We are IntechOpen, the world's leading publisher of Open Access books Built by scientists, for scientists

3,500+

Open access books available

111,000+

International authors and editors

115M+

Downloads

Our authors are among the

Top 1%

most cited scientists

12.2%

Contributors from top 500 universities

Selection of our books indexed in the Book Citation Index in Web of Science™ Core Collection (BKCI)

## Interested in publishing with us? Contact<EMAIL_ADDRESS>
Numbers displayed above are based on latest data collected. For more information visit www.intechopen.com

## **Meet the editor**

Vakhrushev Alexander Vasilyevich received his PhD degree in Technical Sciences from Izhevsk Institute of Mechanical Engineering, Russia, in 1982, and degree of Doctor of Sciences in Physics and Mathematics from the Institute of Continuous Media Mechanics of Ural Branch of Russian Academy of Sciences, Russia, in 2003. Now, he is the head of the Department of "Nanotechnol-

ogy and Microsystems Technics" of Kalashnikov Izhevsk State Technical University and head of the Department of "Mechanics of Nanostructures" of the Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences. He has over 400 publications to his name, including monographs, articles, reports, reviews, and patents. He has received several awards, including an Academician A. F. Sidorov Prize from the Ural Division of the Russian Academy of Sciences for significant contribution to the creation of the theoretical fundamentals of physical processes taking place in multilevel nanosystems and Honorable Scientist of the Udmurt Republic. He is currently a member of the editorial board of several journals, including Computational Continuum Mechanics, Chemical Physics and Mesoscopia, and Nanobuild. His research interests include multiscale mathematical modeling of physical-chemical processes into the nanoheterosystems at nano-, micro-, and macrolevels; static and dynamic interaction of nanoelements; and basic laws relating the structure and macrocharacteristics of nanoheterostructures.

## Contents

#### **Preface XI**

## Preface

In recent years, nanotechnology is the basis for the development of modern production. This determined the urgency of the intensive development of the new direction of mechanics and nanomechanics, for the scientific description of nanotechnological processes and the solu‐ tion of a number of topical nanotechnology problems: reduction of time to prepare for the production, acceleration of technological processes, automation of technological processes, reduction in the cost of production, improvement in the quality of materials and products, preparation of high-performance materials, improvement of the ecology, etc. How are nano‐ technological processes different from traditional technologies and how does nanomechan‐ ics fundamentally differ from classical mechanics? The specific feature of the physical processes in nanoscale is that the key phenomena determining the behavior of a nanoscale system in real time at the macroscale take place at small space and time scales. The proper‐ ties of a nanoscale system depend not only on the properties of its constituent elements but also on the regularities of the spatial arrangement of the nanoscale system and the parame‐ ters of the nanoelement interaction. So, classical physical body mechanics, which is based on the hypothesis of continuum per that all the properties of a body are determined by the me‐ chanics of continuum, cannot be applied to nanoscale systems. In this connection, it is obvi‐ ous that describing of nanosystems requires the use of different physical models and mathematical methods and a detailed complex analysis of the "history" of the nanoscale ma‐ terial existence at different structural scales. Therefore, for nanosystems, we use currently nanomechanics, which allows to describe their behavior and properties at different structur‐ al levels. That is why, the development of nanomechanics is very necessary. Nanomechanics includes different physics and mathematics models: quantum mechanics, molecular dynam‐ ics, mesodynamics, and continuum mechanics. Because of the multilevel nature of nanotech‐ nological processes, the problems of nanomechanics are very complex.

This book presents a collection of eight scientific papers on theoretical and practical advan‐ ces in nanomechanics at different structural levels. Topics included in the book cover a wide range of research in the field of nanomechanics: thermomass theory of nanosystems, defor‐ mation of nanomaterials, interface mechanics of assembly carbon nanotube, nanomechanics on surface, molecular interactions and transformations, nanomechanical sensors, nano‐ beams and micromembranes, nanostructural organic and inorganic materials, green synthe‐ sis of metallic nanoparticles. The main goal of these works is the establishment of the nanosystem macroparameter dependence on its nanoparameters using nanomechanics.

Chapter 1 presents the complete material on the problem of interfacial mechanical behaviors in carbon nanotube assemblies. Chapter 2 presents the complete investigations on regulari‐ ties of deformation at high strain rates and damage and fracture of ultrafine-grained alloys in static and in dynamic loading conditions. Chapter 3 presents the complete material on the

problem of changes in the parameters of thermal conductivity when the size of the nanosys‐ tem changes. In Chapter 4, it is shown how to single out small ligands able to inhibit protein misfolding, to measure energetics of surface-confined ferritin during iron loading, and to realize a universal probe for ammine-based designer medication. Chapter 5 presents the complete experimental investigation, analytical calculation, and numerical simulation by the method of MFE of micromembranes supported by serial-parallel connected hinges. Chapter 6 presents the modified couple stress theory for static, vibration, and buckling analysis of nanobeams. Chapter 7 presents the eco-friendly methods of obtaining nanostructures using plant experimental results of metallic and carbon nanostructures formation *ficus-indica* using the extract from *Opuntia* cladodes. Chapter 8 presents the results of experimental and simu‐ lation study of structure and properties of materials, surface of which was modified by ori‐ ented carbon nanotubes and, additionally, was treated by surface electromagnetic waves.

This book will be useful for engineers, technologists, and researchers interested in methods of nanomechanics and in advanced nanomaterials with complex behavior and their applications.

I would like to express my appreciation to all the contributors of this book. My special thanks to the Publishing Process Manager, Ms. Martina Usljebrka, and other staff of InTech publishing for their kind support and great efforts in bringing the book to completion.

#### **Prof. Alexander Vakhrushev**

Head of the Department of "Mechanics of Nanostructures" Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Head of the Department of "Nanotechnology and Microsystems," Kalashnikov Izhevsk State Technical University, Izhevsk, Russia

## **Interfacial Mechanical Behaviors in Carbon Nanotube Assemblies**

Xiaohua Zhang

problem of changes in the parameters of thermal conductivity when the size of the nanosys‐ tem changes. In Chapter 4, it is shown how to single out small ligands able to inhibit protein misfolding, to measure energetics of surface-confined ferritin during iron loading, and to realize a universal probe for ammine-based designer medication. Chapter 5 presents the complete experimental investigation, analytical calculation, and numerical simulation by the method of MFE of micromembranes supported by serial-parallel connected hinges. Chapter 6 presents the modified couple stress theory for static, vibration, and buckling analysis of nanobeams. Chapter 7 presents the eco-friendly methods of obtaining nanostructures using plant experimental results of metallic and carbon nanostructures formation *ficus-indica* using the extract from *Opuntia* cladodes. Chapter 8 presents the results of experimental and simu‐ lation study of structure and properties of materials, surface of which was modified by ori‐ ented carbon nanotubes and, additionally, was treated by surface electromagnetic waves. This book will be useful for engineers, technologists, and researchers interested in methods of nanomechanics and in advanced nanomaterials with complex behavior and their applications. I would like to express my appreciation to all the contributors of this book. My special thanks to the Publishing Process Manager, Ms. Martina Usljebrka, and other staff of InTech publishing for their kind support and great efforts in bringing the book to completion.

VIII Preface

**Prof. Alexander Vakhrushev**

Ekaterinburg, Russia

Izhevsk, Russia

Institute of Continuous Media Mechanics

Head of the Department of "Mechanics of Nanostructures"

Head of the Department of "Nanotechnology and Microsystems,"

of the Ural Branch of the Russian Academy of Sciences,

Kalashnikov Izhevsk State Technical University,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67764

#### **Abstract**

Interface widely exists in carbon nanotube (CNT) assembly materials, taking place at different length scales. It determines severely the mechanical properties of these assembly materials. In this chapter, I assess the mechanical properties of individual CNTs and CNT bundles, the interlayer or intershell mechanics in multiwalled CNTs, the shear properties between adjacent CNTs, and the assembly-dependent mechanical and multifunctional properties of macroscopic CNT fibers and films.

**Keywords:** carbon nanotube, assembly materials, mechanics, interface

### **1. Introduction**

Carbon nanotubes (CNTs) are hollow cylinders consisting of single or multiple sheets of graphite (graphene) wrapped into a cylinder. After the first observation in 1991 by Iijima [1], extensive work has been carried out to CNTs toward their broad mechanical, electronic, thermal, and optical applications [2, 3]. The fundamental mechanical properties, such as their stiffness, strength, and deformability, have been investigated with extensive theoretical and experimental researches, and been well reviewed, in the past two decades [4–8]. Nowadays, for industrial and engineering applications, CNTs have been assembled into macroscopic materials such as fibers, films, forests, and gels [9–15]. Due to the assembly feature of these materials, the interfacial structure between CNTs always plays a crucial role in determining the tensile or compressive behavior, dynamic response, and coupling phenomenon between

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

multiple physical properties that take place at the interfaces. Therefore, the utilization efficiency of the mechanical property from individual CNTs to their assembly is a sophisticated function of the assembly structure and types of interfacial interactions.

In this chapter, I will review the mechanics of individual CNTs, discuss the sliding friction between CNTs, and report our recent progresses on the fabrication technique and mechanical properties of macroscopic CNT assembly materials. The general features of the assembly design and interface design will be illustrated from the perspective of interface engineering. The chapter is organized as follows. Section 2 contains a brief description of the mechanical properties of individual CNTs, in terms of modulus, strength, compressibility, and deformability. Section 3 describes the interlayer (intershell) sliding of multiwalled CNTs (MWCNTs) and intertube friction between adjacent CNTs, and the strategies to enhance the interfacial frictions. Section 4 discusses the recent investigations on the interfacial mechanics in macroscopic CNT assembly materials, especially CNT fibers and films where the CNTs are highly aligned or highly entangled. Finally, the chapter concludes with a brief summary and gives an outlook on future developments in the field.

## **2. Mechanical properties of carbon nanotubes**

#### **2.1. Young's modulus and tensile strength**

The basic mechanical properties of CNT are strongly related to the basic properties of a graphene sheet. In these materials, carbon atoms are covalently bonded with three nearest carbon atoms in a hexagonal lattice by forming three σ bonds in the sheet plane and one delocalized π-bond over the basal plane. As the sp2 σ bond is shorter and stronger even than the sp3 bond in diamond, the axial elastic modulus of CNT and graphene is super high, as expected to be up to several TPa [6, 7]. The first experimental study on the modulus was based on the analysis of thermal vibration of MWCNTs, which showed a wide range of 0.4–4.15 TPa [16]. Later, the modulus was also estimated by the compressive response using micro Raman spectroscopy and was 2.8–3.6 TPa for singlewalled CNTs (SWCNTs) and 1.7–2.4 GPa for MWCNTs [17]. Direct tensile tests showed the modulus ranged from 270 to 950 GPa for individual MWCNTs [18], and from 320 to 1470 GPa when several SWCNTs bundled together as a CNT rope [19]. Besides the experimental evaluations, theoretical estimations also show the similar results. For example, by using an empirical Keating Hamiltonian with parameters determined from first principles, a modulus ranging from 1.5 to 5.0 TPa was estimated [20]. A molecular dynamics (MD) approach showed a modulus of ~1 TPa and a shear modulus of ~0.5 TPa and predicted that chirality, radius, and number of walls have little effect on the value of Young's modulus [21].

Different from the modulus estimation, measuring the tensile strength of CNTs is a very challenging task. Compared with experiment, it is easier to compute the strength by considering the effects of defects [22, 23], loading rate, temperature [24], and number of walls [25]. Typically, the fraction of CNT involves bond breakage and/or rotation, usually resulting in the formation of specific types of dislocation, such as the pentagon-heptagon (5-7), (5-7-7-5), (5-7-5-8-5) defects [26]. MD simulations showed that CNT under tension behaves as a brittle material at high strain (15%) and low temperature (1300 K), or as a ductile material at low strain (3%) and high temperature (3000 K) [26–28]. Such tensile behaviors depend on the evolution of the dislocation. For example, the (5-7-7-5) dislocation can either separate into two (5-7) pairs to result in a ductile transformation or involve into a crack to result in a brittle fracture. An alternative pathway for the fracture of CNT was also proposed by the direct bond-breaking through the formation of a series of virtual defects at high tensions [23]. These studies were usually based on the consideration of the formation of energy for the dislocations. However, another MD study showed that the fracture behavior is almost independent of the separation energy and to depend primarily on the inflection point in the interatomic potential [22]. The fracture strength should be moderately dependent on tube chirality, and the strength and fracture strain were estimated to be 93.5–112 GPa and 15.8–18.7%, respectively. **Figure 1a** shows two different stress-strain curves for a (20,0) CNT, where the modified Morse potentials with interatomic force peaks at 19 and 13% strain were used. To show the effect of structural defect, a result for a missing atom is provided where the strength was reduced by about 25%.

multiple physical properties that take place at the interfaces. Therefore, the utilization efficiency of the mechanical property from individual CNTs to their assembly is a sophisticated

In this chapter, I will review the mechanics of individual CNTs, discuss the sliding friction between CNTs, and report our recent progresses on the fabrication technique and mechanical properties of macroscopic CNT assembly materials. The general features of the assembly design and interface design will be illustrated from the perspective of interface engineering. The chapter is organized as follows. Section 2 contains a brief description of the mechanical properties of individual CNTs, in terms of modulus, strength, compressibility, and deformability. Section 3 describes the interlayer (intershell) sliding of multiwalled CNTs (MWCNTs) and intertube friction between adjacent CNTs, and the strategies to enhance the interfacial frictions. Section 4 discusses the recent investigations on the interfacial mechanics in macroscopic CNT assembly materials, especially CNT fibers and films where the CNTs are highly aligned or highly entangled. Finally, the chapter concludes with a brief summary and gives

The basic mechanical properties of CNT are strongly related to the basic properties of a graphene sheet. In these materials, carbon atoms are covalently bonded with three nearest carbon atoms in a hexagonal lattice by forming three σ bonds in the sheet plane and one delocalized π-bond over

the axial elastic modulus of CNT and graphene is super high, as expected to be up to several TPa [6, 7]. The first experimental study on the modulus was based on the analysis of thermal vibration of MWCNTs, which showed a wide range of 0.4–4.15 TPa [16]. Later, the modulus was also estimated by the compressive response using micro Raman spectroscopy and was 2.8–3.6 TPa for singlewalled CNTs (SWCNTs) and 1.7–2.4 GPa for MWCNTs [17]. Direct tensile tests showed the modulus ranged from 270 to 950 GPa for individual MWCNTs [18], and from 320 to 1470 GPa when several SWCNTs bundled together as a CNT rope [19]. Besides the experimental evaluations, theoretical estimations also show the similar results. For example, by using an empirical Keating Hamiltonian with parameters determined from first principles, a modulus ranging from 1.5 to 5.0 TPa was estimated [20]. A molecular dynamics (MD) approach showed a modulus of ~1 TPa and a shear modulus of ~0.5 TPa and predicted that chirality, radius, and number of walls

Different from the modulus estimation, measuring the tensile strength of CNTs is a very challenging task. Compared with experiment, it is easier to compute the strength by considering the effects of defects [22, 23], loading rate, temperature [24], and number of walls [25]. Typically, the fraction of CNT involves bond breakage and/or rotation, usually resulting in the formation of specific types of dislocation, such as the pentagon-heptagon (5-7), (5-7-7-5), (5-7-5-8-5) defects [26]. MD simulations showed that CNT under tension behaves as a brittle

σ bond is shorter and stronger even than the sp3

bond in diamond,

function of the assembly structure and types of interfacial interactions.

an outlook on future developments in the field.

