<figure><img src="image_167.png" /><figcaption>**Fig. 85.** (a) Structural relaxation enthalpy and (b) elastic modulus (E) and hardness (H) values as a function of HPT rotation number. The inset in (a) shows differential scanning calorimetry curves of the sample processed with 50 HPT turns, where red and black lines denote the 1st and 2nd heating curves, respectively, and T<sub>g</sub> and T<sub>x</sub> denote the glass transition temperature and crystallization temperature, respectively. The open symbols in (b) denote the data after annealing at 673 K for 1 h [1774].</figcaption></figure>

1779] and its distribution over the sample becomes less uniform [1780]. Serrations on the nanoindentation curves of the HPT-processed BMG are not observed unlike for as-cast BMG, and this can be explained by more homogeneous deformation in the former case due to an increase in amorphous phase structure heterogeneity [1775]. HPT leads to a significant 2.5-fold increase in the strain rate sensitivity parameter from 0.014 to 0.036, while the elastic modulus decreases slightly, from 90 to 85 GPa [1775]. Indents analysis suggests that HPT can lead to an increase in the amorphous alloy microplasticity [1781] and improvement of ductility [1782, 1783].

The structural transformation in amorphous alloys by HPT process-
ing is the result of an extremely high density of shear bands propagating
through the amorphous matrix. TEM data show that the spacings be-
tween shear bands reach 30 nm after HPT processing [1766]. The
spacings between shear bands in Zr-based BMG after HPT for 5 turns can
vary from 500 nm at the center of the sample to 100 nm at the edge
[1784]. Nanohardness measurements across shear bands in the
deformed amorphous alloy show noticeable softening on the distances of
about tens of microns due to free volume increase [1785]. This means
that with the shear band density observed after HPT processing
(Figs. 86a and 86b [1786]), the entire amorphous material undergoes

transformations [1787, 1788], despite some possible slippage between
anvils and a processed specimen that can occur during HPT of hard
BMGs [1784, 1789]. A model has been proposed to explain the strain
accumulation in an HPT-processed specimen with an account for slip-
page [1789]. Furthermore, the accumulative HPT procedure has been
implemented for processing BMGs and hard alloys [59, 1790]. It has
been shown that a Zr-based amorphous alloy undergoes a more pro-
nounced structural transformation after accumulative HPT as compared
to a conventional one. Taken together, SPD provides new opportunities
to understand the plastic behavior of brittle amorphous materials. Such
understanding can eventually contribute to the design of amorphous
materials with improved plasticity and new functionalities.

7.8. Semiconductors

Semiconductors are one of the major components used in the 21st
century and silicon is one of the most important semiconductor mate-
rials for modern electronic devices [1791]. However, bulk crystalline
silicon is not suitable for optical and optoelectronic applications due to
its indirect bandgap of 1.1 eV. The well-known way to overcome this
limitation is the use of nanostructured silicon, which exhibits photo-
luminescence in the visible light region associated with the quantum
confinement effect [1792]. Recently, allotropes of silicon have been of
interest for future electronic devices because they have different elec-
tronic structures [1793]. Among several silicon allotropes, metastable
phases can be obtained by phase transformation from high-pressure
phases. When high pressure is applied to silicon crystals,
diamond-cubic Si-I transforms to metallic Si-II with β-Sn structure at
about 11 GPa, and then it further transforms to orthorhombic Si-XI
(~14 GPa) and simple-hexagonal Si-V (~16 GPa) [1794]. Upon pres-
sure release, Si-II transforms to metastable phases such as rhombohedral
Si-XII and BCC Si-III [1795]. These metastable phases can be obtained by
high-pressure cells [1795, 1796] and indentation experiments
[1797–1799]. However, it is difficult to obtain the bulk samples by these
methods. SPD processing of semiconductor materials has attracted
attention for altering optical and electrical properties because grain
refinement and phase transformation are expected to occur simulta-
neously. Among several SPD techniques, HPT is suitable for processing
brittle semiconductor materials due to constraining in the cavity of an-
vils. Recently, large-scale samples (> 10 mm in diameter) could be
processed by HPT [179]. The first HPT processing of semiconductors
was reported by Bridgeman [20] and further investigated by several
researchers for silicon [1180, 1183] and germanium [1181, 1182]. HPT
processing of semiconductors such as silicon [1184, 1800–1805],
geranium [1185, 1806, 1807] and GaAs [1808] were conducted in
recent years and the main findings were summarized in some overview
articles [512, 1809]. The functional properties of some HPT-processed
semiconductors such as silicon [1810, 1811] and Si<sub>0.5</sub>Ge<sub>0.5</sub> alloy
[1812] were also reported recently.

Fig. 87a shows the XRD profiles of the silicon samples after HPT processing at a nominal pressure of 6 GPa. The XRD profiles consist of Si-III/Si-XII as well as Si-I. The diffraction peak intensities of Si-III/Si-XII increase with increasing the number of anvil rotations. The volume fractions of Si-III and Si-XII after 100 HPT turns are > 0.3 and ~0.2, respectively. The formation of Si-III/Si-XII indicates the strain-induced phase transformation from Si-I to Si-II during HPT processing and phase transformation from Si-II to Si-III/XII during pressure release [8, 1813]. The HPT processing also affects the electrical, optical and thermal properties. The resistivity of the silicon samples (20 Ω-cm) decreases to 0.7 Ω-cm after HPT processing for 100 turns due to the formation of Si-III having a semi-metallic property [1814] with a narrow gap (30 meV) [1815]. A weak broad photoluminescence peak associated with Si-I nanograins appeared in the visible light region after annealing. The thermal conductivity of bulk silicon (~140 W m⁻¹ K⁻¹) was reduced to ~3 W m⁻¹ K⁻¹ after HPT processing for N ≥ 50 [1810]. To investigate the phase transformation of the metastable phases in
<figure><img src="image_168.png" /><figcaption>**Fig. 86.** (a,b) SEM images showing shear bands in a Zr<sub>52.5</sub>Cu<sub>17.9</sub>Ni<sub>14.6</sub>Al<sub>10</sub>Ti<sub>5</sub> metallic glass processed by HPT with 5 rotations, where (b) is a magnified view indicating formation of interacting shear band networks with increaseing strain [1786].</figcaption></figure>

HPT-processed silicon, synchrotron XRD measurements were also per-
formed [1811]. The silicon sample was subjected to HPT processing at a
nominal pressure of 24 GPa for 10 turns, and then cut into ~1 mm strips
for the XRD measurements. The XRD profiles during annealing showed
that the diffraction peaks of Si-III/Si-XII were almost constant up to

433 K, and these peaks gradually decreased at 453 K. New diffraction
peaks corresponding to hexagonal-diamond Si-IV appeared at 463 K. At
473 K, the Si-IV and Si-I diffraction peaks appeared and Si-III/Si-XII
peaks disappeared. These results on the phase transformation of Si-IV
from Si-III during annealing indicate that the combination of HPT pro-
cessing and annealing is effective in obtaining new metastable phases.
[1797, 1816, 1817]. It should be noted that Si-IV has been predicted to
be a semiconductor having a bandgap of 0.95 eV [1814].

Fig. 87b shows XRD profiles of HPT-processed Si<sub>0.5</sub>Ge<sub>0.5</sub> after pure compression and HPT processing for 10 turns. The diffraction peaks correspond to a diamond-cubic phase for the sample without rotation. Additional peaks corresponding to a bc8 phase appear after 10 HPT turns. The formation of bc8-Si<sub>0.5</sub>Ge<sub>0.5</sub> is consistent with the high-pressure experiments at high temperatures [1818]. The lattice constant of bc8-Si<sub>0.5</sub>Ge<sub>0.5</sub> is 0.678 nm, which is in good agreement with the value found from Vegard's law comprising 0.6784 nm. The electrical resistivity increased from ~9 × 10<sup>-3</sup> Ω·cm to ~5 × 10<sup>-2</sup> Ω·cm after compression and decreased slightly to ~3 × 10<sup>-2</sup> Ω·cm after 10 turns of HPT. The decrease in resistivity after HPT is similar to that observed in HPT processing of silicon [1803, 1810], suggesting that bc8-Si<sub>0.5</sub>Ge<sub>0.5</sub> has a semi-metallic property [1812].

SPD processing of silicon and related semiconductors appears a
promising method to achieve novel functional properties through
nanograin refinement and the formation of metastable phases [1456].
Considering the current global crisis concerning semiconductors, such
studies deserve to receive higher attention in the SPD field.

