The increased energy dissipated for adhesion to a rough surface is usually a result of plastic dissipation processes, evidence of which can often be obtained by examining the fracture surfaces. However Gent and Lin have shown that large amounts of energy can also be involved in peeling an elastic material from a rough surface [71]. The energy is essentially used for the elastic deformation of embedded filaments: this energy is lost because when the filaments become free, they immediately relax.
Gent and Lin experimented with rubber bonded to a model aluminum surface, consisting of plates with regular arrays of cylindrical holes. The peel energy was low for the plates in the absence of holes. An energy balance analysis given the ratio of fracture energy for peeling from the material with cylindrical pores G’a to that from a smooth substrate Ga as
(15)
where l is the pore length, a its radius, and ф the ratio of pore area to total area of the plate [71]. Their experimental results demonstrated the essential validity of this relationship. Where pull-out alone occurred the work of detachment for their system increased by up to 20 times.
They further considered the additional energy lost where fracture of strands occurred. An extra term, lUb*, is added to the value of G’a given by Eq. (15). Ub is the energy to break per unit volume, which for the rubber they used is an elastic stored energy. Because this additional term is proportional to the depth of the pores, it dominates for deep pores. For Gent and Lin’s system, it could be several hundred times the work of detachment from a smooth surface.