Toughening Mechanisms in Nanolayered MAX Phase Ceramics—A Review

Advanced engineering and functional ceramics are sensitive to damage cracks, which delay the wide applications of these materials in various fields. Ceramic composites with enhanced fracture toughness may trigger a paradigm for design and application of the brittle components. This paper reviews the toughening mechanisms for the nanolayered MAX phase ceramics. The main toughening mechanisms for these ternary compounds were controlled by particle toughening, phase-transformation toughening and fiber-reinforced toughening, as well as texture toughening. Based on the various toughening mechanisms in MAX phase, models of SiC particles and fibers toughening Ti3SiC2 are established to predict and explain the toughening mechanisms. The modeling work provides insights and guidance to fabricate MAX phase-related composites with optimized microstructures in order to achieve the desired mechanical properties required for harsh application environments.


Introduction
Conventional ceramic materials mainly include glasses, structural clay products, whitewares, refractories, abrasives, cement and the newly developed advanced ceramics. Ceramic materials offer many distinct advantages such as excellent corrosion, wear resistance, high hardness and stiffness, chemical inertness, high-temperature characteristics as well as low density, which make them attractive for applications such as industries [1][2][3][4], medical [5], fuel constituents [6,7] and daily life [8], ranging in size scale from micro-electromechanical systems through large aerospace components. However, ceramic materials are severely limited in various fields of human activities by their mechanical properties [9][10][11]. The Achilles heel of ceramic materials is the low reliability, which is given by the disposition of inherent brittleness to catastrophic fracture with very low energy absorption. One of the macroscopic properties that characterizes this disposition of a ceramic is the fracture toughness (K IC ) which is the resistance of ceramics to incipient cracking or defect generation and the microstructural mechanisms that are the source of such resistance [1]. The fracture toughness can be strongly influenced by microstructure or by the using of various reinforcements. There are two fundamentally different approaches: flaw control and toughening [12]. The toughening mechanisms have been well documented and can be conveniently considered to involve either intrinsic toughening mechanisms or extrinsic toughening mechanisms ( Figure 1) [13]. The intrinsic toughening is an inherent property of the material, which is induced essentially from plasticity and enhances a material's inherent damage resistance. Thus, it is active irrespective of crack size and geometry. The intrinsic toughening is the primary source of fracture resistance in ductile materials [13]. In contrast, most structural ceramics are essentially impossible to be tough intrinsically due to the absence of mobile dislocation activity [13,14] and the extrinsic toughening is the primary source of toughening in ceramics which act primarily behind the tip to impede crack advance. Extrinsic toughening acts to lower the local stress and strain fields at the crack tip without the inherent fracture resistance of the material changed; as it depends on the presence of a crack, it affects only the crack-growth toughness, specifically through the generation of a rising R-curve [13]. So far, a number of extrinsic toughening methods have been developed: transformation toughening, dispersed ductile/brittle particle toughening (microcracking toughening), fiber/lamella bridge toughening [15], whisker toughening [16], the frictional interlocking of grains during intergranular fracture in monolithic ceramics and complex structure toughening etc. Intergranular fracture is generally an essential requirement here for the operation of these mechanisms.
1 Figure 1. Schematic illustrating both intrinsic and extrinsic mechanisms of toughening mechanisms associated with crack extension [13].
MAX phases are a group of new nanolayered ceramics with a general composition of M n+1 AX n [17][18][19][20][21][22] where M is an early transition metal, A is IIIA or IVA element, and X = C or N (n = 1~7). Until now, more than 50 M 2 AX phases (Ti 2 AlC, Cr 2 AlC, Ti 2 SnC etc.), 6 M 3 AX 2 phases (Ti 3 SiC 2 , Ti 3 AlC 2 etc.) and 8 M 4 AX 3 phases (Ti 4 AlN 3 , Nb 4 AlC 3 , etc.) have been discovered and investigated along with many possible solid solution permutations and combinations [18]. In the unit cell of MAX phase, the M and X atoms form two common edges, M 6 X tetrahedron with the stronger covalent bond which is separated by A atomic planes, and the link between A atomic planes and M 6 X tetrahedron is weaker due to the M-A metallic bond. Due to such unique nanolaminated structure, the MAX phases are able to combine metal and ceramic materials demonstrating high thermal and electrical conductivities, excellent machinability and high-temperature oxidation resistance. Recently, MAX phases have attracted much attention due to their special qualities and potential applications in sensors, radiation hardened in nuclear energy and electrochemical energy storage systems [18][19][20][21]. In this content, enhancement of the reliability of these nanolayered MAX phases with desired mechanical properties becomes critical.
The present work gives a critical review of toughening mechanisms for the nanolayered MAX phases. Based on the present toughening work for MAX phases, microstructure-based models were established for a better understanding of the toughening mechanisms of these ceramics with nanolayered structures. Finally, an outlook of future directions for the toughening of these nanolayered ceramics is also provided.

