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Fatigue crack growth in SiC particulates reinforced Al matrix graded composite
Materials Science and Engineering A360 (2003) 191 /196 www.elsevier.com/locate/msea
Fatigue crack growth in SiC particulates reinforced Al matrix graded composite F.M. Xu a, S.J. Zhu a,b, J. Zhao a, M. Qi a, F.G. Wang a,*, S.X. Li c, Z.G. Wang c a
Department of Materials Engineering, Dalian University of Technology, Dalian 116024, China b Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan c Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China Received 17 January 2003; received in revised form 14 May 2003
Abstract The SiC/Al graded composite was fabricated by powder metallurgy processing and its fatigue crack growth behavior was studied. The volume percentage of SiC particulates was distributed from 5 to 30% layer by layer on the cross section. Since the aluminium was dissolved together, there was no evident interface between the two layers with different volume fraction of SiC particulates. Fatigue crack growth was in direction of from 5 to 30% SiC layers under sinusoidal wave-form. The retardation of fatigue crack growth was found when crack propagated from low volume fraction of SiC to high volume fraction of SiC. The crack deflection and branching between two layers were observed, which decreased crack growth rates. In view of crack tip driving force, the plasticity mismatch between the layers shielded crack tip driving force, i.e. decreased the effective J-integral at the tip of the crack as the plastic zone of the crack tip spread from the weaker material into the stronger material. # 2003 Elsevier B.V. All rights reserved. Keywords: SiC/Al graded composite; FGMMC; Fatigue crack growth; Retardation
1. Introduction The concept of functionally graded materials (FGMs) was proposed in 1980s to prepare thermal barrier materials usable not only for space structures and fusion reactors, but also for future space plane systems [1]. Since the structural components of the spacecraft are exposed to high heat load, the material has to withstand severe thermo-mechanical loading. To solve this problem, FGMs were fabricated by using heat-resistant ceramics on the high temperature side and tough metals with high thermal conductivity on low-temperature side. Recent development of FGMs has demonstrated that FGMs have potential for a wide range of thermal and structural applications, including thermal gradient structures, wear parts and metal/ceramic joining. A lot of systems such as Cu/Si3N4, Cu/Al2O3, Al/ Al2O3, Al/AlN, Mo/ZrO2, Ni/MgO, Ni/ZrO2, Ni/TiB2, * Corresponding author. Tel.: /86-411-470-8439; fax: /86-411470-8116. E-mail address: [email protected] (F.G. Wang). 0921-5093/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-5093(03)00397-6
Ni/TiC, Ti/PSZ and others were developed by powder metallurgy, or plasma spraying, or self-propagating high-temperature synthesis or other techniques [1 /3]. However, the applications of FGMs are still very few. One of the most important reasons is lack of understanding for their mechanical behavior, e.g. there is little research on fatigue crack growth in FGMs [4]. Since the stress and strain distributions in FGMs are different from those in uniform materials, mechanical analysis and calculation have been conducted to establish the fundamental relationship between material gradation and mechanical properties of FGMs [2,3]. For example, Erdogan [5] has discussed a number of aspects of fracture mechanics of FGMs. Jin and Noda [6] showed that the crack tip fields in general nonhomogeneous materials are identical to those in homogeneous materials as long as the material properties are continuous and piece-wise continuously differentiable. Compared with the study on mechanics, experimental research on mechanical behavior, particularly cyclicdependent or time-dependent behavior, is not enough. Therefore, the authors selected discontinuously rein-
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forced metal matrix composites (MMCs) to make the volume fraction of reinforcements distribute gradually [4], because the MMCs have been well studied and applied as components in engineering [7 /20]. Thus, it is feasible to compare the mechanical behavior of the functionally graded metal matrix composites (FGMMCs) to the homogeneous MMCs. Since there are the effects of reinforcement on precipitation-hardening and other factors, the effects of volume fraction on fatigue crack growth behavior in Al alloy matrix composites are not simple and contradictory sometimes [7,11,12,16,19]. Generally, increasing the volume fraction of the particulates resulted in higher crack growth resistance at low crack growth rates due to higher crack closure effects [18,19]. However, the fracture of large particulates ahead of the crack tip, the more pores and different precipitation-hardening effects may cause crack growth rates increases with an increase in volume fraction of particulates [11,18]. Therefore, pure Al is selected as the matrix and medium sized particulates as the reinforcements in the present research. The purpose of the present work is to observe fatigue crack growth behavior in a FGMMC, SiC particulates reinforced Al matrix (SiC/Al) graded composite. Whether the mechanisms of fatigue crack growth in MMCs can be used in FGMMCs are to be discussed.