<figure><img src="image_169.png" /><figcaption>**Fig. 87.** XRD profiles of (a) silicon processed by HPT for different rotations (N) [1810] and (b) Si<sub>0.5</sub>Ge<sub>0.5</sub> processed by pure compression (N = 0) and N = 10 turns of HPT [1812].</figcaption></figure>

7.9. *Ceramics*

Plastic deformation of ceramics (including oxides, carbides, nitrides, etc.) is quite difficult under ambient conditions due to their hard and brittle nature. There have been long-term efforts to process these materials by plastic deformation, particularly because of the importance of this issue in geological studies [1819]. The first success in processing these materials by SPD was reported in 1935 when Bridgman recognized high pressure as the key to the plastic deformation of ceramics [20, 1820]. The introduction of HPT and its use for processing ceramics led to similar studies in the last century by other scientists mainly in the fields of geology [1821–1823] and physics [1824–1827]. The combination of HPT [20] with diamond anvil cells [1828] and the introduction of shear (rotational) diamond anvil cells in the 1980 s [1829, 1830] improved the research in this field because of increasing the level of processing pressure and the possibility of *in situ* examinations [8, 366]. Although high-energy ball milling can also introduce deformation in ceramics, pure plastic deformation can be hardly achieved in ceramics by ball milling due to the limited applied pressure [43]. Following a publication in 2010 [1179], which attempted to consolidate ceramic powders by HPT, SPD processing of ceramics to achieve functional properties
became more popular [513]. As discussed earlier in this manuscript, a wide range of ceramics were processed by HPT to achieve various properties including, high hardness [1179], electrocatalysis [960], photocatalysis [844], photoluminescence [583], photovoltaics [665], dielectric properties [840] and ion conductivity for batteries [1831]. The functional properties of ceramics were reviewed in previous chap- ters, but it is worth discussing the structural and microstructural evo- lution of ceramics compared to metals during SPD because there is limited information on this issue.

Phase transformations occur frequently in ceramics, and it was shown that the fraction of both pressure-induced and strain-induced phases increases with increasing strain in ceramics, mainly because of the defect-pressure-strain interactions [1829, 1830]. Fig. 88a shows the phase transformation from the γ phase to the α phase in Al₂O₃ induced by the application of HPT [16]. Moreover, SPD processing has led to the discovery of new hidden or intermediate phases in ceramics [630, 631, 1004]. The structural and phase evolutions in ceramics are principally similar to those in metals and the acceleration of phase transformations by increasing strain during SPD processing of metallic materials was also reported [506, 507].

There are similarities between the microstructural evolution of ce-
amics and metals, but grain refinement in ceramics is more significant
compared to metallic materials [513]. In metallic materials, grain sizes
are usually at the submicrometer level [2, 3], except for some dual-phase
materials, composites, HEAs and intermetallics [38, 290, 922]; however,
grain sizes in SPD-processed ceramics always decrease to the nanometer
level (see Fig. 88b for grain sizes in SiO₂ [609]). The reason for smaller
grain sizes in ceramics, which usually have a high melting point, is due
to their ionic or covalent atomic bondings which make the motion of
dislocations and grain boundaries harder than in metals [1832]. Similar
to metallic materials, it was shown that dislocations can be observed
within the grains of nanoceramics due to their slow movement resulting
from the strong atomic bonding and high Peierls stress [1832]. Another
issue that can be mentioned here is that similar to reports on metallic
materials [38], there is a steady state for grain size due to the occurrence
of dynamic recrystallization and grain boundary migration in ceramics
[513]. When a ceramic with grain sizes smaller than the steady-state
grain size is processed by SPD, a grain coarsening rather than a grain
refinement occurs (see Fig. 88d for grain coarsening in Al₂O₃ processed
by HPT [1831]). Similar grain coarsening was reported during HPT
processing of nanograined metals such as copper and nickel [38, 1834].
Finally, it should be noted that the formation of vacancies is also a
general phenomenon in HPT-processed ceramics. For example, Fig. 88e
shows the formation of vacancies in the TiO₂-ZnO composite confirmed
by electron spin resonance spectroscopy [605] and Fig. 88f shows the
formation of oxygen vacancies in the high-pressure columbite phase of
TiO₂ simulated by the first-principles calculations [1002]. Such va-
cancies, which were frequently reported in SPD-processed metals [306,
1835, 1836], are responsible for various functionalities of ceramics
[513]. Taken together, there are clear similarities between the behavior
of metals and ceramics during SPD, but deeper in situ studies using XRD
and ex situ studies using electron microscopy are needed to clarify the
mechanisms underlying microstructural evolutions in ceramics.

7.10. Polymers

SPD treatments can significantly affect the structure and properties
of polymers. The structural states formed during SPD treatment are
characterized by a variety of possible modes of molecular orientation,
crystalline lamellar and interlamellar amorphous phase arrangement,
degree of macromolecular chain orientation and intermolecular inter-
action. A distinctive feature of SPD methods compared to conventional

polymer processing methods (extrusion, injection molding, forging) is the introduction of uniform, simple shear into the materials, which promotes homogeneous structure and property development throughout the extruded billet and prevents the formation of undesirable so-called skin-core morphology, a reduction in the cross-sectional area of the workpiece, etc. Studies have shown that the structural states of polymeric materials formed by SPD and, thus, their physical and mechanical properties, are mainly determined by the magnitude of the accumulated strain. Activation of phase and structural transitions [1837–1840], strain-induced diffusion [1841], and intercalation and exfoliation of organic and inorganic fillers [1842–1844] can occur in polymers at different absolute values of accumulated strain. These changes depend on both SPD parameters (pressure, temperature, intensity and strain rate) and the structure of polymers (amorphous or semi-crystalline; linear, branched, cross-linked, etc.). SPD is most commonly performed on polymers by two methods: ECAP [226] and equal-channel multi-angle extrusion (ECMAE) [64]. Most studies on ECAP of polymers were limited to the case of 1–2 strain cycles, corresponding to a true strain of 0.8–2.4 (depending on the channel intersection angle). In contrast, ECMAE was used to reach a higher range of strain (6.7–9.1).

For polymers processed at low values of true strain (0.8–2.4), the increase in their elastic modulus and the decrease in tensile strength and plastic properties with increasing strain are typical [65, 1845–1854]. At the same time, the melting temperature and heat distortion temperature decrease (Table 7). The structure rearrangement in this range of true strains is mainly caused by the processes of molecular orientation and amorphization. The behavior of polymer materials processed in the range of high values of true strain (6.7–9.1) is fundamentally different from that of polymer materials deformed at low values of accumulated strain. At high strain levels, there is an increase in both stiffness and strength [64, 1855–1858]. At the same time, the melting temperature, heat distortion temperature and glass transition temperature increase (Table 7) [1859, 1860]. In semi-crystalline polymers, the amorphization process is replaced by the dynamic recrystallization process (strain-induced crystallization) in this range of strain. The accumulation of large values of strain causes the formation of a larger fraction of the crystalline phase in the deformed polymers. With increasing strain, the conformational transitions in semi-crystalline and amorphous polymers proceed more intensively. As a result, the fraction of oriented polymeric macromolecules, their packing density, and the degree of their orientation increase. This contributes to an additional increase in the stiffness and strength of the deformed polymers [1857]. Fig. 89 shows an example of the dependence of tensile strength and strain at break on accumulated strain for high-density polyethylene subjected to ECMAE.

In polymers capable of polymorphic transformations, activation of phase transitions is observed in high strain levels. As a result of SPD treatment, such polymers have different properties than undeformed polymers or polymers treated with low strain values. For example, an increase in the proportion of the more ductile γ phase due to the α→γ transition in polypropylene and polyamide-6 contributed to an increase in their ductility [1838, 1839], and the transition from the α phase to the β phase in polyvinylidene fluoride manifested the piezoelectric effect [1862]. Several semi-crystalline polymers, such as high-density polyethylene, polyoxymethylene and polytetrafluoroethylene, are characterized by an extremely low coefficient of linear thermal expansion values after SPD with strains of 8.5–9.1, which are close to the values of the coefficient of thermal expansion of invar alloys (Table 7) [1863]. The invar effect is achieved by forming a crystal structure in deformed polymers with a high degree of continuity, an extremely high degree of molecular orientation and a strain-induced degree of crystallization. Polymers deformed to high values of true strain (6.7–9.1) exhibit significant molecular orientation. Varying the deformation route results in different patterns of molecular orientation, in particular a biaxial molecular orientation [1857, 1858]. The latter provides a low anisotropy of elasticity and strength properties and a unique opportunity to improve the plastic properties of deformed polymers (Table 7).
<figure><img src="image_170.png" /><figcaption>**Fig. 88.** (a) TEM high-resolution image showing the γ→ α phase transformation in Al₂O₃ by HPT processing for 4 turns at 723 K [16]. (b) TEM High-resolution image showing the formation of nanograins in SiO₂ by HPT processing for 5 turns at 723 K [609]. (c) TEM lattice image of a Lomer-Cottrell dislocation lock formed in TiO₂ by HPT processing for 15 turns at room temperature [1002]. (d) TEM bright-field image (top) and selected area electron diffraction pattern (down), showing grain coarsening from 10 nm to the submicrometer level in Al₂O₃ by HPT processing for 4 turns at 723 K [16]. (e) Electron spin resonance spectra of TiO₂-ZnO composite before and HPT processing for 3 and 5 turns at room temperature, showing the formation of oxygen vacancies in TiO₂ and ZnO [605]. (f) Oxygen vacancies simulated by density functional theory for high-pressure columbite phase of TiO₂ stabilized by HPT processing [1002].</figcaption></figure>

