Calculated c and m coefficients of FGM2 M(T) specimens: 1–4 refer to specimen numbers from innermost (aluminum-rich side) to outermost (SiC-rich side) regions of cylinder
In this study, a functionally graded cylindrical specimen was obtained via centrifugal casting and its fatigue crack behavior was investigated. Aluminum 2014 alloy and SiC were used as matrix material and ceramic particle, respectively. The distribution of SiC and the mechanical properties of material through cylinder wall thickness were varied because of the centrifugal force during centrifugal casting. Variations in microstructure and hardness were examined. A cylindrical specimen was cut through its thickness in four sections through vertical slicing. Tensile strength was tested on each section to determine the mechanical properties that can be varied such as Young’s modulus, tensile strength, and yielding stress. To investigate the effect of variation in the mechanical properties and distribution of SiC particles on fatigue crack behavior, fatigue crack growth tests were applied under tensile cyclic load with stress ratio R = 0.1. The samples were prepared in three separate groups: central notched, single-edge notched on SiC-rich side, and single-edge notched on aluminum-rich side. It was found that SiC distribution affected fatigue crack initiation and propagation. The fatigue life increased up to 350% because of increasing SiC ratio for central notched specimens. Cracks were started out later on the single-edge notched SiC-rich side compared to aluminum-rich side whose fatigue life increased up to 500%. In addition, it was found that unreinforced aluminum material’s fatigue life was lower than that of reinforced material.
- Functionally graded material
- Aluminum matrix
- Crack propagation
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 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 . 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 resistance, 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 continuous 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 mechanical/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 . 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 . For a linear elastic material, stress concentration at the tip can be represented by KI, KII, and KIII, which are stress intensity factors in opening, sliding, and tearing conditions, respectively. Critical value of stress intensity factor Kc must be equal to KI for crack propagation under Mode I load.
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 homogeneous materials.
Under asymmetric loadings, the crack propagates perpendicularly to grading direction, which changes the direction of crack . However, under symmetric loadings, the crack propagates in parallel to grading direction . 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 experiments 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 :
Variable stress region: Crack direction in FGMs is changed by graded mechanical properties (Young’s modulus, E, and the Poisson ratio, υ), but not in homogeneous materials. As a result, fracture loads and crack path are affected by grading material properties.
Crack tip toughness: Since the chemical composition of material changes, internal fracture toughness (K0) becomes a function (K0(a)) that changes according to the position of the grading.
Hardening rate of the crack opening: Change in the microstructure and the chemical composition of graded region changes the characteristics of hardening of the crack opening too. Crack closure as in homogeneous materials depends on not only being on the back of the crack but also the position of the cracks in graded region.
In Equation (1), represents the crack tip stress, (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, the transverse stress, angular functions, and the singularity of crack tip stress. Studies by Delale and Erdogan  and Eischen  showed that the singularity of crack tip stress of continuous or partially graded materials is similar to that of homogeneous materials. Jin and Noda  verified this situation by determining that the angular distribution function of the elastic and plastic crack tip area () is the same.
Also, the studies conducted by Eischen  and Jin and Noda  have shown that FGMs crack tip stress () and displacement () (Eq. (2)) are the same form as homogeneous material. In Equation (2), (α = I, II) represents stress intensity factors, r the distance from crack tip, θ the angle with respect to the plane of the crack, angular functions, the Young’s modulus at crack tip, and 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 . Similar results have been found for dynamically propagated cracks by Parameswaran and Shukla .
Continuous or stepped grading prevents the abnormal stress behavior of cracks when the interface of two materials is combined . Moreover, Delale and Erdogan  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 considering two limit states :
Crack propagation is parallel to grading direction: crack does not digress although effective fracture toughness changes.
Crack propagation is perpendicular to grading direction: asymmetric crack tip zone causes crack to deflect.
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 .
Critical value of stress intensity factor must be equal to for crack propagation under crack opening mode. In the ongoing process, crack growth rates 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 .
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 centrifugal casting. The effect of SiC distribution on the mechanical and fatigue fracture properties was determined and analyzed experimentally.
2. Experimental results and analysis
Two functionally graded aluminum 2014 alloy (1.18% Si, 4.9% Cu, 1.04% Mn, in wt.) matrix materials reinforced with 20% in wt. and 9 μm SiC particles were produced by centrifugal casting. Density of SiC particles is higher than that of aluminum, 3.2 gr/cm3 and 2.8 gr/cm3, respectively. As a result of the centrifugal force effect, the distribution of SiC particles was varied through the wall thickness of the cylinder. More SiC particles were dispersed to the outer diameter of the FGM cylinder under these circumstances, as expected. By changing casting wall thicknesses, two cylinders having different mechanical properties were produced. The specimens were named FGM1 and FGM2, and SiC-rich and aluminum-rich regions were formed on both of FGM1 and FGM2. FGM1’s wall thickness was higher than FGM2’s. This result is compatible with the previous studies on the subject [74–83]. Taking into account the wear, fatigue, and fretting behaviors of FGM from previous studies, an aging process was performed (solutionizing at 500 °C, followed by water quenching and reheating for aging at 145 °C for 10 h, followed by water cooling) [75, 82, 83].
