FE simulation of uniaxial tensile behavior of SiC reinforced AA5083 alloy

ABSTRACT

Reinforcements added to pure AA5083 alloy are known to lower the overall weight while improving the strength of the Metal Matrix Composite (MMC). In this work, Silicon carbide (SiC) particles are added to pure AA5083 in varying quantities (3%, 5%, 7% and 10%), and tested to failure using tensile testing. The stress-strain behavior is decomposed into the elastic and plastic behavior and is validated using Finite Element (FE) modeling. The results exhibited an increase in ultimate tensile strength (UTS) of the MMC up to 5% of SiC. The formation of intermetallic compounds due to reactions at high concentrations of SiC resulted in debonding in the MMC and thus reduction in UTS. In this work, the response of the material between yield and complete failure is characterized using VOCE nonlinear model in FE analysis. It is observed that MMC with 5% SiC has shown maximum UTS (340.34 Mpa), while MMC with 10% SiC content has resulted in the most ductility (27% plastic strain) of all the compositions. Further, MMC with 7% SiC has highest saturation stress (R₀ = 653.09 Mpa) and lowest ductility, while MMC with 10% SiC has lowest saturation stress (R₀ = 115.57 Mpa) and highest ductility.

Keywords
VOCE; AA5083; Plasticity; ANSYS; Metal Matrix Composites

1. INTRODUCTION

The addition of micro and nano reinforcement particles to a metal matrix has shown to have improved the mechanical as well as tribological properties of metal matrix composites (MMCs) [¹]. Such materials with superior strength and lower weight are highly coveted in both the commutable automobile sector as well as military grade vehicles [², ³]. Several studies focused on the addition of a wide range of reinforcements to metal matrices. SINGH et al. [⁴] showed that the addition of SiC particles in Aluminum MMCs has improved the tensile strength but reduced the elongation (or ductility) of the samples. However, the grade of Aluminum matrix and the manufacturing process (whether the sample is stir casted, friction welded or cut from a commercial rolled sample) is not mentioned. It is only logical to compare the pure sample prepared using the same method and in the same conditions as all the other samples. NAGARAJA et al. [⁵] performed a comprehensive study on the addition of Fly Ash and SiC in AA5083 and determined that the mechanical properties are mainly dependent on the sample preparation process. Usually, the reinforcements are of extremely high strength and most studies add them in powder form to the metal matrices. PIERS NEWBERY et al. [³] showed that ball milling at cryogenic temperatures created ultrafine grained structure which improved strength by 50% and tensile elongation by 11%. However, most studies have concentrated on the tribological properties rather than pure mechanical response. GARGATTE et al. [⁶] used liquid stir casting method to add SiC particles to Al-5083 and showed that the reinforcements reduce the wear rate when compared to pure alloy. The same has been corroborated by SOLEYMANI et al. [⁷] not just with SiC, but also with MoS₂ reinforcements. SHYAM KUMAR et al. [⁸] also used friction stir casting to develop Tungsten reinforced AA5083 alloy and proposed that a composite layer on the surface of the MMCs significantly improved the wear properties without affecting the bulk properties. TAZARI and SIADATI [⁹] used cold pressing and sintering for adding SiC nanoparticles to AA5083 and reported impeded grain growth being the reason for improved strength and wear properties of reinforced MMCs. FOO et al. [¹⁰] in an early study found out that at high temperatures during sintering, intermetallic compounds may be created at the SiC-matrix interface, though not in all the cases. These compounds had caused debonding at the interface and can reduce the strength. ALIZADEH et al. [¹¹] proposed that a combined stir casting and squeeze casting technique significantly improved particle distribution which resulted in improved strength and wear properties. JAIN et al. [¹²] demonstrated that Zener-Holloman mechanism and particle stimulated nucleation (PSN) mechanism has been activated during friction stir casting of SiC into AA5083 which resulted in randomly oriented grains. GHOSH and SAHA [¹³] showed that the crack density increases with increase in SiC (direct metal laser sintered) volume beyond 15% and wear resistance reduces beyond 20% volume. When it comes to determining the mechanical response of the reinforced MMCs using FE models, several approaches are being used. Representative or unit volume element approach wherein one single cell with the volume fraction of the reinforcement embedded into the matrix has been the most common form of modeling reinforced composites in finite element modeling [¹⁴]. More advanced techniques such as modeling of the exact shape and volume of the reinforcement into a finite volume has also been done [¹⁵]. However, the bonding of the elements is not a precise science, and it would be computationally expensive to model a macro specimen. BALASIVANANDHA PRABU et al. [¹⁶] studied the interface between the Al matrix and the SiC microparticles at a microscopic scale and concluded that apart from the size of the particles, their orientation also affects the overall response. PENG et al. [¹⁷] has performed a comprehensive 3D multiscale analysis of micro and nano-reinforcements in MMCs. They created Representative Volume Elements (RVEs) to model macroscale responses using FE analysis and estimated progressive damage and fracture. A similar study was done by SAXENA et al. [¹⁸] on reinforcements to Copper MMCs. BAHL and BAGHA [¹⁹] used 2D FE analysis to study the interfacial effects between the reinforcements and the metal matrix and reported that the cohesive layer behaved the same as the matrix before damage. KIM et al. [²⁰] analyzed various interface techniques and microstructure analyses to study their effect on the material properties of the MMCs. MAURYA et al. [²¹] reviewed the reinforcements that are usually added to the Aluminum MMCs.