SPD can be also applied to polymer-based composites as well as for
the consolidation of polymer powders. SPD-treated polymer composites
are characterized by increased physical and mechanical characteristics
compared to untreated composites [1842, 1861, 1864, 1865]. Their
feature is that an increase in the concentration of the filler does not lead
to a decrease in the degree of its dispersion. With an increase in the
accumulated plastic deformation, the improvement in the dispersion of

the filler becomes more pronounced (Fig. 90a-f). This fact is because
high pressure neutralizes the effect of an increase in melt viscosity with
an increase in filler concentration, which hinders the movement of fillers
inside the matrix and prevents their dispersion; however, plastic
deformation promotes effective exfoliation of filler particles without
damage to the polymer matrix. Such a mechanism of filler dispersion
leads to an improvement in the physical properties of polymer
<caption>**Table 7**</caption>

Effects of accumulated true strain during SPD on physical and mechanical properties of polymers (e: true strain, E: elastic modulus, σ<sub>y</sub> - yield strength, ε<sub>b</sub>: strain at break, T<sub>m</sub>: melting temperature, T<sub>g</sub>: glass transition temperature, R: electrical resistance, CLTE: coefficient of linear thermal expansion). The index 0 denotes the corresponding parameters of undeformed polymers [1844, 1861].

<table><thead><tr><th>Polymer</th><th>e</th><th>E/E<sub>0</sub></th><th>σ<sub>y</sub>/σ<sub>y0</sub></th><th>ε<sub>b</sub>/ε<sub>b0</sub></th><th>T<sub>m</sub> or T<sub>g</sub><sup>*</sup>, K</th><th>CLTE×10<sup>6</sup>, K<sup>-1</sup></th><th>R<sub>0</sub>/R</th></tr></thead><tbody><tr><td>High-Density polyethylene</td><td>2.18.5</td><td>1.703.30</td><td>1.403.00</td><td>0.930.92</td><td>398410</td><td>210–7</td><td>–</td></tr><tr><td>Polyoxymethylene</td><td>2.18.5</td><td>1.382.28</td><td>2.074.04</td><td>0.780.94</td><td>439443</td><td>130–5</td><td>–</td></tr><tr><td>Polytetrafluoroethylene</td><td>2.18.5</td><td>1.282.33</td><td>1.322.23</td><td>1.603.10</td><td>–</td><td>220–6</td><td>–</td></tr><tr><td>Polyamide 6</td><td>2.18.5</td><td>1.292.15</td><td>1.612.04</td><td>0.870.91</td><td>495500</td><td>–</td><td>–</td></tr><tr><td>Poly(methyl methacrylate)</td><td>2.18.5</td><td>1.191.23</td><td>1.101.30</td><td>1.501.60</td><td>390405</td><td>–</td><td>–</td></tr><tr><td>Linear Low-Density Polyethylene – 10 wt% Carbon Nanotubes</td><td>2.18.5</td><td>1.201.50</td><td>1.221.31</td><td>1.501.61</td><td>397402</td><td>150–6</td><td>2416</td></tr><tr><td>Cellulose</td><td>1.2</td><td>1.55</td><td>–</td><td>–</td><td>411</td><td>–</td><td>–</td></tr></tbody></table>

<figure><img src="image_171.png" /><figcaption>**Fig. 89.** Influence of the value of accumulated strain on tensile strength and strain at break of high-density polyethylene exposed to ECMAE [1857].</figcaption></figure>

composites. For example, electrical conductivity can be enhanced without a deterioration in mechanical properties with the introduction of conductive nanofillers (carbon nanotubes, carbon nanoplates) into polymers (Table 7) [1844, 1861]. The SPD-consolidated polymer powders (nylon 12, ultra-high molecular weight polyethylene, starch, wood flour, maple hardwood) materials exhibit significantly higher hardness and stiffness compared to reference materials produced by injection molding [1841, 1866–1869]. Strain-induced diffusion, which occurs in this case eliminates the need for the addition of a plasticizer or a binder. Figs. 90g and 90h show SEM images of polypropylene before and after strain-induced consolidation.

In summary, SPD has a high potential to significantly improve the mechanical properties of polymers and achieve new functionalities. The published studies show that SPD-processed polymer materials are characterized by unique physical and mechanical properties that cannot be achieved by other methods, such as (i) an increase in stiffness and strength while maintaining ductility at the level of the original material for semi-crystalline polymers, amorphous polymers and polymer powders, (ii) low coefficient of linear thermal expansion for semi-crystalline polymers and composites, (iii) increased electrical conductivity and strength in the case of polymer composites containing an electrically conductive nanofiller.

## 8. Heterostructured materials processed by SPD

Heterostructured materials are defined as materials composed of at least two different zones with a large difference in mechanical or physical properties [1870]. For structural heterostructured materials, the disparities can be given by coexisting zones with different order scales, defects densities, crystal structure, chemical composition, or crystallographic orientation [1870]. For multidisciplinary hetero-structured materials, the disparities may include electrochemical potential, magnetic sensitivity, optical properties, etc. [44]. SPD processing, including bulk-SPD, surface-SPD and powder-SPD, is one solution to produce heterostructured materials. In the following section, after reviewing the fundamentals and properties of heterostructured materials, the features of two kinds of popular heterostructured materials, namely harmonic-structured materials and gradient-structured

materials, are discussed.

### 8.1. Fundamentals and properties of heterostructured materials

Heterostructured materials are a fast-emerging field that offers a novel solution to various issues in materials science. Increasing both the strength and the strain hardening to avoid the "inevitable" strength-ductility trade-off is one of the most studied issues. Hetero-deformation-induced strengthening and work hardening [1870] by GNDs [1871] serve as the foundation for structural heterostructured materials. The hetero-deformation-induced stress, formerly known as back stress [1872] can be measured by uniaxial loading experiments [1873, 1874]. The hetero-deformation-induced stress accounts for the contribution of both forward stress and back stress [1870]. Back stress cannot be measured from the mechanical testing curves because it cannot be decoupled from the forward stress.

<figure><img src="image_172.png" /><figcaption>**Fig. 90.** (a-f): SEM micrographs of nanocomposites of LLDPE polymer with (a-c) 10 wt% of carbon nanotubes and (d-f) 20 wt% of carbon nanotube addition, after true strains of (a,d) e = 0, (b,e) e = 4.4, (c,f) e = 8.5 [1861]. (g,h) Morphologies of compacted polypropylene powders after strains of (g) e = 0 and (h) e = 8.5 [1841].</figcaption></figure>
The outstanding mechanical properties of heterostructured materials come from the interactive coupling between soft and hard zones (Fig. 91a) [1875]. The differences in flow stress cause a strain gradient between the soft/hard interface and the Frank-Read dislocation source (Fig. 91b) [1875]. To accommodate the strain mismatch near the interfaces, known as zone boundaries in heterostructured materials, GNDs are generated from Frank-Read sources in the soft zone. As a result, hard zones remain elastic while soft zones begin to deform plastically (Fig. 91c) before global yielding. Both soft and hard regions remain under mutual constraints. GNDs pile up against zone boundaries as applied stress increases, causing back stress in soft zones [1870, 1873]. To avoid cross-slip to encourage GND pileup, planar slip promoted by low stacking fault energy or short-range order is desired [1876]. The back stress acts against the dislocation source to curtail the emission of more dislocations [1877]. Simultaneously, the stress exerted by the head of the GND pileup produces forward stress in hard zones [1875, 1878, 1879]. The creation and interaction of GNDs near the zone boundaries will produce a hetero-boundary-affected region [1880]. The back stress strengthens soft zones, while the forward stress makes hard zones easier to deform [44]. As a result, the soft zones sustain larger deformations, while the hard zones act as obstacles to dislocation gliding. Therefore, the heterostructured materials possess higher strain-hardening and strengthening than those obtained in homogeneous nanostructures or coarse materials [1881]. The hetero-deformation-induced strengthening is usually negligibly small in homogeneous materials and not considered

in most classical models, such as the rule of mixtures. As a result, the yield strength and strain hardening of heterostructured materials exceed those predicted by the rule of mixtures [1882]. The hetero-deformation-induced strengthening is dominant in hetero-structured materials, and their properties come from the synergy of multiple strengthening mechanisms given by microstructural defects, e. g. zone boundaries, twins, shear bands, stacking faults, etc. [1883–1885].

