Micromechanical simulation and experimental investigation of aluminum-based nanocomposites

Mohammad Javad Ghasemi.Mohammad Silani.Ali Maleki.Mostafa Jamshidian

Department of Mechanical Engineering.Isfahan University of Technology.Isfahan.84156-83111.Iran

Keywords: Aluminum/nano-silica composites Powder metallurgy Micromechanics

ABSTRACT Ceramic reinforced metal matrix nanocomposites are widely used in aerospace and auto industries due to their enhanced mechanical and physical properties.In this research.we investigate the mechanical properties of aluminum/Nano-silica composites through experiments and simulations.Aluminum/Nanosilica composite samples with different weight percentages of silica nanoparticles are prepared via powder metallurgy.In this method.Nano-silica and aluminum powders are mixed and compressed in a mold,followed by sintering at high temperatures.Uniaxial tensile testing of the nanocomposite samples shows that adding one percent of Nano-silica causes a considerable increase in mechanical properties of nanocomposite compared to pure aluminum.A computational micromechanical model.based on a representative volume element of aluminum/silica nanocomposite.is developed in a commercial finite element software.The model employs an elastoplastic material model along with a ductile damage model for aluminum matrix and linear elastic model for nano-silica particles.Via careful determination of model parameters from the experimental results of pure aluminum samples prepared by powder metallurgy,the proposed computational model has shown satisfactory agreement with experiments.The validated computational model can be used to perform a parametric study to optimize the microstructure of nanocomposite for enhanced mechanical properties.

1.Introduction

The main advantages of composite materials originate from their lightweight.high specific strength.resistance to corrosion,and the potential to absorb energy.Due to high strength and hardness.metal matrix composites applications are increasing in auto and aerospace industries.Metal matrix composites reinforced with discontinuous fibers are produced by different procedures including powder metallurgy.injection casting.mechanical alloying.and various casting methods such as squeeze casting.semisolid casting.and stir casting [1].

Salehi et al.[2]made an aluminum/Nano-silica Nano-foam composite.They prepared aluminum Nano-composite specimens and investigated different weight fractions of Nano-silica reinforcing particles.Their experiments revealed that Nano-composites containing 0.5 and 0.75%weight fraction of Nano-silica.compared to pure aluminum.had a significant increase in their hardness.In addition,Vickers’s hardness increased up to 75%with the increase of Nano-silica weight fraction and subsequently reduced when the Nano-silica weight fraction reached 1%.Using an extrusion process,Issa et al.[3]created an aluminum matrix composite reinforced with Nano-silica particles.They showed that the addition of 1%weight fraction of reinforcing powder to the aluminum matrix results in substantial improvements to the mechanical properties of aluminum/Nano-silica composites compared to pure aluminum.Particularly,the hardness and ultimate tensile strength respectively increased by 41% and 24%.However.a 12.6% reduction in the ductility of Nano-composites in comparison with pure aluminum was reported.Sharifi et al.[4]investigated the effect of adding of 5%,10%.and 15% volume fraction of B4C powder to the aluminum matrix.They observed significant rises in hardness.compressive strength.and corrosion resistance in the 15% volume fraction specimen.Abdizade et al.[5]prepared an aluminum matrix composite by adding different weight fractions of magnesium oxide nanoparticles.They showed that stir casting and powder metallurgy can successfully be used to create aluminum-magnesiumoxide nanocomposites.They investigated the samples with 1.5%,2.5%.and 5% volume fraction of magnesium oxide and reported a 63%increase in hardness.Highest values of hardness were achieved with specimens molded and sintered at 850 and 625°C.respectively.Due to less porosity in the casting method,the compressive strength of the cast specimens was more than the sintered ones.

Recent studies have shown that the corrosion resistance of nanocomposites is profoundly affected by the volume fraction and distribution of the reinforcing particles and their strength and mechanical properties.For example.Alpas and Zhang [6]studied the corrosion behavior of Al-7wt%Si alloy reinforced with silicon carbide(SiC)particles.They performed corrosion tests on both the base and the reinforced alloys with 10%-20% volume fraction of particles,under various loading conditions.Their results show that at lower loads corresponding to the stresses less than the failure strength of particles,SiC particles act as load-carrying particles and hence reduce the corrosion in samples.