**2.1. Young's modulus and tensile strength**

the basal plane. As the sp2

2 Nanomechanics

**2. Mechanical properties of carbon nanotubes**

have little effect on the value of Young's modulus [21].

The tensile strength and the fracture of CNT were also measured directly with experiment [18, 19]. The measurement of 19 MWCNTs showed a strength of 11–63 GPa and a strain at break up to 12% [18]. The failure of MWCNTs was described in term of the "sword-insheath" type fracture, where the outermost shell broke first followed by the pull out of the rest of the shells from the outermost shell. When SWCNTs were bundled to be a rope, the tensile strength was measured to be 13–52 GPa, based on 15 measurements, and the strain at break was up to 5.3%, see **Figure 1b** [19]. The stretchability of CNT was also experimentally obtained by deforming freely suspended SWCNT ropes, where the maximum strain was up to 5.8 ± 0.9% [29]. By measuring the stress-induced fragmentation of MWCNTs in a polymer matrix, the tube strength was up to 55 GPa [30]. Another pulling and bending tests on individual CNTs in-situ in a transition electron microscope (TEM) showed a tensile strength of ~150 GPa, suggesting that the strength is a large fraction of the elastic modulus [31].

**Figure 1.** (a) A strong dependence on the inflection point in the interatomic potential can be seen from the stress-stain curves for a (20,0) CNT, and a missing atom has also a significant effect on strength, reducing it by about 25% [22]. Experimental measurements on MWCNTs are provided for comparison [18]. (b) Eight stress-strain curves obtained from the tensile-loading experiments on SWCNT ropes [19].

#### **2.2. Compressibility and deformability**

Different from the high rigidity and high strength along the axial direction, CNT is relatively compressible and deformable in the transverse direction. When individual SWCNTs are bundled together, significant deformation could occur by van der Waals (vdW) interaction between the adjacent tubes [32]. Fully collapsed MWCNTs were first observed with TEM [33]. Large diameter CNTs could also form the partial and full collapse on substrate [34–36]. The structural deformation can be induced by applying pressure. Various experiments on SWCNT bundles have shown clear evidence of structural deformation or transition [37–42]. MD simulations revealed that the compressibility and deformability are dependent on the tube diameter and the number of walls [43]. By applying a certain high pressure, there could be a circular-to-elliptical shape transition of the tube's cross section for either individual CNTs or their bundles [44–51]. These structural deformations are all reversible upon unloading the pressure. In a different way, a very large force exerted on CNT could still produce reversible and elastic deformation, and that radial mechanical forces might not be capable of cutting a CNT [43]. By examining the ballistic impact and bouncing-back processes, large diameter CNTs could withstand high bullet speeds [52].

Upon compressing, bending, or twisting, structural deformations of CNT become more complicated. With an increasing compression stress, different buckling patterns in CNT at the point of instabilities can be created [53]. As shown in **Figure 2**, each shape change corresponds

**Figure 2.** The strain energy (a) displays four singularities corresponding to shape changes (b–e) with increasing the axial compression [53].

to an abrupt release of energy and a singularity in the stress-strain curve. MD simulations showed that the presence of intertube vdW interactions tends to weaken the CNT bundles under compression [55]. On the other hand, with increasing the tube diameter, the bending modulus was found to decrease sharply [56], as a rippling mode becomes energetically favorable [57, 58]. The modeling on the wavelike distortion indicated that there is a critical diameter at a given load and a CNT length, for the emergence of the rippling mode [59]. It was also found that thick MWCNTs are very prone to develop rippling deformations in bending and twisting, governed by the interplay of strain energy relaxation and intertube interactions [58, 60]. **Figure 3** shows experimental observations of partially collapsed segments in freestanding and twisted MWCNTs with TEM [54].

**Figure 3.** TEM images showing a suspended, fully collapsed, and twisted MWCNT (a), and a freestanding, fully collapsed, and twisted MWCNT (b) on a lacy carbon TEM grid [7, 54].

### **3. Interlayer and intertube interactions**

#### **3.1. Sliding between MWCNT shells**

**2.2. Compressibility and deformability**

4 Nanomechanics

compression [53].

Different from the high rigidity and high strength along the axial direction, CNT is relatively compressible and deformable in the transverse direction. When individual SWCNTs are bundled together, significant deformation could occur by van der Waals (vdW) interaction between the adjacent tubes [32]. Fully collapsed MWCNTs were first observed with TEM [33]. Large diameter CNTs could also form the partial and full collapse on substrate [34–36]. The structural deformation can be induced by applying pressure. Various experiments on SWCNT bundles have shown clear evidence of structural deformation or transition [37–42]. MD simulations revealed that the compressibility and deformability are dependent on the tube diameter and the number of walls [43]. By applying a certain high pressure, there could be a circular-to-elliptical shape transition of the tube's cross section for either individual CNTs or their bundles [44–51]. These structural deformations are all reversible upon unloading the pressure. In a different way, a very large force exerted on CNT could still produce reversible and elastic deformation, and that radial mechanical forces might not be capable of cutting a CNT [43]. By examining the ballistic impact and bouncing-back processes, large diameter CNTs could withstand high bullet speeds [52].

Upon compressing, bending, or twisting, structural deformations of CNT become more complicated. With an increasing compression stress, different buckling patterns in CNT at the point of instabilities can be created [53]. As shown in **Figure 2**, each shape change corresponds

**Figure 2.** The strain energy (a) displays four singularities corresponding to shape changes (b–e) with increasing the axial

Different from SWCNTs, the interlayer interactions in MWCNTs exhibit interesting sliding phenomena during the tensile stretching and self-oscillation. By modeling of the interlayer interaction with different atomic potentials, such as the classic Lennard-Jones (LJ) potential and the registry-dependent Kolmogorov-Crespi (KC) potential (zeroth generation RDP0 [61] and first generation RPD1 [62]), could cause significantly different energy corrugation between graphitic layers [62–65]. Nevertheless, the interlayer sliding has been systematically studied despite the type of atomic potential. Experiments have also shown the interlayer sliding and superlubricity of CNTs.

Experimental measurements on the dependence of the sliding force against the contact length between the MWCNT shells suggested several responsible sources including the surface tension, the shear elastic force, and the edge (tube termination) effect force [66]. The shear strength was found to be 0.08–0.3 MPa depending on the interlayer commensurability. After the inner shells were pulled out from the outer shells, spontaneous retraction was observed with TEM due to the attractive vdW forces between these shells [67]. The interlayer static and dynamic shear strengths were estimated to be 0.43–0.66 MPa. The telescoping motion of an MWCNT also showed an ultralow friction, below 1.4 × 10−15 N per atom (8.7 × 10−4 meV Å−1) [68]. More direct observation of the superlubricity in doublewalled CNTs (DWCNTs) was conducted by extracting the inner shell out from a centimeters-long DWCNT, where the inner-shell friction (vdW force) was estimated to be 1.37–1.64 nN (the total number of atoms was unknown, yet could be over 108 –109 for a tube length of 1 cm) [69], corresponding to a friction force of about 10−6–10−5 meV Å−1 per atom. By following the low-friction induced telescoping, gigahertz oscillators were theoretically proposed based on the oscillatory extrusion and retraction of the inner shells [70–77], and the interlayer commensurability determines the rate of energy dissipation during the oscillation [71]. The friction force between oscillatory layers was estimated to range from 10−17 to 10−14 N per atom, about 6 × 10−6–0.006 meV Å−1 [73]. Similarly, the rotation between CNT shells and the rotational friction was observed or measured by experiments and simulations [78–81]. The rotational friction is a broadband phenomenon, as it does not depend strongly on a specific vibrational mode but rather appears to occur from the aggregate interactions of many modes at different frequencies [82].

At high sliding speeds, the friction between CNT layers was not hydrodynamical, in fact not even monotonic with the sliding speed [83]. A high speed can develop a sharp friction peak and onset parametric excitation of CNT's "breathing" phonon modes. **Figure 4a** shows that there is

**Figure 4.** (a) There is a massive increase in friction at ~1100 m s−1 for the (5,5)@(10,10) DWCNT [83]. (b) The center-ofmass angular momentum *J* CM (top) and the sliding frictional force per inner tube atom (bottom) as functions of the sliding speed [84]. A, B, and C are three resonance regions related the giant friction forces.

a massive increase in sliding friction at a speed of ~1100 m s−1 for a (5,5)@(10,10) DWCNT. The highest friction force could be up to 170 pN, corresponding to ~0.15 meV Å−1 per inner tube atom. The main source of the interlayer friction was believed to be the inner nanotube terminations [85], while the "bulk" friction was unfortunately considered to be irrelevant.

To understand the "bulk" frictional behavior, two groups of studies were carried out [65, 84, 86]; pulling simulations where a constant external force was applied on each atom of the inner tube along the tube axis, and rigid sliding simulations where the inner tube was constrained to slide as a whole at a fixed speed. The pulling simulation revealed a static friction (depinning) force of 0.02 meV Å−1 at 300 K and 0.1 meV Å−1 at 50 K for the (5,5)@(10,10) DWCNT. After the depinning, the speed of the inner tube jumps directly to plateaus. Three speed plateaus are seen at v ≈ 450, 720, and 780 m s−1. This phenomenon is ubiquitous as it is also observed for an incommensurate case where a chiral (11,2) tube slides inside a (12,12). The general occurrence of plateaus and jumps is a natural consequence of frictional peaks for growing the speed. **Figure 4b** shows sharp frictional peaks near *v* ≈ 450, 570, 720, and an important threshold onset near 780 m s−1. These peaks are known to generally arise out of parametric excitation of the "breathing" phonon modes, classified by an angular momentum index *n* (for tangential quantization around the tube axis). Such nonmonotonic force-speed characteristics imply a "negative differential friction," whereby an increasing applied force yields an inner tube sliding speed that grows by jumps and plateaus, rather than smoothly.

The surprise comes from analyzing the two parts of angular momentum *J* = *J* CM + *J*pseudo around the tube axis such as its center-of-mass (rigid body rotation with angular velocity *ω*) and shape-rotation ("pseudorotational") parts [65, 84]. Generally, zero at generic sliding speed due to lack of nanotube chirality, *J* pseudo = −*J*CM = 0, *J*pseudo jumps to nonzero values at the frictional peaks and past the threshold, where *J* pseudo = −*J*CM / ≠ 0, see **Figure 4b**. This is a spontaneous breaking of chiral symmetry occurring in nanoscale friction, whose mechanism is from the third- and fourth-order energy nonlinearities. The inner-tube sliding causes a washboard frequency due to the lattice periodicity *a*CC = 2.46 Å. At the critical frequencies, the '*n* = 5' or '2 + 3 = 5' excitations are observed, where the DWCNT's *n* = 5 mode is resonantly excited or the *n* = 2, 3, 5 modes are jointly excited by the simple matching condition 2 + 3 = 5. Besides these "normal" excitations (labeled A in **Figure 4b**), there are '*n* = 5s' and '2 + 3s = 5' excitations, where the 3s and 5s are the single outer tube's phonon modes. These excitations are labeled B in **Figure 4b**. The two C-peaks in **Figure 4b** are ascribed to the phenomenon of strong stickslip frictions, possibly related to the phonon modes along the tube axis.

#### **3.2. Intertube friction**

Experimental measurements on the dependence of the sliding force against the contact length between the MWCNT shells suggested several responsible sources including the surface tension, the shear elastic force, and the edge (tube termination) effect force [66]. The shear strength was found to be 0.08–0.3 MPa depending on the interlayer commensurability. After the inner shells were pulled out from the outer shells, spontaneous retraction was observed with TEM due to the attractive vdW forces between these shells [67]. The interlayer static and dynamic shear strengths were estimated to be 0.43–0.66 MPa. The telescoping motion of an MWCNT also showed an ultralow friction, below 1.4 × 10−15 N per atom (8.7 × 10−4 meV Å−1) [68]. More direct observation of the superlubricity in doublewalled CNTs (DWCNTs) was conducted by extracting the inner shell out from a centimeters-long DWCNT, where the inner-shell friction (vdW force) was estimated

length of 1 cm) [69], corresponding to a friction force of about 10−6–10−5 meV Å−1 per atom. By following the low-friction induced telescoping, gigahertz oscillators were theoretically proposed based on the oscillatory extrusion and retraction of the inner shells [70–77], and the interlayer commensurability determines the rate of energy dissipation during the oscillation [71]. The friction force between oscillatory layers was estimated to range from 10−17 to 10−14 N per atom, about 6 × 10−6–0.006 meV Å−1 [73]. Similarly, the rotation between CNT shells and the rotational friction was observed or measured by experiments and simulations [78–81]. The rotational friction is a broadband phenomenon, as it does not depend strongly on a specific vibrational mode but rather appears to occur from the aggregate interactions of many modes at different frequencies [82].

At high sliding speeds, the friction between CNT layers was not hydrodynamical, in fact not even monotonic with the sliding speed [83]. A high speed can develop a sharp friction peak and onset parametric excitation of CNT's "breathing" phonon modes. **Figure 4a** shows that there is

**Figure 4.** (a) There is a massive increase in friction at ~1100 m s−1 for the (5,5)@(10,10) DWCNT [83]. (b) The center-of-

speed [84]. A, B, and C are three resonance regions related the giant friction forces.

