Examination of the Stress Distribution in the Tip of a Pencil

[+] Author and Article Information
E. Pogozelski

 State University of New York College at Geneseo, One College Center, Geneseo, NY 14454pogo@geneseo.edu

D. Cole, M. Wesley

 State University of New York College at Geneseo, One College Center, Geneseo, NY 14454

J. Appl. Mech 73(2), 335-337 (May 24, 2005) (3 pages) doi:10.1115/1.2062847 History: Received July 20, 2004; Revised May 24, 2005

The stresses within the tip of a pencil are examined theoretically, numerically, and experimentally to determine the position and orientation of the fracture surface. The von Mises stress is used to evaluate the impact of the normal and shear stresses due to compression, bending, torsion, and shear. The worst-case stress is shown to occur along the top edge of the inclined pencil point, where the normal stress is compressive. The resulting crack propagates diagonally downwards and towards the tip from this initial position, and is frequently observed to contain a cusp.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Forces acting on the pencil tip. Note that the frictional force μ2N points out of the page.

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Figure 2

von Mises Stress distribution in the pencil tip for α=9°, θ=55°, μ=0.15. (a) Vertical axial section of the pencil tip; (b) finite element results for the vertical axial section of the tip.

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Figure 3

Impact of friction and writing angle θ on the axial breaking position x* (for α=9°)

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Figure 4

Computed fracture lines in the z=0 plane as a function of θ (for α=9° and μ=0.1)

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Figure 5

Typical digital photograph of a pencil tip after breaking (θ=30°)



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