Page 108 - Handbook of Adhesives and Sealants

76 Chapter Two

If the adherends are assumed to be unyielding, and the adhesive is
relatively flexible and thick, the greatest stress on the adhesive, oc-
curring at the ends of the joint, may be approximated from the follow-
ing relationship:

S T (k k )(GL/2d)
2
1
where S greatest shear stress in the adhesive due to differential
thermal expansion of the adherends, without considera-
tion for adherend strain
G shear modulus of the adhesive
d thickness of the adhesive
L length of the joint

These theoretical expressions are approximations in that they exclude
the strain capability of either the adhesive or the adherends. Such
strain would tend to relieve some of the stress. The values calculated,
however, are greater than the actual stress and, therefore, conserva-
tive.
Methods of reducing such stresses consist of using flexible materials
or trying to better match the thermal expansion coefficients. The co-
efficient of thermal expansion of adhesive and adherend should be as
close as possible to limit stresses that may develop during thermal
cycling or after cooling from an elevated-temperature cure. As shown
in Table 2.3, polymeric adhesives generally have a thermal-expansion
coefficient an order of magnitude greater than metals. Adhesives can
be formulated with various fillers to modify their thermal-expansion
characteristics and limit internal stresses. A relatively elastic adhe-
sive capable of accommodating internal stress may also be useful
when thermal-expansion differences are of concern.
Once an adhesive bond is made and placed in service, other forces
are at work weakening the bond. The type of stress involved, its ori-
entation to the adhesive, and the rate in which the stress is applied
are important. When a bond separates cohesively, it is because adja-
cent molecular segments have physically moved away from each other.
This could occur from breaking of strong bonds within the molecular
chain or from rupture of weak bonds between the chains. The bond
separation is either rapid (cracking) or slow (creep).
Cracking results when a localized stress becomes great enough to
physically separate adjacent molecular segments. Highly crystalline
or highly crosslinked polymers are likely to crack rather than creep
under stress. When bond separation appears as an adhesive failure,
it is generally because a crack has followed the interface surface or
because some chemical has displaced the adhesive from the adherend
(see below). Cracks may result from internal or external stress.