Toughening in Nanolayered MAX Phases
The fascinating MAX phase ceramics have gained increasing attention due to their fruitful potential applications in industry. Great efforts have been made to investigate the fracture toughness and its enhancement of MAX phases [23]. The toughening mechanisms in MAX phases can be categorized into four basic types: particle toughening, phase-transformation toughening, fiber-reinforced toughening, and texture toughening.

Particle Toughening
The particle toughening is a general concept that refers to impending crack growth by dispersion particles such as TiC [24], Al 2 O 3 [25], ZrC [26], BN [27,28] and carbon nanotubes (CNTs) [29] etc. Unfortunately, these brittle particle reinforcements can modestly enhance the toughness of MAX phases due to lack of plasticity of ceramic particles, and the most common activated toughening mechanisms are crack deflection and crack bridging.
ZrC particles-reinforced Ti 3 AlC 2 composites were obtained by in situ reactive hot-pressing at 1500 • C under a pressure of 30 MPa for 2 h in Ar using Ti, Al, graphite and ZrC powders as starting materials [26], and the fracture toughness of 20 vol % ZrC/Ti 3 AlC 2 composite could reach up to 11.5 ± 1.0 MPa·m 1/2 while the fracture toughness of monolithic Ti 3 AlC 2 was 7.8 ± 0.4 MPa·m 1/2 . As shown in Figure 2, the fracture toughness improvement could be ascribed to energy consuming by ZrC particles and residual stresses in the ZrC/Ti 3 AlC 2 composite derived from the cooling process in the composite preparation.

Toughening in Nanolayered MAX Phases
The fascinating MAX phase ceramics have gained increasing attention due to their fruitful potential applications in industry. Great efforts have been made to investigate the fracture toughness and its enhancement of MAX phases [23]. The toughening mechanisms in MAX phases can be categorized into four basic types: particle toughening, phase-transformation toughening, fiber-reinforced toughening, and texture toughening.

Particle Toughening
The particle toughening is a general concept that refers to impending crack growth by dispersion particles such as TiC [24], Al2O3 [25], ZrC [26], BN [27,28] and carbon nanotubes (CNTs) [29] etc. Unfortunately, these brittle particle reinforcements can modestly enhance the toughness of MAX phases due to lack of plasticity of ceramic particles, and the most common activated toughening mechanisms are crack deflection and crack bridging.
ZrC particles-reinforced Ti3AlC2 composites were obtained by in situ reactive hot-pressing at 1500 °C under a pressure of 30 MPa for 2 h in Ar using Ti, Al, graphite and ZrC powders as starting materials [26], and the fracture toughness of 20 vol % ZrC/Ti3AlC2 composite could reach up to 11.5 ± 1.0 MPa·m 1/2 while the fracture toughness of monolithic Ti3AlC2 was 7.8 ± 0.4 MPa·m 1/2 . As shown in Figure 2, the fracture toughness improvement could be ascribed to energy consuming by ZrC particles and residual stresses in the ZrC/Ti3AlC2 composite derived from the cooling process in the composite preparation. (a) Interface between Ti3AlC2 and Zr, the inset: Backscattering image of area pointed with the white arrow; The Letters "T", and "Z" represent Ti3AlC2, and ZrC, respectively; (b) A crack crossing through Ti3AlC2 grain and ZrC particle [26].
A (TiB2 + TiC)/Ti3SiC2 composite with higher fracture toughness was obtained by hot-pressing at 1500 °C under a pressure of 25 MPa for 2 h in Ar atmosphere by applying TiH2, Si, graphite and B4C powders as starting materials [24]. The microstructures of the (TiB2 + TiC)/Ti3SiC2 composites (10 vol % TiB2) characterized by high-resolution transmission electron microscope (HRTEM) demonstrated clean and clear grain boundaries between the Ti3SiC2 matrix and reinforcements (Figure 3a,b). The fracture toughness of the as-prepared composites was higher than the pure Ti3SiC2 ceramic and other Ti3SiC2-matrix composites [30]. The fracture toughness of the (TiB2 + TiC)/Ti3SiC2 composites increased from about 9 MPa·m 1/2 for the composites with 5 vol % TiB2 reinforcements to 9.55 MPa·m 1/2 for the one with 10 vol % TiB2 reinforcements. However, further increasing TiB2 volume content up to 20 vol % resulted in a reduction of the fracture toughness of the composites [24]. The improvement of the fracture toughness of the composites was due to the very close interatomic distance of close-packed plane of atoms for TiB2 (0.3028 nm) and TiC (0.3055 nm), resulting in a coherent interface with strong binding energy (Figure 3c), which would lead to transgranular fracture and increase fracture energy as well as the residual compressive stress caused by the thermal expansion coefficient mismatch, which could increase the crack propagation resistance [24]. The Letters "T", and "Z" represent Ti 3 AlC 2 , and ZrC, respectively; (b) A crack crossing through Ti 3 AlC 2 grain and ZrC particle [26].
A (TiB 2 + TiC)/Ti 3 SiC 2 composite with higher fracture toughness was obtained by hot-pressing at 1500 • C under a pressure of 25 MPa for 2 h in Ar atmosphere by applying TiH 2 , Si, graphite and B 4 C powders as starting materials [24]. The microstructures of the (TiB 2 + TiC)/Ti 3 SiC 2 composites (10 vol % TiB 2 ) characterized by high-resolution transmission electron microscope (HRTEM) demonstrated clean and clear grain boundaries between the Ti 3 SiC 2 matrix and reinforcements (Figure 3a,b). The fracture toughness of the as-prepared composites was higher than the pure Ti 3 SiC 2 ceramic and other Ti 3 SiC 2 -matrix composites [30]. The fracture toughness of the (TiB 2 + TiC)/Ti 3 SiC 2 composites increased from about 9 MPa·m 1/2 for the composites with 5 vol % TiB 2 reinforcements to 9.55 MPa·m 1/2 for the one with 10 vol % TiB 2 reinforcements. However, further increasing TiB 2 volume content up to 20 vol % resulted in a reduction of the fracture toughness of the composites [24]. The improvement of the fracture toughness of the composites was due to the very close interatomic distance of close-packed plane of atoms for TiB 2 (0.3028 nm) and TiC (0.3055 nm), resulting in a coherent interface with strong binding energy (Figure 3c), which would lead to transgranular fracture and increase fracture energy as well as the residual compressive stress caused by the thermal expansion coefficient mismatch, which could increase the crack propagation resistance [24].