Tensile tests were performed using specimens sliced through the wall thickness and were numbered from 1 to 5 for FGM1 and FGM2 according to their position in the cylinder (from the innermost to the outermost layer). Tensile strength was tested on each section to determine the mechanical properties that can be varied such as Young’s modulus (E), tensile strength (R), and yielding stress (Re) (Figures 1–3). Tensile experiments were conducted using video extensometer at 1 mm/min tensile speed. Obtaining tensile specimens from the cylindrical FGM is shown in Figure 4.
Due to the higher density of SiC particles (relative to aluminum 2014), many more particles were dispersed to the outer diameter of FGM cylinder during centrifugal casting. This produced a gradient in the Young’s modulus, from the inside to the outside layer of cylinder (Figure 1) . It was observed that SiC distribution under centrifugal force and wall thickness of cylinders effected Young’s modulus variation. As wall thickness of cylinder decreased, it was observed that Young’s modulus value (innermost of cylinder) increased from 65 MPa to 84 MPa. Grading functions of FGMs were differed from each other due to the distribution of SiC. Young’s modulus values of the outermost region of cylinders were similar (105–106 MPa). It was observed that wall thickness of FGM and manufacturing process had an impact on the composition and mechanical properties of FGM.
As mentioned above, FGMs’ properties can vary exponentially, linearly, and according to the rule of force. In this study, Young’s modulus variation was calculated according to the rule of force to compare with experimental results using Equations (4) and (5). In these equations, represents Young’s modulus at x point, base material Young’s modulus, reinforcing material Young’s modulus, the width/thickness of FGM, the distance from the starting point, the distance function, and p the gradient exponent. The gradient exponent (p) was calculated using equations as 0.1 and 7 for FGM1 and FGM2, respectively.
Tensile and fatigue crack growth tests were performed with a 5-ton capacity Instron fatigue servo-hydraulic test device. Two cylindrical specimens were cut through their wall thickness in four sections via vertical slicing as shown in Figure 4. Tensile tests were carried out to determine the crack opening properties using video extensometer at 1 mm/min tensile speed.
To investigate the effect of variation in mechanical properties and distribution of SiC particles on fatigue crack behavior, fatigue crack growth tests were applied under tensile cyclic load with stress ratio R = 0.1. The samples were prepared according to the ASTM E647 (2011)  in three separate groups: central notched (middle tension, M(T)), single-edge notched (SE(T)) on SiC-rich side, and single-edge notched (SE(T)) on aluminum-rich side (Figure 5). The test specimens’ dimensions are shown in Figure 6. M(T) and (SE(T)) samples are prepared according to the ASTM E647 (2011) . Samples were processed by laser cutting method. According to the ASTM E647 (2011)  standard, crack length to be opened must be at least 0.2W; sample length L > 0.3. W represents width belonging to the sample. Notch length opened on M(T) specimens 2a = 13 mm, notch length opened on SE(T) a = 5.5 mm . Both tensile and fatigue experiments were applied to these samples. Two digital portable microscopes, as shown in Figure 7, were used to determine the crack beginning from notch tip and propagation of that crack. Applied maximum load determined with respect of minimum yielding stress after tensile tests were applied to central and single-edge notched specimens (Eq. (6)).
For 2a/W < 0.95 situation, M(T) specimens were accepted homogeneous and Equations (5) and (6) were used in calculations. a represents crack half-length. If 2a/W is greater than or equal to 0.95, it is accepted that crack will be instable and then probably fracture will be occur. The stress ratio R = 0.1 and frequency f = 5 Hz were selected as fatigue crack growth experiment parameters. SE(T) specimens’ notch was parallel to the grading direction.
Load-crack tip opening diagrams of M(T) specimens obtained from FGM1 after tensile tests are shown in Figure 8. Here, 1–4 refer to specimen numbers from innermost (aluminum-rich side) to outermost (SiC-rich side) regions of cylinder. It can be understood that Al-rich side fractured at a lower load value. Since SiC rate increased, load carrying capacity of specimens increased. SiC-rich side fractured at a higher load value than the others.
Load-crack tip opening diagrams of SE(T) specimens obtained from FGM2 after tensile tests can be seen in Figure 9. The specimen (SE(T)) on SiC-rich side was fractured at a higher load than the (SE(T)) on aluminum-rich side specimen. Curves are almost continued in the same way until opening value is 0.5 mm. However, it is seen that (SE(T)) on aluminum-rich side specimen fractured when load value is up to 12 kN. On the other hand, (SE(T)) on SiC-rich side specimen continues to open till an 1.6 mm opening value at 20 kN load.