For particle-reinforced metal matrix composites.enhanced mechanical and physical properties are generally achieved by the proper and uniform distribution of particles in the matrix and the minor porosity and the absence of oxide films.Alipour et al.[7]investigated the microstructure and hardness of 7060 cast aluminum nanocomposites reinforced with SiC nanoparticles.In this work.mechanical properties and microstructure of 7068 aluminum nanocomposites prepared by stir casting and reinforced with 1%.2%.3%.and 5% SiC nanoparticles were investigated.Microstructural inspections showed that the presence of SiC nanoparticles results in grain size reduction,which in turn causes a significant increase in the hardness of nanocomposites.However,at high percentages of SiC nanoparticles (5% weight).the particles conglomerate at grain borders and cause a reduction in the hardness of the nanocomposite.

Modeling nanocomposites is of particular interest in investigating the effects of parameters such as particle weight fraction,nominal and true diameter of reinforcing particles.and particle distribution.Micromechanical simulations can be used to gain a better understanding of stress and damage evolution within a representative volume element (RVE) of the nanocomposite.Chawla et al.[8]used the finite element method to simulate a 3D model of an aluminum matrix composite reinforced with SiC particles.Compared to the experimental data.their model offered a good estimation of the mechanical properties and Young’s modulus of the aluminum matrix composites reinforced with 20% of SiC particles.The fracture of nanocomposites was also studied using novel numerical methods such as phase-field [9]and stochastic analysis[10].

Hung-Gou et al.[11]studied the mechanical properties and surface structure of aluminum matrix composites reinforced with SiC nanoparticles via molecular dynamics (MD) simulations.The tensile test of the nanocomposite was simulated under a fixed strain rate and periodic displacement boundary conditions.The effective elastic modulus and yield strength were obtained from the stress-strain curves.The MD simulation results estimated the yield strength of the nanocomposite with 1% weight SiC particles to be significantly higher than the yield strength of the A356 aluminum alloy.Furthermore.MD simulations indicated the tendency of aluminum atoms to arrange around the SiC particles and form a surface layer.a fact that has been validated by experimental findings.

Despite extensive experimental and computational research on particle-reinforced aluminum matrix composites.there is still research gaps in correlating experimental and simulation results.Computer simulations and parametric studies based on a validated micromechanical model can be used to obtain optimum microstructural features for enhanced mechanical properties of the composite.The aim of the present research is to establish and validate a micromechanical model of the nanoparticle reinforced aluminum matrix composites.The preparation of nanocomposite samples and the experimental tests are first described,followed by the presentation of the micromechanical modeling approach.Finally,the experimental and simulation results are compared and discussed.

2.Experiments

We investigate the effect of reinforcing nanoparticles on the mechanical properties of Aluminum/Nano-silica composites.Aluminum/Nano-silica specimens were prepared according to the ASTM E8M-04 standard [12].Tensile tests are performed on both the base metal and the nanocomposite.Fig.1a illustrates the shape and dimensions of the dogbone samples used in uniaxial tensile tests.Tensile tests were performed using a Santam STM-50 machine.

The composite specimens were prepared in a mold via powder metallurgy.The schematic of the mold is shown in Fig.1b.The mold components are made of CK45.as shown in Fig.1c.In short.the powder was compacted and consolidated in the mold.and then specimens were fused in the oven to yield the final composite specimens.The powder material used in this study comprises aluminum powder and Nano-silica powder.Aluminum powder with 99.5% purity and the particle size less than 45μm was purchased from Khorasan powder metallurgy Pte Ltd.Nano-silica powder was made from burning HTV silicone polymer in 700°C for an hour.The prepared powder structure is amorphous.UsingTransmission Electron Microscopy.the silica particle size in the powder was determined to be between 30 nm and 50 nm [3,13].

Fig.1.(a) The shape and dimensions of the specimens used in the tensile tests.(b)Schematic of the mold and pressing process,(c)Image of the mold components made for creating test samples via powder metallurgy.

