Localized Necking Criterion for Strain-Softening Materials

[+] Author and Article Information
C. L. Chow

Department of Mechanical Engineering,  University of Michigan-Dearborn, Dearborn, MI 48128mjie@umich.edu

M. Jie1

Department of Mechanical Engineering,  University of Michigan-Dearborn, Dearborn, MI 48128mjie@umich.edu

X. Wu

Department of Mechanical Engineering,  Wayne State University, Detroit, MI 48202

All the mathematical derivations are performed with the aid of the software MATHEMATICA .


Corresponding author. 4901 Evergreen Road, Room 1340EC, Dearborn, MI 48128. Telephone: (313) 593-4976; Fax: (313) 593-3851.

J. Eng. Mater. Technol 127(3), 273-278 (Feb 21, 2005) (6 pages) doi:10.1115/1.1925283 History: Received April 26, 2004; Revised February 21, 2005

The paper presents the development of a localized necking criterion based on the singularity of acoustic tensor. This criterion is applicable to materials exhibiting strain-softening behavior. The tensor form of the criterion is deployed in simple mathematical expressions, based on which the forming limit diagrams (FLDs) of strain-softening materials can be determined. At the left-hand side of a FLD, or the negative strain ratio region, a closed-form expression of localized band inclination is derived as a function of the strain-ratio value. At the right-hand side of a FLD, or the positive strain ratio regions, the localized band is assumed to be perpendicular to major strain according to the MK [Marciniak and Kuczynski (1967)] model. On both sides of the FLD, the localized necking criteria are analytically expressed by elements of tangent modulus matrix. For the sake of illustration of the proposed criterion, a special case of localized necking employing associative and isotropic plasticity is presented. The material chosen for the illustration is AA-6061 at an elevated temperature. The proposed criterion is also applicable to the formability of other metals at high temperatures and other strain-softening materials such as rocks.

Copyright © 2005 by American Society of Mechanical Engineers
Topics: Tensors , Necking , Acoustics
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Figure 1

Localized necking in sheet metals: (a) Uni-axial to plane strain; and (b) Bi-axial tension

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Figure 2

True stress–true strain curves of AA6061 at 450°C and four levels of strain rate

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Figure 3

Hardening modulus vs equivalent strain for AA6061 at 450°C at four strain rates

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Figure 4

Critical hardening moduli of AA6061 at 450°C

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Figure 5

Predicted forming limits of AA6061 at 450°C at four strain rates with test results




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