Aluminum-silicon cast alloys are prominent group among Al alloys and widely
used in automotive and aerospace applications to produce critical components,
because of good fluidity and castability, higher strength to weight ratio, good
surface finish and better wear resistance in comparison with other aluminum
cast alloys (Venkaltaramani et al., 1995; Prasada-Rao
et al., 2004).
Alloys with 3-5% silicon are utilized in rotors, vessels, valve bodies and
large fan blade fittings. Eutectic alloys containing between 11-13% Si are used
for pistons, cylinders, blocks and heads of engines in automobile and aeronautical
industries (Hegde and Prabhu, 2008). Alloy elements
such as Fe, Cu, Mg and Mn are added Al-Si to achieve the desired properties.
It is common practice in the foundry industries to cast molten metal 100°C above the liquidus temperature which defined as superheat temperature to provide better molten metal fluidity and obtain desired microstructure.
Regarding to this issue, the knowledge of reliable liquidus temperature of alloys is necessary to estimate their corresponding superheat temperature. Since, the data about binary and tertiary phase diagrams of aluminium with other alloying elements are not sufficient, correct determine of liquidus temperature in multi component Al-Si alloys is essential to increase the efficiency of melt treatment and produce high quality components.
|| Variation of grain size with pouring temperature
Grain size: The solidification microstructure of the alloy is dependent
on the superheat temperature, as well as the cooling rate during solidification
(Zhong-wei et al., 2005). It has been reported
that grain refined structure achieved by controlling casting parameters such
as superheat temperature, casting temperature and cooling rate (Conley
et al., 2000). Figure 1 shows the relationship
between grain size and superheat temperature in permanent mold casting, sand
casting and lost foam casting for Al-7%Si. It can be see that grain size of
the alloy increases with increasing the superheat temperature from 700 to 900°C
(Venkaltaramani et al., 1995).
||Microstructure of Al-7Si-0.4Mg alloy at two different pouring
temperatures: (a) 680°C and (b) 710°C
Srinivasan et al. (2006) also obtained same
results in sand cast Al-7Si-0.3 Mg. Figure 2a and b
show the effect of pouring temperature on microstructure of Al-7%Si in two different
pouring temperatures. It is clear that DAS increases with increasing pouring
temperature and in turn reduces the mechanical properties (Srinivasan
et al., 2006).
Moreover, increasing pouring temperature causes to increase fluidity length
of molten metal as shown in Fig. 3 (Rzychon
and Kielbus, 2007).
Calculation and Prediction of liquidus temperature: Differential thermal
analysis (DTA) (Wu and Perepezko, 2000) and Differential
Scanning Calorimeter (DSC) (Dong and Brooks 2005) are
used to determination of liquidus temperatures, the result even for binary alloys
was variable. Also, thermal analysis is applied for calculation of liquidus
temperature based on cooling curve of molten metal. In this condition the result
is dependent to cooling rate and geometry of the mould sample.
Drossel (1981) Eq. 1 to predict the
liquidus temperature of Al-Si cast alloy.
||The effect of pouring temperature on the fluidity length
However, the range of chemical composition is limited for application. Besides,
Eq. 2 has been proposed (Vijayaraghavan
et al., 1996) based on the ternary phase diagram:
This equation can be used just for Al-Si-Cu alloys. Another relationship developed
based on silicon equivalent by Djurdjevic et al.
The result is more accurate compared with Eq. 1 and 2. However, all of the major alloying elements must have eutectic or peritectic reaction with Al.
Due to chemical composition limitation and their assumption to validate above equations, forecast of liquidus temperature based on Artificial Neural Network has drawn attention.
The aim of this study is to use artificial neural network method for the prediction of the liquidus temperature of multi-component hypoeutectic Al-Si alloys, based on their chemical compositions.
Modeling with artificial neural network: Artificial neural network has
been widely used in solving material science problems that involve the manipulation
of several parameters and non-linear interpolation and therefore not easily
amenable to conventional theoretical (Sha and Edwards, 2007)
and experimental approaches.
Since, ANN has been established in the field of material science (Bhadeshia,
1999), researchers utilized this modeling technique in forecasting parameters
in hot working Aluminium alloys (Chun et al., 1999),
prediction of mechanical properties of automotive Al alloys (Emadi
et al., 2001), prediction of porosity formation in Al-Si cast alloy
(Shafyei et al., 2006), forecasting of tensile
and density properties in Al metal matrix composite (Altinkok
and Koker, 2006), modeling creep life behaviuor of aluminium composite (Gupta
et al., 2007), grain size prediction of AA5754 (Lela
et al., 2008), study surface roughness (Caydas
and Hascalyk, 2008) and forecasting the tensile strength of welded A319
cast aluminium alloy (Jayaraman et al., 2009).
This variety of applications demonstrates the capability of artificial neural
network method in the prediction of physical and mechanical properties of aluminium
Artificial neural network theory: A neural network is a system composed of many simple processing elements operating in parallel whose function is determined by network structure, connection strengths and the processing performed at computing elements or nodes.
One of the prominent advantages of ANN is its ability to learn how to do tasks based on the set of data, called training set. There are several types of neural network such as feed forward neural network, Radial Basis Function (RBF) network, Kohonen self-organizing network and etc. As mentioned above, several neurons, which are highly connected to each other in different layers form an ANN.
One of the most frequent types of ANN is feed forward which consists of an
input layer, one or more hidden layers and an output layer (Shafyei
et al., 2006) that has been demonstrated schematically as a three-layer
ANN in Fig. 4.
