On the Effect of SiC Content and Processing Temperature on Relative Density and Hardness of Hot Compacted Aluminum AA 6061 Composite – Mathematical Empirical and Response Surface Approach

The AA6061 is reinforced by adding SiC at various volume fractions and, the mixture is hot compacted at different processing temperatures. The influences of such parameters are investigated on the product relative density along with its relevant Vickers hardness using quantitative and qualitative formulation approach. Empirical relationships are established to relate each of the controlling (independent) parameters (SiC% and hot compaction (HC) temperature), to the composites relative density and the hardness, as dependent variables. The developed models are examined for its adequacy and significance using several statistical criteria. Response surface and contour graphs are established to reflect the relevant function interrelations and, to provide a data base source for the prior design stage. Within the specified experimental domain, first order and nonlinear models are found independently adequate and significant to grasp the functional dependence between the relative density and both SiC and HC temperature. However, second order multiple model with quadratic components of SiC percent is found to best suit the hardness-SiC%-temperature functional relationship. Increasing SiC content is found to reduce the relative density of the composites regardless the hot compaction temperature while, up to about 18 vol.% SiCp relative ratio, it enormously and nonlinearly increases the composite hardness. Further increase in SiC% addition seems not to affect the composite hardness. Relative density of the resulting composite is decreased by increasing HC temperature.


Introduction
Aluminum alloys are notable by vast diversity in industrial application thanks to their many advantages regarding specific strength, corrosion resistance, thermal conductivity, low density, and good workability.On the other hand, their use is limited due to their relatively low yield strength and poor tribological characteristics (Min, 2009;O'Donnel et al., 2001).Therefore, applicability was affected negatively in many circumstances as a result of their reduced hardness and wear resistance (Huang et al., 2004).Recently, the interest to increase aluminum strength has risen and the study of metal matrix composites (MMCs) has been motivated in particular applications such as the aerospace and aeronautic industries.MMCs are considered as outstanding materials to obtain properties that are superior to those of the constituent phases and also to satisfy the above requirements.Aluminum is the most common metal used in MMCs; in particular, particles reinforced Aluminum-based MMCs are focal composites grasping an increasing attention recently thanks to their lightness, higher specific strength, and wear resistance (Senapati et al., 2014;Zakaria, 2014;Mohanakumara et al., 2014).
Aluminium-Silicon alloys, as a matrix material, are frequently selected for their good wear resistance, strength-to-weight ratio, thermal conductivity, ease of fabrication at reasonable cost, high strength at elevated temperature, as well as excellent corrosion resistance.As a result of the previous mentioned properties, the suitability of these alloys for aerospace, automotive and military applications has been evident (Senapati et al., 2014;Rao & Das, 2011).The strengthening of Aluminum and its alloys can be done by dispersing hard particles such as carbides, oxides, or nitrides into the aluminum matrix by using various techniques in the solid or liquid state (Pawar & Utpat, 2014).Al 2 O 3 and SiC reinforcements are two widely used types of reinforcing agents in aluminum metal matrix composites (AMCs).Their use is focused mainly in automotive and aircraft industries due to the importance of material tribological properties in these applications (Senapati et al., 2014;Mazahery & Shabani, 2013).SiC is a covalent material of huge technological attention thanks to its excellent overall properties.It has good thermal shock behavior and mechanical resistance with has high thermal conductivity, oxidation, and erosion resistances (Liu et al., 2010).The SiC as whisker or particle reinforced Al matrix composite (Al-SiC) is perhaps the most successful class of MMCs produced ever (Mandal & Viswanathan, 2013).As a result, AMCs reinforced with SiC particles offer higher modulus, wear resistance, and better dimensional stability than conventional aluminum alloys (Mohanakumara et al., 2014).
Powder Metallurgy (PM) can be used to prepare aluminum composites in the solid state.The process consists of mixing reinforcement particles with the metallic powder, followed by consolidation and sintering processes.Other methods that could be also adopted include mechanical alloying (MA) and mechanical milling (MM), which renders composites with fine and homogeneous distributions of the particles (Mazahery & Shabani, 2013;Showaiter & Youssefi, 2008;Kim et al., 2001).The best properties of PM for fabrication of composites can be obtained when the reinforcement is homogeneously dispersed in the matrix (Ravindran et al., 2013).
MMCs can be reinforced using alternatives such as continuous fibres, discontinuous particles, or whiskers (Yan et al., 2008).Particle-reinforced MMCs possess distinct advantages over fibre reinforced composites regarding low cost and isotropic mechanical properties considerations.Therefore, they are relatively easier to process via powder compared to AMCs reinforced with ceramic whiskers and fibers (Mazahery & Shabani, 2012).The mechanical properties of a composite under loading are typically controlled by the interfaces formed between matrix and reinforcement particles.Generally, a good interface bonding with coherency or semi-coherency is advantageous for better mechanical properties.Conversely, interface with in-coherency degrades its properties, especially with the presence of brittle intermetallic phases (Mandal & Viswanathan, 2013).Discontinuous particles reinforced MMCs have gained much interest recently due to their promising mechanical properties regarding matrix-reinforcement coherency (Mohanakumara et al., 2014;Mazahery & Shabani, 2013;Zhanwei et al., 2014).Additionally, the common problems accompanying the fabrication of continuous reinforced MMCs such as fiber-damage, microstructural heterogeneity, fiber mismatch, and inter-facial reactions are minimized by the use of discontinuous reinforcements (Kalkanl & Yilmaz, 2008).
During the last several decades, optimizing the mechanical properties of the SiC reinforced aluminum alloy composites has been a main point of interest for many researchesrs, for instance (Min, 2009).The improvement of mechanical properties of produced composites could be reached by having a well performed homogenization which would enable uniform distribution of reinforcement particles in the composite matrix.The effectiveness of the powder and the performance of produced components are typically determined by the appropriate relative mixture contents and constituents (Bozic et al., 2010).
In the current study, a quantitative procedure is adopted to explore the effect of the SiC volume fraction and the HC temperature on the physical and mechanical properties of AMCs, and to develop a general approach describing the dependence of the relative density and hardness of the AA6061-SiC composite on SiC content and hot compaction temperature.Based on a previous study (El_Garaihy, 2012), experimental data are used to establish mathematical models of the functional relationship of the aforementioned parameters.Response surface in terms of three dimensions and contours representations are introduced as database reference to help in the design stages.

