Effect of nano-clay addition and heat-treatment on tensile and stress-controlled low-cycle fatigue behaviors of aluminum-silicon alloy: Effect of nano-clay addition and heat-treatment

The objective of the present paper is to investigate the stress-controlled low-cycle fatigue behavior of piston aluminum-silicon (AlSi) alloy reinforced with nano-clay particles and T6 heat-treatment. The piston aluminum-silicon alloy strengthened by 1 wt.% nano-clay particles were prepared by the stir casting method and then subjected to the heat-treatment. The optical microscopy analysis demonstrates that heat-treatment changed the size, morphology, and distribution of silicon phases through the microstructure of the aluminum matrix. In addition to tensile tests, stress-controlled low-cycle fatigue experiments at different loading conditions including the variation of the mean stress, the stress rate, and the stress amplitude were conducted at room temperature. The obtained experimental results showed no clear improvement in either mechanical or fatigue properties of the material. Moreover, the density measurements using the Archimedes method reveal a higher content of the porosity in nano-composite. It was observed that the reinforcement (nano-particles and heat-treatment) can change the cyclic behavior of the AlSi alloy, significantly. The cyclic hardening feature of the AlSi alloy changed to cyclic softening and also the fatigue lifetime and the ratcheting resistance decreased after the nano-particles addition and heat-treatment. Through the microstructural analysis, it was indicated that the neglecting of higher kinematics of age hardening in nano-composite was the major source of mechanical properties reduction. In the end, it was shown that the fatigue lifetime of samples can be described adequately utilizing a modified plastic strain energy technique considering the mean stress effect.


INTRODUCTION
istons in internal combustion engines are one of the critical and heavy-duty components, which are subjected to Low-cycle Fatigue (LCF) and wear damages during engine performance [1,2]. Therefore, the utilized material should provide high resistance under cyclic loadings and also high strength to weight ratio for the fuel consumption and consequently reducing the gas emission. For this purpose, the aluminum-silicon alloys are a potential candidate because of their high strength to weight ratio, good castability, acceptable ductility, and corrosion resistance [3]. There are several concepts available that could achieve improvements in mechanical and fatigue properties through the piston design including the optimized geometries, novel materials, advanced manufacturing processes, and different strengthening methods [1]. One of the most common strengthening methods is the development of metal-matrix composites reinforced with ceramic particles, which have attracted great attention over the past decade [4]. Several studies [5][6][7] had demonstrated the superior mechanical properties of aluminum-matrix nano-composites in comparison to similar micro-composites with the same volume fraction of particles. In the context of the cyclic behavior, LCF properties of particle-reinforced aluminum-matrix composites had been investigated in the literature extensively [8][9][10][11][12]. Results indicate the inferior fatigue lifetime compared to their counterpart monolithic alloys. This was mainly due to the limited ductility of the metal matrix in the presence of the ceramic particles contrary to High-cycle Fatigue (HCF), in which the fatigue lifetime was mostly strength-dependent. Llorca [13] indicated that the particle cracking was the major source of the fatigue crack initiation and growth through the matrix in composites. On the other hand, Wallin et al. [14] pointed out that the particle fracture probability could be decreased by the particle size reduction. Therefore, it was desirable to investigate the LCF behavior of metallic materials reinforced by nano-sized ceramic particulates. Senthilkumar et al. [15] conducted fully reversed LCF tests on two materials including AA2014 aluminum alloy containing micro-and nano-Al 2 O 3 particles and its counterpart micro-composite, which were both followed by hot extrusion and T6 heat treatment. They showed that the hybrid micro/nano-composite offered a higher fatigue lifetime and cyclic hardening at high strain amplitudes in comparison to almost stabilized response of the micro-composite. Azadi et al. [16] conducted fully-reversed strain-controlled LCF experiments on piston aluminum alloys and their counterpart nano-clay reinforced and T6 heattreated nano-composites at different temperatures. They concluded that the fatigue behavior of the aluminum alloys was not influenced significantly by nano-particles and the heat treatment except a lifetime reduction at the temperature of 300 °C due to the over-aging phenomenon. Ghasemi Yazdabadi et al. [17] studied HCF and LCF responses of an aluminum alloy reinforced with nano-SiC particulates prepared by the powder metallurgy route. They showed that the HCF resistance of nanocomposites improved followed by increasing the tensile strength while increasing the volume fraction. However, the LCF lifetime reduced as a result of the limited slip distance of dislocations caused by hard particles. Jabbari et al. [18] conducted strain-controlled LCF experiments on extruded AZ31B magnesium alloy reinforced by nano-Al2O3 particles at different temperatures. They indicated that although the mechanical properties of the material degraded at elevated temperatures, the fatigue lifetime increased as a result of ductility enhancement. Besides, they showed that the Jahed-Varvani model was able to describe the fatigue lifetime of the material appropriately. The common feature of aforementioned LCF tests is that they have been conducted under strain-controlled conditions. However, it is difficult to realize the cyclic loading mode in the actual service condition of the components since strains and stresses are related to each other by some constitutive