Whisker-and Fiber-Reinforced Toughening
In the whisker-and fiber-reinforced ceramic composites, the reinforcements could provide a ceramic matrix with large strains before failure and maintain themselves intact. However, limited work has been performed to investigate the toughening behaviors of fiber-or whisker-reinforced MAX phases due to the high reactivity between the fibers and MAX phase matrix. Most of the work focused on the fabrication of the whisker or fiber/MAX phase composites and the main fibers include SiC fiber [31][32][33], carbon fiber [34] and Al2O3 fiber [35,36].
The reactivity of Ti2AlC or Ti3SiC2 powders with uncoated SiC fibers at the temperature up to 1550 °C were evaluated [31]. The results indicated that the uncoated SiC fibers could be used as reinforcement in Ti3SiC2 but not in Ti2AlC, attributing to the reactivity that no apparent reaction occurred between Ti3SiC2 and SiC fibers, while Ti2AlC could react with SiC fibers to form Ti3(Al1−xSix)C2, TiC and Al1+xTi1−x alloy. To reduce the reaction between the SiC fibers and Al-contained MAX phase, a Ti barrier layer was applied between the SiC fibers and Ti3AlC2 which could effectively hinder the inward diffusion of Al from the Ti3AlC2 matrix [32,33]. In the SiCf/Ti3AlC2 composites prepared at 1250 and 1300 °C, only minor phases of Ti5(Al,Si)3 alloy and TiC, as well as Ti2AlC were detected as interfaces. Compared to the monolithic Ti3AlC2 bulk, the load-displacement curves of as-prepared composites showed a noncatastrophic failure and a step-like fracture model was observed in the fracture surfaces using a field emission scanning electron microscope (FE-SEM, Figure 4) which indicated an improvement of the toughness [32]. Furthermore, Ti2AlC matrix loaded with two type of Al2O3 fibers (20 vol %) was obtained by spark plasma sintering (named as Ti2AlC/720f and Ti2AlC/610f) [36]. The fracture experiments and the post-mortem analysis of the fracture surface by SEM revealed that kinking along with intergranular cracking and delamination played an important role in deformation of Ti2AlC. The dynamic fracture toughness (5.46 MPa·m 1/2 ) was higher than the quasi-static value (4.03 MPa·m 1/2 ) by approximately 35%, and the fracture toughness of the composites reduced when increasing the temperature.