The main factors to consider during the designing of hetero-structured materials can be divided into intrinsic and extrinsic (Fig. 92) [1886]. The former is material-specific and includes crystal structure, crystallographic texture, and those influencing the slip mode, such as stacking fault energy, short-range order, atomic size mismatch and shear modulus. The main extrinsic or processing parameters are stress state, equivalent strain, strain rate, temperature, time and pressure. Intrinsic parameters guide material selection while extrinsic parameters dictate the thermo-mechanical route selection. A description of each effect has been described in detail elsewhere [1886]. The elaboration of hetero-structured materials has to be optimized based on their classification: (i) multimodal structures that can be produced by SPD techniques, SPD plus heat treatments, or powder metallurgy, (ii) gradient structure by surface nanostructuring techniques, (iii) harmonic structure by powder metallurgy, powder metallurgy plus heat treatments and additive manufacturing, (iv) heterogeneous lamella structure by cold working (including SPD) plus partial recrystallization annealing, (v) layered

<figure><img src="image_173.png" /><figcaption>**Fig. 91.** Fundamental of heterostructured materials. (a) Generation and distribution of long-range back and forward stress by geometrically necessary dislocation (GND) pileups near the zone boundary, including generation of GND pileups from a Frank-Read source that produces hetero-deformation induced (HDI) stress. The curve on the left of the boundary is the distribution of forward stress. (b) Distribution of strain gradient with the distance from the zone boundary. (c) Deformation stages (I, II and III) and their effect on dislocation behavior and HDI stress distribution near a zone boundary ($\tau_a$ is the applied shear stress and red circles represent the dislocation source) [44, 1292, 1870].</figcaption></figure>
structure by rolling-based processing, physical or chemical surface
deposition, or additive manufacturing, and (vi) multiphase structure by
heat treatments, cold working (including SPD), powder metallurgy and
additive manufacturing [1887].

Among the key advantages of heterostructured materials is their
ability to produce unique property combinations that are not present in
their individual zones. So far, the most widely explored combinations
are improved mechanical performance with multidisciplinary properties
[1292, 1887]. However, other non-structural multidisciplinary mate-
rials can also be designed. Heterostructured materials are highly desir-
able for a wide range of applications, including structural, biomedical
[1888–1890], biosafety [1891, 1892], optoelectronics [1893, 1894],
energy storage [1895, 1896], catalysis [1891, 1897], photo-
electrochemistry [1898], food processing [1890], etc. These advances in
the development of heterostructured materials contribute to the ongoing
efforts to achieve sustainable energy solutions and more efficient
multidisciplinary components. More detailed descriptions of funda-
mentals, properties and perspectives of heterostructured materials can
be found in recent literature [44, 1292, 1875, 1899, 1900], including
one overview of SPD-processed heterostructured materials [1886].

8.2. *Harmonic-structured materials*

Powder metallurgy is a widely used technique for producing metallic
and ceramic bulk materials by sintering below the melting temperature
[1901–1903]. It is easy to produce high melting point materials by
powder metallurgy because there is no need to melt materials. In addi-
tion, powder metallurgy is suitable for hard-to-deform materials because
it is die-forming and does not require cutting or bending. This section
introduces harmonic structure design [1904] as a new family of heter-
ostructured materials that can be manufactured by powder-SPD com-
bined with powder metallurgy.

As mentioned earlier in this article, high-energy ball milling is a
useful SPD technique for processing powders [43, 153, 1905, 1906]. In
ball milling, plastic strain is introduced in powders by rotating, shaking
or jetting gases in a closed vessel, and the powder collides with each
other or with process media balls. In a single collision, the deformation
energy of the powder is quite small, but with repeated collisions in a
closed vessel, the deformation energy is accumulated in the powder. For
example, in the case of planetary ball milling, Umemoto et al. [1907]
predicted that in a single collision, the energy imparted to the powder is
less than 1 mJ, the equivalent plastic strain is about 1, the increasing
temperature is a maximum of 300 K, the collision time is 10⁻⁵ s, and the
strain rate is as high as 10⁴ s⁻¹. Therefore, quite a large equivalent

plastic strain and UFG powder formation could be expected by long-time
ball milling [1907, 1908]. The ball milling method can also produce
powders with heterogeneous grains by applying different levels of strain
to the interior and surface of the powder depending on the processing
conditions and the size of the powder. Harmonic structure design takes
advantage of the inhomogeneity between the interior and surface of the
powder [1908].

The harmonic structure is a type of heterogeneous and bimodal grain
size microstructure consisting of a three-dimensional UFG network
(Shell) surrounding the coarse-grained clusters (Core), as shown in
Fig. 93a. Fig. 93b shows a cross-sectional SEM image of a pure titanium
powder processed by high-pressure argon gas jet-milling [153], and
Fig. 93c shows a TEM image and a selected area diffraction pattern from
the TEM image taken from the near-surface region (such as the white
square region) shown in Fig. 93b. An equiaxed grain structure with a
grain size in the range of 5 µm to 10 µm was observed in the as-received
powder, although after high-pressure gas milling, the grain size in the
near-surface region became less than 100 nm. A ring-like pattern of the
selected area diffraction pattern indicates the existence of high-angle
boundaries in the HCP structure. The formation of such nanograins
with high-angle boundary structures was attributed to the grain subdi-
vision that occurs in various bulk SPD methods, such as HPT [330,
1909–1911] and ARB [1912–1915]. The ball-milled powder can be
consolidated into any shape by powder metallurgy sintering.

The harmonic structure can be introduced to all metallic materials
and is expected to combine high strength and high ductility. Compared
to the conventional bimodal structure with irregular coarse-grained and
UFG distribution, the harmonic structure has a network of UFG struc-
tures at the macro scale. The isotopically developed UFG network can
provide additional hetero-deformation-induced strengthening in multi-
ple directions during tensile deformation [1870, 1917–1922]. There-
fore, it is noteworthy that the harmonic-structured materials do not have
anisotropic mechanical properties. In addition, the enhanced strain
hardening and suppressed local deformation by the network structure
can achieve a good combination of strength and ductility [1904]. The
effect of stress partitioning on the UFG network structure during
deformation, which is one of the most unique features of
harmonic-structured materials, leads to hetero-deformation-induced
strengthening, resulting in a synergy of micro- and macro-scale me-
chanical properties of the materials [1923–1926]. Fig. 93d shows the
strength and toughness values of the harmonic-structured materials
normalized by the values of the homogeneous coarse-grained structure
[153]. All metallic materials show improvement in strength and
toughness including titanium [1927–1930], copper [1931, 1932], nickel

<figure><img src="image_174.png" /><figcaption>**Fig. 92.** Main intrinsic and extrinsic parameters to select starting materials and processing routes during the design of heterostructured materials [1886].</figcaption></figure>
[1933, 1934], stainless steel [1916, 1935], and Co-Cr-Mo alloys [1936]. This result suggests that harmonic structure design can be a universal, material-independent design guideline for improving mechanical properties [1876, 1937].

This section, thus, describes harmonic-structured materials as a new family of heterostructured materials with high strength and high ductility which can be produced by the powder-SPD process. Innovative mechanical properties in these materials are achieved through macroscopic periodicity and microscopic heterogeneous microstructures. The harmonic-structured materials not only show improvement in tensile properties but also in fatigue or wear properties [1938–1940]. It is expected that further research will reveal more possibilities for harmonic-structured materials in industrial fields, not only for their mechanical properties but also for their potential functional properties.

### 8.3. Gradient-structured materials

Gradient-structured materials can be defined as materials with dramatic heterogeneity in strength from one zone area to another [1941]. The gradient-structured materials are classified as a category of heterostructured materials, and thus, the relevant theories of heterostructured materials can be reasonably used to study gradient-structured materials [1942]. Production of gradient-structured materials is currently feasible with various surface-SPD methods developed in recent decades [1941, 1942]. In the following sections, the fundamentals, mechanical properties and functional properties of gradient-structured materials are discussed.

#### 8.3.1. Fundamentals of gradient-structured materials

The application of gradient structures in metal materials could be traced back to the carburizing and nitriding process, but the gradient structure material was not defined at that time. Until now, compositionally graded structures have also played an important role in

structural materials [1943]. Grain size and twinning gradients generated during tensile tests were frequently used in the past [1944–1948]. The relationship between gradient structure and hardness has been shown in Fig. 94 [1949]. Generally, the hardness of the gradient structure gradually decreases from the surface to the core, which has a certain corresponding relationship with the grain size. At present, research on structures such as defect gradient [1950], phase distribution gradient [1951] and texture gradient [1952–1954] is reported. By regulating the gradient structure, materials with excellent strength and ductility are obtained. The microscopic schematic diagram of various gradient structures is shown in Fig. 95 [1955]. Simulations and experiments confirmed that gradient-structured materials have synergistic effects by interactions between the gradient layer and the coarse-grained layer [1882, 1956–1962]. The traditional strengthening mechanism cannot fully explain the superior combination of strength and ductility of gradient-structured materials, and thus, research on their strengthening mechanism remains open for in-depth exploration.

