provides a path for load transfer between the adherends, These joints add a discontinuity to the structure and are potentially the weakest regions in the structure.

There are a variety of methods for creating these joints the more popular methods include welding, soldering, riveting, bolting and adhesive joining, among all of these methods mentioned adhesive bonding is by far the most widely used due to the fact that it does not require the adherends to be modified in any way, for example riveting and bolting require holes to be machined which cause undesirable stress concentrations ,where as welding and soldering leave a heat affected zone thus causing residual stresses.

As mentioned above methods other than adhesive bonding cause unnecessary stress concentrations thus reducing the strength of the entire structure , Previous research (references) carried out states that mechanical fastening can only achieve a strength of about 50% of the strength of the weakest adherend where as adhesive joints are said to achieve a strength of 80% of the weakest adherend.

Adhesives are becoming more and more popular for creating joints for example the aerospace industry. adhesive bonding distributes stresses over whole bonded area hence reducing stress by reducing the possibility of stress concentrations (compare with riveting and bolting), adhesive bonding does not require any extra equipment other than the adhesive as compared to other method of joining such as welding , as adhesive bonding is done at room temperature the material is free of any heat affected zones, adhesive bonding reduces the weight of the overall structures (high weight efficiency index),adhesive joints have a low cost potential, Despite their numerous advantages adhesive joints are still faced with a number of drawbacks including the fact that the joint cannot be disassembled without damaging the structural components, they are less resistant to chemicals and are more susceptible to age affects and fatigue loading.(thesis fe analysis.pdf)

## Composite Materials

A composite is a material that consists of two other materials and displays desired properties of both constituents, such as compressive strength of resin and tensile strength of fibres, this gives the material enhanced strength without adding any significant weight ,Figure ? shows an Ashby property map displaying the higher Young's Modulus of composites while having a lower density than most other materials such as Aluminium,

Figure 1.1 Ashby Property map for composites

The composite material usually consists of fibres embedded in an epoxy resin matrix,

The three main types of fibre used are:

Glass

Carbon

Aramid (aromatic polyamides, such as Kevlar ).

Matrix

Fibre

Figure 1.2 Long fibre composite material with fibre's embedded in a matrix phase

The research carried out was focused on Carbon fibre reinforced composites, more specifically CFRP ,which are basically composite materials made by reinforcing a resin (usually epoxy) with carbon fibres, Figure ? shows .

In some types of composite, the fibres are oriented randomly within a plane, while in others the material is made up of a stack of differently-oriented "plies" to form a laminate, each ply containing an aligned set of parallel fibres. The choices of composition and of the materials used as matrix and fibre are dependent on the required properties, The CFRP composite material used for the purpose of this research was a had a cross ply alignment , that is the arrangement consisted only of plies oriented at either 90 or 0 degrees.

{((Add details of ply arrangement in appendix ,with figure showing this arrangement{}_

For thousands of years we have been using composites, whether it be in brick walls or concrete, and now, composites are widely used in automotive, aerospace, marine and sports applications. Therefore an understanding of how composite materials behave is crucial to any technological advances.

(http://www.doitpoms.ac.uk/tlplib/fibre_composites/intro.php)

Background

## Mechanics of single lap joint:

The single lap joint is one of the simplest joint to analyse, due to this relative ease of analysis strength prediction of the single lap joint is a very important step for predicting strength of more complex geometries as well

Extensive research of adherend and adhesive properties is necessary for accurate solution of both analytical and numerical analysis

In adhesive bonding load is transmitted from one adhered to the other via the adhesive layer in the overlap region ,when loaded state of mixed stress is developed ,combination of shear stresses parallel to bonded surface and tensile stresses perpendicular to them ,this stress combination arises due to non-collinear tensile stresses in the specimen

Due to the continuously increasing stretching force all stresses superimpose on the overlap region causing adhesive failure.(149.pdf,as wells as mage)

Adhesive joints are intended to transfer load from one adherend to the other simply by a shearing mechanism but due to the eccentricities in loading peel stress is seen in the joint which is one of the major causes of less than expected strength of the joint,plastic bending of the joint can also lead to high strains which less ductile adhesives cannot withstand thus leading to bond failure(Shigley's Mechanical Engineering Design -Richard G.Budynas and J.Keith Nisbett)

Some basic things to look at when creating or analysing joints:

Peel stresses are usually what cause premature failure of sinlge lap joints, they can be reduced by tapering the adherend ends or by increasing bond are at location where peel is likely to occur

The adhesive selected should be as ductile as possible as this gives room for plasticity to occur and thus increasing the toughness of the bond

Some adhesives are affected by the environmental conditions such as exposure to water and solvents which can degrade the performance of the adhesive substantially

Increasing the bond area increases the strength of the bond, after a certain amount of increase in bond area the strength of the bond does not increase further, the bond area should not be exceedingly more than this optimum overlap area as this only increase weight by adding more adhesive.

