10
e.g., below failure stress levels, both the
depth-to-width ratio of the seal and the
modulus of elasticity of the sealant should
8
be kept optimally small. It is in this context
that measurements of the shear modulus or
6
the Young's modulus as a function of tem-
perature appear practical for seal design.
4
Recognizing the limitations of the above
relations beyond small deformations, Payne
2
(1956) and Gent and Lindley (1959) suggested
the following expression for a large defor-
0
1
2
3
4
5
mation, nominal stressstrain relationship of
d/w
Figure 3. Ratio of the apparent modulus to the Young's modu-
a rubber block.
lus, Ea/E, as a function of the depth-to-width ratio d/w.
1
1
σx =
λ - 2 Ea
′
(7)
3
λ
The apparent modulus is thus greater than the
Young's modulus of the associated homogeneous
where λ = 1 + e is the ratio of the deformed seal
plane strain deformation by the value of the sec-
width to the original width. The expression is a
ond term in eq 1, which models the additional
modification of the large, homogeneous deforma-
structural stiffness that arises from the constraint
tion relationship for the simple extension or
of the bond. Gent and Lindley showed that eq 1
uniaxial compression of an elastic material (Treloar
and 5 correctly represented results of load and
1975). The Payne/Gent and Lindley expression
deflection experiments of rubber structures with
accounts for the inhomogeneous deformation in
length-to-width ratios of three. The joint com-
an approximate manner by the use of the appar-
pressions in these experiments were less than 5%
ent modulus of the structure at small strains Ea
and the material modulus of elasticity was ap-
rather than the Young's modulus E. Gent and
proximately 1800 kPa. Lindley (1967) suggested
Lindley presented experimental results which sug-
that eq 1 is applicable up to nominal strains of
gest that, for accuracy consistent with that re-
about 10%.
quired for design of building and pavement seals,
The plane strain structural stiffness, F/∆w,
the relationship of eq 7 is valid for nominal com-
which corresponds to the apparent modulus Ea,
pression strains up to 30%.
is given by
The expression of eq 7 is illustrated by non-
dimensional relationships in Figures 4 and 5. Fig-
F
d
=
Ea .
(6)
ure 4 shows the ratio of the nominal stress to the
∆w w
apparent modulus as a function of nominal com-
pression and extension strain, and Figure 5 shows
In this equation F is the resultant compressive or
similar relationships for the nominal stress di-
extensive force at the interface per unit length
along the seal.
The relationships of eq 1 and 6 describe
0.3
the structural stiffness of a butt joint seal in
0.2
extension or compression and its depen-
Extension
dence on shape factor and elastic modulus.
0.1
The relationship of eq 1 is depicted in Fig-
0
ure 3 in the form of the ratio of the appar-
ent modulus to the Young's modulus, for
0.1
depth-to-width ratios from 0.25 to 5. As
0.2
indicated in the figure, the modulus ratio
Compression
increases from 4/3 to nearly 10 as the depth-
0.3
to-width ratio increases from 0.25 to 5, re-
0.4
vealing that the average normal stress in
0.10
0.20
0
0.10
0.20
e
the seal can increase by a factor of 7 over
Figure 4. Ratio of the nominal stress to the apparent modulus,
this small range of d/w. It is readily ob-
σx /Ea, as a function of nominal compression and extension
served from Figure 3 that in order to keep
the seal stresses at reasonably low levels,
strain, e, for large deformations.
4
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