The excellent properties of gradient-structured materials are attributed to the combined action of multiple strengthening theories [1955]. The theory of dislocation and twin strengthening is a common explanation for the good properties of gradient-structured materials. Increasing dislocation density increases the strength, while the pileup of dislocations generally leads to a significant decrease in the ductility of materials. Twins are believed to contribute to dislocation slip and coordinate deformation while increasing strength and improving the ductility of materials [1881, 1941, 1942]. The Zener-Holloman parameter (Z) has been used to express the effect of deformation on microstructure and mechanical properties as shown in Equation 36 [1963].

$$ \ln Z = \ln \dot{e} + \frac{Q}{RT} \qquad (36) $$

where Q is the activation energy for diffusion, $\dot{e}$ is strain rate and T is deformation temperature (Q is considered to be related to stacking fault

<figure><img src="image_175.png" /><figcaption>Fig. 93. (a) Schematic representation of the harmonic structure. (b) Cross-sectional image of jet-milled pure titanium powder. (c) TEM image of the near-surface region of jet-milled pure titanium powder. (d) Normalized yield strength and tensile toughness of harmonic structured materials [1916].</figcaption></figure>
<figure><img src="image_176.png" /><figcaption>**Fig. 94.** Schematic diagram of gradient grain structure and corresponding microhardness of metallic samples [1949].</figcaption></figure>

energy [1963]). Stacking fault energy has a considerable influence on the pileup of GNDs, which is closely related to the strengthening of heterostructured materials [44]. Hetero-deformation-induced theory can be used to explain the excellent mechanical properties of hetero-structured materials, which has been discussed earlier [188, 1962].

The theory of shear banding and strain delocalization was also used to explain the good ductility of gradient-structured materials. Macroscopically, the orderly and progressive plastic strain of GS material effectively alleviates the local stress concentration of the material, inhibits strain localization, and enables the material to maintain uniform plastic deformation at a higher stress level. Nanometallic materials usually form narrow shear bands after yielding and then fail quickly, while strain localization induced by shear bands seems inevitable. However, in gradient-structured materials, harmful shear bands are used to improve ductility [1941, 1964]. The key mechanical principle to realize the strength-ductility synergistic effect is that the microstructure should be designed by preventing strain localization as far as possible to fully promote the uniformity of plastic flow and realize strain delocalization. This requires that the work hardening capacity or strain rate sensitivity of the material is high enough to stabilize the plastic deformation [1965]. It is difficult for traditional homogeneous materials to meet such requirements, but such effects have been observed in

heterostructured materials [1966, 1967].

In summary, the research of gradient-structured materials as a kind of heterostructured materials is just beginning. In the future, a quantitative understanding of structure-property relationships is vital for rational design and optimization of gradient-structured functional materials with desired performance.

### 8.3.2. *Mechanical properties of gradient structures*

For materials processed by surface-SPD methods based on impacts [1968–1974], contacts [125, 1975] or shocks [1976–1983], there is a gradient microstructure from the treated surface to the bulk region with three zones: (i) a nanostructured layer, (ii) a transition region where grains are subdivided, (iii) a deformed region where grains are plastically deformed [1984]. For materials that exhibit deformation-induced twinning and/or phase transformation, there is a superposed gradient distribution of twins and transformed phases (see Fig. 96) [1985, 1986]. Due to the induced microstructure and other parameters including residual stresses (Fig. 96), surface-SPD methods are able to enhance mechanical properties such as hardness, tensile properties, fatigue and wear resistance [1951, 1987]. Mechanical properties are mainly determined by the induced nanostructured layer, compressive residual stress, work hardening and surface roughness [1988, 1989]. In general, the first two parameters are beneficial for improving the properties of materials either by retarding crack initiation or delaying crack propagation [1990, 1991], whereas surface roughness degrades it by causing local stress concentration [1991, 1992]. As for work hardening induced by surface-SPD, it is complex due to the multiaxial nature of loading [1976], and it can be divided into isotropic hardening (scalar) and kinematic hardening (tensor) [1993]. Isotropic hardening increases the strength of materials, while kinematic hardening can lower the yield stress of material through back stress [1994].

Under low-cycle fatigue, surface-SPD can significantly enhance mechanical strength and alter the cyclic plasticity (hardening and softening) of gradient-structured materials, depending on imposed stress amplitudes [1995]. In terms of fatigue life, both beneficial and harmful effects of surface-SPD have been observed as a function of the material’s type, treatment conditions and load amplitudes [1975, 1995, 1996]. Residual stress relaxation essentially occurs during the first cycles [1997], and the positive effect of compressive residual stress generated by surface-SPD can be quickly reduced or even lost. Significant improvement in fatigue life can thus not be observed, especially for high

<figure><img src="image_177.png" /><figcaption>**Fig. 95.** Micro-schematic diagram of various gradient structures [1955].</figcaption></figure>
<figure><img src="image_178.png" /><figcaption>**Fig. 96.** Generated gradient features including (a) gradient microstructure and residual stress [1971], (b) variation of twin volume fraction [1985] and (c) distribution of phase transformation (B, C and F refer to samples processed by shot peening coverage of 100%, 300% and 1500% respectively) [1986].</figcaption></figure>

load amplitudes [1998]. Improvement in the strength of materials induced by surface-SPD is usually accompanied by a reduction in its ductility [1999, 2000]. Decreased ductility, in some cases, cannot have an improving effect on low-cycle fatigue of materials processed by surface-SPD if the fatigue tests are strain-controlled, especially under high amplitudes [2001].

For high-cycle fatigue, an increase in fatigue resistance due to surface-SPD can usually be observed for various gradient-structured materials under different loading conditions [2002], if no excessive surface defects, such as micro-cracks, are generated by an over-treatment phenomenon. For a given material, the improvement is strongly dependent on treatment conditions which can be optimized according to material behavior [2003]. Under very high-cycle fatigue, extended lives induced by surface-SPD are frequently observed, except for materials with severe surface defects [2004] and excessive interior tensile residual stress [2005, 2006]. For almost all the cyclic loading modes, there is a trend of crack initiation shift from the surface in the high-cycle fatigue regime to the subsurface in the very high-cycle fatigue regime [2004, 2007]. In addition, in the case of subsurface crack initiation, a fish-eye pattern is frequently observed at crack origin, especially for materials that have metallurgical defects such as inclusions and/or crystallographic defects [2008, 2009].

Tribological properties have also been studied for various gradient-structured materials processed by surface-SPD [2010–2013]. In general, a remarkable increase in wear resistance can be observed with respect to coarse-grained counterparts. Several possible mechanisms

potentially involved in improving the tribological performance are: (i) inducing compressive residual stresses [2014, 2015]; (ii) decreasing coefficient of friction [2016, 2017]; (iii) increasing hardness by nano-structured layer and work-hardened region [2018]. However, poor wear resistance of a nanostructured layer can be observed due to its low ductility and toughness easily leading to surface cracks [2019].

Surface-SPD can improve material resistance by retarding crack initiation and delaying crack propagation through strengthened surface and compressive residual stresses. The contributions of grain refinement and that of work hardening to the strength of a structure are rather to increase the crack initiation resistance [1990, 1991]. For crack propagation, however, grain refinement gives rise to a deleterious effect [2020], just like work hardening [2021, 2022], as recapitulated in Fig. 97. As for compressive residual stresses, they usually decrease the crack propagation rate by acting as crack closure stress at the crack tip [2023]. However, the initial residual stresses obtained after surface-SPD cannot be directly used for fatigue analysis because of residual stress relaxation [2024]. In addition, surface-SPD-induced residual stress field and work hardening are associated, and it is difficult to properly separate their contributions through experiments. Their respective effects have thus been investigated using alternative numerical methods [2024, 2025]. The stress-strain curves at different depths can be obtained to provide information about local mechanical behavior. It was highlighted that the presence of residual stress can significantly change the local stress state of materials [2025]. However, more loading modes especially fatigue loading need to be comprehensively investigated in future
work.

### 8.3.3. Functional properties of gradient structures

There are two general ways to impart SPD to the surface in order to enhance the functional properties of gradient-structured materials: (i) applying a constant load onto the surface to be deformed or (ii) repeatedly impacting the surface with harmers or shots [46, 2026]. Many of the latter family of processes, such as SMAT, are derived from conventional shot peening [2027]. UFG structures generated by SPD are usually produced by the generation and accumulation of lattice defects, dividing and refining the initial microstructure into substructures and ultimately fine grains down to the nanoscale. As mentioned in an earlier section, the gradual cumulative strain applied from the surface creates a gradient microstructure which can be seen as a succession of different affected layers, but with a gradual transition. It goes from a refined surface nanocrystalline + ultrafine grain zone towards the surface to a

"plastically deformed layer" in the depth, via a transition zone where the grains are undergoing the subdivision process [2028, 2029]. The transition depth between the different layers depends on the processing parameters which include also the peening temperature. In addition to the obvious modification of the grain size and density of structural defects (dislocations, twins, etc.) through the depth of the samples, the so-called gradient microstructure is very often the combination of different gradients in terms of local texture, phase distribution and residual stresses [138, 1951, 2030-2034]. For example, when martensite forms by transformation-induced plasticity in SMAT-processed stainless steel, the maximum amount of α' martensite is never found in the UFG layer at the vicinity of the extreme surface but within the sub-surface; at a depth of 50-100 µm depending on the processing conditions [1951]. SMAT carried out at cryogenic and room temperatures on a 5553 β-metastable Ti-based alloy also promoted a martensitic transformation and kink bands produced essentially at the sub-surface [2034]. All these

<figure><img src="image_179.png" /><figcaption>**Fig. 97.** (a-c) Some typical mechanical properties of gradient-structured materials including (a) low-cycle fatigue of 316 L steel in different states [1995], (b) high-cycle fatigue of 316 L steel in different states [125] and (c) Tribological properties of an AZ91D magnesium alloy [2012]. (d) Roles played by different parameters on fatigue and wear resistance of gradient-structured materials.</figcaption></figure>
microstructural features can affect the functional properties of
gradient-structured materials.

