# Severe plastic deformation for producing Superfunctional ultrafine-grained and heterostructured materials: An interdisciplinary review

Kaveh Edalati, Anwar Ahmed, Saeid Akrami, Kei Ameyama, Valery Aptukov, Rashid Asfandiyarov, Maki Ashida, Vasily Astanin, Andrea Bachmaier, Victor Beloshenko, et al.

► To cite this version:

Kaveh Edalati, Anwar Ahmed, Saeid Akrami, Kei Ameyama, Valery Aptukov, et al. Severe plastic deformation for producing Superfunctional ultrafine-grained and heterostructured materials: An interdisciplinary review. Journal of Alloys and Compounds, 2024, 1002, pp.174667. 10.1016/j.jallcom.2024.174667. hal-04591805

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Review

# Severe plastic deformation for producing superfunctional ultrafine-grained and heterostructured materials: An interdisciplinary review

Kaveh Edalati<sup>a, *</sup>, Anwar Q. Ahmed<sup>b, c</sup>, Saeid Akrami<sup>d</sup>, Kei Ameyama<sup>e</sup>, Valery Aptukov<sup>f</sup>, Rashid N. Asfandiyarov<sup>g, h</sup>, Maki Ashida<sup>i</sup>, Vasily Astanin<sup>g</sup>, Andrea Bachmaier<sup>j</sup>, Victor Beloshenko<sup>k</sup>, Elena V. Bobruk<sup>g</sup>, Krzysztof Bryła<sup>l</sup>, José María Cabrera<sup>m, n</sup>, Amanda P. Carvalho<sup>o</sup>, Nguyen Q. Chinh<sup>b</sup>, In-Chul Choi<sup>p</sup>, Robert Chulist<sup>q</sup>, Jorge M. Cubero-Sesin<sup>r</sup>, Gregory Davdian<sup>s</sup>, Muhammet Demirtas<sup>t</sup>, Sergiy Divinski<sup>u</sup>, Karsten Durst<sup>v</sup>, Jiri Dvorak<sup>w, x</sup>, Parisa Edalati<sup>y</sup>, Satoshi Emura<sup>z</sup>, Nariman A. Enikeev<sup>g, aa</sup>, Ghader Faraji<sup>ab</sup>, Roberto B. Figueiredo<sup>o</sup>, Ricardo Floriano<sup>ac</sup>, Marjan Fouladvind<sup>ad</sup>, Daniel Fruchart<sup>ad, ae</sup>, Masayoshi Fuji<sup>y, af</sup>, Hiroshi Fujiwara<sup>e</sup>, Marcell Gajdics<sup>b, ag</sup>, Diana Gheorghe<sup>ah</sup>, Łukasz Gondek<sup>ai</sup>, Joaquín E. González-Hernández<sup>r</sup>, Alena Gornakova<sup>s</sup>, Thierry Grosdidier<sup>aj, ak</sup>, Jenő Gubicza<sup>b</sup>, Dmitry Gunderov<sup>g, h</sup>, Liqing He<sup>al</sup>, Oscar Fabian Higuera<sup>am</sup>, Shoichi Hiroswa<sup>an</sup>, Anton Hohenwarter<sup>ao</sup>, Zenji Horita<sup>ap, aq, ar</sup>, Jelena Horky<sup>as</sup>, Yi Huang<sup>at, au</sup>, Jacques Huot<sup>av</sup>, Yoshifumi Ikoma<sup>aw</sup>, Tatsumi Ishihara<sup>a, ax</sup>, Yulia Ivanisenko<sup>ay</sup>, Jae-il Jang<sup>az</sup>, Alberto M. Jorge Jr<sup>ba, bb, bc</sup>, Mie Kawabata-Ota<sup>bd</sup>, Megumi Kawasaki<sup>be</sup>, Tarek Khelfa<sup>bf</sup>, Junya Kobayashi<sup>bg</sup>, Lembit Kommel<sup>bh</sup>, Anna Korneva<sup>q</sup>, Petr Kral<sup>w, x</sup>, Natalia Kudriashova<sup>bi</sup>, Shigeru Kuramoto<sup>bg</sup>, Terence G. Langdon<sup>au</sup>, Dong-Hyun Lee<sup>bj</sup>, Valery I. Levitas<sup>bk, bl</sup>, Cong Li<sup>bm</sup>, Hai-Wen Li<sup>al</sup>, Yongtao Li<sup>bn</sup>, Zheng Li<sup>bo</sup>, Huai-Jun Lin<sup>bp</sup>, Klaus-Dieter Liss<sup>bq</sup>, Ying Liu<sup>bo</sup>, Diana Maritza Marulanda Cardona<sup>br</sup>, Kenji Matsuda<sup>bs</sup>, Andrey Mazilkin<sup>s</sup>, Yoji Mine<sup>bt</sup>, Hiroyuki Miyamoto<sup>bu</sup>, Suk-Chun Moon<sup>bq</sup>, Timo Müller<sup>bv</sup>, Jairo Alberto Muñoz<sup>m</sup>, Maxim Yu. Murashkin<sup>g, aa</sup>, Muhammad Naeem<sup>bw</sup>, Marc Novelli<sup>aj, ak</sup>, Dániel Olasz<sup>b, ag</sup>, Reinhard Pippan<sup>bx</sup>, Vladimir V. Popov<sup>by</sup>, Elena N. Popova<sup>by</sup>, Gencaga Purcek<sup>bz</sup>, Patricia de Rango<sup>ad</sup>, Oliver Renk<sup>ca</sup>, Delphine Retraint<sup>cb</sup>, Ádám Révész<sup>b</sup>, Virginie Roche<sup>ba</sup>, Pablo Rodriguez-Calvillo<sup>cc</sup>, Liliana Romero-Resendiz<sup>bw, cd, ce</sup>, Xavier Sauvage<sup>cf</sup>, Takahiro Sawaguchi<sup>z</sup>, Hadi Sena<sup>cg</sup>, Hamed Shahmir<sup>ch</sup>, Xiaobin Shi<sup>bn</sup>, Vaclav Sklenicka<sup>w, x</sup>, Werner Skrotzki<sup>ci</sup>, Nataliya Skryabina<sup>ae</sup>, Franziska Staab<sup>v</sup>, Boris Straumal<sup>s</sup>, Zhidan Sun<sup>cc</sup>, Maciej Szczerba<sup>q</sup>, Yoichi Takizawa<sup>cj</sup>, Yongpeng Tang<sup>ck</sup>, Ruslan Z. Valiev<sup>g, aa</sup>, Alina Vozniak<sup>cl</sup>, Andrei Voznyak<sup>cm</sup>, Bo Wang<sup>cn</sup>, Jing Tao Wang<sup>bo</sup>, Gerhard Wilde<sup>u</sup>, Fan Zhang<sup>cn</sup>, Meng Zhang<sup>bp</sup>, Peng Zhang<sup>bp</sup>, Jianqiang Zhou<sup>co</sup>, Xinkun Zhu<sup>bm</sup>, Yuntian T. Zhu<sup>cp</sup>

**Abbreviations:** ARB, Accumulative roll-bonding; BCC, Body-centered cubic; EBSD, Electron backscatter diffraction; ECAP, Equal-channel angular pressing; FCC, Face-centered cubic; GNDs, Geometrically necessary dislocations; HCVD, Hard cyclic viscoplastic deformation; HCP, Hexagonal close-packed; HEA, High-entropy alloy; HPS, High-pressure sliding; HPT, High-pressure torsion; HPTE, High-pressure torsion extrusion; RDAC, Rotational diamond anvil cell; SEM, Scanning electron microscopy; SPD, Severe plastic deformation; SMAT, Surface mechanical attrition treatment; TEM, Transmission electron microscopy; t-HPS, Tube high-pressure shearing; UTS, Ultimate tensile strength; UFG, Ultrafine-grained; XRD, X-ray diffraction.

* Corresponding author.

E-mail address: kaveh.edalati@kyudai.jp (K. Edalati).

https://doi.org/10.1016/j.jallcom.2024.174667

<footnote><sup>a</sup> WPI, International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, Fukuoka 819-0395, Japan</footnote>

<footnote><sup>b</sup> Department of Materials Physics, Eötvös Loránd University, ELTE, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary</footnote>

<footnote><sup>c</sup> College of Science, University of Kufa, Najaf 54001, Iraq</footnote>
d Institutes of Innovation for Future Society, Nagoya University, Nagoya 464-8603, Japan

e College of Science and Engineering, Ritsumeikan University, Kusatsu 525-8577, Japan

f Perm State University, Bukireva, Perm 614068, Russia

g Ufa University of Science and Technology, 32 Zaki Validi str, Ufa 450076, Russia

h Institute of Molecule and Crystal Physics UFRC RAS, 71 pr. Oktyabrya, Ufa 450054, Russia

i Seikei University, 3-3-1 Kichijoji-Kitamachi, Musashino-shi, Tokyo 180-8633, Japan

j Erich Schmid Institute of Materials Science of the Austrian Academy of Sciences, Leoben, 8700, Austria

k Donetsk Institute for Physics and Engineering Named after O.O. Galkin, National Academy of Sciences of Ukraine, Pr. Nauki, 46, Kyiv 02000, Ukraine

l Faculty of Mechanical Engineering, Cracow University of Technology, Warszawska 24, Kraków 31-155, Poland

m Department of Materials Science and Engineering EEBE, Universidad Politécnica de Catalunya, c/Eduard Maristany 10-14, Barcelona 08019, Spain

n Fundació CIM-UPC, c/Llorens i Artigas 12, Barcelona 08028, Spain

o Department of Metallurgical and Materials Engineering, Universidade Federal de Minas Gerais, Belo Horizonte, MG 31270-901, Brazil

p School of Materials Science and Engineering, Kumoh National Institute of Technology, Gumi 39177, Republic of Korea

q Institute of Metallurgy and Materials Science, Polish Academy of Sciences, Krakow 30-059, Poland

r Centro de Investigación y Extensión en Materiales (CIEMTEC), Escuela de Ciencia e Ingeniería de los Materiales, Instituto Tecnológico de Costa Rica, Cartago 159-7050, Costa Rica

s Osipyan Institute of Solid State Physics of the Russian Academy of Sciences, Ac. Osipyan Str. 2, Chernogolovka 142432, Russia

t Department of Aerospace Engineering, Samsun University, Samsun 55420, Turkey

u Institute of Materials Physics, University of Münster, Germany

v Physical Metallurgy (PhM), Materials Science Department, Technical University of Darmstadt, Peter-Grünberg-Str. 2, Darmstadt 64287, Germany

w Institute of Physics of Materials, Czech Academy of Sciences, Zizkova 22, Brno 616 62, Czech Republic

x CEITEC – Institute of Physics of Materials, Czech Academy of Sciences, Zizkova 22, Brno 616 62, Czech Republic

y Department of Life Science and Applied Chemistry, Nagoya Institute of Technology, Tajimi 507-0033, Japan

z National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 316-8511, Japan

aa Laboratory for Dynamics and Extreme Characteristics of Advanced Nanostructured Materials, Saint Petersburg State University, 7-9 Universitetskaya nab., St. Petersburg 199034, Russia

ab School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

ac School of Applied Sciences, University of Campinas (FCA-UNICAMP), Pedro Zaccaria, 1300, Limeira 13484-350, Brazil

ad Institut Néel, CNRS & UGA, Grenoble, 38042, France

ae JOMI-LEMAN SA, 1115 route de St Thomas, La Motte-Fanjas 26217, France

af Advanced Ceramics Research Center, Nagoya Institute of Technology, Tajimi 507-0033, Japan

ag Institute for Technical Physics and Materials Science, HUN-REN Centre for Energy Research, Budapest H-1121, Hungary

ah National Institute for Research and Development in Environmental Protection, 294 Splaiul Independentel, 6th District, Bucharest 060031, Romania

ai AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków 30-059, Poland

a) Université de Lorraine, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3 UMR 7239), 7 rue Félix Savart, BP 15082, Metz F-57073, France

ak Université de Lorraine, Laboratory of Excellence on Design of Alloy Metals for low-mass Structures (DAMAS), Metz F-57045, France

al Hefei General Machinery Research Institute Co., Ltd, Hefei 230031, PR China

am Universidad del Atlántico, Faculty of Engineering, Mechanical Engineering Program, Research Group CONFORMAT, Puerto Colombia, Colombia

an Department of Mechanical Engineering and Materials Science, Yokohama National University, Yokohama 240-8501, Japan

ao Department of Materials Science, Montanuniversität Leoben, Johannstraße 12, Leoben 8700, Austria

ap Graduate School of Engineering, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan

aq Magnesium Research Center, Kumamoto University, Kumamoto 860-8555, Japan

ar Synchrotron Light Application Center, Saga University, Saga 840-8502, Japan

as RHP-Technology GmbH, Forschungs- und Technologiezentrum, Seibersdorf 2444, Austria

at Department of Design and Engineering, Faculty of Science and Technology, Bournemouth University, Poole, Dorset BH12 5BB, UK

au Materials Research Group, Department of Mechanical Engineering, University of Southampton, Southampton SO17 1BJ, UK

av University of Quebec in Trois-Rivières (UQTR), 3351 des Forges, Trois-Rivières G9A 5H7, Canada

aw Department of Materials Science and Engineering, Kyushu University, Fukuoka 819-0395, Japan

ax Department of Applied Chemistry, Faculty of Engineering, Kyushu University, Fukuoka 819-0395, Japan

ay Institute for Nanotechnology, Karlsruhe Institute for Technology, Karlsruhe, 76021, Germany

az Division of Materials Science and Engineering, Hanyang University, Seoul 04763, Republic of Korea

ba LEPMI, Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, LEPMI, Grenoble, 38000, France

bb SIMAP, Univ. Grenoble Alpes, CNRS, Grenoble INP, SIMaP, Grenoble, 38000, France

bc DEMa, Federal University of São Carlos, São Carlos, São Paulo 13565-905, Brazil

bd Ritsumeikan Global Innovation Research Organization, Ritsumeikan University, Kusatsu 525-8577, Japan

be School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331, USA

b) Department of Materials Engineering, School of Energy and Electromechanical Engineering, Hunan University of Humanities Science and Technology, Loudi 417000, China

b) Department of Mechanical and Systems Engineering, Faculty of Engineering, Ibaraki University, 4-121-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan

b) Department of Mechanical and Industrial Engineering, Tallinn University of Technology (TalTech), Ehitajate tee 5, Tallinn 19086, Estonia

b) School of Physical Sciences, University of Cambridge, Trinity Lane, Cambridge CB2 1TN, UK

b) Department of Materials Science and Engineering, Chungnam National University, Daejeon 34134, Republic of Korea

b) Iowa State University, Departments of Aerospace Engineering and Mechanical Engineering, Ames, IA 50011, USA

b) Ames National Laboratory, Division of Materials Science & Engineering, Ames, IA 50011, USA

b) Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650093, China

b) School of Materials Science and Engineering & Low-Carbon New Materials Research Center, Anhui University of Technology, Maanshan 243002, PR China

b) School of Materials Science and Engineering, Nanjing University of Science & Technology, Nanjing 210014, China

b) Institute of Advanced Wear & Corrosion Resistance and Functional Materials, Jinan University, Guangzhou 510632, China

b) School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, NSW 2522, Australia

b) Faculty of Engineering, Universidad Militar Nueva Granada, Bogotá, Colombia

b) Graduate School of Science and Engineering, University of Toyama, Toyama 930-8555, Japan

b) Department of Materials Science and Engineering, Kumamoto University, Kumamoto 860-8555, Japan

b) Department of Mechanical Engineering, Doshisha University, Kyoto 640-0394, Japan

b) Anton Paar GmbH, Anton-Paar-Straße 20, Graz 8054, Austria

b) School of Metallurgy and Materials, University of Birmingham, Birmingham B15 2TT, UK

b) Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, Johannstraße 12, Leoben 8700, Austria

b) M.N. Miheev Institute of Metal Physics, Ural Branch of RAS, Ekaterinburg 620108, Russia

b) Department of Mechanical Engineering, Karadeniz Technical University, Trabzon 61080, Turkey

c) Department Materials Science, Montanuniversität Leoben, Roseggerstraße 12, Leoben 8700, Austria
cb LASMIS, University of Technology of Troyes (UTT), Troyes, 10004, France

cc NLMK Belgium Holdings NV, Rue des Rivaux 2, La Louvière 7100, Belgium

cd Department of Design and Engineering, Faculty of Science and Technology, Bournemouth University, Poole, Dorset BH12 5BB, UK

ce Facultad de Química, Departamento de Ingeniería Metalúrgica, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico

cf Univ Rouen Normandie, INSA Rouen Normandie, CNRS, Groupe de Physique des Matériaux UMR 6634, Rouen, 76000, France

cg Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA

ch Department of Materials Engineering, Tarbiat Modares University, Tehran, Iran

ci Institute of Solid State and Materials Physics, Dresden University of Technology, Dresden, 01062, Germany

ci Technology Department, Nagano Forging Co., Ltd, Nagano 381-0003, Japan

ch Department of Advanced Materials Science and Engineering, Faculty of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan

ci Centre of Molecular and Macromolecular Studies, Polish Academy of Sciences, Sienkiewicza Street, 112, Lodz 90001, Poland

cm Kryvyi Rih State Pedagogical University, Gagarin av. 54, Kryvyi Rih 50086, Ukraine

cn School of Materials Science and Engineering, Shanghai University of Engineering Science, Shanghai 201620, China

cp School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China

ep Department of Materials Science and Engineering, Mechanical Behavior Division of Shenyang National Laboratory of Materials Science, City University of Hong Kong, Kowloon, Hong Kong, China

ARTICLE INFO

Keywords:

Severe plastic deformation (SPD)

Nanostructured materials

Ultrafine grained (UFG) materials

Gradient-structured materials

High-pressure torsion (HPT)

A B S T R A C T

Ultrafine-grained and heterostructured materials are currently of high interest due to their superior mechanical and functional properties. Severe plastic deformation (SPD) is one of the most effective methods to produce such materials with unique microstructure-property relationships. In this review paper, after summarizing the recent progress in developing various SPD methods for processing bulk, surface and powder of materials, the main structural and microstructural features of SPD-processed materials are explained including lattice defects, grain boundaries and phase transformations. The properties and potential applications of SPD-processed materials are then reviewed in detail including tensile properties, creep, superplasticity, hydrogen embrittlement resistance, electrical conductivity, magnetic properties, optical properties, solar energy harvesting, photocatalysis, electrocatalysis, hydrolysis, hydrogen storage, hydrogen production, CO₂ conversion, corrosion resistance and biocompatibility. It is shown that achieving such properties is not limited to pure metals and conventional metallic alloys, and a wide range of materials are currently processed by SPD, including high-entropy alloys, glasses, semiconductors, ceramics and polymers. It is particularly emphasized that SPD has moved from a simple metal processing tool to a powerful means for the discovery and synthesis of new superfunctional metallic and nonmetallic materials. The article ends by declaring that the borders of SPD have been extended from materials science and it has become an interdisciplinary tool to address scientific questions such as the mechanisms of geological and astronomical phenomena and the origin of life.

Table of Contents

1. Introduction

2. SPD methods

2.1. Bulk-SPD methods

2.2. Surface-SPD methods

2.3. Powder-SPD methods

2.4. Recent trends in SPD methods

2.4.1. SPD methods with hydrostatic pressure

2.4.2. Upscaling disc sample to rod

2.4.3. Pipe sample processing

2.4.4. Upscaled sheet sample processing

2.4.5. Hard cyclic viscoplastic deformation

2.4.6. Cryogenic-SPD

2.4.7. Ultra-SPD

3. Microstructural features after SPD

3.1. Grain boundaries and related phenomena

3.2. Investigation of non-equilibrium grain boundaries

3.3. Investigation of microstructure by electron backscatter diffraction

3.4. Investigation of microstructure by synchrotron X-ray and neutron diffraction

4. Phase transformations

4.1. Phase transformations in metallic alloys

4.2. Phase transformations in ceramics

4.3. Coupled in situ and theoretical studies of phase transformations

5. Mechanical properties

5.1. Strain hardening

5.2. Anneal hardening

5.3. Creep resistance

5.4. Superplastic deformation

5.5. Low- and room-temperature superplasticity

6. Functional properties

6.1. Electrical conductivity

6.2. Magnetic properties

6.3. Optical bandgap narrowing and solar energy harvesting

6.4. Photocatalytic CO2 conversion

6.5. Photocatalytic hydrogen production

(continued on next column)

(continued)

6.6. Electrocatalytic hydrogen production

6.7. Hydrolytic hydrogen production

6.8. Solid-state hydrogen storage

6.8.1. Thermodynamic tailoring of hydrogen storage materials

6.8.2. Kinetic tailoring of hydrogen storage materials

6.8.3. Activation and air resistance of hydrogen storage materials

6.8.4. Mass sample production for hydrogen storage

6.9. Hydrogen embrittlement resistance

6.10. Corrosion resistance

6.10.1. Corrosion passive film features

6.10.2. Corrosion resistance of steels

6.11. Biomaterials

6.11.1. Biocompatible titanium alloys

6.11.2. Biocompatible magnesium alloys

6.11.3. Innovative biomaterials

7. Ultrafine-grained materials processed by SPD

7.1. Magnesium alloys

7.2. Aluminum alloys

7.3. Titanium alloys

7.4. Iron alloys and steels

7.5. Lattice-softened alloys

7.6. High-entropy alloys

7.6.1. Microstructural and mechanical behavior of Cantor alloy

7.6.2. Hardening behavior of high-entropy alloys

7.6.3. Nanomechanical behavior of high-entropy alloys

7.6.4. Superplasticity of high-entropy alloys

7.6.5. Superfunctional high-entropy alloys and ceramics

7.7. Amorphous and glass materials

7.8. Semiconductors

7.9. Ceramics

10. Polymers

8. Heterostructured materials processed by SPD

8.1. Fundamentals and properties of heterostructured materials

8.2. Harmonic heterostructured materials

8.3. Gradient-structured materials

(continued on next page)
(continued)

8.3.1. Fundamentals of gradient-structured materials

8.3.1. Mechanical properties of gradient structured materials

8.3.2. Functional properties of gradient-structured materials

9. SPD from the Bronze Age to 2024

10. SPD from earthquake to the origin of life

11. Concluding remarks and outlook

Acknowledgments

# 1. Introduction

Severe plastic deformation is receiving significant attention as a powerful process to produce materials with ultrafine grains (UFG) and large fractions of crystal lattice defects such as vacancies, stacking faults, dislocations, twins and grain boundaries [1–3]. These microstructural features of SPD-processed materials lead to their enhanced properties for various applications [4,5]. Although high strength through the Hall-Petch strengthening mechanism is the most known property of SPD-processed materials [6,7], these materials exhibit a wide range of mechanical and functional properties [4,5]. In addition to microstructure control by SPD, the process has other applications such as phase transformation control [8,9], mechanical alloying [10,11] and consolidation of powders [12,13]. The application of SPD has been extended from metallic alloys to a wider range of materials such as polymers [14], carbon [15] ceramics [16], etc. Since the properties of such SPD-processed materials are superior compared to conventional engineering materials, the term superfunctional materials has been recently used for them [17]. As shown in Fig. 1, the number of publications about SPD has experienced a gradual increase since the year 2000, and over 1000 papers are currently published about SPD every year.