Whisker-and Fiber-Reinforced Toughening
In the whisker-and fiber-reinforced ceramic composites, the reinforcements could provide a ceramic matrix with large strains before failure and maintain themselves intact. However, limited work has been performed to investigate the toughening behaviors of fiber-or whisker-reinforced MAX phases due to the high reactivity between the fibers and MAX phase matrix. Most of the work focused on the fabrication of the whisker or fiber/MAX phase composites and the main fibers include SiC fiber [31][32][33], carbon fiber [34] and Al 2 O 3 fiber [35,36].
The reactivity of Ti 2 AlC or Ti 3 SiC 2 powders with uncoated SiC fibers at the temperature up to 1550 • C were evaluated [31]. The results indicated that the uncoated SiC fibers could be used as reinforcement in Ti 3 SiC 2 but not in Ti 2 AlC, attributing to the reactivity that no apparent reaction occurred between Ti 3 SiC 2 and SiC fibers, while Ti 2 AlC could react with SiC fibers to form Ti 3 (Al 1−x Si x )C 2 , TiC and Al 1+x Ti 1−x alloy. To reduce the reaction between the SiC fibers and Al-contained MAX phase, a Ti barrier layer was applied between the SiC fibers and Ti 3 AlC 2 which could effectively hinder the inward diffusion of Al from the Ti 3 AlC 2 matrix [32,33]. In the SiC f /Ti 3 AlC 2 composites prepared at 1250 and 1300 • C, only minor phases of Ti 5 (Al,Si) 3 alloy and TiC, as well as Ti 2 AlC were detected as interfaces. Compared to the monolithic Ti 3 AlC 2 bulk, the load-displacement curves of as-prepared composites showed a noncatastrophic failure and a step-like fracture model was observed in the fracture surfaces using a field emission scanning electron microscope (FE-SEM, Figure 4) which indicated an improvement of the toughness [32].

Whisker-and Fiber-Reinforced Toughening
In the whisker-and fiber-reinforced ceramic composites, the reinforcements could provide a ceramic matrix with large strains before failure and maintain themselves intact. However, limited work has been performed to investigate the toughening behaviors of fiber-or whisker-reinforced MAX phases due to the high reactivity between the fibers and MAX phase matrix. Most of the work focused on the fabrication of the whisker or fiber/MAX phase composites and the main fibers include SiC fiber [31][32][33], carbon fiber [34] and Al2O3 fiber [35,36].
The reactivity of Ti2AlC or Ti3SiC2 powders with uncoated SiC fibers at the temperature up to 1550 °C were evaluated [31]. The results indicated that the uncoated SiC fibers could be used as reinforcement in Ti3SiC2 but not in Ti2AlC, attributing to the reactivity that no apparent reaction occurred between Ti3SiC2 and SiC fibers, while Ti2AlC could react with SiC fibers to form Ti3(Al1−xSix)C2, TiC and Al1+xTi1−x alloy. To reduce the reaction between the SiC fibers and Al-contained MAX phase, a Ti barrier layer was applied between the SiC fibers and Ti3AlC2 which could effectively hinder the inward diffusion of Al from the Ti3AlC2 matrix [32,33]. In the SiCf/Ti3AlC2 composites prepared at 1250 and 1300 °C, only minor phases of Ti5(Al,Si)3 alloy and TiC, as well as Ti2AlC were detected as interfaces. Compared to the monolithic Ti3AlC2 bulk, the load-displacement curves of as-prepared composites showed a noncatastrophic failure and a step-like fracture model was observed in the fracture surfaces using a field emission scanning electron microscope (FE-SEM, Figure 4) which indicated an improvement of the toughness [32]. Furthermore, Ti2AlC matrix loaded with two type of Al2O3 fibers (20 vol %) was obtained by spark plasma sintering (named as Ti2AlC/720f and Ti2AlC/610f) [36]. The fracture experiments and the post-mortem analysis of the fracture surface by SEM revealed that kinking along with intergranular cracking and delamination played an important role in deformation of Ti2AlC. The dynamic fracture toughness (5.46 MPa·m 1/2 ) was higher than the quasi-static value (4.03 MPa·m 1/2 ) by approximately 35%, and the fracture toughness of the composites reduced when increasing the temperature. Furthermore, Ti 2 AlC matrix loaded with two type of Al 2 O 3 fibers (20 vol %) was obtained by spark plasma sintering (named as Ti 2 AlC/720f and Ti 2 AlC/610f) [36]. The fracture experiments and the post-mortem analysis of the fracture surface by SEM revealed that kinking along with intergranular cracking and delamination played an important role in deformation of Ti 2 AlC. The dynamic fracture toughness (5.46 MPa·m 1/2 ) was higher than the quasi-static value (4.03 MPa·m 1/2 ) by approximately 35%, and the fracture toughness of the composites reduced when increasing the temperature.

