0.3
0.2
Extension
0.1
0
0.1
0.2
Compression
0.3
0.4
0.8
0.9
1.0
1.1
1.2
λ
Figure 9. Approximation of the nominal stressstrain response of a
butt joint seal in extension and compression. (From Gent and Lindley
1959.)
the ratio of the nominal stress to the apparent
10%
20%
Young's modulus can be written as
σ
λ2 - λ
=
,
(4)
Ea
3
where σ is the nominal stress acting on the seal
and λ is the extension ratio of the current joint
width to the original joint width. The relation is
depicted in Figure 9. Gent and Lindley illustrated
with experimental results that the approximation
reasonably represents the compression of vulca-
(0.275 in.
6.99 mm)
nized natural rubber blocks with d/w ratios from
(0.300 in.
0.36 to 1.7, and with lengths equal to w, to approxi-
7.62 mm)
mately 25% compression. These results, by the in-
a. Deformed quarter sections at 10% and 20%
fluence of the apparent modulus on the large defor-
joint extension.
173
mation response, provide further elucidation of the
influence of the shape factor on the stress of a seal.
It should be noted, however, that the use of eq 4
implies the applicability of a strain energy func-
tion with the form of the first term in eq 1. Al-
though this term provides a good representation
of rubber constitutive behavior, it does not repre-
sent rubber behavior in general (Treloar 1974).
Cook (1965a, 1965b) later considered the homo-
geneous rubber elasticity relation of eq 4 for seal-
(0.300 in.
7.62 mm)
ant materials, but inappropriately used the equa-
b. Maximum principal stress distribution at 20%
tion directly for the inhomogeneous deformation
joint extension.
of butt joint seal specimens without distinguish-
ing between the material Young's modulus and
Figure 10. Results of numerical analysis of a 1.2-
1.2-cm silicone butt joint seal. (From Catsiff et
the apparent Young's modulus, as shown to be nec-
essary by Gent and Lindley (1959).
al. 1970b.)
13
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