The historical development of SPD was discussed in a recent review paper by 49 active scientists in the field [5]. Such a historical development can be briefly summarized in Fig. 2 [5]. The SPD was known in ancient times in sword making, and it became popular during the transition from the Bronze Age to the Iron Age [18]. The repeated forging and folding that was used for sword making is considered an ancient form of modern accumulative roll-bonding (ARB) [19]. Another transition in the SPD occurred in the 1930 s [20,21] followed by a book in 1952 [22] when Bridgman could apply SPD to a wide range of materials by the introduction of the high-pressure torsion (HPT) method (see details in [23]). It should be noted that superplastic deformation (severe plastic elongation by thermally-activated deformation mechanisms) was also reported in metallic materials in the 1930 s by Pearson [24], which received the term “super-plasticity” in polymer sciences in the 1930 s [25]. The invention of equal-channel angular extrusion/-pressing (ECAP) and ECAP-conform by Segal and his co-workers in the 1970 s was another important development that resulted in scaling up the size of SPD-processed samples by simple shear [26–28]. The

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Number of publications per year about SPD and HPT [Scopus, January 15, 2024].</figcaption></figure>

discovery of the formation of UFG microstructure by SPD was another important finding, which was first reported by Bridgman using X-ray diffraction (XRD) [20–22] and later visualized by transmission electron microscopy (TEM) in a few papers in the 1970 s [29,30] and a book written in Polish in 1976 [31] (the content of the book was summarized in English in [32]). The achievement of low-temperature superplasticity by Valiev and his co-workers in the 1980 s was an important finding that showed the interesting properties of SPD-processed materials with UFG structures and a large fraction of high-angle grain boundaries [33]. An extension of this study to Western and Asian countries [34,35] followed by the publication of a review paper in 2000 [1] resulted in the birth of the modern NanoSPD (nanomaterials by severe plastic deformation) field and eventually in the commercialization of the method for biomedical applications [36].

Despite significant progress in the SPD field, there are some arguments regarding the terminology of SPD. The SPD process was defined as the introduction of large strains in a bulk sample without changing its shape [2]. In SPD processes, the applied pressure should be usually high to avoid the fracture of materials, and the temperature should be below the recrystallization temperature when the objective is to produce UFG materials [37,38]. However, there are comments that the strain level (usually over a von Mises equivalent strain of 6) should be considered as a border of SPD regardless of the method used for the application of such strain levels. Such strains can be sometimes applied at low temperatures by conventional methods such as rolling, wire drawing and extrusion [39]. Moreover, there have been long-term efforts to apply such large strain on the surface of bulk materials [40,41] or in powders [42,43]. Since all these processes follow the same principles, SPD methods can be classified into three broad categories: (a) bulk-SPD, (b) surface-SPD and (c) powder-SPD. Despite such classification, a rigid strain border can be hardly defined for SPD because the microstructure-strain relationships of materials are quite different [5]. Moreover, the objective of SPD is not always the formation of UFG (materials with grain sizes below 1000 nm having high angles of misorientation) or nanograined (materials with grain sizes below 100 nm) materials, but it may be used in lower strain levels to control lattice defects [44] or produce heterostructured materials [45].

Despite significant progress in the field of SPD in recent years, there are limited comprehensive review papers about the field [1–5]. Moreover, available review papers are either old or mainly focus on SPD as a metal processing tool. However, the borders of SPD have been extended to non-metallic materials and various disciplines other than metallurgy. By considering the progressive changes of SPD in terms of concept and research direction, a comprehensive review paper is required to discuss the most recent aspects and future direction. Such a review paper should also clarify the classification of the SPD process and discuss the behavior of various types of materials during severe straining. This article, which was prepared by a large number of active researchers in different aspects of SPD, aims to provide a comprehensive overview of the latest concepts and findings in the field of SPD. The article classifies these findings by considering the processing methods, microstructural and structural features, mechanical and functional properties, and processed UFG and heterostructured materials. At the end of the manuscript, the application of SPD as a potential scientific tool for elucidating some natural phenomena such as earthquakes and the origin of life is briefly mentioned.

# 2. SPD methods

As mentioned in the introduction, the SPD processes can be classified as bulk-SPD, surface-SPD and powder-SPD methods. In bulk-SPD, the goal is to modify the bulk microstructure of a material with reasonably large sizes, although the surface is also affected [1–3]. In surface-SPD, only surface and sub-surface layers are modified, and the core of the sample remains reasonably unchanged [46]. In powder-SPD, the material is in the form of powder, and strain is introduced on the surface layer and core of the powder particles usually by ball milling methods [43].
<figure><img src="image_4.png" /><figcaption>Fig. 2. Illustration of the historical development of SPD. From left to right: sword making by repeated forging and folding (photograph of a sword made in Luristan, Iran, 750–650 BSE), principles of HPT (a drawing by Bridgman, 1935), principles of ECAP (visualization of simple shear by Moire Fringes and coordinate grids reported by Segal, 1970 s), formation of UFG structure by HPT processing (micrographs reported by Erbel, 1976), high strain rate superplasticity in an aluminum alloy processed by ECAP (a work by Valiev, et al., 1997), and commercialization of ECAP-processed titanium for implants [5].</figcaption></figure>

To introduce large levels of strain in the sample, the SPD method should be able to introduce strain at low temperatures without failure of the sample. To satisfy these conditions, high pressure is an important requirement, as indicated by Bridgman decades ago [20–22]. The pressure should be higher than the final yield stress of the material after processing to realize the plastic flow [38]. Furthermore, introducing large shear strains in the material is difficult when the dimensions of the

sample change [2]. For example, if a von Mises strain of 6 is applied by rolling a plate with a thickness of 1 cm, its thickness is reduced to 300 nm, which is not practical. Different methods based on rolling, torsion, forging and extrusion can satisfy the required conditions for SPD processing of bulk material [5]. In most of these methods, the dimensions of the samples remain unchanged; however, some methods result in some dimensional changes in the samples. In this section, SPD

High-Pressure Torsion
(HPT) [Bridgman]

<figure><img src="image_5.png" /></figure>

Twist Extrusion (TE)
[Beygelzimer]

<figure><img src="image_6.png" /></figure>

Equal-Channel Angular
Pressing (ECAP) [Segal]

<figure><img src="image_7.png" /></figure>

$$ \bar{\epsilon}_{ECAP} = \frac{N}{\sqrt{3}} \left[ 2 \cot\left(\frac{\varphi+\psi}{2}\right) + \psi \csc\left(\frac{\varphi+\psi}{2}\right) \right] $$

Multidirectional Forging
(MDF) [Valiahmetov]

<figure><img src="image_8.png" /></figure>

Cyclic Extrusion
Compression (CEC)
[Richert]

<figure><img src="image_9.png" /></figure>

Accumulative Roll-Bonding
(ARB) [Saito]

<figure><img src="image_10.png" /><figcaption>Fig. 3. Schematic illustration of main SPD methods and corresponding equivalent strain [50]. For HPT, N, r and h are the number of turns, distance from the center and disc thickness, respectively. For TE, r, R, and β are radial distance from the center, maximum radial distance from the center, and angle between the extrusion axis and the twist line, respectively. For ECAP, N is the number of passes. For MDF, h₀ and h are the initial and final height of the sample, respectively. For CEC and ARB, N is the number of cycles.</figcaption></figure>
methods are comprehensively reviewed and some recent trends in SPD processing are discussed.

## 2.1. Bulk-SPD methods

In the majority of SPD methods, and particularly the popular methods such as HPT, ECAP and ARB, the introduction of large strain is possible due to no change in the sample dimensions [47]. HPT is becoming increasingly popular because it works at very high pressure and is therefore suitable for all types of metallic and non-metallic materials. In addition, the process can apply extremely large shear strains which are not achievable with other processes. ECAP has the benefit of the big sample size which makes it appropriate for commercial application. ARB is of interest because it is a simple and continuous process. Fig. 3 shows schematics and equivalent plastic strains of the main SPD methods including HPT [20], twist extrusion (TE) [48], ECAP [26], multi-directional forging (MDF) [49], cyclic extrusion compression (CEC) [50] and ARB [19].

Various methods were developed in recent years mainly by modification of major SPD processes to either improve straining conditions, modify the shape and dimensions of samples, or make the process continuous [50]. In most of these processes, the dimensions of the samples remain unchanged. Die structure and corresponding equivalent plastic strain of such SPD methods are summarized in Table 1 [51–109]. In some limited methods, the introduction of high plastic strain on the sample is associated with cross-section change. These methods are included in Table 2 [110–120].

## 2.2. Surface-SPD methods

In surface-SPD, gradient microstructures are generated from the treated surface to the core instead of producing a homogeneous plastic deformation within the bulk of the sample. The materials processed by surface-SPD can take advantages of the characteristics of both the refined surface layer and the coarse-grained core of the sample. When surface properties such as biocompatibility, wear resistance and corrosion resistance are of importance, surface-SPD processes have high technical benefits for commercial applications. Over time, several approaches have been designed to generate surface-SPD. Table 3 contains schematic representations of several surface-SPD methods, which are mainly based on peening, grinding, ultrasound and rolling [121–145]. Among these methods, ultrasonic shot peening (USSP or USP) [41] and surface mechanical attrition treatment (SMAT) [134] have received high attention in producing gradient-structured materials. The methods have a high potential for processing large sheets with enhanced properties. At the end of this article, the mechanical and functional properties of surface-SPD-processed materials with gradient microstructure are reviewed.

## 2.3. Powder-SPD methods

The most known method for inducing SPD in powders is high-energy ball milling, which was developed in the 1960s [43]. In this method, powders of materials together with some hard balls (steel, tungsten carbide, zirconia, alumina, etc.) are introduced into a vial. The strain is introduced by rotation or vibration of the vial which leads to the impact of powders between the balls in dry or wet conditions [146]. In addition to straining, other phenomena such as welding and fracturing occur during the process [43]. The grain sizes achieved by this method are usually smaller than those achieved by bulk-SPD and surface-SPD methods, but the method suffers from contamination by milling media (balls and vial) as well as oxidation [43]. Ball milling followed by high-temperature sintering is a process to make bulk UFG materials, although the size of grains can be large due to the high-temperature effect [147]. Ball milling can be conducted using reactant liquids and gasses which is known as reactive ball milling [148]. Ball milling is

applicable to almost all types of material [149], while bulk-SPD methods (except for HPT) have limited applications to various metallic and non-metallic materials. Ball milling has contributed to the synthesis and discovery of various materials since the last century [150] until now [151,152]. The most popular ball milling methods are shown in Fig. 4, which include attritor milling, vibratory milling, planetary milling and high-pressure gas milling [153].

## 2.4. Recent trends in SPD methods

Although the most focused research direction in the SPD field is the examination of characteristics and properties of SPD-processed materials, there are some efforts on the modification or invention of processing methods. Some efforts focused on making the SPD methods continuous [154]. Despite these efforts, classic methods of ARB [19,155] and ECAP conform [28,156] are still among the most powerful and popular continuous SPD methods. Some studies focused on the application of hydrostatic pressure to make SPD processes more practical in terms of load and energy [157]. Some other studies focused on the modification of the shape and size of the sample to a form that can be more appropriate for practical applications such as rods [158], pipes [159] and sheets [160]. In most of these methods, high pressure plays a critical role. The application of SPD through cyclic viscoelastic deformation is another effort in this regard, although it has been employed by limited groups [161]. SPD processing under extreme processing conditions such as cryogenic temperature [162], ultra-high pressure [15], ultra-high strain rate [163] and ultra-high shear strain (known as ultra-SPD) [164] is another important progress in the field in recent years. In the following sections, some of these recent trends in SPD methods are discussed.

### 2.4.1. SPD methods with hydrostatic pressure

Despite high attraction in SPD during the last three decades, most SPD methods are limited to laboratory-scale experiments. This matter, which prevents the utilization of SPD methods for industrial goals, is mainly relevant to the higher load when processing longer samples [50]. Total processing load includes deformation load ($F_D$), friction load ($F_f$) and required load for the redundant work ($F_R$) [157]. It should be noted that the magnitude of the total processing load is mainly affected by the friction load portion especially when processing long samples [157]. In this regard, an increase in the sample length leads to higher surface contact between the die and the sample, which consequently increases the total processing load remarkably. An increase in the processing load increases the chance of buckling and yielding of the punch. Therefore, any approach that reduces the total processing load opens the opportunity for processing relatively long samples as a requirement for industrial applications [5]. Using high-pressure fluid instead of a solid punch is one of the best candidates, which was implemented in single-pass hydrostatic deformation processes as modified versions of conventional methods. Single-pass hydrostatic deformation processes include hydrostatic extrusion (HE) [165], hydrostatic extrusion integrated with circular equal channel angular pressing (HECCAP) [166], hydrostatic backward extrusion (HBE) [167] and hydrostatic radial forward tube extrusion (HRFTE) [168]. The presence of high-pressure fluid in the gap between die-sample contact eliminates the friction force which is very huge in processing longer samples. This reduces the processing load and makes it possible to process samples with a higher aspect ratio (length to diameter) compared to conventional methods. It was reported that a sample with an aspect ratio of 0.27 with a processing load of ~264 kN was processed by conventional backward extrusion while only a fifth of this load was required in HBE to process a sample with an aspect ratio of 8.5 [167].

The application of high-pressure fluid to SPD methods leads to the development of hydrostatic SPD methods as new counterparts of conventional SPD processes [157] including equal-channel angular hydro-extrusion (ECAH) [169], hydrostatic cyclic extrusion compression
<table><caption>**Table 1**
Die structure and equivalent plastic strain of some SPD methods (references do not necessarily refer to the first publication of each method).</caption><thead><tr><th>Schematics of Process</th><th>Equivalent Plastic Strain</th><th>Schematics of Process</th><th>Equivalent Plastic Strain</th></tr></thead><tbody><tr><td>Incremental HPT (IHPT) [51]</td><td>ε̄<sub>IHPT</sub> = <sup>2</sup>&frasl;<sub>√3</sub> πNr</td><td>Single-task incremental HPT (SIHPT) [52]</td><td>ε̄<sub>SIHPT</sub> = ε̄<sub>IHPT</sub></td></tr><tr><td>Continuous HPT (CHPT) [53]</td><td>ε̄<sub>CHPT</sub> = (1 - s) <sup>πR</sup>&frasl;<sub>√3t</sub></td><td>Tube high-pressure shearing (t-HPS) [54]</td><td>Ȳ<sub>t-HPS</sub> = <sup>θ</sup>&frasl;<sub>ln(R/R<sub>i</sub>)</sub><br>ε̄<sub>t-HPS</sub> = <sup>θ</sup>&frasl;<sub>√3ln(R/R<sub>i</sub>)</sub></td></tr><tr><td>High-pressure tube twisting (HPTT) [55]</td><td>Ȳ<sub>HPTT</sub> = <sup>β</sup>&frasl;<sub>ln(b/a)</sub></td><td>Ring HPT (RHPT) [56]</td><td>ε̄<sub>RHPT</sub> = ε̄<sub>HPT</sub></td></tr><tr><td>High-pressure sliding (HPS) [57]</td><td>ε̄<sub>HPS</sub> = <sup>x</sup>&frasl;<sub>√3t</sub></td><td>High-pressure torsion extrusion (HPTE) [58]</td><td>ε̄<sub>HPTE</sub> = 4 ln(<sup>D0</sup>&frasl;<sub>D1</sub>) + 2 ln(<sup>D1</sup>&frasl;<sub>D2</sub>) + <sup>ω · R · D2</sup>&frasl;<sub>√3 · V · D1</sub></td></tr></tbody></table>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

$$ \begin{aligned} \bar{\epsilon}_{\text{HPTE}} = & 4 \ln \frac{D_0}{D_1} \\ & + 2 \ln \frac{D_1}{D_2} \\ & + \frac{\omega \cdot R \cdot D_2}{\sqrt{3} \cdot V \cdot D_1} \end{aligned} $$

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>Accumulative HPT [59]</td><td>Planar HPT [60]</td><td>Y&#773;<sub>P-HPT</sub> = (2&pi;r &phi; / t) / 360&deg;</td></tr><tr><td>Rotary-die ECAP [61]</td><td>Dynamic-channel angular pressing (DCAP) [62]</td><td>E&#773;<sub>DCAP</sub> = N [ (2 cot(&phi;/2 + &psi;/2) / &radic;3) + (&psi; csc(&phi;/2 + &psi;/2) / &radic;3) ]</td></tr><tr><td>Side extrusion ECAP [63]</td><td>Equal channel multi-angular extrusion (ECMAE) [64]</td><td>E&#773;<sub>ECMAE</sub> = 2 &sum;<sub>i=1</sub><sup>n</sup> (&cot;&theta;<sub>i</sub> / &radic;3)</td></tr></tbody></table>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>Multi-pass die ECAP<br>[50]<br><br><span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><sub>MPECAP</sub> ~ 5<span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><sub>ECAP</sub><br>(for &phi; = 90&deg;)</td><td>ECAP with back pressure<br>[65]<br><br><span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><sub>ECAPBP</sub> = <span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><sub>ECAP</sub></td><td></td></tr><tr><td>ECAP with parallel<br>channel [66]<br><br><span style="font-size: 2.5em; vertical-align: middle;">d</span><br><br><span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><br><br><span style="font-size: 2.5em; vertical-align: middle;">&phi;</span><br><br><span style="font-size: 2.5em; vertical-align: middle;">K</span></td><td>Cyclic extrusion<br>compression angular<br>pressing (CECAP) [67]<br><br><span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><sub>CECAP</sub><br>= &epsilon;<sub>CEC</sub> + &epsilon;<sub>ECAP</sub></td><td></td></tr><tr><td>Extrusion-expansion<br>channel angular pressing<br>(EECAP) [68]<br><br><span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><sub>EECAP</sub><br>= &epsilon;<sub>CEE</sub> + &epsilon;<sub>ECAP</sub></td><td>Twist channel angular<br>pressing (TCAP) [69]<br><br><span style="font-size: 2.5em; vertical-align: middle;">&#773;</span><sub>TCAP</sub><br>= &epsilon;<sub>twist extrusion</sub><br>+ &epsilon;<sub>ECAP</sub></td><td></td></tr></tbody></table>

<figure><img src="image_25.png" /></figure>

$$ \bar{\epsilon}_{MPECAP} \sim 5\bar{\epsilon}_{ECAP} $$

<figure><img src="image_26.png" /></figure>

$$ \bar{\epsilon}_{ECAPBP} = \bar{\epsilon}_{ECAP} $$

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

$$ \bar{\epsilon}_{CECAP} = \epsilon_{CEC} + \epsilon_{ECAP} $$

<figure><img src="image_29.png" /></figure>

$$ \bar{\epsilon}_{EECAP} = \epsilon_{CEE} + \epsilon_{ECAP} $$

<figure><img src="image_30.png" /></figure>

$$ \bar{\epsilon}_{TCAP} = \epsilon_{\text{twist extrusion}} + \epsilon_{ECAP} $$

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>Twist channel multi-<br>angular pressing<br>(TCMAP) [70]</td><td>ECAP conform [28]</td></tr><tr><td>Equal channel angular<br>drawing (ECAD) [71]</td><td>C-shape equal channel<br>reciprocating extrusion<br>(CECRE) [72]</td></tr><tr><td>Torsional ECAP [73]</td><td>Expansion ECAP (Exp-<br>ECAP) [74]</td></tr></tbody></table>

$$ \bar{\varepsilon}_{CECRE} = \bar{\varepsilon}_{ECAP} $$

$$ \bar{\varepsilon}_{Exp-ECAP} = \bar{\varepsilon}_{ECAP} + 4N \ln \frac{D_1}{D_0} $$

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>Repetitive forging using inclined punch (RFIP)<br>[75]</td><td>Pure shear extrusion (PSE)<br>[76]</td><td></td></tr><tr><td>α</td><td>A<br>B<br>C<br>D<br>E<br>F<br>G<br>H<br>I<br>J<br>K</td><td>ε̄<sub>PSE</sub> =<br>2N/√3 √(ln R)<sup>2</sup> + (R<sup>2</sup>−1)/(R<sup>2</sup>+1)<sup>2</sup></td></tr><tr><td>γ̃<sub>RFIP</sub><br>= 2N tan α</td><td></td><td></td></tr><tr><td>Incremental ECAP<br>(IECAP) [77]</td><td>Dual equal channel lateral<br>extrusion (DECLE) [78]</td><td>γ̃<sub>DECLE</sub><br>= cot α + cot β</td></tr><tr><td>α↓</td><td>α'<br>β'</td><td></td></tr><tr><td>Plastic flow machining<br>[79]</td><td>Friction-assisted lateral<br>extrusion process (FALEP)<br>[80]</td><td>γ̃<sub>FALEP</sub> = p/c + c/p</td></tr></tbody></table>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>Channel angular pressing with converging billets (CAPCB) [81]</td><td>Channel angular pressing with converging billets (CAPCB) [81]</td></tr><tr><td>Multiple direct extrusion (SSE) [82]</td><td>Multiple direct extrusion (MDE) [83]</td></tr><tr><td>Vortex extrusion [84]</td><td>Accumulated extrusion (AE) [85]</td></tr></tbody></table>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

