Research Papers

The Bending Mechanics of Aged Paper

[+] Author and Article Information
Andrea K. I. Hall

Heritage Science for Conservation,
The Sheridan Libraries,
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218

Thomas C. O'Connor

Department of Physics and Astronomy,
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218

Molly K. McGath

Heritage Science for Conservation,
The Sheridan Libraries,
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218

Patricia McGuiggan

Heritage Science for Conservation,
The Sheridan Libraries,
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218;
Department of Materials Science and
Johns Hopkins University,
3400 N. Charles Street,
Baltimore, MD 21218
e-mail: mcguiggan@jhu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 15, 2018; final manuscript received March 30, 2018; published online May 8, 2018. Assoc. Editor: Yihui Zhang.

J. Appl. Mech 85(7), 071005 (May 08, 2018) (10 pages) Paper No: JAM-18-1100; doi: 10.1115/1.4039881 History: Received February 15, 2018; Revised March 30, 2018

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.

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Grahic Jump Location
Fig. 1

(Left) Photograph of the experiment showing the paper bending under an added weight (right) and schematic diagram of the cantilever test for paper, where ω is the weight per unit length across a sample, s is the arc length, Ψ is the angle between the horizontal and the line connecting the fixed end and free end position of the paper, ϕ is the angle corresponding to the local deflection and the horizontal, P is the concentrated load at the sample's free end, δ is the amount of maximum deflection, and L is the exposed length of the undeformed sample

Grahic Jump Location
Fig. 2

A schematic illustration of the bending of paper with increasing L/c

Grahic Jump Location
Fig. 3

Cantilever tests of aged paper #1 (a), aged paper #2 (b), copy paper (c), and PET Film (d). Solid points are experimental values and the dashed curve represents the numerical fit. One bending modulus was used for each set of curves.

Grahic Jump Location
Fig. 4

Plots of maximum curvature versus added mass (a) and maximum % strain versus added mass (b)

Grahic Jump Location
Fig. 5

Plot of L/c versus the angle, Ψ. The solid curve is a plot of Eq. (4), the angle Ψ is calculated from the measured deflection, and the L/c values are found from numerical analysis or the single point method, as shown in Table 2.

Grahic Jump Location
Fig. 6

Tensile test of an individual run of aged paper #1. The trend line indicates Young's modulus calculation, beginning at 20% peak load and includes points following that have the smallest deviation from the straight line.

Grahic Jump Location
Fig. 7

Comparison of bending modulus (a) and L/c values (b) with fold endurance number of paper-based samples. The solid lines are guides to the eye. The left curve is a best fit to an inverse polynomial (r2 = 0.88) and the line on the right is a least squares linear fit (r2 = 0.67) to the data.




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