behaviors. Therefore, knowing both the strain and stress fields and the relation between them in a component would allow both stress-and strain-controlled tests to be used to identify the fatigue behavior of the materials [19,20]. An important field of this area is stress-controlled LCF accompanying mean stress, which usually results in ratcheting i.e., the progressive accumulation of the inelastic strain and consequently to premature fatigue failure. The investigation of symmetric and asymmetric stress-controlled LCF behavior of aluminum alloys had been performed during recent years in the literature [21][22][23][24][25][26] but not as extensively as steel and magnesium alloys. In the context of the stress-controlled LCF experiments on metal-matrix composites, the ratcheting deformation in 6061 aluminum alloy reinforced with SiC particulates was systematically discussed by Kang [27] and Kang and Liu [28]. The effects of the particulate volume fraction, the heat treatment, the multiaxiality, the temperature, and some other factors on the ratcheting were discussed. Useful results along their purposes were that the ratcheting resistance of composite increased as the SiC volume fraction enhanced. Besides, the ratcheting behavior of composite had a great time-dependence even at low temperatures, which implied the presence of the creep component in the total ratcheting deformation. Regarding the stresscontrolled LCF loading on nano-composites, Goh et al. [29] investigated the effect of nano-sized Y2O3 particulates addition into magnesium alloys in different volume fractions on the cyclic plastic response under stress-controlled LCF loading. They showed that the intensity of cyclic hardening in nano-composite increased with the volume fraction of reinforcements, which was a result of the forest dislocation's pinning role of dispersed nanoparticles. P Through the above literature review, studies demonstrated the advantage of nano-particles addition [5][6][7][15][16][17][18] and the heat treatment [15,16] on mechanical and fatigue properties improvement of metallic materials. Regardless of the little investigations that were carried out on the strain-controlled LCF behavior of nano-composites [15][16][17][18], there was only one investigation [29] focusing on stress-controlled LCF behavior of metal matrix nano-composites to the author's best knowledge. The promising results of such loading conditions in micro-composites [27][28] and also fewer studies on stresscontrolled LCF behavior of aluminum alloys [21][22][23][24][25][26] in comparison to other metallic materials, motivated the present investigation to be made. Therefore, the objective of this article was to evaluate the effect of the addition of nano-clay particles and the heat treatment on mechanical and stress-controlled LCF properties of piston AlSi alloys.

Materials Processing
he matrix material, which was utilized in the present research, was a cast aluminum-silicon (AlSi) alloy (ENAC-48000). This AlSi12CuNiMg alloy had been widely utilized in the manufacturing of engine pistons in automotive industries. In the primary ingots of this AlSi alloy, the chemical composition is measured as Si: 12.7 wt.%, Ni: 0.8 wt.%, Cu: 1.16 wt.%, Fe: 0.56 wt.%, Mg: 1.00 wt.%, Zn: 0.16 wt.%, Mn: 0.12 wt.% and the aluminum as balance. Two groups of specimens were made in this research, including aluminum alloy specimens reinforced with nano-clay particles and the original un-reinforced alloys for comparison. The fabrication method of original aluminum alloys is a permanent mold gravity casting method described in the following paragraph: The aluminum ingots were first melted and the temperature was held at 700 °C for 2 hours in an electrical resistance furnace [30,31] before pouring them into a permanent steel mold. For the production of 1 wt.%, nano-clay particles reinforced specimens with the stir-casting process, clay (type: montmorillonite K10) as nano-particles with the chemical composition according to Tab. 1 were used. In this research, nano-clay particles were first pre-heated to the temperature of 420 °C for 20 minutes [31,32] to achieve a better wettability of nano-clay particles in the aluminum melt. The nano-particles powder was wrapped in aluminum foil. Then, they were added gradually to the aluminum melt. The clay amount is 2 g by 2 g in order to eliminate any gas accumulations in the aluminum melt. The density of the nano-clay particles (0.5 g/cm 3 ) was lower than that of the molten aluminum. The density of the aluminum alloy was 2.7 g/cm 3 . This causes the floating of nanoparticles in the crucible surface. To get an appropriate distribution of reinforcements in a uniform condition in the molten aluminum alloy, a steel stirrer was used. This stirrer was redesigned in order to have a falling stream in the melt through the casting process. It should be noted that high stirring time and rotational speed can result in better dispersion of nanoparticles in the melt. On the other hand, it caused the degradation of mechanical properties because of the formation of some undesired chemical components and increasing the gas entrapment in the melt [6,30,33]. It should be noted that for the nano-composite, it took 20 minutes to put the molten aluminum in the steady-state condition after adding the nanoclay particles. Then, the resulting composite slurry was poured into the cast-iron mold. After the casting process, all initial cylinders of aluminum alloys and nano-composites were cooled down in the air. Then, the machining process was performed to fabricate the standard-sized samples from initial casted cylinders. For these specimens, the geometry, which is suited for both tensile and fatigue tests, is illustrated in Fig. 1. In addition, mechanical polishing was done to have a mirror-like surface. After machining, the nano-composite specimens were subjected to T6 heat treatment to the following schedule: a solution treatment of the alloy at 500 °C for 1 hour, water quenching and then artificial aging at 300 °C for 2 hours (air-cooled) [16,34].