<figure><img src="image_40.png" /></figure>

$$ \bar{\epsilon}_{MDE} = \frac{2N}{\sqrt{3}} \ln \frac{1}{1-r} \\ = \frac{2N}{\sqrt{3}} \ln 2 $$

<figure><img src="image_41.png" /></figure>

<figure><img src="image_42.png" /></figure>

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>Accumulative press bonding (APB) [86]</td><td>Cyclic expansion extrusion (CEE) [87]</td><td>ε̄<sub>CEE</sub> = 4N ln(d<sub>1</sub>/d<sub>m</sub>)</td></tr><tr><td>Severe forward extrusion (SFE) [88]</td><td>Equal channel forward extrusion (ECFE) [89]</td><td></td></tr><tr><td>Accumulative fold forging (AFF) [90]</td><td>Accumulative back extrusion (ABE) [91]</td><td>ε̄<sub>ABE</sub> = 4N ln((D + 2d)/(5d<sup>2</sup> + 4dD))</td></tr></tbody></table>

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

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<table><caption>**Table 1 (continued)**</caption><tr><td><img src="repetitive_upsetting_and_extrusion_rue.png" alt="Repetitive upsetting and extrusion (RUE) [92]"></td><td><img src="cyclic_closed_die_forging CCDF.png" alt="Cyclic closed die forging (CCDF) [93]"></td><td><img src="ECCDF.png" alt="Elastic strain (ECCDF) [93]" style="vertical-align: middle;"><br>$$ \bar{\varepsilon}_{\text{CCDF}} = \frac{2N}{\sqrt{3}} \ln\left(\frac{H}{W}\right) $$</td></tr><tr><td><img src="repetitive_corrugation_and_straightening_rcs.png" alt="Repetitive corrugation and straightening (RCS) [94]"></td><td><img src="accumulative-roll-bonding_and_folding_arbf.png" alt="Accumulative roll bonding and folding (ARBF) [95]"></td><td><img src="equal_channel_angular_rolling_ecar.png" alt="Equal channel angular rolling (ECAR) [97]"></td></tr><tr><td><img src="continuous-frictional_angular_extrusion_cfae.png" alt="Continuous frictional angular extrusion (CFAE) [96]"></td><td><img src="tension-bonding.png" alt="Tension-bonding (tension-bonding) [96]"></td><td><img src="bend-bonding.png" alt="Bend-bonding (bend-bonding) [96]"></td></tr></table>

<figure><img src="image_49.png" /></figure>

<figure><img src="image_50.png" /></figure>

<figure><img src="image_51.png" /></figure>

<figure><img src="image_52.png" /></figure>

<figure><img src="image_53.png" /></figure>

<figure><img src="image_54.png" /></figure>

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>Conshearing [98]</td><td>Cone-cone method (CCM) [99]</td><td>ε&#773;<sub>CCM</sub> = <sup>2πN.R(x)</sup>/<sqrt>3.t</sup></td></tr><tr><td>Constrained groove pressing (CGP) [100]</td><td>Rubber pad-constrained groove pressing (RP-CGP) [101]</td><td></td></tr><tr><td>Interface sheet constrained groove pressing (ISCGP) [102]</td><td>Friction stir processing (FSP) [103]</td><td></td></tr></tbody></table>

<figure><img src="image_55.png" /></figure>

<figure><img src="image_56.png" /></figure>

<figure><img src="image_57.png" /></figure>

<figure><img src="image_58.png" /></figure>

<figure><img src="image_59.png" /></figure>

<figure><img src="image_60.png" /></figure>

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<table><caption>**Table 1 (continued)**</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>Tubular channel angular pressing process (TCAP)<br>[104]</td><td>ε<sub>TCAP</sub><br>= N / √3 [2 cot(φ<sub>i</sub> + ψ<sub>i</sub>) + ψ<sub>i</sub>cosφ<sub>i</sub>(φ<sub>i</sub> + ψ<sub>i</sub>)] + 4 ln R/R<sub>0</sub></td><td>Parallel tubular channel angular pressing (PTCAP)<br>[105]</td><td>ε<sub>PTCAP</sub><br>= 2 / √3 N [2 cot(φ<sub>i</sub> + ψ<sub>i</sub>) + ψ<sub>i</sub> cos φ<sub>i</sub>(φ<sub>i</sub> + ψ<sub>i</sub>)] + 2 ln R<sub>2</sub>/R<sub>1</sub></td></tr><tr><td>Combined parallel tubular channel angular pressing (Combined PTCAP) [106]</td><td>ε<sub>CPTCAP</sub><br>= ε<sub>PTCAP</sub> + ln R<sub>0</sub><sup>2</sup>/R<sub>0</sub><sup>2</sup> - r<sub>0</sub><sup>2</sup></td><td>ECAP for hollow parts [55]</td><td>ε<sub>ECAPHP</sub> = ε<sub>ECAP</sub></td></tr><tr><td>Rubber pad tube straining (RPTS) [107]</td><td>ε<sub>RPTS</sub><br>= 4 / √3 N [cot φ/2 + ln R<sub>0</sub> + R<sub>0</sub>]</td><td>Cyclic flaring and sinking (CFS) [108]</td><td>ε<sub>CFS</sub><br>= 4 / √3 N [cot(φ<sub>i</sub>/2) + ln R<sub>2</sub>/R<sub>1</sub>]</td></tr><tr><td>Accumulative spin bonding (ASB) [109]</td><td>Y<sub>ASB</sub> = (2(1-r)<sup>2</sup>/r(2-r)) tan θ ln(1/r)</td><td></td><td></td></tr></tbody></table>
<table><caption>**Table 2**
Die structure and equivalent plastic strain of SPD methods with cross-sectional area change.</caption><thead><tr><th>Schematics of process</th><th>Equivalent plastic strain</th><th>Schematics of process</th><th>Equivalent plastic strain</th></tr></thead><tbody><tr><td>ECAP with chocked exit channels (ECAPCEC) [110]<br><img src="ecap_with_chocked_exit.png" alt="ECAP with chocked exit channels (ECAPCEC) [110]" style="width: 200px; height: 200px; margin: auto; display: block;"><br>Chocked angle</td><td>ε̄<sub>ECAPCEC</sub> = ε̄<sub>extrusion</sub> + ε̄<sub>ECAP</sub></td><td>Non-equal channel angular pressing (NECAP) [111]<br><img src="necap.png" alt="Non-equal channel angular pressing (NECAP) [111]" style="width: 200px; height: 200px; margin: auto; display: block;"><br>p<br>c</td><td>Ȳ<sub>NECAP</sub> = p/c + c/p</td></tr><tr><td>Half-channel angular extrusion (HCAE) [112]<br><img src="hcae.png" alt="Half-channel angular extrusion (HCAE) [112]" style="width: 200px; height: 200px; margin: auto; display: block;"><br>Side Up</td><td>ε̄<sub>HCAE</sub> = ε̄<sub>extrusion</sub> + ε̄<sub>ECAP</sub></td><td>Integrated extrusion and ECAP (IEECAP) [113]<br><img src="ieecap.png" alt="Integrated extrusion and ECAP (IEECAP) [113]" style="width: 200px; height: 200px; margin: auto; display: block;"><br>d<sub>0</sub> Φ<sub>1</sub> d<sub>1</sub> Φ<sub>2</sub> K<br>Extrusion ECAP</td><td>ε̄<sub>IEECAP</sub> = ε̄<sub>extrusion</sub> + ε̄<sub>ECAP</sub></td></tr><tr><td>Porthole-equal channel angular pressing (P-ECAP) [114]<br><img src="porthole.png" alt="Porthole-equal channel angular pressing (P-ECAP) [114]" style="width: 200px; height: 200px; margin: auto; display: block;"><br>← →</td><td>ε̄<sub>P-ECAP</sub> = ε̄<sub>ECAP</sub> + ε̄<sub>PE</sub></td><td>Integrating forward extrusion and torsion deformation (IFETD) [115]<br><img src="ifetd.png" alt="Integrating forward extrusion and torsion deformation (IFETD) [115]" style="width: 200px; height: 200px; margin: auto; display: block;"><br>I II III</td><td></td></tr></tbody></table>

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<table><caption>**Table 2 (continued)**</caption><thead><tr><th></th><th></th><th></th></tr></thead><tbody><tr><td>Friction stir back<br>extrusion (FSBE) [116]</td><td>Friction stir tube back<br>extrusion process (FSTBE)<br>[117]</td><td></td></tr><tr><td>Friction stir back<br>extrusion (FSBE) [116]</td><td>Friction stir tube back<br>extrusion process (FSTBE)<br>[117]</td><td></td></tr><tr><td>Friction stir back<br>extrusion (FSBE) [116]</td><td>Friction stir tube back<br>extrusion process (FSTBE)<br>[117]</td><td></td></tr><tr><td>Radial forward extrusion<br>(RFE) [118]</td><td>Radial backward extrusion<br>(RBE) [119]</td><td></td></tr><tr><td>Radial forward extrusion<br>(RFE) [118]</td><td>Radial backward extrusion<br>(RBE) [119]</td><td></td></tr><tr><td>Radial forward extrusion<br>(RFE) [118]</td><td>Radial backward extrusion<br>(RBE) [119]</td><td></td></tr><tr><td>Caliber rolling (CAROL)<br>[120]</td><td></td><td></td></tr><tr><td>Caliber rolling (CAROL)<br>[120]</td><td></td><td></td></tr></tbody></table>

(HCEC) [170], hydrostatic cyclic extrusion expansion (HCEE) [171], hydrostatic twist extrusion (HTE) [172], hydrostatic tube cyclic extrusion compression (HTCEC) [173] and hydrostatic tube cyclic extrusion expansion (HTCEE) [174] as shown schematically in Fig. 5. Five main advantages of utilizing SPD methods with high hydrostatic pressure can be summarized as:

* lower processing load

* higher aspect ratio of the processable sample

* more homogeneous properties

* lower ductility loss

* smaller saturated grain size

Similar to common SPD methods, a decrease in grain size and an increase in dislocation density leads to an increase in yield and ultimate strength in hydrostatic SPD processes [174]. However, in these

processes, ductility loss is usually lower than that in common SPD methods. The strength-ductility paradox is one of the challenges ahead of the industrial application of SPD. As an example, it was reported that pure copper with simultaneously higher ductility and strength is achievable by the hydrostatic TCEE method in comparison with other conventional SPD methods like common TCEE, ECAP and ARB [174]. It was also reported that HCEC applies more homogeneous strain to the sample compared to the common CEC method [170], which results in more uniform grain refinement and mechanical properties after HCEC [175]. Since mechanical properties are a function of grain size, the minimum achievable grain size or minimum saturated grain size is a remarkable parameter in SPD methods, which is highly influenced by hydrostatic pressure [50,175]. As an example, HTE [172] was capable of producing samples with a grain size of 800 nm, which was 50% smaller than that of the TE method [176]. Also, among all SPD methods with high hydrostatic pressure, those that create higher hydrostatic pressure
<table><caption>**Table 3**
Schematic representations of some surface-SPD methods (references do not necessarily refer to the first publication of each method).</caption><thead><tr><th>Process</th><th>Schematics</th></tr></thead><tbody><tr><td>Spherical motion burnishing (SMB) [121]</td><td></td></tr><tr><td>Surface mechanical grinding treatment (SMGT) [122]</td><td></td></tr><tr><td>Conventional deep cold rolling (CDCR) [123]</td><td></td></tr><tr><td>Ultrasonic deep cold rolling (UDCR) [124]</td><td></td></tr><tr><td>Surface mechanical rolling treatment (SMRT) [125]</td><td></td></tr><tr><td>High-pressure surface rolling (HPSR) [126]</td><td></td></tr></tbody></table>

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<table><caption>**Table 3 (continued)**</caption><tr><td>Fast multiple rotation rolling (FMRR) [127]</td><td><img src="image_0_1.png" alt="Fast multiple rotation rolling (FMRR) tool tip model with a sample and a deformation texture layer"></td></tr><tr><td>Vibration-centrifugal hardening (VCH) [128,143]</td><td><img src="image_0_2.png" alt="Vibration-centrifugal hardening tool model with a sample, a platform, and balls"></td></tr><tr><td>Ultrasonic cold forging technology (UCFT) [129]</td><td><img src="image_0_3.png" alt="Ultrasonic cold forging technology (UCFT) tool model with a sample and a gripper"></td></tr><tr><td>Ultrasonic nanocrystal surface modification (UNSM) [130]</td><td><img src="image_0_4.png" alt="Ultrasonic nanocrystal surface modification (UNSM) tool model with a sample, a transducer (vibrator), a ball gripper, and a ball pressure regulator"></td></tr></table>

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<table><caption>**Table 3 (continued)**</caption><tr><td>Rotating pins ultrasonic peening (RPUP) [131]</td><td></td></tr><tr><td>Ultrasonic peening (UP) [132]</td><td></td></tr><tr><td>Ultrasonic impact peening (UIP) [133]</td><td></td></tr><tr><td>Ultrasonic shot peening (USSP) [41]</td><td></td></tr><tr><td>Surface mechanical attrition treatment (SMAT) [134]</td><td></td></tr><tr><td>Surface mechanical impact treatment (SMIT) [135]</td><td></td></tr></table>

<figure><img src="image_61.png" /></figure>

<figure><img src="image_62.png" /></figure>

<figure><img src="image_63.png" /></figure>

<figure><img src="image_64.png" /></figure>

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<table><caption>**Table 3 (continued)**</caption><tr><td>High energy shot peening (HESP) [136]</td><td></td></tr><tr><td>Severe shot peening (SSP) [137]</td><td></td></tr><tr><td>Gradient severe shot peening (GSSP) [138]</td><td></td></tr><tr><td>Abrasive waterjet peening (AWJP) [139]</td><td></td></tr><tr><td>Vibratory peening (VP) [140, 144]</td><td></td></tr><tr><td>Laser shock peening (LSP) [141,145]</td><td></td></tr><tr><td>Friction stir processing (FSP) [142]</td><td></td></tr></table>

<figure><img src="image_65.png" /></figure>

<figure><img src="image_66.png" /></figure>

<figure><img src="image_67.png" /></figure>

<figure><img src="image_68.png" /></figure>

<figure><img src="image_69.png" /></figure>
<figure><img src="image_70.png" /><figcaption>**Fig. 4.** Various types of high-energy ball milling for powder-SPD: (a) attritor milling, (b) vibratory milling, (c,d) planetary milling and (e) high-pressure gas milling [43, 151, 153].</figcaption></figure>

produce samples with better mechanical properties. In this regard, CEC-based methods such as HCEC and HTCEC are more capable of grain refinement compared to CEE-based methods including HCEE and HTCEE [175].

In conclusion, the application of high hydrostatic pressure through a liquid phase provides specific features for scaling up the sample size. Moreover, this strategy improves the microstructure and mechanical properties of the final product.

### 2.4.2. Upscaling disc sample to rod

It is well known that HPT is the most effective method in terms of reachable strain, versatility of treatable materials, grain refinement and processing costs [177,178], but the size of HPT-processed disc samples is small, which prevents the industrial application of this method. Over the past 30 years, numerous other methods of SPD allowing the production of billets and sheets have been developed. A comprehensive overview of these methods can be found in a recent review publication [179]. Typically, multiple processing passes are required to accumulate a significant strain, which is necessary for refining the microstructure of a billet to the sub-micrometer range (one-pass processing is possible in limited methods like ECAP-conform [156]). As a result, integrating these methods into a technological processing chain is challenging, despite the clear advantages demonstrated by SPD-processed materials [36, 180–182]. There have been some attempts to overcome this problem and the introduction of high-pressure torsion extrusion (HPTE) is one of them.

The HPTE method reproduces the stress-strain conditions similar to HPT conditions (i.e. obtaining very high torsional strain in a single pass) but in a rod-shaped sample [183]. The technical detailed description of the method was reported elsewhere [58]. In short, a rod-shaped

specimen is deformed by the punch (moving with the velocity $v$) as well as by the containers (one of them rotates with the velocity $\omega$) (Fig. 6a) in such a way that the entire length of a specimen is torsionally deformed, as a specimen gradually passes through the shear zone. During the deformation, the plastic flow of the billet material follows a spiral pattern, as evidenced using aluminum marker wires embedded in a copper billet (Fig. 6b) [184,185]. To constrain torsional deformation within a thin layer of a billet, and to prevent slippage of the billet in the die, the die design was modified to include special holding elements (Fig. 6a). Similar to HPT, strain distribution at HPTE is not uniform along the billet radius (as well as along the billet height), as follows from FEM calculations of the strain distribution in the billet [58,184,186]. Therefore, HPTE at low strain levels can be used for the processing of gradient structure in the billet, favorable concerning the good balance of strength and ductility [187,188]. On the other hand, at a high enough strain, the microstructure of the billet can be homogenous due to the saturation of grain refinement phenomenon observed at SPD processing [38,189].

By now HPTE was successfully used for processing commercially pure copper [58,190] and aluminum [191], 6101 Al-based alloy, niobium [192], magnesium as well as ZK30 and ZK60 Mg-based alloys. In each case, the mean grain size of the treated metals and alloys has been effectively refined to the submicrometer range. This is illustrated, for example, in Fig. 7a which highlights the microstructure refinement of copper. Both the microhardness and tensile strength of HPTE-processed metals and alloys are significantly higher than those in the annealed state. Uniform elongation is reduced to a few percent, but total elongation remains rather large, similar to the annealed sample (Fig. 7b). This is in agreement with the “strength-ductility paradox” proclaimed for some SPD-processed materials [193]. Therefore, HPTE
<figure><img src="image_71.png" /><figcaption>Fig. 5. Schematics of different SPD methods with high hydrostatic pressure [157].</figcaption></figure>

<figure><img src="image_72.png" /><figcaption>Fig. 6. (a) Schematics of the HPTE process with three billets inside the die [184]. (b) X-ray tomography reconstruction of aluminum wires embedded into the copper billet after HPTE processing with translational velocity $v = 6$ mm/min and rotational velocity $ω = 1$ rpm (aluminum wires are shown in three different colors for better visualization) [185].</figcaption></figure>

appears to be feasible for fabricating metallic rods with small grain size and enhanced mechanical properties in one pass, while other rod-processing SPD methods like ECAP require several passes [193]. HPTE can be also used for processing architecture (gradient and hybrid) samples [194–196]. Application of HPTE to a rod sample with inserted hardening wires leads to a refinement of the matrix microstructure and transforms the shape of wires from straight to helical (Fig. 6b). Such architectures resemble the morphology of natural tissues having high fracture toughness (bones, shells, etc.) [197,198], and can be used for parts operating in special conditions such as shock loading.

In conclusion, there are ways to upscale the sample size and modify the shape by modification of SPD methods, and the HPTE method is one of the successful examples that can be used for processing bulk specimens like rods [158]. The main highlight of this method includes the possibility of accumulating large shear strain in one pass (orders of magnitude larger than in ECAP [27], TE [199] and CEC [87]) under high pressure.

### 2.4.3. Pipe sample processing

Pipes and tubes are of significance in industrial applications, but as shown in Table 1, quite limited SPD methods are available for the processing of pipes. There have been some attempts in recent years for SPD processing of pipes and tube high-pressure shearing (t-HPS) is one
<figure><img src="image_73.png" /><figcaption>**Fig. 7.** (a) Inverse pole figure map of the copper microstructure in the longitudinal cross-section of the billet after HPTE at 373 K with a translational velocity of *v* = 1 mm/min and a rotational velocity of *ω* = 1 rpm [190]. (b) Tensile curves of copper samples in the initial coarse-grained state (initial) and after HPTE at 373 K with a rotational velocity of *ω* = 1 rpm and translational velocities of *v* = 1 mm/min (*v*1ω1) and *v* = 10 mm/min (*v*10ω1) [185].</figcaption></figure>

successful friction-driven process for such an application [54,159]. The t-HPS is different from other friction-driven processes such as HPT [23], where the strain planarity of simple shear is violated [159,200], and high-pressure sliding (HPS), where the achievable strain level is limited by the plunger stroke [57]. Therefore, t-HPS provides a monotonic deformation process characterized by constant shear direction and strain planarity to high strain levels over 2000 [201]. The development of this SPD technique may be classified into three sectors with different names as rotation shear [202], high-pressure tube twisting [203,204] and t-HPS [54], where they include the same core concept of friction-driven azimuthal shear in the tube and independently developed by three different scientific groups. Continuous processing of t-HPS was also investigated [205]. The principle of t-HPS is depicted schematically in Fig. 8 [54,159,200,206,207]: (i) a tube sample is radially constrained between a central mandrel and an outer cylinder; (ii) a sufficiently high hydrostatic pressure is introduced in the tube wall by the four schemes illustrated in Fig. 8, so that frictional forces at the interfaces between the sample-mandrel and the sample-cylinder are sufficiently high to prevent any localized slip between the interfaces; and (iii) a simple shear strain is then produced in the tube wall by fixing the mandrel and rotating the outer cylinder (or vice versa) [54,202,203]. Although t-HPS is different from HPT by the planarity of shear

<figure><img src="image_74.png" /><figcaption>**Fig. 8.** Illustration of t-HPS schemes: (a) compression directly applied on two ends of tube by pressure ring in scheme E1 [54,206], (b) compression directly applied on two ends of tube by stepped mandrel together with stepped cylinder in scheme E2 [200,207], (c) a small tapper angle is introduced to tube and die parts so that compression can be directly applied to the tube wall in scheme W [207,208] and (d) compression directly applied to both ends and wall of tube by stepped mandrel together with stepped cylinder in scheme EW [207,208].</figcaption></figure>

deformation [159,200], it has a strain gradient along the radius of the sample, but it is the reverse of HPT [54,200,208,209].

The microstructure evolution upon t-HPS is distinguished between geometrical parameters, such as grain size and aspect ratio versus crystallographic parameters, such as grain boundary misorientation, high-angle grain boundary fractions and texture. The evolution of geometrical parameters is observed to be consistent with those observed in general SPD processes [159,210]. Fig. 9a presents an example of pure aluminum processed by different SPD methods compared to t-HPS [211–220]. Grain size and aspect ratio demonstrate a clear trend of stagnation at a t-HPS equivalent strain of ~30 [220]. This is consistent with the saturation features of many metals during HPT at equivalent strains between 10 and 30 [38]. This general trend was also demonstrated by Shan and Tóth using different materials like commercially pure aluminum [202,204,221], AA5056 alloy, interstitial-free (IF) steel, copper and magnesium [204,210]. Accompanying this stagnation in the geometrical parameters, the crystallographic parameters evolve continuously in contrast. Fig. 9b shows that the average grain boundary misorientation and high-angle grain boundary fractions increase first at low strain levels, passing through a peak at around the equivalent strain of ~9, and decrease thereafter monotonically. The intensity of the texture sharply decreases at low strain levels, passing through a minimum at an equivalent strain of ~20, and increases monotonically thereafter, where a new texture component gradually dominates [220].