Transformation Toughening
Transformation toughening in MAX phases can be traced back to 2007 [37,38]. A 20 wt % ZrO 2 /Ti 3 AlC 2 was obtained by uniaxial hot-pressing at 1450 • C under a pressure of 20 MPa for 2 h in vacuum and the measured fracture toughness of 20 wt % ZrO 2 /Ti 3 AlC 2 composite was 6.8 MPa·m 1/2 , while the fracture toughness of monolithic Ti 3 AlC 2 was 4.6 MPa·m 1/2 [37]. The SEM observations of the fracture surface indicated that the fracture toughness improvement can be ascribed to the compressive stress in the matrix generated by the ZrO 2 particles transformation process.
In the 3 mol % yttria stabilized tetragonal zirconia ceramics (3Y-TZP) reinforced Ti3SiC2 composites prepared by spark plasma sintering (SPS) at 1300 • C, the fracture toughness could reach 11.94 MPa·m 1/2 with 30 vol % 3Y-TZP additions [38]. Some amount of m-ZrO 2 phase could be found on the fracture surface indicating that the phase transformation of T-ZrO 2 →M-ZrO 2 occurred during the fracture [38]. On the other hand, transformation toughening is not an exclusive toughening mechanism in the zirconia toughened composites (ZTCs). The second phase formed by phase transformation could toughen the matrix through multiple toughening mechanisms to a different degree, such as crack deflection and bridging [39].
Textured nanolayered Nb 4 AlC 3 ceramic with a shell-like microstructure was fabricated by strong magnetic field alignment technology followed by spark plasma sintering [40]. After sintering, the tailored microstructures were schematized and analyzed by SEM and TEM observations ( Figure 5). Figure 6 shows that the texture microstructure can activate the toughening mechanisms of crack deflection, through grain pull-out and bridging in Nb 4 AlC 3 ceramic. Consequently, the fracture toughness of the textured Nb 4 AlC 3 ceramic was extremely high and increased from 7.1 MPa·m 1/2 for the as-grown ceramic to 17.9 ± 5.16 and 11.49 ± 1.38 MPa·m 1/2 along the directions of parallel and perpendicular to the c-axis direction, respectively [40]. Similar work has been reported on other 211 and 312 MAX phases in a spark plasma facility and the fracture toughness of Ti 2 AlC increased from 6.0 MPa·m 1/2 in the as-sintered ceramic to 7.9 MPa·m 1/2 and 6.5 MPa·m 1/2 parallel and perpendicular to the loading direction, respectively, in the deformed ceramic [42].

Transformation Toughening
Transformation toughening in MAX phases can be traced back to 2007 [37,38]. A 20 wt % ZrO2/Ti3AlC2 was obtained by uniaxial hot-pressing at 1450 °C under a pressure of 20 MPa for 2 h in vacuum and the measured fracture toughness of 20 wt % ZrO2/Ti3AlC2 composite was 6.8 MPa·m 1/2 , while the fracture toughness of monolithic Ti3AlC2 was 4.6 MPa·m 1/2 [37]. The SEM observations of the fracture surface indicated that the fracture toughness improvement can be ascribed to the compressive stress in the matrix generated by the ZrO2 particles transformation process.
In the 3 mol % yttria stabilized tetragonal zirconia ceramics (3Y-TZP) reinforced Ti3SiC2 composites prepared by spark plasma sintering (SPS) at 1300 °C, the fracture toughness could reach 11.94 MPa·m 1/2 with 30 vol % 3Y-TZP additions [38]. Some amount of m-ZrO2 phase could be found on the fracture surface indicating that the phase transformation of T-ZrO2→M-ZrO2 occurred during the fracture [38]. On the other hand, transformation toughening is not an exclusive toughening mechanism in the zirconia toughened composites (ZTCs). The second phase formed by phase transformation could toughen the matrix through multiple toughening mechanisms to a different degree, such as crack deflection and bridging [39].
Textured nanolayered Nb4AlC3 ceramic with a shell-like microstructure was fabricated by strong magnetic field alignment technology followed by spark plasma sintering [40]. After sintering, the tailored microstructures were schematized and analyzed by SEM and TEM observations ( Figure 5). Figure 6 shows that the texture microstructure can activate the toughening mechanisms of crack deflection, through grain pull-out and bridging in Nb4AlC3 ceramic. Consequently, the fracture toughness of the textured Nb4AlC3 ceramic was extremely high and increased from 7.1 MPa·m 1/2 for the as-grown ceramic to 17.9 ± 5.16 and 11.49 ± 1.38 MPa·m 1/2 along the directions of parallel and perpendicular to the c-axis direction, respectively [40]. Similar work has been reported on other 211 and 312 MAX phases in a spark plasma facility and the fracture toughness of Ti2AlC increased from 6.0 MPa·m 1/2 in the as-sintered ceramic to 7.9 MPa·m 1/2 and 6.5 MPa·m 1/2 parallel and perpendicular to the loading direction, respectively, in the deformed ceramic [42].

Toughening Models for MAX Phases
The toughening mechanisms in ceramics can be understood and predicted by the modeling work which can contribute insights and theoretical instructions for material design, process development and optimization. Many approaches were applied and developed for ceramic toughening mechanism simulations such as finite element method (FEM), first principles calculation (FPC) [47,48] and the empirical electron theory (EET) of solids and molecules [49][50][51][52].
For a comprehensive understanding of the toughening mechanisms in these nanolayered MAX phase ceramics, SiC particle and fiber-reinforced Ti3SiC2 composites were selected as models and simulated using a primary 3D finite element model (3D-FEM), which is schematically represented in Figure 7. The main material parameters used in 3D-FEM are listed in Table 1. For the SiC fiber toughening Ti3SiC2 MAX phase, the elliptical SiC fibers with a length-diameter ratio of 20:1 was applied in 3D-FEM.