Microstructural Evaluation
For investigating the material microstructure, aluminum alloy and nano-composite specimens were firstly mounted. This job was done with the Struers Citopress embedding device. Then, they were subjected to a five-step grinding process at 300 T rpm and under 4 N. Moreover, the last stage for having smooth surfaces was four-step polishing in the water-based diamond lubricant and also was using the etchant of Keller's reagent solution. Microstructural characterizations before testing were carried out using the optical microscopy (OM) of Keyence VHX5000. In addition, the ICNA energy dry cool 350 was utilized as the energy-dispersive X-ray spectroscopy (EDS). For the image of the field emission scanning electron microscopy (FE-SEM), the JEOL-7200F equipment was also used. Furthermore, the porosity content of the samples as a measure of void spaces in the materials was determined by comparing the measured density of the samples using the Archimedes method with that of their theoretical density. The details of this method were referred to in the literature [35].

Tensile and Fatigue Testing
Uniaxial tensile and LCF experiments were carried out using an automated mechanical testing machine (Instron Servohydraulic testing machine), equipped with the 100 kN load cell. Instron room temperature extensometer was used in order to measure the strain value through the test. Tensile tests were done at a constant strain rate of 2.5×10 -3 s -1 at room temperature, based on the ASTM E8M standard testing procedure [36]. The fatigue tests were carried out in a tension-compression engineering stress-controlled loading mode at room temperature according to the standard fatigue testing procedure of ASTM E466 [37]. The response of materials to varied the stress amplitude, the mean stress and the stress rate were examined and the detailed loading conditions for original aluminum alloys and nano-composites are presented in Tabs. 2 and 3, respectively. It should be noted that σ a was the stress amplitude, σm was the mean stress and σ˙ was the stress rate. Since the cyclic loading condition was tensile-compressive, the stress distribution was uniform on the cross section of the sample. Therefore, cracks would initiate either on the specimen surface (through the gauge length) or inside the sample. However, the fatigue lifetime of samples was defined as the cycle number, corresponding to the first abrupt reduction of the load carrying capacity in the strain amplitude diagram versus the number of cycles. It should be noted that "AlSi" was used for the original aluminum alloy (without reinforcement) and "AlSi_N_T6" referred to the heat-treated nano-composite through the rest of the paper.

