**1. Introduction**

Material is used to perform a design. The design engineer expects some material properties, either single or combinations of one or more properties, from materials for engineering design such as light weight, strength, fatigue strength, high temperature strength, high fracture

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toughness, corrosion resistance, wear resistance, electrical properties, and manufacturability [1, 2]. Although the metallic materials have higher fracture toughness and better thermal shock resistance than the ceramics, their high temperature resistance is lower than of the ceramics. Ceramic materials have low density, good high temperature resistance, and good creep resistance, but their thermal shock resistance is low [2–5]. Man-made polymer materials have been used for the past 100 years because they are lightweight, cheap, highly resistant to corrosion, and wear resistant. Also, the production of polymer materials is much easier than the metallic and ceramic materials. However, their low mechanical strength limits their use in structural design [2]. Composite materials are obtained by combining ceramic, metallic, and/or polymer materials. Thus, the designer can benefit from the superior properties of two different materials simultaneously [2, 4].

Metal matrix composites (MMCs) reinforced with ceramic particles provide the required material properties in many engineering applications. High strength, high corrosion resist‐ ance, and stiffness of MMCs have made them suitable for their use in, particularly, aerospace, aviation, automobile, and mineral processing industry [6, 7]. Particulate reinforced MMC materials are cheaper and have higher abrasion resistance and higher temperature stability than that of materials, and they are being used widely in many areas compared to the contin‐ uous fiber reinforced composites [6, 7].

Functionally graded materials (FGMs) can be considered as a subcategory of composite materials. The microstructure, mechanical, and thermal properties are changed throughout the thickness or width of the material depending on a function [8–10].

The function type and consequently FGMs' properties are primarily related to mechanical/ thermal properties and compatibility of matrix and reinforced materials, FGM thickness or width, and manufacturing method. Function can occur in three different ways depending on the following factors: exponentially, linearly, and according to the rule of force. The mechan‐ ical/thermal properties of material such as Young's modulus, yielding stress, tensile stress, fatigue, and thermal/electrical conductivity properties can vary depending on the function type [4, 8–12].

There are some basic manufacturing methods for graded materials, which include powder metallurgy, physical vapor deposition (PVD), chemical vapor deposition (CVD), plasma spray, thermal spray, combustion synthesis (SHS), centrifugal casting, and polymerization [4, 10, 12– 29]. Recently developed methods are also available: modified stir casting, centrifugal sintering, gradient slurry disintegration and deposition, and powder cold spray before cold isostatic sintering [30–33].

MMCs reinforced with ceramic particles have been used for a long time because they can be easily manufactured. MMCs are inexpensive than the other composite types and have improvable thermal and mechanical properties [7]. When two different types of materials are combined, it can lead to formation of additional thermal and residual stresses. It is known that discontinuities and thermal stress can be decreased on ceramic–metal interface using FGMs [4, 8, 9].

Crack propagation that causes sudden or stepped fracture occurs when stress concentration at the tip of crack overcomes strength of material [34]. For a linear elastic material, stress concentration at the tip can be represented by *K*I, *K*II, and *K*III, which are stress intensity factors in opening, sliding, and tearing conditions, respectively. Critical value of stress intensity factor *K*c must be equal to *K*I for crack propagation under Mode I load.

toughness, corrosion resistance, wear resistance, electrical properties, and manufacturability [1, 2]. Although the metallic materials have higher fracture toughness and better thermal shock resistance than the ceramics, their high temperature resistance is lower than of the ceramics. Ceramic materials have low density, good high temperature resistance, and good creep resistance, but their thermal shock resistance is low [2–5]. Man-made polymer materials have been used for the past 100 years because they are lightweight, cheap, highly resistant to corrosion, and wear resistant. Also, the production of polymer materials is much easier than the metallic and ceramic materials. However, their low mechanical strength limits their use in structural design [2]. Composite materials are obtained by combining ceramic, metallic, and/or polymer materials. Thus, the designer can benefit from the superior properties of two

Metal matrix composites (MMCs) reinforced with ceramic particles provide the required material properties in many engineering applications. High strength, high corrosion resist‐ ance, and stiffness of MMCs have made them suitable for their use in, particularly, aerospace, aviation, automobile, and mineral processing industry [6, 7]. Particulate reinforced MMC materials are cheaper and have higher abrasion resistance and higher temperature stability than that of materials, and they are being used widely in many areas compared to the contin‐

Functionally graded materials (FGMs) can be considered as a subcategory of composite materials. The microstructure, mechanical, and thermal properties are changed throughout

The function type and consequently FGMs' properties are primarily related to mechanical/ thermal properties and compatibility of matrix and reinforced materials, FGM thickness or width, and manufacturing method. Function can occur in three different ways depending on the following factors: exponentially, linearly, and according to the rule of force. The mechan‐ ical/thermal properties of material such as Young's modulus, yielding stress, tensile stress, fatigue, and thermal/electrical conductivity properties can vary depending on the function

There are some basic manufacturing methods for graded materials, which include powder metallurgy, physical vapor deposition (PVD), chemical vapor deposition (CVD), plasma spray, thermal spray, combustion synthesis (SHS), centrifugal casting, and polymerization [4, 10, 12– 29]. Recently developed methods are also available: modified stir casting, centrifugal sintering, gradient slurry disintegration and deposition, and powder cold spray before cold isostatic

MMCs reinforced with ceramic particles have been used for a long time because they can be easily manufactured. MMCs are inexpensive than the other composite types and have improvable thermal and mechanical properties [7]. When two different types of materials are combined, it can lead to formation of additional thermal and residual stresses. It is known that discontinuities and thermal stress can be decreased on ceramic–metal interface using FGMs

the thickness or width of the material depending on a function [8–10].

different materials simultaneously [2, 4].