The t-HPS method has some advantages. For example, tubes with multilayered structures composed of unitary pieces of metals can be fabricated in one step of t-HPS [200]. A detailed comparison between ARB and t-HPS in multilayered laminate synthesis is given in [200]. Moreover, t-HPS provides a new channel to bypass the phase separation in solidification and to synthesize homogeneous alloys directly from monolithic bulk elements, which provides more freedom in the design and synthesis of alloys with enhanced properties. For example, exceptional superplasticity as shown in Fig. 9c is achieved in a Pb-40Sn (wt%) alloy with off-eutectic composition, synthesized from lead and tin bulks in one step of the t-HPS step [201]. The reason for large superplasticity by t-HPS is bypassing the inherent pre-eutectic Pb-rich phase separation during solidification [222]. A similar effect is also observed in other systems [223,224].
<figure><img src="image_75.png" /><figcaption>**Fig. 9.** (a) Evolution of average grain sizes and grain aspect ratios upon increase of t-HPS equivalent strain (grain size obtained from other deformation processing of aluminium with 99.999% purity are also included for comparison) [220]. (b) Evolution of average grain boundary misorientation, high-angle grain boundary fractions and intensity of {110}<110> texture upon increase of t-HPS equivalent strain [220]. (c) Engineering stress-strain curves for the Pb-Sn alloys tested at the initial strain rate of 1.0 × 10⁻³ s⁻¹ at room temperature (inset: appearance of the specimens after pulling to failure) [201].</figcaption></figure>

In summary, although there are limited SPD methods for processing pipes, the newly developed ones such as t-HPS exhibit high potential for various applications such as the generation of UFG structure, fabrication of multilayered laminates from monolithic materials, and synthesizing bulk micro-duplex alloys. The high planarity character of SPD methods for processing tubes makes it possible to produce a sole component shear texture, which challenges the long-standing position of a torsion-based method as a typical simple shear method and this may further bring about new challenges to the existing theory of texture evolution for simple shear [225].

### 2.4.4. Upscaled sheet processing

Despite significant progress in the development of SPD techniques [1–3,32], limited techniques can apply SPD in sheet samples in a continuous process. Among popular methods such as ECAP [193,226], ARB [19,227,228], MDF [229,230] and HPT [20,23], only ARB can process large sheets continuously [154]. There have been various attempts for continuous SPD processing or processing sheets [156, 231–235], but SPD processing of large sheets is still challenging. One of the recent attempts to process large sheets is the application of HPS [57]. The HPS process is similar to HPT because both processes are operated under high pressure, and they are applicable to hard-to-deform and/or less ductile metallic materials due to highly constrained conditions. The
<figure><img src="image_76.png" /><figcaption>**Fig. 10.** (a) Schematic illustration, (b) cross-sectional view and (c) incremental feeding pattern for consecutive 1st, 2nd and 3rd passes of incremental-feeding HPS [160].</figcaption></figure>

major difference between the two processes is that, while the HPT process is used with disc or ring forms of the samples [30,56,177,236, 237], the HPS process utilizes the samples in rectangular sheet forms and sometimes in rod or pipe forms [238,239]. The HPS process has more advantages in upscaling the sample size [179].

A typical example of the upscaling of sheet samples by HPS is the development of incremental feeding HPS (IF-HPS) process as illustrated in Fig. 10a. [160,240]. The incremental feeding, which has been combined with HPT in some studies as well [51,58,60,241], has a high potential for upscaling the sample size without any need to increase the machine capacity. Fig. 10b shows a detailed cross-sectional view including a sheet sample between a plunger and anvils, and Fig. 10c illustrates a strained area that is extended to a larger scale by repeating the operation of sliding and successive feeding. The feeding pattern can be made in one- or two-dimensional directions. Until now, IF-HPS has been successful in enlarging the SPD-processed area to 100 × 100 mm² in a Ni-based superalloy (Inconel 718) [160,240]. It should be noted that it is possible to increase the sizes of rods and pipes by adopting a multi-pass HPS [238,239]. In developing the IF-HPS process, the following three points are important as recently described in detail [160, 242]: (i) the use of flat-type anvils to make sample feeding easier and sheet surface smoother, (ii) the control of the sliding mode determined by the sliding distance and the numbers of the reciprocation of the sliding direction and (iii) the control of the feeding pattern determined by the feeding distance and the feeding direction. The performance of the IF-HPS process was demonstrated with the application to a Ni-based superalloy (Inconel 718) [240], a Ti-6Al-7 Nb (wt%) alloy [243] and commercially available aluminum alloys (A1050, A3105, A5052 and A5182) [242].

As an example of the properties of sheets processed by IF-HPS, Fig. 11 shows the stress-strain curves of the Inconel 718 after HPS processing for a single pass under 4 GPa using (a) flat-type anvils and (b) groove-type anvils. The total elongations reached 220% and 710% for the sliding distances of 10 and 15 mm using the flat-type anvils [240], while they exhibited 770 and 670% using the groove-type anvils for the corresponding sliding distances [244]. The difference is significant when the sliding distance is 10 mm but no difference was observed when the sliding distance is longer than 15 mm [160]. The superplastic

<figure><img src="image_77.png" /><figcaption>**Fig. 11.** Stress-strain curves of tensile specimens extracted from samples processed using (a) flat-type and (b) groove-type anvils of incremental-feeding HPS for sliding distances of 5, 10 and 15 mm (tensile tests were performed at 1073 K with an initial strain rate of 2 × 10⁻² s⁻¹ [160].</figcaption></figure>
behavior of these sheets confirms that SPD could be successfully imparted in them by using IF-HPS.

In conclusion, sheet processing is a key issue in the commercialization of the SPD process. While ARB is still the most practical process for the continuous processing of large sheets, methods like IF-HPS can be used to process large sheets of hard materials under high pressure.

### 2.4.5. Hard cyclic viscoplastic deformation

Despite the potential of SPD in reducing the grain size [3,22,245, 246] and increasing tensile strength and hardness [247–250], the thermal stability of such materials is relatively low depending on their microstructural evolutions [5,251,252]. To have a better balance between the microstructure, mechanical properties and thermal stability, the evolution of these features should be examined step by step during or after SPD processing [253–255]. To study the microstructure and properties evolution of metallic materials before and after SPD, a processing method, called hard cyclic viscoplastic deformation (HCVD), was developed based on viscoplasticity theory [256–260], cyclic ratcheting [261] and Bauschinger effect [262, 263].

The main parameters of HCVD are a strain-controlled deformation process with an amplitude of tension-compression in the range from ±0.2% to ±3.0% with several cycles from 20 to 30 per strain level and a frequency of 0.5–2.5 Hz of cycles [161, 263–269]. The tension-compression cycle is applied at constant strain amplitude, by a strain-controlled system at room temperature (Fig. 12). The load or stress amplitude, which depends on the mechanical properties of the metallic material, is introduced in the viscoplastic region. During HCVD,

the viscoplastic region parameters affect the microstructure and mechanical, physical and chemical properties of the materials. HCVD can be used to study the stability and viability of metallic materials with different microstructures and grain sizes and to predict their suitability over time in harsh environments such as aerospace and defense applications where the strain amplitude is greater than ±0.2% of the strain [268]. It was shown that the microstructure and properties of the material obtained before or after SPD processes alter in HCVD testing. For example, the initial strength properties of a coarse-grained material increase, but the strength properties of a UFG material may decrease. Also, other features of materials such as electrical conductivity, dislocation density, etc., change during HCVD processing [269, 270]. Changes in physical properties (Figs. 13a and 13b) before material failure were reported during HCVD [267].

In summary, the HCVD method can provide information about the behavior of materials, including SPD-processed materials in various extreme operating conditions such as aerospace and defense applications, when the margin coefficient is very small and the deformation can be increased to 0.2% and higher. Such information provided by HCVD can expand the application of SPD in the industry by clarifying the relationships between microstructure, mechanics, physics and chemistry with processing parameters.

### 2.4.6. Cryogenic-SPD

An effective way to obtain high-strength UFG materials is by conducting SPD at cryogenic temperature in liquid nitrogen [5, 271–273]. UFG metals and alloys obtained by cryogenic-SPD exhibit exceptional

<figure><img src="image_78.png" /></figure>

<figure><img src="image_79.png" /></figure>

<figure><img src="image_80.png" /></figure>

<figure><img src="image_81.png" /></figure>

<figure><img src="image_82.png" /><figcaption>**Fig. 12.** (a-c) HCVD stress amplitude versus strain amplitude curves of niobium for viscoplastic tension-compression straining at (a) an amplitude of ε = ±0.1% and corresponding deformation amplitude of v = ±0.01 mm in the base length of 10 mm in elastic regime, (b) ε = ±0.5% and v = ±0.05 mm and (c) ε = ±2.0% and v = ±0.2 mm. (d) HCVD stress amplitude versus time curves at ε = ±2%. (e) Effect of elastic-plasticity on the deflection of the curves during the compression (C) and tension (T) cycles [161].</figcaption></figure>
<figure><img src="image_83.png" /><figcaption>**Fig. 13.** (a) Variation of Vickers hardness versus aging temperature and (b) electrical conductivity versus aging temperature, (c) tensile strength versus elongation and (d) experimental values of stress amplitudes obtained during HCVD testing for 20 cycles at a frequency of 0.5 Hz and a strain amplitude of ±1% for Cu-0.66Cr-0.03Si-0.02Fe-0.016S (wt%) alloy processed under different conditions (initial coarse-grained sample, SPD by indirect extrusion angular pressing IEAP and SPD followed by heat treatment at 723 K IEAP+HT) [267].</figcaption></figure>

mechanical properties in a wide temperature range, especially at cryogenic temperatures, due to the activation of additional deformation mechanisms, such as twinning and phase transitions [274-276]. The coexistence of several deformation paths affects the evolution of the microstructure and deformation mechanisms during cryogenic-SPD. This section reviews the influence of various methods of cryogenic-SPD (ECAP [193], quasi-hydroextrusion [277], HPT [22]) on the mechanical properties of some metals (titanium, zirconium, cobalt), titanium grade 2 alloy and high-entropy alloys (HEAs). The influence of cryo-rolling on the mechanical properties of titanium is also briefly mentioned [278-282]. A more complete review of the results on this topic was given elsewhere [162].

Cryogenic-SPD has received attention, particularly in recent years [283-289]. Such studies were partly motivated by the effectiveness of cryo-rolling in controlling microstructure [278-282]. Cryo-rolling studies on commercially pure titanium grade 2 showed that the material after cryo-rolling demonstrates a higher rate of hardening (due to the rapid growth of twins and a slower dynamic recovery process) than after rolling at room temperature. Titanium exhibits an increase in strength and a finer nanostructure with an average grain size of 30-80 nm (compared to 200 nm after rolling at room temperature). Commercially pure titanium grade 2 was also processed by cryo-ECAP, which led to a decrease in the average grain size and an increase in strength (by about 10%) compared to ECAP at room temperature [283]. The effect of HPT on the structure and mechanical properties of high-purity titanium was also investigated in [284]. The hardness and

strength of nanostructured titanium treated with cryo-HPT is 10–14% higher compared to room-temperature processing due to the smaller average grain size (100 nm instead of 160 nm). A combination of different SPD methods (ECAP and quasi-hydroextrusion) at cryogenic temperature was also applied to commercially pure titanium in a study [285]. A significant increase in the yield strength by a factor of two (from 0.42 GPa at 300 K to 0.86 GPa at 77 K) was achieved using simple shear via ECAP and axisymmetric deformation via quasi-hydroextrusion at 77 K. These results showed that additional modes of plastic deformation with a different set of working sliding systems significantly affect the microstructure and mechanical properties of titanium.

It was reported that extra strengthening by cryogenic-SPD is not limited to titanium and similar results were reported for other metals such as zirconium and cobalt [286, 287]. After HPT at 77 K and 300 K, the average grain sizes are 80 nm and 200 nm for zirconium and 70 nm and 100 nm for cobalt, respectively. The values of microhardness, yield strength and strength under deformation by uniaxial compression after cryo-HPT (at temperatures of 77 K and 4.2 K) are approximately 10% higher than those after HPT at room temperature. These effects are due to the slowdown in the processes of dynamic recovery during cryo-HPT and an increase in the contribution of the twinning process to grain refinement. The effect of cryo-HPT on the structure and strength properties of HEAs was studied as well [288-291]. After cryo-HPT, both hardening and softening processes are observed in HEAs. In some HEAs (CoCrFeNi Mn, CoCrFeNi MnV<sub>0.2</sub>, Co<sub>20</sub>Cr<sub>26</sub>Fe<sub>20</sub>Mn<sub>20</sub>Ni<sub>14</sub>), cryo-HPT results in lower yield strength and microhardness than those after HPT at
<figure><img src="image_84.png" /><figcaption>**Fig. 14.** Inverse pole figure images and (100) pole figures for Co₂₀Cr₂₆, Fe₂₀Mn₂₀Ni₁₄ alloy after cryogenic-SPD via HPT for (a,d,g) 1 rotation, (b,e,h) 3 rotations and (c,f,k) 5 rotations, (d–f) show the grains with sizes smaller than 1 µm (maximum texture intensity is indicated for each pole figure in mrd). (j-m) Inverse pole figure images of Co₂₀Cr₂₆Fe₂₀Mn₂₀Ni₁₄ alloy after cryogenic-SPD via HPT for (j,l) 1 rotation and (k,m) 5 rotations, where (l,m) show the grains with sizes smaller than 1 µm [288].</figcaption></figure>

room temperature. The reasons for such softening may be related to phase transformations (FCC-HCP) and a decrease in the dislocation density [292–295]. Such transformations during and after cryo-HPT are shown in Figs. 14 and 15 [288]. It should be noted that in nano-structured CoCrFeMnNi [274] obtained at certain values of pressure and number of revolutions, subsequent holding at room temperature leads to reverse structural transformations. Despite reported results on HEAs, cryogenic-SPD can generally be considered an effective method for producing high-strength materials that can be used as materials for structural and functional purposes.

<figure><img src="image_85.png" /><figcaption>**Fig. 15.** (a-f) SEM backscatter electron images of Co₂₀Cr₂₆Fe₂₀Mn₂₀Ni₁₄ alloy after cryogenic-SPD via HPT for (a,d) 1 rotation, (b,e) 3 rotations and (c,f) 5 rotations where (d-f) are the magnified images of the corresponding areas highlighted in (a-c). (g-i) TEM images of the Co₂₀Cr₂₆Fe₂₀Mn₂₀Ni₁₄ alloy after 5 rotations of HPT at 300 K, where (g) is a bright-field image, (h) is a dark-field image and (i) is the corresponding selected area electron diffraction pattern. (j) Schematics illustrating the microstructural evolution of Co₂₀Cr₂₆Fe₂₀Mn₂₀Ni₁₄ alloy which accommodates stored strain energy during and after cryo-HPT [288].</figcaption></figure>

<figure><img src="image_86.png" /><figcaption>**Fig. 16.** Schematic illustration of ultra-SPD concept, in which severe shear strains are applied to a material so that the thickness of sheared phases is reduced to the subnanometer level [298].</figcaption></figure>
### 2.4.7. Ultra-SPD

The ultra-SPD concept was defined in 2017 in an attempt to discover new materials by mechanical alloying via SPD [296]. As schematically illustrated in Fig. 16, ultra-SPD is defined as SPD processes in which the applied shear strain significantly increases so that the thicknesses of phases are reduced to the subnanometer level [296]. The shear strain required to achieve these changes depends on the initial phase dimensions and co-deformation behavior of various phases, but it was suggested that the applied shear strain should be over 1000 in ultra-SPD [178]. Besides the original target of ultra-SPD was the synthesis of new materials, it has also raised questions concerning the deformation behavior of materials at the steady state [38, 45]. It was shown that some deviations from the steady-state hardness occur in a few pure metals after ultra-SPD [178]. These observations suggested that there can be new deformation stages beyond stage V of deformation at extremely large shear strains [297].

Among various bulk-SPD methods [1–3, 37, 299], HPT, which applies to disc [3, 177] or ring [56, 300] samples, is currently the only method used to apply ultra-SPD. There are a few reasons that HPT appears as the best candidate for this application. (i) Shear strain can be continuously enhanced in HPT by increasing the number of rotations of anvils with almost no limitations, a fact that was first recognized by Bridgman [20]. (ii) High pressure in HPT makes it applicable to metals with high hardness such as hafnium [301], molybdenum [302] and tungsten [303] and their powder mixtures for mechanical alloying. (iii) The method is one of the most effective methods to introduce lattice defects [304–306] for enhancing dynamic interdiffusion [307, 308] and controlling solid-state phase transformations [9, 10].

The concept of ultra-SPD has been successfully used to synthesize various materials such as binary alloys [309–312], ternary alloys [313–315], HEAs [316, 317], intermetallics [318–321], hydrides [322], oxides [323–325] and oxynitrides [326, 327]. The materials synthesized by this method exhibit interesting properties such as ultrahigh strength, stability at high temperatures, enhanced superplasticity at room temperature, storage of hydrogen at low temperature, compatibility with biological environments, superconductivity and photocatalytic activity for hydrogen and oxygen production and CO₂ conversion, as reviewed in a few papers [164, 298]. Some of the features of materials processed by ultra-SPD are briefly reviewed below.

* Materials processed by SPD usually exhibit poor thermal stability because of large stored energy [328–331], but ultra-SPD can contribute to thermal stability by the generation of supersaturated solid solution and second-phase precipitation. Ultra-SPD-developed supersaturated alloys of aluminum with calcium [311], iron [310], zirconium [332] and lanthanum and cerium [315] exhibit not only high thermal stability but also strengthening through precipitation hardening.

* A combination of high strain and high pressure and their interaction with lattice defects can lead to the formation of hidden phases [8]. In this regard, ultra-SPD could stabilize large fractions of phases that are not formed in equilibrium phase diagrams. The formation of body-centered cubic (BCC) and face-centered cubic (FCC) phases in magnesium alloyed with titanium [333], zirconium [334] and hafnium [335] are the most highlighted examples because these elements are immiscible in magnesium even in the liquid form.

* Nanograined intermetallics are usually produced by two-step processes such as the production of nanopowders followed by high-temperature sintering [43, 336–338]. On the contrary, ultra-SPD synthesizes bulk nanograined intermetallics in a single step. Mg₂X (X: various elements) [339], AlNi [318], Al₃Ni [319, 320] TiAl [321], FeNi [340] and Ni₂AlTi [341] are some intermetallics synthesized by ultra-SPD from elemental powders.

* Materials for orthopedy should have a combination of low elastic modulus, high hardness and good biocompatibility [342]. SPD-processed biomaterials, which are usually based on titanium,

show high hardness and good biocompatibility but suffer from high elastic modulus [36, 343–345]. In a few attempts to produce biomaterials with high hardness and low elastic modulus, ultra-SPD was employed to synthesize various alloys in the Ti-Zr-Hf-Nb-Ta alloy system [312, 317].

* Superplasticity can be usually achieved at homologous temperatures over 0.5, where grain boundary sliding is dominant [346]. Due to the activation of grain boundary sliding at high homologous temperatures, the achievement of room-temperature superplasticity is not possible in conventional magnesium and aluminum alloys. To reduce the superplastic deformation temperature, two strategies can be used [347]: (i) grain refinement which was employed to attain low-temperature superplasticity by conventional SPD processing [33, 348, 349]; and (ii) enhancement of grain boundary diffusion by the engineering of grain boundaries. The second strategy was realized by ultra-SPD in Mg-Li and Al-Zn alloys to attain room-temperature superplasticity for the first time in magnesium and aluminum alloys [350, 351].

* Nb-Ti alloys are the most used superconductors which are industrially produced by several repetitions of wire drawing and long-time annealing [352–355]. Ultra-SPD provides a single-step process to produce Nb-Ti superconductors with properties similar to industrial products [356].