(Shigley's Mechanical Engineering Design -Richard G.Budynas and J.Keith Nisbett)

The line of action of tensile force in a single lap joint is not parallel to the adherend sides as the load is increased the adherends and adhesive layer bend (Figure 2.1), High peel and shear stresses are seen at the ends of the overlap, the peel stresses usually lead to failure.

Figure 2.1. Line of action of tensile force and bending of adherends and adhesive layer

There are two main methods of analysing lap joints a closed form solution and numerical solution. In the first approach a set of equations and boundary conditions are formulated which when solved give stress values for any point in the joint. In the second approach the finite element method is used to analyse the joint with the aid of computational tools ,The ANSYS software package was used for the purpose of the research carried out.

There has been a lot of research on developing a closed form solution by several researchers. Deriving an exact solution is a very hard task to perform mainly due to the non linear behaviour of the adhesive layer and also somewhat due to the complexity of the geometry (the non linear load path)

Figure 2.2 Shear and Peel stresses in adhesive layer of lap joint

The single lap joint is comparatively weaker than other joints but the relative ease of analysis makes it the best choice for comparing CFRP lap joints with Aluminium lap joints.

The simplest lap joint analysis is derived by assuming the adherends to be rigid and the adhesive to only deform in shear. The equation formed gives a shear stress which is more of an average value it is as follows:

Figure 2.3 Geometry of lap joint.

## = =

Equation 2.1

Fig. 2.4. Stresses in single lap adhesive bonded joint: -shear stresses which are parallel to bonded area caused by moving parts that are

Where P is the applied load, b is the width of the adhesive layer and l is the length of overlap ,This equation gives us an idea of the stresses in the adherends and is not accurate enough to determine stresses in the adhesives as it neglects many important factors but this equation is helpful in a way as it tells us that by increasing the area of overlap we can decrease the shear stress .

Figure 2.5. Shear stress distribution given by simplest analysis, where the dashed line gives the shear stress distribution obtained from this analysis.

Volkerson (O. Volkersen, Luftfarhtforschung, vol. 15, pp. 41-47 (1938) )

first proposed his shear lag model in "1938" for bolted joint s which was later developed into an adhesive joint analysis, The main issue with this model is the fact that this solution assumes both adherends to be in pure tension and adhesive to be in shear only with the stresses being constant along the thickness this means that the Volkerson method does not take into account adherend bending and shear deformations which leads to inaccuracies in the final solution

In 1944 Golland and Reissner (Reference) further developed on Volkerson's solution and took into account the eccentricity in the lap joint by including the effects of peel stresses and shear deformations on the joint as well as shear stresses , L.J Hart-Smith (reference) modified the shear lag model to include adhesive plasticity .

All of the methods other than the average stress approach tell us that maximum shear stress occurs at the overlap edges.

Analytical Analysis

## Volkerson Shear Lag model

The average shear stress equation (2.1a) does not give us an accurate depiction of the stresses within the lap joint, as it fails to take into account factors such as the adhesive thickness and modulus, the adherend thickness and modulus, and all other complex geometrical factors such as spew and fillets, Although the Volkerson model also fails to take into account some of these factors it still gives a more accurate depiction of stresses within the joint.The Volkerson shear stress along any point in the adhesive layer "x" is as shown in equation (3.1 a)

Figure 3.1 ,Joint ...

= {(k-1)cosh (l-x) +cosh} (3.1a)

=[ +] (3.1b)

k= + 1 (3.1c)

= (2.1a)

Where:

=Shear stress at x along the bondline

=Overlap length

x=distance along the bond line from centreline

P= Force per unit width

b=width of adhesive layer

=Adhesive shear Modulus

=Young's Modulus of first adherend

=Young's Modulus of second adherend

{{((Data from volkerson in appendix +extra graphs with comparion))}

Assumption:

Adhesive deforms in shear and offers no axial stiffness

Adherends extend, but do not shear

Adherends and adhesive are linear elastic

Fails to take into account:

Load eccentricity, adherend bending, moment equilibrium

Peel stresses (normal stresses)

Singular stresses, spew details

## Golland and Reissner

The Golland and Reissner solution adds and improvement to the Volkerson analysis by taking into account the deflection of the joint due to the eccentric nature of the joint and peel stresses.

