Rate effect in the fracture of rubbers and chemically cross-linked gels

Stationary crack propagation in rubbers and chemically cross-linked gels is studied by a new molecular theory of fracture in polymer networks. The fracture energy G (energy required to create a unit free surface by fracture) as a function of the crack velocity V is shown to obey, when measured in the unit of νlkBT, a master curve as a function of the dimensionless velocity 2tan θV/lβ0(T), where ν is the number density of the network chains, T is absolute temperature, θ is the angle of the crack tip, l is the mean distance between the adjacent cross-links, and β0(T) is the scission rate of the chains. The slope of the master curve in logarithmic scale depends on the nature of chain rupture; it takes a small value 0.16-0.2 in the low velocity region, and exhibits a crossover to the three times larger value 0.5-0.6 in the high velocity region. The ultimate strength G0 as defined by the fracture energy in the limit of zero crack velocity is obtained as a function of the molecular weight of the network chain, the bond energy, and temperature. The theoretical model is applied specifically to peeling and tearing experiments of rubbers and gels to study how the velocity affects the fracture energy in different geometry of network breakage. All results are qualitatively compared with the data reported in the literature.