2. Material and experimental methods The materials used were gradient-distributed SiC particulate reinforced aluminium matrix composites (SiC/Al graded composite), which were fabricated by powder metallurgy techniques. The average size of the aluminium powders was 43 mm and the silicon carbide powders was 7 mm, respectively. Aluminium powders with 5, 10, 15, 20, 25 and 30 vol.% SiC were blended by a ball milling method for 17 h, with the ethanol as dispersant agent and degassed in a vacuum machine. The powders mixed according to the designed value were poured into a metal die. Die wall lubrication was applied by brushing natrium stearate solution. Care was taken to ensure that the powder was distributed evenly within the die cavity. The green components were compacted at 177 MPa. Sintering was carried out at 873 K and at a pressure of 23 MPa with an automatic hot-press machine, using the BN powder as the high temperature lubricant. The hot-pressing was conducted continuously with high-purity argon gas at a pressure of 2 bar and at a flow rate of 0.12 m3 h 1 throughout the sintering process. The thickness of the hot-pressed compact was 10 mm with six layers. The thickness of each layer was 0.5 mm of the middle four layers and 3 mm of the 5 vol.% SiC layer and 5 mm of the 30 vol.% SiC layer.
Fig. 1. Photograph of SiC/Al graded composite showing graded microstructure from 5 to 30% SiC layers.
The microstructures of the SiC/Al graded composite are shown in Fig. 1. In the 30% SiC layer, there are more pores than in other layers, since the sintering temperature and/or pressure may be lower for the 30% SiC composite. It can be seen that the matrix was dissolved together; there was no evident interface between the adjacent layers with different volume fractions of SiC (Fig. 2). However, the pure Al colony exists, which is in the same size as original Al powders (Fig. 2(b)). The single edge notched three point-bending (3PB) specimens were cut from the compact using electrodischarge machining (EDM) and used for fatigue crack growth tests. The height of the specimens was 10 mm, the thickness 5 mm and the length 50 mm. A 2 mm long notch was on the side containing the lowest concentration (5 vol.%) of silicon carbide. Therefore, the direction of fatigue crack growth was from 5 to 30 vol.% SiC layer. Pre-crack from the notch was made by fatigue tests with a decreasing load method. The fatigue crack growth tests were conducted by a Shimadzu servohydraulic testing machine at room temperature according to ASTM E399 guidelines. The frequency of fatigue tests was 20 Hz with a sinusoidal waveform and a stress ratio of 0.1. Crack length was measured using a traveling optical microscope with an accuracy of 10 mm. The crack growth path and fracture surfaces were observed by scanning electronic microscope (SEM) operating at 20 kV.
3. Results and discussions 3.1. Fatigue crack growth rate Fatigue crack length versus number of cycles in SiC/ Al graded composite is shown in Fig. 3. It can be seen that crack growth is not continuous as observed in homogeneous MMCs [11,12]. When the fatigue crack propagates from one layer to another, a decrease in
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identical to those in a homogeneous material if the material properties are continuous and step-wise continuously differentiable. Hence, the stress intensity factor concept can still be used to study the fracture behavior of FGMs [6]. Fig. 4 shows that the variation of the fatigue crack growth rate, da/dN, as a function of the stress intensity factor range, DK, for the SiC/Al graded composite. It is can also be seen that the retardation of fatigue crack growth occurs from one layer to another. In the present specimen, fatigue crack propagates from the less SiC particulates layer to the more SiC particulates layer. Therefore, it is expected the reason for the retardation of fatigue crack growth is the more SiC particulates layer has higher resistance to crack growth. However, the retardation was also observed when fatigue crack propagates from the more SiC particulates layer to the less SiC particulates layer [4]. 3.2. Retardation mechanism of fatigue crack growth
Fig. 2. Microstructures of SiC/Al graded composite showing interfaces between layers: (a) between 5 and 10% SiC; (b) between 15 and 20% SiC.