* The production of magnesium alloys for storing hydrogen at room temperature has been a long-time objective of many research works, but there has been little success in this regard [357, 358]. Ultra-SPD was used for the synthesis of some Mg-based hydrogen storage materials like Mg₂X (X: various elements) [339], Mg-Ti [322, 333],

<table><caption>**Table 4**

Summary of the application of ultra-SPD to various materials [164].</caption><thead><tr><th>Alloy</th><th>Shear Strain</th><th>Characteristics</th><th>Ref.</th></tr></thead><tbody><tr><td>Mg-Li</td><td>7800</td><td>Superplasticity at room temperature</td><td>[351]</td></tr><tr><td>Mg₂X (X: 21 elements)</td><td>5500</td><td>Storing hydrogen</td><td>[339]</td></tr><tr><td>Mg-Ti</td><td>5500</td><td>Storing hydrogen</td><td>[333]</td></tr><tr><td>Mg-Zr</td><td>55000</td><td>Storing hydrogen in new phases</td><td>[334]</td></tr><tr><td>Mg-Hf</td><td>3900</td><td>Biocompatible new phases</td><td>[335]</td></tr><tr><td>Mg-V-Cr</td><td>50000</td><td>Storing hydrogen</td><td>[313]</td></tr><tr><td>Mg₄NiPd</td><td>59000</td><td>Storing hydrogen at room temperature</td><td>[359]</td></tr><tr><td>MgTiCrFe</td><td>12000</td><td>Storing hydrogen</td><td>[314]</td></tr><tr><td>MgTiH₄</td><td>17000</td><td>Storing hydrogen</td><td>[322]</td></tr><tr><td>Al-Ca</td><td>39000</td><td>Thermal stability</td><td>[311]</td></tr><tr><td>Al-Fe</td><td>39000</td><td>Thermal stability</td><td>[310]</td></tr><tr><td>AlNi</td><td>4700</td><td>Enhanced microhardness</td><td>[318]</td></tr><tr><td>Al₃Ni</td><td>4700</td><td>Enhanced microhardness</td><td>[319, 320]</td></tr><tr><td>Al-Cu</td><td>3900</td><td>Quick interdiffusion</td><td>[308]</td></tr><tr><td>Al-Zn</td><td>7800</td><td>Superplasticity at room temperature</td><td>[351]</td></tr><tr><td>Al-Zr</td><td>39000</td><td>Thermal stability and age hardening</td><td>[332]</td></tr><tr><td>Al-La-Ce</td><td>39000</td><td>Thermal stability and age hardening</td><td>[315]</td></tr><tr><td>TiAl</td><td>2000</td><td>Enhanced strength/plasticity</td><td>[321]</td></tr><tr><td>TiV</td><td>5500</td><td>Storing hydrogen with no activation treatment</td><td>[309]</td></tr><tr><td>Ti-Nb</td><td>5900</td><td>Biocompatibility with good strength/elasticity</td><td>[312]</td></tr><tr><td>TiZrHfNbTa</td><td>2000</td><td>Biocompatibility with good strength/elasticity</td><td>[317]</td></tr><tr><td>TiZHfNbTaO₁₁</td><td>7800</td><td>Photocatalytic H₂ evolution and CO₂ conversion</td><td>[323, 324]</td></tr><tr><td>TiZrHfNbTaO₆N₃</td><td>3900</td><td>Photocatalytic H₂ evolution and CO₂ conversion</td><td>[326, 327]</td></tr><tr><td>TiZrNbTaWO₁₂</td><td>3900</td><td>Photocatalytic O₂ evolution</td><td>[325]</td></tr><tr><td>FeNi</td><td>3900</td><td>Quick phase transition</td><td>[340]</td></tr><tr><td>Ni₂AlTi</td><td>4700</td><td>Enhanced microhardness</td><td>[341]</td></tr><tr><td>Nb-Ti</td><td>3900</td><td>Superconductivity</td><td>[356]</td></tr></tbody></table>
Mg-Zr [334], Mg-V-Cr [313] and Mg-V-Ti-Cr-Fe [314], but the most interesting results were reported for Mg-Ni-Pd which could reversibly store hydrogen at room temperature [359].

* Photocatalysis is a clean technology to produce hydrogen and oxygen from water or convert CO₂ to CO under sunlight [360, 361]. Ultra-SPD contributed to this field by the introduction of the first high-entropy photocatalysts such as TiZrHfNbTaO₁₁ [323, 324], TiZrNbTaWO₁₂ [325] and TiZrHfNbTaO₆N₃ [326, 327].

Table 4 summarizes major studies on the application of ultra-SPD, including the compositions of processed materials, applied shear strain and reported characteristics. All these results suggest the high potential of ultra-SPD in exploring new functional materials.

### 3. Microstructural features after SPD

SPD induces large plastic deformation in a piece of sample, and thus, significant microstructural changes are introduced. Since such plastic deformations are introduced at temperatures below the traditional recrystallization temperature and under high pressure, the introduced microstructural features are usually unique and can hardly be introduced by other methods [2, 3]. Continuous refinement of grains and the introduction of various defects during SPD increases the internal energy of the material, leading to the reduction of the temperature for continuous dynamic recrystallization to room temperature [362]. This issue finally leads to the saturation of microstructural evolution, the formation of UFG grains with nanometer or submicrometer sizes, the appearance of high-angle grain boundaries and the weakening or randomization of texture [3, 363]. The saturation of grain refinement to the steady state and parameters influencing the steady-state grain size have been a matter of study for a long time [189, 297, 364, 365]. Impurity atoms, alloying, the addition of a second phase, and reduction of homologous temperature (i.e. reducing the processing temperature or increasing the melting point) are well-known factors that reduce the steady-state grain size [189, 297, 364, 365]. It is well established that in materials with covalent or ionic bondings such as ceramics, the steady state grain size can be lower than in metallic materials due to difficult dislocation slip and grain boundary motion in these materials [365]. There have been some suggestions that the materials with low stacking fault energy can have smaller grain sizes [364], while some studies showed that the steady-state grain size is reasonably independent of stacking fault energy [365]. Moreover, steady-state grain size is independent of pressure if no phase transformation occurs [366]. Besides grain refinement, SPD introduces large fractions of lattice defects such as vacancies [306] and dislocations [305]. Grain boundaries formed by SPD have special features usually not in equilibrium conditions [307] and can sometimes be decorated by segregation or dynamic precipitation [304]. In the following sections, after a discussion of features of high-angle grain boundaries, recent advances in the investigation of the microstructure of SPD-processed materials are reviewed.

#### 3.1. Grain boundaries and related phenomena

SPD drives bulk materials far away from equilibrium and opens up new opportunities to explore hitherto uncharted regions of structure-property correlations with respect to grain size, strain and defect density under extreme conditions [5]. The SPD processing involves the interaction of defects of different dimensionality during deformation and their interrelation with fluxes of solute atoms or with segregation fields under complex elastic strain fields, resulting in chemo-mechanical coupling effects especially accompanying nucleation and precipitation of secondary phases [367]. All of these aspects that result from the complex interactions of defects and solutes strongly affect phase equilibria and phase- and microstructure evolution and stability. Naturally, material properties, such as diffusion rates or the plastic response of SPD-processed materials are controlled by the SPD-induced

microstructure, giving rise to new opportunities for “defect engineering” [368]. For such defect engineering, fundamental aspects of the processing-microstructure-property correlations under these boundary conditions have to be addressed. While most SPD-related work has focused on crystalline materials and microstructures [299, 369], amorphization transformations [370, 371] and deformation-induced structure modifications of bulk metallic glasses [372] present new aspects and additional opportunities that expand the spectrum of SPD-engineered materials with superfunctional properties [180].

A prominent aspect of specific and characteristic microstructural features that are induced by SPD processing of crystalline materials is the appearance of so-called “non-equilibrium” or “deformation-modified” grain boundaries as one of the prominent characteristics of SPD processing [307, 373]. The non-equilibrium grain boundaries in SPD-processed materials were suggested to be characterized by increased elastic strains, enhanced diffusivities and elevated grain boundary energies [374–376]. An in-depth analysis of local strains using geometrical phase analysis from TEM images with atomic resolution [377, 378] revealed an accumulation of defects at the grain boundaries

<figure><img src="image_87.png" /><figcaption>**Fig. 17.** (a) Strain map showing the in-plane rigid-body rotation $ω_{xy}$ for HPT-processed PdAg alloy [377]. (b) Relative enhancement of diffusion rate for non-equilibrium grain boundaries with respect to diffusion along relaxed general high-angle grain boundaries as they are present in the polycrystalline counterparts for SPD-processed nickel [380], copper [381], Cu-0.17Zr (wt%) [382] and Cu-1Pb (wt%) [383] where inverse homologous temperature scale, $T_m/T$, is used for proper comparison. The relative enhancements measured for manganese and iron in additively manufactured CoCrFeNiMn HEA are shown in (b) for comparison [384].</figcaption></figure>
with atomic-scale arrangements [379] and the resulting significant accumulation of strains at such grain boundaries (Fig. 17a). Radiotracer measurements of diffusion rates along such interfaces in SPD-processed metals and alloys confirmed a non-equilibrium state of high-angle grain boundaries in terms of severely enhanced diffusion rates (Fig. 17b), orders of magnitude above those typical of polycrystalline counterparts [379–383].

However, recent results clearly demonstrated that the existence of such a non-equilibrium state of grain boundaries is not limited to SPD-processed materials. In fact, similar grain boundary states have recently been discovered in additively manufactured alloys [384–386], where the processing history did not involve externally applied deformation. In the micrograph and energy-dispersive X-ray spectroscopy mapping of Fig. 18a, the non-equilibrium segregation of manganese atoms at both low-angle and high-angle grain boundaries in an additively manufactured CoCrFeMnNi alloy is indicated. The lack of similar segregation and equiatomic concentrations at grain boundaries has been observed in polycrystalline CoCrFeMnNi alloys [387], which are prominent members of the HEA family. Measurements of tracer diffusion in the additively manufactured alloy revealed a significant enhancement of grain boundary diffusion rates by many orders of magnitude, even exceeding the relative enhancement observed for pure metals or highly concentrated binary alloys (Fig. 17b). This enhancement is exemplified for manganese and iron in Fig. 17b. This unexpected result may be related to the larger configuration space of grain boundary structures in complex, multicomponent alloys. For example, segregation must be taken into account and the structure of grain boundary complexes could also be affected by the presence of minute amounts of alloying elements that are not sufficiently concentrated to allow observation of segregation. The strong enhancement of grain boundary diffusion disappears completely after one-hour annealing treatment at a moderate temperature of 773 K, which has been shown to cause no measurable changes in the microstructure [385].

SPD processing can also serve for bonding or mechanical intermixing at low homologous temperatures. Previous work on HPT-processed HEAs has typically been focused on single-phase solid solutions [388–392]. However, recently the potential for fabricating UFG or even nanocrystalline HEA composites via HPT processing has been analyzed

[370]. For this reason, single-phase equiatomic FCC CoCrFeMnNi and BCC HfNbTaTiZr HEAs were severely co-deformed by HPT, enabling the fabrication of a novel generation of HEA nanocomposites. Bulk nano-composites consisting of alternating elongated nanocrystalline CoCr-FeMnNi and amorphous HfNbTaTiZr nano-lamellae with residual crystalline fractions of HfNbTaTiZr developed (Fig. 18b), exhibiting complex microstructures with vortex-like regions and extremely high hardness. The hardness of the co-deformed BCC-FCC-amorphous nano-composite exceeded both single-phase materials deformed under similar conditions and reached values exceeding 6 GPa. Amorphization during severe co-deformation and the associated defect accumulation and defect interaction at the severely strained heterophase interfaces may represent a rather extreme material response. However, these results highlight the importance of strain-induced modifications that can occur at heterophase interfaces during SPD processing [370].

SPD processing under at least partial confinement and involving high hydrostatic pressure introduces significant structural modifications of metals and crystalline as well as amorphous alloys and drives internal interfaces into states that are denoted as non-equilibrium. The modified grain boundary structure in terms of structural defects (or complexions [393, 394]) affects grain boundary segregation [395, 396] and diffusion [397], and influences strain accumulation [398] or inhibits grain boundary migration by rotational defects [367]. Such modifications are not limited by the SPD processing of materials. Non-equilibrium processing via additive manufacturing drives grain boundaries to similar non-equilibrium states featuring both non-equilibrium segregation and enhanced diffusion [384].

In-depth analysis shows a strong heterogeneity of grain boundary structures [386], segregation response [304, 370, 395, 396], precipitation, amorphization and/or phase decomposition along interfaces with the same macroscopic degrees of freedom [370], and therefore requires new approaches that go beyond purely geometric descriptions of the atomic structure and the related properties of internal interfaces, especially after non-equilibrium processing.

## 3.2. Investigation of non-equilibrium grain boundaries

As mentioned earlier, SPD allows the production of bulk UFG

<figure><img src="image_88.png" /><figcaption>**Fig. 18.** (a) Microstructure and energy-dispersive X-ray spectroscopy chemical maps of additively manufactured CoCrFeMnNi alloy in the as-printed state with pronounced non-equilibrium segregation of manganese [386]. (b) A virtual dark-field image reconstructed from nanobeam diffraction mapping of co-deformed FCC/BCC HEA composite (left panel), individual diffraction patterns revealing crystalline reflections of the FCC CoCrFeMnNi phase (red square), an amorphous halo in the Ta-rich (green square) and an amorphous halo with crystalline reflections at the equiatomic HfNbTaTiZr regions (blue square) and color map of the phases using the value of the intensity-weighted mean of the reciprocal diffraction distance around the first strong crystalline reflections of each nano-beam diffraction pattern (right panel) [370]. Homogenous red and yellow regions fit with the FCC phase. The green regions match the BCC phase and/or the mixed phase regions. The blue regions correspond to a Ta-rich amorphous-nanocrystalline composite.</figcaption></figure>
materials with more attractive properties compared to their coarse-grained counterparts [5]. As will be discussed later, these materials demonstrate higher strength and hardness, increased toughness and wear resistance, and enhanced fatigue strength and superplasticity [182, 347, 399–401]. In UFG materials processed by SPD, the role of grain boundaries is especially high not only because of their high density but also due to their specific state [3]. In the present chapter, specific features of grain boundaries in various materials nanostructured by different modes of SPD are considered in detail.

As mentioned in the previous chapter, grain boundaries in UFG materials processed by SPD are in a non-equilibrium state, which is responsible for the improved mechanical properties [394, 402]. Nazarov worked out a theoretical model, according to which modification in the structure and properties of grain boundaries under the SPD results from the absorption of lattice dislocations, and the non-equilibrium grain boundaries are characterized by excess free energy, higher fields of long-range elastic stresses and larger free volume compared to conventional high-angle grain boundaries [376]. In recent publications, the term deformation-modified grain boundaries is used along with non-equilibrium [307, 373]. It was suggested that localized residual strain fields are located in the near-boundary regions of deformation-modified grain boundaries, rather than long-range elastic stress fields [403]. The specific state of deformation-modified grain

boundaries can be revealed by various methods.

* Firstly, a conclusion about the non-equilibrium state of boundaries in nanostructured materials was made based on TEM. For example, significant elastic distortions near grain boundaries in nanocrystal-line nickel and Ni₃Al were observed by high-resolution TEM [404]. In [405] the “zigzag” stepped configurations of grain boundaries in UFG pure copper and Al-3Mg (wt%) alloy processed by HPT were attributed to their non-equilibrium state. An analogous appearance of grain boundaries was observed in HPT-processed niobium and nickel (Figs. 19a and 19b) [406, 407].

* The state of grain boundaries can be assessed qualitatively and quantitatively by emission Mössbauer spectroscopy [408], which reveals the specific deformation-modified state of grain boundaries in molybdenum, tungsten and niobium [406, 409–411]. In Fig. 19c, the isomer shifts of ⁵⁷Co(⁵⁷Fe) spectral lines versus annealing temperature are compared for coarse-grained and UFG niobium [406]. In coarse-grained niobium, the isomer shifts of both lines (grain-boundary line – component 1 and volume line – component 2) increase slightly with increasing annealing temperature approaching the isomer shift in the regular lattice. In UFG niobium, the isomer shifts of both lines are noticeably lower, especially at low temperatures (673–723 K), because of an excessive free volume, which is one

<figure><img src="image_89.png" /><figcaption>**Fig. 19.** (a,b) Stepwise boundaries in HPT-processed (a) niobium and (b) nickel [407]. (c) Isomer shifts of ⁵⁷Co(⁵⁷Fe) spectral lines versus annealing temperature in coarse-grained niobium (red lines and symbols) and UFG niobium (blue lines and symbols) [406]. (d) Microhardness versus grain size (d) in nickel processed by various techniques [407].</figcaption></figure>
of the main features of the deformation-modified grain boundaries. Above 723 K, the isomer shifts of both lines increase sharply, and after annealing at 873 K, the isomer shift of the volume line of the UFG sample approaches the value for the coarse-grained sample. The increase of isomer shift with increasing annealing temperature is explained by the recovery processes in grain boundaries and near-boundary regions of crystallites.

* The state of grain boundaries can also be revealed by diffusion methods. For example, in [412], an additional free volume was supposed in the deformation-modified boundaries of titanium pro- cessed by ECAP based on the tracer diffusion data. In some publi- cations, it was shown that under the SPD processing, a part of high-angle boundaries acquires the deformation-modified state,

characterized by accelerated atomic transfer [380, 403, 413, 414]. As demonstrated in [415–418], the grain-boundary diffusion co- efficients of cobalt in UFG nickel and niobium processed by HPT are several orders of magnitude higher than in their coarse-grained counterparts, suggesting that non-equilibrium grain boundaries form under SPD processing.

* Additional information on the specific state of deformation-modified grain boundaries can be obtained from the joint analysis of emission Mössbauer spectroscopy and radiotracer data [419]. Based on this approach, it was shown in [420] that grain boundaries in UFG mo- lybdenum processed by HPT are the ultrafast diffusion paths, the coefficients of which are several orders of magnitude higher than those for grain boundaries of recrystallization origin, and this is a

<figure><img src="image_90.png" /><figcaption>**Fig. 20.** (a) Number of scientific documents that included EBSD as keyword since 1994 until now and their distribution according to the research field (information obtained from Scopus data base on June 2023). (b) EBSD system and main calculation and representation techniques [437, 439, 442, 443].</figcaption></figure>
direct part of the evidence for the specific non-equilibrium state of grain boundaries.

In [407], tunneling microscopy was additionally applied to reveal the specific state of grain boundaries in HPT-processed nickel. The relative energy of grain boundaries was determined by the method of etching grooves and calculated from the dihedral angle at the bottom of an etching groove by Equation 1.

$$ \gamma_{\text{rel}} = \frac{\gamma_{\text{gb}}}{\gamma_{\text{s}}} = 2\cos\frac{\Psi}{2} \qquad (1) $$

where $\gamma_{\text{rel}}$, $\gamma_{\text{gb}}$ and $\gamma_{\text{s}}$ are the relative energy of a grain boundary, the grain boundary energy and the energy of a free surface, respectively, and $\Psi$ is the angle at the bottom of the groove. The relative energies of grain boundaries markedly increase with straining, and even at HPT by 0.5 revolutions, $\gamma_{\text{rel}}$ is much higher than in coarse-grained nickel, where it equals 0.30 [421].

Fig. 19d demonstrates the Hall-Petch dependence of microhardness on the square root of the average crystallite size for nickel [329, 380, 407, 422–424], and it is obvious that for grain sizes down to ~ 100 nm the dependence is linear, indicating that the main strengthening factor is grain refinement rather than the specific state of grain boundaries. This conclusion is confirmed by the results of X-ray studies, based on which the level of microstresses was determined. These studies showed that under HPT conditions, the microstress changes from 0.23 GPa for a sample deformed by 0.5 revolutions to 0.35 GPa for a sample deformed by 5 revolutions [407], and this is much less than the total strengthening of nickel after SPD processing.

The main conclusion of this section is that the specific non-equilibrium state of grain boundaries, characterized by excess free energy and larger free volume compared to conventional relaxed high-angle grain boundaries, is formed in metals and alloys under various modes of SPD. This can be revealed by different methods. The contribution of the deformation-modified state of grain boundaries to strengthening is relatively small, and the strengthening mainly results from grain refinement by SPD processing.

### 3.3. Investigation of microstructure by electron backscatter diffraction

UFG materials produced by SPD methods present complex microstructures involving different phases, high density of defects, heterogeneous grain sizes and local texture variations that cannot be characterized by conventional optical microscopy [425]. In this regard, scanning electron microscopy (SEM) coupled with an electron backscatter diffraction (EBSD) detector has gained importance over the years for a thorough microstructure characterization of polycrystalline materials [426, 427]. Fig. 20a proves the continuously growing interest in this technique as the number of published documents has increased in the last thirty years in diverse research fields such as medicine, mathematics, energy, chemistry, physics and materials science. In this technique, an electron beam strikes the surface of a 70° tilted sample, where the diffracted electrons produce a characteristic pattern known as Kikuchi lines on a phosphorous screen (Fig. 20b) [428–430]. This pattern reflects the crystal structure and orientation of the region from which it was generated, so it is recorded and indexed according to the previously selected database [431]. Various in situ and ex situ microstructural measurements can be performed inside the SEM vacuum chamber: After the data acquisition, several microstructural representations and calculations can be obtained: phase identification, texture [432], recrystallized fractions (using local strain indicators like kernel average misorientation KAM and image quality IQ) [433, 434], composition distribution [435], grain size distribution, geometrically necessary dislocations GND and Schmid factor quantifications. These techniques enable the study of grain fragmentation and plasticity of materials [436, 437], characterization of grain boundaries, strain

distribution and microstructural heterogeneity (e.g. grain reference orientation deviation GROD) [438, 439]. EBSD has evolved tremendously during the last decade in terms of software and hardware due to new detectors that enable fast scans (i.e. several samples analyzed in a few hours) and the building up of three-dimensional microstructures at high resolution [440]. Furthermore, the transmission Kikuchi diffraction technique, also known as transmission-electron backscatter diffraction, can overcome some limits of standard EBSD. These constraints include the spatial resolution of around 20 nm and the angular resolution of approximately 1°. This method utilizes TEM samples within the SEM chamber, enabling a greater spatial resolution compared to conventional EBSD. Therefore, it is particularly well-suited for analyzing nanomaterials due to its exceptional sensitivity to small variations in the crystal lattice [441].

EBSD allows for the analysis of several microstructural characteristics. For example, Fig. 21a-c show the microstructure evolution as IQ map with the overlapping low-angle and high-angle grain boundaries for Armco iron after annealing treatment (Fig. 21a) and subsequently ECAP processing by one (Figs. 21b) and 16 ECAP passes (Fig. 21c). This representation highlights the microstructure transformation from the coarse-grained annealed state to a UFG microstructure, passing through a substructure state dominated by a high fraction of low-angle grain boundaries. The transformation from low-angle grain boundaries to high-angle grain boundaries at room temperature (i.e. very low homogeneous temperature) has been described as a continuous dynamic recrystallization process [444]. It is pertinent to note that conducting a successful EBSD analysis necessitates accurately defining microstructural parameters such as the minimum grain size and the minimum grain boundary misorientation to obtain reliable results. Typically, a grain should consist of at least five pixels to be considered as such, and the minimum grain boundary misorientation needed to differentiate between grains falls within the range of 1–5°. It is important to mention that these are general guidelines, and the specific requirements may vary depending on factors such as the crystal structure, sample preparation methods and instrument settings [426].

