Table 1. Chemical composition of work materials
Figure 1. Samples of A1350 casts.
Figure 2. Samples of A380 casts.
Table 2. Input factors and their respective levels for the casts of both alloys shown above.
ing type and cooling medium were kept constant and only pressure was regulated as tabulated in Table 2.
2.5. Regression Models
Regression models are used to predict one variable from one or more other variables. Regression models provide the scientist with a powerful tool, allowing predictions about past, present, or future events to be made with information about past or present events. In order to construct a regression model, both the information which is going to be used to make the prediction and the information which is to be predicted must be obtained from a sample of objects or individuals  -  . The relationship between the two pieces of information is then modeled with a linear transformation equation. Then in the future, only the first information is necessary, and the regression model is used to transform this information into the predicted.
Multiple regression analysis is a statistical tool for understanding the relationship between two or more variables. Multiple regressions involves a variable to be explained called the dependent variable and additional explanatory variables that are thought to produce or be associated with changes in the dependent variable Multiple regression also may be useful in determining whether or not a particular effect is present, in measuring the magnitude of a particular effect, and in forecasting what a particular effect would be, but for an intervening event  -  .
The linear regression was carried out using the regression line Equation.
The constants a and b can be calculated from the expressions:
And the multiple regression was carried out using the multiple regression Equation where the equations for the constants are:
The RMSE of a model prediction with respect to the estimated variable X model is defined as the square root of the mean squared error:
where Xobs is observed values and X model is modeled values at time/place i.
3. Results and Discussions
3.1. Hardness Test
The hardness values were measured using the Rockwell hardness testing machine (model AVERY 6402 England), available at the work shop of the Science and Technology Complex (SHEDA) Abuja. The indents formed were measured on B scale with a minor load of 10 kg, major load of 100kg but before the hardness test, the surfaces of the samples were cleaned thoroughly by removing dirt, scratches and oil.
The results obtained from the hardness tests on the cast samples of both alloys are represented in Figure 3.
Figure 3. Variation of hardness with applied pressure for both alloys.
The figure shows that hardness values for both alloy casts follow similar pattern with increased applied pressure similar to work by Ming et al.  . The regression model is:
The root mean square error was found to be RMSE = 0.46
The root mean square error was found to be RMSE = 0.28, where P is pressure.
3.2. Tensile Test
The specimen bars produced from the samples of both alloys were subjected to tensile tests in accordance with the ASTM E8 standard test method for tension testing of metallic materials using a Hounsfield tensiometer with maximum load of 500 KN available at the workshop of the Science and Technology Complex (SHEDA) Abuja, Nigeria. The test specimen size was 100.4 mm length and gauge length of 45 mm was marked on the samples. The specimen were mounted by their ends into the holding grips of the testing machine and locked securely. The machine then elongated the specimen at constant rate and at the same time the instantaneous load applied was measured using an extensometer and recorded. The results obtained from the tensile tests on the cast samples are represented below in Figure 4 and Figure 5.
The figures show that tensile strengths for both alloy castings and elongations followed similar pattern also with increase in applied pressure similar to works by Ming et al.  . The regression model is:
The root mean square error was found to be RMSE = 2.67
The root mean square error was found to be RMSE = 1.41, where P is pressure.
Yield Strength Result
The results of the yield strength obtained from the tensile tests on both alloy cast samples are represented in Figure 6.
Figure 4. Variation of tensile strength with applied pressure for both alloys.
Figure 5. Variation of elongation with applied pressure for both alloys.
The figure shows that the yield strengths for both alloy casts also followed similar pattern with applied pressure.
The regression model is:
The root mean square error was found to be RMSE = 0.06
The root mean square error was found to be RMSE = 0.50, where P is pressure.
3.3. Impact Test Results
The impact tests of the samples of both alloys were conducted using the Avery Denison test machine available at the work shop of the Science and Technology Complex (SHEDA) Abuja, Nigeria. Impact tests of the samples of both alloys were carried out using the charpy V notch test method. All specimens were notched at the centre to about 2 mm depth with a root radius of 0.25 mm at angle of 450 according to the standard of the machine used. Impact tests conducted for each sample were in accordance with ASTM E23 “standard method for notched bar impact testing of metallic materials”. The expended energy was measured and recorded for each specimen. The results obtained from the impact strength tests are represented below in Figure 7.