The particular property of the UFG structures is the significantly high-volume fraction of high-angle grain boundaries with high energy and free volume resulting in the so-called non-equilibrium grain boundaries. The related increase in intergranular energy densities has an influence on the surface reactivity and the atomic transport along boundaries during chemical diffusion [373]. Thus, in addition to modifying mechanical properties through the influence of UFG, residual compressive stresses and potential stress raisers can be created on the surface by surface-SPD, which would affect the chemical and mecha-nochemical properties of the materials [2002, 2035–2037]. Conse- quently, surface-SPD has been used for several applications in which the favored atomic transport is beneficial, as discussed below.

The enhanced diffusion of chemical species after surface-SPD has been used to improve corrosion resistance as well as to optimize ther-mochemical surface treatments via “duplex” treatments. The most widely investigated process is the nitriding treatment, but pack bro-mizing, aluminizing, chromizing as well as plasma electrolytic oxidation have also been investigated successfully (See [2038], for further reading). For the case of nitriding, the enhanced atomic mobility after mechanical surface treatment generates a thicker diffusion layer for a given nitriding temperature/duration or allows reducing the nitriding temperature [2038–2040]. The latter is of importance when considering austenitic stainless steels. Indeed, by nitriding at a temperature as low as 573 K, a single-phase expended austenite is created without precipita-tion of Cr-rich precipitates which are detrimental to corrosion resis-tance. Also, SMAT carried out before nitriding allows producing a much harder surface layer due to the combination of two hardening mecha-nisms: strain hardening due to remaining structural defects and solid solution hardening due to the presence of the N-enriched expended austenite [2038]. An important issue with the “duplex” treatments is the contamination that can be introduced during surface-SPD by the peen-ing media that are also able to transfer chemical elements from the working chamber, locally modifying the chemical composition of the treated surfaces [2038, 2041, 2042]. This contamination acts as a bar-rier to the external atomic flux. For example, it leads to the formation of reduced or discontinuous nitriding layers [2038, 2041] so that the chemical etching [2042] or mechanical polishing [2043, 2044] must be used as an intermediary stage to remove the surface contamination and, thereby, improve further the quality and thickness of the nitrided layers.

Using surface-SPD for modifying the corrosion properties faces the same challenges as nitriding treatment. Plastic deformation improves the corrosion resistance in a passive environment whereas it increases the dissolution rate in a non-passive environment. SMAT has been used for example on a 301 stainless steel to facilitate the diffusion of Cr from the bulk towards the surface to form a stronger passivation film [2045]. Also, the effect of the surface contamination was demonstrated by modifying, for example, the nature of the peening shots during SMAT for a 2024 Al-based alloy [2046]. While the use of ceramic peening balls improved the corrosion resistance by the formation of a dense passive film, the Fe-containing layer induced by SMAT with steel balls led to the diminution in the corrosion resistance.

Surface-SPD is now finding new applications for the hydrogen sector. As hydrogen produces no greenhouse gas emissions when it burns, hydrogen will be the preferred alternative to fossil fuels for decarbon-izing both transport and industry. In addition to producing enough green hydrogen near the offtake sites using renewable energies, the storage and transportation of large amounts of hydrogen are other important issues for the hydrogen sector. For hydrogen storage, the objective is to use metallic materials as solid-state hydrogen tanks by storing the hydrogen in reversible metallic hydrides. Bulk-SPD induces structural defects and fine grains in metals which can be used to activate them as well as to optimize their hydrogen absorption/desorption kinetics [1077]. Instead of using high-energy ball milling to introduce structural defects and fine grains, the bulk-SPD techniques have the major

advantage of avoiding the complexity of handling highly reactive and pyrophoric powders [1077, 1753, 1754]. A very good example of the high potential of SPD has been demonstrated for the activation of TiFe via groove rolling or HPT [181]. While hydrogen absorption was extremely limited in the coarse-grained TiFe annealed sample because of difficult activation, the HPT-processed samples could fully store hydrogen reversibly at room temperature and were not deactivated by long-time exposure to the air [1137]. However, in some materials like the Ti-V-Cr alloys, the large number of structural defects generated by bulk-SPD can act as trap sites, impeding the hydrogen desorption reversibility. In the case of these Ti-V-Cr materials, the surface-SPD method of SMAT could be used successfully to activate the material while preserving reversibility [2047]. As summarized in Fig. 98, the nanostructure and cracks present at the surface of the SMAT-processed sample could act as a pathway for hydrogen transport through the oxide layer and activate the material while the hydrogen atoms could be stored in the defect-free subsurface and bulk from where reversibility was possible [2047, 2048]. Compared to bulk-SPD, an additional advantage of surface-SPD route is that they can be more easily scaled up. Thus, mechanical surface treatment inducing surface gradients can then be regarded as having a high potential for elaborating activated indus-trial hydrogen storage materials.

Transportation applications based on hydrogen as a fuel also require preventing the hydrogen embrittlement phenomenon. Since the hydrogen is absorbed and diffused from the surface, surface function-alization has been studied to prevent or reduce phenomena like hydrogen embrittlement. Surface functionalization can take the form of surface chemistry modifications like coatings and mechanical surface treatments [2049]. It was reported that the increase in hydrogen trap sites due to the surface structural refinement associated with the for-mation of a compressive residual stress gradient is beneficial for limiting the hydrogen embrittlement resistance. It was proposed that the high density of defects associated with the accumulation of hydrogen in the shot-peened deformed layer is responsible for creating a mismatch be-tween the treated surface and the non-deformed core, leading to the formation of sub-surface cracks which will then propagate toward the surface and not the core [2050, 2051]. However, the distinct influence of hydrogen trap site density and residual stress is not clear [2052] and phase transformation may also be of importance [2053]. Fig. 99 illus-trates that gradient-structured FCC CrMnFeCoNi HEAs can exhibit a good combination of a high yield stress and good ductility under a hydrogen environment [1235]. Due to the formation of surface nano-twins under SMAT (Figs. 99a and 99b), as opposed to the fully nano-structured sample produced by HPT which led to brittle failure in the presence of hydrogen, the SMAT-processed gradient samples showed a 2-3 times higher yield stress than the coarse-grained material coupled with a fair amount of ductility (Fig. 99c). Such improvement is expected as long as the hydrogen content is kept under a critical level to prevent the hydrogen-enhanced localized plasticity mechanisms. As depicted by the sequence of SEM images given in Fig. 99d-f, the presence of the gradient structure containing nanotwins was associated with a combi-nation of both intergranular (enlarged in Fig. 99e) and transgranular (Fig. 99f) surface cracking mechanisms [1235].

Gradient-structured materials appear to exhibit high potential for various functional applications. Although research in this regard is rather limited compared to the mechanical properties of these materials, there are clear trends to examine the functionality of these materials for various applications and particularly in the energy sector. Despite these gradient-structured materials are currently produced by surface-SPD methods such as SMAT and laser shot peening, which can be operated remotely, various metal forming, machining and welding methods or some SPD methods like equal-channel angular sheet extrusion can be also modified to produce such materials [2054–2057].
<figure><img src="image_180.png" /><figcaption>**Fig. 98.** (a-c) EBSD of cross section of SMAT-processed Ti₁₀V₇₅Cr₁₅ where (a) is a misorientation map, (b) is grain boundary map and (c) is internal misorientation map (treated surface is at bottom) [2047]. (d) pressure-composition isotherms for SMAT-processed Ti₁₀V₇₅Cr₁₅, indicating reversible hydrogen storage at room temperature without the need to an extra activation treatment [2047]. (e) Schematics of the effect of surface-SPD on hydrogen storage behavior and activation of Ti-V-Cr alloys [2047].</figcaption></figure>

## 9. SPD from the Bronze Age to 2024

SPD has been a part of human life for centuries and was used first in food-making and later in strategic tool-making. Sword making in the Bronze Age or at least during the transition from the Bronze Age to the Iron Age by Repeated forging and folding is perhaps the first success in commercializing the SPD process [5, 18]. The scientific interests in SPD which originated from geology at the beginning of the last century led to the invention of some new SPD methods such as HPT [20–22] and ECAP [27, 28] which are still the most popular [177, 193] even at the beginning of the year 2024. As discussed in previous chapters, SPD has been expanded in different directions in the 21st century and used to control microstructural and structural features to achieve novel mechanical and functional properties in a wide range of materials. To have an idea about the latest research trends in the SPDD field, some major articles published in 2024 are briefly reviewed in this section.