EBSD representations like GROD and GND can evaluate the microstructure heterogeneity and the lattice curvature following Equations 2 and 3, respectively [436, 448].

$$ \text{GROD}_{ij} = \Delta(\theta_{ij}, \theta_{\text{avg}}) \qquad (2) $$

$$ \rho_{\text{GND}}^{(2D)} = \frac{1}{b} \sqrt{\alpha_{12}^2 + \alpha_{13}^2 + \alpha_{21}^2 + \alpha_{23}^2 + \alpha_{33}^2} \qquad (3) $$

where $\theta_{ij}$ is the misorientation at the position $(i, j)$, $\theta_{\text{avg}}$ represents the grain average misorientation, $b$ is the magnitude of Burgers vector and $\alpha_{ij}$ represents the five components of the Nye's tensor that can be determined from two-dimensional mapping. Fig. 21d-e illustrates the GROD maps of interstitial free steel across the sheet thickness after cold symmetric and asymmetric rolling, respectively. This analysis proves that the asymmetric rolling process gives rise to microstructure heterogeneity across the sheet thickness. At the same time, the deformation on the symmetric rolled material is evenly distributed in different zones of the sheet. The large GROD values close to the sheet surfaces after asymmetric rolling emphasize a higher density of dislocations and faster grain refinement than in the symmetrically rolled sample due to the velocity gradient and the intense shear strain component (i.e. faster texture randomization than in symmetric rolling) [442, 449]. In view of GNDs and texture evolution in heterostructured materials, Fig. 21f displays the GND maps considering the slip systems for commercially pure titanium after two passes by equal-channel angular sheet extrusion (an ECAP-based technique applied to sheets to create heterogeneous materials, with a specific focus on plane geometry deformation). These maps and the pole figures suggest that dislocation activity occurs primarily on the basal and prismatic planes rather than pyramidal planes (larger Burgers vector and, therefore, a higher resolved shear stress for
<figure><img src="image_91.png" /><figcaption>**Fig. 21.** (a-c) Armco iron processed by (a) zero, (b) one and (c) 16 ECAP passes [445, 446]. (d,e) Grain reference orientation deviation (GROD) maps for interstitial free steel processed by (d) cold symmetric rolling and (e) asymmetric rolling [442]. (f) Geometrically necessary dislocations (GND) and pole figures for commercially pure titanium after two passes of equal-channel angular sheet extrusion (ECASE) [439]. (g) Schmid factor evolution for low-carbon 1020 steel after heat treatment (HT) and four ECAP passes [447]. (h) Phase maps for an austenitic stainless steel processed by one ECASE pass [437].</figcaption></figure>
dislocations to slip), which is indicative of the titanium low formability capacity at room temperature and the strong material anisotropy [439, 450]. Regarding plasticity, Fig. 21g shows the Schmid factor evolution for low-carbon steel processed by ECAP at room temperature. In this plot, the initial heat-treated and four ECAP pass processed materials present similar distributions, indicating that the low-carbon steel can withstand more significant amounts of plastic deformation even when the ductility after four ECAP passes is almost neglectable [447, 451]. EBSD also enables the evaluation of phase transformation from austenite to martensite on steels like the austenitic stainless steel 304 L processed by equal-channel angular sheet extrusion, which creates a heterogeneous material across the sheet thickness, as indicated in Fig. 21h. The aforementioned results demonstrate the efficacy of the EBSD technique in characterizing materials with homogenous coarse, homogeneous UFG, and heterostructured microstructures.

The information obtained by EBSD leads to a better understanding of the microstructural and mechanical properties of different SPD-processed metallic materials. Fig. 22a-c compiles results from different SPD processes, like ECAP, ARB, and HPT, concerning the grain boundary misorientation examined by EBSD [443, 445, 446, 452–475]. Thus, metallic materials processed by ARB present a faster transition from low-angle grain boundaries to high-angle grain boundaries with less accumulated strain than ECAP and HPT. However, all the processes suggest a plateau state after von Mises plastic strains larger than seven, which is associated with the slowing of grain fragmentation, i.e. saturation of the grain size reduction and low ductility [445]. In this sense, metallic materials subjected to SPD techniques are characterized by high yield strength but low ductility, limiting their application, as indicated in Fig. 22d. To overcome this strength-ductility paradox, the newly emerging research field of heterostructured materials appears as a solution (Fig. 22d) [443, 452]. EBSD characterization thus plays a crucial role in understanding the property-microstructure relation and hardening mechanisms of SPD-processed materials.

### 3.4. Investigation of microstructure by synchrotron X-ray and neutron diffraction

The investigation of microstructure evolution during SPD and under extreme conditions can be accomplished in reciprocal space using various diffraction techniques, including X-ray, synchrotron and neutron diffraction. A portrayal of Laue-Bragg interference is depicted in Fig. 23a [476], where $\lambda$ is the wavelength, $\theta$ is the Bragg angle, $k_i$ and $k_f$ are the incoming and scattered wavevectors, respectively, $d$ is the lattice spacing and $G$ is the reciprocal lattice vector. Lab-scale XRD and its line profile analysis have been effectively employed to study the microstructural evolution and phase transformation of bulk nano-structured metals processed through SPD [477–481]. Such reflection-type XRD, having a limited penetration depth [482], presents unique opportunities to unveil microstructural heterogeneity even when different planes and sections are scanned within SPD-processed metals. Some examples of such capability are different textures at local and global regions of ZK60 discs after HPT [483] and heterogeneous phase transformation and order-to-disorder transformation in a TiAl intermetallic compound through HPT [484]. By contrast, synchrotron X-ray and neutron diffraction techniques, both in penetration-type settings [485, 486], complement each other, providing distinct measurement capabilities and offering valuable insights into dynamic microstructural changes [476, 487].

High-energy synchrotron X-rays enable the penetration of millimeters into metals using a micro- to nano-scale beam, revealing precise local probing of interest with a high reciprocal space resolution providing the through-thickness microstructural information [476,

<figure><img src="image_92.png" /><figcaption>**Fig. 22.** High-angle grain boundary (HAGB) fractions for different metallic materials processed by (a) ECAP (Armco iron [446], steel 1020 [447], duplex steel [453], pure copper [454], Cu-0.2Mg [455], Cu-0.5Mg [455], pure aluminum [456], AA8079 [457], Al-0.13Mg [457], AA6060 [458], AA6082 [459], Mg-based alloy [460] and commercially pure titanium [461]), (b) ARB (Armco iron [462], interstitial free (IF) steel [463], TRIP (transformation-induced plasticity) steel [464], stainless steel [465], AA1050 [466] and Al/SiC composite [466]) and (c) HPT (AA6061 [467], Cu-0.17Zr [468], Cu-Ni-Si [469], pure copper [470] and pure magnesium [471]). (d) Yield strength and elongation evolution for UFG, coarse-grained and heterostructured materials (sandwich stainless steel [472], Cu-Ni-Cr-Si [473], hierarchical stainless steel [474] and bimodal stainless steel 316 L [475]).</figcaption></figure>
<figure><img src="image_93.png" /><figcaption>**Fig. 23.** (a) A portrayal of Laue–Bragg interference [476]. (b) Position-dependent microstructure map constructed by a series of high-energy XRD (HEXRD) patterns with an enlarged representative diffractogram [488]. (c) A contour plot showing neutron diffraction patterns with time and temperature [489].</figcaption></figure>

490]. The technique of high-energy XRD with a micro-beam is utilized at beamline BL02B1, SPring 8, Japan, [491] by scanning the local region of an HPT-induced diffusion-bonded Al-Mg metastable alloy over the disc surface, enabling a mapping of heterogeneous phase fractions and microstructure over the whole sample volume [488]. Fig. 23b showcases the position-dependent microstructure of the HPT-deformed Al-Mg disc, where the map is constructed from a series of high-energy XRD patterns, with an enlarged representative diffractogram aiding in the visualization of heterogeneous phase fractions and microstructure across the

entire sample volume [488]. The polymorphous phase transformation as a function of plastic strain is demonstrated during the nanostructuring and diffusion bonding of aluminum and magnesium through HPT.

Neutrons offer the advantage of integrating over larger sample volumes [476], rendering them highly suitable for targeted investigations, especially in the context of titanium alloys [487, 492], where their diverse diffraction contrasts can effectively detect order and disorder structures. Neutron diffraction characterization facilitates the study of time-resolved structural changes, thereby elucidating the evolution

<figure><img src="image_94.png" /><figcaption>**Fig. 24.** A heterogeneous phase transformation observed by laser-scanning confocal microscopy (LSCM) at the cross-sections of the HPT-processed CoCrFeNiMn alloy disc edges upon heating [499].</figcaption></figure>
mechanisms and transitions in bulk samples [493]. The incorporation of additional parameters such as heating or cooling enables real-time characterization of crystallographic changes with varying temperatures. A neutron diffraction study on a nanostructured 316 L stainless steel under a heating-cooling cycle was conducted at the iMATERIA beamline BL20 [494, 495] located within J-PARC, Japan [496, 497]. A contour plot showing neutron diffraction patterns against time and temperature is shown in Fig. 23c. The neutron diffraction data were analyzed and the structural evolution in the nanostructured stainless steel is described by the changes in relative lattice expansion and contraction, crystallite size, micro-strain and dislocation density with heating through 1300 K [489]. This technique elucidates the detailed structural relaxation behavior upon heating with detailed transition temperatures of the bulk nanostructured alloy after HPT [498]. A recent report displayed a comprehensive summary of the utilization of the synchrotron X-ray and neutron diffraction techniques on SPD-processed nanostructured materials [499].

In the context of characterization techniques for capturing the heterogeneously appearing microstructural recovery upon heating of nanostructured metals, in situ examination by laser-scanning confocal microscopy with a heating system [500–502] demonstrates a preliminary result on a nanostructured CoCrFeNi Mn HEA after HPT for 15 turns [499]. A series of micrographs taken at arbitrarily selected temperatures upon heating from 373 to 923 K at a rate of 10 K/min is shown in Fig. 24 displaying a gradual and heterogeneously occurring phase transformation upon heating at a similar disc edge region of the HPT-processed CoCrFeNi Mn HEA [499]. Microstructural recovery is visible mainly due to the phase separation of the alloy [503–505]. The delayed multi-phase microstructure formation during recovery is evident in the middle-height region of the nanostructured HEA disc after HPT. At the central section, the morphology of the multi-phases appears more equiaxed, in contrast to the elongated structure along the shear pattern observed in the surface regions. This characterization method serves as an excellent preliminary technique for in situ and ex situ nanoscale microstructural and mechanical testing and the interpretation of local diffraction studies as previously stated.

In summary, the novel and unique microstructural characterization techniques via synchrotron X-ray and neutron diffraction present not only alternative and complementary approaches but also go beyond by allowing in situ observations and incorporating time and temperature scales. This integration of real-time and localized monitoring enhances our ability to gain a deeper understanding of the heterogeneity in nanostructures across multiple length scales.

## 4. Phase transformations

In addition to microstructural evolutions, crystal structure evolutions through strain-, pressure- and temperature-induced phase transformations are another feature of SPD. The history of SPD has a close relation to phase transformations [20], and the topic is still of high interest [8, 9, 15]. It is well established that SPD can affect both the thermodynamics and kinetics of phase transformations and contribute to the discovery of new phases [8, 9, 15]. The SPD-induced phase transformations were reported in various elements including titanium [506], zirconium [507], hafnium [508], cobalt [509], bismuth [510], carbon [511], silicon [15], germanium [512] and phosphorous [20]. Phase transformations and solid-state reactions in alloying systems containing two or more elements were frequently observed after SPD [10, 11] and particularly in the systems with full immiscibility in the solid and liquid forms (e.g. Mg-Ti [333], Mg-Zr [334] and Mg-Hf [335]) after ultra-SPD [164]. Phase transformations by SPD are not limited to metallic materials as such transformations were reported in various nano-metallic materials such as oxides [513], nitrides [514], hydrides [515], etc. In this section, after reviewing phase transformations in metallic materials and ceramics, recent findings on coupling theoretical studies with in situ experiments are discussed.

### 4.1. Phase transformations in metallic alloys

Along with grain refinement, SPD can cause various phase transformations in metals and metallic materials [516]. Titanium, zirconium and hafnium, along with iron, cobalt and bismuth, belong to the metals in which allotropic phase transformations occur when temperature or pressure changes. These phase transformations make it possible to design mechanical and heat treatments to control the properties. Metallic alloys after SPD usually do not contain the same phases as before processing with SPD. SPD can drive the phase transformations both in the bulk and in grain boundaries of alloys. In turn, the SPD-driven bulk phase transitions can be divided into three large groups.

* The first group of phenomena includes competition between decomposition and formation of a solid solution. During the decomposition of a supersaturated binary solid solution, particles of a second phase form and grow, and the concentration of the alloying element in the solid solution decreases. During the formation of a supersaturated solid solution, particles of the second phase dissolve during SPD, increasing the concentration of the second component in the solid solution [517–520]. It is well known that during SPD (especially during HPT), a stationary state (or steady state) can be reached with the strain increase [521]. It turns out that, as a rule, when the decomposition and formation of a solid solution compete, a certain stationary concentration is established. Interestingly, this concentration usually is equal to the solubility of the second component at some elevated temperature called effective temperature ($T_{eff}$) [522]. Most frequently, $T_{eff}$ significantly exceeds the room temperature being usually the temperature of SPD treatment [523].

* The second group of phenomena includes SPD-driven amorphization of crystalline phases [524–527], or nanocrystallization from an amorphous phase [528–530]. Interestingly during HPT, one, two, or several different amorphous phases can appear [531].

* The third class of phase transformations during SPD is observed in metals that possess several allotropic modifications at different temperatures or pressures. In this class of phenomena, the SPD-driven transformations in titanium and its alloys are best studied.

Titanium alloys are one of the most important classes of materials in modern technologies [532–534]. Pure titanium (like zirconium or hafnium) can exist in three crystallographic modifications, namely the low-temperature α-Ti with a hexagonal close-packed crystal structure (space group P63/mmc), the high-temperature β-Ti with a body-centered cubic structure (space group Im3m), and the high-pressure ω-Ti with a hexagonal structure (space group P6/mmm). Many SPD studies are devoted to the change in the properties and structure of titanium and its alloys, such as pure titanium [535–540], binary titanium alloys like Ti-Al [541, 542], Ti-Mg [333, 543], Ti-Fe [544, 545], Ti-Ni [546, 547], Ti-Co [548, 549], Ti-Mo [550, 551], Ti-Nb [552, 553], Ti-Hf [554], Ti-V [309, 555], ternary alloys like Ti-Nb-Zr (TNZ) [556, 557], Ti-Nb-Ta [558], quaternary Ti-Nb-Ta-Zr (TNTZ) [559, 560] and quinary Ti-Al-Zr-Mo-V (TA15) [561]. However, only a small portion of these works concern HPT-induced phase transformations in titanium and its alloys.

In a recent study, HPT processing of various binary titanium alloys with β stabilizers (iron, cobalt, nickel, molybdenum and niobium) was studied [544]. Before HPT, the samples were annealed and contained (i) pure β-phase, (ii) α+β mixture with different portions of phases, (iii) α' or α'' martensites, (iv) the mixture of α-Ti and respective intermetallic phase. It was observed that HPT can lead to various phase transitions in the alloys. In particular, the metastable high-pressure ω phase and α' martensite could form [544]. The orientation relationship between the lattices of β-Ti and α/α'-Ti is described as
$$ (0001)_a \parallel (110)_\beta; \langle 1120 \rangle_\alpha \parallel \langle 111 \rangle_\beta \quad [562] $$
As shown in Fig. 25a, at low
<figure><img src="image_95.png" /></figure>

<figure><img src="image_96.png" /><figcaption>**Fig. 25.** (a) Dependence of the ω phase volume fraction of HPT-treated Ti-Fe alloys on the iron concentration (samples were pre-annealed at 1233 K, 1273 K, 893 K, 873 K) [544]. (b) Data gathered from the literature [545, 563–566] for the lattice periods in Ti-Fe alloys measured for ω-phase (a~ω~ filled squares) with the values $\sqrt{2} a_{\beta}$ for β phase (open symbols). Vegard law straight lines are shown in (b) for the β (thin) and ω (thick) phases which intersect at ~4 wt% of iron [567].</figcaption></figure>

iron concentrations, the fraction of the ω phase after HPT is modest and amounts to about 40% [563–566]. With an increase in the iron content, the portion of the ω phase in the alloy after HPT also increases. It reaches almost 100% at an iron concentration of 4 wt%. Then it begins to decrease with increasing iron concentration and drops to 10–30% at 10 wt% of iron. It is important to mention that, despite the diffusion-like mass transfer during HPT, the transformation of the β phase into the ω phase occurs according to the martensitic mechanism and is associated with a certain orientation relationship between the β-phase and the ω-phase. It turns out that the lattice period of the β and ω phases changes with the addition of iron but in different ways. In both cases, the lattice period decreases with the addition of iron, but in the β phase, it decreases more rapidly. Fig. 25b shows that in the Ti-Fe alloys at a concentration of about 4 wt% of iron, the lines for the lattice period a~ω~ and $\sqrt{2} a_{\beta}$ in β and ω phases intersect. The intersection point corresponds to the lowest lattice mismatch. It greatly facilitates the β-to-ω transformation. As a result, almost 100% of the crystal volume is converted after five HPT revolutions into the ω phase. A micrograph obtained at earlier stages of deformation of Ti-Fe alloy, namely after 1/10 of HPT revolutions, is shown in Fig. 26 and 26b clearly shows how the ω phase (shown in turquoise) surrounds the remains of the α phase (shown in red). Between the α phase and the ω phase, a shell of the β phase is visible (shown in green). It was also shown that the replacement of iron by cobalt in a titanium alloy leads to an increase in the lattice mismatch between α, β and ω phases and to the incomplete transformation of these phases into the ω phase [548].

The composition of phases (similar to their grain size) reaches the steady state value (e.g. after about 1.5 HPT revolutions). In some cases, the equifinality of the SPD-driven phase transitions is observed [568]. Equifinality means that the composition and portion of phases after HPT do not depend on the composition and portion of phases before SPD [519]. However, pre-SPD treatment can sometimes influence the phase transformations. For example, if the Ti-based alloys are annealed below the temperature of eutectoid decomposition of the β phase, they contain only α phase or the mixture of α phase with the corresponding intermetallic compound. In this case, the α phase has no chance to "use" the intermediate layer of the β phase to transform into the ω phase during HPT. Thus, the formation of the ω phase is more complicated and can be completely suppressed if the α phase contains enough diluted alloying atoms. Moreover, if the intermetallic compound exists in a certain

<figure><img src="image_97.png" /><figcaption>**Fig. 26.** (a) Bright field TEM micrograph of the Ti-4Fe (wt%) sample pre-annealed at 1223 K quenched in water and treated by HPT (7 GPa, 0.1 rot, 1 rpm). (b) Phase map of a red outlined area in (a). The α phase is shown in red, the β phase is shown in green and the ω phase is shown in turquoise. The elongated α grain is surrounded by a layer of β phase embedded in ω matrix. The elemental analysis for the black outlined area is shown in the insets in the upper part of (b) [562].</figcaption></figure>
concentration interval, HPT can lead to the composition change in such solid solution based on the intermetallic compound.

The HPT-driven phase transitions can be martensitic (i.e. without or almost without mass transfer) or diffusional (i.e. with mass transfer). For example, in the case of martensitic β-to-ω or α-to-ω phase transitions in titanium alloys, certain orientation relations between β and ω or α and ω phases were observed. In the case of diffusional phase transitions, the rate of mass transfer during HPT at room temperature is several orders of magnitude higher than that of conventional bulk diffusion at room temperature [569]. This is especially remarkable since the high pressure itself (i.e. without shear strain) decreases the rate of mass transfer [570, 571]. The type of phase transformation (martensitic or diffusional) and chemical composition can affect the thermal stability of phases. The thermal stability of the ω phase obtained by HPT has been studied by the *in situ* XRD at high temperatures. It was shown that the ω phase in the HPT-treated Ti-based alloys with β stabilizers can remain in the samples

up to 773–873 K. This temperature range is much higher than in pure titanium (~453 K). Alloying with niobium or molybdenum increases this temperature to 573–623 K. In Ti–Co alloys, the ω phase remains stable up to 673 K and in the Ti–Fe alloys even up to 823 K [567, 572].

Phase transformations can take place not only in the bulk but also in grain boundaries. They include faceting-roughening transitions [573], as well as wetting [574], prewetting [575–577] or premelting [578, 579] transformations. The significance of SPD-driven grain boundary phase transformations was reported in a few recent studies [580, 581]. The HPT-driven bulk and grain boundary phase transitions open a new way for tailoring, grain size, phase composition and properties of metallic materials. In turn, it gives the new instrument in the hands of engineers to design materials for special applications such as titanium alloys for medical applications.

<figure><img src="image_98.png" /><figcaption>**Fig. 27.** (a,b) Influence of plastic shear strain on the fraction of high-pressure phases in (a) TiO₂ [582] and (b) Y₂O₃ [583] after HPT processing. (c,d) Formation of dislocations during phase transformations of (c) ZrO₂ [584] and (d) TiO₂ [582] after HPT processing. (e,f) Grain size effect on the stability of high-pressure (e) TiO₂-II [582] and (f) monoclinic Y₂O₃ [583] after HPT processing.</figcaption></figure>
## 4.2. Phase transformations in ceramics

Phase transformation induced by SPD is not limited to metallic materials and such phase transformations were reported in a wide range of ceramics (e.g. ZrO₂, BaTiO₃, ZnO, TiO₂, Y₂O₃, SiO₂, Al₂O₃, VO₂, BN, etc.). Among bulk-SPD methods, HPT is currently the only method used for controlling phase transformations in ceramics due to the high processing pressure in this method. Processing by HPT provides some unique features for the phase transformation of ceramics. (i) The fraction of the high-pressure phase increases with increasing the applied shear strain, as shown in Fig. 27a for TiO₂ [582] and Fig. 27b for Y₂O₃ [583]. (ii) Phase transformation can occur at a pressure below the transition pressure under static compression (e.g. reduction of pressure from 11 to 15–6 GPa in monoclinic-to-cubic phase transformation of Y₂O₃ shown in Fig. 27b). (iii) Dislocations contribute to the acceleration of phase transformation and the reduction of transition pressure (e.g. see dislocations observed during phase transformation of ZrO₂ in Fig. 27c [584] and TiO₂ in Fig. 27d [582]). (iv) High-pressure phases formed by HPT can remain stable after releasing pressure, particularly in grains with small nanoscaled sizes, as shown in Fig. 27e for TiO₂ [582] and in Fig. 27f for Y₂O₃ [583]. The stability of HPT-induced phases is a striking issue because such phases can be used for different applications. Zinc oxide (ZnO) is one successful example that its high-pressure phase was utilized for photocatalysis, as described below in detail.