The figure shows that impact strengths for both alloy casts followed similar pattern also with applied pressure. The trends are similar for the two alloys as both followed similar pattern.
The regression model is:
The root mean square error was found to be MSE = 0.0006
The root mean square error was found to be MSE = 0.00024, where P is pressure.
4. Metallographic Examination
Microstructures of both alloy samples were investigated by means of a scanning electron microscope (SEM) available at the physics laboratory at Science and Technology Complex (SHEDA) Abuja and the metallurgical microscope available at metallurgy laboratory available at the Federal University of Technology Minna.
Figure 6. Variation of Yield strength with applied pressure for both alloys.
Figure 7. Variation of Impact strength with applied pressure for both alloys.
Preparation of the samples for micro examination involved mainly sampling, polishing and etching. Samples measuring 26 mm × 15 mm × 5 mm were cut from the castings with the help of a hacksaw. The samples were filed and ground. Grinding was done in succession on a bench grinder using silicon carbide abrasive papers of 220 - 320 - 400 and 600 grits, the samples were polished in the usual manner with final polishing being carried out by hand, and they were etched in aqueous solution containing 2.5% HNO3, 1.5% HCL and 1% HF acid (etched with Keller’s reagent) for 20 to 60 seconds. Etching was done to make visible the grains of the samples under different pressures conditions.
4.1. Scanning Electron Microscope Analysis (SEM)
Microstructures of the samples were investigated by means of a scanning electron microscope (SEM) available at the physics laboratory at Science and Technology Complex (SHEDA) Abuja. Samples after preparation were placed to the multi-stub sample holder by the help of double sided conductive aluminum tape and mounted unto the sample chamber and an electron gun switched on which passed an accelerating voltage of 20 kv and probe current of 227 pA through the samples at a working distance of 6.0mm. SEM was done to make visible porosity pores across the microstructures of the samples under the different pressure conditions.
4.2. Number of Grains
The variations of the number of grains with applied pressure are presented in Figure 8 for both alloys. As shown in the figure, number of grains also followed similar pattern in both alloy casts with applied pressure as they both showed variations in the number of grains across the varying applied pressures similar to work by ying-hui et al.  .
The regression model is:
The root mean square error was found to be MSE = 7.35
The root mean square error was found to be MSE = 6.86, where P is pressure.
4.3. Grain Size
Figure 9 shows the variation also of grain sizes with varying pressure for both alloys. The figure shows that finer grains were obtained with increased applied pressure as the trend are also similar and followed same pattern in both alloy castings similar to work by Ying hui et al.  .
The regression model is:
The root mean square error was found to be MSE = 0.28
Figure 8. Variation of number of grains with applied pressure for both alloys.
Figure 9. Variation of grain size with applied pressure for both alloys.
The root mean square error was found to be MSE = 0.28, where P is pressure.
4.4. Microstructure Analysis
The microstructures of the samples of both alloys at varying pressures consisted of a primary α phase, peritectic β phase and ternary eutectic phase (β + η + ε), where α phases appeared as nodular when the pressure reached 1400 kg/cm2 (seen in Figure 10), also the eutectic structure (β + η + ε) was not found in the samples at 1400 kg/cm2, while the (η + ε) phases appeared between grains. The primary α phases appeared as elongated at 1050 kg/cm2 pressure (seen in Figure 11) and with 700 kg/cm2 pressure, α phases solidified as coarse grains and the eutectic structure (β + η + ε) phases appeared between grains (Figure 12).
In the lower pressure samples, scanty grains were seen and they were not homogeneously distributed (Figure 13 and Figure 14). In the solidification process of both alloys, the primary phase α precipitates first from liquid phase and then the hypoeutectic reaction follows. However, at high pressure, the degree of these two reactions becomes
Figure 10. SEM (Scanning Electron Microscope) and DEM (Digital Electron Microscope) of sample 1 of both alloys with pressure of 1400 Kg/cm2.
