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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__ *T _{g}*, 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
**c _{i}
** 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

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 [

_{}
(1)

Where
** c
** is the moisture concentration,

(2)

_{}

The diffusivity changes very little with moisture content, and thus the
solution to Equation (1) is given by [__3__]:

_{}
(3)

** N
** is the number of summation terms and

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 [__4__]. 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:

_{}
(4)

where *W _{i}* and

**(a)**

**(b)**

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

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