CM (top) and the sliding frictional force per inner tube atom (bottom) as functions of the sliding

mass angular momentum *J*

6 Nanomechanics

–109

for a tube

to be 1.37–1.64 nN (the total number of atoms was unknown, yet could be over 108

In most of the cases, individual CNTs are bundled together as a CNT rope, owing to the strong aggregation tendency between adjacent CNTs. As mentioned above, experimental measurement showed a tensile strength just up to 13–52 GPa [19], far below the ideal strength for individual CNTs. The easy sliding between adjacent CNTs has become a severe problem hindering their engineering applications. For example, slip rather than breakage of individual CNTs was observed in the fracture test of polymers reinforced by CNT bundles [87]. As CNTs can contact with each other in parallel way or at certain cross angles, the interfacial shear strengths between CNTs should be discussed separately.

The static and kinetic frictions between two perpendicular CNTs were investigated experimentally. A coefficient of friction of 0.006 ± 0.003 was obtained by sliding an MWCNT perpendicularly on a SWCNT surface, and the shear strength was derived to be 4 ± 1 MPa [88]. The shear strength was one to two orders of magnitude larger than the intershell shear strength of 0.05 MPa for MWCNTs in vacuum, possibly due to the presence of water at the intertube interface in ambient. A following experiment, namely a vertical friction loop measurement, was proposed to characterize the adhesion and friction properties between CNTs [89]. An MWCNT tip was ramped in the vertical direction against a suspended SWCNT. During ramping, a stick-slip motion was found to dominate the sliding, attributed to the presence of defectinduced or amorphous-carbon-associated high energy points on the tip surface. Surprisingly, the coefficients of static friction and shear strength were finally evaluated to be about 0.2 and 1.4 GPa, respectively.

MD simulations showed that the sliding behaviors and interfacial shear strengths between two crossly contacting CNTs are much more complicated than the frictions between CNTs and graphite, graphite and graphite, and the inner and outer shells of MWCNTs [90]. The simulation was performed on two SWCNTs in contact at different cross angles. For the parallel contact, the axial interfacial shear strengths between the zigzag-zigzag (~0.25 GPa) and armchair-armchair pairs (~0.5 GPa) are two orders of magnitude larger than those of CNTs having different chiralities (0.5–1 MPa). CNTs with diameters larger than 1 nm will slide relatively from an AB stacking position to the next nearest AB stacking position while smaller ones do not slide through AB stacking positions. For two cross contacting CNTs, the magnitude of interfacial shear strength is much less dependent upon tube chirality. The highest value of shear strength was reported to be about 1 GPa in SWCNT bundles, however, still as quite low as to be improved for applications in high-performance composite materials [91].

#### **3.3. Strategies to improve the intertube load transfer**

A molecular mechanics modeling showed that in order to make the strength of a CNT bundle as high as that of the lowest value of individual CNTs (11 GPa), the contact length should be up to ~3800 nm, by assuming the CNTs are bundled together without changing their circular cross sections [63]. With considering the vdW-force-induced radial deformation [32], the intertube distance-of-closest changes from 3.34 to 3.25 Å for (10,10) CNT bundles, the required contact distance for 11 GPa can decrease to ~1300 nm. This implies that the key to improve the intertube load transfer is the interface design between CNTs.

Twist is an effective way to induce strong radial deformation for CNT bundles. **Figure 5a** shows the cross sections obtained from MD simulations with increasing the twist level and **Figure 5b** shows the corresponding transferred load due to the shape deformation at twist angles of 0, 30, 60, 90, 120, 150, 180, and 210° [63]. It was observed that the individual CNTs start to collapse in the cross section, and therefore, more atoms are in close contact. For the case of no twist, a force of only ~0.048 eV Å−1 is transferred to the center tube, while at 120° the transferred load increases to 1.63 eV Å−1. Clearly, the radial deformation strongly depends on the twist angle, which consequently changes the nature of the contact and contributes to a new interlayer tribology.

The static and kinetic frictions between two perpendicular CNTs were investigated experimentally. A coefficient of friction of 0.006 ± 0.003 was obtained by sliding an MWCNT perpendicularly on a SWCNT surface, and the shear strength was derived to be 4 ± 1 MPa [88]. The shear strength was one to two orders of magnitude larger than the intershell shear strength of 0.05 MPa for MWCNTs in vacuum, possibly due to the presence of water at the intertube interface in ambient. A following experiment, namely a vertical friction loop measurement, was proposed to characterize the adhesion and friction properties between CNTs [89]. An MWCNT tip was ramped in the vertical direction against a suspended SWCNT. During ramping, a stick-slip motion was found to dominate the sliding, attributed to the presence of defectinduced or amorphous-carbon-associated high energy points on the tip surface. Surprisingly, the coefficients of static friction and shear strength were finally evaluated to be about 0.2 and

MD simulations showed that the sliding behaviors and interfacial shear strengths between two crossly contacting CNTs are much more complicated than the frictions between CNTs and graphite, graphite and graphite, and the inner and outer shells of MWCNTs [90]. The simulation was performed on two SWCNTs in contact at different cross angles. For the parallel contact, the axial interfacial shear strengths between the zigzag-zigzag (~0.25 GPa) and armchair-armchair pairs (~0.5 GPa) are two orders of magnitude larger than those of CNTs having different chiralities (0.5–1 MPa). CNTs with diameters larger than 1 nm will slide relatively from an AB stacking position to the next nearest AB stacking position while smaller ones do not slide through AB stacking positions. For two cross contacting CNTs, the magnitude of interfacial shear strength is much less dependent upon tube chirality. The highest value of shear strength was reported to be about 1 GPa in SWCNT bundles, however, still as quite low as to be improved for applications in high-performance composite materials [91].

A molecular mechanics modeling showed that in order to make the strength of a CNT bundle as high as that of the lowest value of individual CNTs (11 GPa), the contact length should be up to ~3800 nm, by assuming the CNTs are bundled together without changing their circular cross sections [63]. With considering the vdW-force-induced radial deformation [32], the intertube distance-of-closest changes from 3.34 to 3.25 Å for (10,10) CNT bundles, the required contact distance for 11 GPa can decrease to ~1300 nm. This implies that the key to

Twist is an effective way to induce strong radial deformation for CNT bundles. **Figure 5a** shows the cross sections obtained from MD simulations with increasing the twist level and **Figure 5b** shows the corresponding transferred load due to the shape deformation at twist angles of 0, 30, 60, 90, 120, 150, 180, and 210° [63]. It was observed that the individual CNTs start to collapse in the cross section, and therefore, more atoms are in close contact. For the case of no twist, a force of only ~0.048 eV Å−1 is transferred to the center tube, while at 120° the transferred load increases to 1.63 eV Å−1. Clearly, the radial deformation strongly depends on the twist angle, which consequently changes the nature of the contact and contributes to a

improve the intertube load transfer is the interface design between CNTs.

1.4 GPa, respectively.

8 Nanomechanics

new interlayer tribology.

**3.3. Strategies to improve the intertube load transfer**

**Figure 5.** (a) Change in cross section at the mid-length of a SWCNT bundle with increasing the twist level and (b) the corresponding load transfer ability as a function of twist angle [63].

Even a slight structural deformation could cause an improved load transfer. For example, when a DWCNT was slightly bent into a curved one, the energy transfer between the two tubes becomes much faster than that between two straight tubes [81]. Slight displacement of the inner tube could add a large degree of disturbance to the DWCNT's original state of equilibrium and thus present strong inertia to oppose the extraction process, indicating the importance of the inner tube as structural support for the outer tube [92].

Pressure-induced structural phase transition could be a new strategy to improve the intertube load transfer [51]. For a CNT bundle containing 16 (23,0) SWCNTs, the intertube static friction can be improve from 0.1 eV Å−1 per atom to 0.4–0.45 eV Å−1 after all the tubes collapse under pressure higher than 0.5 GPa, see **Figure 6**. Due to the large tube diameter, the collapsed CNT structure

**Figure 6.** The intertube friction force can be increased by a factor of 1.5–4, depending on tube chirality and radius, when all tubes collapse above a critical pressure and when the bundle remains collapsed with unloading down to atmospheric pressure [51].

can be well maintained even by unloading the pressure down to 0.05 GPa. In order to realize a 10 GPa tensile strength, the minimum tube length should be just 167 nm, much smaller than the length of 1090 nm before the phase transition. For a CNT bundle containing totally different tube chiralities, the dynamic friction force can be improved from 0.0017 to 0.0026 eV Å−1 after the phase transition. Such study also indicated that fewwalled large-diameter CNTs could be very important for engineering applications due to the easy ability to induce the collapse phase transition.

Covalent bonding between the shells in MWCNTs or between adjacent CNTs can increase the interlayer and intertube shear strength by several orders of magnitude [93–95]. The covalent intershell bonds can be formed due to the on-shell vacancies or intershell interstitials. According to the types of defect, the force needed to initiate sliding of the shells varies from 0.08 to 0.4 nN for a single vacancy to 3.8–7.8 nN for two vacancies, an intershell interstitial, and an intershell dimer [93]. Therefore, small-dose electron or ion irradiations are suggested to partially transfer the load to the nanotube inner shells. MD simulations revealed that interwall sp3 bonds and interstitial carbon atoms can increase load transfer between DWCNT walls and that interwall sp3 bonds are the most effective [95]. Similarly, by using moderate electron-beam irradiation inside a TEM, stable links between adjacent CNTs within bundles were covalently formed [94]. At a high irradiation energy of 200 keV, there was a substantial increase in effective bending modulus and thus an increase in shear modulus for low doses, while a long irradiation time rather damaged the well-ordered structure of tubes (**Figure 7**). At 80 keV, electrons were shown not to damage isolated CNTs but had enough energy to lead to the formation

**Figure 7.** Behavior of bending modulus as a function of received dose for two incident electron energies [94]. For 200 keV, the modulus increases on short exposures, due to cross-linking and degrades at higher exposures because of structural damage. The bundle irradiated with 80-keV electrons shows a much stronger and sharper increase of the bending modulus.

of mobile interstitial atoms in the confined space between adjacent CNTs. As a result of the newly formed covalent bonds, a huge increase of the bending modulus by a factor of thirty was observed (**Figure 7**). However, a long-time dose at low energies could still cause the accumulation of damage to the structure, making the mechanical performance to decrease eventually.

Even without introducing covalent bonding between the sp2 layers, the existence of structural defects in either CNT layer could lead to a sharp increase in friction and energy dissipation rate [64].

However, besides the tube structure, defect level, and intertube contact, there are many other issues in macroscopic CNT assembly materials. For example, the CNT packing density, alignment, entanglement, aggregation size, and surface functionalization could be important structural parameters, as to be discussed below.

## **4. Carbon nanotube assembly materials**

So far, CNT fibers, films, forests, and gels are well-known and typical macroscopic assembly materials where the CNTs are the main constituents, especially at a mass fraction much more than 50% [10]. For example, CNT fiber is a one-dimensional assembly containing millions of individual tubes [9, 11–13, 15]. It has been found that CNT fibers could have much higher specific modulus and specific strength than those of commercial carbon and polymeric fibers. For the composite materials, there have been two different applications of CNTs such as a dispersion-based fabrication by using CNTs as reinforcing fillers in a polymer matrix [96, 97] and an assembly-based fabrication by directly assembling CNTs into composites [14]. In the former, the CNT content is strongly limited to be no larger than ~5 wt%, while in the latter, a small amount of polymer molecules (about 20–30 wt%) are used to strengthen the interfaces between CNTs. To describe these macroscopic CNT materials, different structural parameters are proposed and investigated in the past decade.

#### **4.1. CNT fibers**

can be well maintained even by unloading the pressure down to 0.05 GPa. In order to realize a 10 GPa tensile strength, the minimum tube length should be just 167 nm, much smaller than the length of 1090 nm before the phase transition. For a CNT bundle containing totally different tube chiralities, the dynamic friction force can be improved from 0.0017 to 0.0026 eV Å−1 after the phase transition. Such study also indicated that fewwalled large-diameter CNTs could be very important for engineering applications due to the easy ability to induce the collapse phase transition. Covalent bonding between the shells in MWCNTs or between adjacent CNTs can increase the interlayer and intertube shear strength by several orders of magnitude [93–95]. The covalent intershell bonds can be formed due to the on-shell vacancies or intershell interstitials. According to the types of defect, the force needed to initiate sliding of the shells varies from 0.08 to 0.4 nN for a single vacancy to 3.8–7.8 nN for two vacancies, an intershell interstitial, and an intershell dimer [93]. Therefore, small-dose electron or ion irradiations are suggested to partially transfer the load to the nanotube inner shells. MD simulations revealed that interwall

bonds and interstitial carbon atoms can increase load transfer between DWCNT walls and

irradiation inside a TEM, stable links between adjacent CNTs within bundles were covalently formed [94]. At a high irradiation energy of 200 keV, there was a substantial increase in effective bending modulus and thus an increase in shear modulus for low doses, while a long irradiation time rather damaged the well-ordered structure of tubes (**Figure 7**). At 80 keV, electrons were shown not to damage isolated CNTs but had enough energy to lead to the formation

**Figure 7.** Behavior of bending modulus as a function of received dose for two incident electron energies [94]. For 200 keV, the modulus increases on short exposures, due to cross-linking and degrades at higher exposures because of structural damage. The bundle irradiated with 80-keV electrons shows a much stronger and sharper increase of the

bonds are the most effective [95]. Similarly, by using moderate electron-beam

sp3

10 Nanomechanics

that interwall sp3

bending modulus.

CNT fiber can be produced by the coagulation-based "wet spinning" [98–101], the "direct spinning" from a CNT aerogel [102–104] or similarly from a pre-formed CNT film [105], and the "forest spinning" based on vertically aligned CNT forests [106–108]. A CNT fiber with a diameter of ~10 μm usually contains more than 106 individual CNTs. Such assembly feature is different from those well-known fibers for many years, which are usually a solid structure without internal interfaces. CNT fiber can also be considered a continuous length of interlocked "filaments" (CNT bundles), where the bundles are formed during the CNT growth rather than in the spinning process. As I have pointed out recently [109], although also being called as CNT yarn, CNT fiber is indeed not a yarn because the CNT bundles are not macroscopically processable. On the contrary, the basic components of a yarn, the long and parallel or interlocked filaments, are usually processable objects with a width larger than several micrometers [110].

