Chain pullout energy

The problem of evaluating the fracture energy Gic of polymer interfaces is represented in Fig. 1. Material A is brought into contact with material B to form an A/B interface, the weld is fractured and the strength is related to the structure of the interface through microscopic deformation mechanisms. If interpenetration is limited, chain pullout and perhaps chain fracture may occur. Such an interface is weak and may be modelled using the Nail Solution discussed below. 

Low molecular weight When M < Me (region A, O Fig. 2.9) only short lengths of polymer chain are involved in the fracture process, which occurs by chain pullout. The fracture energy is low, up to about 1 J/m. ... 

Fracture behavior in this region can be treated using the nail solution where the weak interface is modeled as if the two sides were nailed together with Z nails per unit area, each of length L. The analysis shows that the fracture energy associated with chain pullout, G, increases with and with Z. To this friction term must be added a surface energy term, so that... 

The toughness of an interface will be expected to be related to the depth of interpenetration of the chains. Wool (1995) has argued that the fracture energy, G, for chain pullout, is proportional to the square of the interface thickness, which, via Eq. 2.6, gives... 

Here, the polymer-polymer laminate (see Figure 1) is modelled as a cantilever beam comprising two planks of wood, nailed together by S nails (molecnlar chains) per unit area with penetration length L. A simple analysis of the energy required to pullout the molecules leads to expressions for the fracture energy of the form... 

When M < Me, the role of entanglements is no longer present and Eqns. 2 and 3 cannot be used since Gie = 0 at Me. However, the Nail solution applies for weak interfaces (see Eqn. 3 in Polymer-polymer adhesion models) and the chain segments simply pullout at fracture such that (Gic-Gq) M, where Gq is the surface energy term, and we obtain. 

Further Evans (67) examined the energy required to pull a chain out of a tube. The energy for pullout of a chain end, Ep, is given by... 

---