6.6: Summary of Fractures in Bio-Based Polymers

6.6 Summary of Fractures in Bio-Based Polymers

A theory of fracture of entangled polymers was developed that was based on the vector percolation model of Kantor and Webman [6], in which the modulus E is related to the lattice bond fraction p, via E ~ [ p ? p _c] ^?. The Hamiltonian for the lattice was replaced by the engineering strain energy density function of the bulk polymer, U = ? ²/2 E, and p was expressed in terms of the normalized entanglement density, using the entanglement molecular weight, M _e. The polymer fractured critically when p approached the percolation threshold p _c, which was accomplished by utilizing the stored strain energy in the network to randomly fracture [ p ? p _c] bonds. The fracture energy was found to be G _{1 c} ~ [ p ? p _c]. When applied to interfaces of width X, containing an areal density ? of chains, each contributing L entanglements, the percolation term p ~ ? L/ X, and the percolation threshold was related to ? _c, L _c, or X _c. This gave a unified theory of fracture for the virgin state of polymers in the bulk and a variety of polymer interfaces. The percolation theory has also been applied successfully to fracture of thermosets (Chapter 7), carbon nanotubes [88], and fracture of polymer solid interfaces [83 87].