PALANIYANDI and VEEMAN [²²] indicated the extraordinary performance of Aluminium MMCs was the low density that obtained after alloying. Ultimate tensile strength, compressive strength and impact toughness improves with the addition of reinforced particle. GOVINDAN and RAGHUVARAN [²³] stated that when the weight % of reinforcement rises, the elastic strength increases gradually, and toughness will be limited resulting in an increase in matrix rigidity. S. IYENGAR et al. [²⁴] reviewed that the increased tensile strength is attributed to good dispersion and interfacial bonding between the particles and Aluminium metal matrix. WOLF et al. [²⁵] inferred the mechanical strength of the composites were superior to the matrix material, especially for the aluminum alloy composites which showed significant increase on the UTS. NANJAN and MURALI [²⁶] has observed the enhancement of mechanical properties of the stir casted metal matrix composites. BARMOUZ et al. [²⁷] has discovered the formation of the intermetallic phases between the base metal and reinforced particles in the casted specimens. CAO et al. [²⁸] has discovered that the behavior of the reinforced particles changes with the processing parameters. GUKENDRAN et al. [²⁹] concluded that the introduction of reinforcements into aluminium enhances the mechanical properties of the composites considerably.

In this work, the stress-strain curves of the SiC reinforced AA5083 prepared by stir-casting method are analyzed to characterize the material response in both the elastic and plastic regime with emphasis on the plasticity behavior. Influence of the SiC particles on the strength and ductility of the MMCs is studied and the FE parameters that influence the response of the MMCs in the nonlinear regime are identified.

2. MATERIALS AND METHODS

The sample was prepared as per ASTM E8/E8M – 13a [³⁰] as shown in Figure 1. The subsize specimen which is the smallest of all the 3 specified sizes was chosen (to minimize material usage). The steps involved in sample preparation and the microstructure analysis of the specimens is already documented in a previously published work [³¹].

Figure 1:
ASTM standards for tensile testing [³⁰].

The experimental procedure is as follows. The sample is placed in the grips exactly for 20 mm from both ends and was loaded at a rate of 1 mm/min until failure. A servo hydraulic 100 kN INSTRON 8801 universal testing machine is used for experimentation. 5 different types of specimens are tested. Apart from the pure AA5083 specimen, samples made with the addition of 3%, 5%, 7% and 10% SiC to pure AA5083 are tested. Every aspect of the experiment is carefully documented to replicate the process in using FE Analysis. The specimens exhibited classic brittle failure with little to no necking as shown in Figure 2. However, based on the final length of the specimens, a significant elongation can be observed though no necking has occurred. The complete stress strain curves of the tests are published in KUMAR et al. [³¹]. Once the experimental data is obtained, further analysis is performed as explained in the subsequent sections.

Figure 2:
(a) Prepared and tested samples (b) sample before testing (c) sample after testing.

