The cyclic stretching
measurements in various geometries including
uniaxial, planar, unequal, and equal biaxial extension reveal the
distinctive features of the internal fracture in the double network
(DN) hydrogels with high toughness, which are composed of the rigid
and brittle first network and the soft and ductile second network.
The initial modulus, residual strain after unloading, dissipated energy
(D), dissipation factor (Δ; the ratio of D to input strain energy), and the ultimate elongation of
network strands (λi,m*) in each loading–unloading
cycle are evaluated as a function of the imposed maximum elongation
in the i-direction (λ
i,m, i = x, y) in each cycle. The modulus reduction and Δ depend on the
stretching mode when compared at the same λ
i,m, but each of them exhibits a universal relation independently
of the stretching mode when the corresponding magnitude of the deformation
tensor (m
m; m
m = (I
1,m
2 – 2I
2,m)1/2 where I
1,m = λ
x,m
2 +
λ
y,m
2 + λ
z,m
2 and I
2,m = λ
x,m
2λ
y,m
2 + λ
y,m
2λ
z,m
2 + λ
z,m
2λ
x,m
2) is used as a variable. This
is in contrast to that Δ of the filler-reinforced elastomers,
which undergo apparently similar mechanical hysteresis, which shows
the corresponding universal relation using I
1,m as a variable. The difference in governing variable indicates
that the influence of the cross-effect of strains (λ
i
λ
j
; i,j = x,y,z and i ≠ j) on
Δ is pronounced in the DN gels whereas it is minimal in the
filled elastomers. Characteristically, λ
i,m* is close to λ
i,m in every
type of deformation, indicating that in the end of the loading most
of the chains with lower extensibility than λ
i,m undergo fracture whereas most of the long chains with higher
extensibility than λ
i,m remain intact.
The elongation λ
i,m* has no appreciable
cross-effect of strains in contrast to the modulus reduction as well
as Δ.