Each node is composed of four main elements which are input, weighted connection, activation function and output. Basically, the inputs are information received from the preceding layer which is of the form:
where, Xj is the net input, Xi are inputs from the previous layer, Wij are weights entered node j, which are values assigned to the connections between nodes and express the effect of an input set on the node, bj is the bias associated with node j and n is the number of nodes. The bias neurons do not have any input. They just affect the neurons of the next layer by emitting a constant output value across the weighted connections. Details are shown in Fig. 5 for better understanding.
|| A processing element (neuron) operation
To avoid the numerical overflows due to very large or very small values, normalization
of the inputs is necessary which could be minmax function formulated as follows
(Sola and Sevilla, 1997):
Normalization limits the range of the output values into [0, 1] where data can be retrieved by the reverse method of normalization.
Another element of a neuron is activation function which shows the internal activation level and the other one is output (Y) which is generally obtained as a function of inputs and determined as follows:
A multilayer network, in general, learns much faster when the activation function
is represented by a hyperbolic tangent. Hence, the activation function f in
the hidden layer is selected as hyperbolic tangent sigmoid transfer function.
The hyperbolic tangent can make the network non-linear whose strength is determined
by the weight Wij. The output Y is therefore a non-linear function of Xj. The
function usually chosen to be the hyperbolic tangent because of its flexibility
and faster convergence (Bhadeshia 1999).
There are three types of learning in neural network which are supervised learning, unsupervised and reinforcement learning.
To illustrate how a neural network works and to estimate how accurate a neural
network is, the data set is divided into two categories:
||Training category which includes the weights associated with
||Test category which verifies the network predictions for instances that
are not learnt previously
The supervised learning method procedure is as follows: A training process
starts by introducing an input vector to the input layer and distributing it
throughout the network to the output layer. At each observation, the output
vector, which is produced from the output nodes, is compared with the target
vector and errors are calculated.
To minimize the error, the weights are recalculated according to the difference
between output and target vector and the training process turns back to the
previous layer to update the weights and train the network again with new values.
This kind of training is called backpropagation training algorithm (Shafyei
et al., 2006).
ANN structure and training: However, based on the definition of network structure and components, there are several ANN models trained and tested using training data sets. Here, in this study, we use feed forward neural network structure (Fig. 4). The ANN consists of element concentrations and liquidus temperature in the input and the output layers, respectively.
The number of hidden layers and neurons within each hidden layer can be varied
based on the complexity of the problem and the dataset. In our study, only one
hidden layer is used while the neurons within this layer varies from 2 to 12.
The optimal configuration was based upon minimizing the difference between the
neural network predicted values and the desired outputs. A total dataset of
156 samples were selected from AnyCast software, Binary phase diagram of aluminium
and previous published works (Byczynski, 1997; Djurdjevic
et al., 1998; McDonald et al., 2004;
Robles-Hernandez et al., 2005) to train and test
the network where 15 of them applied as the test set. Also, the range of input
data used for prediction of liquidus temperature is shown in Table
|| Maximum and minimum of input parameters
The data applied to the process of learning and testing have been normalized by means of the minmax function that transforms the domains of variables to range [0,1].
The hyperbolic tangent sigmoid transfer function which demonstrated in Eq. 7 was used as the activation function in the hidden layer and a linear transfer function was used in the output layer.
Furthermore, the learning algorithm used in the proposed methodology is Levenberg-Marquardt backpropagation.
RESULTS AND DISCUSSION
As explained before, number of neurons in each hidden layer varies according to the intricacy of the problem. Therefore, it should be selected in such a way to minimize the network performance function.
The network performance function is measured according to the Mean Square Error (MSE). The variation of network performance function with the number of hidden neurons is shown in Fig. 6. It illustrates that a hidden layer with 8 neurons results in minimum MSE. So, the ANN model trained by 7 neurons as input layer, 8 neurons in hidden layer and one neuron as the output. It was also implemented using feed forward backpropagation neural network.
The investigation is shown in Fig. 7 and 8
using a regression analysis. Regression is a method of determining relationships
among different data in order to predict future behavior or results. The regression
of training and test steps are shown. As the figures depict, the training and
test step regression results are 0.99109 and 0.97981, respectively.
To compare the accuracy of the proposed methodology with the methods developed by Drossel, Vijayaraghavan and Djurdjevic for calculation of liquidus temperature in Al-Si cast alloy, Fig. 9 and 10 have been plotted.
||Variation of network performance function with the number
of hidden neurons
|| Training step regression
As it can be figured out, the predicted values have more convergence to the real data compared to developed equations for input test data. Although, djurdjevic equation shows better prediction than other two equations, suggested ANN model is more efficient.
Not only reliable and accurate prediction of liquidus temperature helps to obtain desired microstructure result in improving mechanical properties of Al-Si cast alloy, but also, it assists to provide required viscosity and surface tension of molten metal for better fluidity to produce high quality Al-Si casting components.
As the results show, the proposed ANN gives satisfactory results to predict the liquidus temperature.
|| Testing step regression
||Comparison of predicted values with drossel, vijayaraghavan
||Linear regression of predicted values compared with developed
It has been shown that the application of artificial neural networks is accurate to forecast different phenomena in material science. Hence, in this investigation, the ANN with one hidden layer and eight units in the hidden layer has been used to predict the liquidus temperature of Al-Si cast alloys. The research shows that ANN performs well in prediction of liquidus temperature when compared to the experimental measurements. Furthermore, the model obtained from ANN can be used in the modeling of the solidification behavior of aluminum-silicon alloys.
The authors would like to acknowledge Universiti Teknologi Malaysia for providing research facilities and the ministry of science and technology of Malaysia for financial support.