3. RESULTS AND DISCUSSION

3.1. Experimental results

The results obtained from the UTM (INSTRON) are shown in Table 1. These parameters are based on the Engineering Stress-Strain data calculated using the initial length and cross-section area of the samples.

Table 1
Experimental data

Composite	Elastic Modulus (Mpa)	Experimental
		Tensile Stress at Yield (0.2% Offset) (Mpa)	Ultimate Tensile stress (Mpa)
Pure AA5083	56302	117.78	238.31
AA5083 + 3% SiC	66999	127.35	256.61
AA5083 + 5% SiC	64165	127.68	263.73
AA5083 + 7% SiC	67699	129.53	254.37
AA5083 + 10% SiC	60504	118.98	243.75

Figure 3 shows the stress strain data of the pure AA5083 sample obtained the INSTRON UTM. The linear region of the stress-strain data is not exactly clear from the curve and needs closer examination (Figure 4) to identify the linear and non-linear regions.

Figure 3:
Stress-strain curve of the Pure AA5083 sample.

Figure 4:
Close-up of the linear region of the stress strain curve of Pure AA5083 sample.

3.2. Plasticity analysis

The major objective of this work is to analyze the plastic region of the stress-strain curve. Hence, it is first required to separate the data into elastic and plastic regions. The decomposition of the experimental stress-strain data into elastic and plastic regions is a challenging task since the identification of the linear region of the stress-strain curve is not an exact science. One has to make a decision on how much non-linearity is acceptable in the elastic portion of the curve. The “Elastic Modulus” and “Tensile stress at yield (0.2% offset)” data obtained from INSTRON (Table 1) is taken as reference.

However, analysis of the linear elastic region is not the intent of this paper. This paper considers the yield point (Tensile Stress at Yield (0.2% Offset) obtained from the instrument as the starting point for further analysis. As such, the procedure adopted here to separate the elastic and plastic regions is as follows:

$${\epsilon }_p={\epsilon }_t-{\epsilon }_E={\epsilon }_t-\sigma /E$$ (1)

where ε_p, ε_t, ε_E, σ, E are true plastic strain, true total strain, true elastic strain, true stress and Young’s modulus respectively [³²]. Since the experimentation only involves uniaxial tests, the equivalent stress and strain are the same as the total stress and strain [³³]. For multiaxial loads, the calculations involve lot more complexity. For finding out true stress strain values, the experimental stress-strain data (also called engineering stress-strain or nominal stress-strain) is converted as follows:

The true strain ε is calculated from engineering strain ‘e’ as follows:

$$\epsilon =ln(e+1)$$ (2)

The true stress σ is obtained from engineering stress, ‘s’ as follows:

$$\sigma =\frac{P}{A_0}(e+1)=s(e+1)$$ (3)

The tensile stress at yield point (σ.) obtained from experimental data is shown in Table 1 is taken as the reference for the onset of yielding. The strain at that point (maximum true elastic strain) is subtracted from the subsequent true strain value so that only the plastic strain values are remaining. The true stress values thus obtained are listed in Table 2. In this work, rather than making observations with this data, a nonlinear plasticity model is used to fit the data up until the failure point. It has to be noted here that the plasticity model can only predict the path of the stress-strain curve and not the breaking stress. The breaking stress usually depends on the imperfections in the samples which are not taken into consideration in the theoretical model.

Table 2
True stress values of yield and ultimate tensile strength values.

Composite	True
	Tensile Stress at Yield (0.2% Offset) (Mpa)	Ultimate Tensile stress (Mpa)
Pure AA5083	119.08	296.22
AA5083 + 3% SiC	128.67	306.17
AA5083 + 5% SiC	129.12	340.34
AA5083 + 7% SiC	130.94	293.24
AA5083 + 10% SiC	120.39	317.26

Based on these numbers, the results of the Pure AA5083 are taken for reasoning. Figure 3 shows the entire stress strain curve of the sample and Figure 4 shows the close up of the elastic region of the curve. It can be clearly seen that the slope (56302 MPa) as interpreted by the inbuilt software does not accurately fit the data.