Toughening Models for MAX Phases
The toughening mechanisms in ceramics can be understood and predicted by the modeling work which can contribute insights and theoretical instructions for material design, process development and optimization. Many approaches were applied and developed for ceramic toughening mechanism simulations such as finite element method (FEM), first principles calculation (FPC) [47,48] and the empirical electron theory (EET) of solids and molecules [49][50][51][52].
For a comprehensive understanding of the toughening mechanisms in these nanolayered MAX phase ceramics, SiC particle and fiber-reinforced Ti3SiC2 composites were selected as models and simulated using a primary 3D finite element model (3D-FEM), which is schematically represented in Figure 7. The main material parameters used in 3D-FEM are listed in Table 1. For the SiC fiber toughening Ti3SiC2 MAX phase, the elliptical SiC fibers with a length-diameter ratio of 20:1 was applied in 3D-FEM.

Toughening Models for MAX Phases
The toughening mechanisms in ceramics can be understood and predicted by the modeling work which can contribute insights and theoretical instructions for material design, process development and optimization. Many approaches were applied and developed for ceramic toughening mechanism simulations such as finite element method (FEM), first principles calculation (FPC) [47,48] and the empirical electron theory (EET) of solids and molecules [49][50][51][52].
For a comprehensive understanding of the toughening mechanisms in these nanolayered MAX phase ceramics, SiC particle and fiber-reinforced Ti 3 SiC 2 composites were selected as models and simulated using a primary 3D finite element model (3D-FEM), which is schematically represented in Figure 7. The main material parameters used in 3D-FEM are listed in Table 1. For the SiC fiber toughening Ti 3 SiC 2 MAX phase, the elliptical SiC fibers with a length-diameter ratio of 20:1 was applied in 3D-FEM.  In fracture mechanics, there are three types of basic fracture modes, as shown in Figure 8: Mode I Opening model, Mode II Shearing mode and Mode III Tearing mode, where (x1, x2, x3) is the local Cartesian coordinate system centered at the crack front with the x1-axis perpendicular to the crack front, the x2-axis perpendicular to the crack plane, and the x3-axis along the crack front. In those modes, the stress-intensity factor, K, is a parameter describing the field of the crack tip which only correlates to the loads and geometries. In the present study, Mode I, the opening mode, was selected for SiC particle and fiber-reinforced Ti3SiC2 composites where the stress-intensity factor, KI, can be expressed by the following formula and be obtained from the extended finite element method (EFEM) by using an ABAQUS/CAE 2016 software package.
In the formula, σ22 is the biaxial stress in the vicinity of the crack tip, x1 and x2 are Cartesian coordinates at x1-axis and x2-axis, respectively, a is the crack length and r is the radius for a 3D penny-shaped crack.  Figure 9a represents the finite element mesh for the composite of SiC particle-reinforced Ti3SiC2 matrix, and Figure 9b shows the boundary conditions applied on the top and bottom sides of the In fracture mechanics, there are three types of basic fracture modes, as shown in Figure 8: Mode I Opening model, Mode II Shearing mode and Mode III Tearing mode, where (x 1 , x 2 , x 3 ) is the local Cartesian coordinate system centered at the crack front with the x 1 -axis perpendicular to the crack front, the x 2 -axis perpendicular to the crack plane, and the x 3 -axis along the crack front. In those modes, the stress-intensity factor, K, is a parameter describing the field of the crack tip which only correlates to the loads and geometries. In the present study, Mode I, the opening mode, was selected for SiC particle and fiber-reinforced Ti 3 SiC 2 composites where the stress-intensity factor, K I , can be expressed by the following formula and be obtained from the extended finite element method (EFEM) by using an ABAQUS/CAE 2016 software package.

