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TECHNICAL PAPERS

Upsetting of Cylinders: A Comparison of Two Different Damage Indicators

[+] Author and Article Information
H.-P. Gänser

Institute of Mechanics, Montanuniversität Leoben, Leoben, Austriae-mail: gaenser@unileoben.ac.at

A. G. Atkins

University of Reading, Reading, United Kingdom

O. Kolednik

Erich Schmid Institute of Materials Science, Austrian Academy of Science, and Institute of Metal Physics, Montanuniversität Leoben, Leoben, Austria

F. D. Fischer

Christian Doppler Laboratory for Micromechanics of Materials, Institute of Mechanics, Montanuniversität Leoben, Leoben, Austria

O. Richard

Institut Français de Mécanique Avancée, Aubière, France

J. Eng. Mater. Technol 123(1), 94-99 (Feb 15, 2000) (6 pages) doi:10.1115/1.1286186 History: Received May 25, 1999; Revised February 15, 2000
Copyright © 2001 by ASME
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References

Figures

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Experimental fracture lines for the compression of cylindrical specimens. After Kudo and Aoi 16, from Atkins 13.
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Finite element model. The strain paths and the damage indicators are monitored at point “A,” (a) undeformed state, (b) deformed state.
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Different strain paths, measured at point “A,” obtained by variation of the geometry H/D and of the friction coefficient μ. The data of the reference geometry H/D=1 are shaded.
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Hydrostatic stress at point A as a function of the equivalent strain for different values of the friction coefficient μ, for the reference geometry H/D=1
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Failure lines obtained by the Hancock–Mackenzie damage indicator D1(R=1.5). Influence of the calibration parameter ε0, for the reference geometry H/D=1 and different friction coefficients (dotted lines represent the strain paths).
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Failure lines obtained by the Hancock–Mackenzie damage indicator D1(R=2). Influence of the calibration parameter ε0, for the reference geometry H/D=1 and different friction coefficients (dotted lines represent the strain paths).
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Failure lines obtained by the Atkins damage indicator D3. Influence of the parameters c and c1, for the reference geometry H/D=1 and different friction coefficients (dotted lines represent the strain paths).
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Failure line obtained from the Hancock–Mackenzie damage indicator D1 using the parameters R=2,ε0=0.5 (dotted lines represent the strain paths)
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Failure line obtained from the Atkins damage indicator D3, using the parameters c=0.3,c1=3 (dotted lines represent the strain paths)
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Failure points obtained from micromechanical simulations using a tensile instability criterion in hoop direction (Gänser 24). A result for εz=0, although not obtainable by the upsetting of cylinders, is also included. Note that the failure points do not lie exactly on a straight line. Also shown are a least square line fit, line “a,” and a fit for a slope of −0.5, line “b” (dotted lines represent the strain paths).

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