Microstructure Characterization
he optical micrographs of original aluminum alloys (AlSi) and heat-treated nano-composites (AlSi_N_T6) were depicted in Fig. 2-5. As a first observation, the finer microstructure of AlSi_N_T6 compared to AlSi alloys could be observed. It was commonly confirmed that the addition of hard particles to the metal-matrix materials resulted in reduction of the grain size [5,30], which was generally related to the pinning role of particles at the grain boundaries during the solidification. Such a phenomenon in the nano-composites can improve the mechanical strength of the matrix material through the Hall-Petch effect [38]. Considering Figs. 4 and 5, in the microstructure of AlSi alloys, four different phases could be distinguished. The first phase was the aluminum (α-Al) matrix with the white color. The second one is the AlSi phase with the dendritic morphology that is homogeneously distributed in the matrix. The third one is the silicon (Si) phase as a gray-colored area and finally, intermetallic phases as black-colored and light gray-colored script-like areas. Similar phases could be found in AlSi_N_T6, but a change in the shape and also the distribution of both Si phases and intermetallic phases could be observed as a result of the nano-particles addition and the heat treatment. In the following paragraphs, a discussion on the size and morphology of both Si and intermetallic phases, which can determine the mechanical and fatigue behavior of the material has been performed. As could be observed qualitatively in Fig. 5, the content of the Si phase was increased for AlSi_N_T6 compared to AlSi alloys. This could be a result of the presence of about 50% SiO 2 in the chemical composition of nano-clay particles according to Tab. 1. As reported in the literature [39], the Si phase in the piston aluminum alloys was usually detected to exist in two types including the flake shape and the coarse primary blocky shape, in which the primary Si phase had a dominant role in the determination of mechanical properties [40][41]. Based on reports in the previous research [16], the circularity of the Si phase increased as a result of the heat treatment that implied a higher number of blocky shape Si particles compared to the needle shape ones in AlSi_N_T6. This result was consistent with the reports in the literature [42][43][44], which states that after the heat treatment, Si particles tend to become spherical. Such results can cause an improvement in the mechanical properties [40,44]. Besides, the size of blocky Si particles increased as a result of nano-particles and the heat treatment, which could be a source of reduction in fatigue lifetime and mechanical properties in the base metal [43]. The distribution of intermetallic phases was similar in both AlSi alloy and also AlSi_N_T6. However, it was demonstrated quantitatively in the previous research [16] that the content of these phases and their sizes in AlSi-N_T6 were lower than the base AlSi alloys. Lower content and size of intermetallic phases were reported to cause better fatigue performance [45][46].    To study the material microstructures more accurately, the FE-SEM images were depicted in Fig. 6-7 for both AlSi alloys and AlSi_N_T6. The Intermetallic phases could be distinguished easily from the rest of the microstructure. As it could be observed, the intermetallic phases in AlSi_N_T6 have a nearly needle-shaped morphology, which could act as stressconcentration sites and eventually reduce mechanical properties [47]. For the determination of the dominant chemical element of intermetallic phases, the EDS results for AlSi_N_T6 were depicted in Fig. 8. Both Si and intermetallic phases could be found through the aluminum matrix. The elements, which have percentages of more than 1% including Al, Si, Cu, Mg, and O according to Tab. 1, were presented. As it could be observed, two main intermetallic phases including Cu-rich and Mg-rich could be distinguished. The presence of such intermetallic phases could result in the improvement of mechanical properties [48]. It is widely accepted that nano-particles have a high tendency to attract each other and create agglomerations as a result of their high surface to volume ratio. The agglomerations are a possible site for the crack nucleation and therefore, could be the reason for achieving undesirable mechanical properties compared to the original metal matrix. Nevertheless, reaching completely distributed single nano-particles is quite impossible in most cases [7]. The dispersion of nano-particles in the metal matrix is highly dependent on the processing route. Fig. 9-10 demonstrates the FE-SEM images of the surface of AlSi_N_T6 sample at two typical sites. Fig. 9 exhibits the nano-clay particle distribution in the aluminum matrix. A highly magnified FE-SEM image for AlSi_N_T6 at a clustered particle site is depicted in Fig. 10 and its counterpart EDS results in Fig. 11. The elements, which had percentages more than 1% including Al, Si, Cu, Mg, and O according to Tab. 1, were presented. From Fig. 11, it was easy to recognize the nano-particles dispersed in the aluminum matrix by focusing on the two most abundant elements including Si and O in the nano-clay chemical composition. Observations indicated that the dispersion of nano-particles was proper but not perfect and so desirable and therefore, some small degrees of agglomerations were detected in the microstructure.

Density Measurement
It could be observed in Fig. 7 that some black tiny areas were present in the microstructure of AlSi_N_T6, which represents the micro-porosity areas. It has been indicated in several studies [7,[49][50] that an enhancement in micro-porosity content would be achieved after nano-particles addition to the metal matrix, which results in mechanical properties degradation. Such a phenomenon was mainly attributed to poor wettability features of ceramic particulates [7,49], which stimulated the pore nucleation at nano-particles sites or agglomeration sites. The results of the pore measurement of both AlSi and AlSi_N_T6 using the Archimedes method are presented in Tab. 4. As it could be seen in Tab. 4, the porosity content of AlSi_N_T6 has increased in comparison to its counterpart AlSi alloy following the reports in the literature [7,[49][50].

Tensile Properties
The tensile flow curves of AlSi alloys and AlSi_N_T6 are depicted in Fig. 12. Moreover, the measured mechanical properties corresponding to tensile curves were presented in Tab. 5. Based on the results, AlSi_N_T6 showed different tensile properties compared to AlSi alloys. The yield strength and also the ultimate tensile strength in the nano-composite reduced by 7% and 5% respectively. In addition, the elastic modulus decreased by 21%. However, the elongation percent increased by about 2.5 times with respect to AlSi alloy.

