The Force-Elongation Curve of a Thin Fibrous Network

Specimens from low-density weblike handsheets were tested in a tensile tester. In a test the direction of extension was frequently reversed and the specimen reextended to obtain a series of force-elongation curves. For Kraft woodpulp specimens the force-elongation behavior was well represented by an exponential equation involving three parameters: a modulus of elasticity C ₂, a length parameter x _c related to average segment length between network bonds, and an elongation value x ₀ at which the curve starts. The unstrained length of a specimen l increases, and the parameters x _c and C ₂ tend to decrease with each successive reextension curve. For a series of specimens of increasing area density representative values of x _c /l tend to decrease and C ₂ to increase. For a series of specimens made from pulps beaten increasing amounts representative values of x _c /l tend to decrease and C ₂ to increase. Some features of the tensile behavior can be modeled by a system of parallel Filaments of equal length to which longer parallel filaments with an exponential length distribution have been added. Upon extension the filaments assume load successively, thus simulating the force-elongation behavior of a paper network. By thinking in terms of this model it is possible to anticipate intuitively much of the behavior of a paper network.