Strength and ductility of nanomaterials processed by SPD
The yield stress σy of polycrystals at low temperatures obeys the well-known Hall-Petch relationship:


where d is the grain size. According to this relationship, one can expect an increase of the yield stress and a related increase of the ultimate strength σUTS of the material, when the grain size is reduced down to the nanometer range.

Experiments show that, indeed, nanocrystals have a much higher strength than their coarse-grained counterparts. However, the nanocrystals prepared by the most of synthesis methods such as inert gas condensation, ball milling etc., are essentially brittle. Traditional metal forming operations such as cold rolling, extrusion etc., increase the strength of metals, but also result in a significant reduction in the ductility.

In general, any material having high strength exhibits low ductility irrespectively of its treatment. This trend is illustrated by the figure in which the strength and ductility of a number of common metals fall consistently within the lower-left yellow-colored area of the figure: high strength is accompanied by low ductility and the high ductility by low strength. Cold rolling (the reduction in thickness is marked by each data point) of Cu and Al increases their yield strength but decreases their elongation to failure (ductility). Nanostructured Ti and Cu obtained by ECAP, when appropriately processed, fall well out of this trend exhibiting extraordinary combinations of both high strength and high ductility.

Figure 1. Paradox of high strength and ductility in nanostructured materials

Underlying processes resulting in such extraordinary behavior of SPD-processed nanostructured materials are not fully understood yet. It is believed, that this is due to the formation of mainly high-angle grain boundaries with a nonequilibrium structure that facilitates the operation of grain boundary sliding.

This result demonstrates the possibility of tailoring microstructures by SPD techniques to produce nanostructured metals and alloys that have a combination of high strength and high ductility that has a high practical importance.

Literature Recommended for Further reading

  1. Y.T. Zhu and T.G. Langdon, Fundamentals of Nanostructured Materials by Severe Plastic Deformation, JOM, Oct. (2004) p.58-63.
  2. R.Z. Valiev, I.V. Alexandrov, Y.T. Zhu and T.C. Lowe, Paradox of strength and ductility in metals processed by severe plastic deformation, J. Mater. Res., 17(1) (2002) p.5-10.