3.3. Analytical parameter identification

The VOCE model mainly used to capture work hardening characterizes yield stress in the material using an exponential saturation term in addition to a linear term as shown in Eqn (4) below:

$${\sigma }_Y={\sigma }_{{}_0}+R_0{\widehat{\epsilon }}^{pl}+R\infty \left(1-exp\left(-b{\widehat{\epsilon }}^{pl}\right)\right)$$ (4)

where the user-defined parameters R_∞, the difference between the saturation stress and the initial yield stress, R₀, the slope of the saturation stress and, b, the hardening parameter that governs the rate of saturation of the exponential term ${\widehat{\epsilon }}^{pl}$ is the accumulated equivalent plastic strain. Eqn (4) shows the progression of yield stress beyond the initial yield stress σ₀. To apply this model, the plastic strain (${\widehat{\epsilon }}^{pl}$) is to be separated from the total strain and the initial yield stress (σ₀) must be identified from the experimental data. MASTRONE et al. [³⁴] followed an iterative procedure to obtain the Voce parameters for a ductile material. In this work, the initial yield stress is constrained to be the same as obtained from the experiment and the rest of the parameters are optimized using a Generalized Reduced Gradient (GRG) nonlinear method without any constraints.

The curve fits to the actual true plastic stress to equivalent plastic stress are as shown in Figure 5 and Table 3. The figure clearly shows the higher stress response for certain MMCs over others. Another inference that can be made from Figure 5 is the amount of equivalent plastic strain. Assuming that the elastic strain can be re-covered, the amount of equivalent plastic strain is considered as the ductility of the material. The maximum ductility can thus be seen for 10% SiC added MMC with a value of 0.27 or 27% followed by 5% SiC added MMC with 25%.

Figure 5:
GRG curve fits of all the materials used.

Table 3
The VOCE parameters obtained by fitting the experimental data with Eqn (4) using the GRG method.

	Pure AA5083	AA5083	AA5083	AA5083	AA5083
		+3% SiC	+5% SiC	+7% SiC	+10% SiC
σ 0	119.0838	128.6714	129.1231	130.9448	120.3919
R 0	361.6365	579.7463	329.3432	653.0933	115.5742
R ∞	106.7094	83.3625	136.1315	76.6707	179.6840
b	16.2338	23.8436	13.2070	26.7469	9.3645

The plot of these parameters along with the Elastic Modulus (E) has been shown in Figure 6. The following observations are made from these plots: The elastic modulus (E) and σ₀ follow a similar trend and higher for MMCs compared to the pure AA5083, but a clear drop can be observed at 10% SiC. The R₀ and b values which show a similar trend, shows that the highest slope of the saturation stress or the fastest rise after yield point is observed in the 7% SiC MMC. The R_∞ values which represent the ductility or the longest strain between the saturation (break) and yield is highest for the 10% SiC which had an equivalent plastic strain of close to 27% before break. Though the exact reason of the break can only be ascertained using microscopic analysis, the most likely reason is the sudden debonding of the interfacial layer due to high slopes of the stress.

Figure 6:
The variation of (a) elastic modulus, E (b) initial yield stress, σ₀ (c) slope of the saturation stress, R₀ (d) difference between the saturation stress and the initial yield stress, R_∞ (e) hardening parameter, b.

3.4. Finite element analysis

ANSYS 15.0 Academic version is used for the analytical evaluation of the material response. The 1/8th symmetric model of the specimen is modeled as shown in Figure 7. The dimensions of this model are given in Figure 1. The details of the element type used, and material properties are shown in Table 4.

Figure 7:
Modeling of 1/8^th symmetric model from the full tensile testing specimen.

Table 4
Element type and material models used in FEA.

Element Type	Material model (Required Parameters)
SOLID186 (20-node bricks)	Nonlinear inelastic rate independent isotropic hardening Mises plasticity model
	Elastic Modulus: (Table 1) Poisson’s ratio: 0.3 Initial Yield Stress, σ0 (Table 3) Linear Coefficient, R0 (Table 3) Exponential Coefficient, R∞ (Table 3) Exponential Saturation Parameter, b (Table 3)

The model is built as 4 volumes to control the mesh size and also for application of boundary conditions. The left most volume and the adjacent filleted volume of the model are fine meshed, whereas the right most volume is coarse meshed. The coarse meshed volume is the region that is fixed inside the grips of the vice during experimentation. The mesh is shown in Figure 8. The total number of brick elements is 4920 and the total number of nodes is 23773.

