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elastic anisotropy of hcp metal crystals and polycrystals

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IJRRAS 6 (4) ● March 2011 Tromans ● Elastic Anisotropy <strong>of</strong> Hcp Metal Crystals <strong>and</strong> Poly<strong>crystals</strong><br />

(a) E data<br />

(a) E data<br />

(a) E data<br />

Tb<br />

Dy<br />

0.5<br />

0.5<br />

0.5<br />

Tm<br />

X3<br />

Pr<br />

Hf<br />

Os<br />

Ru<br />

Ho<br />

1.0<br />

0<br />

X3<br />

0<br />

X3<br />

0.5<br />

0.5<br />

1.0<br />

1.0<br />

0.5<br />

0.5<br />

1.0<br />

1.0<br />

0<br />

0.5<br />

0.5<br />

1.0<br />

0.5<br />

0.5<br />

0.5<br />

Gd<br />

Os<br />

Pr<br />

Tm<br />

Hf<br />

Ho<br />

Ru<br />

Tb<br />

Dy<br />

Gd<br />

475<br />

(b) G data<br />

Ru<br />

Pr<br />

(b) G data<br />

Ho<br />

(a) G data<br />

(a) (b)<br />

Figure 12. Normalized polar diagrams: Os, Pr Tm Hf, (top);). Ho, Ru (middle) <strong>and</strong> Tb, Dy, Gd (bottom)<br />

.(a) E data: (b) G data.<br />

In the group Os, Pr, Tm <strong>and</strong> Hf, it is Tm which exhibits the most isotropic E <strong>and</strong> G behaviour. The least isotropic is<br />

Pr with a pronounced distorted circle in the X3 direction. The normalised anisotropic behaviours <strong>of</strong> Ho <strong>and</strong> Ru are<br />

almost identical despite the large differences in the moduli <strong>of</strong> each <strong>metal</strong> (c.f. Figs. 7 <strong>and</strong> 8). The normalized values<br />

<strong>of</strong> the moduli for the <strong>metal</strong>s Gd, Tb <strong>and</strong> Dy are virtually indistinguishable. In fact they are so similar that in both the<br />

Tb<br />

Dy<br />

0.5<br />

0.5<br />

0.5<br />

X3<br />

0<br />

X3<br />

1.0<br />

0<br />

0.5<br />

0.5<br />

0.5<br />

1.0<br />

X3<br />

0.5<br />

1.0<br />

0<br />

0.5<br />

0.5<br />

1.0<br />

0.5<br />

0.5<br />

0.5<br />

Os<br />

Gd<br />

Os<br />

Pr<br />

Tm<br />

Hf<br />

Ho<br />

Ru<br />

Tb<br />

Dy<br />

Gd

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