Twist is the most fundamental treatment to make the CNTs assembled into a continuous fiber with a circular cross section. The as-spun fiber is relatively loose with noticeable spaces between CNTs or CNT bundles when the twist angle is small. Increasing the twist angle is an effective method to densify CNT fibers and thus improves the friction coefficient between the CNTs. **Figure 8** shows the strength-twist relationship for different CNT fibers [111–113]. All studies showed that the highest fiber strength was found at a twist angle of 15–20°. However, with further increasing the twist, the load (upon stretching) compresses the fiber rather than acts totally along the fiber axis due to the twist angle between the CNTs and the axis, making the utilization efficiency to decrease at high twist angles. The experimental observations that the strength initially increases with twist angle and then decreases are almost the same as those in traditional textile yarns. Nevertheless, the constituent CNTs are different from the filaments in a textile yarn; the CNTs are hollow cylinders and can deform the cross section under pressure due to a structural phase transition [44–49]. For those fibers spun from fewwalled CNTs (wall numbers smaller than 6), it can be seen that beyond the optimal twist angle, an additional strength peak is at large twist angle of 27–30°. This second peak arises from the collapse transformation of the CNT hollow structure, which renders the CNT bundles much stronger and reduces the bundle cross-sectional area.

Solvent densification is another interfacial treatment to CNT assemblies, due to a large capillary force [114, 115]. Therefore, liquid infiltration by using water, ethanol, acetone, or dimethyl sulfoxide (DMSO) is also often used in the method of array spinning to densify CNT fibers [116–119]. Although the densification process does not improve nanotube orientation, it enhances the load transfer between the nanotubes, thus ensuring that most of them are fully load-bearing. For example, the fiber diameter was shrunk from 11.5 to 9.7 μm after acetone shrinking [117]. However, the role of solvent is hardly known as the capillary force can be influenced by the solvents volatility (boiling point), surface tension, and interaction with CNT surfaces. By comparing various solvents including the nonpolar solvents of *n*-hexane, cyclohexane, cyclohexene, toluene, and styrene, polar protic solvents of glycerine, methanol, ethanol, water, ethylene glycol, and 1,3-propanediol, and polar aprotic solvents of

**Figure 8.** (a) Double-peak strength behavior of CNT fibers with increasing twist angles [111]. The surface twist angle (*θs* ) depends on the twisting and drawing speeds (*vt* and *vd* ) by *θs* = arccos {(*vd* /*vt* )/[(π*d*f ) 2 + (*vd* /*vt* ) 2 ]1/2}, where *d*f is the fiber diameter and is >10.5 μm. (b) Dependence of yarn tensile strength on helix angle for forest-spun MWCNT fibers [112]. The fiber diameter was ~20 μm. (c) Relationship between the fiber's specific strength and tenacity with the surface twist angle [113].

ethyl acetate, acetone, acetonitrile, *N,N*-dimethylformamide (DMF), DMSO, and *N*-methyl-2-pyrrolidone (NMP), only few highly polar solvents show high densifying ability to CNTs, namely DMF, DMSO, NMP, and ethylene glycol, despite of their high boiling points and low evaporation rates [118]. These solvents increased the fiber strength from 864 MPa (dryspun) or 1.19 GPa (ethanol) to 1.14–1.35 GPa (DMF, DMSO, NMP) or 1.33–1.58 GPa (ethylene glycol). Clearly, the solvent polarity shows a key role in determining the capillary, as the polarity induced attractive binding energy with CNT (*E*ind) goes up quadratically with the solvent's local dipole moment *μ*, by *E*ind = −*μ*2 *α*/(4π*ε*0 )2 *r*6 , where α is the static polarizability of CNT, *ε*0 is the vacuum permittivity, and *r* is the distance between the dipole moment and the CNT surface [120, 121].

Twist is the most fundamental treatment to make the CNTs assembled into a continuous fiber with a circular cross section. The as-spun fiber is relatively loose with noticeable spaces between CNTs or CNT bundles when the twist angle is small. Increasing the twist angle is an effective method to densify CNT fibers and thus improves the friction coefficient between the CNTs. **Figure 8** shows the strength-twist relationship for different CNT fibers [111–113]. All studies showed that the highest fiber strength was found at a twist angle of 15–20°. However, with further increasing the twist, the load (upon stretching) compresses the fiber rather than acts totally along the fiber axis due to the twist angle between the CNTs and the axis, making the utilization efficiency to decrease at high twist angles. The experimental observations that the strength initially increases with twist angle and then decreases are almost the same as those in traditional textile yarns. Nevertheless, the constituent CNTs are different from the filaments in a textile yarn; the CNTs are hollow cylinders and can deform the cross section under pressure due to a structural phase transition [44–49]. For those fibers spun from fewwalled CNTs (wall numbers smaller than 6), it can be seen that beyond the optimal twist angle, an additional strength peak is at large twist angle of 27–30°. This second peak arises from the collapse transformation of the CNT hollow structure, which renders the CNT bun-

Solvent densification is another interfacial treatment to CNT assemblies, due to a large capillary force [114, 115]. Therefore, liquid infiltration by using water, ethanol, acetone, or dimethyl sulfoxide (DMSO) is also often used in the method of array spinning to densify CNT fibers [116–119]. Although the densification process does not improve nanotube orientation, it enhances the load transfer between the nanotubes, thus ensuring that most of them are fully load-bearing. For example, the fiber diameter was shrunk from 11.5 to 9.7 μm after acetone shrinking [117]. However, the role of solvent is hardly known as the capillary force can be influenced by the solvents volatility (boiling point), surface tension, and interaction with CNT surfaces. By comparing various solvents including the nonpolar solvents of *n*-hexane, cyclohexane, cyclohexene, toluene, and styrene, polar protic solvents of glycerine, methanol, ethanol, water, ethylene glycol, and 1,3-propanediol, and polar aprotic solvents of

**Figure 8.** (a) Double-peak strength behavior of CNT fibers with increasing twist angles [111]. The surface twist angle

diameter and is >10.5 μm. (b) Dependence of yarn tensile strength on helix angle for forest-spun MWCNT fibers [112]. The fiber diameter was ~20 μm. (c) Relationship between the fiber's specific strength and tenacity with the surface twist

) by *θs*

= arccos {(*vd*

/*vt* )/[(π*d*f ) 2 + (*vd* /*vt* )2

]1/2}, where *d*f

is the fiber

and *vd*

(*θs*

angle [113].

12 Nanomechanics

) depends on the twisting and drawing speeds (*vt*

dles much stronger and reduces the bundle cross-sectional area.

In addition to twisting and liquid densification, polymer impregnation is another effective treatment to enhance the mechanical properties of CNT fibers. The polymers are introduced to bridge nonneighboring CNTs, such as polyethyleneimine (PEI) [122], polydopamine (PDA) [123], polyvinyl alcohol (PVA) [105, 118, 124], polyacrylate [125], polyvinylidene fluoride (PVDF) [126], epoxy [105], polyimide (PI) [118, 127], and bismaleimide (BMI) [118, 128]. **Figure 9** shows several typical stress-strain curves for polymer-reinforced CNT fibers, such as PI, BMI, PEI, and PDA [118, 122, 123]. The enhanced mechanical properties of CNT fibers with polymer impregnation are attributed to couplings between the CNT network and polymer chains occurring at the molecular level. As a result, the sliding between CNTs can be remarkably hindered by the polymer network, especially that formed by the cured thermosetting polymers. Therefore, more external strain can be transferred to the CNTs as shown in **Figure 10**, where the Raman peaks of CNTs downshift to a lower wavenumber by different values under axial strains [105]. Both PVA and epoxy enhanced the downshifts, corresponding to the improved load transfer between CNTs. The cured thermosetting polymer network also shows advantages in improving the fiber modulus, as indicated by the largest change in G'-peak wavelength. Similarly, PI and BMI are other efficient thermosetting polymers for producing high-modulus CNT fibers [118, 127, 128]. However, other polymers might be good at improving the fiber's stretchability and toughness by preventing the sliding-induced fiber fracture, possibly due to the polymer wrapping around the CNT connections [126], cooperative deformation mechanisms of the soft and hard segments [125], iron-mediated covalent cross-linking [122], or cross-linked polymeric binders [123].

**Figure 9.** (a) Stress-strain curves of dry-spun, ethanol-densified, ethylene-glycol-densified, PI-reinforced, and BMIreinforced CNT fibers [118]. (b) Stress-strain curves of PEI-catechol-reinforced CNT fibers, including one after addition of Fe(III) [122]. (c) Stress-strain curves of as-drawn CNT fiber, CNT/PDA fiber, and CNT/(pyrolyzed PDA) fiber [123].

**Figure 10.** Variations of Raman spectra under strain in different systems [105]. (a) Typical G' band Raman spectra of epoxy- and PVA-infiltrated CNT fibers. (b) Downshifts of the peak position in different systems.

The structure of CNT fiber is hierarchical, with CNTs self-assembling into bundles and the bundles forming an aligned network in the fiber [129, 130]. Other assembly parameters also include the tube waviness or straightness [131], which can also result in different elasticity and modulus for CNT fibers. Notice that the above-mechanical improvements are irrelevant to the microstructure of individual CNTs but are relevant to the macroscopic assembly parameters. From the point of view of tube structure, fewwalled CNTs have shown advantages in producing high-performance fibers, rather than the ideal SWCNTs [131]. For the SWCNTs, usually 1–1.5 nm in diameter, simulations and experiments have shown that a certain high pressure (hundreds of MPa) is necessary to introduce even a slight deformation of their cross sections. That means, the intertube contact area is far limited compared with the overall circumference of the cross section. While for the fewwalled tubes, the tube diameter can be large up to ≥5 nm, making it much easy to deform the cross section and increase the contact area. Experiments even have shown, upon certain twisting and/or tensioning, collapse of fewwalled tubes were possibly introduced [111, 132].

Furthermore, covalent interface engineering could be an efficient posttreatment for the asproduced CNT fibers. Acid treatment could introduce rich hydroxyl, methyl/methylene, and carbonyl groups onto CNT surfaces, which also made CNT fibers shrunk slightly, or more densified. Such treatment enhanced the load transfer between CNTs, according to a theoretical study [94], and thus resulted in an increase in fiber strength and modulus [133]. Recently, by using an incandescent tension annealing process (ITAP), where the current-induced Joule heating increase the temperature of CNT fiber up to 2000°C in vacuum, sp3 covalent bonding was observed in CNT fibers [134]. As a result, the fiber modulus could be improved from 37 to 170 GPa, once the ITAP was performed with maintaining a high tension on the fiber.

In order to further improve the utilization efficiency of the individual CNT's mechanical properties in CNT fibers, more effort should be paid to the delicate combining of the choice of CNT structure, controlling in CNT packing density, alignment, and straightness, and intertube mechanics engineering by polymers or covalent functionalization.

#### **4.2. CNT films**

The structure of CNT fiber is hierarchical, with CNTs self-assembling into bundles and the bundles forming an aligned network in the fiber [129, 130]. Other assembly parameters also include the tube waviness or straightness [131], which can also result in different elasticity and modulus for CNT fibers. Notice that the above-mechanical improvements are irrelevant to the microstructure of individual CNTs but are relevant to the macroscopic assembly parameters. From the point of view of tube structure, fewwalled CNTs have shown advantages in producing high-performance fibers, rather than the ideal SWCNTs [131]. For the SWCNTs, usually 1–1.5 nm in diameter, simulations and experiments have shown that a certain high pressure (hundreds of MPa) is necessary to introduce even a slight deformation of their cross sections. That means, the intertube contact area is far limited compared with the overall circumference of the cross section. While for the fewwalled tubes, the tube diameter can be large up to ≥5 nm, making it much easy to deform the cross section and increase the contact area. Experiments even have shown, upon certain twisting and/or tensioning, collapse of fewwalled tubes were

**Figure 10.** Variations of Raman spectra under strain in different systems [105]. (a) Typical G' band Raman spectra of

epoxy- and PVA-infiltrated CNT fibers. (b) Downshifts of the peak position in different systems.

Furthermore, covalent interface engineering could be an efficient posttreatment for the asproduced CNT fibers. Acid treatment could introduce rich hydroxyl, methyl/methylene, and carbonyl groups onto CNT surfaces, which also made CNT fibers shrunk slightly, or more densified. Such treatment enhanced the load transfer between CNTs, according to a theoretical study [94], and thus resulted in an increase in fiber strength and modulus [133]. Recently, by using an incandescent tension annealing process (ITAP), where the current-induced Joule

was observed in CNT fibers [134]. As a result, the fiber modulus could be improved from 37 to

In order to further improve the utilization efficiency of the individual CNT's mechanical properties in CNT fibers, more effort should be paid to the delicate combining of the choice

170 GPa, once the ITAP was performed with maintaining a high tension on the fiber.

covalent bonding

heating increase the temperature of CNT fiber up to 2000°C in vacuum, sp3

possibly introduced [111, 132].

14 Nanomechanics

CNT films are another important macroscopic material with high mechanical performances. Various processing methods have been developed to produce CNT films by using preformed CNT assemblies, among which these two methods are of great importance: the layer-by-layer stacking of aligned CNT sheets and the stretching on entangled CNT webs [14]. Despite of the fabrication methods, there are also many common problems concerning with the interface mechanics, as the CNT fibers do.

For instance, liquid densification is widely used to CNT films [135–137], and polymer impregnation can remarkably improve the interfacial load transfer [138–143]. Different from CNT fibers where the tubes are assembled with the aid of twisting, there is more freedom to tune the assembly structure. The CNTs can be got superaligned by stretching the films in a wet environment [135], or by microcombing before they are layer-by-layer stacked [136]. After improving the CNT alignment, the pure CNT films could be as strong as 3.2 GPa in tensile strength, with a Young's modulus of 124–172 GPa [135, 136]. **Figure 11** shows the stress-strain curves for the CNT films being both densified and superaligned. Once these aligned CNTs were impregnated with polymers, especially thermosetting polymers, the film's strength and modulus could be further improved. At a mass fraction of 50–55% for CNT, the CNT/BMI composite films exhibited a strength of 3.8 GPa and a modulus of 293 GPa [139]. Such superior properties are derived from the long length, high mass fraction, good alignment, and reduced waviness of the CNTs.

The stretching on entangled CNT webs is another way to obtain highly aligned CNT films. With the aid of BMI impregnation and curing, the strength and modulus of the CNT/BMI composite films could be improved from 620 MPa and 47 GPa (un-stretched) to 1600 MPa and

**Figure 11.** Stress-strain curves for CNT films obtained by a stretch-dip-drying method (a) [135] and a microcombing method (b) [136]. The films treated with acetone (ADD) and ethanol (EDD) were much stronger than the as-spun and spray-wound (SW) films. The films after microcombing had a larger Young's modulus than the ADD and EDD films.

