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
Predicting the life-time of an adhesive joint is a significant, as yet unsolved, problem for industry  . The area has been extensively investigated, with various approaches proposed and used in attempts to predict joint durability  . 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 
, 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.
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.
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.
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 . 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  . 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 type||Failure surface||Failure stress (MPa)|
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.
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.
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