slope of the curve can be found. This means retardation of fatigue crack growth occurs at transition region between two layers. For non-homogeneous materials, it is still argued that whether the stress intensity factor can be used to evaluate the fatigue crack growth rate, but the results by Jin and Noda [6] showed that the crack tip fields are
Fig. 3. Fatigue crack length versus number of cycles in SiC/Al graded composite. A. Between 5% SiC and 10% SiC; B. Between 10% SiC and 15% SiC; C. Between 15% SiC and 20% SiC; D. Between 20% SiC and 25% SiC.
In order to understand the phenomenon of retardation of fatigue crack growth at transition region between two layers, the fatigue fracture surfaces and the crack path were examined and analyzed with a SEM. Fig. 5(a) and (b) show fractographs of the fatigue fracture surfaces at transition region between two layers for the SiC/Al graded composite. It can be seen that there are steps at transition region between two layers which means the change of the crack growth direction occurs. The dimples can be observed in the less volume fraction of SiC particulates layers or in the last stage of crack growth. SiC particulates in the dimples can be found (Fig. 5(c)). The ductile fatigue striations are seldom observed in 5% SiC layers, which may occur in original Al colony as shown in Fig. 2(b). The addition of SiC particles brings about brittleness in the materials and
Fig. 4. Fatigue crack growth rate as a function of stress intensity factor range in SiC/Al graded composite (numbers in the figure denote the crack length). A. Between 5% SiC and 10% SiC; B. Between 10% SiC and 15% SiC; C. Between 15% SiC and 20% SiC; D. Between 20% SiC and 25% SiC.
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Fig. 5. Fracture surfaces of fatigue crack growth in SiC/Al graded composite. (a) Transition region between 15 and 20% SiC layers; (b) transition region between 20 and 25% SiC layers; (c) dimples and particulates in 15% SiC layer; (d) fatigue striations in 5% layer.
constrains plastic deformation in the matrix of the SiC/ Al graded composite. Therefore, the fracture surface becomes flat with increasing volume fraction of SiC particulates. Fig. 6 shows the tortuous crack propagation path. The deflection and branching of fatigue crack occurs at transition region between two layers in SiC/Al graded composite. It is known that crack branching yields an increase in the crack surface with increased energy consumption. It was reported that crack branching decreases the local stress intensity factor at the crack tip [14]. After branching, the fatigue crack propagates along one of branched cracks. This crack deflects from its original propagation direction. The deflection of crack can decrease the fatigue crack growth rate [15]. There are two kinds of crack deflections: one is crack deflection at transition region between two layers and the other is periodic crack deflection by SiC particulates. The effects of crack deflection at transition region between two layers can be evaluated by a model as shown in Fig. 7. The stress intensity factor at the main pffiffiffiffiffiffi crack (line OA) tip is: KI /Fs/ pa; KII /0. Where KI and KII are model I and model II stress intensity factor, respectively. When the crack is approaching B at the transition region the deflection occurs. The crack tip will
bear tensile stress and shearing stress at the same time though there is only tensile stress far away. The stress intensity factor at the crack tip can be expressed as the function of nominal applied stress intensity factor [16]: kI F11 KI F12 KII kII F21 KI F22 KII
(1) (2)
where: u 1 3u cos cos 4 2 4 2 3 u 3u sin F12 sin 4 2 2 1 u 3u F21 sin sin 4 2 2 1 u 3 3u F22 cos cos 4 2 4 2
F11
3
(3) (4) (5) (6)
Here, u denotes the kink angle. Then the effective stress intensity factor of deflected crack is: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k kI2 kII2 F (u)KI (7) When the effect of deflection was considered, the
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Fig. 6. Fatigue crack path in SiC/Al graded composite. SEM micrograph showing crack deflection and branching (indicated by an arrow) in the transition region from 20 to 25% SiC layer.
