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Page 2 of 9 Valiev. Microstructures 2023;3:2023004 https://dx.doi.org/10.20517/microstructures.2022.25

where σ is the lattice friction stress and k is the Hall-Petch coefficient. According to Equation (1), the
HP
0
strength of the material increases with decreasing average grain size.
Based on this connection, there is significant interest in achieving ultrafine-grained (UFG) structures in
metallic materials with an average grain size of less than 1 µm and predominantly high-angle grain
boundaries, which may be implemented by using severe plastic deformation (SPD) processing
[3-5]
techniques .

For this purpose, at present, the most popular SPD processing techniques are equal-channel angular
pressing (ECAP) and high-pressure torsion (HPT). The deformation processing of materials by SPD was
the first key step that initiated comprehensive studies of the mechanical properties of bulk nanomaterials
and is now the basis for their innovative applications (see reviews and books on this topic) [5-10] .

The past two decades have witnessed detailed analyzes of the effect of reducing the grain size to the
nanoscale on the strength of materials. Although many studies have observed an increase in strength with
decreasing grain size following Equation (1), this relationship is often violated for nanosized grains (less
than 100 nm). Thus, the Hall-Petch curve deviates from the linear relationship at lower stress values and its
[2]
slope k becomes negative (curve 1, Figure 1) . This problem has been extensively analyzed in many
HP
experimental and theoretical studies. In addition, several recent studies have shown that UFG materials may
exhibit significantly higher strengths than that predicted by the Hall-Petch relation for the range of ultrafine
grains (curve 2, Figure 1) . The nature of such superstrength may be related to the influence of various
[5,6]
nanostructural features observed in SPD-processed metals and alloys located in the grain interior
(dislocation substructures, nanosized particles of secondary phases and nanotwins) and at grain
boundaries .
[10]

In this regard, the task herein is to analyze the nature of the superstrength of UFG materials and various
strengthening mechanisms, including both the known ones related to the presence of nanoparticles and
other nanostructural features and the new ones related to the influence of grain boundary structures in UFG
materials.

EXPERIMENTAL OBSERVATIONS
In the last decade, a number of studies on the strength properties of various nanostructured metals and
alloys, including Al alloys [11,12] , steels [13,14] and titanium materials , have been performed in our laboratory in
[15]
collaboration with colleagues from other institutions. In all cases, a significant increase in the strength of the
material was observed during grain refinement by SPD techniques, with yield stress values significantly
exceeding the values calculated by the Hall-Petch equation. This is illustrated in Figure 2 for the yield
[11]
stress values of the UFG Al alloys 1570 and 7475 with grain sizes of ~100 nm, which are significantly higher
than the Hall-Petch ratio calculations for closely related Al alloys with similar grain sizes.

It is important that in all these and our other works [16-19] , the formation of nanoclusters and solute
segregations at grain boundaries was observed along with the formation of the UFG structure. This is clearly
seen, for example, when studying the SPD-processed alloys with the use of three-dimensional atom probe
tomography [Figure 3] , as well as in Figure 4, which demonstrates observations of the nanostructural
[12]
features of the alloy 7075 after HPT at two different temperatures (room temperature and 200 °C) .
[20]