Materials
The investigated aluminum alloy AA6061 (supplied by Powders Company Limited) was received in the form of powders 30 µm in average size, Figure 1a.AA6061 particles were characterized by irregularity in shape with variation in size from 10-to-75 µm.The as-received SiC powders (supplied by American Elements Company) were used as reinforcement.As shown in Fig. 1b, SiC powder was characterized by non-uniformity in shape with particles size ranging from 1-to-5 µm with an average size of 2 µm.

NonlinearModeling
However, to detect the possible nonlinear nature of the independent variables, a nonlinear model is usually proposed in the form (Myres et al., 2012;Kowalski, 1977): where a's are the model coefficients to be determined by the nonlinear regression procedures using the experimental data.
Regression statistical routine is used together with the experimental data to reach the most adequate and significant relationship between each of the dependent variable; relative density (RD) and Vicker's hardness (H V ), and the independent variables; AA6061 percentage in the alloy (Al%) and compact temperature (T HC ).
Regression routine is one of the most familiar statistical tool to detect the influence of more than one independent variables are involved.This is a necessity if a response surface is required.Using regression analysis asseses and estimates the effect of each individual variable on the measured response together with the possible interaction effect among all involved variables.As in many modeling and forecasting techniques, such as neural network, genetic algorithm, etc, regression analysis uses the most widely used ordinary least squares analysis.Such a fitting technique is included as a toolbox facility in many commercial programs such as MathWork and MatLab.Least squares method creats the best fit line or surface through all of the available data points so as to minimize error sum of squares.Fitting a regression model requires several assumptions of which the assumption that the errors are uncorrelated random variables with mean zero and constant variance.Also, tests of hypotheses and interval estimation require that the errors are normally distributed.There are a number of advanced statistical tests that can be used to examine whether or not these assumptions are true for any given regression equation (Myres et al., 2012;Kowalski, 1977).
Through the current study, a fitting strategy is followed so as to begin with the first-order model of form (2) then; interaction among dependent variable and their possible quadratic and nonlinear trend are examined using model structures ( 3) and ( 4).Fitting procedures are terminated once the best model is detected.Model adequacy and significant is judged through many criteria which can be defined as follow: sometimes denoted as coefficient of determination, measures the percentage of variation in the response variable R explained by the explanatory variable x.Thus, it is an important measure of how well the regression model fits the data.The value of R 2 is always between zero and one.R 2 of unity or, 100%, means all variability are grasped while 50% or below, indicates the the predictionmay be poor.Student t statistics value usually measures the influence strength (weight) of an estimated coefficient for a specivic independent variable x i through comparing its estimated value to its calculated standard error.For a variable to be significant, t statistics absolute value must not be less than 2.0.As indicated above, F ratio (F-test) indicates the ratio of regression mean squares to the residuals mean squares for a set of independent variables and number of data points (degrees of freedom).This has a preset threshold value from special statistical tables where greater value is not always a judgment of model superiority.
Further statistical judgment (hypothesis tests) is performed by observing the trends of each of the residuals pattern and the normal distribution of the predicted values (Douglas et al., 2012).Based on the selected best model, a surface response representation is introduced in terms of 3-dimensional graphs and contours which will be demonstrated in the following section.

