The effect of moisture migration within an adhesive joint can adversely affect the adhesive bond in three ways:
· Degradation of the bulk adhesive properties (chemical, physical and mechanical)
· Degradation of the adherend/adhesive interfacial adhesion properties
· Degrade the properties and induce dimensional changes of adherends
Water permeation in polymers generally lowers the glass transition temperature Tg, thus lowering the maximum operating temperature. The effects of moisture will often be irreversible (e.g. loss of interfacial strength). Volumetric swelling due to moisture absorption, if significant, may induce additional stresses within the bonded joint compromising the durability of the joint, and therefore should be included in durability modelling of the adhesive.
Moisture degradation effects can be managed through good design and manufacturing procedures:
· Correct selection of an adhesive with low water permeability
· Coating (encapsulating) the exposed edges of the joint with a water resistant sealant
· Use of a suitable primer/coupling agent will improve interfacial durability – a fluid primer that wets the surface will tend to fill discontinuities on the adherend surface
The modelling approach described below is concerned with the weakening of the bulk adhesive and mass diffusion is considered to be the primary transport process. Consequently, weakening of the joint due to moisture absorption is assumed to occur through plasticisation of the adhesive and the failure is cohesive in nature. In fact, interfacial failure plays a predominant role in the moisture resistance of the bonded joint. The subject is a very complicated one, primarily due to the coupled mechanical-diffusion response that influences the joint behaviour.
A scheme is presented below that enables the redistribution of stresses in bonded joints due to moisture ingress to be assessed. The modelling procedure consists of two phases:
· Modelling the moisture absorption in an adhesive joint, and
· Modelling the mechanical-diffusion interaction.
Figure 1: Graphical representation of one-dimensional diffusion problem
The first step in assessing the environmentally degraded response of bonded joints is finding the temporal and spatial distribution of moisture within the adhesive layer. Assuming a rectangular plate is taken to be infinitely long in the y- and z- directions (Figure 1), the moisture content inside the plate varies only in the x-direction (i.e. one-dimensional). Initially the moisture concentration ci inside the plate is uniform. The plate is suddenly exposed to a moist environment and as a result the exposed faces instantaneously reach the equilibrium moisture concentration ca , which remains constant. Further exposure will result in moisture diffusion into the bulk material.
The moisture uptake through the thickness of an infinite plate is given by Fick’s law, which assumes water penetration into a material is dependent on the moisture concentration gradient ¶ c/ ¶ x and time :
Where c is the moisture concentration, x is the thickness coordinate, Dx is the moisture diffusivity of the material (i.e. speed at which the moisture is diffused or penetrates in the x-direction), t is time and the boundary conditions are:
The diffusivity changes very little with moisture content, and thus the solution to Equation (1) is given by :
N is the number of summation terms and c(t) is the instantaneous concentration.
Equation (3) is used to compute the moisture distribution at the nodal co-ordinates within the adhesive, assuming the only concentration gradient is along the bond length. Figure 2 shows the moisture distribution for different time periods up to 12 days within a single-lap joint. Comparisons between the bulk and joint diffusion behaviour indicate that care needs to be taken if the calculated value of the diffusion coefficient of bulk adhesives is used to predict the extent of water penetration in an adhesive joint. Diffusion coefficient for a bonded joint can be an order of a magnitude higher than for the bulk adhesive. The differences between bulk and joint behaviour are attributed mainly to interfacial effects or capillary diffusion.
Figure 2: Predicted moisture concentration distributions along the adhesive layer (half-model)
The resulting moisture distribution along the overlap, shown in Figure 2, indicates that the moisture content in the joint is far from the equilibrium moisture content state after 12 days of water immersion. The moisture profile is symmetric and decreases steadily from saturation level of 10% at the overlap ends to a dry state at the centre of the overlap. However, the one-dimensional diffusion theory is expected to underestimate the moisture concentration at the wider end of the overlap. This is because one-dimensional expressions cannot take into account changes in bond line thickness.
In cases where the geometry is irregular and/or the problem is no longer one-dimensional, a simple analytical solution is not available. An improved scheme, utilising a transient finite element technique developed at NPL enables the assessment of three-dimensional moisture uptake . This approach yields more accurate representations of the moisture concentration field and it can be sequentially coupled with a mechanical analysis.
Modelling the mechanical-diffusion interaction requires the moisture-dependent mechanical properties of the adhesive to be determined experimentally. These need to be obtained from bulk tests performed on the specimens that have been exposed to hot/wet conditions at varying periods of time. Typical tensile stress-strain data obtained from tests conducted on conditioned specimens are shown in Figure 3. It can be seen, that the result of increased exposure time was to reduce the elastic modulus and the yield stress of the adhesive. The strain to failure steadily increases with conditioning time and noticeable plasticisation and necking occurs in specimens that were conditioned for up to 5 days. Test samples tested after 12 days of water immersion failed at far lower strain levels. This brittle failure mode was attributed to the chemical degradation of the epoxy resin due to the extended period of environmental conditioning.
Figure 3: Stress-strain curves for different water immersion periods
It is recommended that weight uptake measurements to be carried out for each bulk test specimen, as well as, for one traveller specimen for each conditioning time period. All specimens should be dried and weighed prior to being immersed in water. Weight is recorded as a function of time and the percentage moisture content, M, calculated by:
where Wi and W0 are the initial and final weight of the specimen. The moisture uptake is plotted as a function of exposure time in Figure 4(a), while Figure 4(b) shows the reduction of the elastic modulus and Poisson’s ratio with increasing moisture content.
Figure 4: Water immersion of AV119 epoxy adhesive samples
The moisture-dependent stress-strain data, shown in Figure 3, provides the full non-linear description of the bulk adhesive properties for use in the finite element model. Using the analytical solution for the moisture profile along the overlap, a different material curve is used for each element in the adhesive layer. The material properties corresponding to any mass uptake of water are determined by interpolation between the two adjacent curves. The reader is directed towards references [4, 5]. Using non-linear elastic-plastic analysis it is possible to determine the distribution of stresses and strains along and across the bond-line as a function of exposure time. As the adhesive absorbs moisture the material plasticises and as a result the shear stress (Figure 5) and peel stress (Figure 6) at the ends of the overlap decrease (stress relief) and the plasticity zones (Figure 7) increase.
Figure 5: Shear Stress Distribution Along the Centre of Bondline with exposure time
Figure 6 : Peel Stress Distribution Along the Centre of Bondline with exposure time
Figure 7: Plastic strain magnitude (left) unconditioned and (right) condition (12 days)
Note: The “apparent” joint strength could in principle increase with exposure time due to stress relief at the ends of the bond-line. In reality, the joint strength decreases as a result of the combined effect of interfacial degradation and reduction in mechanical properties of the adhesive. Numerical modelling needs to account for not only changes in adhesive properties due to environmental exposure, but also degradation of the adherend/adhesive interfacial properties.
Next: Finite Element Approaches for Modelling Interfaces