122 GPa, 1800 MPa and 150 GPa, and 2088 MPa and 169 GPa after being stretched by 30, 35, and 40%, respectively [140]. By further introducing surface functionalization for CNTs, the strength and modulus were surprisingly improved up to 3081 MPa and 350 GPa, respectively [141].

However, the direct stacking of CNT sheets and stretching on CNT webs could not avoid the CNT aggregation due to the vdW interactions. As shown in **Figure 12a** and **b**, the aggregation size was up to hundreds of nanometer [143]. Such aggregation of nanometer-sized components has become a severe problem in paving the way to stronger materials [144]. In the aggregation phase, the intertube load transfer is not as efficient as at the CNT-polymer interface. Thus, such aggregation phase becomes the weak parts in the composites and hinders further reinforcement. In an ideal structure, the nanometer-sized components should be uniformly distributed in the matrix without forming any aggregation phases. Therefore, all the interfaces can play roles in shear load transfer. As inspired by the formation process of natural composite structures, the BMI resins were infiltrated into CNT webs before any stretching was performed. Since the liquid treatment just densifies the CNT network without inducing CNT aggregation, the impregnation before stretching causes each CNT or CNT bundle uniformly covered by a thin layer of polymers. Therefore, the following stretching could just align the CNTs but avoid the aggregation due to the thin layer of polymer, resulting in an optimized composite structure. By adapting a multistep stretching process, the final

**Figure 12.** Comparison of CNT assembly structure for different films [143]. (a,b) CNT aggregation in the layer-by-layer stacking of array-drawn CNT sheets and the stretched dry films composed by entangled CNTs, respectively. (c) The small-sized CNT bundles did not aggregate but were surrounded by BMI polymers and uniformly distributed. (d, e) 750°C treated CNT/BMI composite films where the stretching was performed before and after resin impregnation, respectively, showing the aggregation and unaggregation. (f) Cross section of the optimal CNT/BMI composite structure by using focused ion beam treatment, indicating an aggregation size of 20–50 nm for the CNTs.

composite film exhibited superior mechanical performances. The highest tensile strength and modulus were up to 5.77–6.94 and 212–351 GPa at a CNT-to-resin mass ratio of 7:3 and a stretching magnitude of 34% [143].

**Figure 12c** shows the morphology of the optimized CNT/BMI composites, where the CNT bundles were found to be uniformly distributed and aligned. To characterize the aggregation of CNTs, thermal treatment and focused ion beam treatment were used. After being heated to 750°C to decompose the polymers, the remaining CNTs were found to be aggregated/ unaggregated if the stretching was performed before/after the polymer impregnation, see **Figure 12d** and **e**. The direct observation of the cross section with focused ion beam treatment showed an aggregation size of just 20–50 nm (**Figure 12f**), a size for the bundling that was still difficult to avoid during the growth process.

On the whole, for the macroscopic CNT assemblies, the interface mechanics becomes much more complicated as the material exhibits a collective dynamics from the constituent CNTs. Assembly parameters, including CNT packing density, alignment and/or entanglement, twisting level, cross-linking, and aggregation size, are found to be critical for the mechanical properties. By controlling the interface mechanics in the CNT assemblies, we can not only optimize the mechanical properties, but also introduce multifunctionalities, as discussed below.

#### **4.3. Multifunctionalization by interface engineering**

122 GPa, 1800 MPa and 150 GPa, and 2088 MPa and 169 GPa after being stretched by 30, 35, and 40%, respectively [140]. By further introducing surface functionalization for CNTs, the strength and modulus were surprisingly improved up to 3081 MPa and 350 GPa, respectively

However, the direct stacking of CNT sheets and stretching on CNT webs could not avoid the CNT aggregation due to the vdW interactions. As shown in **Figure 12a** and **b**, the aggregation size was up to hundreds of nanometer [143]. Such aggregation of nanometer-sized components has become a severe problem in paving the way to stronger materials [144]. In the aggregation phase, the intertube load transfer is not as efficient as at the CNT-polymer interface. Thus, such aggregation phase becomes the weak parts in the composites and hinders further reinforcement. In an ideal structure, the nanometer-sized components should be uniformly distributed in the matrix without forming any aggregation phases. Therefore, all the interfaces can play roles in shear load transfer. As inspired by the formation process of natural composite structures, the BMI resins were infiltrated into CNT webs before any stretching was performed. Since the liquid treatment just densifies the CNT network without inducing CNT aggregation, the impregnation before stretching causes each CNT or CNT bundle uniformly covered by a thin layer of polymers. Therefore, the following stretching could just align the CNTs but avoid the aggregation due to the thin layer of polymer, resulting in an optimized composite structure. By adapting a multistep stretching process, the final

**Figure 12.** Comparison of CNT assembly structure for different films [143]. (a,b) CNT aggregation in the layer-by-layer stacking of array-drawn CNT sheets and the stretched dry films composed by entangled CNTs, respectively. (c) The small-sized CNT bundles did not aggregate but were surrounded by BMI polymers and uniformly distributed. (d, e) 750°C treated CNT/BMI composite films where the stretching was performed before and after resin impregnation, respectively, showing the aggregation and unaggregation. (f) Cross section of the optimal CNT/BMI composite structure

by using focused ion beam treatment, indicating an aggregation size of 20–50 nm for the CNTs.

[141].

16 Nanomechanics

Besides load transfer at the intertube interfaces, energy dissipation is also a common interfacial phenomenon. As CNT fiber is formed by assembling millions of individual tubes, the assembly features provide the fiber with rich interface structures and various ways of energy dissipation, including the internal viscosity and intertube friction [109]. Therefore, a modified Kelvin-Voigt model was adopted, where an elastic spring *K*, a viscous damping coefficient *η*, and an intertube friction *f* are connected in parallel [145]. Due to the friction, there exists a friction-dependent component in loss tangent, which is not dependent on the frequency. As shown in **Figure 13**, the loss tangent was nonzero (about 0.045) for the dry-spun CNT fibers, while that for the T300 carbon fiber was nearly zero due to the absence of interfaces. When the CNT fibers were densified

**Figure 13.** The frequency dependence of loss tangent for the dry-spun CNT fiber, ethylene-glycol-densified CNT fiber, and T300 carbon fiber [109].

by ethylene glycol, the CNTs became constrained, corresponding to reduced loss tangents, see **Figure 13**. Based on the friction-based Kelvin-Voigt model, the damping performance of CNT fibers can be tuned in a very wide range. The introduction of thermosetting polymers further decreases the loss tangent, while plying CNT fibers into a yarn increases the loss tangent [109].

The CNT entanglement provides another way to enhance the damping ability [146]. The as-produced CNT films based on an injection chemical vapor deposition exhibited a loss tangent of 0.37–0.42 at 200 Hz [146], or 0.2 at 50 Hz [143]. After the network was stretched and strengthened with BMI, the loss tangent could decrease remarkably down to about 0.05 at 50 Hz [143].

When an electric current is passing through CNT assemblies, there exist parallel currents along the aligned CNTs. The collective electromagnetic force between parallel current can cause a volume contraction for the assembly [147]. Based on such mechanism, CNT fibers can be developed as electromechanical actuator. Detailed study revealed that the electromechanical coupling is quite complicated beyond the actuation [128]. For example, when a current passes through a CNT fiber, the fiber's modulus could decrease remarkably due to the current-induced weakening in C−C σ bond. Besides the electromechanical coupling, the current could induce a strong Joule heating, making the fiber temperature to increase very sharply. Such electrothermal coupling can be used for fast curing to the impregnated thermosetting resins at a moderate temperature of 200–300°C [128], or for the formation of intertube sp3 covalent bonding at a high temperature of 2000°C in vacuum [134].

## **5. Conclusion**

The control of interface mechanics is a key strategy to develop high-performance CNT assembly structures. High tensile properties (strength up to 3–6 GPa and modulus up to 200–350 GPa) can be obtained for aligned CNT fibers and films, corresponding to an improved utilization efficiency of CNT's mechanical properties. Furthermore, the dynamical performance and multifunctionalities both depend strongly on the interface between CNTs, also in terms of CNT packing density, alignment, entanglement, twisting level, cross-linking, and aggregation size. For future development of high-performance CNT assembly materials, more delicate design on the multiscale interfaces is required. I hope this review could cast lights for the interface design ranging widely from the nanometer scale to the macroscopic scale.

### **Acknowledgements**

The author thanks Prof. Xingao Gong of Fudan University, Prof. Erio Tosatti of the International School for Advanced Studies, and Prof. Qingwen Li of Suzhou Institute of Nano-Tech and Nano-Bionics for their kind collaborations, which are the important sources for this chapter. Financial supports from the National Natural Science Foundation of China (11302241,<PHONE_NUMBER>8), Youth Innovation Promotion Association of the Chinese Academy of Sciences (2015256), and National Key Research and Development Program of China (2016YFA0203301) are acknowledged.

## **Author details**

by ethylene glycol, the CNTs became constrained, corresponding to reduced loss tangents, see **Figure 13**. Based on the friction-based Kelvin-Voigt model, the damping performance of CNT fibers can be tuned in a very wide range. The introduction of thermosetting polymers further decreases the loss tangent, while plying CNT fibers into a yarn increases the loss tangent [109]. The CNT entanglement provides another way to enhance the damping ability [146]. The as-produced CNT films based on an injection chemical vapor deposition exhibited a loss tangent of 0.37–0.42 at 200 Hz [146], or 0.2 at 50 Hz [143]. After the network was stretched and strengthened with BMI, the loss tangent could decrease remarkably down to about 0.05

When an electric current is passing through CNT assemblies, there exist parallel currents along the aligned CNTs. The collective electromagnetic force between parallel current can cause a volume contraction for the assembly [147]. Based on such mechanism, CNT fibers can be developed as electromechanical actuator. Detailed study revealed that the electromechanical coupling is quite complicated beyond the actuation [128]. For example, when a current passes through a CNT fiber, the fiber's modulus could decrease remarkably due to the current-induced weakening in C−C σ bond. Besides the electromechanical coupling, the current could induce a strong Joule heating, making the fiber temperature to increase very sharply. Such electrothermal coupling can be used for fast curing to the impregnated thermosetting resins at a moderate temperature of 200–300°C [128], or for the formation of intertube sp3

The control of interface mechanics is a key strategy to develop high-performance CNT assembly structures. High tensile properties (strength up to 3–6 GPa and modulus up to 200–350 GPa) can be obtained for aligned CNT fibers and films, corresponding to an improved utilization efficiency of CNT's mechanical properties. Furthermore, the dynamical performance and multifunctionalities both depend strongly on the interface between CNTs, also in terms of CNT packing density, alignment, entanglement, twisting level, cross-linking, and aggregation size. For future development of high-performance CNT assembly materials, more delicate design on the multiscale interfaces is required. I hope this review could cast lights for the interface design

The author thanks Prof. Xingao Gong of Fudan University, Prof. Erio Tosatti of the International School for Advanced Studies, and Prof. Qingwen Li of Suzhou Institute of Nano-Tech and Nano-Bionics for their kind collaborations, which are the important sources for this chapter. Financial supports from the National Natural Science Foundation of China (11302241,<PHONE_NUMBER>8), Youth Innovation Promotion Association of the Chinese Academy of Sciences (2015256), and National Key Research and Development Program of China (2016YFA0203301) are acknowledged.

covalent bonding at a high temperature of 2000°C in vacuum [134].

ranging widely from the nanometer scale to the macroscopic scale.

at 50 Hz [143].

18 Nanomechanics

**5. Conclusion**

**Acknowledgements**

#### Xiaohua Zhang

Address all correspondence to<EMAIL_ADDRESS>
1 Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, Suzhou, China

2 Jiangsu Key Laboratory of Engineering Mechanics and Department of Engineering Mechanics, School of Civil Engineering, Southeast University, Nanjing, China

## **References**

[29] Walters DA, Ericson LM, Casavant MJ, Liu J, Colbert DT, Smith KA, Smalley RE. Elastic strain of freely suspended single-wall carbon nanotube ropes. Applied Physics Letters. 1999;**74**(25):3803–3085

[13] Miao M. Yarn spun from carbon nanotube forests: production, structure, properties and

[14] Zhang X, Yu X, Zhao J, Li Q. Bio-inspired design and fabrication of super-strong and multifunctional carbon nanotube composites. In: Berber MR, Hafez IH, editors. Carbon Nanotubes - Current Progress of Their Polymer Composites. Rijeka, Croatia: InTech -

[15] Di J, Zhang X, Yong Z, Zhang Y, Li D, Li R, Li Q. Carbon-nanotube fibers for wearable

[16] Treacy MMJ, Ebbesen TW, Gibson JM. Exceptionally high Young's modulus observed

[17] Lourie O, Wagner HD. Evaluation of Young's modulus of carbon nanotubes by Micro-

[18] Yu M-F, Lourie O, Dyer MJ, Moloni K, Kelly TF, Ruoff RS. Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science. 2000;**287**(5453):637–640

[19] Yu M-F, Files BS, Arepalli S, Ruoff RS. Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties. Physical Review Letters. 2000;**84**(24):5552–5555

[20] Overney G, Zhong W, Tománek D. Structural rigidity and low frequency vibrational

[21] Lu JP. Elastic properties of carbon nanotubes and nanoropes. Physical Review Letters.

[22] Belytschko T, Xiao SP, Schatz GC, Ruoff RS. Atomistic simulations of nanotube fracture.

[23] Dumitrică T, Belytschko T, Yakobson BI. Bond-breaking bifurcation states in carbon

[24] Wei C, Cho K, Srivastava D. Tensile strength of carbon nanotubes under realistic tem-

[25] Liew KM, Wong CH, He XQ, Tan MJ, Meguid SA. Nanomechanics of single and multi-

[26] Bernholc J, Brabec C, Nardelli MB, Maiti A, Roland C, Yakobson BI. Theory of growth and mechanical properties of nanotubes. Applied Physics A. 1998;**67**(1):39–46

[27] Nardelli MB, Yakobson BI, Bernholc J. Brittle and ductile behavior in carbon nanotubes.

