STOCHASTIC-ANALYSIS OF PAPER TOUGHNESS

The fracture toughness of paper is modeled by considering bond rupture and fibre failure as stochastic energy-consuming processes at the mic roscopic level. The toughness per fibre is given by W-fibre = N(fibre) w(f) + L(pull)w(1), where N-fibre is the fraction of broken fibres, L( pull) pull-out fibre length, w(f) fibre rupture energy and w(1) bondin g energy per unit fibre length. We derive the functional dependence of L(pull) on N-fibre and fibre length 1(f). The energies w(f) and w1 ar e phenomenological parameters that include possible pre-rupture plasti c deformation in the fibres. The connection between w(f) and fibre str ength is discusses. Fibre and bond rupture are argued to be complement ary: fracture toughness decreases when either bonding becomes proporti onately much stronger than the fibres or vice versa. This mechanism is illustrated with a rate equation which compares the typical energy of fibre pull-out oto that of fibre rupture.