The Bending Mechanics of Aged Paper

Abstract

Brittleness in paper is one of the primary reasons library books are removed from circulation, digitized, or have their access limited. Yet, paper brittleness is difficult to characterize as it has multiple definitions and no single measurable physical or chemical property associated with it. This study reevaluates the cantilever test as applied to aged papers. In this nondestructive test, the deflection of a strip of paper held horizontally is measured across its length. The deflection data are then fit to nonlinear bending theories assuming large deflection of a cantilever beam under a combined uniform and concentrated load. Fitting the shape of the deflection profiles provides bending and elastic moduli, the bending length, and confirms that the paper sheets respond linearly. The results are compared to those calculated from a simplified single point measurement of the maximum deflection of the cantilevered sample. Young's modulus measured by the cantilever test is lower for paper-based materials than that measured by tensile testing, and the bending modulus was found to correlate with the destructive Massachusetts Institute of Technology (MIT) fold endurance test.

Determining effective bending stiffness of fabrics and other materials from tests involving an added weight

“…37 This is not true; the curvature at every point of the ring must have the same sign, as pointed out by Pan. 3 ) The shape of the deformed ring with w = 0 is symmetric about a horizontal line as well as the vertical line passing through the support.…”

“…just self-weight) has been used extensively to determine the bending stiffness of a strip of material, starting with Peirce 2 . A cantilever with self-weight w and vertical tip load F was considered in that paper and in papers by Grosberg and Swani 23 , Potluri et al 24 , Be´lendez et al 18 , de Bilbao et al 5 , Kimiaeifar et al, 20 Liang et al 12 and Hall et al, 3 among others.…”

“…The entire profile of the cantilever was measured in experiments described in Clapp et al, 25 de Bilbao et al, 26,5 Liang et al 6 and Hall et al 3 In the last of these, profiles were obtained for three types of paper and for a thin film, each subjected to several tip loads F. Predictions of the bending stiffness (divided by the strip thickness) determined from these profiles were compared to predictions based simply on the tip deflection.…”

“…Price 10 , Hall et al. 3,4 ) or other material. Some previous investigations have included such an added load to the cantilever and hanging ring tests.…”

“…Hall et al. 3,4 ), prepreg (e.g. de Bilbao et al., 5 Liang et al., 6 Alshahrani and Hojjati, 7,8 Boisse et al.…”