The mixed Aluminum/Nano-silica powder with 0%,1%.2%.and 3%weight of Nano-silica was first weighted and mixed.The mixture of aluminum/Nano-silica powder had to be grinded.The milling process was done using a planetary ball mill machine.Ball to powder ratio was eight and the milling process was done in an argon atmosphere with the angular velocity of 300 revs per minute.Each step of the milling process produced 25 g of aluminum/silica powder.Finally,the mold was used for the compaction process.The maximum pressure of the hydraulic pump in the pressing machine was 4000 bar.Using a pressure gauge,the appropriate pressure was applied on the surface of the specimens.

For the sintering process.a vacuumed furnace was used.Both the pure aluminum samples and the aluminum/silica nanocomposite samples were sintered in a similar manner.An important aspect of the sintering process is the highly sensitive nature of its progress to temperature [14].Increasing the sintering temperature results in enhancing the mechanical properties of the sintered material through optimizing cavity morphology.Generally,the highest possible temperature results in better bonds and continuity in the sintered specimens.Considering the melting temperature of pure aluminum at 650°C and the furnace temperature tolerance of 35°C,the sintering temperature was set to 615°C.The heating rate was 10°C per second and samples were kept for 2 h at 615°C after which the furnace was turned off,and specimens were cooled inside.

Fig.2 illustrates the microstructure of 1%,2%,and 3%aluminum/Nano-silica nanocomposites after the sintering process without etching.For comparison,the microstructure of the pure aluminum specimen is also shown in this figure.The black dots in these micrographs represent the pores in the nanocomposite specimens.For the 3% aluminum/Nano-silica nanocomposite sample.the increased weight fraction of nanoparticles has led to the intensification of the agglomeration phenomenon and consequently.the increase in porosity percentage.

The sintered samples were directly used in tensile tests.A quasistatic tensile deformation was applied by setting the speed of clamps to 1 mm per minute.For each specimen.the tensile tests were repeated three times.Fig.3 shows the experimental stressstrain curves for pure aluminum and aluminum/Nano-silica composite samples with 1%.2%.and 3% weight percentages of Nanosilica particles.This figure demonstrates that the addition of reinforcing nanoparticles increases the tensile strength and yield strength of the material and reduces the sample ductility.The sample with 1% Nano-silica particles shows an optimum ductility and toughness compared to the samples with more nanoparticle weight percentage.The decreased ductility for increased nanoparticle percentage can be attributed to the presence of voids.as shown in Fig.2.

Fig.3.Experimental Stress-strain curves of aluminum/Nano-silica composite samples with different weight percentages of Nano-silica particles obtained from uniaxial tensile tests.

3.Simulations

In order to numerically simulate the tensile test of the nanocomposite.the Abaqus software package was employed.A python script is written to generate the RVE of the nanocomposite material[15].Setting prescribed values for the size and weight percentage of nanoparticles,the python script generates three-dimensional RVEs with a random distribution of spherical nanoparticles.

The RVE is meshed by Tetrahedral elements.The number of elements and nodes in the RVE for 1%weight nanocomposite were 15083 and 21133,respectively.To simulate the uniaxial tensile test,one face of the RVE is normally pulled with a steady displacement rate while symmetry boundary conditions are applied on all other faces.The experimental micrographs have shown that with increasing the weight percentage of nanoparticles.the probability of having voids increases.Therefore,voids were introduced into the RVE model.Particularly.for each 1% weight fraction of Nano-silica particles.0.1% volume fraction of randomly distributed spherical voids were added to the RVE.A sample nanocomposite RVE and its finite element mesh are shown in Fig.4.

For simulating the deformation process of nanocomposite RVE,proper material models are to be assigned to the matrix material and the reinforcing particles.In this study,the aluminum matrix is modeled as an elastoplastic material.including damage.Damage evolution in the aluminum matrix is simulated using a ductile damage model that predicts damage initiation due to nucleation,development,and coalescence of cavities[16].This model assumes that the equivalent plastic strain at damage initiation is a function of the equivalent plastic strain rateand the stresstriaxiality parameter η=-p/q with p being the pressure stress and q the equivalent Mises stress.Damage initiation criterion is expressed by the following equation:

Fig.2.Microstructure of aluminum/Nano-silica composites after the sintering process without etching:(a)pure aluminum,(b)1%Nano-silica,(c)2%Nano-silica,(d)3%Nano-silica.