Cyclic behaviors
The results of cyclic deformation had been presented focusing on mean stress, stress amplitude, and stress rate effects, respectively. where the horizontal axis is located at the mean stress axis. The softer response of AlSi_N_T6 means a higher plastic strain amplitude and as a consequence a wider hysteresis loop. Besides, the width of hysteresis loops of AlSi alloys demonstrated a decreasing trend, which implies the cyclic hardening behavior, whereas the mentioned width has an increasing trend in AlSi_N_T6, which indicates the cyclic softening behavior of the material. Such an observation had been approved by the evolution of plastic strain amplitude of samples in Fig. 16. It could be seen in Fig. 16 that the AlSi alloys experience a decreasing trend of plastic strain amplitude over cycles, which implies the cyclic hardening feature of piston aluminum alloys. However, the cyclic hardening feature of monolithic alloys had been changed to a cyclic softening feature after the nano-particles addition and the heat treatment. Besides, as it was reported in the literature [22,23], a higher value of mean stress has resulted in higher responded plastic strain amplitude and also a higher rate of cyclic hardening in the case of AlSi alloys and a higher rate of cyclic softening in the case of AlSi_N_T6.       Fig. 17 indicates another evidence of the cyclic hardening/softening feature of the samples. As it could be observed in Fig. 18, AlSi alloys demonstrated a nearly constant mean strain over cycles, which increased as the mean stress increased. However, after the nano-particles addition and the heat treatment, the mean strain demonstrated an ascending order over cycles, which implies the ratcheting deformation. The rate of ratcheting strain (mean strain), increased as the applied mean stress increased. It is shown in the introduction that cyclic stress loadings with non-zero mean stresses could result in the ratcheting response. Nevertheless, the ratcheting strain for AlSi alloys showed no significant trend counting for the ratcheting behavior even though the applied mean stress for two tests was positive.
On the other hand, the applied mean stress in Fig. 13 was zero but still, the ratcheting deformation could be observed in AlSi_N_T6.  In the mentioned tests, the mean stress was equal to zero and the stress rate had been set to 100 MPa/s. As commonly noted in the literature [22,23], with increasing the stress amplitude, the strain amplitude also increased and exhibited a higher degree of hardening in the case of the AlSi alloy and softening in the case of AlSi_N_T6. From Fig. 19, a great difference between the response of as-cast AlSi alloys and AlSi_N_T6 to stress amplitude variations could be observed. First of all, despite the zero applied mean stress on these tests, the mean strains were non-zero. This fact could be also confirmed from the curves of the mean strain versus cycles in Fig.  22. Generally, the asymmetrical behavior of the material under fully-reversed cyclic loadings was related to the different deformation mechanisms operating in tension and compression. The tests related to AlSi alloys in Fig. 22 illustrated the tensile mean strain, which implied the larger deformation resistance of the material under tension than compression. However, a nearly constant mean stress sustained most of the fatigue lifetime. This positive mean strain increased as the stress amplitude increased. That was in an agreement with the results in the literature [18,19]. The addition of nano-particles and the heat treatment changed the mean strain response of the material completely. The responded mean strain in AlSi_N_T6 was non-zero under fully-reversed stress-controlled loading similar to AlSi alloys, but with increasing the stress amplitude, the mean strain continuously decreased. It seems that the resistance of the material to the tensile deformation decreased with increasing the stress amplitude and as a consequence, the mean strain changed the polarity from tensile to compression. It could be observed in Figs. 19 and 22 that under the stress amplitude of 220 MPa, the mean strain was completely compressive. Besides, the mean strain was not constant during cycles and despite zero applied mean stress, a ratcheting deformation in tests with stress amplitudes of 200 and 220 MPa had been observed.  Figs. 23-26 depict the test results regarding the stress rate effect. In the mentioned tests, the mean stress was equal to zero and stress amplitude had been set to 210 MPa. It should be noted that experimental data for 10 MPa/s of the stress rate on AlSi_N_T6 were eliminated from these figures, due to have only two cycles of loading for the sample. From Figs. 24 and 25, it could be claimed that both the AlSi alloys and AlSi_N_T6 nano-composites presented a ratedependent response. The viscosity effect or the time-dependent response normally occurred at high temperatures as a consequence of the creep phenomenon, but it was shown that some materials experienced the viscosity effect even at room temperature. In such materials, the variation in the stress rate influenced the cyclic response [27]. Besides, the sensitivity of nano-composites to the stress rate variations was larger than their counterpart AlSi alloys. Increasing the stress rate, the strain amplitude of AlSi alloys changed negligibly contrary to AlSi_N_T6, which the change of the strain amplitude was significant. The common feature observed in the literature [24][25][51][52][53], was that with increasing the stress rate, the ratcheting strain decreases in rate-dependent alloys. Considering Figs. 23

Fatigue Lifetime prediction
The fatigue life of the samples has been investigated through this sub-section. Generally, in the LCF regime, the strainbased models have been utilized to predict the fatigue lifetime but in the special case of stress-controlled LCF loading, the validity of these models is questionable because of unusual changes in maximum and mean strains during stress-controlled fatigue tests. Therefore, the stress-based models were utilized to predict the fatigue lifetime. Such models [54][55] are presented originally for the high-cycle fatigue (HCF) regime, but some investigations [56][57] demonstrated the validity of these models for the LCF applications. The classical models like stress-and strain-based models were limited by a constant condition during the fatigue loading, for example, the constant temperature or the constant loading rate. Besides, they were restricted to uniaxial loading. The generalization of such models to multiaxial cases needs the consideration of equivalent forms of the stress and the strain or utilizing the critical plane theories [57]. Noting such difficulties, the energy-based models overcome these problems and even though, they consider both the stress and strain parameters in their formulations. Using such models facilitates the consideration of different loading conditions, the damage accumulation in samples and components with notches.