effective stress intensity factor of whole cracks is given by: P a F (u) KI FD KI (8) DKeff Pi i ai Where FD denotes deflection factor and ai is the length of the ith crack. The deflection prediction of this model leads to a total growth distance is larger than the total fatigue crack length, a. The parameters were approximately measured based on the fatigue crack path of FGMMC (Fig. 7), the model predicts that the effective stress intensity factor range, DKeff is about 93pct of the nominal applied DKI . The crack deflection by single SiC particulate is relatively small (Fig. 6) although this may be important for homogeneous MMCs. The principal effects of particulates on fatigue crack growth in homogeneous MMCs are roughness-induced crack closure (e.g. due to periodic crack deflection by SiC particulates) in the wake of crack tip [17 /19]. The crack closure decreases the effective stress intensity factor at crack tip, and therefore, decreases fatigue crack growth rate. Thus, fatigue crack growth rates decrease with an increase of volume fraction of SiC particulates. This is one of the reasons for the retardation of fatigue crack growth from less SiC particulates to more SiC particulates layers. However, this can not explain the retardation of fatigue
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crack propagates from the more SiC particulates layer to the less SiC particulates layer [4]. Recently, effects of plasticity mismatch between the layers on the shielding or amplification of crack tip driving force were examined by finite element analyses [21,22]. The numerical studies reveal that the effective Jintegral at the tip of the crack becomes smaller than the remotely applied J, as the plastic zone of the crack tip begins to spread across the interface from the weaker material into the stronger material [21,22]. The experimental results (Figs. 3 and 4) showing retardation of fatigue crack growth are consistent with this numerical analysis. There was no interface between the adjacent layers since aluminium matrix was dissolved together. But the deformation and rupture are different due to the change of volume fraction of SiC. When crack propagating from one layer to another, the stress /strain field of the crack tip change. In our research, the direction of crack propagation is from low strength layer to high strength layer, the crack spreads easily to the direction of the biggest shearing force owing to the increase of plastic deformation ability; this may be the main cause of crack deflection and branching.
4. Conclusions The gradient-distributed SiC particulate reinforced aluminium matrix composites (SiC/Al graded composite), were fabricated by powder metallurgy processing. Since the aluminium was dissolved together, there was no evident interface between the two layers with different volume fraction of SiC particulates. However, the retardation of fatigue crack growth was found when crack propagated from low volume fraction of SiC to high volume fraction of SiC. The crack deflection and branching at interfaces were observed, which decreased crack growth rates. This could be explained in view of crack tip driving force, the plasticity mismatch between the layers shielded the crack tip driving force, i.e. decreased the effective J-integral at the tip of the crack as the plastic zone of the crack tip spread across the interface from the weaker material into the stronger material.
Acknowledgements The authors gratefully acknowledge Shenyang National Laboratory for Materials Science for partial funding for this research.
References Fig. 7. Schematic diagram showing a model of crack deflection.
[1] L.M. Sheppard, Ceram. Bull. 71 (1992) 617.
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[2] S. Suresh, A. Mortensen, Fundamentals of Functionally Graded Materials, Institute of Materials, London, UK, 1998. [3] A. Mortensen, S. Suresh, Int. Mater. Rev. 40 (1995) 239. [4] F.M. Xu, M. Qi, S.J. Zhu, J. Zhao, F.G. Wang, S.X. Li, Z.G. Wang, Acta Mater. Sinica 38 (2002) 998. [5] F. Erdogan, Comp. Eng. 5 (1995) 753. [6] Z.H. Jin, N. Noda, ASME J. Appl. Mech. 61 (1994) 738. [7] S. Suresh, A. Mortensen, A. Needleman, Fundamentals of Metal Matrix Composites, Butterworth-Heinemann, Stoneham, MA, USA, 1992. [8] S.J. Zhu, L.M. Peng, Q. Zhou, Z.Y. Ma, K. Kucharova, J. Cadek, Mater. Sci. Eng. A282 (2000) 273. [9] S.J. Zhu, D. Mukherji, W. Chen, Y.X. Lu, Z.G. Wang, R.P. Wahi, Mater. Sci. Eng. A256 (1998) 301. [10] S.J. Zhu, L.M. Peng, Z.Y. Ma, J. Bi, F.G. Wang, Z.G. Wang, Mater. Sci. Eng. A215 (1996) 120. [11] Y. Sugimura, S. Suresh, Metall. Trans. A 23A (1992) 2231.