[28] Nardelli MB, Yakobson BI, Bernholc J. Mechanism of strain release in carbon nanotubes.

devices and smart textiles. Advanced Materials. 2016;**28**(47):10529–10538

Raman spectroscopy. Journal of Materials Research. 1998;**13**(9):2418–2422

modes of long carbon tubules. Zeitschrift fur Physik D. 1993;**27**(1):93–96

nanotube fracture. Journal of Chemical Physics. 2003;**118**(21):9485–9488

perature and strain rate. Physical Review B. 2003;**67**(11):115407

walled carbon nanotubes. Physical Review B. 2004;**69**(11):115429

Physical Review Letters. 1998;**81**(21):4656–4659

Physical Review B. 1998;**57**(8):R4277–4280

for individual carbon nanotubes. Nature. 1996;**381**(6584):678–680

applications. Particuology. 2013,**11**(4):378–393

20 Nanomechanics

Open Access; 2016. pp. 73–93. Chapter 3

1997;**79**(7):1297–1300

Physical Review B. 2002;**65**(23):235430

[61] Kolmogorov AN, Crespi VH. Smoothest bearings: interlayer sliding in multiwalled carbon nanotubes. Physical Review Letters. 2000;**85**(22):4727–4730

[44] Elliott JA, Sandler JKW, Windle AH, Young RJ, Shaffer MSP. Collapse of single-wall carbon nanotubes is diameter dependent. Physical Review Letters. 2004;**92**(9):095501

[45] Zhang XH, Sun DY, Liu ZF, Gong XG. Structure and phase transitions of single-wall carbon nanotube bundles under hydrostatic pressure. Physical Review B. 2004;**70**(3):035422

[46] Zhang XH, Liu ZF, Gong XG. Comment on collapse of single-wall carbon nanotubes is

[47] Sun DY, Shu DJ, Ji M, Liu F, Wang M, Gong XG. Pressure-induced hard-to-soft transition

[48] Ye X, Sun DY, Gong XG. Pressure-induced structural transition of double-walled carbon

[49] Gadagkar V, Maiti PK, Lansac Y, Jagota A, Sood AK. Collapse of double-walled carbon nanotube bundles under hydrostatic pressure. Physical Review B. 2006;**73**(8):085402

[50] Chang T. Dominoes in carbon nanotubes. Physical Review Letters. 2008;**101**(17):175501

[51] Zhang X, Li Q. Enhancement of friction between carbon nanotubes: an efficient strategy

[52] Mylvaganam K, Zhang LC. Ballistic resistance capacity of carbon nanotubes.

[53] Yakobson BI, Brabec CJ, Bernholc J. Nanomechanics of carbon tubes: instabilities beyond

[54] Yu M-F, Dyer MJ, Chen J, Qian D, Liu WK, Ruoff RS. Locked twist in multiwalled car-

[55] Liew KM, Wong CH, Tan MJ. Tensile and compressive properties of carbon nanotube

[56] Poncharal P, Wang ZL, Ugarte D, De Heer WA. Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science. 1999;**283**(5407):1513–1516

[57] Lourie O, Cox DM, Wagner HD. Buckling and collapse of embedded carbon nanotubes.

[58] Arroyo M, Belytschko T. Nonlinear mechanical response and rippling of thick multi-

[59] Liu JZ, Zheng Q, Jiang Q. Effect of bending instabilities on the measurements of mechanical properties of multiwalled carbon nanotubes. Physical Review B. 2003;**67**(7):075414

[60] Qian D, Liu WK, Subramoney S, Ruoff RS. Effect of interlayer potential on mechanical deformation of multiwalled carbon nanotubes. Journal of Nanoscience and

walled carbon nanotubes. Physical Review Letters. 2003;**91**(21):215505

to strengthen fibers. American Chemical Society Nano. 2010;**4**(1):312–316

linear response. Physical Review Letters. 1996;**76**(14):2511–2514

bon-nanotube ribbons. Physical Review B. 2001;**64**(24):241403

diameter dependent. Physical Review Letters. 2004;**93**(14):149601

of a single carbon nanotube. Physical Review B. 2004;**70**(16):165417

nanotubes. Physical Review B. 2005;**72**(3):035454

Nanotechnology. 2007;**18**(47):475701

22 Nanomechanics

bundles. Acta Materialia. 2006;**54**(1):225–231

Physical Review Letters. 1998;**81**(8):1638–1641

Nanotechnology. 2003;**3**:185–191

[93] Huhtala M, Krasheninnikov AV, Aittoniemi J, Stuart SJ, Nordlund K, Kaski K. Improved mechanical load transfer between shells of multiwalled carbon nanotubes. Physical Review B. 2004;**70**(4):045404

[77] Li B, Chang T. Tunable dual-frequency oscillators of carbon nanotubes. Journal of

[78] Fennimore AM, Yuzvinsky TD, Han W-Q, Fuhrer MS, Cumings J, Zettl A. Rotational

[79] Zhang S, Liu WK, Ruoff RS. Atomistic simulations of double-walled carbon nanotubes

[80] Servantie J, Gaspard P. Rotational dynamics and friction in double-walled carbon nano-

[81] Cai K, Cai H, Yin H, Qin QH. Dynamic behavior of curved double-wall carbon nanotubes with rotating inner tube. Royal Society of Chemistry Advances. 2015;**5**(38):29908–29913

[82] Cook EH, Buehler MJ, Spakovszky ZS. Mechanism of friction in rotating carbon nanotube bearings. Journal of the Mechanics and Physics of Solids. 2013;**61**(2):652–673

[83] Tangney P, Cohen ML, Louie SG. Giant wave-drag enhancement of friction in sliding

[84] Zhang XH, Santoro GE, Tartaglino U, Tosatti E. Dynamical chiral symmetry breaking in

[85] Tangney P, Louie SG, Cohen ML. Dynamic sliding friction between concentric carbon

[86] Zhang X-H, Tartaglino U, Santoro GE, Tosatti E. Velocity plateaus and jumps in carbon

[87] Ajayan PM, Schadler LS, Giannaris C, Rubio A. Single-walled carbon nanotube polymer composites: strength and weakness. Advanced Materials. 2000;**12**(10):750–753

[88] Bhushan B, Ling X, Jungen A, Hierold C. Adhesion and friction of a multiwalled carbon nanotube sliding against single-walled carbon nanotube. Physical Review B.

[89] Bhushan B, Ling X. Adhesion and friction between individual carbon nanotubes measured using force-versus-distance curves in atomic force microscopy. Physical Review

[90] Li C, Liu Y, Yao X, Ito M, Noguchi T, Zheng Q. Interfacial shear strengths between car-

[91] Salvetat J-P, Briggs GAD, Bonard J-M, Bacsa RR, Kulik AJ, Stöckli T, Burnham NA, Forró L. Elastic and shear moduli of single-walled Carbon nanotube ropes. Physical Review

[92] Kok ZKJ, Wong CH. Molecular dynamics simulation studies of mechanical properties of different carbon nanotube systems. Molecular Simulatio. 2016;**42**(15):1274–1280

actuators based on carbon nanotubes. Nature. 2003;**424**(6947):408–410

(DWCNTs) as rotational bearings. Nano Letters. 2004;**4**(2):293–297

carbon nanotubes. Physical Review Letters. 2006;**97**(19):195901

sliding nanotubes. Physical Review Letters. 2009;**102**(12):125502

nanotubes. Physical Review Letters. 2004;**93**(6):065503

bon nanotubes. Nanotechnology. 2010;**21**(11):115704

2008;**77**(16):165428

B. 2008;**78**(4):045429

Letters. 1999;**82**(5):944–947

nanotube sliding. Surface Science. 2007;**601**(18):3693–3696

tubes.  Selective interaction in a polymer—single-wall carbon nanotube composite. Journal of Physical Chemistry B. 2003;**107**(2):478–482

[106] Jiang K, Li Q, Fan S. Spinning continuous carbon nanotube yarns. Nature. 2002;**419**

[107] Zhang M, Atkinson KR, Baughman RH. Multifunctional carbon nanotube yarns by

[108] Li Q, Zhang X, DePaula RF, Zheng L, Zhao Y, Stan L, Holesinger TG, Arendt PN, Peterson DE, Zhu YT. Sustained growth of ultralong carbon nanotube arrays for fiber

[109] Zhao J, Zhang X, Pan Z, Li Q. Wide-range tunable dynamic property of carbon-nano-

[110] Hearle JWS, Hollick L, Wilson DK. Yarn Texturing Technology. Boca Raton: CRC Press;

[111] Zhao J, Zhang X, Di J, Xu G, Yang X, Liu X, Yong Z, Chen M, Li Q. Double-peak mechan-

[112] Fang S, Zhang M, Zakhidov AA, Baughman RH. Structure and process-dependent properties of solid-state spun carbon nanotube yarns. Journal of Physics: Condensed

[113] Miao M, McDonnell J, Vuckovic L, Hawkins SC. Poisson's ratio and porosity of carbon

[114] Liu H, Li S, Zhai J, Li H, Zheng Q, Jiang L, Zhu D. Self-assembly of large-scale micropatterns on aligned carbon nanotube films. Angewandte Chemie International Edition.

[115] Chakrapani N, Wei B, Carrillo A, Ajayan PM, Kane RS. Capillarity-driven assembly of two-dimensional cellular carbon nanotube foams. Proceedings of the National

[116] Zhang X, Jiang K, Feng C, Liu P, Zhang L, Kong J, Zhang T, Li Q, Fan S. Spinning and processing continuous yarns from 4-inch wafer scale super-aligned carbon nanotube

[117] Liu K, Sun Y, Zhou R, Zhu H, Wang J, Liu L, Fan S, Jiang K. Carbon nanotube yarns with high tensile strength made by a twisting and shrinking method. Nanotechnology.

[118] Li S, Zhang X, Zhao J, Meng F, Xu G, Yong Z, Jia J, Zhang Z, Li Q. Enhancement of carbon nanotube fibres using different solvents and polymers. Composites Science and

[119] Qiu J, Terrones J, Vilatela JJ, Vickers ME, Elliott JA, Windle AH. Liquid infiltration into carbon nanotube fibers: effect on structure and electrical properties. American

downsizing an ancient technology. Science. 2004;**306**(5700):1358–1361

tube-based fibers. Advanced Materials Interfaces. 2015;**2**(10):1500093

ical properties of carbon nanotube fibers. Small. 2010;**6**(22):2612–2617

spinning. Advanced Materials. 2006;**18**(23):3160–3163

nanotube dry-spun yarns. Carbon. 2010;**48**:2802–2811

Academy of Sciences. 2004;**101**(12):4009–4012

arrays. Advanced Materials. 2006;**18**(12):1505–1510

(6909):801–801

26 Nanomechanics

2001

Matter. 2010;**22**(33):334221

2004;**43**(9):1146–1149

2010;**21**(4):045708

Technology. 2012;**72**(12):1402–1407

Chemical Society Nano. 2013;**7**(10):8412–8422

[146] Liu Q, Li M, Gu Y, Wang S, Zhang Y, Li Q, Gao L, Zhang Z. Interlocked CNT networks with high damping and storage modulus. Carbon. 2015;**86**:46–53

[133] Meng F, Zhao J, Ye Y, Zhang X, Li Q. Carbon nanotube fibers for electrochemical applications: effect of enhanced interfaces by an acid treatment. Nanoscale.

[134] Di J, Fang S, Moura FA, Galvão DS, Bykova J, Aliev A, de Andrade MJ, Lepró X, Li N, Haines C, Ovalle-Robles R, Qian D, Baughman RH. Strong, twist-stable carbon nanotube yarns and muscles by tension annealing at extreme temperatures. Advanced

[135] Wang Y, Li M, Gu Y, Zhang X, Wang S, Li Q, Zhang Z. Tuning carbon nanotube assembly for flexible, strong and conductive films. Nanoscale, 2015;**7**(7):3060–3066

[136] Zhang L, Wang X, Xu W, Zhang Y, Li Q, Bradford PD, Zhu Y. Strong and conductive dry carbon nanotube films by microcombing. Small. 2015;**11**(31):3830–3836

[137] Di J, Hu D, Chen H, Yong Z, Chen M, Feng Z, Zhu Y, Li Q. Ultrastrong, foldable, and highly conductive carbon nanotube film. American Chemical Society Nano.

[138] Liu W, Zhang X, Xu G, Bradford PD, Wang X, Zhao H, Zhang Y, Jia Q, Yuan F-G, Li Q, Qiu Y, Zhu Y. Producing superior composites by winding carbon nanotubes onto a

[139] Wang X, Yong ZZ, Li QW, Bradford PD, Liu W, Tucker DS, Cai W, Wang H, Yuan FG, Zhu YT. Ultrastrong, stiff and multifunctional carbon nanotube composites. Materials

[140] Cheng Q, Bao J, Park J, Liang Z, Zhang C, Wang B. High mechanical performance composite conductor: multi-walled carbon nanotube sheet/bismaleimide nanocomposites.

[141] Cheng Q, Wang B, Zhang C, Liang Z. Functionalized carbon-nanotube sheet/bismaleimide nanocomposites: mechanical and electrical performance beyond carbon-fiber

[142] Jiang Q, Wang X, Zhu Y, Hui D, Qiu Y. Mechanical, electrical and thermal properties of aligned carbon nanotube/polyimide composites. Composites Part B. 2014;**56**:408–412

[143] Han Y, Zhang X, Yu X, Zhao J, Li S, Liu F, Gao P, Zhang Y, Zhao T, Li Q. Bio-inspired aggregation control of carbon nanotubes for ultra-strong composites. Scientific Reports.