A review of the paper published in 2024 suggests that there are still attempts to develop new or modified bulk-SPD methods [2057–2061]. These attempts are mainly to enhance the properties, modify the shape

of samples or scale up the final product [2062, 2063]. There are also attempts to develop new surface-SPD methods or combine the existing methods with other processes [2064, 2065]. One issue that can be understood clearly from the literature survey is the high interest of researchers in processing additively manufactured alloys by bulk-SPD [2066, 2067] or surface SPD [2068, 2069]. A combination of 3D printing and SPD was also employed with the objective of enhancing the strength-ductility synergy [2070, 2071]. Cryogenic-SPD to achieve enhanced mechanical properties such as high strength and high ductility is used by some researchers [2072], while the thermal stability of these materials is still a matter of investigation [2073]. There are reports to use the concept of ultra-SPD to synthesize materials and the synthesis of novel Al-Au alloys [2074], HEAs [2075] and high-entropy ceramics [2076] are some reported results. Deep evaluation of microstructure by different *ex situ* characterization methods is still popular as there are still many questions in this regard, but there are clear trends to use *in situ* methods as well [2077, 2078]. Understanding the importance of grain boundaries and related phenomena such as segregation and diffusion are other microstructure-related studies [2079–2081], while there are also
<figure><img src="image_181.png" /><figcaption>**Fig. 99.** Illustration of the effect of SMAT on the modification of the hydrogen embrittlement resistance of a CrFeMnCoNi HEA: (a-b) SEM and EBSD images of surface nanotwins induced by SMAT before hydrogen charging, (c) tensile stress-strain curves before (black) and after (red) hydrogen charging for gradient-structured samples produced by two different SMAT processing conditions or fully nanostructured sample produced by HPT, (d-f) SEM images of a fractured specimen after hydrogen charging revealing both intergranular enlarged in (e), and transgranular enlarged in (f) [1235].</figcaption></figure>

various studies on structure-related studies such as phase trans-
formations [2082–2084]. While most of these studies are experimental,
there are some efforts to use theoretical or numerical approaches such as
atomistic modeling [2085], first-principles calculations [1004, 2086],
molecular dynamic simulations [2087], crystal plasticity simulations
[2088], finite element analysis [2089] and machine learning [2090].

A survey of publications in 2024 indicates that the investigations of
mechanical and functional properties for different applications are the
most popular research topics. There are numerous publications on such
properties and application after processing by bulk-SPD including
hardness [2091], strain hardening [2092], anneal hardening [2093],
ductile-brittle fracture transition [2094], fatigue resistance [2095,
2096], creep resistance [2097, 2098], shape memory effect [2099],
superconductivity [2100], magnetic properties [2101–2103], electro-
magnetic interference shielding [2104], thermoelectric properties
[2086], battery application [2105, 2106], photocatalytic CO₂ conver-
sion [2076], photocatalytic hydrogen production [2077], solid-state
hydrogen storage [2107–2109], corrosion resistance [2110, 2111] and
biomedical devices [2112–2114]. Materials processed by surface-SPD
were also investigated for different properties including wear resis-
tance [2115, 2116], fatigue resistance [2117, 2118], superplasticity
[2119] and corrosion resistance [2120]. There have been also attempts
to combine bulk-SPD with laser treatment or replace bulk-SPD with
powder-SPD to produce materials that need a large specific surface area
such as photocatalysts [2076, 2121]. One of the latest research trends is
the application of SPD to biomolecules to simulate their mechano-
chemical behavior which is of interest in understanding the origin of life
[2122]. This last issue will be discussed in more detail in the next
session.

10. SPD from earthquake to the origin of life

Although SPD methods are at the early stages of commercialization,

they have significantly contributed to scientific issues regarding the
behavior of materials under deformation. Among various SPD methods,
HPT is perhaps the most powerful tool for fundamental studies because
strain, pressure, temperature and strain rate can be controlled in this
method with high precision [20]. Although HPT is currently used mainly
for metal processing [23, 2123]; however, high pressure in the method
makes it applicable to almost any kind of material including
hard-to-deform materials such as ceramics [2124, 2125]. From the
historical point of view, Bridgman employed the first HPT facility to
process different kinds of metallic and nonmetallic substances including
rocks and organic materials [20]. The application of HPT to rocks is
accompanied by plastic deformation, phase transformations and snap-
ping, an observation that suggested a mechanism for the occurrence of
deep-seated earthquakes by plastic deformation of rocks [20] which is
still of interest in geology [646]. The first press release of HPT to the
public by Bridgman in 1935 had the title of “Scientist Makes Miniature
Earthquake”, as shown in Fig. 100a [23]. The HPT has continued its way
as a scientific tool in clarification of different phenomena, and under-
standing the origin of life is one of its latest contributions that was press
released in a TV program in 2022, as shown in Figs. 100b and 1c [2126].

One of the most essential biomolecules for life on Earth is protein,
but the formation of the first protein molecules from amino acids in the
early Earth conditions (about four billion years ago) is not well under-
stood yet. Following the discovery of amino acids in meteorites,
particularly Murchison and Tagish Lake meteorites, the hypothesis of
delivery of biomolecules and their polymerization by high-pressure
impacts through small solar system bodies (meteoroids, asteroids and
comets) has received high attention [2127, 2128]. Despite high interest
in this hypothesis, simulations of astronomical impacts by high-pressure
shock experiments have not led to the formation of proteins from amino
acids so far [2129, 2130]. Neglecting the strain effect can be one
explanation for little success in the polymerization of amino acids by
shock experiments [2131], while straining can practically occur in such
impacts due to high pressure, as schematically shown in Fig. 100b [2132]. Since some studies reported clear changes by straining in organic materials [2133, 2134], the strain effect should be included in the astronomical impact simulations.

For simulating the behavior of biomolecules under astronomical impacts, a recent study processed glycine amino acid by HPT under 1 and 6 GPa at ambient temperature [2126]. A loud explosion occurred during the HPT processing of glycine which can be recognized from the appearance of HPT anvils after the process, as shown in Fig. 100c. The gas phase could not be analyzed in this study, but examination of the solid phase by XRD (Fig. 101a), Raman spectroscopy (Fig. 101b) and nuclear magnetic resonance spectroscopy (Figs. 101c and 101d) indicate the stability of large amounts of glycine and the formation of some amounts of alcohol. The presence of large amounts of glycine after such severe HPT processing conditions justifies the stability of glycine reported in meteorites [2127, 2128]. The detection of ethanol confirmed that polymerization of glycine did not occur but its decomposition to alcohol and nitrogen-containing molecules happened by HPT processing. Despite the absence of polymerization, these findings are of importance because alcohol and nitrogen-containing groups are essential molecules for the development of organic materials on the Earth [2135]. Furthermore, both alcohol and glycine were detected in some comets [2136, 2137] and simulations by HPT suggested a possible mechanism for the formation of alcohol in comets by pressure and strain effects. These findings suggested that further studies by SPD under high pressure can be of importance from the “operational” view [2138] for a better understanding of the origin of life.

## 11. Concluding remarks and outlook

Severe plastic deformation (SPD) processing and the science of the design and synthesis of ultrafine-grained (UFG) materials by this process continuous its progress, although the focus of the field shows a transition from structural materials with enhanced mechanical properties to superfunctional materials with superior functional properties. This article attempts to highlight the most recent progress in the field and give new insight into the future of SPD. There are now various SPD methods for producing samples with appropriate shapes, large sizes and

continuous processing for commercial applications (Chapter 2). Microstructure and phase transformation of severely deformed materials, which have a significant effect on their properties, are studied much deeper with advanced characterization methods and theoretical studies in recent years (Chapter 3 and 4). Mechanical properties of severely deformed materials including high hardness and strength particularly at room temperature as well as creep resistance and superplasticity particularly at high temperature are widely studied (Chapter 5). However, the general trend is to study the functional properties of these materials for various applications including electric/magnetic properties, catalytic performance, hydrogen-related functionalities (hydrogen production, hydrogen storage and hydrogen embrittlement resistance), corrosion resistance and biocompatibility (Chapter 6). The application of SPD has been now extended from the production of UFG metallic materials such as magnesium, aluminum, titanium and iron alloys to various kinds of metallic and non-metallic materials such as high-entropy alloys, glasses, semiconductors, ceramics and polymers (Chapter 7). Another trend in the SPD field is to produce heterostructured materials including harmonic-structured and gradient-structured materials because these materials can show better properties for some particular applications compared to UFG materials (Chapter 8). These research trends continue to expand in different directions in the year 2024 (Chapter 9), and one of the latest trends in the SPD field is the investigation of the mechanisms behind certain natural phenomena, including the origin of life (Chapter 10).