[12] J.K. Shang, W. Yu, R.O. Ritchie, Mater. Sci. Eng. A102 (1988) 181. [13] Z.M. Sun, J.B. Li, Z.G. Wang, W.J. Li, Acta Metall. 40 (1992) 2961. [14] M. Levin, B. Karlsson, Composites 24 (1993) 288. [15] S. Suresh, Metall. Trans. A 16A (1985) 249. [16] T.L. Anderson, Fracture Mechanics, second ed, CRC Press, Florida, USA, 1998. [17] K. Li, X.D. Jin, B.D. Yan, P.X. Li, Composites 23 (1992) 54. [18] J. Llorca, Prog. Mater. Sci. 47 (2002) 283. [19] J.J. Mason, R.O. Ritchie, Mater. Sci. Eng. A231 (1997) 170. [20] G. Liu, J.K. Shang, Acta Mater. 44 (1996) 79. [21] Y. Sugimura, P. Lim, C.F. Shih, S. Suresh, Acta Metall. 43 (1995) 1157. [22] A.S. Kim, S. Suresh, C.F. Shih, Int. J. Solids Struct. 34 (1997) 3415.
Fatigue crack growth in SiC particulates reinforced Al matrix graded composite F.M. Xu a, S.J. Zhu a,b, J. Zhao a, M. Qi a, F.G. Wang a,*, S.X. Li c, Z.G. Wang c a
Department of Materials Engineering, Dalian University of Technology, Dalian 116024, China b Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan c Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China Received 17 January 2003; received in revised form 14 May 2003
Abstract The SiC/Al graded composite was fabricated by powder metallurgy processing and its fatigue crack growth behavior was studied. The volume percentage of SiC particulates was distributed from 5 to 30% layer by layer on the cross section. Since the aluminium was dissolved together, there was no evident interface between the two layers with different volume fraction of SiC particulates. Fatigue crack growth was in direction of from 5 to 30% SiC layers under sinusoidal wave-form. The retardation of fatigue crack growth was found when crack propagated from low volume fraction of SiC to high volume fraction of SiC. The crack deflection and branching between two layers were observed, which decreased crack growth rates. In view of crack tip driving force, the plasticity mismatch between the layers shielded crack tip driving force, i.e. decreased the effective J-integral at the tip of the crack as the plastic zone of the crack tip spread from the weaker material into the stronger material. # 2003 Elsevier B.V. All rights reserved. Keywords: SiC/Al graded composite; FGMMC; Fatigue crack growth; Retardation
1. Introduction The concept of functionally graded materials (FGMs) was proposed in 1980s to prepare thermal barrier materials usable not only for space structures and fusion reactors, but also for future space plane systems [1]. Since the structural components of the spacecraft are exposed to high heat load, the material has to withstand severe thermo-mechanical loading. To solve this problem, FGMs were fabricated by using heat-resistant ceramics on the high temperature side and tough metals with high thermal conductivity on low-temperature side. Recent development of FGMs has demonstrated that FGMs have potential for a wide range of thermal and structural applications, including thermal gradient structures, wear parts and metal/ceramic joining. A lot of systems such as Cu/Si3N4, Cu/Al2O3, Al/ Al2O3, Al/AlN, Mo/ZrO2, Ni/MgO, Ni/ZrO2, Ni/TiB2, * Corresponding author. Tel.: /86-411-470-8439; fax: /86-411470-8116. E-mail address: [email protected] (F.G. Wang). 0921-5093/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-5093(03)00397-6
Ni/TiC, Ti/PSZ and others were developed by powder metallurgy, or plasma spraying, or self-propagating high-temperature synthesis or other techniques [1 /3]. However, the applications of FGMs are still very few. One of the most important reasons is lack of understanding for their mechanical behavior, e.g. there is little research on fatigue crack growth in FGMs [4]. Since the stress and strain distributions in FGMs are different from those in uniform materials, mechanical analysis and calculation have been conducted to establish the fundamental relationship between material gradation and mechanical properties of FGMs [2,3]. For example, Erdogan [5] has discussed a number of aspects of fracture mechanics of FGMs. Jin and Noda [6] showed that the crack tip fields in general nonhomogeneous materials are identical to those in homogeneous materials as long as the material properties are continuous and piece-wise continuously differentiable. Compared with the study on mechanics, experimental research on mechanical behavior, particularly cyclicdependent or time-dependent behavior, is not enough. Therefore, the authors selected discontinuously rein-