[144] Wagner HD. Nanocomposites: paving the way to stronger materials. Nature Nanotechn

[145] Murayama T. Dynamic measurement of interfilament friction on staple yarns. Journal

mandrel under a poly(vinyl alcohol) spray. Carbon. 2011;**49**(14):4786–4791

2012;**4**(23):7464–7468

28 Nanomechanics

2012;**6**(6):5457–5464

Materials. 2016;**28**(31):6598–6605

Research Letters. 2013;**1**(1):19–25

composites. Small. 2010;**6**(6):763–767

2015;**5**:11533

ology. 2007;**2**(12):742–744

Advanced Functional Materials. 2009;**19**(20):3219–3225

of Applied Polymer Science. 1979;**24**(6):1413–1417

[147] Guo W, Liu C, Zhao F, Sun X, Yang Z, Chen T, Chen X, Qiu L, Hu X, Peng H. A novel electromechanical actuation mechanism of a carbon nanotube fiber. Advanced Materials. 2012;**24**(39):5379–5384

## **Mechanical Behavior of Nanostructured and Ultrafine-Grained Metal Alloy under Intensive Dynamic Loading**

Vladimir A. Skripnyak and Evgeniya G. Skripnyak

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68291

#### Abstract

Researches of the last years have allowed to establish that the laws of deformation and fracture of bulk ultrafine-grained (UFG) and coarse-grained (CG) materials are various both in static and in dynamic loading conditions. The influence of average grain size on the yield stress, the tensile strength, and the compression strength was established for metal alloys with a face-centered cubic (FCC), a body-centered cubic (BCC), and a hexagonal close-packed (HCP) structures. The study of the microstructure of the alloys after severe plastic deformation (SPD) by the electron backscatter diffraction (EBSD) technique showed the presence of a bimodal grain size distribution in the UFG alloys. Metal alloys with a bimodal grain size distribution possess a negative strain rate sensitivity of the yield stress and higher ductility at quasi-static strain rates. In this chapter, we will discuss the regularities of deformation at high strain rates, damage, and fracture of ultrafine-grained alloys.

Keywords: nanostructured metals, ultrafine-grained alloys, severe plastic deformation, high strain rates, yield stress, spall strength

#### 1. Introduction

During the last decade, the interest in research of mechanical behavior of ultrafine-grained (UFG) and nanostructured (NS) metal alloys has been risen sharply [1–13]. Compared to their coarse-grained counterparts, UFG and NS metals exhibit significantly higher static yield strength, hardness, but lower tensile elongation. Ultrafine-grained materials produced by severe plastic deformation (SPD) methods exhibit a high strength, good damping properties, and superplastic properties over a limited range of strain rates at high temperatures. The increase of UFG material strength can be explained on the behavior of dislocation at submicrometer grain size. Laws of plastic deformation operating at room temperature for

coarse-grained metals usually are based on dislocation mechanisms [1–9]. When grain size is decreased in nanometer range, dislocation activity becomes difficult. Therefore, plastic deformation resulting to dislocation nucleation and motion limits ductility of NS and UFG materials. Strain rate sensitivity of flow stress also depends on grain size [9–11].

Similarity of mechanical behavior of materials in wide range of loading conditions takes place for metals combining into several groups [14]. Metal alloys with face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) crystalline lattices can be related to three groups. Mechanical behavior of these groups of metals has to be described by various constitutive models [2–4]. We can expect that UFG metals with FCC, BCC, and HCP lattices will have various laws of plastic deformation at high strain rates also.

Mechanical behavior of NS and UFG materials under shock wave loading requires understanding of fundamental laws of the deformation and failure mechanisms at high strain rates.

## 2. Mechanical behavior of nanostructured and ultrafine-grained metal alloys

Important information about mechanical behavior of nanostructured and ultrafine-grained materials under dynamic loading is contained in the experimental data on high-speed interaction of plates; results of tests on compression and tension by using a split-Hopkinson pressure bar (SHPB), also known as Kolsky bar test; and results of tests using high-rate servo-hydraulic machine Instron VHS.

Experimental results obtained from the tests of metals and alloys by these methods showed that the patterns of deformation in ultrafine-grained and coarse-grained materials are different not only under quasi-static but also intense dynamic loading.

The free surface profiles of shock wave in the UFG Ti-6Al-2Sn-2Zr-2Mo-Si titanium alloy are shown in Figure 1.

The metal plate was loaded with shock pulses, which were obtained by the impact of thin aluminum. The metal plate was loaded with shock pulses, which were obtained at impact thin aluminum plates at a speed of 650 m/s [13, 15].

The movement of the back surface of the plates when exposed to a shock pulse was recorded using a laser Doppler interferometer VISAR with subnanosecond time resolution [15].

Shock wave in UFG alloys has the two-wave structure as in CG alloys. The shock wave in the UFG alloys has a double structure in coarse-grained alloys. Elastic precursor propagates with the longitudinal sound speed. The bulk compression wave or the plastic wave propagates through compressed material with the bulk speed of sound.

Curves 1 and 2 correspond to specimens with grain size ~300 nm, and the Curve 3 corresponds to coarse-grained specimen with grain size of 20 μm [13, 15]. The thicknesses of UFG specimens 1 and 2 were 0.835 and 6.36 mm, respectively. The thickness of coarse-grained specimen was 10 mm.

Mechanical Behavior of Nanostructured and Ultrafine-Grained Metal Alloy under Intensive Dynamic Loading http://dx.doi.org/10.5772/intechopen.68291 33

Figure 1. Free surface velocity profiles.

coarse-grained metals usually are based on dislocation mechanisms [1–9]. When grain size is decreased in nanometer range, dislocation activity becomes difficult. Therefore, plastic deformation resulting to dislocation nucleation and motion limits ductility of NS and UFG

Similarity of mechanical behavior of materials in wide range of loading conditions takes place for metals combining into several groups [14]. Metal alloys with face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) crystalline lattices can be related to three groups. Mechanical behavior of these groups of metals has to be described by various constitutive models [2–4]. We can expect that UFG metals with FCC, BCC, and HCP

Mechanical behavior of NS and UFG materials under shock wave loading requires understanding of fundamental laws of the deformation and failure mechanisms at high strain rates.

Important information about mechanical behavior of nanostructured and ultrafine-grained materials under dynamic loading is contained in the experimental data on high-speed interaction of plates; results of tests on compression and tension by using a split-Hopkinson pressure bar (SHPB), also known as Kolsky bar test; and results of tests using high-rate servo-hydraulic

Experimental results obtained from the tests of metals and alloys by these methods showed that the patterns of deformation in ultrafine-grained and coarse-grained materials are different

The free surface profiles of shock wave in the UFG Ti-6Al-2Sn-2Zr-2Mo-Si titanium alloy are

The metal plate was loaded with shock pulses, which were obtained by the impact of thin aluminum. The metal plate was loaded with shock pulses, which were obtained at impact thin

The movement of the back surface of the plates when exposed to a shock pulse was recorded

Shock wave in UFG alloys has the two-wave structure as in CG alloys. The shock wave in the UFG alloys has a double structure in coarse-grained alloys. Elastic precursor propagates with the longitudinal sound speed. The bulk compression wave or the plastic wave propagates

Curves 1 and 2 correspond to specimens with grain size ~300 nm, and the Curve 3 corresponds to coarse-grained specimen with grain size of 20 μm [13, 15]. The thicknesses of UFG specimens 1 and 2 were 0.835 and 6.36 mm, respectively. The thickness of coarse-grained specimen

using a laser Doppler interferometer VISAR with subnanosecond time resolution [15].

not only under quasi-static but also intense dynamic loading.

through compressed material with the bulk speed of sound.

aluminum plates at a speed of 650 m/s [13, 15].

2. Mechanical behavior of nanostructured and ultrafine-grained metal

materials. Strain rate sensitivity of flow stress also depends on grain size [9–11].

lattices will have various laws of plastic deformation at high strain rates also.

alloys

32 Nanomechanics

machine Instron VHS.

shown in Figure 1.

was 10 mm.

The Hugoniot elastic limit (HEL) (dynamic elastic limit) for an elastic plastic material can be calculated by the formula [15, 16]

$$
\sigma\_{\rm HEL} = (1/2)\rho\_0 \mathbf{C}\_{\rm L} u\_{\rm HEL} \tag{1}
$$

where σHEL is the Hugoniot elastic limit, r0 is the initial mass density, CL is the longitudinal speed of sound, and upHEL = ufsHEL/2 is the maximum particle velocity in the elastic precursor.

The average strain rate in the elastic precursor is measured by the ratio [16]

$$
\dot{\varepsilon}\_{eq}^{HEL} = \frac{1}{2} \frac{u\_{pHE}}{\mathbb{C}\_L \Delta t\_{HEL}},\tag{2}
$$

where ΔtHEL is a time, which is achieved by the amplitude of the elastic precursor.

The calculated ratio of the bulk modulus of nanostructured titanium to the bulk modulus of coarse-grained titanium agrees with experimental data. Sound velocities of materials can be calculated by relations [16]

$$\mathbf{c}\_{\mathbf{s}} = \sqrt{\mu}/\rho, \quad \mathbf{c}\_{\mathbf{b}} = \sqrt{\mathbf{B}/\rho}, \quad \mathbf{c}\_{\mathbf{L}} = \sqrt{\mathbf{c}\_{\mathbf{b}}^2 + (4/3)\mathbf{c}\_{\mathbf{s}}^2} \tag{3}$$

where Cs, Cb, CL are the shear, bulk, and longitudinal sound velocities; B is the bulk modulus; and μ is the shear modulus.

The effective bulk modulus B of nanostructured material can be determined by the equation

$$B = B^{(c)}\mathcal{C}^{(c)} + B^{(g)}\mathcal{C}^{(g)} + B^{(t\dagger)}\mathcal{C}^{(t\dagger)},\tag{4}$$

where B(c) is the isentropic bulk modulus of a crystalline phase; B(g) ≈ 0.45B(c) and B(tj) ≈ 0. 5B(c) are the bulk modulus of a grain boundary phase and the bulk modulus of material near the triple junctions correspondingly; and C(c), C(g), and C(tj) are the volume fractions of these phases correspondingly.

The volume fraction of the triple junction and the volume fraction of grain boundaries were described by the equations

$$\mathbb{C}^{(\mathcal{g})} = \beta^{(\mathcal{g})} \exp \left( -a^{(\mathcal{g})} d\_{\mathcal{S}} / b \right), \tag{5}$$

$$\mathbf{C}^{(\dagger)} = \beta^{(\dagger)} \exp\left(-\alpha^{(\dagger)} d\_{\S}/b\right),\tag{6}$$

where dg is the grain size; b is the modulus of the Burgers vector; and β(g), β(tj), α(g), and α(tj) are the constants of a material.

The values of C(g) and C(tj) versus grain size are shown in Figure 2.

As the grain size is decreased into the nanometer range (<100 nm), the volume of grain interfaces sufficiently increased. The calculated ratio of the bulk modulus of nanostructured materials to the bulk modulus of coarse-grained materials is demonstrated in Figure 2.

Figure 2. Volume fractions of grain boundary phases versus grain size for titanium. Filled square denotes the experimental data [17].

From Eqs. (3)–(6), it follows that the longitudinal and bulk sound velocities for the UFG and CG alloys differ insignificantly. Thus, in the absence of pores and microcracks, UFG and CG alloys have close values of mass density, elastic moduli, and sound velocities Cs, Cb, and CL.

The dynamic yield stress of the material σy acting on the shock adiabat is determined by the formula [15, 16]

$$
\sigma\_Y = \sigma\_{\rm HEL} \frac{1 - 2\nu}{1 - \nu},
\tag{7}
$$

where ν is Poisson's ratio.

The effective bulk modulus B of nanostructured material can be determined by the equation

where B(c) is the isentropic bulk modulus of a crystalline phase; B(g) ≈ 0.45B(c) and B(tj) ≈ 0. 5B(c) are the bulk modulus of a grain boundary phase and the bulk modulus of material near the triple junctions correspondingly; and C(c), C(g), and C(tj) are the volume fractions of these

The volume fraction of the triple junction and the volume fraction of grain boundaries were

Cð Þg ¼ βð Þg exp �αð Þg dg=b

Cð Þ tj ¼ βð Þ tj exp �αð Þ tj dg=b

where dg is the grain size; b is the modulus of the Burgers vector; and β(g), β(tj), α(g), and α(tj) are

As the grain size is decreased into the nanometer range (<100 nm), the volume of grain interfaces sufficiently increased. The calculated ratio of the bulk modulus of nanostructured materials to the bulk modulus of coarse-grained materials is demonstrated in Figure 2.

B/B0

The values of C(g) and C(tj) versus grain size are shown in Figure 2.

0 10 20 30 40 50 60 70 80

d g (nm)

Figure 2. Volume fractions of grain boundary phases versus grain size for titanium. Filled square denotes the experimen-

phases correspondingly.

34 Nanomechanics

described by the equations

the constants of a material.

0,0

C(tj) C(g)

C(gb)

0,2

0,4

B/B0 , C

tal data [17].

(g), C

(tj), C

(gb)

0,6

0,8

1,0

B ¼ Bð Þc Cð Þc þ Bð Þg Cð Þg þ Bð Þ tj Cð Þ tj ; ð4Þ

; ð5Þ

; ð6Þ

The experimental results in Figure 1 showed that the UFG and CG titanium alloys have similar amplitude values of the elastic precursors at the equivalent distances to the free surface of the samples. Thus, the Hugoniot elastic limits of UFG and CG titanium alloys can be the same. But the quasi-static yield strength of titanium alloys depends on grain size in accordance with the Hall-Petch relation, as shown in Figure 3.

Filled symbols show experimental data for titanium alloys [13, 18] and magnesium alloys [7, 8, 19].

Experimental investigations indicate that the prevailing deformation mechanisms are changed for the grain size below ~100 nm. The Hall-Petch relation (Eq. (8)) is satisfied for many polycrystalline materials, but the values of coefficients σ0 and k are changed at the

Figure 3. The yield strength of HCP alloys versus the inverse square root of the grain size.

Figure 4. Free surface velocity versus time in UFG and CG copper.

grain size about several hundred nm (range UFG) and 30–20 nm (range NS) as shown in Figure 3. Filled symbols show experimental data for titanium alloys [13, 18] and magnesium alloys [7, 8, 19]:

$$
\sigma\_s = \sigma\_0 + k d\_g^{-1/2},
\tag{8}
$$

where σ0 is the yield strength, dg is the grain size, σ0, and k are the material constants.

Figure 4 shows shock wave profiles in UFG and CG copper specimens [15, 20, 21]. Copper refers to isomechanical group of materials with the FCC lattice [15]. Curve 1 corresponds to UFG structure of specimen with grain size of ~500 nm. Curve 2 is received for a material in which fine grains occupied only 85% of volume. These experimental results testify that the Hugoniot elastic limit (HEL) and the spall strength (σsp) of copper sharply decrease with the decrease of the relative volume occupied with UFG structure.

The solid Curve 1 corresponds to CG specimen, and dashed Curve 2 corresponds to UFG specimen. The HEL of UFG copper M2 (~0.4 GPa) is about twice that of polycrystalline alloy.

Precipitate-strengthened aluminum, magnesium alloys, copper, and some other metals possess a high strength and ductility. The presence of nanoparticles and precipitate phases influences on the yield stress and the spall strength of UFG alloys under shock wave loadings.

