We applied the theory of absolute reaction rate studies by Eyring to the process of layer structure formations of carbon black filled rubber vulcanizates due to three-dimensional stresses. The ratio of fracture surface energies (Γ
rad/Γ
lat)
t corresponding to the degree of layer structure formation is approximated by the following equation. The ratio of fracture surface energies is 1 at the initial state and β
∞ at the final state.
(Γ
rad/Γ
lat)
t=β
∞-(β
∞-1)×exp[-exp{-U(σ
x)/kT}•t]
U(σ
x)=U
0-α•(σ
x)
n, n≈2
where, β
∞ is the ratio of fracture surface energies at the final state, σ
X is the maximum principal tensile stress,
U0 is the activation energy at σ
X=0, α and
n are constants,
k is Boltzmann′s constant and
T is absolute temperature. There is a relationship between critical fracture surface energies at the crack-occurring time and the principal tensile stress, which is exhibited by the following equation.
(Γ
rad/Γ
lat)
tc•(σ
x)
m=C
where, tc is the crack-occurring time,
m and
C are constants. The ratio of critical fracture surface energies, degree of layer structure formation, changes of dynamic and fracture properties at the crack-occurring time become smaller compared with those in the initial state as the stress increases.
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