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forced metal matrix composites (MMCs) to make the volume fraction of reinforcements distribute gradually [4], because the MMCs have been well studied and applied as components in engineering [7 /20]. Thus, it is feasible to compare the mechanical behavior of the functionally graded metal matrix composites (FGMMCs) to the homogeneous MMCs. Since there are the effects of reinforcement on precipitation-hardening and other factors, the effects of volume fraction on fatigue crack growth behavior in Al alloy matrix composites are not simple and contradictory sometimes [7,11,12,16,19]. Generally, increasing the volume fraction of the particulates resulted in higher crack growth resistance at low crack growth rates due to higher crack closure effects [18,19]. However, the fracture of large particulates ahead of the crack tip, the more pores and different precipitation-hardening effects may cause crack growth rates increases with an increase in volume fraction of particulates [11,18]. Therefore, pure Al is selected as the matrix and medium sized particulates as the reinforcements in the present research. The purpose of the present work is to observe fatigue crack growth behavior in a FGMMC, SiC particulates reinforced Al matrix (SiC/Al) graded composite. Whether the mechanisms of fatigue crack growth in MMCs can be used in FGMMCs are to be discussed.
2. Material and experimental methods The materials used were gradient-distributed SiC particulate reinforced aluminium matrix composites (SiC/Al graded composite), which were fabricated by powder metallurgy techniques. The average size of the aluminium powders was 43 mm and the silicon carbide powders was 7 mm, respectively. Aluminium powders with 5, 10, 15, 20, 25 and 30 vol.% SiC were blended by a ball milling method for 17 h, with the ethanol as dispersant agent and degassed in a vacuum machine. The powders mixed according to the designed value were poured into a metal die. Die wall lubrication was applied by brushing natrium stearate solution. Care was taken to ensure that the powder was distributed evenly within the die cavity. The green components were compacted at 177 MPa. Sintering was carried out at 873 K and at a pressure of 23 MPa with an automatic hot-press machine, using the BN powder as the high temperature lubricant. The hot-pressing was conducted continuously with high-purity argon gas at a pressure of 2 bar and at a flow rate of 0.12 m3 h 1 throughout the sintering process. The thickness of the hot-pressed compact was 10 mm with six layers. The thickness of each layer was 0.5 mm of the middle four layers and 3 mm of the 5 vol.% SiC layer and 5 mm of the 30 vol.% SiC layer.
Fig. 1. Photograph of SiC/Al graded composite showing graded microstructure from 5 to 30% SiC layers.
The microstructures of the SiC/Al graded composite are shown in Fig. 1. In the 30% SiC layer, there are more pores than in other layers, since the sintering temperature and/or pressure may be lower for the 30% SiC composite. It can be seen that the matrix was dissolved together; there was no evident interface between the adjacent layers with different volume fractions of SiC (Fig. 2). However, the pure Al colony exists, which is in the same size as original Al powders (Fig. 2(b)). The single edge notched three point-bending (3PB) specimens were cut from the compact using electrodischarge machining (EDM) and used for fatigue crack growth tests. The height of the specimens was 10 mm, the thickness 5 mm and the length 50 mm. A 2 mm long notch was on the side containing the lowest concentration (5 vol.%) of silicon carbide. Therefore, the direction of fatigue crack growth was from 5 to 30 vol.% SiC layer. Pre-crack from the notch was made by fatigue tests with a decreasing load method. The fatigue crack growth tests were conducted by a Shimadzu servohydraulic testing machine at room temperature according to ASTM E399 guidelines. The frequency of fatigue tests was 20 Hz with a sinusoidal waveform and a stress ratio of 0.1. Crack length was measured using a traveling optical microscope with an accuracy of 10 mm. The crack growth path and fracture surfaces were observed by scanning electronic microscope (SEM) operating at 20 kV.
