A simple, two-constant, constitutive relation, applicable over the entire range of strains, is proposed for rubber networks. Behavior in simple extension is derived as an example.
Strength of adhesion depends upon the rheology of an adhesive as
well as upon its interaction with a
substrate. This is shown by studies using model joints prepared
with different amounts of interlinking
between two rubber sheets. The fracture energy G per
unit of interfacial area appears to be a product
of two terms: G = G
o [1 +
f(R,T)], where
G
o is the intrinsic (chemical) strength of the
interface and f(R,T),
usually much larger than unity, reflects energy dissipated
viscoelastically within the adherends at a crack
speed R and temperature T. Values of
G
o range from virtually zero for nonbonded
sheets up to the threshold
tear strength of rubber, 50−80 J/m2, in proportion to the
density of interfacial bonds. Values of G are
as
much as 1000× greater at high speeds and low temperatures. Like
adhesion, the tear strength of a soft
rubbery solid is also increased by internal energy losses and shows the
same marked dependence upon
rate of tearing. By comparing the rate R at which tear
strength increases by a certain factor with the
angular frequency ω at which the elastic modulus μ increases by the
same factor the length δ of the
dissipative zone at the crack tip can be estimated: δ =
R/ω. But values obtained in this way are only
about
1 Å, too small to represent an actual dissipation zone in rubber.
It seems likely instead that fracture takes
place intermittently, the crack growing at high speed and then
stopping. A possible mechanism of crack
stopping is by splitting at the crack tip. Indeed, tip blunting
can be inferred by comparing tear strength
with resistance to cutting, when blunting is suppressed. Cutting
resistance increases much more slowly
with increasing rate and decreasing temperature. Thus, much of the
observed tear strength of soft adhesives
and soft solids is attributed to crack-tip blunting. Further
research is needed to establish the exact nature
of the blunting process and how it is related (as it clearly is) to
viscoelastic and dissipative properties.
Attention is drawn to other unresolved issues in adhesion
science.
An unusual rupture process is described. It consists of the sudden appearance of internal cracks in bonded rubber cylinders at a well-defined and comparatively small tensile load. The cracks occur in all the vulcanizates examined, and in particularly weak rubbers are found to cause failure. Their appearance may also lead to marked changes in the load-deflection relationship. A theoretical treatment is presented on the basis of a proposed criterion for crack formation. It is assumed that they form when the negative hydrostatic pressure component of the applied stress reaches a critical value. It is shown by means of the theory of large elastic deformations that a critical value of the negative pressure exists at which any cavity in the rubber will burst, and the calculated value is shown to be in satisfactory agreement with experiment. Moreover, the theory successfully predicts the observed dependence of the cracking stress on the Young's modulus of the rubber, its virtual independence of the rubber strength and extensibility, and the general form of the observed variation of cracking stress and crack disposition with the thickness of the testpiece.
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