PEEL STRESSES volky and g theo

Graph showing comparsion between results obtained from both methods for one geom

Numerical Solution

## Finite element analysis

With the introduction of more advanced computers the finite element method is gaining more popularity as it gives an approximation as to what the solution is without the need to create a prototype.

The finite element method calculates a solution for the above mentioned problem (Finite element analysis :Theory and practice by M.J Fagan) by subdividing the assembly into elements which are interconnected at nodes, after discretisation of problem equations for each element are calculated and assembled to give system equations which are then tabulated with input data from material properties and loading conditions to give a solution

Given unlimited computer resources the finite element method would be able to solve any given stress problem with great accuracy, however as these resources are limited the FE method still has room to evolve.

The finite element method gives an approximate solution, the accuracy of the result depends mainly on the mesh density ,the element type, the accuracy of geometric representation, the element shape and the boundary conditions used.

Every FE analysis requires some sort of validation method, as mentioned previously the FE method is an approximate solution hence the need for validation this can be done by correlating the results to some analytical or experimental solution , an exact match is not expected due to errors in experimental solution and assumptions made in analytical solution but the solution's should show a close enough match.

Using the ANSYS software package a finite element analysis was performed on different geometries of both CFRP and aluminium alloy lap joints to determine the peel and shear stress distribution in the adhesive layer. Both two-dimensional and three dimensional analysis were done using Plane 82 and Solid 45 elements respectively, For the purpose of validation the stresses from the FE analysis will be compared to those from the Golland and Resisner solution to determine the validity of the FE solution.

The adhesive properties modelled in ANSYS came from Araldite slow set resin manufactured by Araldite.inc .The material properties for the CFRP and Aluminium adherend came from uniaxial tensile tests . All materials properties used are as listed below:

Material Property

Araldite Adhesive

Aluminium Adherend

CFRP Adherend

(MPa)

2300

71000

## ???

(MPa)

2300

71000

## ???

(MPa)

2300

71000

## ???

Poisson's Ratio

0.35

0.34

## ???

## Three-Dimensional Elastic Solution's

Results from the 3d analysis showed that stresses did not vary across the width of the adhesive, hence a 2d model was an accurate simplified depiction of the lap joint.

The geometry of the modelled lap joint and the material properties used were taken from actual experiments performed at The University of Sheffield, details of the experiments are explained in detail later. The adhesive was modelled with dimensions shown in Figure 4.2,The overlap length was varied for reasons explained in 5.1, F or validation of FEA model and comparison between different FEA element types and inputs an overlap length of "12.5 mm" is used in all of Section 4 .Figure 4.1 shows the boundary conditions being applied to the 3 dimensional model, the light blue region at the edges shows the parts of the lap joint that are constrained ,the figure fails to display the adhesive edges ,they are modelled to be square ,in reality this is rarely the case as the adhesive is squeezed out and forms a fillet or a circular shape when the adherends are pushed together, the effects of including the fillet in modelling are discussed later.

The element used for modelling the problem of Solid 45

The vertical displacement of both adherends was constrained at the ends to accurately display the constraints imposed by the tensile testing machine, the lower adherend also had its x-displacements constrained at the free end, A force equivalent to 10kN was applied to the upper adherend in the positive x-direction.

As the model is a three dimensional the computing time is significantly increased due to the large number of elements and nodes, to reduce computing time and resources the lap joint was modelled with symmetry boundary conditions which halves the computing time, The mesh density in the overlap region was refined until values for peel and shear stresses converged, this was done for an accurate solution.

The solution from the FE analysis were compared with the Golland and Reissner ,although the results do not show an exact match due to the simplifications and assumptions buil into the analytical solution however a similar trend was seen as shown in Figure ?............................................

({{{{EXPLANATION OF G AND R VS FEA AND VOLKERSON WITH BRIEF EXPLANATION AND FIGURES SHWOING THE SIMILARITIES AND DIFFERENCES}}

Figure 4.1 Boundary conditions applied to Three-dimensional model

Figure 4.2, Geometry of lap joint ,where a=25 mm, s=2.0mm,b=80mm, Î´=0.18mm, "l" the overlap length is varied with three different values 12.5mm,20mm and 35mm

## Two-Dimensional Elastic Solution's:

For the purposed of the two dimensional-analysis the Plane82 element was used to model both adherends and the adhesive layer, the Plane82 element is an 8 node isoparametic element which gives solutions for both plane stress and plane strain cases, Plane strain assumes that the width of the element approaches infinity while plane stress assumes the width to be very small, The single lap joint considered has a width of 25 mm which cannot be completely considered a plane stress or plane strain case rather somewhere in between, to investigate this further FEA analysis was done for both cases and results compared with the three dimensional model whose sole purpose was to determine the effect of the width on the solution.

