Discussion
Which one of the following samples of high-purity aluminium (Al) single crystal will plastically yield at the lowest applied load under ambient conditions? Loading axis is along the direction shown in the schematic.
Answer: D
The sample loaded along [123], (iv), yields first.
Aluminium is FCC and slips on {111}\(\langle 110 \rangle\) systems. Yield begins when the resolved shear stress on the most favourable system reaches the critical value, \(\tau_{c} = \sigma\cos\phi\cos\lambda\), so the load needed is smallest for the orientation with the largest Schmid factor \(m = \cos\phi\cos\lambda\).
- [100] and [101]: maximum m is about 0.41.
- [111]: maximum m is about 0.27.
- [123]: a single-slip orientation near the middle of the standard triangle, with m close to the ideal 0.5 (about 0.47).
So [123] needs the lowest load. [111] is the hardest orientation, and [100] and [101] lie in between.
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