SPD has shown great potential for the formalization of property-microstructure relationships for a few decades, but the field can move to the discovery of original materials that exhibit unique functionalities for particular applications like energy materials. In this regard, the field needs to be empowered by using various advanced analysis and in situ characterization methods. Moreover, close collaboration with theoretical scientists is necessary, particularly for functional properties related to energy applications. Biomaterials and hydrogen-related materials have currently a great positioning in many countries, and interesting findings reported for SPD-processed materials in these applications can lead to a faster transition from the laboratory scale to industry adoption. For such a transition to industry and commercialization, scaling up the sample size by using methods with enlarged processing capacity or with

<figure><img src="image_182.png" /><figcaption>**Fig. 100.** (a) The first press release about HPT in 1935, highlighting the potential of the method for geological studies and the mechanism of deep-seated earthquakes [23]. (b) A television program on TV Cultura channel in 2022 about the application of HPT for understanding the origin of life [2126].</figcaption></figure>
<figure><img src="image_183.png" /><figcaption>**Fig. 101.** (a) XRD profiles, (b) Raman spectra and (c,d) nuclear magnetic resonance spectra for glycine amino acid before and after treatment by HPT under 1 and 6 GPa [2126].</figcaption></figure>

continuous processing capability is essential. Studies conducted in very recent years confirm that SPD can move from a metal processing technique to a multidisciplinary tool for various studies that need close connection with scientists from the fields of physics, chemistry, mathematics, geology, astronomy, life sciences and many aspects of engineering.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

Kaveh Edalati thanks Mitsui Chemicals, Inc. for a research fund and the MEXT, Japan for Grants-in-Aid for Scientific Research (JP19H05176, JP21H00150 and JP22K18737).

Kei Ameyama was supported by JSPS KAKENHI via Grant Number JP18H05256.

Maki Ashida thanks the support by the Japan Science Promotion Society for Grant-in-Aid for Early-Career Scientists (Grant Number JP21K17007).

Andrea Bachmaier has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (Grant No. 757333 and 101069203).

Elena V. Bobruk was supported by the Ministry of Science and Higher Education of the Russian Federation under project No. 13.2251.21.0196 (grant agreement No. 075-15-2023-443).

Nguyen Quang Chinh thanks the KDP-2021 Program of the Ministry of Innovation and Technology from the source of the National Research,

Development and Innovation Fund, the Hungarian-Russian Research program (TET) through Grant No. 2021-1.2.5-TET-IPARI-RU-2021-00001, the Hungarian Scientific Research Fund OTKA through Grant number K143216 for the research support.

In-Chul Choi was supported in part by the National Research Foundation (NRF) of the Korean government (MSIT) under Grant No. 2022R111A3063805.

Robert Chulist acknowledges Project No. 2020/37/B/ST5/03267 of the National Science Centre of Poland.

Jorge M. Cubero-Sesin would like to thank Vicerrectoría de Investigación y Extensión, Instituto Tecnológico de Costa Rica for financial support from grant VIE-CF-1490033.

Sergiy Divinski is grateful to the German Research Foundation (DFG) for financial support.

Karsten Durst was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 405553726 – TRR 270, project A08.

Nariman A. Enikeev acknowledges the support by the Mega-grant State Program (agreement 075-15-2022-1114 dated 30.06.2022).

Roberto B. Figueiredo acknowledges FAPEMIG and CNPq for financial support.

Ricardo Floriano thanks the Brazilian funding agency São Paulo Research Foundation (FAPESP) for grant No. 2022/03024-7 and the National Council for Scientific and Technological Development (CNPq) for grant No. 407900/2021-7.

Joaquín E. González-Hernández would like to acknowledge Dirección de Posgrado, Instituto Tecnológico de Costa Rica for a doctoral program scholarship.

Thierry Grosdidier would like to acknowledge the support of the French Government through the program "Investissements d'avenir" operated by the French National Research Agency (ANR) and referenced
to as ANR-11-LABX-0008-01 ('LabEx DAMAS').

Dmitry Gunderov was supported partly by the Russian Science Foundation project 22-19-00347.

Liquing He thanks the support from the National Natural Science Foundation of China (No. 52171205, 52101249), Anhui Provincial Natural Science Foundation (No. 2108085QE191) and Youth Science and Technology Fund Project of China Machinery Industry Group Co., Ltd. (No. QNJJ-ZD-2022-01).

Zenji Horita acknowledges the support by a Grant-in-Aid for Scientific Research (A) from the MEXT, Japan (JP19H00830).

Yoshifumi Ikoma would like to thank the support by Grant-in-Aid for Scientific Research (B) (Grant No. JP18H01384) from the Japan Society for the Promotion of Science.

Jae-il Jang was supported by the National Research Foundation (NRF) of the Korean government (MSIT) under Grant No. 2022R1A5A1030054 and RS-2023-00273384.

Alberto M. Jorge Jr acknowledges the São Paulo Research Foundation - FAPESP (Brazil) under the grant FAPESP #2021/06546-1.

Megumi Kawasaki was supported by the National Science Foundation of the United States through Grant No. CMMI-2051205.

Shigeru Kuramoto was supported by the Iketani Science and Technology Foundation.

Terence G. Langdon was supported by the European Research Council under ERC Grant Agreement No. 267464-SPDMETALS.

Dong-Hyun Lee was supported by the National Research Foundation (NRF) of the Korean government (MSIT) under Grant No. 2021R1F1A1048393.

Valery I. Levitas received support from NSF (CMMI-1943710, DMR-2246991, XSEDE MSS170015), Iowa State University (Vance Coffman Faculty Chair Professorship and Murray Harpole Chair in Engineering), HPCAT through DOE-NNSA's Office of Experimental Science of Argonne National Laboratory (Contract No. DE-AC02-06CH11357).

Huai-Jun Lin thanks the financial support from the National Natural Science Foundation of China (No. 52071157), and the Guangdong Basic and Applied Basic Research Foundation (No. 2024B1515020010).

Klaus-Dieter Liss acknowledges the Japan Synchrotron Radiation Research Institute and SPring-8 under Proposal No. 2018B1219, the Ibaraki Prefectural Government and the J-PARC facility under the 2019 Overseas Academic User Program of the Ibaraki Neutron Beamline BL20 with proposal number 2019PM2014.

Diana Maritza Marulanda Cardona thanks to Universidad Militar Nueva Granada, Colombia.

Suk-Chun Moon acknowledges the University of Wollongong for the use of facilities in the High-Temperature Microscopy Laboratory.

Maxim Yu. Murashkin acknowledges the support by the Mega-grant State Program (agreement 075-15-2022-1114 dated 30.06.2022).

Muhammad Naeem thanks the Asia-Oceania Neutron Scattering Association (AONSA) for the award of the AONSA Young Research Fellowship (AONSA-YRF-2022).

Marc Novelli would like to acknowledge the support of the French Government through the program "Investissements d'avenir" operated by the French National Research Agency (ANR) and referenced to as ANR-11-LABX-0008-01 ('LabEx DAMAS').

Dániel Olasz thank the KDP-2021 Program of the Ministry of Innovation and Technology from the source of the National Research, Development and Innovation Fund, the Hungarian-Russian Research program (TÉT) through Grant No. 2021-1.2.5-TÉT-IPARI-RU-2021-00001, the Hungarian Scientific Research Fund OTKA through Grant number K143216 for the research support.

Vladimir V. Popov's contribution was carried out within the State Assignment of the Russian Federation on themes 'Pressure' and 'Function'.

Elena N. Popova's contribution was carried out within the State Assignment of the Russian Federation on themes 'Pressure' and 'Function'.

Oliver Renk acknowledges funding from the Austrian Academy of

Sciences via the Innovation Fund project IF 2019-37.

Liliana Romero-Resendiz acknowledges the funding from the European Union's Horizon 2022 Research and Innovation Programme under the Marie Sklodowska-Curie Action (MSCA) with project number 101103048, Programa de Apoyo a la Investigación y el Posgrado (PAIP-50009223) of the Chemistry College of Universidad Nacional Autónoma de México (UNAM), and Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (PAPIIT)-UNAM under grant number IA102724.

Vaclav Sklenicka acknowledges financial support provided by the Technology Agency of the Czech Republic under Grant No. TH02000018/004.

Boris Straumal thanks the Russian Ministry of Science and Higher Education (contract no. 075-15-2021-945 grant no. 13.2251.21.0013).

Yoichi Takizawa acknowledges the New Energy and Industrial Technology Development Organization (NEDO) for The Strategic Core Technology Advanced Program.

Yongpeng Tang is grateful to the Japan Science and Technology Agency (JST) for collaborative research based on industrial demand "Heterogeneous structure control: Towards innovative development of metallic structural materials".

Ruslan Z. Valiev was supported partly by the Ministry of Science and Higher Education of the Russian Federation under project No. 13.2251.21.0196 (grant agreement No. 075-15-2023-443), and partly by the Mega-grant State Program (agreement 075-15-2022-1114 dated by June 30, 2022).

Jing Tao Wang was supported by the National Natural Science Foundation of China (Grant No. 52074160).

Gerhard Wilde is grateful to the German Research Foundation (DFG) for financial support.

Yuntian T. Zhu acknowledges the support from the Ministry of Science and Technology of China (2021YFA1200202), the National Natural Science Foundation of China (11988103), the Hong Kong Research Grants Council (GRF-11214121) and the Hong Kong Institute for Advanced Study of City University of Hong Kong.

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