Number of cyclic load-crack propagation diagram of M(T) samples obtained from FGM2 with stress ratio R = 0.1 condition is shown in Figure 10. Here, 1–4 refer to specimen numbers from innermost (aluminum-rich side) to outermost (SiC-rich side) regions of cylinder, and specimens fractured at 12,880, 27,000, 34,000, and 48,000 number of cyclic loads, respectively. It can be seen that the fatigue life increases to almost 350% because of increase in SiC rate.
Number of cyclic load-crack propagation diagram of SE(T) samples obtained from FGM1 (both of SiC-rich side and aluminum-rich side) with stress ratio R = 0.1 is shown in Figure 11. It was determined that the crack growing rate increased after 14,400 cycles for the aluminum-rich side SE(T) sample. However, after 28,800 cycles, the crack growing rate increased dramatically and after 36,850 cycles, sample fractured in a short time. On the other hand, SiC-rich side SE(T) sample’s crack growth rate was very slow up to 13,000 cycles under the same cyclic load and after 13,000 cycles, the growth rate increased gradually. Crack growth rate increased dramatically after 190,000 cycles and sample fractured in a short time after 214,000 cycles. Under the same fatigue load, it was determined that the SiC-rich side SE(T) sample had fatigue life more than 500% compared to the aluminum-rich side SE(T) sample.
Number of cyclic load-crack propagation diagram of SE(T) samples obtained from FGM1 and FGM2 aluminum-rich side with stress ratio R = 0.1 condition is shown in Figure 12. A sample belonging to FGM2 displays a quick fracture behavior compared to FGM1. Whereas FGM2 sample fractured at 36,850cycles, FGM1 sample fractured at 238,000 cycles. FGM1’s fatigue life was increased 1.5-fold compared to FGM2’s fatigue life, which is explained by Young’s modulus variation seen in Figure 1. Graphics show differences in variation of Young’s modulus. SiC distribution in FGM2 increases from the innermost region to the outermost region till 0.2 times wall thickness, and then the rise slows down. In FGM1’s inner region, distributions of SiC and in parallel with Young’s modulus are higher than in the FGM2’s. The Young’s modulus determined as E = 85 GPa innermost of cylinder wall thickness does not visually increase by 0.75 times wall thickness.
After the fatigue crack growth experiments finished, c and m, which are material-dependent coefficients of the Paris-Erdogan equation (Eq. (3)), were found for each FGM2 M(T) specimens. The crack propagation behavior of the samples, which were from the inner diameter to the outside diameter of the cylinder numbered from 1 to 4, was observed differently in each of the samples. Therefore, the c and m coefficients were observed different from each other. The FGM’s c and m coefficients are shown in Table 1.
FRANC2D finite elements program have been developed by the fracture group of Cornell University . The program is usually used for fracture mechanics and fatigue analysis. In this study, FRANC2D analysis was done for FGM2 M(T) specimens. The finite element model can be seen in Figure 13. It was accepted that the M(T) specimen was homogeneous in itself while modeling in FRANC2D. According to the analysis, obtained results from experimental and finite element modeling were similar to each other as seen in Figure 14.
|c||10−8||10−8||2 × 10−9||6 × 10−9|
In the literature, studies related to FGM have mostly focused on determining FGMs’ thermal properties using experimental, analytical, and numerical methods. FGMs’ fatigue and fatigue fracture behaviors have been tested using numerical and analytical methods and improved new approaches are developed to date. However, there are hardly enough experimental studies to support this.
In conjunction with this study, mechanical properties and fatigue crack propagation behavior were analyzed experimentally. The results can be summarized as follows:
FGMs can be manufactured easily by centrifugal casting. It is possible to obtain FGM having different properties by changing casting parameters, FGM thickness, and casting weight from reinforced mixture.
Since SiC density is higher than aluminum, it is dispersed mostly to the outer region of material because of the centrifugal force during centrifugal casting. Therefore, hardness, composition, and mechanical properties change throughout the FGM thickness.
Crack propagation behaviors of single-edge notched (SE(T)) on SiC-rich side and single-edge notched (SE(T)) on aluminum-rich side specimens are different from each other under the same fatigue load. Fatigue crack propagation both begins later and has long fatigue life on SiC-rich side.
Each middle tension M(T) specimen obtained by slicing wall thickness as four sections shows different crack propagation behaviors. As SiC rate increases, crack begins and propagations are delayed under the same experimental conditions. After all, fatigue life increases to approximately 350%.
p < 1 seems to be more advantageous than p > 1 condition after crack propagation experiments of FGM when crack propagation starts from single-edge notched (SE(T)) aluminum-rich side considering the gradient exponent.
This study was supported by the Scientific Research Department of Pamukkale University as a PhD. Thesis via Project 2009FBE006 . Some parts of this study were presented in the 16th International Conference on Machine Design and Production.