3. Results and discussions 3.1. Fatigue crack growth rate Fatigue crack length versus number of cycles in SiC/ Al graded composite is shown in Fig. 3. It can be seen that crack growth is not continuous as observed in homogeneous MMCs [11,12]. When the fatigue crack propagates from one layer to another, a decrease in
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identical to those in a homogeneous material if the material properties are continuous and step-wise continuously differentiable. Hence, the stress intensity factor concept can still be used to study the fracture behavior of FGMs [6]. Fig. 4 shows that the variation of the fatigue crack growth rate, da/dN, as a function of the stress intensity factor range, DK, for the SiC/Al graded composite. It is can also be seen that the retardation of fatigue crack growth occurs from one layer to another. In the present specimen, fatigue crack propagates from the less SiC particulates layer to the more SiC particulates layer. Therefore, it is expected the reason for the retardation of fatigue crack growth is the more SiC particulates layer has higher resistance to crack growth. However, the retardation was also observed when fatigue crack propagates from the more SiC particulates layer to the less SiC particulates layer [4]. 3.2. Retardation mechanism of fatigue crack growth
Fig. 2. Microstructures of SiC/Al graded composite showing interfaces between layers: (a) between 5 and 10% SiC; (b) between 15 and 20% SiC.
slope of the curve can be found. This means retardation of fatigue crack growth occurs at transition region between two layers. For non-homogeneous materials, it is still argued that whether the stress intensity factor can be used to evaluate the fatigue crack growth rate, but the results by Jin and Noda [6] showed that the crack tip fields are
Fig. 3. Fatigue crack length versus number of cycles in SiC/Al graded composite. A. Between 5% SiC and 10% SiC; B. Between 10% SiC and 15% SiC; C. Between 15% SiC and 20% SiC; D. Between 20% SiC and 25% SiC.
In order to understand the phenomenon of retardation of fatigue crack growth at transition region between two layers, the fatigue fracture surfaces and the crack path were examined and analyzed with a SEM. Fig. 5(a) and (b) show fractographs of the fatigue fracture surfaces at transition region between two layers for the SiC/Al graded composite. It can be seen that there are steps at transition region between two layers which means the change of the crack growth direction occurs. The dimples can be observed in the less volume fraction of SiC particulates layers or in the last stage of crack growth. SiC particulates in the dimples can be found (Fig. 5(c)). The ductile fatigue striations are seldom observed in 5% SiC layers, which may occur in original Al colony as shown in Fig. 2(b). The addition of SiC particles brings about brittleness in the materials and
Fig. 4. Fatigue crack growth rate as a function of stress intensity factor range in SiC/Al graded composite (numbers in the figure denote the crack length). A. Between 5% SiC and 10% SiC; B. Between 10% SiC and 15% SiC; C. Between 15% SiC and 20% SiC; D. Between 20% SiC and 25% SiC.
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Fig. 5. Fracture surfaces of fatigue crack growth in SiC/Al graded composite. (a) Transition region between 15 and 20% SiC layers; (b) transition region between 20 and 25% SiC layers; (c) dimples and particulates in 15% SiC layer; (d) fatigue striations in 5% layer.