Therefore, a hysteresis energy-based model would be selected in this article in order to describe the fatigue lifetime of both AlSi and AlSi_N_T6 samples.  The power-law formulation describing the relationship between the energy related damage parameter P and fatigue lifetime Nf has been described as follows [57]: Where A and B are two material constants. The energy related damage parameter that has been utilized in this investigation is the plastic strain energy density to represent the fatigue damage inside the material. The plastic strain energy at each cycle had been reported to be representative of the necessary energy for the crack propagation [58]. Such a plastic strain energy is equal to the area of the stress-strain hysteresis loop, which could be written as follows [57]: The literature [56] suggests that the plastic strain energy could be approximated as the product of the stress range, Δσ, and the plastic strain range, Δε p , determined at the mid-life hysteresis loop, instead of integrating the hysteresis area over cycles. It has been known primarily that the tensile mean stress has a detrimental effect on the fatigue lifetime [59][60], while the compressive mean stress has a beneficial effect. Therefore, the influence of mean stress has been embedded in lifetime prediction models as an additional parameter. It had been indicated in the "Cyclic behaviors" section that in some tests, the ratcheting phenomenon had been observed. Generally, the effect of ratcheting on the fatigue lifetime had been considered as the effect of the mean stress on the lifetime [61][62]. Therefore, in this investigation, the mean stress effect on the fatigue lifetime has been considered as an additional factor. The plastic strain energy damage parameter has been modified to the following formulation [57]: Where m1 and m2 are two material constants. The value of material constants is calibrated using experimental data by a regression approach. The values of these parameters for both AlSi and AlSi_N_T6 had been reported in Tab. 6. Figs. 27-28 depictes the regression analysis on fatigue data of both AlSi and AlSi_N_T6 in a logarithmic scale analyzed by the plastic strain energy (PSE) model and its counterpart corrected version based on the mean stress effect. The coefficient of determination (CD) or the value has been considered for evaluating fitting capability of the lifetime model. The related formulation of the CD parameter has been presented in the literature [57]. As it could be observed, the coefficient of determination (CD) of AlSi_N_T6 data was smaller in value than AlSi data since the scatter in nano-composite data was larger. It is interesting to note that the mean stress correction factor in the energy model could enhance the accuracy of the model significantly, especially in the case of AlSi_N_T6. This argument could be proved by noting the CD parameter as its value increases in the PSE model with the addition of the mean stress effect. Besides, it has been proven that the dissipated plastic strain energy has a reverse relationship with the fatigue lifetime, which implied a negative slope in the following diagrams. Such a negative slope had not been seen for AlSi_N_T6 based on the uncorrected model but after the embedding of the mean stress correction factor into the models, the mentioned condition has been satisfied.  Table 6: The martial constants of un-corrected and corrected plastic strain energy based on mean stress effect for both AlSi and AlSi_N_T6.  By the extrapolation of the fitted curve for AlSi_N_T6, as a claim, it could be predicted that for lower stress/strain amplitudes, the fatigue lifetime for the heat-treated nano-composite specimens could be equal to or higher than that for non-heat-treatment samples. Fig. 29 illustrates the scatter-band analysis for both AlSi alloys and AlSi_N_T6 with the consideration of uncorrected and corrected plastic strain energy models. It could be observed that the scatter-band for AlSi_N_T6 data had significantly wider than the data corresponding to AlSi alloys. Such results explained the higher value of CD for AlSi alloys in comparison to nano-composites. It was seen that the energy model with the correction factor presented a smaller scatter-band in both cases of AlSi and AlSi_N_T6 samples in comparison to the un-corrected plastic strain energy model. It could be observed in Fig. 29 that the scatter-band parameter for AlSi alloys with the un-corrected model was about 2.5, while the corrected model presented the value of 1.6. Furthermore, in the case of AlSi_N_T6, the scatter-band in the uncorrected model was about 5000, while with the addition of the mean stress correction factor, the scatter-band parameter decreased considerably to about 3. It could be claimed that the present energy approach had a satisfying accuracy in the stress-controlled LCF lifetime prediction. The addition of a mean stress correction factor could enhance the accuracy of the model and also provide good results for the fatigue lifetime prediction in ratcheting-fatigue interaction cases. The simplicity and the consideration of both stress and strain parameters were other advantages of the presented model. As it could be seen in Figs. 27-28, the addition of the reinforcement by nano-clay particles and the heat treatment influenced the fatigue lifetime significantly. In many samples, the fatigue lifetime decreased more than 50%. Such a result was in an agreement with the literature [9][10][11].

