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Valiev. Microstructures 2023;3:2023004 https://dx.doi.org/10.20517/microstructures.2022.25 Page 5 of 9

processing, including HPT in different regimes and annealing procedures [Table 1], are provided in our
[22]
previous work . Table 1 also shows the structural parameters of Ti measured by X-ray and TEM analysis
after processing.

Figure 5 shows the stress-strain engineering curves of the samples during tensile tests. In the initial state, the
character of the curve is typical for the materials obtained by hot rolling. After reaching the yield point, a
gradual increase in stresses to maximum values is observed, followed by a decrease due to strain
localization. The character of the curve changes significantly after HPT. A decrease in the uniform strain, a
significant increase in the strength parameters and a decrease in ductility are observed. High-temperature
annealing of the deformed state leads to the development of recrystallization and complete leveling of the
hardening effect from the formation of the UFG structure and distortions of the crystal lattice. Additional
HPT leads to a rapid increase in the material strength but a significant loss of ductility. However,
subsequent annealing at 350 °C to relieve the stresses provides an increase in ductility while maintaining
high strength. A summary of the changes in mechanical properties is presented in Table 2.

As seen from Tables 1 and 2, the structural parameters of CP Ti Grade 4 differ significantly in various states
and therefore may contribute differently to the strength properties of the material.

The contributions of various microstructural parameters to the overall strength of the material are
important to be calculated for establishing the basic mechanisms of hardening after the combined
deformation-heat treatment of CP Ti Grade 4, as well as for understanding the nature of its superstrength
state. Following Refs. [2,5,9,23] , the calculation may be realized by considering the additive contribution of such
strengthening mechanisms as grain boundary (σ ), dislocation (σ ), solid solution (σ ) and dispersion (σ )
ss
dis
gb
Or
strengthening to the flow stress:

where σ ≈ 80 MPa and is the frictional stress of the crystal lattice in Ti [15,24] .
0
Following the known relations for these strengthening mechanisms [such as grain boundary hardening
(Hall-Petch strengthening), dislocation hardening, solid solution and dispersion hardening (Orowan
equation)] and considering the microstructural data in Table 2, the contributions of different strengthening
mechanisms to UFG Ti strength were calculated. Their comparison with experimental data from
mechanical tests is provided in Table 3.

Various strengthening mechanisms contribute to the strength of UFG Ti. However, their contributions in
the state with the highest strength (σ = 1340 MPa) are noticeably less than this value, which means that the
T
deformation of UFG Ti in such a state may also be affected by a different strengthening mechanism. Similar
conclusions have been made for other UFG metallic materials, including Al alloys [11,12] and a number of
steels [13,14] . Such a strengthening mechanism may be related to the state of grain boundaries in UFG
materials, their non-equilibrium structure containing grain boundary dislocations and the grain boundary
segregation of alloying elements [10,25] .

Recent model calculations in Ref. show [Figure 6] that the formation of segregations of impurities or
[26]
alloying elements at grain boundaries may significantly inhibit the dislocation nucleation at grain
boundaries, thereby contributing to the additional hardening of UFG materials. Simultaneously, computer
simulations [27,28] and experimental studies [11,12,14,17-19] provide convincing evidence of the formation of grain