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initial rigid body rotation. The plastic flow is
larger along the Y-axis because the flow stress is
softer in the Y-direction given the yield surface
shape for this material. In this calculation, the
strong axis of the yield surface was initially
oriented along the Z-axis (perpendicular to the
loading direction (X-axis). This configuration
produces an elliptical footprint with some
flattening along 450 lines.FIGURE 3. Taylor Cylinder calculations showing
Euler-Rodrigues angle and vectors for an isotropic (top)
and anisotropic (bottom) yield surface description for
Ta.. Linear gradients in rotation angle (radians)
from 0.0 to 0171 (isotropic) and 0.0 to 0.9135
(anisotropic) are realized.
STRETCHING ROD PROBLEM
Plastic tensile instability (necking) is an important
consideration for a variety of stretching rod
deformation processes. A potential stabilization
mechanism for the rod necking problem is yield
anisotropy. The stability of a stretching metal rod
has dependencies that include the material flow
stress (a ), density (p), axial strain rate (k), rod
radius (a), and the initial distribution of geometric
perturbations (7,8). Romero (8) defines the
following isotropic dimensionless number P(t)
based upon these parameters:1(t)= Jpi2(t)a2 (t)/ a(t)
Perturbations are stable (no necks should develop
on the rod surface) for '(t) > 1. As the rod is
stretched, "(t) decreases. For r(t) < 1,
perturbations can become unstable. Note that the
stability equation indicates a softer flow stress
produces a more stable rod geometry. Our
numerical study of rod topology consists of a
comparison of two anisotropic cases (0 and 90"
initial rotation about the 1 or X axis). The Ta rod
has an initial radius of 0.213-cm, an initial length
of 0.852-cm and an average strain rate of- 104 1/s.
Figure 4 shows that the deformed cross section
shapes are not circular but elliptical. The calculated
topologies show a strong sensitivity to the yield
surface coefficients (a) or yield surface
orientation for the tensile plastic instability
problem.cross section shape
comparison at center of rod
at -2C pa
2 or Y
9tFIGURE 4. Comparison of rod cross sections at -25 s
for 0" and 900 initial rotation angles about the X axis.
REFERENCES
1. Clancy, S. P., Burkett, M. W., Maudlin, P. J., J. Phys.
IV France 7 Colloq. C3 (DYMAT 97), 735-740 (1997).
2. Maudlin, P. J. and Schiferl S. K., Comput. Methods
AppL. Mech. Engrg. 131 (1996) 1-30.
3. Kolian, K. S., et al., Proceeding of the Conference on
Numerical Simulations and Physical Processes related to
Shock Waves in Condensed Media, Oxford, England,
September 1997.
4. Maudlin,P. J., Bingert, J. F., Gray III, G. T., L J.
Plasticity, accepted for publication, May 2001.
5. Hill, R., The Mathematical Theory of Plasticity
(Oxford University Press, London, (1950).
6. Taylor, G. 1., I. Theoretical Considerations. Proc. R.
Soc. Lond. A 194, 289 (1948).
7. Walsh, J. M., J. Apple. Phys., 56 (7) 1 (1984).
8. Romero, L. A., J. Apple. Phys., 65, 3006 (1989).(4)
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Synchrotron-based high-pressure research in materials science, article, Date Unknown; [Los Alamos, New Mexico]. (https://digital.library.unt.edu/ark:/67531/metadc930753/m1/4/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.