Effect of SiC Content and Compact Temperature on the Relative Density
The aforementioned fitting strategy is used to establish a relationship between the relative density (RD), as a dependent variable, and AA6061 percent in the alloy and compact temperature (T HC ) as independent variables using the experimental data listed in Table 1.To get rid of computational error arises during fitting process at zero SiC%, AA6061 content (Al%) is transformed and coded so that the value is always greater than zero (Al% = 100% -SiC%).
A first-order linear model of form (2) was obtained taking the form:   Same fitting procedures and strategy, which has been explained in the last section, are followed to develop a functional interrelationship between the alloy hardness (Vickers Hv) as a dependent variable and both of the AA6061 content (Al%) and HC temperature (T HC ) as influential independent variables.Applying a first order linear multiple form (2) didn't lead to satisfactory general statistical outcome.To resolve such an emerged problem, the partial plots are considered to reveal the individual real natural dependence of Hv on each of Al% and T HC , Figure 7. Hardness-AA6061 content, Figure 7a, exhibits a strong indication of second-order (quadratic) trend while an almost linear trend is noticed regarding hardness-temperature dependency, Figure 7b.Consequently, a second-order multiple regression of form (3) is proposed.Using Stepwise procedure in linear regression routine, which determines the maturity of each individual independent variable to be included into the final equation, the following second order linear model is obtained: with less correlation factor R2 of 87.7 and, therefore, it is of less predictability than model ( 7) to values of Hv as a relation to both AA6061 content (Al%) and HC temperature (T HC ).This may be observed from Figure 9 where both models are examined against the experimental values.As shown by Figure 9.b, nonlinear model exhibits larger deviations from the experimental values especially for experiments Nos. 1, 2, 3, 13 and 14 with overestimation trend.For the rest of cases, an approximate trend is observed for both models credibility.However, both models tend to represent the effect of reducing AA6061% or, increasing SiC%, on the hardness of the composite.It is obvious that a reinforced disc has a Hv-value higher than the monolithic alloy.However compact temperature seems to have a limited influence on the hardness.At higher HC temperature, the grain coarsening increases thus lower HV-values result.
Figure 10 shows a 3-D surface response along with a contour graph of the functional Hv-Al%-T HC relationship.The effect of HC temperature has a higher impact of the hardness of monolithic material than on the composite.As SiC percent increases up to 18 %, hardness increases reaching its ultimate value.Further increase in SiC content seems not to affect composite hardness which is slightly and linearly decreases according to a temperature-dependent pattern.
The hardness distribution results showed that good sintering was achieved in the case of AA6061 with or without SiC reinforcement even at the 400°C sintering temperature and adhesion between particles increase as the sintering temperature increase.When temperature rises, the resulting heat leads to the expansion of an aluminum particle making a wider contact with the neighbor particle.As a result, voids between particles are reduced.Furthermore, increasing HC temperature up to 500°C usually leads to strain softening due to grain coarsening as shown in Figure 6.
The presence of the SiC increased the composite hardness as they carry some of the load applied to the material (load transfer from the matrix to the reinforcement due to the difference in the elastic constant).The increase in the Hv-values of the composite can be attributed to the high hardness of the reinforcement.So mainly the interaction is either aluminum with aluminum particles which adhere properly or aluminum with SiC in which adhesion is enhanced by the presence of SiC particle.11, where at 20% SiC composite, the hardness drops due to the weak contact among SiC particles and, as aresult, higher probability of more than two particle cluster together occurs, Figure 11.Additionally, such decrease in hardness of the AA6061-20% SiC p composite can be attributed to the decreasing of the composite compressibility which resulted in increasing voids.The porosity volume fraction dominated the behavior of the composite which resulted in deterioration of the overall hardness of the discs.This probably reflects mixing difficulties in obtaining a uniform particle distribution at high volume fraction for this process, there being a higher number of nucleation sites present for the cracks to form as a result of the particle clusters.Increasing SiC content is found to reduce the relative density and to increase the hardness of the composites.However, the surface response and the contour graphs interestingly explained that adding greater than (15 to 20%) SiC% to the composite does not benefit increasing of its hardness.HC temperature showed a negative trend (decrease) in each of the composite relative density and its hardness.
Figure Following base alloy density m loading di applied lo monolithic emission s etched sam 3. Data Pr 3.1 Linear To establi dependent 2012; Myr Figure 3.Comparison of experimental and predicted data for both linear and nonlinear models Figure 4 s temperatur temperatur associated /°C) and t stresses inc graphs em temperatur particles (w brittle SiC junctions a Figure 5. T increase in coalesced i Figure 7. Partial relation between hardness and each of AA6061 content and temperature Figure

Figure 11 SEM
Figure 11 SEM Micrograph for AA6061-20% SiC showing the segregation of SiC particles along boundaries and triple points, arrows point at SiC particles