SiC Particle-Reinforced Ti3SiC2 MAX Phase
In the formula, σ 22 is the biaxial stress in the vicinity of the crack tip, x 1 and x 2 are Cartesian coordinates at x 1 -axis and x 2 -axis, respectively, a is the crack length and r is the radius for a 3D penny-shaped crack. In fracture mechanics, there are three types of basic fracture modes, as shown in Figure 8: Mode I Opening model, Mode II Shearing mode and Mode III Tearing mode, where (x1, x2, x3) is the local Cartesian coordinate system centered at the crack front with the x1-axis perpendicular to the crack front, the x2-axis perpendicular to the crack plane, and the x3-axis along the crack front. In those modes, the stress-intensity factor, K, is a parameter describing the field of the crack tip which only correlates to the loads and geometries. In the present study, Mode I, the opening mode, was selected for SiC particle and fiber-reinforced Ti3SiC2 composites where the stress-intensity factor, KI, can be expressed by the following formula and be obtained from the extended finite element method (EFEM) by using an ABAQUS/CAE 2016 software package.
In the formula, σ22 is the biaxial stress in the vicinity of the crack tip, x1 and x2 are Cartesian coordinates at x1-axis and x2-axis, respectively, a is the crack length and r is the radius for a 3D penny-shaped crack.  Figure 9a represents the finite element mesh for the composite of SiC particle-reinforced Ti3SiC2 matrix, and Figure 9b shows the boundary conditions applied on the top and bottom sides of the  Figure 9a represents the finite element mesh for the composite of SiC particle-reinforced Ti 3 SiC 2 matrix, and Figure 9b shows the boundary conditions applied on the top and bottom sides of the geometry respect to the X axis and Y axis respectively. The geometry displacement at the X axis direction is constrained to zero. Figure 10 illustrates the maximum principal stress distribution at the onset of crack propagation predicted by the fracture model for the composite with 6.8 vol % SiC reinforcement. The corresponding value of the stress-intensity factor, K I , obtained from this simulation is 6.26 MPa·m 1/2 . As shown in Figure 10, the SiC particles can prevent crack from propagating and lead to stress concentration at the crack tip and the stress-intensity factor K I can be considered as a critical factor for fracture toughness (K I = K IC = 6.26 MPa·m 1/2 ), which demonstrates a sufficient reinforcement to enhance the toughness of monolithic Ti 3 SiC 2 MAX phase [30]. geometry respect to the X axis and Y axis respectively. The geometry displacement at the X axis direction is constrained to zero. Figure 10 illustrates the maximum principal stress distribution at the onset of crack propagation predicted by the fracture model for the composite with 6.8 vol % SiC reinforcement. The corresponding value of the stress-intensity factor, KI, obtained from this simulation is 6.26 MPa·m 1/2 . As shown in Figure 10, the SiC particles can prevent crack from propagating and lead to stress concentration at the crack tip and the stress-intensity factor KI can be considered as a critical factor for fracture toughness (KI = KIC = 6.26 MPa·m 1/2 ), which demonstrates a sufficient reinforcement to enhance the toughness of monolithic Ti3SiC2 MAX phase [30].

SiC Fiber-Reinforced Ti3SiC2 MAX Phase
Similar to SiC particle-reinforced Ti3SiC2 MAX phase, Figure 11 shows the finite element mesh and boundary constraint for the SiC fiber-reinforced Ti3SiC2 composite. In the finite element mesh geometry respect to the X axis and Y axis respectively. The geometry displacement at the X axis direction is constrained to zero. Figure 10 illustrates the maximum principal stress distribution at the onset of crack propagation predicted by the fracture model for the composite with 6.8 vol % SiC reinforcement. The corresponding value of the stress-intensity factor, KI, obtained from this simulation is 6.26 MPa·m 1/2 . As shown in Figure 10, the SiC particles can prevent crack from propagating and lead to stress concentration at the crack tip and the stress-intensity factor KI can be considered as a critical factor for fracture toughness (KI = KIC = 6.26 MPa·m 1/2 ), which demonstrates a sufficient reinforcement to enhance the toughness of monolithic Ti3SiC2 MAX phase [30].

SiC Fiber-Reinforced Ti3SiC2 MAX Phase
Similar to SiC particle-reinforced Ti3SiC2 MAX phase, Figure 11 shows the finite element mesh and boundary constraint for the SiC fiber-reinforced Ti3SiC2 composite. In the finite element mesh

