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TECHNICAL PAPERS

Plasticity in the Thickness Direction of Paperboard Under Combined Shear and Normal Loading

[+] Author and Article Information
N. Stenberg, C. Fellers, S. Östlund

STFI, Box 5604, SE-114 86 Stockholm, Sweden

J. Eng. Mater. Technol 123(2), 184-190 (Jan 02, 2001) (7 pages) doi:10.1115/1.1352747 History: Received April 24, 2000; Revised January 02, 2001
Copyright © 2001 by ASME
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References

Figures

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In (a) the creasing process is shown step by step. First a male die punches a line close to which permanent defects are introduced in the paperboard (1 and 2). When the paperboard is bent, it is deformed along the weakened line (3) with delaminations in the creased zone. In (b) one feature of paperboard printed in offset is shown. The ink tack makes the paper follow the printing cylinder and this introduces shear and normal interlaminar stresses that can sometimes cause delamination.
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The principal directions of paper coincide with the directions in the paper machine: MD for the machine direction, CD for the cross machine direction and ZD for the thickness direction
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A five-layer commercial paperboard was used in the experiments. The outer layers consisted of Chemical Bleached Kraft (CBK) and the material in the inner layers was Chemical Thermo-Mechanical Pulp (CTMP).
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The Arcan device for out-of-plane testing of paperboard. The fixture restricts the deformation of the test piece to two perpendicular directions. The test piece is glued between the two parts of the front. The diameter of the front is 200 mm.
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The structural thickness (ts), is the average of the thickness measured, within a specified area, at a discrete number of points in the sheet between two opposite micrometers 9
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Test piece positioned between the two parts of the front using a slow-curing stiff epoxy adhesive
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Setup for nonproportional biaxial loading of the test piece. In the figure tensile loading in the thickness direction is shown. Compressive loading is obtained by changing the position of the roller allowing the wires to go in the opposite direction.
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Stress-strain curve in the thickness direction for a uniaxial tensile test on a typical paperboard material. Upon unloading from a point below the peak stress the slope of the unloading-reloading curve is approximately the same as the initial elastic stiffness.
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Schematic illustrations showing the principle for determination of the initial yield point (Y0). In (a) a typical stress-strain curve with an initially linear behavior is shown. The linear part is the elastic part of the curve. In (b) the elastic part of the curve is removed to give the yield stress as a function of the plastic strain. The initial yield point (Y0) is defined as the intercept of the derived curve with the stress-axis.
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Failure surface in strain-space. The stars (★) represent data from tests in MD and the open circles (○) data from tests in CD. The dash-dot (CD) and solid (MD) curves are fits to the data using Eq. (6).
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Failure surface in stress-space. The stars (★) represent data from tests in MD and the open circles (○) data from tests in CD. The dash-dot (CD) and solid (MD) curves are fits to the data using Eq. (6).
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Failure surface and initial yield surface in CD. Two different sets of data are presented in the figure. One set is from tests with a rotated Arcan front (★) and one set is from shear tests with a constant normal force (○). The curves are fits to the data using Eq. (6).
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Prediction of tensile test based on data from a shear-stress strain curve in CD. The prediction using Eqs. (6) and (9) and an associative flow law is shown together with data from ten tests.
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Prediction of a shear test in CD with a normal compressive stress of 0.38 MPa based on data from pure shear test in CD. The prediction using Eqs. (6) and (9) and an associative flow law is shown together with data from ten tests.
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Prediction of the strain in the thickness direction when a test piece is subjected to shear under a constant compressive stress of 0.33 MPa. The prediction using Eqs. (6) and (9) and an associative flow law is shown together with data from ten tests.

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