(Invited) Distinctive Characteristics of Internal Fracture in Tough Double Network Hydrogels Revealed By Various Modes of Stretching
Authors: MAI Thanh-Tam , Matsuda Takahiro , Nakajima Tasuku , Gong Jian Ping , Urayama Kenji 
Published: February 2020

Double network hydrogels (DN gels) known as the extremely high mechanical strength, i.e., elastic modulus of 0.1–1.0 MPa, ultimate tensile stress of 1-10 MPa, ultimate tensile strain of 1000–2000%, and tearing fracture energy of 100–2000 J m-2, were first reported by some of present authors.1 DN gels are composed of the two contrasting and well-entangled chemically cross-linked networks: The 1st network is formed by rigid and brittle polyelectrolyte, while the 2nd network is made of soft and ductile neutral polymer. A key of the high mechanical performance of the DN gels is the internal fracture of the chains in the rigid and brittle 1st network which are served as the sacrificial chains. The irreversible fracture of sacrificial network strands is clearly recognized by the irreversibly mechanical softening in the loading-unloading stretching, known as the Mullins effect.2 The internal bond fracture of the DN gels was investigated by using uniaxial deformation in most earlier studies. Uniaxial deformation, however, gives a limited basis for the comprehensive understanding of the nonlinear mechanical behavior, because it is only a particular one among physically admissible deformations of elastomeric materials. To our knowledge, the Mullins effect of tough DN gels has not yet been characterized by various modes of biaxial stretching.
The present study employs several types of biaxial deformation, i.e., planar extension (PE), unequal biaxial extension (UB, with a ratio of 1/2 for the nominal strains in the two directions (μ = ε
y/ε
x)), equibiaxial extension (EB), and uniaxial tension (U) for the characterization of the internal fracture in tough DN gels (Fig. 1).3 In the biaxial extensions, the sheet samples were deformed with the constant crosshead speeds of V
x and V
y in two orthogonal directions (x- and y-directions) by using the custom-built biaxial tester,4 and the resulting tensile force was measured in each direction. In EB, the specimens were stretched equally in the x- and y-directions with the same stretching speed (V
x = V
y). In PE, the specimens were stretched uniaxially in the x-direction, while the dimension in the y-direction was kept unchanged. In UB, the specimens were stretched unequally with V
y /V
x = 0.5 corresponding to ε
y/ε
x = 0.5. For the investigation of the internal fracture during loading, the specimens were stretched with the loading-unloading cycles using various degrees of the maximum elongation (λ
m) in each type of extension.

Fig. 2 shows the nominal stress-elongation relation of loading-unloading cycles for DN-gels under equibiaxial extension (μ
= 1) in x-direction. The numerals denote the values of λ
m in each cycle. The solid and dashed curves indicate the loading and unloading processes, respectively. The analysis of the loading-unloading curves provides the initial modulus (A
i, i=U, PE, UB and EB), energy dissipation (D), and the dissipation factor (Δ, defined as the ratio of D to the input strain energy). The modulus ratio (A
i/A
0
i, which A
0
i denotes the corresponding A
i of virgin sample) and Δ depend on the stretching mode when compared at the same λ
i,m (i=x,y), but each of them exhibits a universal relation independently of the stretching mode when the corresponding magnitude of 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
2
λ
y,m
2 + λ
y,m
2
λ
z,m
2 + λ
z,m
2
λ
x,m
2)­ is used as a variable (Fig. 3). This is in contrast to that Δ of the filler-reinforced elastomers, which undergo apparently similar mechanical hysteresis, show the corresponding universal relation using I
1,m as a variable.4 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.
In addition, ultimate elongation of network strands in each cycle (λ
im
*, i=x,y) as a function of λ
im in various deformation modes was also investigated. 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.

Reference

(1) Gong, J.P. Katsuyama, Y.; Kurokawa, T.; Osada, Y. Adv. Mater.
2003, 15 (14), 1155–1158.
(2) Mullins, L. J. Rubber Res.
1947, 16 (12), 275–289.
(3) Mai, T.-T.; Morishita, Y.; Urayama, K. Soft Matter
2017, 13 (10), 1966–1977.
(4) Mai, T.-T.; Matsuda, T.; Nakajima, T.; Gong, J.P.; Urayama, K. 2018, submitted.

Figure 1