Mechanical properties of ceramics reinforced with allotropic forms of carbon

Progress in Materials Science 128 (2022) 100966 Available online 7 May 2022 0079-6425/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Mechanical properties of ceramics reinforced with allotropic forms of carbon Víctor Morales-Fl´ orez * , Arturo Domínguez-Rodríguez Dpto. Física de la Materia Condensada, Universidad de Sevilla, Av. Reina Mercedes s/n, 41012 Seville, Spain ARTICLE INFO Keywords: Carbon nanotubes Graphene Carbon nanofibers Mechanical properties Alumina Zirconia ABSTRACT For decades, enormous investigation effort has been devoted to the fabrication of new ceramic matrix composites with enhanced mechanical properties. One of the most explored strategies is the addition of carbon allotropic phases such as carbon nanotubes, graphene, and carbon nanofibers due to their outstanding properties. In this review, the main fabrication protocols considered for the synthesis of the ceramic composites based on alumina and zirconia are shown, and their mechanical properties and the changes achieved by the addition of carbon allotropes are presented and discussed. Under particular circumstances, significant improvements in properties such as fracture toughness and wear at low temperature, or creep behavior and superplasticity at high temperature have been accomplished. Nevertheless, some critical aspects such as the homogenization of the carbon allotropes within the matrix are still lacking consolidated responses, which suggest that the potentialities of this reinforcing strategy have not yet been completely exploited. In summary, this work collects the fabrication strategies, major results, and main controversies of two decades of scientific research on the improvement of the fabrication methods and mechanical properties of ceramic matrix composites. Abbreviations: ASB, Aluminum-tri-sec-butoxide; ASTM, American society for testing materials; ACP, Aqueous colloidal procedure; BNNT, Boron nitride nanotubes; CMC, Ceramic matrix composite; CNB, Chevron notched beam; CNF, Carbon nanofiber; CNT, Carbon nanotube; CIP, Cold isostatic pressing; COF, Coefficient of friction; CTAB, Cetyltrimethylammonium bromide; CVD, Chemical vapor deposition; CVI, Chemical vapor infiltration; DCM, Direct crack measurement; DLS, Dynamic light scattering; DWCNT, Double-walled carbon nanotube; EDX, Energy-dispersive x-ray spectroscopy; EELS, Electron energy loss spectroscopy; f-CNT, Functionalized carbon nanotube; f-MWCNT, Functionalized multi-walled carbon nanotube; f-SWCNT, Functionalized single-walled carbon nanotube; FEM, Finite element method; FGM, Functionally gradient materials; FWHM, Full width at half maximum; GBS, Grain boundary sliding; GNP, Graphene nanoplatelets; GO, Graphene oxide; GPL, Graphene platelet; HFIHS, High frequency induction-heated sintering; HIP, Hot isostatic pressing; HP, Hot pressing; HTB, High-temperature background; HV, Hardness Vickers; irGO, In situ reduced graphene oxide; LBA, Load bearing ability; LEM, Lawn, Evans and Marshall; MWCNT, Multi-walled carbon nanotube; PAN, Polyacrylonitrile; PEG, Polyethylene glycol; PEI, Polyethyleneimine; PVB, Polyvinyl butyral; rGO, Reduced graphene oxide; RRT, Round-Robin tests; SCF, Surface crack in flexure; SDS, Sodium dodecyl sulphate; SEM, Scanning electron microscopy; SENB, Single-edged notched beam; SEPB, Singleedged pre-cracked beam; SEVNB, Single-edged V-notched beam; SPD, Superplastic deformation; SPS, Spark plasma sintering; SWCNT, Single-walled carbon nanotube; TEM, Transmission electron microscopy; t-MWCNT, Thermally annealed multiwall carbon nanotube; UPLA, Ultrashort pulse laser ablation; VIF, Vickers indentation fracture; XPS, X-ray photoelectron spectroscopy; YTZP, Yttria-stabilized tetragonal zirconia polycrystals; µWS, Microwave sintering. * Corresponding author at: Dpto. Física de la Materia Condensada, Universidad de Sevilla, Av. Reina Mercedes s/n, E41012 Seville, Spain. E-mail addresses: [email protected] (V. Morales-Fl´ orez), [email protected] (A. Domínguez-Rodríguez). Contents lists available at ScienceDirect Progress in Materials Science journal homepage: www.elsevier.com/locate/pmatsci https://doi.org/10.1016/j.pmatsci.2022.100966 Received 17 September 2020; Received in revised form 15 July 2021; Accepted 30 April 2022 Progress in Materials Science 128 (2022) 100966 2 1. Introduction Ceramic materials have been a very extensive active field of research in the last decades owing to their excellent physical properties such as high-temperature stability, chemical inertness, strength, hardness, and wear resistance together with relatively low densities in comparison to metallic materials. The awakening of this new golden age of ceramic materials can be established in 1975, when Garvie et al. published their article “Ceramic steel?” on zirconia-based ceramics in Nature [1]. Since then, the market value of the global advanced technical ceramics has risen up to $56.70 billion in 2015, considering research, industry, and applications [2]. Thus, ceramics are currently present in a vast set of diverse and sophisticated engineering applications such as superplastic forming [3,4], hightemperature superconductors [5], gas sensors [6], ferroelectric capacitors [7], thermal barriers [8,9], tissue engineering [10,11], leading edges [12], armors [13,14], cutting tools [15], spacecraft [16], separation membranes [17], solid oxide fuel cells [18], engines [19], laser hosts [20], electronic and optoelectronic devices [21,22], water remediation systems [23], and drug delivery [24], among others. Alumina (Al 2 O 3 ) and yttria-stabilized tetragonal zirconia polycrystals (YTZP) (ZrO 2 ) are two of the most frequently considered ceramic matrixes in scientific research and in industry, with special relevance in different advanced industrial sectors and for hightemperature structural applications due to their high oxidation resistance. This review will focus on results obtained regarding the fabrication methods and the mechanical properties of ceramic matrix composites (CMCs) based on alumina or YTZP at low as well as high temperatures. Nevertheless, the inherent brittleness of hard materials such as ceramics due to the ionic-covalent bonding energy character has restricted many different structural applications. So, this limitation has been a continuous driving force that has encouraged researchers to look for new approaches with the aim of improving their fracture toughness. Nature, which is one of the most inspiring sources for engineering solutions, has already confronted this challenge by “designing” composite microstructured materials such as nacre [25,26]. Mimicking nature, a huge number of new ceramic-matrix micro- or nanostructured composites have been proposed, pursuing the occurrence of new toughening mechanisms such as increasing tortuosity of crack propagation or increasing the work of fracture. One of the most explored strategies for toughening materials is the addition of a second reinforcing phase. In the case of ceramic matrixes, the use of reinforcing phases such as whiskers (SiC, Al 2 O 3 ) [27–31], particles (ceramic, metal) [32,33], or long or short fibers (alumina, mullite, Si 3 N 4 , βSiC) [34–38], has been an effective practice to convert the brittleness into toughness. Besides, since the discovery of the different allotropic forms of carbon such as carbon nanotubes (CNTs) [39] and graphene [40], both with exceptional thermal, mechanical, and electric properties and outstanding multifunctional features, they have been used as new additives to overcome the problem of the high brittleness described above, among other purposes, and have been introduced in a variety of alumina or zirconia matrixes. Thus, hundreds of articles have been published related to CNT–alumina, graphene–alumina, CNT–YTZP, or graphene–YTZP composites, with a sustained increasing trend, as can be seen in Fig. 1, concerning novel synthesis protocols, or research on different physical properties such as mechanical, thermal, or electrical properties. After decades of study, results on the mechanical properties of ceramic matrix reinforced by the inclusion of carbon allotropes as reinforcing agents are confusing and not conclusive. Furthermore, there are also several works explicitly questioning the plausibility of the expected mechanical improvements and they indicate limitations of the reinforcement by the inclusion of carbon allotropes into ceramic matrixes and significant scattering of the reported results [41–48]. Moreover, there is a general consensus that three major causes of this controversy on the mechanical reinforcement are related to the preparation procedures [46,49,50]. Firstly, the problems in obtaining composites that are homogeneous on a micrometric or submicrometric scale typically result in a badly dispersed system of carbon allotropes, which are commonly found as aggregates or bundles, instead of individualized entities. In particular, CNTs present enormous problems to be dispersed due to the van der Waals interactions, which lead them to become entangled and to form bundles [51], hindering the formation of stable suspensions to prepare Fig. 1. Publications on a) CNT–alumina and graphene–alumina and b) CNT–zirconia and graphene–zirconia. Source: Web of Knowledge (July 2020). V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 3 homogeneous composites. Besides, there are also graphene-doped composites that suffer reductions in their mechanical resistance due to residual pores caused by the agglomeration of graphene nanoplatelets (GNPs), which give rise to notches and defects. Secondly, the union between the grains of the ceramic matrix and the carbon allotropes is not always satisfactory. For example, it was reported that reinforcement of 3YTZP by CNTs was not achieved due to the poor union between the nanotubes and the matrix [52]. And thirdly, several works have shown that the carbon allotropes are typically located in the grain boundaries of the ceramic matrix [44,48,53–58]. But it has also been suggested that this location is not the most efficient for the mechanical reinforcement of the composite material. Instead, the intragranular location has been proposed as a true reinforcement strategy given that toughening mechanisms such as bridging or pullout may indeed arise and will significantly increase the fracture energy and hinder crack propagation [49,59–61]. Therefore, the efficiency of the reinforcement of ceramics with carbon allotropes is strongly dependent on how the reinforcing phase elements are dispersed in the matrix, how are they bonded to the matrix, and where they are located with respect to the grains of the matrix. This is why optimization of the synthesis strategies in order to achieve the correct dispersion of the reinforcing phase, its proper union with the ceramic matrix, and its intragranular location is still an important challenge to which great research efforts are devoted. To obtain a good homogenization of the CNTs, several techniques have been used such as conventional powder processing, functionalization of the CNTs by acid treatment, colloidal processing, sol–gel processing, heterocoagulation, charge stabilization techniques, and novel in situ growth of CNTs by catalytic chemical vapor deposition (CVD) [54]. To improve the chemical bonding between the CNTs and the matrix, strategies such as the growth of CNTs in situ, or the use of coated CNTs have been considered [54]. Recently, the sol–gel technique has been used in alumina reinforced with CNTs to incorporate the nanotubes within the alumina grains [59,60]. In summary, research on ceramic materials is facing one of the most interesting challenges existing today, namely, transfer of the intrinsic outstanding mechanical properties of carbon allotropes that cannot be exploited on a microscopic scale to the macroscopic world through the preparation of compounds with new and improved physical properties. The mechanical properties of ceramics can be divided into properties at low temperature and those at high temperature. At low temperature, wear resistance, hardness, and fracture toughness are the most commonly studied properties and they have enormous relevance from a technological point of view. Moreover, many high-temperature structural applications require ceramic materials; therefore, there is significant interest in the study of high-temperature mechanical properties of these reinforced ceramic composites. In particular, plasticity has been widely researched by creep experiments at high temperatures. Mechanical loss measurements have also been used to study the high-temperature mechanical behavior since the grain boundary sliding (GBS) mechanism has been invoked as the main mechanism controlling plasticity and this mechanism is a potential source of energy dissipation [62–65]. Thus, creep experiments together with mechanical spectroscopy, a non-destructive technique, are very useful techniques to explore the hightemperature deformation mechanisms. Finally, it is worth mentioning that there is also a general discussion about the most reliable techniques for the assessment of the fracture toughness of ceramic materials. In the literature, different standard test methods are available such as the single-edged precracked beam (SEPB), single-edged notched beam (SENB), single-edged V-notched beam (SEVNB), chevron notched beam (CNB), and surface crack in flexure (SCF). Other measurement techniques such as Vickers indentation fracture (VIF) crack length, double-torsion technique [66] or nanoindentation (also called instrumented indentation) [67] can be found as well, besides critical reviews of these different techniques and their suitability [68,69]. But, after decades of research, the results are not conclusive. 1.1. Carbon allotropes Currently, a wide variety of allotropic forms of carbon are available for the reinforcement of different materials, and within each form, there are also very different options. At a glance, materials scientists now have easily available CNTs, graphene, fullerene, carbon nanofibers (CNFs), also referred to as whiskers, for fabrication of and research on new materials. Among them, the outstanding physical properties of CNTs, graphene, and CNFs make them the most considered carbon phases for reinforcement purposes. 1.1.1. Graphene Graphene was discovered, individualized, and characterized at the University of Manchester in 2004 [40]. It consists of a monolayer of sp 2 bonded carbon atoms arranged in a honeycomb lattice, with a theoretical specific surface area of 2630 m 2 /g. Graphene is a zero-gap semiconductor and displays remarkable electron mobility at room temperature (mobilities of 250,000 cm 2 V −1 s −1 have been achieved). Graphene also exhibits an extremely high thermal conductivity and values of up to 5300 Wm −1 K −1 have been reported [70–72]. Monolayer graphene is the one-atom single layer material, but there are other different forms in which flat sheets of sp 2 -hybridized carbon atoms can be found. Some efforts towards standardization of the nomenclature were reported by Papageorgiou et al. in 2017 [71]. In Fig. 2, different types of graphene are summarized. Thus, it is also possible to find few-layer graphene (two to five sheets piled on top of each other) and multi-layer graphene (five to ten sheets), both commonly referred to just as graphene. When more than ten of layers of graphene are stacked, they form graphite. When graphene-based materials are below 250 nm in size, they are called graphene nanosheets, nanoplates, or nanoplatelets (GNPs); above this size, they are called graphene microplatelets or micrographite. Graphene can be obtained by different fabrication procedures, namely, bottom-up and top-down procedures [73]. In addition to the pristine (unoxidized) graphene, graphene oxide (GO) is the most used form of graphene. It consists of oxidized graphene layers decorated mostly with epoxide and hydroxyl groups in the basal planes, and with carbonyl and carboxyl groups at the edges [74,75]. These functional groups make GO strongly hydrophilic, which allows it to be easily dispersed and swell in water [76]. Unlike graphite, GO is an electrical insulator, which restricts its convenience for the fabrication of conductive composite materials. Moreover, GO can be chemically reduced in order to obtain reduced graphene oxide (rGO) through the restoration of the network of C-C sp 2 bonds. The V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 4 functional groups containing oxygen in GO can be removed by different procedures, such as microwaves, ion bombardment, as well as electrochemical, chemical or thermal reduction [77]. Additionally, it has also been reported the reduction of GO to graphene during the sintering process of ceramic composites [55]. The chemical processing from pristine graphite to GO and then to rGO has been researched by Raman spectroscopy and X-ray photoelectron spectroscopy (XPS). Firstly, the Raman spectrum of the pristine graphite exhibits a prominent G peak at 1581 cm −1 , corresponding to the first-order scattering of the E2g mode [79]. Secondly, the G band in GO spectrum is broadened and shifted to 1594 cm −1 and the D band at 1363 cm −1 becomes prominent. These features reveal the decrease in the in-plane sp 2 domains, probably due to a high oxidation ratio [74]. Thirdly, the Raman spectrum of the rGO also shows the G and D bands (at 1584 and 1352 cm −1 , respectively) but with an increased D/G intensity ratio compared to that in GO, indicating that new graphitic domains were created [79]. The presence of graphene and its evolution to GO and rGO were also studied by XPS [58,71]. For example, it has been reported that the pristine graphene shows a sharp peak at a binding energy of 285 eV [80]. In addition, the reduction efficiency of the GO can be estimated from the change in the intensity of the vibrations at the C – O and C – – O peaks due to the reduction process and by evaluating the carbon-to-oxygen (C/O) ratio [81,82]. Thus, while in GO the C/O ratio is typically 2:1 to 4:1, in rGO, the oxygen content has been reduced and the C/O ratio can rise up to ~18:1 [83]. In addition, there are many other chemically modified types of graphene, functionalized with very different chemical groups [82] or even exotic geometries, such as large graphene nanoribbons (>200 nm long and <10 nm wide). Regarding the mechanical properties, graphene exhibits an intrinsic tensile strength of ~130 GPa [84] and an elastic modulus of 2.4 TPa [85], which means that it is the strongest material ever tested. In addition, it shows a higher capacity to distribute the forces from an impact than any known material. A hypothetical film of the strongest steel of the same thickness as graphene would have a 100 times weaker 2D failure (tensile) strength. In Table 1, the highest reported values of the mechanical properties of graphene are summarized. Obviously, these outstanding mechanical properties make graphene a suitable candidate for many potential applications, including reinforcing composites. However, prediction of the mechanical properties of graphene is extremely challenging due to the varied chemical composition and impurities, the presence of grain boundaries (boundaries of areas of well-ordered carbon atom arrangements), or topological defects, such as wrinkles or ripples that effectively soften the in-plane stiffness of the graphene [58,86]. Therefore, research on the mechanical properties of graphene is still at the beginning and further systematic studies are required to clearly understand the influence of the graphene on the mechanical properties of the CMCs. 1.1.2. Carbon nanotubes A carbon nanotube consists of a single atomic layer of carbon (graphene) rolled up into a tube with a diameter as low as 0.33 nm Fig. 2. Classification scheme of the different graphene-based materials according to three fundamental properties: number of graphene layers, average lateral dimension, and atomic carbon/oxygen ratio. Reproduced from [78] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 5 [108], and length as high as 6 mm [109] (the so-called single-walled carbon nanotube, SWCNT). When two or more layers of graphene are rolled up concentrically we have double-walled carbon nanotubes (DWCNTs) and multi-walled carbon nanotubes (MWCNTs) respectively. MWCNTs are described as an arrangement of concentric cylinders of graphene single layers, separated approximately 0.42 nm, and with an external diameter as high as 140 nm. The rolling direction of the graphene layers can be defined by a vector (n,m) on the hexagonal lattice and defines their alignment, also generally referred to as chirality: zig-zag (m =0), armchair (m =n), or chiral (m ∕=n) [110]. Besides, they can be easily functionalized (f-CNTs) by attaching different chemical groups such as hydroxyl or carboxyl groups and many others [111,112]. Since CNTs were discovered by Iijima in 1991 [39], they have attracted international scientific interest due to their combination of singular mechanical properties, for example, for MWCNTs, a Young’s modulus of 1.8 TPa [98] and fracture strength of up to 63 GPa [100]; for SWCNTs, a Young’s modulus of 1.47 TPa for a CNT diameter of 3.0 nm, decreasing by more than one order of magnitude as the diameter increases up to 20.0 nm [102]; tensile strength of 52 GPa [96]; thermal properties, for example, for SWCNTs, conductivity of 3500 Wm −1 K −1 , and for MWCNTs, 3000 Wm −1 K −1 [72]); and electrical conductivity of up to 10 4 S/cm (though strongly dependent on chirality), as well as low density, flexibility, thermal stability in an argon atmosphere or under vacuum [113,114] and a very large aspect ratio. Thus, different kinds of CNTs have different mechanical strengths as well as different affinities to the ceramic matrix due to variations in the tubular structure, number, and crystallinity of the graphene layers, the type or amount of surface defects, the surface chemistry, and so on. Together with that, there are other factors such as purity, length of nanotubes, inner and outer diameters, functionalization, types of functionalization, specific surface area, and wall thickness, which will involve variations in the mechanical or structural induced reinforcement phenomena. For example, it was shown that thermal annealing was effective for improving both the axial strength and Young’s modulus of MWCNTs by factors of up to ~18.9 as the mechanical properties increase with the rise in the degree of crystallinity of the MWCNTs and with a lower degree of defect concentration in the structure [115]. In Table 1, the maximum reported values of the mechanical properties of CNTs are summarized. It has been possible to characterize the performance of individual nanotubes, revealing amazing behaviors under mechanical stress. For example, load experiments where failure of the MWCNTs was monitored have been carried out [46,100]. It was observed that they broke in the so-called sword-in-sheath mechanism as the failure