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Research Papers

Hybrid Bishop-Hill Model for Elastic-Yield Limited Design With Non-orthorhombic Polycrystalline Metals

[+] Author and Article Information
Ribeka Takahashi

 Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602ribekat@byu.net

Dikshya Prasai

 Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602pdikshya@gmail.com

Brent L. Adams

 Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602b_l_adams@byu.edu

Christopher A. Mattson

 Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602mattson@byu.edu

J. Eng. Mater. Technol 134(1), 011003 (Dec 06, 2011) (12 pages) doi:10.1115/1.4004829 History: Received April 08, 2011; Accepted July 29, 2011; Revised July 29, 2011; Published December 06, 2011; Online December 06, 2011

A method is presented for adapting the classical Bishop-Hill model to the requirements of elastic/yield-limited design in metals of arbitrary crystallographic texture. The proposed Hybrid Bishop-Hill (HBH) model, which will be applied to ductile FCC metals, retains the “stress corners” of the polyhedral Bishop-Hill yield surface. However, it replaces the ‘maximum work criterion’ with a criterion that maximizes the projection of the applicable local corner stress state onto the macroscopic stress state. This compromise leads to a model that is much more accessible to yield-limited design problems. Demonstration of performance for the HBH model is presented for an extensive database for oxygen free electronic copper. The design problem considered is a hole-in-a-plate configuration of thin sheets loaded in uniaxial tension in arbitrary directions relative to the principal directions of material orthorhombicity. Results obtained demonstrate that HBH-based elastic/yield limited design is capable of predicting complex and highly nonintuitive behaviors, even within standard problems.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 5

A variation in yield strength with respect to the applied tensile load direction in anisotropic plates with a circular hole

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Figure 6

(a) As-received. Maximum intensity: 1.639 × random and (b) as-received and annealed. Maximum intensity: 1.748 × random.

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Figure 7

98% cold worked. Maximum intensity: 5.534 × random and (b) 98% cold worked and recrystallized. Maximum intensity: 3.714 × random.

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Figure 8

(a) 58% cold worked. Maximum intensity: 3.390 × random, (b) 58% cold worked and annealed. Maximum intensity: 2.827 × random, and (c) 58% cold worked and recrystallized. Maximum intensity: 2.816 × random.

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Figure 9

Cube texture. Maximum intensity: 36.796 × random

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Figure 4

The stress states around a circular hole in 98% cold worked plate. The solid line indicates the yield surface of the material, and the dotted line indicates the stress states around the hole. When the stress states (σθ ) touch the yield surface (σθY), the material is considered to be yield. The applied stress is along the sample rolling direction.

Grahic Jump Location
Figure 3

A variation in yield strength with respect to the applied tensile load direction in anisotropic plates

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Figure 2

Property Closure

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Figure 1

A geometry of anisotropic hole-in-plate problem

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