An accurate solution from the two-dimensional analysis requires a very fine mesh especially in the regions of interest, these regions of interest are the areas where failure is likely to initiate due to the high stresses, the refined mesh is shown in Figure 4.3. Solving a two-dimensional model even with a refined mesh does not take as much processing time as a three -dimensional model would, hence this simplification to the model is a necessary one

Figure 4.3 Refined mesh used for Plane 82

## plane stress

graph

## plane strain

Figure 4.4 Boundary condition applied to plane82 model

show boundary c

Mesh density,element consideration,element shape considerations,adhesive layer modelling,plane strain or plane stress

The results obtained from plain stress as plain strain solutions showed a close match to the Golland and Reissner solution

## graph showing plane stress vs plain strain results (ADD G AND R TO GRAPHS)-CHANGE GRAPHS TO 12.5 MM GEOM

Figure 4.4 Peel stress distribution in adhesive layer

Figure 4.5 Shear stress distribution in adhesive layer

## FE Result Analysis

Figure 4.6 Shear stress distribution from FEA and Volkerson

graph showing comparison between 2d and 3d analysis

comparions between 2d pstress and pstarin and g and r and 3d

## Limitations of FE analysis

## FEM analysis: package,elemt type (2d 3d why ? ,which is better?,mesh refinement,material prop "adhesive,adherends", results analysis ,which results looked at,what do they mean", geometry and loading (figure)

Graph comparison volkerson,g s and FE METHOD and experimental at end

Optimisation of Geometry

-Shear stresses occur at any place where there is a relative change in stiffness in the adherends ,abrupt changes in stiffness lead to larger peak stresses ,gradual changes give a more uniform shear stress distribution (bridge -02 pdf)

overlap length (optimum equation),why 12.5mm??:graph of overlap against failuire load

Theoretically it is possible to increase the strength of the joint by increasing overlap area , however after an optimum overlap length is reached the strength of the joint does not increase further this is because at short overlap lengths all adhesive material is under high stress whereas for longer overlap lengths the ends of the overlap are the areas under the highest stress and thus develop a plastic zone at the ends , Before any FE analysis or physical testing was done an optimum overlap length needed to be estimated so that resources were not wasted ,this was done by using the following equation:

Optimum overlap length = 30 .t.R =30*(0.18)*

(149.pdf)

(background)

Adhesives have low strength and stiffness as compared to most other materials, thus increasing the the overlap region has an effect of increasing the load transfer region ,this larger area reduces stress (mechanical methods of joining such as riveting and bolting increase the stress)

## Increasing Overlap Length

## Adding a taper

increases load transfer area and decreases peak stresses(other methods reducing adhesive shear modulus, increasing adhesive thickness,in actuality there is always some fillet (ansys analysis of lap joint other stuff.pdf)

The effects of adding a 45â° fillet to the single lap joint was investigated, the taper was created at the unloaded end of the lap joint as shown in Figure 5.1 , the results obtained show that both the adhesive peel stress and the adhesive shear stress are reduced , if the

Figure's 5.1 and 5.2 show the peel and shear stress distributions in a joint with a 45Â° taper, the stress values are in MPa and as the results are from plain stress solution hence all values will be divided by the width of the joint to determine the actually stress values.

45â°

Figure 5.1 Peel Stresses "" in a 45Â° tapered lap-joint, stress values are in MPa

Figure 5.2 Shear Stresses "" in 45Â° tapered lap-joint, stress value's in MPa

{{(FIGURE SHWOING STRESSES IN TAPERED REGION

The graph in Figure 5.3 shows

## Changing the edge shape (fillet)

Figure 5.4 Shear stress "" distribution in lap-joint with fillet, values in MPa,264.12

Figure 5.5 Peel stress "" distribution in lap-joint with fillet, values in MPa,223.6MPa

{{{(FIGURE ....)

## Optimised geometry (Reverse Tapering and an adhesive fillet)

## {{(FIGURE USING)}}

Parametric Study

## Failure Criteria

## failure criteria :adhesive failure,adherend failure,adding taper,adding fillet,weird personal taper

In applying a yield criterion, the resistance of material is given by its yield strength , Yield strengths are most commonly found by performing tensile tests, The occurrence of failure can for isotropic materials can be expressed simply by relating the failure strength of material found from a unaxial test the applied force. As for orthotropic materials failure is determined by relating the applied force in a specific direction to the failure strength in that direction hence failure occurs when force in any direction exceeds strength in that specific direction .