was probably restricted to the outer shell of the MWCNT, which was attached to the pulling device. In this regard, SWCNTs have been proposed as a more efficient reinforcing agent as the sword-in-sheath mechanism is not possible [53,116], and therefore, the load will be distributed throughout the nanotubes, ensuring that the outermost layer does not shear off. Nevertheless, other experiments have studied the load-bearing ability of MWCNTs embedded in Al 2 O 3 [117,118] through tensile-bending tests. Protruding MWCNTs of the surface of a fracture were loaded inside a scanning electron microscopy (SEM) device with the help of a nano-manipulator. The MWCNTs showed an exceptional mechanical performance even in highly deflected MWCNTs, and an effective load-bearing ability between the CNTs and the ceramic matrix was observed. Moreover, CNTs have been shown to be a very versatile phase to chemically functionalize. Procedures such as the acid treatment are very popular and are known to cut the CNTs and to involve the adsorption of negatively charged functional groups along the CNT and at their cut-ends [119]. Other procedures such as CNT dispersion into polysaccharide water solutions lead to non-covalent Table 1 Maximum reported mechanical values of alumina, yttria-stabilized tetragonal zirconia polycrystal (YTZP), carbon nanofibers (CNFs), carbon nanotubes (CNTs) and graphene at room temperature. ▴ YTZP, 90 nm grain size; YTZP, pressureless sintered at 1650 ◦C, 705 nm grain size; ♠ Very homogeneous precursor powder with a mean particle size of 100 nm; ♣ 3YTZP; ◊ micron-sized carbon fibers; ¶ derived from a fracture strength of 63 GPa; ▸ computer simulation; +bundles; †in-plane E 2D <700 N/m, assuming thickness of 0.335 nm; §tensile strength of pre-cracked sample; * out-of- plane bending rupture stress of 42 N/m, assuming a thickness of 0.335 nm; # maximum stress in shear experiment in the absence of out-of-plane deformations; ‡nanoindentation bending breaking stress at “grain boundaries”. More details can be found in the references indicated in brackets. K IC (MPa⋅m 1/2 ) except where indicated E (GPa) H (GPa) Strength (GPa) Al 2 O 3 Polycrystal 5.0 [87] 416 [88] 20.1 [69] 3-point bending: 1.3 [89] Shear: 184 [87] Compressive: 3.5 [88] Single crystal 2.1 [69] 425 [69] 21.8 [69] ZrO 2 17.0 ▴ [90] 217 [91] 14.7 ♠ [92] Tensile: 0.7 [93] Flexural: 1.5 ♣ [94] Compressive: 2.9 [87] CNF 965 [95] Fracture: 3.5 [96] Tensile: 20 ◊ [97] Shear: 15 [95] CNT MWCNT 1.240 ¶ J/kg [96] 1800 [98] Radial Young’s modulus: 80.8 [99] Bending: 14 [96] Fracture: 63 [100] SWCNT 2.7 ▸ [101] 1470 [96] Tensile: 52 + [96] Bulk modulus: 8.5 [98] Shear: 6.5 [102] Graphene 4.0 [103] ~2000 † [104] Monolayer: 2400 [85] Bilayer: 2000 [85] GO: 40 [105] rGO: 250 [106] Fracture: <9.5 § [103] Intrinsic tensile: 130* [84] Shear: 97 # [107] Bending: 35 ‡ [72] V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 6 functionalization [120]. In addition, the presence of hydroxyl groups facilitates the dispersion of the CNTs in aqueous media as it changes the wetting behavior of the CNTs from hydrophobic to hydrophilic [121,122]. Hydroxyl groups also promote the formation of bonds between the CNTs and the host matrix in composite materials [49]. The functionalization and the presence of defects in the CNTs have been characterized by techniques such as Raman spectroscopy [122,123]. Thus, the intensity of the D band, which is typically due to the disordered sp 3 -hybridized carbon acting as impurities and defects in the carbon nanotube structure, with respect to the intensity of the G band, is related to the number of defects present in the wall structure of the CNTs [110]. Until the arrival of CNTs, no previous material had exhibited such a combination of outstanding mechanical, electronic, and thermal properties. Thus, CNTs were considered ideal, not only for a wide range of applications but also as advanced filler material in composites in particular. But concerning the mechanical properties of ceramic composites reinforced by CNTs, there are several reviews showing contradictory results at low temperature [42,54] as well as at high temperature, where even papers by the same research group found opposite results [54,124–128]. To understand these discrepancies, it is necessary to consider the nature of CNTs and the processing conditions to obtain novel engineered CMCs [129]. The diversity of types of CNTs also contributes to the scattering of the mechanical performance of the reinforced ceramic composites. In addition, considering that the graphene sheets have higher surface-to-volume ratios than SWCNTs due to the inaccessible inner nanotube surface to the ceramic matrix, the graphene sheets are expected to be potentially more favorable for altering all matrix properties [76]. 1.1.3. Carbon fibers Carbon fibers (the so-called carbon whiskers) are graphitic structures that have been known since 1889 when they were observed to grow, probably as a nuisance, from carbon containing gases in contact with metallic catalysts [130]. In the 1960s, carbon fibers were developed as one of the important industrial materials for modern science and technology, and were produced from various carbon precursors via the melt-spinning process. In the twenty-first century, carbon fibers have been grown from the vapor phase with diameters of the order of 100 nm and lengths between 20 and 100 µm [96,130–132]. In particular, carbon fibers whose diameter is <1 µm are referred to as CNFs. These small dimensions involve a much higher surface area per unit mass than conventional carbon fibers, which allows much greater interaction surface between the CNFs and the composite matrixes. They can be produced by several techniques such as CVD or electrospinning of polymers, which are subsequently converted into CNFs. Polyacrylonitrile (PAN) is one of the major precursors for the production of carbon fibers through wet-spinning or melt-spinning [133]. Moreover, CNFs have been also processed through acid treatments (e.g., nitric or sulfuric) in order to create oxygen-containing surface groups [134]. The characterization of the oxidation process by XPS showed an increase of the O:C ratio of 60%. It was also shown that the presence of oxide groups considerably increased the wettability of the CNFs. The structure of the graphitic layers in carbon fibers includes a wide range of arrangements, such as piled-up GNPs, fishbone-like configurations, graphene ribbons, or amorphous bulk carbon. Unlike CNTs, which consist of graphene layers rolled up into a hollow cylinder, CNFs have various forms depending on the manner of stacking of the graphene layers [135]. The different degrees of crystallinity are typically controlled by the atomic arrangement of the catalyst particle surface in contact with the solid carbon [130,136]. The carbon fibers also exhibit outstanding physical properties, such as electrical conductivity of 10 6 S/m, thermal conductivity of 1000 W/mK, tensile strength of 20 GPa, and Young’s modulus from 100 to 1000 GPa, given that the anisotropic structure of hexagonal graphite single crystals strongly influences their elastic properties [95,135] (see Table 1 for the highest reported mechanical values of CNFs). In this regard, the strength with respect to normal layer separation and tangential relative sliding is much lower because of the weaker (van der Waals) contacts between the adjacent graphene planes. In the ceramic materials science, CNFs have been proposed as a reinforcement phase thanks to their advantages, such as their dispersibility and their low price, compared to SWCNTs or MWCNTs. This review aims to compile the most relevant results on the fabrication methods and the mechanical properties of CMCs reinforced with carbon allotropes found in the literature. Next, Section 2 shows a revision of the problems and advantages of the different procedures for synthesizing the ceramic composites, paying special attention to their influence in the mechanical characterization. Section 3 collects the relevant discussions on the toughening phenomena in CMCs, starting from classical models on fiber-reinforced ceramics to their application on CMCs with carbon allotropes. Section 4 addresses the problem of the mechanical properties at low (ambient) temperature, explaining in detail the different sources of discrepancies and remarking on current controversies such as the different techniques for measuring the fracture toughness. Section 5 will explain the most important results and discussions with regard to the mechanical properties at high temperature. Finally, Section 6 will set out the major conclusions and possible future trends of the research on reinforcing ceramics with carbon allotropes. 2. Fabrication strategies 2.1. Requirements for an efficient mechanical reinforcement Currently, a major milestone still to be accomplished is to achieve the optimum incorporation of nanostructured carbon allotropes into the ceramic matrix in such a way that the resulting composites exhibit significant mechanical reinforcement in an unquestionable way. An ideal situation involves a fully dense composite with a perfect dispersion of carbon allotropes throughout the ceramic matrix, avoiding any damage of the allotropes during the processing, ensuring an optimum bond between the allotropes and the ceramic matrix, and confirming the intragranular location of the allotropes. In other words, for the carbon allotropes to produce a remarkable reinforcement of ceramics, the following characteristics are critical [49,54,137,138]. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 7 2.1.1. Optimization of the properties of the allotropes Impurities and defects have to be extremely controlled since they may be critical for several aspects, especially the mechanical properties. Purification by acid treatments, sonication or heat treatments under oxidant atmospheres can lead to damages or disintegration of the carbon allotropes during processing and during either dispersion or consolidation [139]. The use of oxidized or functionalized allotropes may facilitate their dispersion in aqueous media [121,122] and their bonding to the matrix [49], but also involves the presence of more structural defects than are found in the pristine ones [122,123], worsening their mechanical behavior [115]. Furthermore, it is well know that the high-temperature treatments required for ceramic consolidation can deteriorate the carbon allotropes [140,141]. Moreover, dispersion procedures based on ultrasound should be employed with care, giving that the acoustic waves are also known to produce mechanical damage and deteriorate the carbon allotropes [142]. 2.1.2. Homogeneous dispersion of the carbon allotropes The absence of agglomerations and a homogeneous distribution of the carbon allotropes throughout the composite are two of the most relevant requirements for an efficient composite fabrication. This is particularly important for CNTs, given that they tend to form aggregates, coils, ropes or bundles due to van der Waals forces as a consequence of their high surface area and high aspect ratio. Hence, a distribution of CNTs in which individual CNTs are separated from each other is still a major challenge for the ceramic community [143]. The aggregations of the carbon allotropes typically lead to pores and defects in the matrix, reduces the interaction through the carbon-matrix interface, and hinder a good distribution of the forces, worsening the mechanical performance. For example, clustering of the carbon allotropes can serve as microcracks, promote the formation of cracks, and facilitate their propagation, reducing their resistance [50,138,144]. In this regard, graphene is more suitable than CNTs because it does not form agglomerates so easily when it is treated appropriately, but its homogeneous dispersion is also a major challenge. Finally, the use of MWCNTs has also been suggested due to their lower tendency to agglomerate compared to SWCNTs [145]. The strategies for preparing of ceramic composite materials with carbon allotropes are devoted to the development and optimization of procedures for dispersing the allotropes and for obtaining stable suspensions of individualized allotropes ready to be added into the composite fabrication processes [146–148]. Magnetic stirring, sonication, plasma, and other physical techniques are being considered for the preparation of these dispersions. In particular, the use of ultrasound (low-power ultrasound in ultrasonic baths or high-power ultrasound by probe sonicators) is widely considered because ultrasonic waves are the most effective way to disperse CNTs as they break the van der Waals’ attractive force that exists among tubes due to the strong shear force induced in the liquid medium by cavitation, which entails a process of bubble formation, growth, and collapse [149]. Furthermore, some physical–chemical techniques such as modification of the pH, the use of surfactants, salts, and debundling agents of distinct nature are also very popular. The use of functionalized allotropes is also a strategy to facilitate the dispersion, given that the presence of hydroxyl or carboxyl groups on the surface of the allotropes will help to achieve good dispersion [121,150–153]. Accordingly, some strategies were reported in order to assess the quality of the dispersion of the allotropes, or, at least, to reveal differences due to different fabrication procedures. Typically, direct observation by SEM of tenths of images of the carbon allotropes within the matrix is considered to estimate the quality of the dispersion of the allotropes. Despite that these observations are limited to small portions of the samples, they are considered to support statistically questionable conclusions [45,122,123,126,154–157] and even served to define a dispersion index to quantify the quality of the dispersion [158]. Other techniques based on chemical analyses such as electron energy loss spectroscopy (EELS) [54] or energy-dispersive x-ray spectroscopy (EDX) [159] for local estimations have been considered and the width of the embedded clusters of carbon were statistically analyzed, understanding the presence of small clusters as a better dispersion. However, so far, the community of composite scientists lacks a reliable and accurate tool to precisely characterize the degree of dispersion provided by each routine at relatively large scale, to provide a quantitative evaluation of the dispersion homogeneity in a statistically reliable scale. Nevertheless, there are already published works with large-scale analyses based on spectroscopy [150,160,161], small-angle x-ray scattering [162,163], small-angle light scattering [164] that may mean useful proposals for the fabrication of ceramic composites. 2.1.3. Optimum bonding between the carbon allotropes and the matrix As a general assumption, the allotropes must be bonded to the matrix so that they can carry the loads and exhibit enough ability to bear stress. Nevertheless, in the framework of strengthening ceramics, the type of bonding is a subtle feature widely commented in the community because strong bonds may favor different strengthening mechanisms than weak bonds. For example, a “tight” interface bonding between CNTs and the ceramic matrix is desirable [159,165] as it will contribute on bearing loads. In addition, middle strong interfacial bonds were also reported as preferable to ensure a good load transfer [52] as the lack of reinforcement was attributed to poor bonding between carbon allotropes and the ceramic matrix [52,144,166]. However, computer simulation also revealed that too strong bonds are counter-productive [167]. This controversy was coped with suggesting the complexity of the feature, assuming that the carbon allotropes must be “sufficiently” [53] or “suitably” [138] bonded to the matrix and it is widely discussed below in Section 3. Hence, is generally accepted that weak bonds should be avoided in order to effectively use the carbon allotropes as efficient reinforcements. In this regard, the use of functionalized CNTs or graphene with reactive groups such as hydroxyls is an option [168–170] they present dangling atoms and functional groups, which improve bonding with the matrix [58]. The use of functionalized carbon allotropes led to different types of bonds in CMCs such as Al-O-C bridging oxygens [171,172] or hydrogen bonds [169]. 2.1.4. The intragranular location of the carbon allotropes The carbon allotropes should be located in such a way that true reinforcement phenomena may arise as, for example, toughening mechanisms in their most efficient way, namely, significantly increasing the fracture energy and the toughening effects on V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 8 intergranular crack propagation [46,49,59–61]. However, the conventional grain boundary location of the carbon allotropes may not exhibit efficient toughening mechanisms. The low chemical compatibility between CNTs and alumina results in a weak interface strength, so the load cannot be efficiently transferred to the CNTs [61]. In addition, the presence of the carbon allotropes in the grain boundaries may produce grain-boundary weakness promoting intergranular fracture along grain boundaries [63,138]. It was reported that the intragranular location leads to increase the strength of the carbon-matrix bonding [49] and favors the transgranular fracture mode, increasing therefore the fracture toughness of the composite [59,173]. The influence of the location of the carbon allotropes with the toughening mechanisms is discussed in Section 3. 2.2. Powder processing Different approaches have been carried out to deal with the synthesis of CMCs considering the previously mentioned critical characteristics and to achieve a perfect dispersion of the carbon allotropes throughout the ceramic matrix; for example, conventional powder processing methods are based on applying shear forces to deagglomerate CNTs or graphene by milling, stirring, or applying ultrasound in wet media; colloidal processing, in which dispersants, surfactants, or acid treatments are based on surface modification with the aim of increasing the stability of liquid suspensions of the allotropes; sol–gel processing, which aims to “freeze” the dispersed carbon allotropes within the liquid sol by the formation of a solid gel network; and in situ growth of CNTs by CVD, in which CNTs are grown directly on the surface of ceramic matrix grains due to the presence of metal impurities on the surface, which act as catalysts [54]. 2.2.1. Estimation of the carbon content Along these years of research on CMC with CNTs, many inconsistent data have been considered and conflicting results have been reported, mainly because the authors did not use identical CNTs [174]. But in the literature, the carbon content is typically controlled by the vol.% in the ceramic composites [175], considering the density of the ceramic matrix and that of the selected carbon allotrope. However, the selection of one specific density implies geometry. Hence, different values of the density such as 1.3 g/cm 3 [128] or 1.8 g/cm 3 [176] for SWCNT, 2.0 g/cm 3 [122] or 2.10 g/cm 3 [158,177] for MWCNT, and 2.2 for GO [43] have been considered without giving special details of the characteristics of the CNTs or GO, or simply assuming the value given by the providers. This practice is specifically delicate in the case of CNTs as their density is strongly dependent of their geometry. In order to clarify this issue, an interesting research on the density of CNTs with different features was performed by Laurent et al. [174]. Currently, it is well known the large diversity of types of CNT that do exist, and even hollow carbon nanofibers are sometimes noted as CNTs. It is also known that there are very different lengths, diameters, crystallinity, defect proportion, different levels of purity or functionalization. However, the fact that different types of CNTs do not have the same weight nor the same density is ignored very often, specially by manufacturers. Calculations based on the length of the C-C bonds in the curved graphene sheets of 0.1421 nm, and the distance between concentric shells (inter-shell distance) in MWCNT is d w–w =0.340 nm, allow the following expressions. Firstly, the density of one SWCNT, ρ SWCNT , can be estimated by: ρ SWCNT =4 ρ s D(1) where ρ s is the surface density of the one single graphene sheet 0.76⋅10 −7 g/cm 2 and D is the diameter of the SWCNT. In Eq. (1) it can be seen how the density is strongly dependent on the diameter of the tube. In the case of MWCNTs, the inner diameter and the number of walls are critical geometrical parameters that affect their density. This dependence can be expressed as a function of the mass of the MWCNT, M MWCNT : MMWCNT = ρ S π L[ndint +2dw−w∑ n−1 i=1 i](2) where L, d int and n are the length, inner diameter and number of walls of the MWCNT, respectively. Thus, the density of the MWCNT, ρ MWCNT , is: ρ MWCNT =4 ρ S[n dout −2dw−w∑n−1 i=1i d2 out ](3) Accordingly, once a density is considered, an outer diameter is implicitly assumed depending on the number of walls, which is, in fact, a very fluctuating quantity. 2.2.2. Conventional powder processing Conventional powder processing was the first method commonly applied in the dispersion of second phase particles in ceramic composites and was considered as the first approach to disperse CNTs throughout the ceramic matrix. The absence of any driving force impedes the deagglomeration and homogenous distribution of the carbon allotropes, especially CNTs, from the ceramic powder particle surface into the bulk of the mixture. Mixing of raw CNTs and dry ceramic particles has been performed under dry conditions or in solution with ultrasonication [178–180], followed by ball milling, or by attrition milling, to obtain CNT–alumina composites V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 9 [53,145,181–188] and CNT–zirconia composites [189–200]. Functionalized CNTs have also been considered through conventional ball milling procedures in ethanol [201,202]. Nevertheless, ultrasonication and ball milling could damage CNTs, producing a shortening of CNTs, which might lead to a less efficient reinforcement or an undesirable effect on the physical properties of CNT–ceramicmatrix composites [142]. Finally, the wet blends are dried, crushed, and sieved before the densification stage [203]. Suspensions of mechanically mixed powders have also been frozen in liquid nitrogen in order to avoid CNT agglomeration after stirring and ultrasonication [204,205]. Then, the frozen suspensions were freeze-dried in order to obtain the precursor powder. The precursor powders of CNT–alumina [206] and CNT–zirconia [207,208] composites have also been submitted to specific dried procedures such as spray drying. In this procedure, powder particles dispersed in an aqueous organic binder to form a slurry, and the slurry was passed through an atomizing orifice into a chamber with hot gas flowing where the atomized droplets dried to form micron-sized agglomerates of spray-dried powders. Graphene–alumina ceramic composites have also been fabricated by conventional powder processing [56,209–217], using dry grinding [218], ball milling [55,156,219–224], or ethanol [225], or acetone [226] suspensions. Freeze-drying has also been considered for these composites [227] as well as the spray drying technique [206]. Zirconia has been doped with graphene using conventional techniques such as ball milling [228–232], magnetic stirring of aqueous suspensions [233], or ultrasound [234] with previously deagglomerated GNPs [235]. Besides, Zou et al. [236] synthesized GO–ZrO 2 composites by impregnating a preform of partially pressured porous ZrO 2 pellets with a graphene suspension. Zeng et al. [237] compared in situ reduced GO (irGO) and previously reduced GO as reinforcing agents, mixing the precursors with magnetic agitation accompanied by a sonication bath. L´ opez- Pernia et al. [238] compared different conventional homogenization procedures for the synthesis of GO–ZrO 2 composites, involving ultrasonic agitation of isopropyl suspensions of GNPs, ball milling, and dry conditions, and concluded that “high-energy planetary ball milling in dry conditions without previous ultrasonication resulted in the best performance in terms of microstructural homogeneity”. CNFs have also been added to alumina-based ceramic matrixes by conventional powder methods such as ball-milling, considering submicrometric alumina particles and CNF suspensions in ethanol with small amounts of different dispersants such as polyvinyl butyral (PVB) [239,240] or KV9056 [241]. Moreover, zirconia has also been doped with CNFs with the help of dispersant (dodecyl Maranil) in water medium, followed by spray drying [242–245]. 