Discussion
The microstructure, tensile, and stress-controlled LCF behaviors of AlSi alloys and AlSi_N_T6 nano-composites have thoroughly described in previous sections. It had been shown that the piston aluminum alloy presented a weaker and softer behavior in both tensile and fatigue experiments after the nano-particles addition and the heat treatment. In the two following sections, the role of nano-particles and the heat treatment on such a behavior will be discussed.

Effect of nano-clay particles
Most of the studies [3][4][5][6][7][30][31][32][33][34][35][49][50][51][52] had proved that the nano-particles addition to the aluminum alloy results in an enhancement of mechanical properties. Such an enhancement had been attributed to several strengthening mechanisms including Hall-Petch strengthening, enhanced dislocation density, Orowan strengthening, and load transfer effect. As it had shown in Tab. 5, the results of the present investigation were in contradiction with mentioned studies. It has been reported in the literature [7,30] that beyond a threshold nano-particles volume/weight fraction, the strength and elongation of Aluminum Matrix Nano-composites (AMNCs) would be declined as a result of excessive presence of particle agglomerations and micro-porosities. Also, very high casting temperature, stirring velocity, and time had been reported [30] to produce degraded mechanical properties in the stir-casting process. Since the elongation of AlSi_N_T6 in the present investigation has increased after the nano-particles addition and the heat treatment, the nano-particles cannot be considered as the major source of the poor performance of AlSi_N_T6. Particle agglomerations and micro-porosities would decrease the yield and ultimate tensile strengths as well as ductility of the material because of providing potential sites for crack initiation and accelerating the crack propagation. It has been indicated in Figs. 9-10 that some degrees of agglomerations are present in AlSi_N_T6. Nevertheless, with a qualitative comparison with similar micrographs of AMMNCs [6,7,30,51] the dispersion of nano-particles demonstrated no intensive heterogeneity and there were no large agglomerations (larger than 1 micrometer) exist in the microstructure of AlSi_N_T6.
The higher porosity content in AlSi_N_T6 in comparison to the AlSi alloy had been reported in Tab. 4. It had been shown [63] that the aluminum alloy with 10 wt.% nano-clay particles corresponding to 3.60% porosity content still offered enhanced strength and decreased ductility in comparison to the monolithic alloy. Particle agglomerations and micro-porosities were characteristic features of nano-composites. Their formation was inevitable during the processing of such materials; however, it was reported that nano-composites processed by the compo-casting method [49], the ultrasonic cavitation [46], and the extrusion after casting [50] offered lower agglomerations and porosities content in comparison to the stir-casting method. It had been observed in Figs. 23-26 that AlSi_N_T6 produced a cyclic softening behavior with more plastic strain amplitudes regarding the AlSi monolithic alloy. It had been proved in the literature [8][9][10][11][12]27,28] that the dislocation hindering role of ceramic particles results in a higher rate of cyclic hardening response and also the lower exhibited plastic strain. The response of nano-composites is the same but more effective in that way because of more particulate content in comparison to microparticles with the same volume fraction. The results of the present investigation also disagree with the mentioned phenomena. Such a poor fatigue performance of AlSi_N_T6 also follows the tensile properties. In general, it could be claimed that particle agglomerations and micro-porosities were not able to increase the ductility alongside the material strength reduction. The nano particles affected the response of AlSi_N_T6 but it could be claimed that the major source of poor performance of AlSi_N_T6 was the heat treatment.