In Figure 5, shock wave profiles in precipitate-strengthened aluminum alloy AA6063T6- AlMg0.5Si0.4 are shown [6].

Mechanical Behavior of Nanostructured and Ultrafine-Grained Metal Alloy under Intensive Dynamic Loading http://dx.doi.org/10.5772/intechopen.68291 37

Figure 5. Free surface velocities versus time in UFG and CG aluminum alloy AA6063 T6.

grain size about several hundred nm (range UFG) and 30–20 nm (range NS) as shown in Figure 3. Filled symbols show experimental data for titanium alloys [13, 18] and magnesium

Time (nanoseconds)

0 100 200 300 400 500 600

~ 2.95 GPa

~ 2.05 GPa Copper M2

d g

d g

~0.5 mm

~110 mm

σs ¼ σ0 þ kd�1=2

Figure 4 shows shock wave profiles in UFG and CG copper specimens [15, 20, 21]. Copper refers to isomechanical group of materials with the FCC lattice [15]. Curve 1 corresponds to UFG structure of specimen with grain size of ~500 nm. Curve 2 is received for a material in which fine grains occupied only 85% of volume. These experimental results testify that the Hugoniot elastic limit (HEL) and the spall strength (σsp) of copper sharply decrease with the

The solid Curve 1 corresponds to CG specimen, and dashed Curve 2 corresponds to UFG specimen. The HEL of UFG copper M2 (~0.4 GPa) is about twice that of polycrystalline alloy.

Precipitate-strengthened aluminum, magnesium alloys, copper, and some other metals possess a high strength and ductility. The presence of nanoparticles and precipitate phases influences on the yield stress and the spall strength of UFG alloys under shock wave loadings.

In Figure 5, shock wave profiles in precipitate-strengthened aluminum alloy AA6063T6-

where σ0 is the yield strength, dg is the grain size, σ0, and k are the material constants.

decrease of the relative volume occupied with UFG structure.

g ; ð8Þ

alloys [7, 8, 19]:

0

Figure 4. Free surface velocity versus time in UFG and CG copper.

50

100

150

Free surface velocity (m/s)

36 Nanomechanics

200

250

300

σ sp

2 1 σHEL < 0.2 GPa

σ sp

350

AlMg0.5Si0.4 are shown [6].

Curves 1, 2, and 3 correspond to AA6063T6 alloy after two and eight passes of equal-channel angular pressing (ECAP) and without ECAP, respectively. Coarse-grained alloy specimens had a grain size of ~100 μm. UFG structure was created by repeated ABC ECAP passes. Nanoparticles of Mg2Si were formed by means of thermal treatment of alloy before ECAP treatment. The HEL of coarse-grained AA6063T6 was equal to ~0.33 GPa, and the spall strength was equal to ~1.29 GPa, whereas the HEL values of UFG alloy were ~5.7% higher (~0.35 GPa), and the spall strength was equal to ~1.48 GPa. Thus, the spall strength and the yield strength of UFG alloys depend not only on grain size but also on concentration and sizes of phase precipitates.

The Hugoniot elastic limit of ultrafine-grained metal alloys and their coarse-grained counterparts is not significantly different. The rate of elastic precursor attenuation is above in UFG alloys, than in coarse-grained counterparts.

The tensile strength at high strain rate can be determined from the analysis of shock wave profiles shown in Figures 1, 4, and 5. These values correspond to the spall strength. The spall strength is determined by formulas [15, 16]

$$
\sigma\_{\rm sp} = (1/2)\rho\_0 \mathbb{C}\_b \{ \Delta u\_{\rm f} + \delta \}, \qquad \delta = (\hbar/\mathbb{C}\_b - \hbar/\mathbb{C}\_L) \cdot |\dot{u}\_1|, \tag{9}
$$

where σsp is the spall strength; r0 is the initial mass density; Cb is the bulk speed of sound in the shock-compressed material; Δufs is the difference between the maximum speed of the free surface of the target and speed in front of the spall pulse; δ is the amendment, to account for the velocity gradients at the free surface in front of spall pulse and in the front; h is the thickness of the target; CL is the longitudinal sound velocity; and u\_ 1 is the change in the free surface velocity in time in front of the spall pulse.

The spall strength σsp of copper specimen with grain size of 500 nm is ~2.95 GPa, whereas the spall strength of specimen with grain size of 100 μm is only ~ 2.05 GPa. The spall strength of UFG and CG copper is shown in Figure 6.

The spall strength of UFG and CG and single crystal aluminum alloys is shown in Figure 7.

Filled symbols show experimental data for Al single crystal [15], AD1 [15], AMg6 [15], and AA6063T6 [6].

These results correlate with data on the increasing of the quasi-static yield stress of FCC metals at a decrease of grain sizes (Figure 8). Experimental data [4–6, 18, 20, 21] for copper and aluminum alloys are shown by the filled symbols.

Changes of curve slope both FCC and HCP metal alloys (Figures 3 and 8) testify to peculiarities of the mechanical behavior of UFG alloys when the grain size varied from 1000 to ~10 nm.

Bulk UFG alloys usually have a dispersion of grain size appearing at their manufacturing by severe plastic deformation (SPD) methods. A specific volume, which is occupied with UFG structure, influences on the HEL and the spall strength of alloys.

Figure 6. The spall strength of UFG and CG copper.

Mechanical Behavior of Nanostructured and Ultrafine-Grained Metal Alloy under Intensive Dynamic Loading http://dx.doi.org/10.5772/intechopen.68291 39

Figure 7. The spall strength of UFG and CG aluminum alloy AA6063 T6.

the velocity gradients at the free surface in front of spall pulse and in the front; h is the thickness of the target; CL is the longitudinal sound velocity; and u\_ 1 is the change in the free

The spall strength σsp of copper specimen with grain size of 500 nm is ~2.95 GPa, whereas the spall strength of specimen with grain size of 100 μm is only ~ 2.05 GPa. The spall strength of

The spall strength of UFG and CG and single crystal aluminum alloys is shown in Figure 7.

Filled symbols show experimental data for Al single crystal [15], AD1 [15], AMg6 [15], and

These results correlate with data on the increasing of the quasi-static yield stress of FCC metals at a decrease of grain sizes (Figure 8). Experimental data [4–6, 18, 20, 21] for copper and

Changes of curve slope both FCC and HCP metal alloys (Figures 3 and 8) testify to peculiarities of the mechanical behavior of UFG alloys when the grain size varied from 1000 to

Bulk UFG alloys usually have a dispersion of grain size appearing at their manufacturing by severe plastic deformation (SPD) methods. A specific volume, which is occupied with UFG

surface velocity in time in front of the spall pulse.

aluminum alloys are shown by the filled symbols.

Figure 6. The spall strength of UFG and CG copper.

structure, influences on the HEL and the spall strength of alloys.

UFG and CG copper is shown in Figure 6.

AA6063T6 [6].

38 Nanomechanics

~10 nm.

Figure 8. The yield strength versus the inverse square root of the grain size.

## 3. Dissipation of mechanical energy during deformation of ultrafinegrained and coarse-grained titanium and zirconium alloys

Research of deformation localization and fracture mechanisms of NS and UFG alloys was investigated by a combination of structure-sensitive methods [1, 2, 22–27]. The high sensitivity of modern infrared (IR) thermal vision systems in combination with the opportunity of noncontact continuous temperature and strain measurements gives us important information on processes of damage and fracture. Recently, it has been shown that UFG titanium has a peak of an internal friction at temperatures of 450–500C, which results from the processes of recovery and recrystallization [22]. Experimental data were obtained about the deformation and thermal characteristics of the UFG and CG VT1-0 alpha titanium alloy and E110 zirconium alloy [26–28]. The mechanical tests were performed by means of servo-hydraulic machine Instron VHS 40/50–20. These specimens were nanostructured by means of a combined method of severe plastic deformation (SPD).

The residual stresses in the specimens were relieved by means of annealing. Samples from UFG titanium and zirconium were converted to coarse grain using a high-temperature annealing. The forces were registered by the sensor DYNACELL with accuracy up to 0.2%.

The obtained curves of true stress—true strain were used for determination of the yield strength, the strength, and the strain to failure. The temperature distributions on the specimen surface under tension with constant strain rate were registered by using the FLIR system SC7700M series infrared camera.

IR thermograms were registered with maximum recording frequency of 115 Hz. The resolution was ~20 micron and the image format is of 640 512 mm.

The thermal camera was at a distance of 0.4 m from the specimen. The software of the FLIR system SC7700M was used for interpretation of the registered data [24]. The reflection surface of the samples was close to the "absolutely black body" through the use of carbon blackening.

The thermal vision system allowed one to record not only the specimen's surface temperature distribution but also the current dimensions of specimen during the deformation. The specimen size, the loading force, and the loading times were recorded in the process of quasi-static tensile tests. Engineering true stress, strain, and true strain were calculated using recorded data.

True stress-strain curves of coarse-grained VT1-0 titanium and E110 zirconium specimens under tension are shown in Figures 9 and 10, respectively. True stress-true strain curves are marked as Curve 1. Curve 2 corresponds to the engineering stress and strain diagrams. Figures 9 and 10 also showed the temperature distribution on the surface of the samples for several increasing strains.

Temperature change is caused by dissipation of mechanical energy during plastic deformation.

The stress-strain curve has a parabolic ascending branch, which passes into the descending portion having a negative coefficient of strain hardening. True stress-strain diagrams of UFG

Mechanical Behavior of Nanostructured and Ultrafine-Grained Metal Alloy under Intensive Dynamic Loading http://dx.doi.org/10.5772/intechopen.68291 41

Figure 9. Stress-strain curves of coarse-grained VT1-0 titanium.

3. Dissipation of mechanical energy during deformation of ultrafine-

Research of deformation localization and fracture mechanisms of NS and UFG alloys was investigated by a combination of structure-sensitive methods [1, 2, 22–27]. The high sensitivity of modern infrared (IR) thermal vision systems in combination with the opportunity of noncontact continuous temperature and strain measurements gives us important information on processes of damage and fracture. Recently, it has been shown that UFG titanium has a peak of an internal friction at temperatures of 450–500C, which results from the processes of recovery and recrystallization [22]. Experimental data were obtained about the deformation and thermal characteristics of the UFG and CG VT1-0 alpha titanium alloy and E110 zirconium alloy [26–28]. The mechanical tests were performed by means of servo-hydraulic machine Instron VHS 40/50–20. These specimens were nanostructured by means of a combined method

The residual stresses in the specimens were relieved by means of annealing. Samples from UFG titanium and zirconium were converted to coarse grain using a high-temperature annealing. The forces were registered by the sensor DYNACELL with accuracy up to 0.2%.

The obtained curves of true stress—true strain were used for determination of the yield strength, the strength, and the strain to failure. The temperature distributions on the specimen surface under tension with constant strain rate were registered by using the FLIR system

IR thermograms were registered with maximum recording frequency of 115 Hz. The resolu-

The thermal camera was at a distance of 0.4 m from the specimen. The software of the FLIR system SC7700M was used for interpretation of the registered data [24]. The reflection surface of the samples was close to the "absolutely black body" through the use of carbon blackening. The thermal vision system allowed one to record not only the specimen's surface temperature distribution but also the current dimensions of specimen during the deformation. The specimen size, the loading force, and the loading times were recorded in the process of quasi-static tensile tests. Engineering true stress, strain, and true strain were calculated using recorded

True stress-strain curves of coarse-grained VT1-0 titanium and E110 zirconium specimens under tension are shown in Figures 9 and 10, respectively. True stress-true strain curves are marked as Curve 1. Curve 2 corresponds to the engineering stress and strain diagrams. Figures 9 and 10 also showed the temperature distribution on the surface of the samples for

Temperature change is caused by dissipation of mechanical energy during plastic deformation. The stress-strain curve has a parabolic ascending branch, which passes into the descending portion having a negative coefficient of strain hardening. True stress-strain diagrams of UFG

tion was ~20 micron and the image format is of 640 512 mm.

grained and coarse-grained titanium and zirconium alloys

of severe plastic deformation (SPD).

40 Nanomechanics

SC7700M series infrared camera.

data.

several increasing strains.

Figure 10. Stress-strain curves of coarse-grained E110 zirconium.

Figure 11. Stress-strain diagrams of ultrafine-grained VT1-0 titanium alloy.

VT1-0 titanium and E110 zirconium specimens under tension are shown in Figures 11 and 12, respectively.

Curves of true stress-true strain are shown as Curve 1. Curves of engineering stress and strain are marked as Curve 2. The insets show the temperature distribution on the specimen surface under certain deformations.

Dimensions of specimens at thermograms for UFG titanium and zirconium alloys showed that the fractional decrease in the area at fracture of specimens is twice less ones in comparison with values of CG alloys. Deformation localization in the zone of necking caused a significant growth of true flow stress and increase of the hardening coefficient. Deformation localization is accompanied by local temperature rise.

The maximum temperature on the surface of CG titanium specimen raised proportionally to the strain rate up to a certain level (in the range from 50 to 55C) and then increased sharply on ~510C (up to the temperature 58.4560.54C) due to the localization of the plastic deformation near damages or crack.

The analyses of IR thermograms showed that character of temperature changing under deformation of UFG and CG titanium specimens is different. These results indicate that macroscopic regularities of strain localization in the UFG and CG titanium and zirconium alloys differ.

The maximum temperature of the UFG sample is directly proportional to strain rate and reaches a temperature of 50–58 C, after that the temperature did not change much [28].

Mechanical Behavior of Nanostructured and Ultrafine-Grained Metal Alloy under Intensive Dynamic Loading http://dx.doi.org/10.5772/intechopen.68291 43

Figure 12. The diagram of ultrafine-grained E110 zirconium alloy.

VT1-0 titanium and E110 zirconium specimens under tension are shown in Figures 11 and 12,

Curves of true stress-true strain are shown as Curve 1. Curves of engineering stress and strain are marked as Curve 2. The insets show the temperature distribution on the specimen surface

Dimensions of specimens at thermograms for UFG titanium and zirconium alloys showed that the fractional decrease in the area at fracture of specimens is twice less ones in comparison with values of CG alloys. Deformation localization in the zone of necking caused a significant growth of true flow stress and increase of the hardening coefficient. Deformation localization is

The maximum temperature on the surface of CG titanium specimen raised proportionally to the strain rate up to a certain level (in the range from 50 to 55C) and then increased sharply on ~510C (up to the temperature 58.4560.54C) due to the localization of the plastic deforma-