Figure 8:
Mesh of the FEA model.

3.5. Boundary conditions

Since the model is 1/8th symmetric, the 3 faces of the model (i.e. areas along xy = 0, yz = 0 and xz = 0) are constrained with symmetric boundary conditions as shown in Figure 9(a). The symmetry conditions imply that the surfaces cannot move along their normal. All the nodes within the grips are coupled in the direction of motion so that they move together. For loading, the load applied can be either displacement controlled or load controlled. The choice of load control greatly affects the convergence of the solution. However, that description is beyond the scope of this paper. Here, the optimum convergence occurs with force control where the actual force (obtained from experiment) is distributed uniformly on all the nodes that are constrained in the grips (Figure 9(b)). The load is applied in steps using auto time stepping. Since the material model chosen is rate independent, the rate at which the load is applied does affect the solution.

Figure 9:
(a) Symmetry boundary conditions on the areas (b) force applied on the coupled nodes in the x-direction.

The stress plot (in the x-direction) for the pure AA5083 sample is shown in Figure 10(a) where the maximum stress is expected to occur because of the minimum amount of cross-section. The stress-strain plot at the global origin i.e. the middle of the fill specimen is taken for evaluating the stress and strain data as shown in Figure 10(b).

Figure 10:
(a) Axial stress plot at maximum deformation and (b) the stress strain curve on the smallest section.

The stress-strain curves obtained using FE analysis is compared with the experimental data and the fit is shown in Figure 11. The plot shows only the fit of best composition of MMC (AA5083 + 5% SiC) and the pure AA5083 alloy. The FE result closely matched the experimental results in all the categories, but due to cluttering of the data, only 2 sets of data is presented here. Hence, this process of material property extraction for FE analysis can be used for MMCs.

Figure 11:
The stress strain curves obtained from FEA in comparison to experimental data.

4. CONCLUSIONS

The algorithm performed by the commercial software inbuilt in the equipment for interpretation of experimental data depends on the regression algorithm used and manual interpretation of data need to be performed as per the standard procedure. This can be seen from the calculation of Young’s modulus and Initial Yield Stress values as seen in Figure 4.

Though the mode of failure appears to be brittle and no necking can be seen, there is significant amount of elongation in the MMCs before failure (27% for 10% addition of SiC).

Even though, ductility is significant, the material failure shows a brittle characteristic rather than classical ductile failure. The brittle fracture is because of the manufacturing process involved in preparing the samples. A rolled sample will exhibit classic ductile fracture but a cast specimen as in this case will have imperfections which will lead to sudden crack formation and propagation which leads to brittle failure.

Addition of Silicon carbide (SiC) particles to pure AA5083 in varying quantities (3%, 5%, 7% and 10%) has resulted in increased ultimate tensile strength (UTS) of the MMC upto to 5% SiC, but as the SiC content increased further, the strength has deceased. This result can be attributed to the formation of intermetallic particles that seem to have formed due to reactions at high concentrations of SiC.

When it comes to final failure, a clear trend has not been observed. However, the 10% SiC MMC has shown the most equivalent plastic strain (27%) which is a measure of ductility.

The highest slope of the saturation stress or the fastest rise after Yield point is observed in the 7% SiC MMC. It is also the MMC with the least amount of plastic strain before failure.

Looking at the overall result, the MMC with 5% SiC has the optimum combination of ductility and ultimate tensile strength.

Finally, the results have shown that the plastic material properties extracted with the process described here are adequate for Finite Element Analysis of materials in the nonlinear domain.

5. ACKNOWLEDGMENTS

The authors thank Dr. Rajeswara Resapu, Associate Professor, Department of Mechanical Engineering, GITAM (Deemed to be University) for his valuable suggestions in regards to Finite Element Modeling and Analysis.

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Publication Dates

• Publication in this collection
  26 Feb 2024
• Date of issue
  2024

History

• Received
  08 June 2023
• Accepted
  15 Jan 2024