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.

References

References
1.
Ashby
,
M. F.
, 2005,
Materials Selection in Mechanical Design
,
3rd.
,
Butterworth-Heinemann
,
San Francisco
.
2.
Juvinall
,
R. C.
, 1967,
Engineering Considerations of Stress, Strain, and Strength
,
McGraw-Hill
,
New York
.
3.
Canova
,
G. R.
,
Kocks
,
U. F.
,
Tome
,
C. N.
, and
Jonas
,
J. J.
, 1985,
“The Yield Surface of Textured Polycrystals
,”
J. Mech. Phys. Solids
,
33
(
4
), pp.
371
397
.
4.
Lequeu
,
P.
,
Gilormini
,
P.
,
Montheillet
,
F.
,
Bacroix
,
B.
, and
Jonas
,
J. J.
, 1987,
“Yield Surfaces for Textured Polycrystals—II. Analytical Approach
,”
Acta Metall.
,
35
(
5
), pp.
1159
1174
.
5.
Hill
,
R.
, 1948,
“A Theory of the Yielding and Plastic Flow of Anisotropic Metals
,”
Proc. R. Soc.
London,
193
(1033), pp.
281
297
.
6.
Taylor
,
G. I.
, 1938,
“Plastic Strain in Metals
,”
J. Inst. Met.
,
62
, pp.
307
324
.
7.
and
Bishop
,
J. F. W.
and
Hill
,
R.
, 1951,
“A Theoretical Derivation of the Plastic Properties of a Polycrystalline Face-Centered Metal
,”
Philos. Mag.
,
42
, pp.
1298
1307
.
8.
Bishop
,
J. F. W.
, and
Hill
,
R.
, 1951,
“A Theory of the Plastic Distortion of a Polycrystalline Aggregate Under Combined Stresses
,”
Philos. Mag.
,
42
, pp.
414
427
.
9.
Ahzi
,
S.
, and
M’Guil
,
S.
, 2005,
“Simulation of Deformation Texture Evolution Using an Intermediate Model
,”
Solid State Phenom.
,
105
, pp.
251
258
.
10.
Adams
,
B. L.
,
Kalidindi
,
S. R.
, and
Fullwood
,
D. T.
, 2008,
Micro Structure Sensitive Design for Performance Optimization,
2nd ed.
,
BYU Academic Publishing
,
Provo
.
11.
Fullwood
,
D. T.
,
Niezgoda
,
S. R.
,
Adams
,
B. L.
, and
Kalidindi
,
S. R.
, 2010,
“Mi-crostructure Sensitive Design for Performance Optimization
,”
Progress Mater. Sci.
,
55
(
6
), pp.
477
562
.
12.
Lekhnitskii
,
S. G.
, 1968,
Anisotropic Plates
,
1st ed.
,
Gordon and Breach Science Publishers
,
New York
.
13.
Bunge
,
H. J.
, 1982,
Texture Analysis in Materials Science: Mathematical Methods
,
Butterworth and Co.
,
London
.
14.
Wright
,
S. I.
,
Adams
,
B. L.
, and
Kunze
,
K.
, 1993,
“Application of a New Automatic Lattice Orientation Measurement Technique to Polycrystalline Aluminum
,”
Mater. Sci. Eng., A
,
160
(
2
), pp.
229
240
.
15.
Prager
,
W.
, and
Hodge
,
P. G.
, 1968,
Theory of Perfectly Plastic Solids
,
Dover
,
New York
.
16.
Chin
,
G. Y.
, and
Mammel
,
W. L.
, 1967,
“Computer Solutions of the Taylor Analysis for Axisymmetric Flow
,”
Trans. Met. Soc. AIME
,
239
, pp.
1400
1405
.
17.
Clausen
,
B.
,
Leffers
,
T.
,
Lorentzen
,
T.
,
Pedersen
,
O. B.
, and
Van Houtte
,
P.
, 2000,
“The Resolved Shear Stress on the Non-Active Systems in Taylor/Bishop-Hill Models for FCC Polycrystals
,”
Scr. Mater.
,
42
, pp.
91
96
.
18.
Adams
,
B. L.
,
Nylander
,
C.
,
Aydelotte
,
B.
,
Ahmadi
,
S.
,
Landon
,
C.
,
Stucker
,
B. E.
, and
Ram
,
G. D. J.
, 2008,
“Accessing the Elastic-Plastic Properties Closure by Rotation and Lamination
,”
Acta Mater.
,
56
, pp.
128
139
.
19.
Kalidindi
,
S. R.
,
Knezevic
,
M.
,
Niezgoda
,
S.
, and
Shaffer
,
J.
, 2009,
“Representation of the Orientation Distribution Function and Computation of First-Order Elastic Properties Closures Using Discrete Fourier Transforms
,”
Acta Mater.
,
57
(
13
), pp.
3916
3923
.
20.
Knezevic
,
M.
, and
Kalidindi
,
S. R.
, 2007,
“Fast Computation of First-Order Elastic-Plastic Closures for Polycrystalline Cubic-Orthorhombic Microstructures
,”
Comput. Mater. Sci.
,
39
(
3
), pp.
643
648
.
21.
Van Houtte
,
P.
, 1988,
“A Comprehensive Mathematical Formulation of an Extended Taylor-Bishop-Hill Model Featuring Relaxed Constraints, the Renouard-Wintenberger Theory and a Strain Rate Sensitivity Model
,”
Textures Microstruct.
,
8–9
, pp.
313
350
.
22.
Kocks
,
U. F.
,
Tome
,
C. N.
, and
Wenk
,
H.-R.
, 1998,
Texture and Anisotropy: Preferred Orientations in Poly Crystals and Their Effect on Materials Properties
,
Cambridge University
,
New York
.
You do not currently have access to this content.