2.2.3. Colloidal processing In order to obtain carbon-reinforced CMC with homogeneous microstructure and adjustable properties, a very close contact between the allotropes and the matrix is essential. With this aim, CNTs are typically coated with ceramic particles in colloidal suspensions by adjusting the surface chemistry, changing the pH, and stabilizing the suspensions as well as by increasing the repulsion between CNTs, which prevents agglomeration and facilitates homogeneous dispersion of CNTs throughout the ceramic matrix grains [126,246–248]. Heterocoagulation of nanoparticles occurs when two stabilized suspensions are mixed. It is the most considered coating process. During heterocoagulation, the electrical attractive force between the opposite charges of CNTs and the ceramic particles is the driving phenomenon that promotes the coating of the CNTs. In addition, the modification of the CNTs’ surface chemistry requires their functionalization since, typically, commercial CNTs exhibit low amounts of surface charge, and therefore, they are poorly dispersed in any medium. Besides, commercial CNTs generally contain impurities, such as amorphous carbon and metal particles from CVD catalysts. Therefore, before the preparation of any dispersion of CNTs in a solution containing ceramic powders, a previous acid treatment is frequently used to purify and improve the dispersion of CNTs in the appropriate solvent. In addition, this previous treatment of CNTs is generally done in a mixture of concentrated acid (sulfuric, nitric, or hydrochloric) with the help of ultrasound, which promotes purification and shortening of CNTs, functionalizing the CNTs by charged groups (carboxyl or hydroxyl) [119,249–251]. Poyato et al. [248] illustrated how acid treatment of SWCNTs enhances their colloidal stability in aqueous solutions with a pH as high as 12, selectively eliminates small-diameter metallic SWCNTs, and enhances their stability in aqueous suspensions with Al 2 O 3 nanoparticles at a high pH. Detailed description of the colloidal-based procedures can be found in [252]. Organic surfactants or dispersants are typically considered to change the surface properties of both ceramic nanoparticles and CNTs. Moreover, the bundles of CNTs are generally dispersed using dispersants and ultrasound. Anionic surfactants in particular can change the effective surface charge from negative to positive, while cationic surfactants can yield the opposite effect. Some of the most used anionic surfactants are sodium dodecyl sulfate (SDS) [61,185,253] and polyacrylic acid [254,255], while common cationic surfactants are polyethylene glycol (PEG) [61] and polyethyleneimine (PEI) [253–255]. Nevertheless, the use of surfactants can also add impurities in the final CMC during surfactant removal, which is typically performed by an oxidizing calcination treatment. Fan et al. [61] investigated the heterocoagulation process after acid treatment of SWCNTs to implant SWCNTs throughout the Al 2 O 3 matrix grains. With this purpose, Al 2 O 3 particles were dispersed in a PEG solution, in which Al 2 O 3 is electropositive, and SWCNTs were dispersed in SDS at a pH of 9.0. When electronegative SWCNTs and electropositive Al 2 O 3 solutions are mixed, SWCNTs are coated with Al 2 O 3 particles due to electrostatic attraction, resulting in the deposition of SWCNTs in the grain boundaries and into the ceramic matrix grains after sintering. Heterocoagulation processes have been used not only for Al 2 O 3 -based matrixes [185,255–258] but also for ZrO 2 [259–261] and with f-CNTs [262]. Zhou et al. [263] compared zirconia-based composites prepared by heterocoagulation using polyacrylate acid and cetyltrimethylammonium bromide (CTAB) followed by different drying techniques: vacuum drying or spray drying. They found that the heterocoagulation treatment played a crucial role in the homogeneous dispersion of the CNTs in the matrix. In contrast, aqueous colloidal processing of SWCNTs and Al 2 O 3 at pH 12.0 involves electrostatic repulsion between individual acidtreated SWCNTs and individual Al 2 O 3 grains owing to the negative surface charge of both acid-treated SWCNTs and Al 2 O 3 grains [248,264]. As a consequence, a well dispersed, charge-stabilized suspension is obtained, wherein SWCNT are uniformly and homogeneously distributed throughout the Al 2 O 3 grain boundaries and retain this structure after sintering [57]. Inam et al. [265] researched V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 16 3. Reinforcing mechanisms in composite ceramics The brittle nature of ceramic materials and their low fracture resistance and fracture toughness are some of the most important technological drawbacks of ceramics for low-temperature applications, given the relatively high values of stiffness or hardness and low densities of ceramics, especially if compared with other stiff and hard materials such as metals. The Ashby diagrams [385] permit the comparison of the different mechanical properties, allowing discussion between the different types of materials at a glance. In Fig. 7, an example of an Ashby chart is shown, in which the values of the fracture toughness and Young’s moduli for the different types of materials are compared. The ceramics in general (light yellow ellipse in Fig. 7) exhibit the highest values of the Young’s modulus and hardness despite exhibiting much lower densities than metals. However, the much lower values of fracture toughness of ceramics in comparison to metals are apparent. Explicitly, the low fracture toughness has impeded the reliability of the mechanical response of ceramic materials, and consequently, it continues to limit their applications. Achieving more reliability upon mechanical stresses is still a challenge, and the most common approach to improve the mechanical reliability of ceramics is to increase the fracture resistance. The general theory of fracture was developed in the first half of the 20th century, based on Linear Elastic Fracture Mechanics and Table 3 (continued) Carbon content Relative density (%) Sintering method Sintering details Source (wt.%) selected allotrope 0.5 t-MWCNT 98.8 PS 1400 ◦C, Ar/H 2 , 1 h T-annealing: 1200 ◦C [158] 98.0 T-annealing: 1800 ◦C 0.5 MWCNT 98.5 SPS 1500 ◦C, 20 MPa, vacuum, 10 min [139] f-MWCNT 0.5 Graphene 98.1 SPS 1500 ◦C, 50 MPa, vacuum, 10 min [211] 1.0 t-MWCNT 96.8 PS 1400 ◦C, Ar/H 2 , 1 h T-ann: 1200 ◦C [158] 94.0 T-ann: 1800 ◦C 1.1 GO 99 SPS 1300 ◦C, 75 MPa, vacuum, 5 min [43] CNF 1.2 MWCNT 99.5 – 100 SPS +PS 1650 ◦C, 25 MPa, 5 min +pressureless 1000 ◦C, 6 h [49] 1.3 f-MWCNT 99.8 SPS 1025 ◦C +1450 ◦C, 60 MPa, Ar, 10 min +10 min [59] 1.4 f-SWCNT 99.7 SPS 1300 ◦C, 75 MPa, 5 min [176] 1.5 MWCNT 89.8 SPS 1400 ◦C, 40 MPa, 10 min [177] 98.6 1600 ◦C, 40 MPa, 10 min 1.9 MWCNT 95.5 SPS 1500 ◦C, 20 MPa, vacuum, 10 min [293] 1.9 MWCNT 92.6 SPS 1500 ◦C, 20 MPa, vacuum, 10 min [139] f-MWCNT 96.5 2.0 GO 99.0 SPS 1450 ◦C, 35 MPa, vacuum, 4 min [210] 2.0 Carbon black ~84 SPS 1400 ◦C, 100 MPa, 3 min [186] >99 1800 ◦C, 100 MPa, 3 min MWCNT ~77 1200 ◦C, 100 MPa, 3 min ~88 1400 ◦C, 100 MPa, 3 min >99 1800 ◦C, 100 MPa, 3 min 2.0 f-MWCNT–GNP 99 HP 1650 ◦C, 40 MPa, Ar, 60 min [345] 98 SPS 1650 ◦C, 40 MPa, 10 min 2.0 rGO 99 SPS 1450 ◦C, 35 MPa, 4 min vacuum [56] 2.3 f-SWCNT 99.8 SPS 1300 ◦C, 75 MPa, 5 min [176] 2.6 f-MWCNT 99.4 SPS 1025 ◦C +1450 ◦C, 60 MPa, Ar, 10 min +10 min [59] 2.8 Graphene 99 SPS 1350 ◦C, 50 MPa, 5 min [55] 3.3 SWCNT 100 SPS 1150 ◦C, 63 MPa, vacuum, 3 min [53] 3.5 MWCNT ~85 SPS 1100 ◦C, 100 MPa, 3 min [186] >99 1400 ◦C, 100 MPa, 3 min 3.8 MWCNT 92.1 SPS 1500 ◦C, 20 MPa, vacuum, 10 min [293] 4.8 SWCNT 100 SPS 1150 ◦C, 63 MPa, vacuum, 3 min [183] 97.8 1550 ◦C, 63 MPa, vacuum, 3 min 4.8 f-SWCNT 100 SPS 1300 ◦C, 75 MPa, 5 min [176] 4.8 SWCNT 94.9 SPS 1550 ◦C, 40 MPa, vacuum, 3 min [124] f-SWCNT 97.6 4.8 SWCNT 95.1 SPS 1450 – 1550 ◦C, 40 MPa, vacuum, 3 – 10 min [44] 5.0 MWCNT >99 SPS 1200 ◦C, 100 MPa, 3 min [186] 5.6 SWCNT 85.8 SPS 1150 ◦C, 63 MPa, vacuum, 3 min [53] 95.2 1150 ◦C, 63 MPa, vacuum, 3 min 100 1150 ◦C, 63 MPa, vacuum, 3 min 5.6 SWCNT 93.9 SPS 1550 ◦C, 40 MPa, vacuum, 3 min [248] f-SWCNT 97.6 5.8 Graphite 97.7 SPS 1450 – 1550 ◦C, 40 MPa, vacuum, 3 – 10 min [44] 6.0 MWCNT 88.3 SPS 1500 ◦C, 20 MPa, vacuum, 10 min [293] 10.0 83.1 V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 17 the fracture phenomena were described thoroughly in classical texts such as [386–388]. This description includes the definition of the concept of fracture toughness as the material’s intrinsic resistance to the propagation of defects, which is driven by its microstructure and is independent of the particular flaws. Within this formalism, the evolution and eventual spontaneous growth of a crack is driven by an energy balance: once an external stress is applied, the elastic energy is stored in the material as elastic strain; next, when a flaw in the material starts a fracture, the stored elastic energy is released as surface energy employed in the formation of the new interfaces of the solid in the fracture surfaces. The extremely high hardness values of the ceramic materials impede the release of crack energy to be dissipated through other mechanisms such as the plastic phenomena. This conflict between strength and toughness has been interestingly exposed by Ritchie in [25]. Then, the balance between the energy rate required by the increasing crack interfaces and the energy rate released as the crack grows drives the spontaneous propagation of the fracture up to percolation and fatal failure of the material. Thus, if no other process releases stored elastic energy than the creation of the crack interfaces, the work of fracture can be equal to twice the thermodynamic surface energy γ, that is, Γ I =2γ, in which the subscript “I” refers to fracture mode I. Hence, the toughening mechanisms can be defined as “the different inelastic deformation processes that produce dissipation of energy, reducing the elastic energy accumulated in the material at the start of fracture and/or contributing to delaying the growth of the crack during its propagation” [389]. Therefore, the reinforcing ability of embedded phases such as CNTs or GNPs in the ceramic matrixes may involve an increase of the intrinsic resistance to the propagation of defects in the composite. The specific contribution of the different carbon allotropes to the increase of the fracture toughness, considering the different reinforcing mechanisms that they may exhibit, is still being experimentally researched and theoretically modeled. 3.1. Extension of the classical theory of fracture mechanics to composites Before reviewing specific results on CMC with carbon allotropes, a short reminder of the classical theory will be of great help. The energy balance associated with the propagation of a crack can be briefly summarized as follows: on the one hand, the surface energy can be expressed as U surf =4γ m c (the total length of the crack is 2c and there are two surfaces for the crack) in terms per unit of sample thickness, where the superscript m refers to the ceramic matrix. On the other hand, the released energy term (per unit of sample thickness) can be estimated as U elast = πσ 2 c 2 /E, where E is the Young’s modulus and σ is the applied stress. This formalism is widely explained in common fracture mechanics reference manuals (e.g. [390]). Assuming the irreversibility of the interface formation, it can be seen that, for a given applied stress, σ F , there is a critical crack size above which the energy release rate due to the elastic term is higher than the release energy rate due to the new interface, and therefore, above this critical size, the crack propagates spontaneously. In essence, this approach states that the balance between the elastic energy release driving term and the dissipation energy retarding term governs the evolution of the crack. Hence, as stated by Irwin [387], the propagation of the crack will start once the applied stress and the crack size cause a characteristic parameter, the stress intensity factor, to reach a critical value, K Ic , which depends exclusively on the material, known also as the fracture toughness. Thus, K Ic is defined as Fig. 7. Ashby chart comparing fracture toughness and Young’s modulus (reproduced from [385] with permission). The ceramics in general (light yellow ellipse) and technical ceramics such as Al 2 O 3 in particular exhibit the highest Young’s modulus values. However, the much lower values of fracture toughness of ceramics in comparison to metals are apparent. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 18 KIc = EΓIc √(4) where E is the Young’s modulus and Γ Ic is the critical value of the work of fracture, which, as explained before, is Γ Ic =2γ m in pure brittle fracture. For example, research has been carried out on the work of fracture in monocrystalline alumina through the preferred cleavage plane that gives a value of 6 J/m 2 [391]. But, in addition to the surface energy, there are other processes in the material that dissipate the stored energy, specific toughening mechanisms in polycrystalline ceramic materials typically due to the interaction between the crack and the microstructure [392,393]. Since the grain boundaries are low-density regions where defects and residual stresses are concentrated [389], polycrystalline alumina have exhibited values of the work of fracture between 10 and 46 J/m 2 [394–396]. Considering those values of the work of fracture, and the typical alumina value of E =400 GPa give K Ic values between 2 and 4.5 MPa⋅m 1/2 , which match reasonably well with experimental values. In this theoretical framework, the inclusion of reinforcing phases such as fibers or carbon allotropes is expected to introduce new toughening phenomena in the ceramic matrixes [144,392,397]. Thus, the contributions of these new toughening phenomena can be included in the classic fracture formalism based on the energy balance approach through an extension of previous Eq. (4) [393], by adding a new term Γreinf Ic : KIc = E(Γm Ic +Γreinf Ic ) √(5) where the superscript m refers to the ceramic matrix, and the superscript reinf refers to the reinforcing phase. It is well known that the increase of the fracture resistance of ceramic materials and reduction of their brittleness by the addition of new toughening phenomena that help to dissipate the crack energy without deterioration of other outstanding physical properties of the ceramic, have been in the focus of materials scientists for a very long time, and are still consuming large scientific resources, as corroborated by this review. Actually, one of the most ancient toughening strategies consists of using pseudo one-dimensional fillers as toughening inclusions in brittle materials, which dates back to about 4000 BCE, when materials like straw or asbestos were used to reinforce construction materials [96]. This recurrent idea has been continuously essayed and it was boosted some decades ago with the fabrication of silica-based composites with carbon fibers [398] or with SiC microfibers [399]. Interestingly, Becher and Wei [400] reported an increase of almost twice the fracture toughness, from 4.6 ±0.4 to 8.7 ±0.9 MPa⋅m 1/2 , by the addition of 20 vol% of SiC microfibers, which was also increased up to 10 MPa⋅m 1/2 later when working with fine grained alumina [397]. In addition, Niihara [401] achieved an increase of the fracture toughness of the pure alumina from 3.5 to 4.8 MPa⋅m 1/2 , by the addition of SiC nanoparticles. Since then, several works have been performed in order to test the specific role of the fibers in the toughening mechanisms and the proposed theoretical models [144,392,400,402]. In the last two decades, similar theoretical and experimental work has been done with the focus on the role of nanostructured carbon allotropes, mainly carbon nanotubes. This chapter will collect and discuss the specific efforts in the theoretical and experimental study of the toughening mechanisms when working with carbon allotropes in alumina and zirconia based CMCs. 3.2. Lessons from earlier reinforcement strategies Before discussing how the toughening mechanisms are performed by carbon allotropic reinforcements, some basic lessons from earlier works on reinforcing ceramic composites deserve consideration. The following question has often been laid out: what is the most appropriate amount of carbon allotropes in a ceramic matrix, in order to maximize the reinforcement of CMC? From the theoretical point of view, some answers have been given. From works on fiber-reinforcements, it was suggested that the amount of fibers must be dense enough and uniform enough that spaces of the order of the typical flaw size in the ceramics (i.e., 20–50 μ m) do not exist between the fibers [144]. The most common types of carbon allotropes such as CNTs, CNFs or GNPs will fulfill this requirement. In addition, a brittle material’s resistance to fracture should increase as the distance between the dispersed inhomogeneities decreases [388]. This implies that the fibers may be small compared to the flaw size, a requirement clearly satisfied by the micron-sized carbon allotropes. Actually, this major dependence between the average distance between ligaments and the typical flaw size in fiberreinforced ceramics has been known for a very long time as was clearly shown by Hasselman and Fulrath [403]. Currently, the translation of these basic ideas to the CMC reinforced with carbon allotropes, and questions as, e.g., what is the maximum amount of carbon allotropes that will maximize the reinforcing phenomena, are still under development. Although several questions about the toughening mechanisms have been widely researched and theorized, the specific performance of the carbon allotropes such as what are their major toughening mechanisms, how their specific reinforcing mechanisms involve an increase of the fracture toughness, or what are the specific material characteristics to be improved, is still under study and research. In the following, attention will be paid to those specific phenomena due to low-dimensional nanostructured reinforcing phases such as CNTs, CNFs, or GNP. 3.3. Crack bridging, crack debonding and pullout The toughening mechanisms performed by the ligaments, either fibers, CNTs, CNFs, or GNPs, are designed to act behind the crack tip, by imposing a strong closure force that opposes the separation of the crack surfaces. There is a collection of different interrelated mechanisms and concepts, such as crack pinning, crack deflection, crack bending, crack bridging, or pullout when describing fracture and toughening models, and they are typically described separately. Despite this, they are quite intuitively related, since the ligament V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 19 is embedded in the matrix, the separating stress acts on the matrix and on the ligament, and the ligament may execute the different toughening phenomena, jointly and/or consecutively, as, e.g., partial strain will precede debonding, and it will inexorably precede pullout. At this point it is worth remarking that the location of the ligament within the matrix and how it is bonded to the matrix will be critical issues for the efficiency of these toughening mechanisms. These points will be discussed later. Here, the phenomena are described in terms of the energy dissipation exhibited by the different toughening processes [392,397]. Based on the energy balance approach, the contribution to the toughness due to a given mechanism can be expressed by particularizing the additional term Γreinf Ic from Eq. (5) for the corresponding toughening mechanism, such as the crack-bridging phenomena. It has also been described in terms of a balance of the mechanical energy release [393] by the crack tip term (surface crack) and shielding terms (microstructure of the matrix, reinforcement phases). In essence, it is assumed that there is a competition between different mechanisms in the energy balance, and their relative importance will govern the crack evolution. In Fig. 8, different moments of the response of a bridging ligament are sketched. Although they can occur jointly, they have been schematized separately for an easier discussion. The simplest response of the ligament will involve no debonding, so, once the ceramic parts are separated, the mechanical response will rely exclusively on the ligament (step “c” in Fig. 8). In this case, the absence of debonding is expected to give very small values of the energy change, though an estimation can be made for carbon nanotubes. In this case, the energy change will be the work of fracture of one single ligament, let’s say, one CNT. Thus, in a brittle fracture of a given material, the work of fracture can be estimated through the area below the stress–strain curve. Thence, in the case of a “no debonding” bridging event, although the Young’s modulus of the CNT, E CNT , can reach values above 1 TPa, the area subjected to strain is very small, suggesting that the contribution to the work of fracture may be very low. Nevertheless, let the strained length of the ligament in the “no debonding” event be estimated in the range of the grainboundary width, namely u 0 ~ 10 nm [404]. Then, the elemental strain d ε can be written in terms of the elemental displacement du as u 0 d ε =du. Thus, the work of fracture due to the process in step “c” of the scheme of Fig. 8 can be estimated by ΔΓ1 Ic =1 2ECNT u0 ε 2 F(6) where the superscript “1′′ refers to one single CNT and ε F is the fracture strain of the CNT which has been estimated close to 0.15 [100,405]. If, in addition to the closure force to union of the crack surfaces, the ligaments are partially debonded or pulled out, the effectiveness of the reinforcement can be much greater. Besides, the contribution due to these two phenomena increases with the length of the ligaments, which is especially relevant in the case of CNTs or CNFs, given their extremely high aspect ratio. In partially debonded ligaments (step “d” in Fig. 8), the expression of Eq. (6) is analogous to Becher’s expression for a partially debonded ligament, where the debonded length of the ligament l db equals u 0 [397]. It can be seen how the contribution of energy change will increase as the term u 0 rises. The length of the debonded part of the ligament can be assessed in terms of the ligament radius, r, and the ratio between the fracture surface energy of the bridging ligament (γ CNT ) and that of the reinforcement-matrix interface (γ i ), that is, γ CNT /γ i . Moreover, on average, with the ligaments, CNTs, CNFs, or even GNPs randomly orientated, there is an orientational factor to take into account, together with the fractional area covered by the ligaments with respect to the total area of the crack, which is ultimately related with the carbon content. Thus, the critical fracture toughness in mode I in the case of elastic stretching of partially debonded CNTs will include an energy release term Γreinf Ic as shown in Table 4 [397]. An interesting estimation of the value of the additional energetic term was made for an aluminoborosilicate matrix with 10 wt% of MWCNT [155], and it was found a value of Γbridging Ic ~ 24 J/m 2 , which is quite similar to the values of the work of fracture previously mentioned (10–46 J/m 2 ). Furthermore, the presence of frictional forces between the partially debonded ligament and the matrix may impose a shear strength against the strain of the ligament. Thus, in balance, not all the debonded ligament is equally stressed, but the stress varies linearly along the partially debonded ligament. The residual stress that can appear at the ligament-matrix interface due to the difference in thermal Fig. 8. Crack scheme of a portion of material submitted to a tensile stress, with ligaments within the crack opening. The situation of the ligament at the crack tip is detailed: several relevant moments are sketched, where two zones of the matrix (squares) are linked by a ligament (black vertical line): a) non-strained system, prior to the application of the stress; b) strained system: matrix and ligament are strained due to the external tensile stress; c) no debonding occurs and the elastic response of the ligament is opposing the crack advance until fracture strain of the ligament is reached; d) partial debonding occurs at the crack zone, the matrix zones relax and the strained portion of the ligament increases; e) pullout of the ligament. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 20 expansion coefficients of the ligament and the matrix is coupled to the interfacial sliding resistance, and hence to the strength and toughness of the composite [324,376]. In the case of CNTs, the thermal expansion coefficient is nearly zero, and essentially isotropic, in contrast to carbon fibers, which are highly anisotropic. This could yield significant differences between CNTs and CNFs. On the other hand, the thermal expansion coefficient for the alumina matrix is of the order of 10 −5 K −1 . Thus, the radial compression to which the CNTs are subjected puts the interface in compression, hindering possible interfacial sliding, which may lead to toughening. In this case, a shear resistance term, τ i , that will act along all the interface between the debonded ligament surface in contact with the matrix, has to be included in the discussion, yielding the fracture toughness term to be expressed as shown in Table 4 [397]. On the other hand, if the debonding of the ligament and the creation of new interfaces between the ligament and the matrix is the only contribution considered [406], the additional term of the work of fracture can be expressed as shown in Table 4. Some estimations of this additional energy term of work of fracture due to debonding were made assuming values of the interface energy γ i for inorganic matrixes of the order of 4 J/m 2 , and a value of 8 J/m 2 was obtained [406]. This value is relatively low, indicating that the contribution of this mechanism alone will not supply significant toughening. It should also be highlighted that fabrication problems such as bad dispersions of the reinforcing phase that will reduce the total interface between the matrix and the ligaments, the formation of weaker bonds, or the accumulation of impurities or porosities at or near the interface reducing the lower γ i , will reduce the frictional and debonding contribution [144]. Finally, the pullout of the ligament will be favored when the matrix-ligament interface is relatively weak. But in this case, the pullout and previous bridging phenomena could be reduced as the crack may be deflected along the matrix-ligament interface before the ligament exhibits bridging phenomena [397]. Thus, the extent of pullout may be quite reduced, especially in the case of short lengths of the reinforcing phases. Therefore, in the case of CNTs, their high aspect ratio can minimize pullout and maximize partial debonding and efficient bridging due to the high extent of the relative interfacial bonding and adjusting the interfacial clamping stresses. The energy involved in these phenomena can be written in terms of the sliding shear stress for the pullout [406], allowing the energy term to be written as shown in Table 4. It can also be seen how all these mechanisms scale with the square root of the amount of reinforcing phases, that is, the effectiveness of these mechanisms rises as the content of ligaments increases [144]. Additionally, Chen et al. [407] asked specifically if “thermal residual stresses contribute to the improved fracture toughness of carbon nanotube/alumina nanocomposites” and they concluded that these high and highly localized compressive residual stresses may be responsible for immobilized dislocations and this phenomenon could enhance the toughness of the composite. Thus, considering that the residual thermal stress, σ rt , depends linearly on the temperature change, it can be expressed as σ rt = EΔ α ΔT(7) where  E is a weighted Young’s modulus that depends on the Young’s modulus of the matrix and the ligament and on the volume fraction, and Δ α and ΔT are the differences in the thermal expansion coefficient and the temperature, respectively. Then, an analytical estimation of the change of the fracture toughness (ΔK c ) due to this phenomenon was proposed, based on an additive formulation for the contributions of the grains (ΔK cg ) and the grain boundaries (ΔK cb ), separately, namely: ΔK c =ΔK cg +ΔK cb . Hence, the change of the fracture toughness of the grains can be expressed as follows: ΔKcg = − 2 σ rt  2(λ−d) π √(8) where d is the average grain size and λ is a geometrical parameter that can be correlated with the volume fraction through λ= 1.085d/ V* √. On the other hand, the contribution to the change of the fracture toughness of grain boundaries, ΔK cb , due to the residual thermal stresses is given by ΔKcb = σ rt  π d √(9) Table 4 Detailed proposed expressions for the additional energy release term of the critical fracture toughness (Γreinf Ic in Eq. (5)) for fiber-reinforced CMC, adapted for the case of CNTs. V* is the volume fraction of the CNTs, σ F,CNT , r CNT and E CNT are the strength, radius and Young’s modulus of the CNTs; τ i , is the shear resistance term at the ligament-matrix interface; l CNT is the length of the CNTs; τ po is the shear stress needed to pull out the ligament. Toughening mechanism Γreinf Ic Details Reference Bridging, elastic V* 12 rCNTγCNT ECNTγi σ 2 F,CNT Elastic stretching of partially debonded CNTs. The length of the debonded part can be estimated in terms of r CNT , and the ratio γ CNT /γ i . [397] Bridging, frictional V*rCNT σ 3 F,CNT 6ECNT τ i Frictional forces between the partially debonded ligament and the matrix [397] Debonding 2V*lCNTγi rCNT The energy release due to the creation of new interfaces between the ligament and the matrix [406] Pullout V*l2 CNT τ po rCNT The energy release term involved in this phenomenon depends on the sliding shear stress for the pullout. [406] V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 21 3.3.1. Experimental evidences of bridging, debonding and pullout The toughening mechanisms observed in the ceramic composites with CNTs have been widely discussed. Among them, the crackbridging phenomenon (Fig. 8c and d) has been frequently reported. This can be seen by electron microscopy and can be found in a variety of samples, as shown in Fig. 9. Typically, SEM images reveal straightforwardly how taut CNTs hold together the two sides of the crack as the cracks propagate along the matrix. Some works have estimated that MWCNT can bridge a maximum of ~100 nm of crack opening [155] before fracturing. For example, the crack-bridging reinforcement effect has been reported in CNT-3YTZP composites [63,204] and several CNT–alumina composites [45,49,120,183,185,356,363,375,408–411]. Curiously, despite the random nature of these composites, the alignment of the bridging CNTs perpendicular to the crack surfaces due to the stretching is apparent, as can be seen in Fig. 9 [165,375]. It has been shown how the initially randomly oriented bridging CNTs orientate perpendicular to the crack surfaces as the crack propagates. The propagation of the crack on CNT-alumina composites was thoroughly examined by Liu et al. [375], and a series of SEM images performed in a fixed location as the crack propagates along the sample are shown. In addition, their experimental results showed that crack bridging was helping to sustain wider crack openings than those corresponding to a pure alumina matrix. They used the analyses of the crack opening displacement (COD) in order to quantify this effect at a given point of the crack. Thus, the bridging stress function, P(u), is a decreasing function of the crack opening, u, and it can be approximated as follows: P(u) = PM(1−u u∞)(10) where P M is the maximum bridging stress, and u ∞ is the COD at the mouth of the crack when the crack-bridging zone length reaches steady-state [375]. Fitting the experimental values resulted in a P M value of 56 MPa and a 2u ∞ of 0.98 μ m. The influence of the length of the CNTs on their toughening ability was researched by Kasperski [120]. He compared 1.5 and 10 μ m length MWCNTs, and concluded that the mechanical locking by the alumina matrix in short CNTs would not extend very far, allowing for pullout at low tensile stresses. This idea was revised in the work by Fan et al. [61], and it was considered in order to assess the interfacial shear strength, τ i , between SWCNT and alumina grains (Fig. 8d), achieving a value as high as τ i ~ 1 GPa. Higher values of the shear strength up to ~2.3 GPa were even reported in the case of MWCNT [409]. This intense interaction can be explained in terms of a strong bonding between CNTs and the alumina grains. If this interfacial strength is attributed only to the radial residual thermal stress between CNTs and the matrix, the estimated value is σ =310 GPa, a much lower value than the calculated value of τ i , which indicates that, in addition to the mechanical bonding, the fabrication procedure (heterocoagulation method) allowed the formation of a diffusion layer between the CNTs and the matrix that increased the bonding strength. Fig. 9. SEM micrographs of taut CNTs bridging the two sides of the crack, a) reprinted from [63] and b) reprinted from [165] with permission; c) detailed bridging CNT (reprinted from [356] with permission); d), e) and f) SEM micrographs of a fixed location at different moments as the crack propagates in alumina-based composite with 10 wt% of MWCNT (reprinted from [375] with permission). V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 22 The presence of protruding CNTs and outcrops in the fracture interface has also been claimed as a proof of the bridging and pullout phenomena (Fig. 8e) [63,293,332,383,409]. Once the crack surfaces start to separate, the bridging CNTs appear perpendicularly aligned to the surfaces and to the crack propagation direction [165,256], providing a closure stress across the surface. Several examples of these CNTs can be seen in Fig. 10a. Moreover, the debonding of single CNTs has been reported by Yamamoto et al. [383]. In Fig. 10b it can be seen how a single CNT located on the grain boundary and parallel to the surface was debonded and left the trace on the grains. The pullout of the CNTs has also been reported in the fracture surface of the alumina composites [49,53,139,304,356,408,412]. Commonly, CNTs protruding from the fracture surface seen by SEM have been understood as evidence of pullout phenomena [139] but broken MWCNTs with clean cuts or by the sword-and-sheath mechanisms are also frequently reported, indicating the existence of a high interfacial strength that involves MWCNT failure and limiting the pullout contribution to the toughening [411]. Then, when pullout occurs, holes are expected to be left on the matrix socket, and this is not usually reported. Nevertheless, explicit reference to these holes observed by SEM is made in [409]. In this work, the authors reported the presence of MWCNT in two different locations, namely, intergranular and intragranular locations, and the different locations involved differences in the pullout mechanism. They affirmed that the shorter pullout lengths observed at the intragranular positions suggested a higher interfacial shear strength in this type of location of the MWCNT. The pullout stress of a single CNT was specifically researched by several authors who characterized tensile tests where the CNTs of the fracture surfaces were mechanically loaded with a nano-manipulator inside a SEM device. Thanks to these experiments, the failure force has been found to be between 5 and 14.4 μ N [117,118,139,383]. Furthermore, Cho et al. [406] performed an estimation of the energy contribution thanks to the pullout mechanism based on some generic values from the literature. Hence, they reported a value of 1 J/m 2 , considering a length of the nanotubes of 100 nm and an extraordinarily low generic value of the sliding shear stress. In the case of graphene-based reinforced composites, there is experimental evidence of graphene providing similar toughening mechanisms, namely, bridging, debonding and pullout. For example, GNPs were observed bridging cracks in graphene-alumina CMCs [58,221,273,382] and in graphene-reinforced zirconia-alumina composites [413]. In Fig. 11, some GNPs can be seen bridging the two sides of the propagating crack. The occurrence of pullout was also reported in the cracks of alumina composites [273,414]. In addition, GNP pullout has also been observed in zirconia-based composites by Zeng et al. [233] and in alumina-based composites [220]. Fig. 10. Fracture surface from MWCNT-alumina composites: a) protruding CNTs can be clearly seen emerging perpendicularly to the crack surface; b) the trace of the debonded CNT is shown in the grain boundaries. Reprinted from [383] with permission. Fig. 11. SEM images showing the microstructure of graphene–alumina: a) crack bridging by graphene nanosheets (indicated by arrows) between alumina grains (reprinted with permission from [58]), scale bar is 1 µm; b) GNP bridging the two sides of a crack. Reprinted from [221] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 23 Typically, during the fabrication of the samples by conventional procedures, the graphene sheets are embedded between the grains, that is, wrapping the ceramic grains, which results in a very high contact area and high interfacial friction between the GNPs and the surface area of the grains [223,229,382,413,415,416]. When the crack reaches a GNP, if the bonding between the GNP and the matrix is weak enough for the crack to be deflected along the interface, the GNP remains intact and the composite can be toughened by the debonding mechanisms [55]. Thus, the graphene-matrix interface is characterized by the critical shear stress needed to debond the graphene and the shear resistance. In the case of pulling out the GNP, it is assumed that the energy required to pull out a graphene sheet from the ceramic matrix has to be much greater than that needed to pull out a nanotube or a nanofiber due to the larger specific surface area of GNPs and their more intimate contact with the ceramic grains. Moreover, the relevance of the dimensions of the GNP was researched by comparing GNP additions of different sizes, selected by centrifugation [58]. It was reported that the best reinforcement was found for an intermediate aggregate size (~20 μ m). The largest GNP (~100 μ m, aggregates) were considered to act as defects instead of as a reinforcement, which is consistent with the observation that the problems in the dispersion of the GNP such as folded GNPs can cause the graphene to act as brittle graphite [382]. And, in the case of the smallest GNPs (~10 μ m), it was stated that the crack-bridging effect could be weaker due to their smaller dimensions. It is also worth highlighting the work by Zhang et al. [417] with GNP-reinforced hydroxyapatite. They reported that the energy dissipated by the pullout of GNPs decreased as the number of graphene layers in the GNPs increased due to the weak van der Waals interaction between the layers. Finally, a reported consequence of the presence of CNTs in the ceramic matrix and the reinforcing mechanisms is the change of the fracture mode. Thus, it was stated that the strong bonding between CNT and the alumina grains reinforced the weak bonding between the respective alumina grains and it was responsible for the change in the fracture mode, from intergranular to transgranular [418]. Similar results were also obtained by Lee et al. [45], who also reported a transition of the fracture mode from transgranular to intergranular as the MWCNT content increased. This change in fracture mode was also reported by Satam et al. [59], and it was explained in terms of the change in the location of the reinforcing agents, as the intragranular location exhibited stronger bonds between the CNT and the grains, and this feature involved the change of fracture mode to transgranular. Analogously, a similar change in the fracture mode has also been observed by the addition of graphene in alumina-based composites [382], and in YTZP-based composites [229], though no such change in the fracture mode can be found in the literature [221]. It was also indicated that the firm bonds between GNP and the matrix offered support to the grain boundaries to efficiently transfer the stress from one grain to another. 3.4. Crack deflection From the point of view of the geometry of the crack, when the crack front arrives at the ligaments, it can be deviated out of the plane of the crack. This process is known as crack deflection. Actually, this phenomenon cannot be only attributed to fiber-reinforcements, yet it was initially considered as an energy absorbing mechanism [393] in ceramic glass with elongated embedded crystals. It can take place when there are paths in the ceramic matrix that exhibit lower resistance to crack propagation than an average plane perpendicular to the tensile stress. For example, it can appear along the grain boundaries as it is known that, typically, they require half the fracture surface energy of a single crystal [419]. In this regard, Wiederhorn [420] established that the value of K Ic for a polycrystalline material should be approximately twice that of a single crystal due to the mere geometric effect of the presence of the grain boundaries in the deflection phenomena. Besides, the deviation of the crack path can also be due to the presence of residual stresses that typically develop in the materials that present thermal expansion anisotropy [376,389]. Nevertheless, crack deflection processes can be found where the crack deviates towards the ligament-matrix interface, which can be easy paths for propagation, depending on the bonding strength. As shown in Fig. 8d, this process started by the debonding of part of the embedded ligament, allowing the crack to propagate perpendicularly (downwards, parallel to the ligament in Fig. 8d), with respect to the original crack propagation direction (which was rightwards in Fig. 8). This phenomenon should not be confused with the deviation of the crack due to crack bridging by CNTs, which is also commonly labeled “crack deflection” (see, e.g., Fig. 9b). In particular, it has been stated that the crack deflection mechanism is favored when the ligament-to-matrix modulus ratio is somewhat lower than 2 [400], which is a rather low ratio compared to the moduli ratio between, for example, alumina and CNTs or GNPs. In any case, this mechanism hinders the crack growth, increasing the resistance of the material to fatal fracture. The presence of weak bonds between the matrix and the ligaments or badly dispersed ligaments reduces the interfacial surface energy γ i , but promotes the crack deflection along the interface. Although this has been claimed as the most interesting reinforcing route [167], it has also been stated that crack deflection due to fiber-reinforcement actually weakens the material [324]. Interestingly, Faber and Evans [421] showed that the most effective morphology of reinforcing embedded phases for increased toughening is the rod shape, and that the toughening effect increases with increasing aspect ratio, which is especially interesting in the case of CNTs, GNPs and CNFs. Due to all considerations, the deflecting toughening effect is expected to increase with the volume ratio of the ligaments, and it was found so, up to a maximum of 20 vol% in the case of microfibers. But, as mentioned before, incorporating this amount of CNTs, homogeneously dispersed and completely individualized, is largely beyond the current fabrication technologies. The crack deflection with CNTs was researched in an ordered system based on in situ grown CNTs in a porous alumina matrix (Fig. 12). It can be seen how the crack intersects the successive CNT-matrix interfaces and is deflected surrounding the CNTs, carrying out the phenomenon of crack deflection. This result means that the CNT-matrix interface has a sufficiently lower energy, relative to that of the crack propagation through the CNT cross-section itself, that deflection and surrounding the CNT is the preferable path [324]. It has been found that full dense composites allowed the crack to grow along