ZnO is a well-known ceramic semiconductor with versatile properties for optoelectronic and biochemical applications [585–590] including applications such as ointment, pigment and vulcanization [591, 592]. ZnO exhibits an allotropic transformation from a wurtzite crystal structure to a rocksalt crystal structure as the pressure increases to more than ~6 GPa according to a pressure-temperature phase diagram [593, 594]. For photovoltaic and photocatalytic applications [595–599], the rocksalt structure is more attractive than the wurtzite structure because its band gap is in the range of 1.2–2.6 eV so that it can absorb visible light [600–602], while the band gap of the wurtzite structure is as high as 3.1–3.4 eV so that its light absorption is limited to the range of UV light [596, 603]. Nevertheless, the rocksalt structure is not stable at ambient pressure, and thus, stabilization at ambient pressure is required for its practical use. A striking report in 2017 [604] that the rocksalt structure can exist at ambient pressure when ZnO is strained under high pressure using HPT, which is mainly known as a metal processing method [2, 20, 23, 177]. Although enhanced photocatalytic activity was realized on the HPT-processed ZnO-containing samples [604–606], the fraction of the rocksalt phase was marginal, and thus, further attempts were made to enhance its fraction.

In a recent study, high pressure was applied to HPT-processed ZnO and the change in the fraction of the rocksalt structure was examined using *in situ* synchrotron high-energy XRD analysis in SPring-8, Japan [607]. A high-pressure application system including a heating unit as illustrated in Fig. 28a [608] is adopted for this XRD experiment, of which principle was introduced earlier [57] and modification was made to this *in situ* experiment [608]. The rocksalt structure in the sample processed by HPT under 6 GPa for 3 turns disappeared with heating to temperatures higher than 433 K under ambient pressure. However, its fraction increased to 100% after heating above 353 K by applying pressures more than ~9 GPa, and remained stable after cooling down to room temperature even after unloading to ambient pressure. In contrast, the formation of the rocksalt phase was considerably suppressed for the ZnO powder without processing by HPT (only a minor fraction was formed above 453 K under 12 GPa). Fig. 28b shows a pressure-temperature phase diagram reproduced from a report by Bayarjargal and Winkler [593]. Open symbols and closed symbols represent phase regions corresponding to the wurtzite structure and the rocksalt structure, respectively. Fig. 28b also includes the results by Decremps et al. [594], where the transformation point from rocksalt to the wurtzite structure is marked by open blue squares and that from wurtzite to the rocksalt structure by closed blue squares. The present

<figure><img src="image_99.png" /><figcaption>**Fig. 28.** (a) Schematic illustration of high-pressure application system for *in situ* XRD analysis at SPring-8, Japan [607]. (b) Temperature-pressure phase diagram of ZnO. Open and closed circles are reproduced from Bayarjargal and Winkler [593] for wurtzite and rocksalt structures, respectively. Open and closed blue squares are from Decremps et al. [594], representing transformation points from rocksalt to wurtzite structure and from wurtzite to rocksalt structure, respectively. Star symbols represent results of HPT-processed ZnO in which rocksalt occupies 100% [607].</figcaption></figure>

results are plotted as marked by star symbols in red. Inspection of Fig. 28b reveals that the presence of the rocksalt structure under high pressures is well consistent with the reports by Bayarjargal and Winkler [593] and Decremps et al. [594]. However, the presence of the rocksalt structure is also confirmed under ambient pressure and temperature. This exceptional result arose because the strain introduced in the sample by the HPT process generates internal pressure due to the mutual interaction of dislocations as argued in earlier papers [8, 584, 609].

In summary, SPD methods and particularly HPT are powerful tools to control phase transformations in ceramics. Such phase transformations, such as stabilization of 100% of the rocksalt ZnO phase which was confirmed by *in situ* high-energy XRD experiments, open a new path for the employment of these phases in functional applications such as photocatalysis.

## 4.3. *Coupled in situ and theoretical studies of phase transformations*

SPD under high pressure is mostly studied postmortem after pressure release, as reflected in old [1], recent [23, 182, 236] and latest [5] reviews. Here, recent *in situ* experimental and theoretical studies of coupled SPD, strain-induced phase transformations under high pressure
<figure><img src="image_100.png" /><figcaption>**Fig. 29.** (a) Schematic of RDAC. (b) Phase-field approach results showing dislocation pileup in the left grain produces a step at the grain boundary (superdislocation) with a strong stress concentrator leading to phase transformation and dislocation slip in the right grain [624]. (c) Molecular dynamics results showing dislocation pileup in the right grain produces a step at the grain boundary in Si-I phase and amorphization in the left grain [623].</figcaption></figure>

obtained under compression in diamond anvil cell (DAC) or compression and torsion in rotational diamond anvil cell (RDAC) [8, 366] are summarized. In RDAC (Fig. 29a), two diamond anvils compress the sample within or without a gasket, like in traditional DAC, to high pressure. Then torque is applied, leading to the superposition of large shear-dominated straining on compression. The X-ray beam is directed along the axial direction for the characterization of the material. The utilization of XRD with synchrotron radiation allowed one to determine the radial distribution of volume fraction of phases and pressure [610–614], dislocation density and crystallite size in each phase [613, 614] and find the main laws of their evolution and interaction. Coupling with the finite element simulations of the sample behavior [615–617] allows the determination of fields of all components of the stress and plastic strain tensors and volume fraction of the high-pressure phase [618, 619] and provides a better understanding of ways to control

occurring transformations and corresponding microstructural evolution. Atomistic [620–622], nanoscale [514, 623–625] (Fig. 29) and scale-free phase-field simulations [626, 627] allow elucidation of the main physical mechanisms of the plastic strain-induced drastic reduction in phase transformation pressure (by one to two orders of magnitude [8, 612, 628, 629]), the appearance of new phases [630–632] and strain-controlled phase transformation kinetics [8, 610, 611, 619] in comparison with hydrostatic loading. Combining *in situ* experiments with multiscale theory potentially leads to the formulation of methods to control strain-induced phase transformation evolution and designing economic synthetic paths for the defect-induced synthesis of desired high-pressure phases, nanostructures and nanocomposites. It should be noted that *in situ* XRD during HPT [633, 634], HPS [608] and compression [607] were also attempted. However, XRD patterns in these cases are averaged over very heterogeneous fields, and just one value is measured for the prescribed load. Thus, it is much less informative than the axial diffraction measurements in RDAC. XRD in perpendicular geometry for the rotational Drickamer apparatus [635–637] has also a large error bar.

It was found that the study of strain-induced phase transformations is significantly simplified when steady states for microstructure and pressure-dependent yield strength are reached before the initiation of strain-induced phase transformations [610, 611]. For such a case, it was shown that (a) the minimum pressure for the strain-induced α-ω phase transformation in zirconium, and the pressure-dependent yield strength $\sigma_y(p)$ of ω-Zr are independent of plastic strain tensor $\epsilon_p$ and strain path $\epsilon_p^{path}$; (b) crystallite size and dislocation density in a single phase ω-Zr are in addition independent of pressure; (c) crystallite size and dislocation density in ω-Zr and (with some outliers) α-Zr during phase transformation are independent of pressure, plastic strain tensor, and strain path and depend on the volume fraction of the high-pressure phase only. It was also found for zirconium [610, 611] and olivine [613] that there is a correlation between the Hall-Petch effect of the grain/crystallite size on the yield strength [638] and the minimum pressure for the strain-induced phase transformation, with corresponding theoretical justification. Similar results, including correlation for the inverse Hall-Petch effect [638] and the minimum pressure for the strain-induced phase transformations, were found for silicon [612]. Namely, in the region when the yield strength increases with the reduction in grain size, the minimum pressure for the strain-induced phase transformation reduces; while for smaller nanoscale grain sizes, the yield strength reduces, and the minimum pressure for the strain-induced phase transformation increases. These *in situ* results are consistent with results for $Y_2O_3$ [583], $TiO_2$ [582, 639] and $ZnO$ [604], obtained with TEM: after phase transformation by HPT processing, the recovered high-pressure phases have smaller grain sizes and initial low-pressure phases have larger grain sizes. However, since TEM results are obtained *ex situ*, various other interpretations are possible [366], i.e. they are not conclusive.

The obtained results imply that the factors and mechanisms that affect the steady grain size (see original papers [364, 365, 640–642] and reviews [189, 643, 644]) and dislocation density [645] are important for controlling strain-induced phase transformations. They change the general wisdom that plastic shear is responsible for reducing phase transformation pressure. In fact, any mode of straining and strain paths that belong to some classes lead to the same phase transformation pressure and steady microstructure. For example, variations of crystallite size and dislocation density in the ω-Zr phase after $\alpha \rightarrow \omega$ phase transformations are shown in Figs. 30a and 30b, respectively. Since the plastic strain tensor and its path, as well as pressure strongly vary with radius and increasing load, approximate independence of the crystallite size and dislocation density and of the radius and load indicates that they reached steady values, which are independent of pressure, plastic strain tensor and its path. This issue is further discussed in Fig. 30c in which schematic of the evolution of the yield surface $f(s, \epsilon_p, \epsilon_p^{path}) =$
<figure><img src="image_101.png" /><figcaption>**Fig. 30.** (a,b) Radial distribution of (a) crystallite size and (b) dislocation density in the ω-Zr phase for three compression steps after full transformation. Pressures in the upper right corner designate maximum pressure at the sample center [614]. (c) Schematic of the evolution of the yield surface $f(s, \epsilon_p, \epsilon_p^{\text{path}}) = \sigma_y(p)$ until it reaches the fixed surface of perfect plasticity $\varphi(s) = \sigma_y^1(p)$ in “5D” space of deviatoric stresses $s$ at fixed pressure $p$, after which the material deforms like perfectly plastic, isotropic, and independent of $\epsilon_p$ and $\epsilon_p^{\text{path}}$ (for some classes of straining paths, several other fixed surfaces of perfect plasticity $\varphi^i(s) = \sigma_y^i(p)$ with larger yield strengths $\sigma_y^i(p)$ can be reached) [614].</figcaption></figure>

$\sigma_y(p)$ until it reaches the fixed surface of perfect plasticity $\varphi(s) = \sigma_y^1(p)$ in “5D” space of deviatoric stresses $s$ at fixed pressure $p$ is illustrated [614]. The initial yield surface and $\varphi(s) = \sigma_y^1(p)$ are isotropic (circles). Two other yield surfaces depend on $\epsilon_p$ and $\epsilon_p^{\text{path}}$, and acquire strain-induced anisotropy, namely shifted centers $O_1$ and $O_2$ (back stress) and ellipsoidal shape due to texture. When the yield surface reaches $\varphi(s) = \sigma_y^1(p)$, the material deforms like perfectly plastic, isotropic with the fixed surface of perfect plasticity. However, for α-Zr for some classes of straining paths, several other fixed surfaces of perfect plasticity $\varphi^i(s) = \sigma_y^i(p)$ with larger yield strengths $\sigma_y^i(p)$ (due to larger steady dislocation density and smaller crystallite size can be reached.

In situ studies [614] lead to a key question: for which classes of plastic strain and strain path (and maybe pressure path), the material remains in each of the steady states, and for which loading classes, the material behavior jumps from one steady state to another? This question is just a translation into the language of plasticity theory of known technological problem: why different SPD technologies lead to different steady microstructures and how to design the loading process to reduce the grain size and phase transformation pressure and increase dislocation density and strength. It is also shown that incomplete phase transformation is a much more effective way to reduce the grain size to produce nanocomposite materials with controllable strength and ductility than SPD alone [366, 610, 611]. In addition, SPD under normal pressure, e.g. by rolling, leading to one of the steady states followed by compression or HPT at relatively low pressure, is a more economical way to produce nanostructured high-pressure phases and nanocomposites than HPT of annealed materials. The possibility of manipulating synthetic paths may lead to new economic technologies at relatively low pressures, room temperature, and without catalysts, e.g. for cubic and hexagonal diamond, cubic and wurtzite BN, Si-III, etc. Application of the concept of plastic strain-induced phase transformations (instead of pressure-induced phase transformations) [8] may also change various geological interpretations, like the mechanism of the deep-focus earthquakes [646] and the appearance of microdiamonds in the Earth’s crust [629]. Application of ultra-SPD [178] may lead to discoveries in strain-induced phase transformation. Still, the entire field of fundamental study of SPD and plastic strain-induced phase transformation is in its infancy; one needs to find whether the above results are valid for other materials and material classes and to find a much more detailed theoretical description at each of the four scales.

## 5. Mechanical properties

The most visible effect of SPD, particularly in metallic materials, is the enhancement of mechanical properties such as strength and hardness, mainly due to the grain refinement effect [3] and the Hall-Petch mechanism [6, 7]. Some studies, however, suggested that the strengthening of these materials by the dislocation hardening mechanism can be quite significant [45]. Hardening by other factors like precipitation, twins, segregation, phase transformation and spinodal decomposition was also reported in these materials [305, 647]. Materials after severe plastic deformation do not always exhibit hardening, and it was shown that softening can occur in pure metals with low melting temperatures, despite a decrease in grain size and an increase in dislocation density [399]. Such behavior, which was reported in lead, tin, indium and aluminum with ultrahigh purity, was attributed to the contribution of thermally-activated phenomena [399, 648]. In magnesium, which also has a low melting temperature, it was shown that storage of HPT-processed samples for several years leads to increasing grain size, decreasing dislocation density and an unusual increase in hardness via anneal hardening [649]. Softening can occur in some metallic alloys by unusual grain coarsening, phase transformation or the activation of thermally-activated phenomena such as grain boundary sliding [38, 650]. Despite some exceptions mentioned above, strength usually
increases after SPD processing and this strengthening is not accompanied by a complete loss of plasticity, as recognized by Segal et al. after ECAP processing [27]. HPT studies have also shown that SPD-processed materials can exhibit a good combination of strength and plasticity, although their work hardening and uniform ductility are limited [194]. A large number of studies attempted to enhance the ductility of SPD-processed materials and there is quite good progress on this issue [182, 651].

Studies on the mechanical properties of SPD-processed materials can be classified as: (i) torque measurements which originated from Bridgman's works on HPT in the 1930s [20], (ii) hardness-strain behaviors which can provide quick information about the microstructural evolution and the occurrence of steady state [400], (iii) tensile, compression and bending properties which are of significance for commercialization of SPD-processed materials [305], (iv) superplasticity which occurs frequently in SPD-processed materials due to large fraction of grain boundaries [652], (v) fatigue properties [653], (vi) creep properties [654], (vii) wear resistance [655], (viii) fracture toughness [656], etc. In the following sections, some recent findings on strain hardening, anneal hardening, creep resistance, superplasticity and hydrogen embrittlement resistance of SPD-processed materials are discussed. Other mechanical properties are reviewed in other chapters of this article.

## 5.1. Strain hardening

As mentioned earlier, SPD is effective not only for grain refinement [1, 657, 658] but also in the generation of various kinds of defects, particularly dislocations [2, 659] which accordingly can enhance

strength. Moreover, SPD can fragment intermetallic phases into nano-sized in alloys containing elements with low diffusivity and low solubility [178], such as Al-Fe [310], Al-Ca [311], Al-Zr [332], Al-RE (RE: rare earth elements) [315], Mg-Ca [660], Mg-Ti [322] and Mg-Zr [334], and further enhance the strength. The contribution of grain boundaries to strengthening can be estimated using the Hall-Patch relationship [6, 661, 662].

$$ \Delta\sigma_{GB} = \frac{k}{\sqrt{d}} \qquad (4) $$

where k is the Hall-Petch coefficient and d is the average grain size. The contribution of dislocations can be estimated through the Bailey-Hirsch relationship [663].

$$ \Delta\sigma_{\rho} = \alpha M G b \sqrt{\rho} \qquad (5) $$

where α is a constant, M is the Taylor factor, G is the shear modulus, b is the Burgers vector, and ρ is the dislocation density. The HPT process, which is operated under high pressure for processing various materials [181, 512, 609, 664–667], is believed to be the most effective SPD technique for hardening through grain refinement and dislocation generation [668, 669]. However, the sample in the HPT process is a disc that experiences heterogeneous strain distribution [154, 177], but methods such as ARB and HPS produce sheets that experience more homogenous strain [670–672]. HPS has the benefits of HPT for hardening because it can be applied under high pressure, but its merit is that it applies to sheets [673–676], rods [238, 677–679] and pipes [239]. The pressure in ARB is not as high as HPT and HPS, but it is still effective

<figure><img src="image_102.png" /><figcaption>Fig. 31. (a) TEM bright-field images of aluminum after five and 10 ARB cycles. (b) Nominal stress-strain curves at a strain rate of $1 \times 10^{-5}$ s$^{-1}$ for aluminum after 0, 1, 3, 5 and 10 ARB cycles. (c) Nominal stress-strain curves with strain rates ranging from $1 \times 10^{-2}$ to $1 \times 10^{-5}$ s$^{-1}$ for HPS-processed aluminum. (d) Plots of yield stress against the number of ARB cycle at a strain rate of $1 \times 10^{-5}$ s$^{-1}$, including value of HPS-processed sample and values calculated by grain boundary and dislocation hardening [675].</figcaption></figure>
in enhancing strain hardening in sheets [19, 227].

Fig. 31a displays typical TEM microstructures of sheets after ARB processing, revealing elongated grains well-developed after five and 10 cycles along the rolling direction, with mean grain thicknesses of 310 and 240 nm, respectively [675]. A significant grain refinement is evident when compared with the mean grain size after annealing, which is 31 µm. Concurrently, Fig. 31b demonstrates a significant strain hardening by increasing ARB cycles. The strain rate dependence of the nominal strength is observed in sheets processed by HPS (Fig. 31c) [675], a fact that was also reported in ARB-processed sheets [679, 680]. A comparison of the yield stress of aluminum processed by HPS and ARB with the calculated strength through Equations 4 and 5, is shown in Fig. 31d. It was shown that yield strength by the HPS process is comparable to those obtained by the ARB process for similar equivalent strains (a sliding distance of 15 mm for HPS compared to 10 ARB cycles).

It is concluded that strain hardening of pure metals can be simply justified through Hall-Petch and dislocation hardening mechanisms when grain sizes are at the submicrometer level. Strain hardening becomes more complicated by the presence of second phases and precipitates [310, 658]. Moreover, breaks in the Hall-Petch mechanisms can occur when grain sizes are reduced to the nanometer level [681].

## 5.2. Anneal hardening

Cold working increases the strength of metallic materials. Especially for severe plastic strains, strength levels of up to 1/3 of the theoretical

strength can be reached [682, 683]. Subsequent heat treatment generally reduces strength as the microstructure is gradually transferred back to the state before cold deformation [434, 684]. However, for sufficiently fine grain sizes and restricting the heat treatment to the recovery regime (i.e. avoiding recrystallization or grain growth), further strengthening instead of a softening, can be observed [671, 685–690]. This extra strengthening increases with annealing temperature until grain coarsening initiates (Fig. 32a). First reports on this subject date back to the 1960s [691–693] and were related to ordering phenomena. However, examination of nanostructured metals in the past decades indicated that anneal hardening can also occur for single-phase metals and alloys, where decomposition or ordering can be excluded. This is also evident from isothermal annealing curves, showing a constant hardness plateau after a rapid initial increase (Fig. 32b) [685, 694], which contrasts with precipitation or decomposition sequences (e.g. see [503]).

For single-phase metals, the hardening is hence a consequence of the reduction of available inter- and intragranular defects, accompanied by solute or impurity segregation to grain boundaries [671,685–687,689, 690]. The required temperatures for the annihilation of dislocations at high-angle boundaries thus perfectly agree with those leading to the maximum anneal hardening increment (Fig. 32c) [695, 696]. The loss of existing dislocation debris requires the activation of dislocation sources after the heat treatment to realize plastic strain [671, 697, 698]. For sufficiently fine grain sizes, these sources are predominantly located at grain boundaries [699] and are relaxed during the annealing treatment

<figure><img src="image_103.png" /><figcaption>Fig. 32. (a) Hardness after isochronal (30 min) annealing of 316 L steel processed by HPT at ambient temperature (grain growth occurs above 823 K) [687]. (b) Isothermal annealing of 316 L steel processed by HPT for different times [694]. (c) Hardness of several nanostructured FCC materials after 30 min annealing as a function of annealing temperature (temperatures for the annihilation of lattice dislocations in high-angle grain boundaries are highlighted) [695, 696]. (d) Hardness of various nanostructured nickel and Ni-Mo alloys as a function of annealing temperature (annealing time <1 h), indicating that the temperature leading to the maximum hardness stays almost unaffected, despite large differences in grain size [690].</figcaption></figure>
[685, 697, 698, 700], enhancing the stresses needed to operate these sources [697]. The activation stress of a grain boundary source could be additionally affected by solute or impurity segregation [701]. For example, different extents of anneal hardening were reported for different solutes but similar grain sizes such as in Ni-W and Ni-Mo alloys [685, 688]. However, active interactions of segregated atoms with propagating dislocations are not expected from strain rate jump tests at ambient and elevated temperatures. At least for the studied strain rates and temperatures, a positive rate sensitivity was measured in any case [702].

The extent of the anneal hardening can be significant and may even double the strength of the nanostructures [688, 703], making it attractive to further improve the mechanical properties of SPD-processed materials. Apart from a few exceptions [704], the strength increment was found to increase with decreasing grain size [685, 688, 702]. This is reasonable, since according to Equation 6 [705, 706], the time, t, to annihilate dislocations at grain boundaries (apart from material constants such as atomic volume Ω, shear modulus G, and boundary width δ) depends only on the boundary diffusivity, D<sub>GB</sub> and the grain size d.

$$t \sim \frac{k_B T d^3}{G \Omega \delta D_{GB}} \quad (6)$$

While smaller grain sizes recover faster and thus allow for a larger hardening, the temperatures leading to the maximum hardness increase are not significantly dependent on grain size [690]. This is evident by comparing specimens with different grain sizes, either synthesized by SPD at different temperatures or by comparing SPD-processed alloys with batches prepared by deposition techniques (allowing usually for

smaller grain sizes), as shown in Fig. 32d. The pronounced dependence of boundary diffusivity on temperature may explain this result.

As the microstructural stability is crucial for the fatigue strength of nanostructures [707, 708], and cyclically induced grain coarsening depends on the (micro)plastic strain amplitude [709, 710], anneal hardening should also have a pronounced effect on the fatigue strength. Since the loss of dislocation debris and the hardening of dislocation sources shift the onset of plasticity to higher stress levels, the fatigue limit should be significantly influenced by anneal hardening. Indeed, this has been observed for nanostructured nickel and 316 L austenitic steel [711, 712], allowing for an additional 60% increase in the fatigue strength compared to the as-HPT deformed condition (Fig. 33a) [712, 713].