Effect of heat treatment
The studies on AMNCs have accounted for the T6 heat treatment as an improver of mechanical properties [7,51,[63][64][65][66] and also the fatigue properties [51,[67][68][69] but such a positive effect has not been observed in the results of the present investigation. It could be claimed that the poor performance of AlSi_N_T6 was related to the excessive aging time and temperature of the T6 process. As it had been indicated in Figs. 2-5, the size and the circularity of Si particles within the microstructure of AlSi alloys enhanced after the nano-particles addition and the heat treatment. The spheroidization and the size reduction of eutectic Si particles have been reported to be the results of the solution treatment and artificial aging, respectively during T6 heat treatment [67]. Besides, the nano-particles addition had some effects on the size reduction of the eutectic Si as a result of enhanced Si particles nucleation at the nano-particles site. Such a change in the morphology could explain the significant strengthening and the increase in the ductility [51,66]; however, the reduction in the size of Si particles had not been met in this research. This observation implied a T7 over-aged state of AlSi_N_T6. It has been reported in several studies [51,68] that the presence of the nano-reinforcement could change the aging kinetics of the material. The segregation of elements like Mg at the matrix-reinforcement interface and grain boundaries, which resulted in the prevention of forming Mg2Si or MgZn2 precipitates, had been reported to reduce the precipitation hardening and subsequently, the detrition of mechanical properties. Regarding the above statements, it is necessary to use the lower aging time and temperature in comparison to those normally used in the literature for nano-composite materials [65] and inevitably optimize the heat treatment parameters with the objective of reaching the optimum strength and ductility combination in aluminum-based nano-composites. Such a work could be reserved for the future work. The weaker and softer behavior of AlSi_N_T6 during tensile tests could explain the cyclic softening behavior under stresscontrolled LCF loading. As it was reported in the literature [67], the excess aging time or temperature during T6 heat treatment could result in cyclic softening of the A356 alloy and subsequently producing severe plastic deformation in the material. Therefore, the wrongly chosen aging time and temperatures for AlSi_N_T6 appeared as the lower resistance of AlSi_N_T6 against the applied cyclic stress. It was obvious in Fig. 26 that the reduced ability of AlSi_N_T6 to the tensile deformation noting on the compressive mean strain in AlSi_N_T6 nano-composites even though the applied mean stress was zero. Therefore, AlSi_N_T6 accommodated the deformation mostly by the compressive deformation. Such an anisotropy in tension and compression conditions could explain the ratcheting deformation in AlSi_N_T6, as could be observed in Fig. 18.

CONCLUSIONS
n this research, tensile and stress-controlled LCF properties of piston AlSi alloys, with and without heat treatment besides nano-clay particles was investigated. The obtained experimental data showed the following highlights and behaviors:  The heat treatment could increase the size and circularity of the silicon phases.
I  Some small degrees of agglomerated nano-particles are detected in the microstructure.  The porosity content of AlSi alloy was enhanced after the nano-particles addition.  The mechanical properties of the AlSi alloy decreased after the nano-particles addition and the hat-treatment.  The cyclic response of the AlSi alloy after the nano-particles addition and the heat treatment changed from a cyclic hardening feature to a cyclic softening feature.  The resistance of the AlSi alloy against the ratcheting deformation reduces after the nano-particles addition and the heat treatment. The ratcheting deformation was observed in some nano-composite samples, even at zero mean stress.  A tensile mean strain is observed in many tests at fully-reversed stress cycling. Such a result implied the decreased resistance of the material against the tensile deformation, especially for nano-composite.  Nano-composite presented a rate-dependent response even at room temperature, unlike its counterpart monolithic alloy.  The fatigue lifetime of nano-composite was mostly less than 50% in comparison to its counterpart monolithic alloy.  It was shown that the major source of mechanical and fatigue properties degradation of nano-composite was related to the excessive aging time as a result of neglecting the higher aging kinetics in nano-composite.  The fatigue lifetime prediction of samples was done using a plastic strain energy approach. It was shown that the addition of a mean stress correction factor to the model could enhance the accuracy of the model considerably. For the further investigation, the fracture surface analysis could be performed on the failed sample (after the tests), in order to find the failure mechanism and the fracture behavior of the material. Moreover, this report could be considered to find the influence of the nano-clay addition and the heat treatment on the fracture behavior and the failure mechanism of studied materials, besides the effect of the mean stress, the stress amplitude and the stress rate. Moreover, performing a higher number of LCF testing on nano-composite samples with a pre-designed plan for loading conditions could help the researcher to investigate the material behavior in a high accurate state.