the interfaces between CNTs and alumina matrix V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 24 grains (see, for example, [53,183,407]), or CNF and alumina [422], promoting the increase of the fracture toughness. In Fig. 13, the change in the propagation direction of the crack due to the presence of one CNT is shown and characterized [423]. Nevertheless, in CNT-reinforced CMCs, the crack deviation along the CNT-ceramic interface is not commonly reported in the literature, unlike crack bridging or pullout. On the contrary, crack deflection along the graphene-ceramic matrix is very eloquently shown in several works. It is worth recalling that the 2D graphene is soft when bearing a bending force but rigid when bearing a tensile force. So, when a crack generated by external force propagates and meets perpendicularly with a GNP, it is arrested and deflected in-plane, resulting in the formation of crack deflection, as can be seen in Fig. 14. This process has been reported in several works, such as [58,220,382]. Given the two-dimensional nature of the GNPs, the deflection can occur in different directions, as shown in Fig. 15, unlike the case of one-dimensional ligaments such as CNTs or CNFs. Once the crack reaches the GNP perpendicularly, it can be singly deflected (Fig. 15b), or it can even be branched, or “forking”, and deflected in two opposite directions (Fig. 15c). The crack branching mechanism is a well-known mechanism [144] through which the crack develops several paths around or through a ligament or other reinforcing element due to the relative orientation of preferred fracture surfaces, such as grain boundaries or the ligament-matrix interface, and it can be promoted by providing preferred propagation directions along the GNP-alumina interface. In addition, considering the increased contact area and large GNPs that provide long deflection paths, the efficiency of the toughening mechanisms brought by GNPs can be much greater than that in CNT- or CNF-reinforced composites. Hence, following this discussion on the crack deflection phenomena, a controversy between weak bonds, which favor crack deflection, and strong bonds, which enhance crack bridging, was opened [46] and it is still a subject of debate. This debate was also laid out in the following terms: the interfacial adhesion should be strong enough “so that the ceramic matrix is able to transfer applied load to CNT reinforcement” [138], and because, in the case of very poor bonding, CNT may act as microcracks or flaws, resulting in a deterioration of the mechanical properties of the composite [406]. First discussions about this point were supplied by R¨ odel [393,424], who concluded that “crack deflection with interface debonding allows a reinforcing element to be strained to a sufficiently large degree Fig. 12. SEM photograph showing the deflection of the crack path along the consecutive CNT-matrix interfaces. Reprinted from [324] with permission. Fig. 13. a) Scanning electron microscopy image showing crack deflection in MWNT aluminum oxide composite; b) sketch of the crack deflection mechanism. Reprinted from [423] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 25 such as to guarantee closure forces up to a large crack opening”. Additional answers were achieved by computer simulation (which will be detailed below), but some ideas may be advanced in this section. It was interestingly concluded that “the interface should not be too weak” but “it should not be too strong” [167]. Finally, Zhan et al. [53] focused explicitly on CNT-reinforced systems and concluded that the CNTs should be “efficiently bonded”. 3.5. Specific toughening mechanisms for carbon allotropes Some specific mechanisms that have been reported exclusively in CMC reinforced with carbon allotropes may be remarked upon in this section. For example, in CNT-reinforced CMCs the presence of shear bands due to the propagation of the crack has been reported [324]. The performance of this ordered system allowed the observation of this novel nanocomposite failure model. It can be seen how the deformation of the composite is accommodated by the collapse or the distortion of the CNT forming shear bands (Fig. 16). Thus, this feature is a CNT-specific phenomenon so it can also be understood as new mechanisms of releasing energy that can contribute to the toughening of the CNT-reinforced composites. In addition, an MWCNT-specific toughening mechanism has been reported due to the breaking of the outer walls (the sword-on- sheath mechanism, discussed below in Section 3.6), and it can also contribute to the toughening of the composite [425]. This unique multiwall-type failure entails an effective load transfer from the ceramic matrix to the external wall, and, subsequently, also to other inner walls, in a successive manner, of the individual MWCNTs that are generally supposed to be unable to bear load. One last feature specific of the CNTs is the stretching/disentangling toughening typically due to the presence of carbon nanotubes at the Fig. 14. SEM image showing the microstructure of graphene–alumina composites and the crack deflection by a graphene nanosheet indicated by the arrow (reprinted from [220] with permission). Fig. 15. A schematic explanation of some of the toughening mechanisms that may be favored in ceramic composites with graphene: the twodirection deflection mechanism. GPL: graphene platelet. Reprinted from [413] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 32 where E is the Young’s modulus, H is hardness, P is the indentation force, c is half the crack length, and §and n are empirical values. This equation should be applied only if a median-radial crack is developed, if the thickness of the specimen is great enough to allow the development of this type of crack, if the test surface is free of pre-existing stresses before indentation and, finally, if the microstructure of the ceramics, such as the grain size, is small enough in comparison with the crack extension to avoid possible disruption of the crack patterns [461]. The values of §and n are determined by averaging data from different materials [460], either numerically by the use of finite element analysis [462] or with a proposed model such as the wedge-loaded half-penny crack by Shetty et al. [463]. All of them basically follow the Eq. (13) with slightly different values of §and n. Table 1 of [461] gives the values of §and n. For n =1/2, Anstis et al. [69] obtained a value of §=0.016 ±0.004 with an accuracy better than 30–40% in a number of ceramic materials. Also for n =1/ 2, a value of 0.018 was found by Miyoshi (article in Japanese, not referenced here) and 0.023 was reported by Shetty [463]; for n =0, Lawn and Fuller [464] and Tanaka [465] found almost the same value: § = 0.0726 and § = 0.0725, respectively. The type of crack determines the form of the equation to be used to determine the toughness. As indicated in [458], the most widely used are shown in Table 5, where E is the Young’s modulus (GPa), H is the hardness (GPa), P is the indentation force (N), l is the average crack length (10 −3 m), c is the average length (10 −4 m), and ν is the Poisson’s ratio. Even though the application of the VIF method to assess fracture toughness varies with the selection of the equations, it is a useful tool for certain materials such as ceramics. The equations in the table are the most frequently used for different types of cracks developed under the indent [69,469,470]. Currently, there are >40 variations of the fracture toughness VIF model and none are completely satisfactory, creating much confusion since they are optimized for particular materials or indentation conditions. When measuring indentation fracture toughness in brittle solids or ceramic materials, Niihara’s equation tends to overestimate the fracture toughness [467] whereas Miyoshi’s equation [468] tends to underestimate it. The same trend has been found in silicon nitride [470]. Therefore, to assess fracture toughness in general, the equation to be used depends on the ceramics. Interesting reviews on these tests and the problems using VIF can be found in refs. [327,330,471]. 4.1.2. Comparative between VIF and SENB The first fracture mechanics test based on flexural loading for brittle materials was the SENB (also standing for single-edge-notched bend [472]) test. Currently, is one of the most considered methods in scientific research devoted to the advanced ceramics and, in particular, to the CMC with carbon allotropes and there is extensive literature reporting the use of this technique explaining deeply the details of the procedure [68,69]. It consists in bending a bar with a specific geometry, in with a notch is cut in one of the narrow sides. Thus, the experiments are based on the consideration a machined (not true) crack. Because of the absence of a true crack, SENB data should not be trusted. In addition, due to the machining of the notch, is typically assumed that there are induced cracks at the root of the crack, which is frequently incorrect. This feature may involve the overestimation of the fracture toughness measured by SENB. Since it was proposed by Davidge and Tappin in 1968 [473], improved versions of the morphology of the notch have been proposed [455], such as SEVNB, SEPB or CBN [456,457,474]. Several works have been faced the controversy of the fracture toughness methods and the reliability of VIF method, in comparison to SENB-based procedures. Thus, whereas the usability and popularity of the VIF method is widely considered, some authors considered it as unacceptable [475], as the stress distribution around the crack is unclear. Other studies such as that by Wang et al. [44] stated that the VIF method is an indirect toughness-testing technique and the validity of the toughness results depends critically on the elastic/anelastic contact of the material being tested. In this regard, a variety of conclusions have been found experimentally, such as either significant toughening up to a two-fold increase or the absence of toughening effects. A recent criticism of the VIF method can be found in the review article by Miyazaki and Yoshizawa [462]. This paper discusses the suitability of the identification of the fracture toughness with the “indentation fracture resistance” measured by VIF. It also shows a comparison from 22 literature reports focusing on new formulae for the VIF method and comments on the comparative results observed during international Round-Robin Test (RRT) standardization trials. RRTs are an experimental methodology performed independently by different laboratories and different scientists using the same method and same materials on different equipment. Hence, some international collaborative projects have been performed, for example, to measure the fracture toughness of alumina with the participation of 23 laboratories [476] or of silicon Table 5 Set of equations to be used depending on the crack type. Palmqvist crack system equations Median crack system equations Shetty [466]: KIC =0.04285 1 (1− ν 2)(HP/l)1/2 Niihara [467]: KIC =0.0123(E/H)2/5(HP/l)1/2 Anstis [69]: KIC =0.016(E H)1 2(P/c3/2) Niihara [467]: KIC =0.0309(E H)2 5(P/c3/2) Miyoshi [468]: KIC =0.018(E H)1 2(P/c3/2) V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 33 nitride and fine-grained zirconia–alumina composites, with the participation of 18 laboratories [477,478]. It was concluded that crack length measurements were equipment-sensitive and highly subjective and there is also the problem that the equations are all suspect. There is poor reproducibility of the results between the different laboratories and, consequently, between the values of the fracture toughness obtained between the standard direct method and VIF. Moreover, Miyazaki and Yoshizawa [462] suggested that the low optical resolution of the microscope used to measure the crack-length in VIF is the origin of the poor reproducibility associated with this test. In practically almost all works, the cracks were measured using an optical microscope and the accuracy of the toughness values was questionable. Besides, surface porosity or damage due to unsuccessful polishing can make the crack length measurements unreliable [44,479]. In contrast, when the cracks are measured with differential interference contrast illumination [69,469] or using powerful optics with a traveling stage for relatively large cracks [462], the measurement of the fracture toughness is more reliable. Nevertheless, Miyazaki and Yoshizawa [462] affirmed that the major source of discrepancies between data from standardized methods compared with those obtained by VIF is not related with inherent features of the VIF method, but with the lack of the essential experimental conditions for such a comparison. Another recent review of this issue was performed by Relias and Ngai [458]. They confirm that the VIF method is a useful tool for fracture toughness estimation and they stated that one of the key steps is the selection of the system of equations considering the crack morphology. Some specific experimental comparisons between the use of VIF and SENB to measure the toughness have been made for alumina reinforced with CNTs and graphene with carbon contents between 0 and 6 wt% and for YTZP reinforced with MWCNT contents between 0 and 5 wt% (results and references are compared in Fig. 22). In the case of YTZP, while at 0 and 0.5 wt% the two methods give almost the same results with values of 6 and 6.5 MPa⋅m 1/2 respectively, when the concentration of MWCNTs increases, the difference between the two methods increases too, changing from 8 MPa⋅m ½ with SENB to 11 MPa⋅m ½ with VIF [63]. Thomson et al. [50] also compared SENB and VIF measurements in alumina-based composites with SWCNT or DWCNT. They found non-systematic differences between the two methods, with the SENB values being in some cases +15% greater and in other cases −30% lower in comparison to the values obtained by the VIF method. Other works by Yamamoto et al. [256] and Ahmad et al. [363,412] also compared the two techniques on reinforced alumina with CNTs. While Yamamoto et al. confirmed that higher values were obtained by VIF, Ahmad reported the opposite behavior, finding higher values by SENB. Finally, Porwal et al. [55] performed a comparative study on graphenereinforced alumina using the two techniques and reported very similar values with graphene contents up to ca. 3.0 wt%. Thus, considering these specific comparison works, it is true that in some cases VIF usually gives higher values than SENB, but the lowest values can also be found by VIF. Typically, VIF tests are performed in specific areas of the sample previously selected by the researcher by direct observation, in order to avoid defects, pores, or CNT aggregations, which are more likely to be present at high CNT contents. But these fabrication flaws are not avoidable in the SENB method, which involves a large volume of sample and therefore yields lower toughness values. However, there is significant scattering in these two methods, VIF and SENB, which reveals the major influence of preparation methods on the mechanical performance that typically result in different densities, defects, or differences in bonding and CNT dispersion throughout the matrix. Therefore, it can be concluded that other factors beyond the selection of the method, VIF or SENB, are critical for the toughness values given that no systematic overestimation is found for VIF with respect to SENB. More results obtained from both techniques are also compared in Fig. 23 and Fig. 26. 4.1.3. Toughness of alumina-reinforced ceramics Results of the fracture toughness measured in CNT–alumina composites by the VIF, SENB, and SEPB methods are plotted in Fig. 23a. The results show discrepancies due to various factors such as the choice of sintering process, method of characterization and assessment of the fracture toughness, and dispersion of the CNTs within the matrix, among others. The figure also shows that the increase of the fracture toughness is proven at low CNT additions (<2 wt%). As a general remark, no specific differences can be Fig. 22. Comparison between different techniques for the determination of fracture toughness by SENB (black symbols) and VIF calculations (red symbols) on reinforced alumina (solid symbols) and zirconia (open symbols) with different carbon allotropes: circles, graphene–Al 2 O 3 [55]; open triangles, CNT–ZrO 2 [63]; all the rest, CNT–Al 2 O 3 [50,256,363,412]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 34 established between the different calculation methods, except for high CNT contents (>4 wt%), where results are very scarce and no conclusion can be drawn. It can also be observed that the tendency of reinforcement of Al 2 O 3 with low CNT contents (<2 wt%) is clearly revealed by the VIF and SENB methods, whereas SEPB does not reflect the same trend. Nevertheless, SEPB values are found to be below VIF values, especially for high CNT contents, which is consistent with the specific comparative research by Miyazaki and Yoshizawa [480]. Also, for high CNT contents, the trend of VIF results is not clear, and the tendency of SENB results is to decrease. The fracture toughness of the reference samples of pure alumina considered for the different works spans from 2.2 to 5.7 MPa⋅m 1/2 , Fig. 23. Fracture toughness for reinforced alumina-based composites with different carbon allotropes: a) CNT-reinforced, data from: VIF [42,45,50,53,116,122,177,182,183,187,188,202,213,254–256,287,290,291,326,356,357,363,364,374,412], SENB [44,46,50,61,120,139,158,185,246,256,292,293,312,332,356,363,371,375,376,412], SEPB [335]; b) graphene-reinforced, data from: VIF [43,55,56,168,210,213,214,220,221,223,224,382], SENB [55,58,156,216,219,267,273]. Average trends are shadowed for clarity for the VIF and SENB models. c) CNF-reinforced; the VIF method was considered in these three works: data from [43] (red squares), [239] (black circles), and [240] (blue triangles). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 35 a wide range that makes it even more difficult to establish unquestionable toughening results due to the inclusion of the CNTs and beyond the mere differences in the synthesis procedures. Nevertheless, Zhan et al. [53,364] and Lee et al. [45] reported outstanding improvements of the fracture toughness in >4.0 wt% CNT–Al 2 O 3 composites sintered by SPS, almost 300% higher than the fracture toughness of their own reference pure alumina, with values of up to 11.2 MPa⋅m 1/2 for samples with 4.3 wt% CNTs. Finally, despite the claimed problems in obtaining well dispersed CNTs within the ceramic matrix, several groups reported studies with CNT contents of >10 wt%, but with a clearly defined decreasing trend of the fracture toughness [293,312,376]. Other carbon allotropes such as different types of graphene or CNFs have also been embedded in alumina matrix with the aim of increasing the composite toughness. The results obtained from different studies considering graphene are plotted in Fig. 23b. Regarding the increase of the fracture toughness, the addition of graphene into alumina ceramics gives results similar to those obtained by using CNTs. Besides, the VIF method, which is used considerably more often, gives higher values than the SENB method, but both show similar trends, namely with increasing values up to carbon contents of 2 wt%, and decreasing ones for higher carbon contents. Extraordinary results have been reported by Lee et al. [168]: up to K IC =10.1 MPa⋅m 1/2 for an rGO content of 1.1 wt%, representing a 150% increase in the fracture toughness with respect to their own reference pure alumina. Unfortunately, there are no other studies confirming such an outstanding toughening effect. Finally, the inclusion of CNF in alumina matrix has scarcely been researched. Only two research groups, Ueda et al. [239,240] and Cano-Crespo et al. [43], have reported studies of alumina reinforced with CNF using the VIF method. The results are collected in Fig. 23c, where some increasing trends are suggested, and the maximum fracture toughness value is 5.6 MPa⋅m 1/2 for composite with 0.4 wt% CNF content [239]. Moreover, the strong dependence of mechanical properties such as the fracture toughness on density is well known, as revealed in Fig. 24, where the tougher composites are obviously the denser ones, achieving a toughness of 9.7 MPa⋅m 1/2 , nearly three times that of pure alumina. When the density decreases, the entangling network structure seems to disappear in samples with density ρ <86% of the theoretical density, whereas stronger bonding of ropes with the matrix occurs in the sample with a density of 95%. These results suggest that the extent of interfacial bonding might be a factor in increasing the toughness of the composites [53]. The influence of the type of reinforcement phase or the sintering procedures on the toughening of ceramic composites can also be discussed with respect to the detailed results plotted in Fig. 25a and b. In Fig. 25a, MWCNT- and SWCNT-reinforced composites have been compared considering only VIF measurements in order to neglect any effect of the methodology. It has been stated that SWCNTs may be a better reinforcing phase given the absence of the sword-in-sheath effect that appears in the MWCNTs [53,139,481]. However, in the light of the research studies, this premise cannot be confirmed without doubt: below 4 wt%, the fracture toughness of MWCNT-reinforced alumina is clearly above that obtained for SWCNTs. Nevertheless, the few works studying CNT concentrations beyond 4 wt% suggest that SWCNTs show a better reinforcing effect, whereas reinforcement by MWCNTs seems to become saturated. In Fig. 25b, the fracture toughness values of the CNT–alumina samples sintered by SPS procedure are compared with values from samples sintered by other procedures such as HP or pressureless sintering. The comparative proves that better results are obtained from samples sintered by SPS, especially for high CNT content, in coherence with the conclusions of specific comparative reports [345,346]. Thus, several studies have been focused on the improvement of the fracture toughness of alumina by the addition of CNTs. The results show a large scattering in the values of the fracture toughness, probably due to the wide range of types of nanotubes, the very different degrees of CNT dispersion, and the extreme difficulty in achieving a fully homogeneous microstructure. These results open doubts on the reproducibility of the mechanical behavior of CNT-based CMC. Moreover, although the fracture toughness measured by Vickers indentation is sometimes questioned, the results obtained by this method do not present significant variations from the others (as can be checked in Fig. 23). Thus, as mentioned before, VIF has attained considerable popularity because of its relative ease of application and the difficulty obtaining the standard size in ceramic materials required for other methods. Fig. 24. Fracture toughness of alumina composites versus CNT content and in function of the density of the composites. Data from [53]. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 36 4.1.4. Toughness of zirconia-reinforced ceramics Zirconia-based ceramic composites have also been reinforced with different carbon allotropes. In Fig. 26 the results of CNT-, graphene-, and CNF-reinforcing studies are plotted. The plots of CNT- and graphene-reinforced zirconia also show the different techniques considered for the measurement of K IC , namely SENB and VIF, and for the latter, the different expressions considered: Anstis, Evans, Niihara, and Shetty [458]. The fracture toughness of the CNT-reinforced zirconia shows, in general, a mild increasing trend for increasing CNT contents (Fig. 26a). But, surprisingly, a very wide dispersion is found, even for the pure zirconia samples. The two different models considered, SENB and VIF, exhibit similar average results, given that the three reported SENB series can be found within those obtained by VIF. But it is remarkable that the SENB studies give contradictory trends: Mazaheri et al. [63] show a well-defined increase of K IC from 5.75 to 10.6 MPa⋅m 1/2 while values reported by Kasperski et al. [204] exhibit the opposite trend, that is, a decrease with increasing CNT content from the value of 10.3 MPa⋅m 1/2 found for pure zirconia to half of that for 6.3 wt% CNT. Besides, the use of different expressions for VIF measurements does not involve any significant systematic shift: although there are not enough samples for reliable statistics, the currently reported values obtained by Anstis’ expression include both the maximum and minimum reported values, namely 1.7 MPa⋅m 1/2 for 0.7 wt% CNTs [192] and 15.2 MPa⋅m 1/2 for 5 wt% of CNTs [65]. Mazaheri et al. [63], by means of both VIF and SENB tests, found a significant improvement of the mechanical properties in 5 wt% MWCNT–3YTZP composites with respect to monolithic 3YTZP. They reported an improvement of the fracture toughness from 5.75 up to 10.6 MPa⋅m 1/2 by VIF and from 6.0 up to 8.0 MPa⋅m 1/2 by SENB. Such an effect was argued to be due to the pinning effect of MWCNTs restricting grain-boundary sliding. Duszov´ a et al. [207] sintered monolithic zirconia and CNT–ZrO 2 composites by hot pressing, and found fracture toughness values of up to 6.24 MPa⋅m 1/2 . Regarding the types of CNTs, in Fig. 26a it can be seen that, on average, similar results are found when using SWCNTs or MWCNTs (an analogous result to that obtained for alumina composites: see Fig. 25a). Bocanegra-Bernal et al. [116] explicitly compared the findings for both allotropes, and found that at very low CNT contents (0.01 wt%) the use of SWCNTs led to lower toughness (3.25 MPa⋅m 1/2 ) than the use of MWCNTs (4.7 MPa⋅m 1/2 ); that is, 45% tougher samples were obtained when considering MWCNTs instead of SWCNTs. As a general consideration, the comparison of the results suggests that neither the selection of the measurement technique nor the selection of the VIF expression is a critical choice. Instead, other factors such as differences in sample fabrication conditions or accuracy when measuring may have led to the large dispersion of the results. Nevertheless, in spite of this great dispersion of the results, the increasing trend of the average fracture toughness of the studied sample series thanks to the addition of the CNTs can be confirmed, at least up to 5 wt% CNTs. Fig. 26b plots the different reported results for the reinforcing strategy of the addition of graphene. Again, it is notable that, except for the outstanding results obtained by Chen et al. [229], for very low contents, similar behavior is found no matter what measurement technique is considered. All the reported studies confirm a significant increase in K IC for small amounts of added graphene, below 0.5 wt%. Beyond this content, most of the studies report a decrease of the fracture toughness. It is also worth paying attention to the different types of graphene that are being considered, namely rGO or GO. In this regard, recent works by Cano-Crespo et al. [47] and Zeng et al. [233] considered GO and found some of the highest values among all the series. It has been suggested that the functional groups of the GO can facilitate stronger attachments between the graphene sheets and the ceramic grains, which would involve stronger toughening mechanisms. In fact, a specific comparison was performed by Zeng et al. [233], showing that GO is a better reinforcing agent than the rGO. But, up to now, there are not enough works to make this idea a major conclusion. Moreover, 3YTZP with the addition of 1–3 wt% graphene was prepared but no significant increase of the toughness was observed (Fig. 26b). The analyses of the fracture surfaces show indications of strong pullout effects and that the bonding of the matrix and Fig. 25. a) Fracture toughness of alumina-reinforced composites with different contents of MWCNTs or SWCNTs. MWCNT data from the following references: [45,50,116,122,177,182,187,188,202,255,256,287,290,291,326,356,357,363,374] and SWCNT data from: [50,53,116,183,364]; b) Comparative of fracture toughness from samples with different sintering procedures. Data from [45,122,139,158,182, 185,213,255,256,312,333,356,363,412]. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 37 (caption on next page) V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 38 reinforcement is relatively weak, probably because the contact areas are perfectly smooth. However, crack deflection was facilitated but the stress transfer to the reinforcement was not strong enough. On the other hand, the results indicate that fabrication approaches seem to give convenient microstructures for composites with low graphene contents but higher graphene fractions result in a broad graphene size distribution and the appearance of multilayer lamellae [228,232,380]. Finally, there are some very recent works considering CNFs as reinforcing agents for zirconia and reporting some different results (Fig. 26c). For example, Cano-Crespo et al. [47] reported a 15% increase of the fracture toughness due to the addition of 0.5 wt% CNFs. However, the works by Duszov´ a et al. [244] and Dusza et al. [359] reported decreases in the values of K IC , except for the sample sintered by SPS, for which the maximum value was obtained: 6.4 MPa⋅m 1/2 with the addition of 0.75 wt% CNFs. Its hot-pressed counterpart exhibited lower values of fracture toughness as expected, due to the larger grain size obtained by this technique. 4.1.5. General assessment of the toughening strategies In these epigraphs, the reported results on the toughening researches have been compiled and compared. Moreover, the different techniques for toughness measurements and the different carbon allotropes have been compared and discussed. In the light of these results, some ideas can be mentioned: •There is a large dispersion of the results. Preparation strategies are the major source of dispersion, involving disparity of allotrope types, fabrication routes, and densification strategies, resulting in significant differences in densities, homogeneity of the carbon suspensions, and carbon location, among other parameters. Furthermore, K IC is highly sensitive to features such as the grain size, porosity, or homogeneity of the carbon dispersion, especially in the case of the SENB method. Besides, the VIF method was claimed to be very sensitive to the accuracy of the indentation length measurement. •The toughening of the ceramic composites by the addition of the carbon nanostructured allotropes is confirmed, although more research work is needed to confirm some reported outstanding results. Values of up to 11.2 MPa⋅m 1/2 for 4.3 wt% MWCNTs [45] and 10.5 MPa⋅m 1/2 for 1.12 wt% graphene [168] in the case of Al 2 O 3 , have been reported. In the case of ZrO 2 , values of 15.2 MPa⋅m 1/2 with 5.0 wt% MWCNTs [65] and 15.3 MPa⋅m 1/2 with 0.01 wt% graphene [229] have also been published. •On average, no major differences have been found between the different carbon allotropes in comparative studies, although in the case of CNFs the toughening mechanisms are largely less investigated. •The consideration of different methods of toughness measurements is not a key feature. The VIF and SENB methods give the same values within the scattering of the reported results, given that the most critical parameters involve sample preparation. Similarly, it is also revealed that the multiplicity of expressions available for KIC calculation by the VIF method is not critical. •Finally, it is plausible that the “saturation” of the toughening effect, that is, the lack of significant toughening for high carbon contents (above 2.0 wt%) or even the decrease of the fracture toughness for increasing carbon contents beyond a given weight percentage may be due to the dispersion problems found in the preparation of carbon-containing composites [49,256,382]. Typically, when the CNTs appear forming coils or bundles, and are located among the grains, they may include porosity or act as impurities instead of as reinforcing agents. Even though the large efforts invested in solving this specific experimental issue, coils or bundles usually still appear in carbon-containing CMCs, hindering the achievement of the desired toughening effects. In this regard, despite it has been proposed a parameter to estimate the quality of the dispersion based on large SEM analyses [139,158], thorough techniques based on a large and statistically reliable scale are still desirable. 4.2. Hardness The hardness of reinforced ceramic composites has been extensively studied. Although hardness is measured using Vickers indentations without any sophisticated equation, a significant scatter of the values can be observed; several factors can cause this, such as the applied load, the processing techniques used, which can yield different structural parameters that dramatically affect the hardness such as grain size or density, or dispersion of the carbon allotropes, which can reduce the densities of the composites. In addition to the decreasing dependence of the theoretical maximum density of the composites with increasing carbon content, in the case of the samples obtained by pressureless sintering, an additional decrease of the experimental density has been reported (Fig. 6). In the following sections, the reported hardness values for alumina and zirconia composites have been compiled and compared in Fig. 27 and Fig. 28. It can be clearly observed that the hardness decreases when the concentration of carbon allotropes increases for both CNTs and graphene and for the two most popular ceramic matrixes, alumina and zirconia. One additional consideration deserves the attention of this review in order to discuss and compare the mechanical properties of CMCs. It is well known that the average size of the ceramic grains is significantly affected by the presence of CNTs or GNPs [45,63,139,145,225,264,273,352,382]. In particular, it has been shown how the incorporation of the carbon allotropes into the polycrystalline ceramic matrix limits the grain growth, resulting in a monotonic trend of decreasing average grain size with the Fig. 26. Zirconia-based ceramics reinforced with different carbon allotropes: a) CNT-reinforced, VIF with Anstis’ model data from [52,63,65,179,192,193,208,259–261,377,379,482], VIF with Niihara’s model [178,201,263], VIF with Evans’ model [116], VIF with Shetty’s model [190,207,302], SENB V-notched data from [63,204], and UPLA-notched from [483]. The use of MWCNTs and SWCNTs is indicated by solid and open symbols, respectively; b) graphene-reinforced, data from references included in the plot. Open symbols stand for GO and solid symbols for graphene or rGO; c) CNF-reinforced, data from [47] (blue triangles), [244] (red circles), and [359] (squares). Open and solid black symbols stand for samples sintered by SPS and hot pressing, respectively. Average trends are shadowed in a) and b), and dashed arrows highlight the data series in c), for clarity. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 39 increasing carbon content. Actually, the change in the grain size of a ceramic matrix is really significant in the mechanical performance of polycrystalline ceramic matrixes due to known phenomena such as the boundary strengthening. This effect has been described as the well-known Hall-Petch effect, regarding to which, mechanical properties such as tensile yield strength and hardness scales inversely with square-root of the grain size. Moreover, other mechanical properties such as fracture toughness may be also affected by this grain size effect on hardness, giving the dependence on the work of fracture with the grain size [484] and the direct relationship between toughness and hardness. Therefore, the values of the mechanical properties are expected to change with the carbon content due to merely the change on the grain size, not due to any specific reinforcing phenomena accomplished explicitly by the inclusion of the reinforcing phase [158,353,394,397,419,425]. Nevertheless, the mechanical behavior was specifically researched in sample series with different grain sizes, and the influence of the grain size was found negligible within the range of the studied sizes, namely, from 0.29 to 3.30 μ m [485], and from 0.32 to 1.20 μ m [430]. This microstructural contribution to the change of the mechanical properties should be considered in order to assess and the actual effects of the incorporation of the reinforcements. 4.2.1. Hardness of alumina-based composites In the case of CNT-reinforced alumina, the results for composites using different types of CNTs have been plotted separately in Fig. 27a. It can be observed that no significant difference is found between the use of SWCNTs and MWCNTs, although higher hardness is suggested for SWCNTs at high carbon concentrations (>5 wt%). The maximum value of the hardness decreased from 25 to 12.5 GPa when the MWCNT content increased from 0 to 5.0 wt%, while it decreased from 20.2 to 14 GPa on increasing the SWCNT content from 0 to 6.0 wt%. The decreasing trend in HV with increasing SWCNT content observed for these SWCNT–Al 2 O 3 composites has been explained by the presence of higher SWCNT quantities at grain boundaries [176]. It is worth remarking that the scattering of the measured values of hardness for pure alumina samples spans from 25 GPa [188] to 14.73 GPa [202] in samples reported to have full relative density but very different average grain sizes: 4 and 0.3 µm, respectively (inverse Hall-Petch behavior). Besides, a surprising increase of the hardness for a very small amount addition of CNTs is found in some cases: Inbaraj et al. [287] Fig. 27. Hardness of reinforced Al 2 O 3 with different carbon allotropes. a) CNT-reinforced alumina: different works with MWCNTs (black squares) and SWCNTs (red dots) are differentiated. MWCNT data from [42,46,49,59,120,122,177,187,202,287,291,335,356,357] and SWCNT data from [42,176,357,364]; b) graphene-reinforced alumina data from [55,56,156,168,211,213,216,219–221,223–225,267,382] and GO-reinforced alumina data from [43,56,210,214,268,272]. Shadows highlight average trends as a guide for the eye only. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 40 found that the hardness increased from 19.6 to 20.4 GPa with the addition of 0.5 wt% MWCNTs; Morales-Rodriguez et al. [176], Mo et al. [49], Sarkar and Das [356], and Yi et al. [202] reported similar increases. Only two authors have discussed this initial increase: Mo et al. [49] argued that the sol–gel procedure allowed more efficient incorporation of CNTs within the alumina matrix and the achievement of better interfacial strength between the CNTs and alumina matrix. Thus, sol–gel samples will present enhanced mechanical performance in comparison to conventional synthesis procedures in which the CNTs are generally agglomerated and intergranular so the load transfer from the matrix to the nanotube cannot be high. However, Sarkar and Das [356], who studied a Fig. 28. Hardness of ZrO 2 reinforced with different carbon allotropes: a) with CNT, where functionalized MWCNTs and SWCNTs are indicated by open symbols (f-MWCNTs and f-SWCNTs, respectively). Data for MWCNTs from [52,63,116,178,179,190,192–194, 204,205,208,244,259–261,263,483], for f-MWCNT from [302], for SWCNT from [482], and for f-SWCNT from [377–379]; b) with graphene (open symbols indicate the use of rGO); c) with CNFs. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 41 conventionally mixed sample, argued that the excellent flexible nature coupled with the very high energy absorption capability of MWCNTs offered improvements in hardness. For CNT contents higher than 1.5 wt%, hardness decreases as expected given the presence of coiled and aggregated CNTs, which act as defects with no load-carrying ability. The reported hardness values of alumina composites with graphene are plotted in Fig. 27b. In this case, the general decreasing trend of the hardness as the carbon content rises is well defined. Moreover, the use of GO or graphene has been emphasized, and, again, no significant difference is observed within the set of reported results. But an increase in the hardness for small additions of carbon is also present. Hence, Centeno et al. [268] found an increase from 16 to 17.5 GPa on adding 0.22 wt% GO and Broniszewski et al. [214] reported an increase from 16.6 to 19.4 GPa on adding 1.0 wt% GO. A similar effect was reported for the addition of graphene by Liu et al. [223], with the hardness rising from 18.8 to 23.7 GPa with the addition of 0.17 wt% graphene. This feature has been explained by the fact that the introduction of GNPs into the alumina results in refinement of the grains, which is essential to improve the toughness and hardness. However, similarly to CNT–alumina composites, this feature has not been deeply discussed. 4.2.2. Hardness of zirconia-based composites The hardness of zirconia-based ceramic composites has also been investigated by several groups. In Fig. 28, the reported values of hardness of zirconia reinforced by CNTs, graphene, and CNFs are plotted. The general decreasing trend observed previously for the alumina-based composites is also confirmed in the case of zirconia reinforced with all the considered carbon allotropes. But, again, very large scattering is found for all the carbon contents. For instance, pure zirconia samples exhibited hardness values from 16.12 GPa [116] to 4.6 GPa [228] (Fig. 28a and Fig. 28b, respectively). When CNTs are used (Fig. 28a), the addition of nanotubes within the matrix produces a decrease of the hardness in almost all cases; this decrease is smaller than 6 % for the lowest CNT contents considered (e.g. [63,190,194]). The use of different types of CNTs, namely MWCNTs or SWCNTs, functionalized or non-functionalized, is highlighted in Fig. 28a. Considering the comparison of the results, it makes no difference whether MWCNTs or SWCNTs are used, since all the SWCNT-reinforced composites exhibit hardness values similar to those found for MWCNT-reinforced composites. In particular, the first research, published by Sun et al. in 2005 [52], focused on zirconia composites obtained by the colloidal route and sintered by SPS. They found a sustained decrease of the hardness from 13.24 to 9.71 GPa when the MWCNT content increased from 0 to 1.0 wt%. Furthermore, Poyato et al. [377] reported a decrease in HV on increasing the carbon content of SWCNT–3YTZP composites up to 5.3 wt%. They argued that this result was a consequence of a SWCNT weakening effect on interfacial cohesion between ceramic grains. Poyato et al. [379] also synthetized 3YTZP composites by colloidal processing and SPS with low SWCNT contents (0.17, 0.34 and 0.52 wt%) and obtained similar values of HV in comparison with the monolithic 3YTZP ceramic, in opposition to what it was reported before. The difficulty of drawing a conclusion about the effect of the CNTs on the mechanical properties of these composites is clearly shown when even the same authors obtained contradictory results. And more recently, Gallardo-L´ opez et al. [378] sintered SWCNT–3YTZP composites using SPS together with several modifications of the colloidal processing technique and also found a decrease in hardness, which is attributed to an enhanced SWCNT dispersion. In addition, whereas Duszov´ a et al. [207] sintered monolithic zirconia and CNT–ZrO 2 by hot pressing and found that the hardness decreased from 13.95 to 8.3 GPa through the addition of 1.07 wt% MWCNTs, other authors such as Mazaheri et al. [63], Su´ arez et al. [190], Bocanegra-Bernal et al. [116], and Kim et al. [194] found no significant variation of the hardness upon CNT addition. Finally, the use of f-CNTs is also found to be not significant on average, within the limited set of reported results, except for a single work by Bocanegra-Bernal et al. [116], who reported the highest hardness value of 17.1 GPa with the addition of 0.01 wt% f-SWCNTs. The use of graphene has also been studied for reinforcing zirconia-based composites. The reported values are plotted in Fig. 28b. In this case, the same general decreasing trend is found, and an increase can also be observed for the lowest graphene concentrations (e.g. [233–236]). For example, Gallardo-L´ opez et al. [235] reported a significant decrease in the hardness of zirconia composites obtained by conventionally mixing powders and sintering by SPS, from 13.9 to 8.5 GPa on adding 3.7 wt% GNPs. An analogous fabrication procedure was employed by Chen et al. [229], who found no significant differences in hardness for carbon concentrations of up to 0.05 wt%. Obradovic and Kern [232] synthesized zirconia composites by the colloidal route and found a similar decrease of the hardness, from 13.7 to 8.23 GPa upon the addition of 1.42 wt% graphene. Moreover, sophisticated fabrication procedures such as mixing by impregnation followed by microwave sintering involved no significant differences up to 0.4 wt% [236]. It is worth remarking on the study by Zeng et al. [233] in which the effects of GO and rGO were compared. They prepared zirconia composites with carbon contents of up to 0.2 wt% by mixing powders with magnetic stirring and ultrasound, and sintered the samples by SPS. The hardness values showed a slight increase in both cases: from 12.74 to 13.26 GPa with the use of 0.2 wt% GO and to 13.75 GPa with 0.2 wt% rGO. Finally, CNF-reinforced zirconia composites have also been the object of study and a few results are reported in the literature, as shown in Fig. 28c. Duszov´ a et al. [244] sintered CNF–ZrO 2 and found a decrease in the values of HV. Dusza et al. [359] achieved a decrease of hardness and fracture toughness for CNF–zirconia composites sintered by hot pressing and SPS with the addition of 1.12 and 1.87 wt% CNFs with respect to pure zirconia. Also, zirconia samples reinforced with 1.12 wt% of CNF and 1.12 wt% GO, and consolidated by SPS were studied by Cano-Crespo et al. [47] in order to evaluate the fracture toughness and HV; a slight increase in fracture toughness and a small decrease in HV were found in both composites. This is in agreement with the results reported by Shin and Horn [380] for composites with mass fractions of 0.3, 1.0, 1.7 and 2.3 wt% rGO, which suggests that neither phase qualitatively improves the mechanical properties of the monolithic material. 