However, anneal hardening drastically shortens ductility (Fig. 33b) [671, 712, 714]. This is not because of an embrittlement effect (e.g. induced by impurity segregation), as can be deduced from the microductile fracture surfaces for as-deformed and annealed state (Fig. 33c). The loss of ductility and early failure is related to an enhanced tendency for strain localization, as defect generation after the heat treatment softens the material. Allowing grain growth (d > 500 nm), the strain softening can be balanced by hardening from dislocation-dislocation interactions [715], but the full strengthening potential is not exploited due to the coarsening. Current research activities aim to identify strategies to avoid strain localization without negating anneal hardening. Manipulation of the grain boundary structure, for instance by introducing nanometer-thick amorphous films [716, 717], or by applying slight plastic strains after the anneal hardening treatment [718, 719], seems promising in this regard (Fig. 33d). Future work should thus elaborate processing strategies to synthesize materials with dedicated

<figure><img src="image_104.png" /><figcaption>Fig. 33. (a) Fatigue S-N (stress-cycle to failure) curves showing the effect of anneal hardening (recovery) on the quasi-static strength and the fatigue limit of a nanocrystalline 316 L austenitic steel prepared by HPT at room temperature [712]. (b) Representative engineering stress-strain curves of a uniaxial tensile test obtained on the same samples as in (a), indicating that anneal hardening drastically shortens the elongation to failure [712]. (c) Representative images of fractured tensile specimens and the corresponding fracture surfaces of a nanocrystalline 316 L steel in HPT-processed (black) and anneal-hardened (red) conditions [712]. (d) Schematics showing the general problem of the strength-ductility trade-off applying especially for anneal hardened metals, and potential solutions to this problem [690].</figcaption></figure>
boundary structures, but also to understand the effect of post-anneal deformation. This could pave the way towards unprecedented combinations of strength and ductility.

### 5.3. Creep resistance

Creep is defined as the time-dependent plastic strain under constant applied stress and/or load at a given temperature. The various deformation mechanisms operating during creep can be defined in terms of the creep rate given by an established phenomenological relationship [720].

$$ \dot{\epsilon} = \frac{ADGb}{kT} \left(\frac{b}{d}\right)^p \left(\frac{\sigma}{G}\right)^n \quad (7) $$

where D is the diffusion coefficient, G is the shear modulus, b is the Burgers vector, k is Boltzmann's constant, T is the absolute temperature, d is the grain size, σ is the applied stress, p is the exponent of the inverse grain size. n is the stress exponent which is equal to 1/m where m is the strain rate sensitivity and A is an appropriate dimensionless constant. The value of D is given by:

$$ D = D_o \exp\left(-\frac{Q}{RT}\right) \quad (8) $$

where D_o is a frequency factor, Q is the activation energy for the creep process and R is the gas constant. It follows, therefore, that the creep mechanism is defined by the specific values of Q, n (or m), p and A and these values may be determined by conducting appropriate creep experiments. A mechanism of creep deformation can be particularly identified through knowledge of the stress exponent n using the following equation [721]:

$$ n = (\partial \ln \dot{\epsilon} / \partial \ln \sigma) T \quad (9) $$

The creep behavior of polycrystalline materials with conventional coarse grain sizes is well described through a series of constitutive equations that delineate different deformation mechanisms [721-724]. According to the value of the stress exponent n, the following types of creep regions can be classified in which corresponding operating deformation mechanisms exist: diffusion-based processes (n = 1) [725-727], a combination of diffusion and dislocation-based processes such as grain boundary sliding (n = 2) [721, 723, 728, 729] and Harper-Dorn creep (n = 1) [730, 731], the power-law controlled mechanisms like viscous glide creep (n = 3) [724] and power-law creep by glide and climb of dislocations (n = 4-7) [721, 723, 724]. At extremely high applied stresses, a power-law breakdown region with very high values of n is observed [722, 732].

Recent progress in producing UFG materials by SPD processing [5, 180] together with factors like reduced grain sizes, microstructure instability, non-equilibrium grain boundaries, very high intragranular dislocation densities and increasing diffusivity resulted in significantly different creep behavior of UFG materials in comparison with coarse-grained materials. Therefore, questions naturally arise about whether the creep deformation and fracture mechanisms in UFG materials are similar to those operating in coarse-grained counterparts, as reviewed in several publications [654, 733-739]. Most studies were performed on pure metals or model binary alloys to separate the basic mechanisms related to grain refinement and microstructure. However, creep experiments have been limited to a narrow range of testing temperatures and stresses because of the instability of non-equilibrium grain boundaries. Further, the experimental results and their interpretations by different authors are not in agreement with each other due to different SPD processing techniques and routes used [740]. It was reported that in pure aluminum and copper, under the same loading conditions, the measured minimum creep rate $\dot{\epsilon}_{min}$ in the SPD-processed materials with ultrafine grain size was slower and the time to fracture (creep lives $t_f$) was longer than in the same material in a coarse-grained

state [5, 735, 738, 740-746]. However, such positive effects dramatically decrease with increasing value of imposed strain. Microstructural analysis showed that after the first ECAP pass grain boundaries were predominantly low-angle ones and high-angle grain boundary fraction in SPD-pressed specimens significantly increased with increasing value of imposed strain [735]. This implies that high-angle grain boundaries have a lower strengthening effect in creep than low-angle grain boundaries [747]. The important conclusion from the creep experiments on UFG pure materials with unstable microstructure is that conventional creep mechanisms, already proposed for coarse-grained materials, may be used also to explain the creep behavior in UFG materials [735-737, 746].

The creep behavior of reasonably stable precipitation and oxide dispersion strengthened structural materials processed by various SPD techniques [654, 748-753] in principle matches the behavior of coarse-grained materials [721-724]. The best way to confirm this view is to compare the resultant creep characteristics of UFG materials with those attained in unprocessed conditions of the same material. To illustrate the creep behavior of polycrystalline materials, it is most informative to use creep curves, which represent graphically the time dependence of creep strain. Fig. 34a shows schematically three creep stages after instantaneous strain $\epsilon_0$ upon loading: a primary or transient creep (Stage I), a secondary or steady-state creep (Stage II), and a tertiary or accelerated creep (Stage III) ending up creep fracture. Figs. 34b, 34c and 34d show the real creep curves of the precipitate-strengthened Zr-2.5 Nb (wt%) alloy [754], the austenitic stainless S304H steel [755] and the heat-resistant high chromium ferritic-martensitic P92 steel [750, 756], respectively. Inspection of these figures leads to the following observations. First, the processing by SPD has a detrimental effect on creep life. Generally, UFG precipitate-strengthened materials exhibit shorter creep lives than the coarse-grained ones under the same loading conditions which limits their engineering utility. Second, it appears that the pertinent ductility (fracture plasticity) enhancement is associated with the increase in the fraction of high-angle grain boundaries. Third, in some cases, the grain refinement after a higher number of SPD operations (e.g. a higher number of ECAP passes) could result in a dramatic decrease in the creep resistance (see Fig. 34b).

In a similar way as in Equation 7, the equation for the time to fracture, $t_f$ is given by [757, 758]:

$$ t_f = B(\sigma)^m \exp(Q_f / kT) \quad (10) $$

where B is a material constant, $m = -(\partial \ln t_f / \partial \ln \sigma)_T$ is the stress exponent of the time to fracture, and $Q_f$ is the activation energy for the time to fracture. Fig. 35 shows stress dependences of the minimum creep rate $\dot{\epsilon}_{min}$ (Figs. 35a and 35c) and the time to fracture (Figs. 35b and 35d) [754, 756, 759-762]. Determined values of the stress exponents n and m imply that UFG structural materials obey the power-law relationship and suggest that occurring creep deformation mechanisms are similar to those operating in the same coarse-grained materials [654, 736]. However, such a conclusion is based on mostly short-term creep experiments at medium and high applied stresses where intergranular (dislocation) mechanisms are dominant. By contrast, diffusion-controlled grain boundary-mediated processes are important at low applied stresses.

In summary, creep mechanisms in UFG structural materials across all stress scales are not clearly resolved at present due to the complexity of the phenomenon. Long-term creep tests should be carried out to properly evaluate the creep strength of UFG materials under service conditions.

### 5.4. Superplastic deformation

When metal samples are pulled in tension they generally fail at relatively low elongations, typically in the range of ~10-50%. But under some conditions, much larger elongations may be achieved and this
<figure><img src="image_105.png" /><figcaption>Fig. 34. (a) Schematic representation of a creep curve. (b) Creep curves for Zr-2.5 Nb (wt%) cladding alloy [754]. (c) Creep curves for austenitic S304H steel [755]. (d) Creep curves for creep-resistant P92 steel with 9 wt% Cr [756].</figcaption></figure>

becomes important because of the potential for using these materials in forming operations. Relatively high elongations, of the order of a few hundreds of percent, were first reported in the scientific literature about one hundred years ago [763, 764] but it was only later, in 1934, that a report appeared from Pearson in England documenting a remarkable tensile elongation of ~1950% in a near-eutectic Bi-Sn alloy together with a similar high elongation of ~1505% in a Pb-Sn alloy when these samples were pulled to failure at room temperature [24]. The result for the Bi-Sn alloy is shown in Fig. 36 where the tensile sample has been coiled after failure to facilitate the recording of a photographic record. Although this result was unique and truly remarkable, it attracted little interest in western scientific circles where it remained simply a laboratory curiosity. Nevertheless, similar investigations were undertaken in the Soviet Union and numerous reports appeared in the Russian literature describing the potential for achieving high elongations in various metals when pulling in tension. In fact, it was the translation of the Russian word *sverkhplastichnost', meaning “ultrahigh plasticity”, that led to the introduction of the new word of “superplasticity” in the English language literature when it first appeared in Chemical Abstracts in 1947 [765].

It was the publicity from these Russian articles, and especially the publication of a comprehensive review of the Russian results [766], that prompted establishing a superplastic testing facility at M.I.T. and the

subsequent demonstration that superplastic forming provided the potential for fabricating, relatively easily, complex curved shapes that may be used for many industrial applications [767]. This represented the nucleus of the modern superplastic forming industry which now processes many thousands of tons of sheet metals and produces beautifully curved products that have many applications in numerous consumer and architectural applications and especially in fabricating the bodies and many major parts for the aerospace and automotive industries. A review was presented earlier describing the transition of superplasticity from a laboratory curiosity to a major tool in modern industrial metal forming operations [768]. Full details of superplastic forming are now available [769, 770] including overviews [771–774] and descriptions of the development of applications in specific industries such as in the manufacture of cars [775].

Superplastic flow is a diffusion-controlled creep process and it is reasonable to anticipate that it will be governed by the conventional rate equation that is used to denote the steady-state creep rate in all crystalline materials. Specifically, in high-temperature creep, the steady-state creep rate for all flow mechanisms is expressed through a general creep relationship (Equation 7) [723, 776], given in the previous chapter. Early tests were conducted in superplasticity where tensile specimens were pulled at the same high temperature but using a different strain rate for each sample and these results showed that the
<figure><img src="image_106.png" /><figcaption>**Fig. 35.** Stress dependences of (a,c) the minimum creep rate $\dot{\varepsilon}_{\min}$, and (b,d) the time to fracture $t_f$ for (a,b) Zr-2.5 Nb (wt%) alloy [754] and (c,d) P92 steel [756]. The creep results for coarse-grained materials published by Pahutova *et al.* [759], Hasegawa [760], Sawada *et al.* [761], and Lee *et al.* [762] are also listed.</figcaption></figure>

<figure><img src="image_107.png" /><figcaption>**Fig. 36.** An exceptional superplastic elongation of ~1950% in a Bi-Sn alloy, reported by Pearson [24].</figcaption></figure>

flow stress varied with the strain rate through three distinct regions where region I at low strain rates was not superplastic with a value of $m \approx 0.2$, region II at intermediate strain rates exhibited superplastic flow with $m \approx 0.5$ and region III at high strain rates was again not

superplastic with $m \approx 0.2$ [777]. These results demonstrate that the strain rate sensitivity is close to ~0.5 in superplastic flow and comprehensive sets of experiments, covering a range of experimental variables, showed that superplastic flow required a small grain size, typically less than ~10 µm, and a temperature typically higher than ~0.5$T_m$ where $T_m$ is the absolute melting temperature [778]. By using experimental data to construct deformation mechanism maps for superplastic materials [779], it was established that the critical grain size delineating the onset of superplastic flow is a grain size equal to or smaller than the equilibrium grain size that forms within the grains under creep conditions. These equilibrium grain sizes are similar for metals [720], ceramics [780] and geological materials [781, 782].

In superplasticity, the polycrystalline grains remain essentially equiaxed so that the dominant flow process is grain boundary sliding [783] but this must be accompanied by the occurrence of some intragranular slip to prevent the opening of cracks at the grain boundaries. Experimental evidence is available confirming the occurrence of this slip [784–787] including some recent reports where tests were conducted on a superplastic Al-Mg-Li alloy [788–790]. Using experimental results, a model for superplasticity was developed where grain boundary sliding occurs on a boundary and thereby produces a stress concentration at a triple point, this leads to slip in the next grain so that the dislocations pass through the grain and pile up at the opposite grain boundary in the absence of any subgrain boundaries and finally the rate of flow is
controlled by the climb of these dislocations into the boundary. For these conditions, the superplastic strain rate is given by the general creep relationship with $D = D_{gb}$ for grain boundary diffusion, $n = 2$, $p = 2$ and with A having a value of ~10. Based on the available experimental data, superplasticity is now defined as an elongation of at least 400% and a strain rate sensitivity close to $m \approx 0.5$ so that the stress exponent is $n \approx 2$ [346].

The requirement of a small grain size for superplasticity was achieved initially in the superplastic forming industry by subjecting metals to appropriate thermo-mechanical treatments but these procedures were not capable of producing grain sizes smaller than ~2–3 µm. This situation changed in 1988 with a Russian publication showing that a much smaller grain size may be achieved using the procedure now known as HPT [33]. This report introduced the processing of metals using SPD techniques and this approach has now been adopted and investigated in many laboratories around the world. Thus, materials have been processed to give submicrometer or nanometer grain sizes using the procedures of HPT [177], ECAP [193] and very recently using the new processing technique of t-HPS [54, 159]. To obtain a direct comparison with the very early work of Pearson [24], recent investigations have been conducted using t-HPS on various Bi-Sn alloys that are close to the eutectic structure [223]. An example of the excellent superplasticity that may be attained by t-HPS is shown in Fig. 37 where an elongation of 2320% was achieved after processing through 100 turns and pulling to failure at room temperature [224].

In summary, superplasticity refers to a tensile elongation of at least 400% and a strain rate sensitivity close to ~0.5. This requires a very fine grain size, typically smaller than ~10 µm, and in practice, exceptionally small grain sizes, in the submicrometer or nanometer range, may be achieved using SPD processing. Recent experiments using these new SPD techniques have demonstrated the potential for achieving excellent superplastic properties.

## 5.5. Low- and room-temperature superplasticity

As mentioned earlier, high-temperature plastic flow, including superplasticity, can be expressed by the general creep equation (Equation 7) [791]. The temperature dependence of superplasticity arises from the presence of the diffusion coefficient in the general creep equation. The creep equation shows that decreasing grain size increases strain rate and decreases the temperature of superplasticity. Such an effect of grain size on superplasticity leads to two types of superplasticity: low-temperature superplasticity and high-strain rate superplasticity. As the most effective grain refinement techniques, SPD methods have been used effectively to attain significant grain refinement leading to low-temperature superplasticity. Al-, Mg- and Ti-based alloys are the most commonly studied alloy systems to achieve low-temperature superplasticity using SPD. Details of SPD processing of these alloys and principles of grain refinement were described in detail in a previously published overview paper

<figure><img src="image_108.png" /><figcaption>**Fig. 37.** Appearance of Bi-43Sn (wt%) samples after processing by t-HPS for 100 turns and pulling to failure at 298 K [224]: the elongation of 2320% exceeds the elongation of 1950% reported in early experiments by Pearson [24].</figcaption></figure>

[792]. In this section, superplastic elongation values in the severely deformed alloys and their microstructural origin are described.

Low-temperature superplastic elongations reported in severely deformed alloys are shown in Fig. 38a-d. In general, elongation to failure of Mg-based alloys is scattered in a wide range between 330% and 1330% [793–801] with an exception of 2400% which is the highest low-temperature superplastic elongation in severely-deformed alloys (Fig. 38a). Ti-based alloys, on the other hand, exhibit superplastic elongations between 474% and 1400% (Fig. 38b) [802–809]. Relatively lower superplastic elongations below 700% were reported in the Al-based alloys (Figs. 38c and 38d) [810–823]. As an extreme example of low-temperature superplasticity, some low-melting point alloys exhibited superplastic elongation even at room temperature [824–831]. Mostly, the Al-Zn alloy system has been studied to attain room-temperature superplasticity. The highest elongation at room temperature was reported in the ECAP-processed Zn-0.3Al alloy as 1000% (Fig. 39) [829].

The main reason for high superplastic elongations in the severely deformed alloys was stated to be their equiaxed and UFG microstructure having large grain boundary area leading to easy grain boundary sliding as the main deformation. However, more recently it was shown that engineering grain-boundary composition and diffusion could also be used to achieve low-temperature superplasticity. Diffusion coefficient *D* in the creep equation should be equal to the coefficient for grain boundary diffusion for grain boundary sliding. The coefficient of diffusion depends strongly on the deformation temperature, and a higher temperature brings about a higher diffusion coefficient. Thus, the diffusion coefficient should be increased without increasing temperature to achieve low-temperature superplasticity. Besides the UFG microstructure, zinc segregation at the difficult-to-slide Al/Al grain boundaries was stated to be the main reason for lowering the superplastic temperature of HPT-processed Al-4.8Zn-1.2Mg-0.14Zr (wt%) alloy [811, 812]. Segregation of zinc at grain boundaries accelerates diffusion and enhances sliding which results in superplasticity at lower temperatures [811, 812]. A similar result was also reported in the friction-stir-processed Mg-9Li-1Zn (wt%) alloy [799, 832]. The β phase (lithium solid solution) particles precipitated at the grain boundaries and triple junctions contributed to the stress relaxation and accommodated grain boundary sliding [832]. It was also specified that lithium segregation at Mg-rich α/α phase boundaries increases the boundary diffusivity and contributes to phase boundary sliding at relatively low temperatures leading to high superplastic elongation of 1104% in Mg-9Li-1Zn alloy [799]. All these results show that besides the UFG formation, controlling the grain boundary composition and grain-boundary segregation using a proper SPD method and alloying element selection is effective for low- and room-temperature superplasticity (e.g. addition of lithium, sodium, calcium, strontium, selenium, bismuth and tellurium to magnesium can enhance the diffusivity) [351, 833].

The effect of grain-boundary segregation on the mobility of grain boundaries was reported to lead to the achievement of room-temperature superplasticity in Al-30Zn (at%) [351] and Mg-8Li (wt%) [350] alloys. One of the most interesting results of grain boundary engineering to attain room-temperature superplasticity was reported in the Al-Zn alloy [351]. It was reported that 200 turns of HPT did not cause further grain refinement compared to lower strains but resulted in the segregation of zinc atoms at α/α grain boundaries. High zinc concentration enhanced grain-boundary diffusion along these boundaries and made them favorable for grain boundary sliding. Thus, improved diffusivity at the α/α boundaries activated grain boundary sliding as the main deformation mechanism and brought about high superplastic elongation in Al-30Zn at room temperature [351]. HPT processing of Mg-8Li alloy also resulted in the segregation of lithium atoms at the α/α boundaries and enhanced diffusion capability of these boundaries [350]. Such a modification on the grain boundaries resulted in a high superplastic elongation of 440% at room temperature corresponding to
<figure><img src="image_109.png" /><figcaption>**Fig. 38.** The variation of superplastic elongation values with strain rate at different temperatures in severely-deformed alloys: (a) Mg-based alloys, (b) Ti-6Al-4 V (wt %) alloy, (c) 7xxx series of Al-based alloys and (d) other Al-based alloys [792].</figcaption></figure>

<figure><img src="image_110.png" /><figcaption>**Fig. 39.** Room temperature superplastic elongations of some severely deformed alloys [792].</figcaption></figure>

0.35T_m which is the lowest homologous temperature for the low-temperature superplasticity in the severely deformed metals.

Regarding the results summarized above it can be concluded that besides UFG formation, the type and chemical composition of grain boundaries also play an important role in decreasing the temperature for superplasticity. Thus, modification of the grain boundaries via SPD can be considered a promising way to achieve low- and room-temperature superplasticity.

## 6. Functional properties

Although SPD-processed materials primarily received attention for

their mechanical properties, there is a general trend in the field toward functional properties. Since these materials show more than one functionality and their functional properties are superior to conventional engineering materials, they are sometimes referred to as multifunctional or superfunctional materials. A review of the recent literature published on the functional properties of SPD-processed materials suggests that the main investigated functional properties include: electromagnetic properties (electrical conductivity [834, 835], superconductivity [836, 837], thermoelectric properties [838, 839], dielectric properties [840] and magnetic properties [841]), thermal conductivity [842], catalytic properties (catalyst [843], photocatalyst [844] and electrocatalyst [845]). hydrogen-related applications (hydrogen storage [846], hydrogen production [847] and hydrogen embrittlement [848]), corrosion resistance [849], irradiation resistance [850], biocompatibility [851], etc. In the following sections, the main functional properties of SPD-processed materials are reviewed.

### 6.1. Electrical conductivity

Electrical conductivity (σ_E, S/m) is a property of materials defined as the capability to allow electron flow under an applied electric field [852–854], or the inverse of electrical resistivity (ρ, Ωm) and calculated using Equation 11.

$$ \sigma_E = \frac{1}{\rho_E} \qquad (11) $$

According to the International Annealed Copper Standard (IACS%), the electrical conductivity can be expressed as a percentage of that of annealed copper (100 IACS%). Conductive metallic materials should exhibit high strength and good ductility, with high thermal stability and electrical conductivity. For pure metals, the main scattering mechanism consists of the interaction between conduction electrons and the