76 Advances in Functionally Graded Materials and Structures

uous fiber reinforced composites [6, 7].

type [4, 8–12].

sintering [30–33].

[4, 8, 9].

There are many analytical and numerical studies on fatigue and fracture mechanics of FGMs [34–51]. Theoretical crack propagation analyses of FGMs indicate that the crack tip stress is different from that of the homogeneous material [34, 38–40]. The studies on the subject demonstrate that grading direction and function affect the crack propagation. It is found that FGMs have shown better performance at increasing crack growth compared with homogene‐ ous materials.

Under asymmetric loadings, the crack propagates perpendicularly to grading direction, which changes the direction of crack [43]. However, under symmetric loadings, the crack propagates in parallel to grading direction [42]. Crack propagation experiments in grading materials have been carried out using the following: direction of crack propagation (in parallel to grading direction) under different loading cycles (regularly increasing or decreasing loading [53–54], periodic mechanical loading [50–52], and periodical thermal loading [58–59]). In the experi‐ ments where crack propagation was perpendicular to the grading direction, fracture happened quickly [60–62]. Therefore, the effect of grading on the stress concentration factor could not be calculated. Compared to homogeneous material, FGMs' fracture behavior is altered by FGM composition and properties by four of the following [63]:


In Equation (1), *σij* represents the crack tip stress, *Kα* (*α* = I, II, III) stress intensity factors, *θ* the angle with respect to the plane of the crack, *r* the distance from crack tip, *δ* the Kronecker delta, *σ<sup>T</sup>* the transverse stress, *f ij* (*α*) (*θ*) angular functions, and 1 / *r* the singularity of crack tip stress. Studies by Delale and Erdogan [35] and Eischen [39] showed that the singularity of crack tip stress of continuous or partially graded materials is similar to that of homogeneous materials. Jin and Noda [41] verified this situation by determining that the angular distribution function of the elastic and plastic crack tip area ( *f ij* (*θ*)) is the same.

$$
\sigma\_{\vec{\boldsymbol{\eta}}} = \frac{K\_a}{\sqrt{2\pi r}} f\_{\vec{\boldsymbol{\eta}}}^{(a)} \left( \boldsymbol{\theta} \right) + \delta\_{\mathbf{i}1} \delta\_{\mathbf{i}\uparrow} \sigma\_{\mathbf{r}} + A\_a \sqrt{2\pi r} w\_{\vec{\boldsymbol{\eta}}}^{(a)} \left( \boldsymbol{\theta} \right) \tag{1}
$$

Also, the studies conducted by Eischen [39] and Jin and Noda [41] have shown that FGMs crack tip stress (*σij* ) and displacement (*ui* ) (Eq. (2)) are the same form as homogeneous material. In Equation (2), *Kα* (*α* = I, II) represents stress intensity factors, *r* the distance from crack tip, *θ* the angle with respect to the plane of the crack, *gi* (*α*) (*θ*) angular functions, *E*tip the Young's modulus at crack tip, and *υ*tip the Poisson ratio at crack tip. These results mean that the stress intensity factor is a determinative fracture parameter for FGMs just like in homogeneous material [67]. Similar results have been found for dynamically propagated cracks by Para‐ meswaran and Shukla [68].

$$u\_i \approx \frac{K\_a \left(2 + 2\nu\_{\rm tip}\right)}{E\_{\rm tip}} \sqrt{\frac{8r}{\pi}} g\_i^{(a)}(\theta) \tag{2}$$

Continuous or stepped grading prevents the abnormal stress behavior of cracks when the interface of two materials is combined [69]. Moreover, Delale and Erdogan [35] found that the effect of spatial variation of the Poisson ratio on the stress singularity can be neglected.

Fracture behavior depending on orientation in the grading region can be defined by consid‐ ering two limit states [63]:


In the cracks that are parallel to the direction, stress at the crack tip region becomes symmetric and it is expected that crack opens toward the grading direction. FGM crack tip stresses in graded regions are significantly lower than in materials with combinations of two material properties [37, 70, 71]. Stress intensity factor of FGMs is found to be greater than that of homogeneous materials. Material grading profile and position of the crack effect stress intensity factor too. When grading step increases, its value increases [35, 37, 42, 72]. Grading format also effects the stress intensity factor. If exponential value *n* is bigger than 1 (*n* > 1), the stress intensity factor is in tendency to decrease compared to *n* < 1 situation [70–72]. Spatial composition changes, which have an important effect on effective fracture toughness of the FGM composites, can effect thermal stress distribution throughout its width. Growing fracture toughness depends on residual stresses partially [53, 64, 73]. As residual stresses change by composition of FGM, compressive stresses increase the resistance of crack against growing fracture [64].

Critical value of stress intensity factor *Kc* must be equal to *K*<sup>I</sup> for crack propagation under crack opening mode. In the ongoing process, crack growth rates d*a* / d*N* in every period can be found by using Paris Equation (Eq. (3)), where *N* is the number of cycles to failure, *c* and *m* are material constants [34].

$$\frac{\text{d}a}{\text{d}N} = c\Delta K^m \tag{3}$$

Studies related to FGMs' fatigue and fatigue fracture behaviors have been conducted using numerical and analytical methods and new approaches are developed to date. However, there are hardly enough experimental studies to support this.

In this study, aluminum 2014 matrix reinforced with SiC FGM was manufactured via centri‐ fugal casting. The effect of SiC distribution on the mechanical and fatigue fracture properties was determined and analyzed experimentally.