Fig.4.A sample nanocomposite RVE and its finite element mesh.

where ωDis a state variable that steadily increases with plastic deformation.The model is to be supplemented by the equivalent fracture strain at damage initiation as well.

Along with the damage initiation criterion.Abaqus employs a damage evolution definition.It is assumed that damage evolution is directly correlated with plastic displacements and aluminum fracture energy.When the conditions for damage initiation are satisfied.the damage parameter increases according to the following equation [17]:

where L is a characteristic element length,is the equivalent plastic displacement after damage initiation,andis the effective fracture plastic displacement.

The damage parameters can be estimated from the uniaxial tensile stress-strain curve of the nanocomposite.Isight software was used to calculate the damage parameters.The software uses the experimental stress-strain curves of pure aluminum samples to calculate the material parameters of the elastoplastic and damage models through the definition of a reverse problem.For the sintered aluminum sample.the fracture strain 0.189.stress triaxiality parameter η = 2.1.and=1 is obtained.For aluminum.the modulus of elasticity 61 GPa.the Poisson’s ratio 0.29.and the density ρ=2710 Kg/m3was used.The equivalent plastic displacement at fracture defined as uf=2Gf/σywas set to 0.37 where σyis the yield stress and Gfis the fracture energy of aluminum [18].The aluminum fracture energy of Gf=16 MPa is used in this study [16].

The Nano-silica particles with a size range from 30 nm to 50 nm were randomly distributed within the RVE.Particle distribution in the matrix is assumed to be fully discrete.Nano-silica particles are assumed to be linear elastic with Young’s modulus 74 GPa and the Poisson’s coefficient 0.23 [21].To investigate the effect of nanoparticle weight percentage.the simulations are performed for nanocomposite RVEs with 1%.2%.and 3% weight of Nano-silica.

The average strain and stress theorems were used to calculate the effective properties of nanocomposites.Considering a given RVE with boundary ?！鮥n the domain Ω□,the space of admissible displacements u is denoted by U□.To guarantee that macro-scale stressand macroscale strainare admissible.the Hill-Mandel macro-homogeneity condition must be satisfied as follows:

where δε corresponds to δu.The Hill-Mandel macro-homogeneity condition is essentially equivalent to equality of the macro-scale and micro-scale virtual works.

Regarding the post-yield strain softening behavior of nanocomposite.the first order homogenization and hierarchical multiscale method is discouraged [19,20].However.the intend of the current study is not to capture the precise softening behavior of nanocomposites.Rather.the focus is on the yield stress and the ultimate strength as well as the hardening behavior which justifies the employed first order homogenization and hierarchical multiscale method.

Regarding the particle-matrix interface conditions.detailed modeling of the interface demands high computational costs.In metal matrix composites,the principal strengthening mechanisms are grain refinement,Orowan,and load transfer.Such mechanisms are effective in the presence of a proper interface between the matrix and the reinforcement particles.In other words.the enhancement of mechanical properties by the addition of reinforcement particles indicates the formation of sound bonding at the interface [3].Therefore.based on the increased strength of the nanocomposite samples compared to the pure aluminum sample and for computational efficiency.the reinforcement-matrix interface is assumed to be perfectly bonded.In the case of weak bonding,MD simulations can be employed to characterize the interphase region formed at the reinforcement-matrix interface [22,23].

In order to find the appropriate size for the RVE.a successive sample enlargement test was performed in this study.Fig.5 shows the Elastic modulus versus RVE size for 2% Aluminum/Nano-silica composite.This figure clearly shows that for the RVE size of 1×1×1 mm3and above,the variation of elastic modulus is negligible i.e.the RVE size convergence has achieved.

Fig.5.Elastic modulus of 2% aluminum/Nano-silica composite versus RVE size.