constrains plastic deformation in the matrix of the SiC/ Al graded composite. Therefore, the fracture surface becomes flat with increasing volume fraction of SiC particulates. Fig. 6 shows the tortuous crack propagation path. The deflection and branching of fatigue crack occurs at transition region between two layers in SiC/Al graded composite. It is known that crack branching yields an increase in the crack surface with increased energy consumption. It was reported that crack branching decreases the local stress intensity factor at the crack tip [14]. After branching, the fatigue crack propagates along one of branched cracks. This crack deflects from its original propagation direction. The deflection of crack can decrease the fatigue crack growth rate [15]. There are two kinds of crack deflections: one is crack deflection at transition region between two layers and the other is periodic crack deflection by SiC particulates. The effects of crack deflection at transition region between two layers can be evaluated by a model as shown in Fig. 7. The stress intensity factor at the main pffiffiffiffiffiffi crack (line OA) tip is: KI /Fs/ pa; KII /0. Where KI and KII are model I and model II stress intensity factor, respectively. When the crack is approaching B at the transition region the deflection occurs. The crack tip will
bear tensile stress and shearing stress at the same time though there is only tensile stress far away. The stress intensity factor at the crack tip can be expressed as the function of nominal applied stress intensity factor [16]: kI F11 KI F12 KII kII F21 KI F22 KII
(1) (2)
where: u 1 3u cos cos 4 2 4 2 3 u 3u sin F12 sin 4 2 2 1 u 3u F21 sin sin 4 2 2 1 u 3 3u F22 cos cos 4 2 4 2
F11
3
(3) (4) (5) (6)
Here, u denotes the kink angle. Then the effective stress intensity factor of deflected crack is: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k kI2 kII2 F (u)KI (7) When the effect of deflection was considered, the
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Fig. 6. Fatigue crack path in SiC/Al graded composite. SEM micrograph showing crack deflection and branching (indicated by an arrow) in the transition region from 20 to 25% SiC layer.
effective stress intensity factor of whole cracks is given by: P a F (u) KI FD KI (8) DKeff Pi i ai Where FD denotes deflection factor and ai is the length of the ith crack. The deflection prediction of this model leads to a total growth distance is larger than the total fatigue crack length, a. The parameters were approximately measured based on the fatigue crack path of FGMMC (Fig. 7), the model predicts that the effective stress intensity factor range, DKeff is about 93pct of the nominal applied DKI . The crack deflection by single SiC particulate is relatively small (Fig. 6) although this may be important for homogeneous MMCs. The principal effects of particulates on fatigue crack growth in homogeneous MMCs are roughness-induced crack closure (e.g. due to periodic crack deflection by SiC particulates) in the wake of crack tip [17 /19]. The crack closure decreases the effective stress intensity factor at crack tip, and therefore, decreases fatigue crack growth rate. Thus, fatigue crack growth rates decrease with an increase of volume fraction of SiC particulates. This is one of the reasons for the retardation of fatigue crack growth from less SiC particulates to more SiC particulates layers. However, this can not explain the retardation of fatigue
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crack propagates from the more SiC particulates layer to the less SiC particulates layer [4]. Recently, effects of plasticity mismatch between the layers on the shielding or amplification of crack tip driving force were examined by finite element analyses [21,22]. The numerical studies reveal that the effective Jintegral at the tip of the crack becomes smaller than the remotely applied J, as the plastic zone of the crack tip begins to spread across the interface from the weaker material into the stronger material [21,22]. The experimental results (Figs. 3 and 4) showing retardation of fatigue crack growth are consistent with this numerical analysis. There was no interface between the adjacent layers since aluminium matrix was dissolved together. But the deformation and rupture are different due to the change of volume fraction of SiC. When crack propagating from one layer to another, the stress /strain field of the crack tip change. In our research, the direction of crack propagation is from low strength layer to high strength layer, the crack spreads easily to the direction of the biggest shearing force owing to the increase of plastic deformation ability; this may be the main cause of crack deflection and branching.
4. Conclusions The gradient-distributed SiC particulate reinforced aluminium matrix composites (SiC/Al graded composite), were fabricated by powder metallurgy processing. Since the aluminium was dissolved together, there was no evident interface between the two layers with different volume fraction of SiC particulates. However, the retardation of fatigue crack growth was found when crack propagated from low volume fraction of SiC to high volume fraction of SiC. The crack deflection and branching at interfaces were observed, which decreased crack growth rates. This could be explained in view of crack tip driving force, the plasticity mismatch between the layers shielded the crack tip driving force, i.e. decreased the effective J-integral at the tip of the crack as the plastic zone of the crack tip spread across the interface from the weaker material into the stronger material.
Acknowledgements The authors gratefully acknowledge Shenyang National Laboratory for Materials Science for partial funding for this research.
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