In order for full utilisation of adhesive joints strength prediction is an important step whereby one

The failure modes of adhesively bonded joints can be split into four major categories:

Adherend Failure

Cohesive Failure

Adherend-Adhesive Interfacial Failure

Out of plane adherend failure

## Adhesive Failure

The failure analysis of composite material lap joint is complex due to the fact that the mode of failure differs depending on the bonding method and adhesive properties.

There are two types of failure criteria one is stress-strain bases the other is fracture mechanics based, the stress strain based criteria may not be suitable due to stress or strain singularities in bonded joint ,the fracture mechanics criterion is not suitable as there is no crack initiation phase in the failure of the joint ,Both of these methods consider only one failure mode whereas various failure modes may appear depending on the material properties and adhesive method used, another common drawback is the fact that both of these methods do not consider the plastic behaviour of the adhesive ,some local parts of the adhesive become plastic due to high stress concentrations before final failure,

To predict failure , the adhered and adhesive are considered separately

Failure of adhesive layer: cohesive failure and interfacial failure of adhesive, other is delamination failure of composite adherends, the criterion used to determine the progressive adhesive failure is an elastic-perfectly plastic model, In this prediction it is assumed that plastic regions initiate at edges of the overlap region due to high stress concentrations ,the plastic region propagates along the adhesive layer as load increases ,When overall region of adhesive layer becomes plastic failure is predicted to occur.

Figure 6.1 Elastic-Perfectly plastic material model for adhesive

(best.pdf -all failure)

## Adherend Failure

## Failure of CFRP adherend

The carbon fibre adherend in question is a cross ply with symmetry, An anisotropic yield criterion is used for defining failure in carbon fibre reinforced plastics due to their orthotropic nature.

The Hill criterion as described below has been used as a failure criterion for orthotropic composite materials with reasonable success.

H+ F+ G +2N+2L+2M

Equation 6.1

Let , and be the unaxial tensile strengths in the three directions, and let , and be shear ultimate tensile strengths on the respective orthogonal planes. H,F,G,N,L and M are empirical constants for the material and can be evaluated from the various tensile strengths as follows:

H+G=, H+F=, F+G=,

Equation's 6.2

2N=, 2L=, 2N=,

Equations 6.3

(Mechanical behaviour of materials , Engineering methods for deformation, fracture and fatigue by Norman .e Dowling)

## Failure of aluminium adherend

As aluminium adherends are isotropic, failure can easily be predicted by basic failure criteria such as the maximum stress criterion which predicts failure to occur when stress in a specific direction exceeds strength in that direction, The Von Mises stress predictions a safer approximation.

Equation "6.4" describes the Von Mises failure criterion , where , and are principal stresses.

++ =2

Equation 6.4

For aluminium is equal to 210 MPa

Experimental Analysis

A limited amount of tensile tests were performed for selected geometries for verification of FE and analytical solution as well as for determining their accuracies.

All tests were carried out t the University of Sheffield using an ---- machine

## Experimental analysis:surface preparation, eccentricity in loading(how it was dealt with), errors and justification,mode of failure (pictures)

## List of tables ,figures

-machinery to be used

## Materials used orientation

## Surface preparation and Eccentricity in loading

Surface preparation can have a significant effect on the strength of a bonded joint, For good adhesion properties the adherend surfaces in contact with the adhesive are sandblasted so that friction between the surfaces increases thus giving a stronger bond.

As discussed earlier in section "2.1" the single lap joint creates an eccentricity in loading ,to reduce the effects of the eccentricity the ends of the lap joint are bonded to ...

{{(figure SHOWING ECCENTRICTY LAP CRAG SHEAR TEST}}

## Testing sequence -method

The test specimen must be carefully aligned in the jaws of the test machine to avoid induced bending, The tensile load should be increased uniformly to cause failure within 30-90 seconds ,when environmental conditioning is required it should be undertaken on the complete specimen after manufacture.

## Calculations and Results analysis

The mean shear stress at failure is given by :

## =

Equation 7.1

Accurately measured values of "w" the width of the adhesive/adherend and "l" the length of the overlap must be used

## Mode of failure

-Pictures

Conclusions and Recommendations

Figure 8.1 Increasing efficiency of lap joint with increased contact, reduced eccentricity

## CFRP VS ALUMUNIUM LAP JOINTS (UTS COMPARISON)

## EXPERIMENTAL RESULTS VS FINITE ELEMENT RESULTS (ACCURACY AND VALIDATION)

## Suggested Improvements to current methods of analysis and testing

## Errors -inclusions etc

References