Subscribe to our newsletter to receive the latest news and events from TWI:

# Predicting adhesive joint life-times (February 2002)

R S Court, S M Tavakoli* and M P F Sutcliffe+

* TWI Ltd, Cambridge
+ Dept of Engineering, University of Cambridge

Paper presented at 25th AMAS and WCARP-II conference on 10-14 February, 2002, in Orlando, Florida, USA

## 1. Introduction

Predicting the life-time of an adhesive joint is a significant, as yet unsolved, problem for industry [1] . The area has been extensively investigated, with various approaches proposed and used in attempts to predict joint durability [2] . In the work presented here, a theoretical model using large-scale bridging concepts has been applied to the problem of joint durability and has been validated against ageing tests on a range of single lap-shear joints.

## 2. Development of theoretical model

The novel method used in this work to represent the adhesive joint is based on a crack-bridging model [3] , which models the large-scale bridging (LSB) conditions where the damage zone in the adhesive layer is large in comparison with the size of a crack. This contrasts with previous models for adhesive joints which have used theories based on continuum mechanics or linear elastic fracture mechanics.

The LSB model uses a force-displacement relationship to describe the material properties of the adhesive, implemented using spring elements in a finite element (FE) model. A schematic diagram of the 2-D FE model is shown in Fig.1, with the spring elements used for the shear and normal forces shown separately for clarity, although they were used simultaneously in the model. The tensile springs undergo the deformations shown in Fig.2. These deformations can be used to develop the relationship shown in Eqn.1 and 2, linking the adhesive's stress-strain response with the geometry of the model and the required force-displacement input data for the spring elements in the LSB FE model:

F 2 = σ.w.l ss and δ 2 = ε n.t a (1 & 2)

where, F 2 is the force, δ 2 is the displacement, w is the sample width, l ss is the spacing of the spring elements, t a is the adhesive layer thickness, σ and ε n are the tensile stress and strain respectively. A similar relationship was developed for the shear springs.

Fig. 1. Schematic diagrams of finite element model for single lap-shear joints
Fig. 2. Diagram of relationship between geometry, stress-strain and force-displacement for normal spring elements

The approach to modelling the joint life-time is based on the changes that occur to the mechanical properties of the adhesive due to the ageing process. Samples of the two-part acrylic (Quickbond 5002) and one-part epoxy (ESP4582) adhesives were hot-wet aged at 40°C and 95% relative humidity (RH) and tested in tension. Fig.3 shows the effect of ageing on the tensile properties of the acrylic adhesive. After 3300 hours of ageing, there were significant reductions in strength, modulus and failure strain for the acrylic adhesive. The epoxy's failure stress (50MPa) was reduced by 25% and the failure strain (1.5%) by 33%.
Fig. 3. Tensile response for acrylic adhesive aged for various times at 40°C and 95% relative humidity

## 4. Joint preparation and ageing

Three combinations of substrate and adhesive were used to make single lap-shear joints: PMMA-acrylic, aluminium-acrylic and aluminium-epoxy. Substrate thickness was 1.6mm for PMMA and 3mm for aluminium alloy 5251. Before bonding, substrates were all grit-blasted, degreased and the Al5251 substrates coated with a silane pre-treatment, SIP from Permabond. The adhesive layers were 0.1-0.2mm thick.

The joints were aged at 40°C and 95% (RH) for up to 13600 hours. Joints were removed after various ageing times and tested in tension.

## 5. Results

### Theoretical model

Results from the LSB FE model for PMMA-acrylic joints are given in Fig.4, which shows the predicted shear stress distribution in unaged and aged joints, at similar values of average applied shear stress. There is a marked change in the shear stress distribution due to the effects of hot-wet ageing, with reductions in the peak stresses at the ends of the joint overlap. Similar results were recorded for the normal stress distributions and for aluminium-acrylic or epoxy joints.
Fig. 4. Shear stress distributions from LSB FE model of unaged and aged PMMA-acrylic single lap-shear joints

### Joint ageing experiments

The average shear failure stresses at each ageing time were measured and the average values from three joints are shown in Fig.5 and 6.
Fig. 5. Average shear stresses at damage initiation and final failure versus ageing time for PMMA-acrylic lap-shear joints
Fig. 6. Average shear failure stress versus ageing time for Al5251-acrylic and Al5251-epoxy lap-shear joints

Reductions in joint final failure strengths were seen for all three joint types. For the PMMA-acrylic joints a video imaging technique was developed allowing the initiation of damage within the joint to be observed and related to the applied load [4]. Damage initiation occurs at around 50% of the final failure stress. All aged joints showed cohesive failure in the adhesive, near to the interface, with no evidence of adhesion or interfacial type failure.

## 6. Validation of adhesive joint model

A comparison of the predictions from the LSB model with the experimental results from joint ageing was performed, making use of various types of failure surface [5] . The experimental results showed no evidence of a change in failure mechanism, which indicates that in this work, the joint performance and hence life-time is controlled by changes in the mechanical properties of the adhesive due to ageing. A comparison of the predicted and experimental failure stresses is shown in Table 1.

Table 1. Predicted and experimental failure stresses for lap-shear joints.

Joint typeFailure surfaceFailure stress (MPa)
PredictedExpt
PMMA-ac un Principal stress 3.5 2
PMMA-ac ag Principal stress 1.0 0.85
Al-ac unaged tension 19.5 22
Al-ac aged tension 7 13
Al-ep unaged shear 18.9 18
Al-ep aged shear 11 15

## 7. Conclusions

A simple and accurate model has been developed for adhesive joints based on LSB concepts, implemented in a 2-D FE analysis. The results from the model were compared with experiment and showed good potential for predicting joint lifetimes, where failure was controlled by the adhesive's properties.

## 8. Acknowledgements

This work was undertaken as part of the TWI - University of Cambridge Post-Graduate Training Partnership. Financial support from EPSRC, DTI and TWI is acknowledged, as is supply of materials and advice from Permabond.

## 9. References

1. M. Davis & D. Bond, Int. J. Adhesion & Adhesives, 1999, 19, 91-105.
2. A.J. Kinloch, Predicting the lifetime of adhesive joints in hostile environments, PAJ-MTS Project 3, Report 5, AEA-ESD-0082, AEA/Imperial College, UK, 1994.
3. G. Bao & Z. Suo, Appl. Mech. Rev., 1992, 45, 355-366.
4. R.S. Court, M.P.F. Sutcliffe & S.M. Tavakoli, Int. J. Adh'n & Adhesives, 2001, 21, 455-463.
5. R.S. Court, The long-term durability of adhesive joints, PhD thesis, University of Cambridge, UK, 2001.