4.Results and discussion

The simulated stress-strain curves of aluminum/Nano-silica nanocomposites obtained from finite element simulations are shown in Fig.6.As shown in this figure.the simulations demonstrate the same trend as in the experimental results.Particularly,the yield strength of nanocomposite increases with increasing the weight percentage of Nano-silica.even for low percentages of reinforcing nanoparticles.However.increasing the weight fraction of reinforcing nanoparticles in this type of composites results in the reduction of the yield strain.

Our primary simulations have shown that the elastoplastic material model without damage cannot predict the stress reduction during plastic straining.In other words.the inclusion of a damage model helps to detect the stress reduction due to the evolution of damage in the RVE.as observed in the experiments.A detailed analysis of the simulation results revealed that with straining the RVE.the damage increases around the reinforcing particles and eventually reaches its critical value.

In Fig.7.the stress-strain curves of aluminum/Nano-silica nanocomposites obtained from simulation are compared with experimental results.This figure shows that the numerical results are in good agreement with experimental results.Fig.8 illustrates the comparison of yield strength in experimental and numerical simulations.This figure verifies that micromechanical simulations can successfully predict the yield strength of nanocomposites.

Fig.6.Simulated stress-strain curves of aluminum/Nano-silica composite samples with different weight percentages of Nano-silica particles obtained from finite element simulations.

Fig.7.Comparison between the simulated and experimental stress-strain curves of aluminum/Nano-silica composites with (a) 1% Nano-silica.(b) 2% Nano-silica.(c) 3%Nano-silica.

The good agreement between the simulation and experimental results can be attributed to the proper phenomenological micromechanical model of the RVE and the precise determination of the input data.The over-estimation of the simulated stress at some points can be credited to the simplification assumption that particle distribution is fully discrete.Since a perfectly discrete distribution of particles in the aluminum matrix is experimentally very hard to achieve,the probability of particle agglomeration and alignment in the loading direction exists.This would cause higher strength in the loading direction and less strength in other directions,especially in the direction perpendicular to the particle alignment direction.As Fig.7 shows.this difference is clearer in the plastic region.In addition,the uncertainty of input variables for the linear region of the stress-strain curve is an important factor to affect the results.Nevertheless.proper assumptions for the material model have ledto a good agreement between experimental and simulation results.

Fig.8.Comparison between the simulated and experimental yield strength of nanocomposites with different nanoparticle weight percentages.

In summary.the micromechanical model of the RVE has been able to well capture the deformation process of aluminum/Nanosilica Nanocomposites.Such a model can be used in a parametric study to computationally optimize the microstructure characteristics of the nanocomposite.

5.Conclusion

An experimental and numerical study on aluminum/silica nanocomposites was performed to examine the effect of adding silica nanoparticles on enhancing the mechanical properties of the nanocomposite.Aluminum/Nano-silica composite samples were prepared via powder metallurgy.Uniaxial tensile testing of the specimens shows that adding silica nanoparticles causes an increase in yield stress and a decrease in yield strain.Our experimental results prove that amorphous Nano-silica powder is a suitable reinforcement for aluminum matrix composites.Compared to pure aluminum.a 16% increase in ultimate tensile strength and a 20% increase in the yield strength of the 1% Nanosilica samples was observed.Abaqus finite element package was used to numerically simulate the tensile deformation of the nanocomposites.Python scripting in Abaqus was employed to generate the RVE of the nanocomposite.An elastoplastic material model,along with a ductile damage model,was used for aluminum matrix and Nano-silica particles were assumed to be linear elastic.The uniaxial stress-strain curve of the pure aluminum was used to calibrate the model parameters for the aluminum matrix.The simulation results demonstrated a good agreement with experiments.Analysis of the micromechanical simulations revealed that the evolution of damage around the reinforcing nanoparticles cause the stress drop in the stress-strain curve and.finally the failure of the tensile specimen.The validated computational model used in this study can be employed to conduct a parametric study for the design of the optimized microstructure of the nanocomposites.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors would like to thank the financial support of the Iran National Science Foundation (INSF).