4.2.3. Weibull distribution The scattered values of the mechanical properties of brittle materials are typically characterized by the Weibull statistical distribution [486]. Briefly, it considers the presence of defects and flaws in the material as a major cause of failure and states that the V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 48 where D 0 is a frequency factor, Q is the activation energy, T is the temperature, and R is the gas constant. In each case, n and Q were experimentally measured from the corresponding dependence of ˙ ε , firstly on σ at constant T, and secondly on T at constant σ , respectively. Besides, an important aspect concerns the type of loading and the testing procedure used for the characterization of the creep of the samples. Hence, tensile tests are typically the most relevant method but they are difficult and expensive to do. Instead, compressive uniaxial tests are frequently performed, as they require an easier loading system. Moreover, the bending tests are easy to perform and are quite inexpensive, and they are used quite often even though, in this method, the stress state is not homogeneous throughout the complete volume of the sample. From a theoretical point of view, the creep mechanisms can be characterized by the parameters n and p of Eq. (15). However, very often, the concurrence of two (or more) creep mechanisms can appear, or they can occur sequentially. Thus, a complete analysis of the stress–strain relation cannot be done by only considering one single exponent expression and by one parameter. At high enough temperatures (above half of the melting temperature), the creep behavior of materials can be controlled by three different phenomena: the recovery creep, that is, the non-conservative motion of dislocations (recovery creep); the diffusional creep, that is, the mere transport of matter; or the GBS, which is accompanied by the transport of matter. The dominant creep mechanisms controlling the creep behavior depend on the structures, microstructures, and stress solicitations. In a general way and for a generic compound A α B β (monolithic ceramic), D is given by the effective molecular diffusion coefficient Deff mol [494]: Deff mol =Deff ADeff B α Deff B+βDeff A (17) Replacing Deff A and Deff B by their corresponding effective expressions, in terms of the different mechanisms, Deff A=Dl A+10( σ μ )2 Dp A+ π δ dDGb A(18) in which the superscripts indicate the path for diffusion: l is the lattice, p is the pipe diffusion, and Gb is the grain boundary; δ is the grain boundary-thickness and the prefactors of DP A and DGb A are taken as 10( σ μ )2 and π δ d respectively [495]. The same expression is valid for the species B. For example, in the case of YTZP, it has been shown that dislocations have not been observed in the deformed superplastic regime [496]. So, neglecting the pipe diffusion and, if Deff A is much higher than Deff B, it can be established that the motion of the slowest diffusing species along the easiest path is the process that controls the creep rate, and the effective diffusion Deff mol will be Deff B. In addition, if we assume a grain-boundary thickness δ =1 nm, the term π δ d can vary by several orders of magnitude depending on the grain size. Thus, Eq. (15) can be written as: ˙ ε ∝A σ n Tdp(Dl+ π δ dDGb)(19) Therefore, depending on the activation energies of the diffusion coefficientsDGb, multiplied by the term π δ d, the effective diffusion coefficient can be smaller than Dl. This is summarized in Fig. 35: As shown in the figure, the dashed lines (3) and (4) correspond to the effective grain-boundary diffusion coefficient π δ dDGb for nanometric (30 nm) and micrometric (1 µm) grain sizes, respectively. In addition, the transition temperatures T 1 and T 2 for lattice to Fig. 35. Grain-boundary diffusion D Gb and lattice diffusion D l coefficients vs the inverse of T, in arbitrary units. Dashed lines (3) and (4) represent effective grain-boundary diffusion π δ dDGb for nanometric and micrometric grains, respectively. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 49 grain-boundary diffusion for the two ranges of grain size are also indicated. For temperatures lower than T 2 , the plasticity is controlled by the diffusion along the grain boundary, although no plasticity is expected under these conditions. In nanometric specimens, such a transition can occur below T 1 when grain-boundary diffusion can be expected. 5.2. Creep of monolithic alumina and zirconia The ceramic materials can be classified into two classes: oxide ceramics and non-oxide ceramics. In the first class, Al 2 O 3 and YTZP are the two most studied ceramic matrixes, and SiC and Si 3 N 4 are the most studied in the second. Al 2 O 3 is a stoichiometric ceramic in which impurities play a critical role given that a small amount can affect the mechanical behavior dramatically. At high temperatures, the creep behavior strongly depends on the diffusion coefficients of the species controlling the plasticity, as explained in the previous section (Eq. (15)). Additionally, it has been reported that there is a very large dispersion of the values of the diffusion coefficients [497] and the mechanical properties [498], and therefore, the same occurs for the creep parameters. In the case of YTZP, it has been shown that at high temperature, this ceramic behaves superplastically. Superplasticity can be defined as the capacity of a polycrystalline material to display very large elongations at elevated temperature. Superplasticity is observed in different types of materials, such as metals or ceramics. This phenomenon occurs typically in polycrystalline materials with grain sizes close to a few micrometers for metals and less than one micron in the case of ceramics. Superplasticity was first observed in a 3 mol% YTZP with a grain size of 0.4 µm and deformed at 1450 ◦C and 3⋅10 −4 s −1 [499]. In other words, regarding the microstructure, the microscopic features of a superplastically deformed polycrystal, such as grain size or form factor, remain unchanged after deformation. In addition, it is generally accepted that this deformation is mainly accomplished by GBS. Clear evidence of GBS during ceramic superplasticity was shown for the first time by R. Duclos [500], who reported the relative motion of the grains during the creep of YTZP. During GBS, the motion of the mass center of any rigid grain can be described as a combination of translation and rotation. Thus, the relative motion of two adjoining grains can be described by two components: parallel, which is associated with the shear motion and corresponds to the GBS phenomenon, and perpendicular to their common grain boundary. Statistically, the pure shear motion can be associated with a mean flight time, δ τ S , and the perpendicular motion, which is mostly driven by diffusional processes along a mean characteristic time, δ τ D , is the creep rate controlling mechanism. The model developed in [501,502] considered a cylindrical polycrystalline sample with an average grain size d, and subjected to a constant uniaxial compressive stress σ (Fig. 36). The condition of constant volume during plastic deformation may be established as zdS +Sdz =0, where S is the cross-sectional area and z is the height of the sample. During compression, the strain rate can be written as follows: ˙ ε = − d ˙ Z Z=d ˙ S S(20) where the dots denote derivation with respect to time. In conditions of constant volume, the net deformation is produced by a constant number of grains N moving stochastically by a Markov process. During pure shear motion, the velocity of the center of a grain is α d δ τ S, with α being a numerical constant. Generally, α depends on the type of the grains. For example, in the case of 2D hexagonal grains, α ≈ 0.07 [502], and in materials with almost equiaxed grains, α ≈0.5, that is, α d is the radius of the sphere circumscribing an average grain [502]. Under the restriction of a constant volume, the strain rate is given by. ˙ ε =2 α δ τ S (δ τ S+δ τ D)2(21) Thus, in order to obtain the strain rate as a function of stress and temperature, the characteristic times δ τ S and δ τ D have to be estimated. The characteristic diffusion time (δ τ D ) is straightforwardly obtained from diffusion theory [494] and can be written as [501]. δ τ D=d2 σ ΩDeff kT (22) where Ω is the atomic volume of the diffusing species that control the accommodation processes. In the case of δ τ S , it depends on the grain-boundary mobility motion controlled by the curve of the grain boundary, the gradient of the surface energy being the driving force, i.e., by the propensity to minimize the interfacial surface energy γ by flattening the grain-boundary surface [502]. Hence, the velocity of flattening is proportional to its mean curvature and the grain-boundary mobility µ, which is proportional to the grainboundary diffusivity D Gb : μ =Ω 2 π kTδDGb (23) where D Gb is the diffusion coefficient along the grain boundary of thickness δ. When the mobility of the grain boundaries is limited by solute drag (impurities) and the grain boundaries are pinned due to second phase particles (“Zener drag”), then the characteristic mean flight time δ τ S is given by [501]. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 50 δ τ S=7d3 48γδ μ (24) By combining Eqs. (22), (23), and (24), we obtain a value of β, the ratio δ τ S /δ τ D : β=7 πσ dDeff mol 24γDGb (25) where σ is the effective stress, i.e., the difference between the applied stress and the threshold stress (if that exists), d is the grain size, and γ is the grain-boundary free energy [126]. An estimation of β can be empirically obtained depending on the material considered, as has been shown in [501,502]. Moreover, considering typical values of σ ~ 50 MPa, γ =0.15 J/m 2 , d ~ 0.3 µm, and δ ~ 0.1 nm, the estimated value of β is ~0.09. Thus, considering the relationship between β and σ and taking the logarithms in Eq. (19), n can be expressed as follows [501]: n= ∂ ln˙ ε ∂ ln σ T=2 1+β(26) Considering the small value obtained for β, a stress exponent value n close to 2 is obtained, which is in good agreement with the experimental results. Hence, this model indicates that during the superplastic flow, the stress exponent is continuously reduced from n =2 to n =1 with increasing stress and grain size [503]. 5.3. Creep of ceramic composites and threshold stress 5.3.1. Creep of CNT-zirconia composites As a general rule, when ceramics are submitted to a creep experiment, as the mechanism of GBS is more difficult, the creep response is reduced, as explained by Bravo-Le´ on et al. [504]. This was corroborated by creep compression tests, such as those performed by Ionascu and Schaller [199], on samples of pure zirconia and samples doped with 1.5 wt% CNTs and 1.5 wt% SiC whiskers at 1550 K under an applied stress of 6 MPa, in which the observed creep strain is much smaller in composites than in pure zirconia (Fig. 37). Thus, it was concluded that the addition of SiC whiskers or CNTs increases the creep resistance of the zirconia. Actually, compression creep tests have been more widely used to study the mechanical behavior of these allotropic materials. Creep experiments have been analyzed using the creep equation (Eq. (15)), which can be expressed in a simpler form: ˙ ε ∝ σ nd−pexp(−Q RT )(27) in which it should be remembered that the parameters n and Q give information about the mechanism controlling the plasticity. In the case of 3YTZP, Castillo-Rodríguez et al. [126,127,129] performed creep experiments on monolithic 3YTZP and 1.0 wt% SWCNT- reinforced 3YTZP. The specimens were subjected to creep tests at temperatures between 1100 and 1200 ◦C in order to research the influence of the addition of SWCNTs on the high-temperature deformation mechanisms in zirconia. Higher creep rates and slightly higher values of the stress exponent were found for SWCNT–3YTZP nanocomposites (n ~ 2.5) compared to monolithic 3YTZP (n ~ 2.0). The main results and stress exponents are summarized in Fig. 38. Nevertheless, the activation energy in pure 3YTZP (Q =715 ±60 kJ/mol) experienced a decrease of ~25% due to the presence of 1.0 wt% SWCNTs (Q =540 ±40 kJ/mol). This high activation energy value could come from the yttrium segregation at the grain boundaries. SEM images confirmed that there was no microstructural evolution in the specimens due to creep. In addition, Raman spectroscopy measurements showed that the SWCNTs were not deteriorated during the creep tests. These results suggest that the high- Fig. 36. Macroscopic deformation in compression of a cylindrical sample of radius R and height z. Reprinted from [502] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 51 temperature deformation mechanism is GBS accommodated by grain-boundary diffusion, which is affected by the segregation of the yttrium and the presence of SWCNTs at the grain boundaries. In this regard, the addition of the carbon allotropes facilitates the occurrence of the superplastic behavior. In [377], the literature data are reviewed in detail, and it is confirmed that the mechanism controlling plasticity in YTZP is the GBS (superplasticity). Thus, zirconia-based composites exhibited higher creep strain rates in comparison to pure zirconia. Lakki et al. [505] performed creep tests under constant stresses in the range 2.5–300 MPa and compared the creep and internal friction of YTZP. It was assumed that the materials behave superplastically, so the flow process is GBS accommodated by diffusional processes; that is, the creep equation can be written as expressed in Eq. (27), in which the power-law relationship between the creep rate and stress is presented. In addition, the existence was postulated of a threshold stress σ 0 below which the sample does not behave superplastically, in order to explain the plastic behavior of fine-grained YSZP. For example, plastic deformation at elevated temperatures (1300 – 1450 ◦C) of 3 and 4 mol% YSZP with fine grain size (d <1 μ m) has been studied at very low stresses (<10 MPa) [504]. In these materials, extensive internal cavitation has been found for a few percent of strain, instead of the superplastic behavior exhibited at intermediate and high stresses, along with a change of the stress exponent. These features are explained on the basis of a gradual inhibition of the GBS to accommodate the macroscopic strain when decreasing the stress below a given value, supporting the existence of a threshold stress for the GBS mechanism. More details on the physical origin of this threshold can be found in [506]. Moreover, it has been reported that, in the case of YSZP, this threshold depends on T and d [507]. Several considerations have been postulated to explain the existence of the threshold stress, such as the inhibitory effect of dispersed particles on grain boundaries, migration or Zener pinning, the inefficiency of grain boundaries as defect sources and sinks, pinning of boundary dislocations by ledges, etc. However, in the case of YTZP it has been explained by the yttrium segregation at the grain boundaries, which is the origin of the threshold stress and has been extensively explained in [507] and described by the following empirical equation: σ 0=C dexp(Q0 RT)(28) where C is a constant, Q 0 is an energy term, and d is the grain size. The constants C and Q 0 are estimated to be C =5⋅10 −4 MPa⋅ μ m and Q 0 =120 ±30 kJ⋅mol −1 . Thus, with the characteristic grain size given in µm, the threshold stress is obtained in MPa, and corresponds to the theoretical value of the threshold stress. An explanation of how the experimental values are obtained is given in [501]. The same Fig. 37. Strain versus time for creep compression tests (T =1550 K, σ =6 MPa) in pure, CNT-doped, and SiCw-doped 3YTZP. Data from [199]. Fig. 38. Log-log plot of the strain rate (creep rate) versus applied stress at different temperatures, for monolithic 3YTZP and SWCNT–3YTZP samples. The obtained mean values of the stress exponent n are indicated. Reprinted from [126] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 52 dependence on the threshold stress has been shown to account successfully for a wide set of materials, with Horton [508] being the first to use the threshold stress in a bycrystal of Al with 0.5 mol% Fe. Moreover, the Al-Zn-Mg-Cu-Mn alloy [509] is another good example giving evidence of the same dependence. The influence of the threshold stress in the behavior of the creep rate is sketched in Fig. 39. Hence, the expected power law-like behavior of the creep rate with the applied stress (linear behavior in log–log representation) is displayed once the applied stress σ exceeds the threshold, as shown in the creep law, which was expressed in simplified form in Eq. (27). In this regard, the representation can be modified by subtracting the stress threshold, σ 0 , namely, the stress that implies the maximum linearity of the creep rate. The following table (Table 6) gives a comparison between the theoretical and experimental values of the threshold stress. The experimental estimation of the stress threshold has been performed following this criterion [501], and the theoretical values were estimated using Eq. (28). As already indicated, the SWCNT-3YTZP and the MWCNT-3YTZP are superplastic. As shown in [507,510], in the creep equation for superplasticity, the true stress is given by σ - σ 0 , where σ is the applied stress and σ 0 a threshold stress. For the conditions used in typical creep experiments (e.g. Fig. 38), σ 0 can reach values clearly over 10 MPa, whereas the superplastic behavior does not occur at stresses of 6 MPa. The influence of the fabrication process and the quality of the dispersion of the CNTs in the ceramic matrix were also assessed. Hence, 3YTZP matrix composites containing 1.0 wt% SWCNTs were fabricated by SPS at 1250 ◦C, following different procedures, with the objective of improving the distribution of the nanotubes in the ceramic matrix, as indicated by Castillo-Rodriguez et al. [129] (the results are plotted in Fig. 40). The specimens were subjected to a creep test at 1200 ◦C to analyze the possible relationship between the creep behavior with the quality of the dispersion of the SWCNTs. This study confirmed, again, that the presence of nanotubes in the 3YTZP sample leads to an increase in the creep rate in comparison to monolithic pure zirconia. In addition, the creep resistance of these nanocomposites is reduced as the distribution of the SWCNTs in the matrix is improved, that is, as the sizes of the SWCNT agglomerates are smaller, a higher concentration of SWCNTs in the grain boundaries is found. This result suggests that SWCNTs may play a role as a lubricant that facilitates the GBS phenomenon during deformation of these composites and, consequently, prompts the superplastic behavior. In these studies, two types of SWCNTs were used: one with a typical length of 0.5–1.5 µm and a diameter of 4–5 nm (samples labeled Fig. 39. The influence of the stress threshold in the creep rate representation is shown: a) typical log–log representation of the creep rate vs. stress, showing non-linear regime for low stress values; b) corrected stress values by subtracting the threshold stress makes the log–log representation linear. This criterion is applied to estimate the stress threshold. Table 6 The experimental and theoretical values of the threshold stress for different temperatures and grain sizes. Data from [501]. Experimental conditions Threshold stress (MPa) Temperature (K) Grain size (µm) Experimental Theoretical 1573 0.3 8 ±3 6.9 1585 0.3 4 ±2 3.6 1595 0.3 3 ±1 2.0 1605 0.3 4 ±2 2.1 1673 0.3 6 ±2 2.3 1673 0.3 4 ±2 1.4 1689 0.3 2 ±1 0.7 1623 0.3 7 3 1573 – 1673 0.3 9 6 1723 0.5 5.5 3.6 1623 0.5 7.2 6.1 V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 53 “1” in Fig. 40) and the other with a length of 1–5 µm and a diameter of ~1.5 nm (samples labeled “2” in Fig. 40). Both were functionalized and sonicated in an ultrasonic bath. SPS was used to sinter the powders. All details can be found in [129]. The values of the stress exponent n have been obtained for all the tested samples. Pure 3YTZP shows values of n =2.3. In this case, the deformation was displayed primarily by GBS accommodated by diffusion of the cationic species throughout the lattice. The obtained values of the stress exponent n for the SWCNT–3YTZP composites were found to be between 1.9 and 2.7, similar to the obtained value for monolithic pure 3YTZP. These values of the stress exponents indicate that GBS is occurring in both pure 3YTZP and SWCNT- based composites within the considered temperature and stress ranges of the reported experiments. It is also observed that better dispersion of the CNTs gives a lower creep resistance, while the worst CNT dispersion gives a higher creep resistance [129]. The same authors repeated the creep experiments with YTZP containing SWCNTs or MWCNTs [127]. The results (Fig. 41) indicate that the monolithic 3YTZP is, again, more creep-resistant than the composites with CNTs. This behavior is independent of the type of CNT, although the composites with MWCNTs are more creep-resistant than the ones with SWCNTs. Moreover, the grain size and form factor showed no change after sample deformation in all cases, suggesting that GBS is the deformation mechanism responsible for the high-temperature mechanical behavior. These microscopic observations [127] indicate that the superplasticity is the mechanism that controls the plasticity. The softening exhibited by the nanocomposites SWCNT–3YTZP and MWCNT–3YTZP compared to monolithic 3YTZP may be due to the mentioned lubricant effect of the nanotubes located at the grain boundaries caused by the weaker interfacial bonding between them and the ceramic matrix. Therefore, the CNT facilitates the occurrence of the GBS during high-temperature deformation and, accordingly, the composites exhibit higher creep rates (and lower creep resistance) in comparison to the pure 3YTZP. 5.3.2. Creep of CNT-alumina composites Zapata-Solvas et al. [124,125] studied the creep behavior in 5.8 wt% SWCNT–alumina under uniaxial compression at temperatures Fig. 40. Log-log plot of the creep (strain) rate vs. applied stress for different samples: pure 3YTZP and SWCNT–3YTZP composites. In the plot, the average values of the stress exponent n are indicated for each sample. The legend in the figure indicates the different functionalization procedures for the SWCNTs and the different processes to obtain the precursor powders, involving an ultrasonic bath or sonication probes for mixing and hotplate or freeze-drying for drying. Details can be found in the source. Reprinted from [129] with permission. Fig. 41. Log-log plot of the strain (creep) rate versus stress for