Figure 11. SEM (Scanning Electron Microscope) and DEM (Digital Electron Microscope) of sample 2 of both alloys with pressure of 1050 Kg/cm2.
greater due to the fact that the eutectic point in both alloys moves to the direction of rich Al, thus the quantity of remaining liquid phase is reduced greatly. On the other hand, because the melting points of both alloys are elevated at high pressure, the degree of super-cooling increases, thus the nucleate rate of primary reaction increases largely during solidifying. This is also the reason for microstructure refining, In addition, the remaining phase is in deep super-cooling state when temperature is dropped to the eutectic point. Therefore, the improvement of mechanical properties is attributed to eliminating of micro-pores in the alloys caused by higher pressure. On the other hand, it is because of the microstructure refining as the applied pressure is increased that increased tensile strength and hardness are attributed to. It can be deduced that the eutectic reaction was restrained while the primary reaction was promoted in both alloys at higher pressure similar to works by   .
In Figure 10 and Figure 11 above, at pressures of 1400 kg/cm2 the SEM and DEM of both alloys samples showed fine grain structures that produced elongated pattern and the grains were finely and cohesively arranged. The much concentrated grains were
cohesively arranged and evenly distributed due to good compatibility of the grain structure which is absolutely, evenly distributed in an attractive manner and perfectly embedded with one another and as pressure was being lowered to 1050 kg/cm2 in Figure 11, the SEM and DEM of both alloys showed spherical dimples characteristics of grain types and showing also fine grains and also the much concentrated grains were cohesively arranged and evenly distributed.
Figure 12. SEM (Scanning Electron Microscope) and DEM (Digital Electron Microscope) of sample 3 of both alloys with pressure of 700 Kg/cm2.
Figure 13. SEM (Scanning Electron Microscope) and DEM (Digital Electron Microscope) of sample 4 of both alloys with pressure of 350 Kg/cm2.
In Figure 12, as the pressure was further lowered to 700 kg/cm2, the microstructure of both alloy samples showed that the grains were cohesively arranged and appeared in parabolic-shaped characteristic appearance. The SEM and DEM show also, ductile aluminum of transgranular fracture surface leaving spaces between the grains which obviously show not very fine grains.
In Figure 13, as the pressure was lowered to 350 kg/cm2, the micrograph of both alloys samples showed spherical characteristic of grain types showing big grain sizes. It
was also clearly shown that the grains were scanty because of coarse grain sizes that depict porosity susceptibility over time.
In Figure 14 at gauge pressure, the microstructure and micrograph of both alloys samples showed deformation that is worsened and the degree of deformation so great. The grains clearly show no morphology that is obvious, probably due to low pressure. The microstructure clearly shows obvious porosity in the sample that solidified at low pressure.
Based on the investigation results, the following conclusions can be drawn:
1) The hardness of both alloys varied in similar manner with pressure as the hardness values of both alloys increased with increase in applied pressure. Also the model that was fitted to the experimental data showed linear relationship with the actual data in view of the small error generated by them.
Figure 14. SEM (Scanning Electron Microscope) and DEM (Digital Electron Microscope) of sample 5 of both alloys with pressure of 0 Kg/cm2.
2) Tensile and yield strengths of both alloys also varied in similar manner with pressure as both strengths increased with increase in applied pressure. Also the model that was fitted to the experimental data showed linear relationship with the actual data in view of the small error generated by them.
3) The impact strengths of both alloys were observed to vary in similar manner across the different applied pressures in the casting process as the impact strengths of both alloys increased with applied pressure. Also the model that was fitted to the experimental data showed linear relationship with the actual data in view of the small error generated by them.
4) The number of grains increased with applied pressure for both alloys. Also the grains became finer with applied pressure for both alloys. The model that was fitted to the experimental data showed linear relationship with the actual data in view of the small error generated by them.
5) The SEM and DEM showed different morphologies that were distributed across the samples of both alloys under varying applied pressures as both showed structural changes (granular, lamellar, coarse etc.) due to pressure variation. The fine grains which were homogenously distributed on micrographs of both alloys at 1400 kg/cm2 can effectively block the movement of dislocations, thus increase the strength and plasticity of both alloys.
6) For all the models developed, a close relationship with the experimental results were underlying in view of the small errors generated by them and can be used to predict the experimental values of this research.
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