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TECHNICAL PAPERS

Chip Formation in Cellular Materials

[+] Author and Article Information
Ralf Laternser, Hans-Peter Gänser, Lars Taenzer, Alexander Hartmaier

Hilti Corp., Corporate Research, P.O. Box 333, FL-9494 Schaan, Liechtenstein

J. Eng. Mater. Technol 125(1), 44-49 (Dec 31, 2002) (6 pages) doi:10.1115/1.1526126 History: Received December 01, 2001; Revised April 30, 2002; Online December 31, 2002
Copyright © 2003 by ASME
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Figures

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Linear cutting process: (a) Experimental setup. The saw tooth is moving with constant velocity in horizontal direction. (b) Cutting directions. The present investigations concentrate on tangential cutting, where the plane perpendicular to the saw tooth may be assumed as isotropic and, averaging the differences between earlywood and latewood, homogeneous. (c) Two-dimensional plane strain finite element model of unit thickness. The saw tooth is moving with constant velocity in horizontal direction, taking off a pre-defined chip from the work piece. The ligament between the chip and the bulk of the work piece is modeled by cohesive zone elements (dotted line).
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(a) Yield surface; p denotes the hydrostatic stress (negative hydrostatic pressure), q the von Mises equivalent stress; refer to the main text for the parameters. (b) Evolution of the yield surface due to hardening.
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Bi-linear softening curve for cohesive zone elements: ligament stress σ versus crack opening δ. Independent softening curves may be defined for crack opening in tension (mode I) and in shear (mode II); refer to the main text for the coupling between both modes.
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Linear cutting process (chip thickness 250 μm), deformed plot of the finite element model: contours of volumetric strain; arrows indicate the forces in the cohesive zone due to mode I (normal) and mode II (tangential) crack opening.
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Linear cutting process (chip thickness 250 μm), energy flow: consumed work W versus tool displacement s. “Deformation” denotes the energy stored elastically in the chip and the bulk of the work piece, and dissipated by plastic deformation. “Crack opening” denotes the work dissipated in the cohesive zone due to mode I (normal) and mode II (tangential) crack opening. After a tool displacement of about 0.5 mm, a stationary regime with constant cutting force is reached, leading to a linear W-s curve in this diagram.
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Linear cutting process, stationary cutting force versus chip thickness. The total cutting force may be split up into a contribution due to elastic-plastic deformation of the chip and bulk of the work piece (curve “deformation”), and a contribution from the cohesive zone (“crack opening”). The contribution from elasto-plastic deformation shows a near-linear dependence on the chip thickness, whereas the contribution from cracking is roughly constant.
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Linear cutting (chip thickness 250 μm): influence of the relative fracture energy on the stationary cutting force (Gf0 is the fracture energy of spruce). Either the stress for failure (“stress scaling”, filled symbols) or the nodal displacement for failure (“displacement scaling”, open symbols) are varied, while the other quantity is held constant. It is seen that the energy consumed by elasto-plastic deformation (“deformation”) is depending markedly on the shape of the softening curve, and not only on the relative fracture energy.

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