pure 3YTZP sample (circles), and the composites SWCNT–3YTZP (triangles), and MWCNT–3YTZP (squares). Solid and empty symbols correspond to the different considered temperatures: 1200 and 1100 ◦C, respectively. The average values of the stress exponents n are also indicated in the plot. Reprinted from [127] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 54 of 1300 and 1350 ◦C in an Ar atmosphere. The obtained values of the strain rate are plotted in Fig. 42. In contrast to the results observed in zirconia, CNT–alumina composites exhibited creep rates about two orders of magnitude lower than the pure alumina, that is, they found that the composites with CNT were more creep-resistant than the pure alumina matrix of the same grain size (0.5 µm). The increase in the creep resistance was explained in terms of a reduction of the GBS due to partial blocking of this mechanism by CNTs located at Al 2 O 3 grain boundaries. Interestingly, Chen and Xue [511] gave evidence that no threshold stress existed in alumina polycrystals, in which no segregation at the grain boundaries has been described. This feature could explain the differences between alumina and zirconia. Also, 5.8 wt% SWCNT-reinforced Al 2 O 3 samples were prepared by two different methods, conventional powder processing and aqueous colloidal processing. Both samples were compared with pure alumina, and the different strain rates measured can be seen in Fig. 43. Two main differences are observed in the creep resistance of SWCNT-reinforced Al 2 O 3 that were processed differently. A better distribution of the SWCNTs throughout the matrix is achieved by the aqueous colloidal procedure, and accordingly, a higher fraction of the surface boundaries of the Al 2 O 3 grains is in contact with the SWCNTs. Therefore, the hindering effect of the creep is higher in the composite with better dispersed CNTs. Moreover, two composites of alumina reinforced with 5.8 wt% SWCNTs, one with a heterogeneous and the other with a homogenous distribution of SWCNTs at the grain boundaries, were deformed at temperatures of 1300 and 1350 ◦C [125]. Fig. 44 shows the steady-state strain rate versus the stress for the heterogeneous and homogeneous SWCNT–alumina composites, at two different temperatures: a) 1300 ◦C and b) 1350 ◦C. In both types of composites, the strain rate was much lower than in pure alumina, although the composites with homogeneous distribution of the SWCNTs were more creep-resistant. At moderate stress, the steady-state creep rate for pure alumina is about 240 times higher than that for the corresponding homogeneous composite and only about 80 times higher when compared with the heterogeneous composites [125]. In coherence with the previous results, the better homogenization of the CNTs allows a greater effect in obstructing the creep mechanisms. Fig. 42. Log-log plot of strain rate (steady-state creep rate,) (˙ ε )versus stress ( σ ) for the SWCNT–alumina composite at two temperatures: 1300 and 1350 ◦C. Solid lines are linear fits. The trends of the creep behavior versus stress at 1300 and 1350 ◦C for pure alumina with similar grain size of ~0.5 µm taken from the literature [512] are also included for comparison (dashed lines). Reprinted from [124] with permission. Fig. 43. Strain rate versus stress for 5.8 wt% SWCNT-reinforced Al 2 O 3 obtained by conventional powder processing and aqueous colloidal processing. The trend of the pure Al 2 O 3 data taken from [512] is also included as a solid line for comparison. Reprinted from [54] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 55 However, these results do not seem to be in agreement with what was found by Estili et al. [154], who observed a much lower flow stress in the fully dense 12.2 wt% acid-treated MWCNT–Al 2 O 3 composites (40 MPa) than in pure monolithic α -Al 2 O 3 with an initial grain size of 150–350 nm (110 MPa) after deformation at 1400 ◦C and a strain rate of 10 −4 s −1 . In Fig. 45, both creep behaviors are compared. This result is explained by the dynamic grain growth during deformation in pure alumina, whereas in the composite, the MWCNTs located in the grain-boundary area significantly contribute to the preservation of the microstructure of the Al 2 O 3 matrix by obstructing the dynamic grain growth, even up to ~0.44 of strain. The grain size after deformation in pure alumina was between 0.5 and 1 µm, although in any case, the composites were more creep-resistant than the monolithic alumina, as found by Zapata-Solvas et al. [54,124,125]. Fig. 44. Log-log representation of the strain (creep) rate (˙ ε )versus uniaxial stress ( σ ) at two different temperatures, for two SWCNT–alumina samples fabricated by different procedures that lead to different SWCNT distributions. Solid lines are linear fittings. The creep data at the same temperatures for pure alumina with similar grain size (~0.5 µm) taken from the literature are also included as dashed lines for comparison. The shaded area in the a) panel is limited by creep data (1300 ◦C) from [512] for alumina composites reinforced with 6.0 and 18 vol% SiC whiskers. Reprinted from [124] with permission. Fig. 45. Uniaxial stress–strain behavior for 12.2 wt% MWCNT–Al 2 O 3 full-dense composite at high temperature (data from [376,425]) and pure Al 2 O 3 registered at 1400 ◦C. Tests were conducted with an initial strain rate of 10 −4 s −1 in Ar atmosphere. Reprinted from [154] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 56 In addition, Castillo-Rodriguez et al. [128] performed creep experiments at temperatures between 1200 and 1250 ◦C on alumina and 1.4 wt% SWCNT–alumina. The data showed a similar mechanical behavior (Fig. 46), indicating that the addition of CNTs seems to have a negligible effect on the strain rate, as found by Estili et al. [154]. Along the fabrication procedure, there are several sources of error that can explain the differences in the creep behavior between alumina and alumina reinforced with CNTs that can affect the creep rate values by more than one order of magnitude, such as the nature and dispersion of the CNTs, the processing techniques used to consolidate the ceramic, and, in this case, what type of alumina is compared with the composites. In the case of Zapata-Solvas et al. [54,124,125], alumina data from the literature was used, in opposition with the data of Castillo-Rodriguez, where the same alumina was used to fabricate the pure sample and the composites [128]. Al 2 O 3 is a very stoichiometric ceramic, and so, it is very sensitive to the presence of impurities. There exists a wide variety of alumina with a large dispersion in the values of the kinetics of the diffusion processes [497] and the mechanical properties [498], which is probably the main source of the discrepancies found among the different authors. Recently, Gopalan and Chokshi [372] published a paper on compression creep experiments in alumina and CNT-reinforced alumina composites and concluded that the creep at high stresses is not influenced by the presence of CNTs at grain boundaries, in agreement with the results presented by Castillo-Rodriguez et al. [128]. However, there is a big difference because Gopalan and Chokshi claimed that the mechanism at high stresses is consistent with a (Nabarro-Herring or Coble) diffusion creep mechanism and an interfacecontrolled diffusion creep process at lower stresses, in opposition to what has already been published [493,501,506]. This mechanism was suggested by Berbon and Langdon [513] based on the creep data of Owen and Chokshi [514]. Jimenez-Melendo and Domínguez-Rodríguez [506] published a detailed analysis of the model suggested in [372] and concluded that there were several reasons for rejecting it, which they enumerated in detail. Nowadays, GBS has been identified as the mechanism controlling creep in fine-grained ceramics such as alumina and YTZP and in ceramics reinforced with CNTs. All the articles cited in this review except [372] accept GBS as the mechanism controlling the mechanical behavior at high temperature. This conclusion is based on the microstructure of the samples after deformation, that is, no elongation of the grains was found in the direction perpendicular to the applied stress, indicating that the form factor of the grains remains unchanged. This characteristic is contrary to what happens in diffusional creep (Nabarro-Herring or Coble), in which the grains change the form factor and become elongated in the direction perpendicular to the applied stress. It is worth highlighting a different effect observed by Huang et al. [515] on the addition of boron nitride nanotubes (BNNTs) to an alumina matrix. They demonstrated that “a small addition of BNNTs can dramatically enhance the high-temperature plasticity of engineering ceramics”. The creep curves of pure alumina and BNNT–alumina samples clearly show “an inspiring brittle-to-ductile transition in Al 2 O 3 ceramics, even at a moderate temperature (1300 ◦C)” through the addition of 0.5 wt% BNNTs. They also observed that the plasticity is improved (reducing the strain-hardening) and the flow stress decreases when the amount of BNNTs increases from 0.5 to 2.5 wt% compared to pure alumina. It was, for the first time, demonstrated that the addition of a small amount of nanotubes can drastically increase the high-temperature superplastic deformation (SPD) of engineering ceramics. In contrast, it was confirmed that the addition of microsized or nanosized boron nitride powders has a negligible effect on the superplasticity of these ceramics. As stated by Huang et al. [515], “the underlying SPD-enhancement mechanism is discussed in terms of the inhibition of the static and dynamic grain growth of the matrix and the energy-absorption mechanism of BNNTs”. The revealed ability of BNNTs to increase the SPD behavior makes them an encouraging phase for the fabrication of cost-effective composite ceramics with improved mechanical properties. Now, it has also been found that YTZP reinforced with the addition of SWCNTs [124,127] or SWCNTs and MWCNTs [125] can improve the high-temperature SPD of engineering zirconia-based ceramics. Fig. 46. Log-log representation of the strain (creep) rate–stress for Al 2 O 3 and SWCNT–Al 2 O 3 ceramic composites. The average stress exponents n for the different temperatures are also indicated. The data were normalized to a grain size of d =0.5 μ m and a grain size exponent p =2 was considered. Reprinted from [128] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 57 5.3.3. Creep of graphene−, CNF−, and micrographite–ceramic composites As already mentioned, the research on the mechanical properties of composites with different types of graphene, and mainly at high temperature, is still at an early stage. To our knowledge, only very few articles are related to the high-temperature plasticity of ceramic composites with carbon allotropes based on alumina or zirconia. Alumina-based CMCs reinforced with GO or CNFs were fabricated using SPS and the high-temperature plasticity was analyzed [271]. In order to quantitatively estimate the dependence of the creep resistance, ˙ ε d2 with the applied stress is shown in Fig. 47. As a general rule, it can be affirmed that the GO-reinforced alumina samples are more creep-resistant than the CNF-reinforced ones. For example, at 1200 ◦C, a difference between the strain rates of around one order of magnitude was found, but it was also found that this observed difference in the creep resistance is strongly dependent on the testing temperature. Hence, as stated by Cano-Crespo et al. [271], “when the temperature increases, both composites tend to have similar creep properties. At 1250 ◦C, the creep resistance differs by less than half an order of magnitude. Therefore, for very high-temperature applications, graphene and CNFs cannot provide effective creep resistance to alumina”. In contrast, the graphene-reinforced alumina composites are more creep-resistant at mediumrange temperatures. Thus, these results give rise to a remarkable theoretical feature: since creep behavior is controlled by GBS in both types of samples, it can be deduced that the grain mobility in the graphene-reinforced samples is much lower than in the CNF- reinforced ones. Besides, the results also confirm that the microstructural characteristics are quite stable during creep deformation, which is consistent with the GBS as the deformation mechanism with no significant increase in porosity. It is also noteworthy to highlight the high ductility observed in the composites, with observed final strains as high as 50% at 1200–1250 ◦C while constant the microstructure. On the other hand, zirconia has also been reinforced with graphene and CNFs, and the high-temperature plasticity has been studied at temperatures of 1200 and 1250 ◦C [47,235]. The changes in the creep resistance of the zirconia induced by the addition of these two Fig. 47. Dependence of the creep resistance (steady-state creep rate multiplied by the square of the grain size) with the applied uniaxial compressive stress for monolithic pure Al 2 O 3 , GO–Al 2 O 3 , and CNF–Al 2 O 3 at different temperatures: a) 1200 ◦C and b) 1250 ◦C. Reprinted from [271] with permission. Fig. 48. Log-log representations of the dependence of the steady-state strain (creep) rate versus the applied uniaxial compressive stress for three different samples: pure monolithic ZrO 2 , GO–ZrO 2 , and CNF–ZrO 2 at the indicated testing temperatures a) 1200 ◦C and b) 1250 ◦C. Reprinted from [47] with permission. V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 64 The Table 7 summarizes the obtained parameters estimated from the creep experiments discussed before. 6. Conclusions and future trends The compilation of research results concerning the reinforcement of alumina-based and zirconia-based CMCs through the addition of nanostructured carbon allotropes presented in this review illustrates the direction of the efforts of the scientific community of ceramic researchers. Since the beginning of this century, the astonishing and seductive mechanical properties of the new nanostructured carbon allotropes that were being discovered, synthesized, and individually controlled and characterized encouraged the community of ceramic reinforcers to look for the best way to transfer the nanoscopic mechanical properties of these carbon allotropes to the macroscopic ceramic composites hosting them. Thus, thousands of papers have been devoted to designing the best synthesis protocols that can achieve the maximum enhancement of the mechanical properties of the ceramic composites. However, as can be seen in this work, all the different proposed strategies yield roughly comparable results within a high scattering, and none of them achieves a significantly better reinforcement than the rest. The reinforcement achieved up to now suggest that there is still work to do in order to maximize the contribution of the embedded carbon allotropes to the mechanical behavior. Therefore, investigations and discussions are still focusing on all the fabrication steps, from the very initial precursors to the final densification and also from the subsequent basic mechanical characterization and the models that may be used to understand the results that may, ultimately, confirm the rise of the mechanical properties such as fracture toughness or creep resistance. In particular, several preparation strategies have been tested and compared: •Different reinforcing phases were considered, such as SWCNTs, MWCNTs, f-CNTs, GNPs, GO, rGO, irGO, and CNFs. In the light of the comparison results, no single type of reinforcing phase can be selected as the best one on average. •Different precursors for the ceramic matrix were used such as fine grained powder or chemical liquid precursors such as alkoxides or salts. Liquid precursors have been under consideration lately in order to face the problems of the homogenization and the carbon location (intergranular/intragranular), and it has been suggested that the intragranular location leads to improved mechanical properties. •Different mixing procedures were tested looking for the best homogenization of the starting powders, such as ball milling, ultrasonic probes, or the use of surfactants or liquid precursors in order to carry out mixing at a molecular level and to achieve a better and more homogenized composite. •Different sintering techniques such as hot pressing, hot isostatic pressing, microwaves, or SPS have been used and compared. Significant structural differences have been reported regarding the grain size or anisotropy and regarding the integrity of the carbon phases after processing. But, although SPS has proven to lead to samples with slightly better mechanical properties, no major differences were found. •Different models have been considered in order to understand the fracture toughness. There are a variety of them, concerning not only the applied experimental technique to measure toughness (SENB, VIF, …) but also empirical models to understand and interpret the results (Niihara, Anstis, …). Despite the VIF method has been questioned, considering the differences between values and trends observed by the different methods, it is an option. All these possible strategies have been thoroughly explored by the community over the years, but this variety makes the comparison a very difficult task, especially at a quantitative level. It should be remarked that the most important source of the scattering of the results is the preparation strategy, so the control and the reproducibility of the fabrication process are the most important challenges. As an example, one only has to check the large scattering found even for the mechanical values of the reference ceramic samples without carbon. Nevertheless, some important results can be stated, namely: •As a general result, the addition of a low content of reinforcing carbon allotrope gives better results independently of the technique considered. •In particular, the fracture toughness of alumina and zirconia was increased by the addition of low carbon quantities: 2.0 wt% CNTs or 1.0 wt% graphene in the case of alumina and 1.5 wt% CNTs or 0.5 wt% graphene in the case of zirconia. Higher carbon contents typically involve dispersion problems, implying a decrease of the toughness given that the badly dispersed allotropes act as defects in the matrix. This is especially true in the case of macroscopic techniques such as SENB, in which testing badly dispersed areas cannot be purposely avoided. On the contrary, in microscopic techniques such as VIF the indentation area can be accurately selected. •Hardness typically decreased with the inclusion of carbon allotropes, but some consistent increasing trends were reported due to the inhibition of grain growth by the presence of the allotropes. •The presence of carbon allotropes clearly improved the wear behavior of the ceramics, typically thanks to the formation of so-called tribofilms. This was found to be true for all the allotropes in both ceramic matrixes. Significantly, there is no problem at high carbon contents because the small dispersion defects are not critical for the formation of the protective tribofilm. •In the case of alumina reinforced with carbon allotropes, the creep resistance is almost unchanged. However, in the case of YTZP reinforced with the allotropes, YTZP is more creep resistant because the composite behaves superplastically. One conclusion can be clearly drawn: this review highlights the major relevance of the fabrication procedure for the mechanical V. Morales-Fl´ orez and A. Domínguez-Rodríguez Progress in Materials Science 128 (2022) 100966 65 properties of the composite. Thus, different procedures lead to different densities, different grain sizes, different qualities of the dispersion of the carbon allotropes, different locations of the carbon allotropes within the matrix, different bonds between reinforcing phase and matrix grains, and so on. Therefore, several challenges are still ahead and they define the future tasks to be done in order to unambiguously define the most efficient way to embed nanostructured carbon allotropes within a ceramic matrix from the point of view of the enhancement of the mechanical properties of the composite. In summary: •Homogenization of the carbon allotropes should be ensured, even at an individual level. This feature should be experimentally verified, and several groups are working on it by the use of strategies such as coating of the carbon allotropes, very low concentrated colloidal suspensions prepared with surfactants and checked by vibrational spectroscopy, X-ray photospectroscopy or smallangle scattering experiments. These techniques, among others, may allow a set of results to measure and quantify the degree of homogenization of the composite. •Characterization and quantification of the types of bonds between the carbon allotropes and the ceramic grains should be performed. Experimental techniques to research the chemical environment of the species in the composites are currently casting some light on this feature. •The location of the carbon allotropes within the matrix should be unambiguously resolved and quantified, given that different mechanical contributions should be expected from either intergranular or intragranular location of the carbon allotropes. Finally, although it seems that finding the most efficient recipe to maximize the ceramic matrix reinforcement is still a challenge, there is a question that experimental laboratories should keep in mind: what is the maximum theoretical enhancement of the mechanical properties of the ceramic composite that can be expected? In this regard, a theoretical ceiling should be developed in order to optimize the direction of the experimental efforts and eventually to assess the success of the current experimental works. Nonetheless, there are already interesting papers discussing the new toughening mechanisms that may appear in the composites and others that discuss these new phenomena from a theoretical point of view. But quantification of their effect, especially as a function of the structural parameters of the composite, and estimation of the theoretical maxima are still needed. Techniques such as computer simulation or the performance of mechanical tests at a nanoscopic scale, such as nanoindentation tests or even indentation–SEM coupled stations, may reveal important aspects to be considered for the construction of a complete theoretical description of the mechanical response of the ceramic composites under stress. Any progress in these theoretical aspects will complement the enormous experimental research that is being developed towards the fabrication of new engineered ceramic matrix composites with superior mechanical properties. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments Projects P12-FQM-1079 and PAIDI 2020-P20_01121 from Junta de Andalucía, and project PGC2018-094952-B-I00 from the Spanish Ministerio de Ciencia, Innovaci´ on y Universidades. V. 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