SiC Fiber-Reinforced Ti 3 SiC 2 MAX Phase
Similar to SiC particle-reinforced Ti 3 SiC 2 MAX phase, Figure 11 shows the finite element mesh and boundary constraint for the SiC fiber-reinforced Ti 3 SiC 2 composite. In the finite element mesh (Figure 11a), the seed point distribution on the inner ellipse SiC fiber edge are 16 points and the seed distribution on the cubic edge of Ti 3 SiC 2 matrix are 6 points at its high dimension, 4 points at its long dimension and 1 point at its wide dimension. For the boundary constraint, as shown in Figure 11b, the displacement of the top of Ti 3 SiC 2 matrix constraint to −4 × 10 5 mm in the U 1 direction, −2 × 10 5 mm in the U 2 direction and 0 mm in the U 3 direction, the displacement of the bottom of Ti 3 SiC 2 matrix constraint to 4 × 10 5 mm in the U 1 direction, −2 × 10 5 mm in the U 1 direction and 0 mm in the U 3 direction. Consequently, Figure 12 shows the predicted maximum principal stress distribution at the onset of crack propagation for the proposed SiC fiber-reinforced Ti 3 SiC 2 composites with 5 vol % reinforcements . The predicted maximum principal stress is 176.2 MPa. The higher the maximum principal stress, the stronger the fiber can prevent crack from initiating. The stress-intensity factor K I computed from 3D-FEM method is 12.65 MP·m 1/2 indicating a significant improvement in the toughness of the Ti 3 SiC 2 MAX phases.
Materials 2017, 10, 366 9 of 12 (Figure 11a), the seed point distribution on the inner ellipse SiC fiber edge are 16 points and the seed distribution on the cubic edge of Ti3SiC2 matrix are 6 points at its high dimension, 4 points at its long dimension and 1 point at its wide dimension. For the boundary constraint, as shown in Figure 11b, the displacement of the top of Ti3SiC2 matrix constraint to −4 × 10 5 mm in the U1 direction, −2 × 10 5 mm in the U2 direction and 0 mm in the U3 direction, the displacement of the bottom of Ti3SiC2 matrix constraint to 4 × 10 5 mm in the U1 direction, −2 × 10 5 mm in the U1 direction and 0 mm in the U3 direction. Consequently, Figure 12 shows the predicted maximum principal stress distribution at the onset of crack propagation for the proposed SiC fiber-reinforced Ti3SiC2 composites with 5 vol % reinforcements. The predicted maximum principal stress is 176.2 MPa. The higher the maximum principal stress, the stronger the fiber can prevent crack from initiating. The stress-intensity factor KI computed from 3D-FEM method is 12.65 MP·m 1/2 indicating a significant improvement in the toughness of the Ti3SiC2 MAX phases.  The successful prediction of toughness of the SiC particle and fiber-reinforced Ti3SiC2 using 3D-FEM can provide insight and valuable guidance to the experimental work to fabricate MAX phase-based composites with optimized microstructures to obtain the desired mechanical properties. However, more modeling prediction should be done to further optimize the microstructures of the composites to achieve the required properties for their applications.  Figure 11a), the seed point distribution on the inner ellipse SiC fiber edge are 16 points and the seed distribution on the cubic edge of Ti3SiC2 matrix are 6 points at its high dimension, 4 points at its long dimension and 1 point at its wide dimension. For the boundary constraint, as shown in Figure 11b, the displacement of the top of Ti3SiC2 matrix constraint to −4 × 10 5 mm in the U1 direction, −2 × 10 5 mm in the U2 direction and 0 mm in the U3 direction, the displacement of the bottom of Ti3SiC2 matrix constraint to 4 × 10 5 mm in the U1 direction, −2 × 10 5 mm in the U1 direction and 0 mm in the U3 direction. Consequently, Figure 12 shows the predicted maximum principal stress distribution at the onset of crack propagation for the proposed SiC fiber-reinforced Ti3SiC2 composites with 5 vol % reinforcements. The predicted maximum principal stress is 176.2 MPa. The higher the maximum principal stress, the stronger the fiber can prevent crack from initiating. The stress-intensity factor KI computed from 3D-FEM method is 12.65 MP·m 1/2 indicating a significant improvement in the toughness of the Ti3SiC2 MAX phases.  The successful prediction of toughness of the SiC particle and fiber-reinforced Ti3SiC2 using 3D-FEM can provide insight and valuable guidance to the experimental work to fabricate MAX phase-based composites with optimized microstructures to obtain the desired mechanical properties. However, more modeling prediction should be done to further optimize the microstructures of the composites to achieve the required properties for their applications. The successful prediction of toughness of the SiC particle and fiber-reinforced Ti 3 SiC 2 using 3D-FEM can provide insight and valuable guidance to the experimental work to fabricate MAX phase-based composites with optimized microstructures to obtain the desired mechanical properties.
However, more modeling prediction should be done to further optimize the microstructures of the composites to achieve the required properties for their applications.

Conclusions
This paper reviews the toughening mechanisms for a family of nanolayered MAX phases and the related composites. Based on the experimental results, SiC particle and fiber toughening MAX phase models were established for a better understanding of the toughening mechanisms and prediction of the improvement of the toughness, which may contribute with insights and theoretical instructions for material design, process development, and optimization. Meanwhile, it also opens many perspectives in toughening those nanolayered ceramics: (1) To apply these nanolayered MAX phases as higher performance and reliable structural components, a further tailoring of the microstructure should be done to enhance both strength and toughness. Through additional microstructure modification e.g., by grain size control, it is probable that the flexural strength or fracture toughness can be further enhanced. (2) For the fiber toughening MAX phases, more work should be done to optimize the interface between MAX phase and fibers, e.g., by selecting different fibers which could be phase equilibrium with MAX phase during the high-temperature processing or by new processing methods that can consolidate the composites with fast densification technology to reduce or avoid the reaction between the fibers and MAX phase matrix. (3) The modeling work presented here is just a first attempt to predict the improved toughness of the MAX phase-based composites by using 3D-FEM. However, more modeling parameters such as selection of proper reinforcements, the volume fraction of reinforcement as well as size and dimensions of the reinforcements etc. need to be further investigated and refined, which may provide valuable theoretical guidelines for material design, process development, and optimization.
Success in addressing these points may expand MAX phases and related composites to numerous structural and high-temperature applications.