Gliwice, Poland. 401 Sunset Avenue, Windsor, Ontario, Canada, N9B 3P4.

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1 Artificial neural network modelling of the influence of chemical composition and cooling rate on the liquidus and solidus temperature for hypoeutectic aluminium alloys L.A. Dobrzanski 1a R. Maniara 1b, J. H. Sokolowski 2a, 1a, b Institute of Engineering Materials and Biomaterials, Konarskiego Str. 18A, Gliwice, Poland 2a Light Metals Casting Technology Group, Room 212A, Essex Hall, 401 Sunset Avenue, Windsor, Ontario, Canada, N9B 3P4. 1a leszek.dobrzanski@polsl.pl, 1b rafal.maniara@polsl.pl, 2a jerry@uwindsor.ca, Abstract The detailed knowledge of initial and finish temperature of transformations occurring during solidification of aluminium alloys allows determination of many technological parameters that enable operation of casting process in order to achieve a suitable cast structure, which has a direct impact on mechanical properties of produced objects. In the literature are reported four equations to determinate liquidus temperature and one equations to determinate solidus temperature for hypoeutectic aluminium alloys. There is however, no algorithm for calculation of cooling rate influence on the liquidus and solidus temperature. The paper presents a method of artificial neural network application in determination of the liquidus and solidus temperature for hypoeutectic aluminium alloys cooled with different cooling rate. The influence of cooling rate on the liquidus and solidus temperature change of solidified alloy has been estimated using, three types of artificial neural networks: MLP neural networks multilayer perceptron, RBL neural networks Radial Base Function, Generalized Regression Neural Networks (GRN) with sub-sample learning algorithms. A laboratory experiment has been carried out in order to check the correctness of an artificial neural network models. 1. Introduction Cast aluminum alloys are important construction material, which is used in various fields of technology. Because of their low density, relatively low melting point, good heat and electrical conduction, low thermal expansion coefficient, good castability and low casting shrinkage, they are mainly used in car manufacturing as piston castings, cylinder head castings, engine blocks, structural supporting reinforcements and absorbing crash impact elements. Aluminum alloys are also widely used in production of household goods, as well as in telecommunication and information technology. Apart from silicon silumins contain, either single or in combinations, the following alloy additions: Cu, Fe, Mg, Mn, Ni, Co, Cr, Mo, W, V, which are to improve mechanical and physicomechanical properties of silumins. In the last decade there has been a growing interest in the CAE software that allows modelling and controlling of casting processes. Effective application of CAE software packages as Magma, Calphad, Pro-Cast, Thermo-Calc or NovaFlow & Solid, reduces evidently time and cost of designed constructions and leads to increased work output and higher quality of products. The CAE software packages that support designing processes of casting technology allow the following: - cavity filling and metal solidification simulation, - heat exchange simulation, - shrinkage flow forecasting, - microporosity and air bubbles production forecasting,

2 - metal structure forecasting etc. For most forecast and simulated parameters phase equilibrium diagrams are used and on their basis initial and finish temperatures of transformations occurring during solidification of alloys are determined. Currently two- and three-component phase equilibrium diagrams have been thoroughly examined. Unfortunately, there are not sufficient data concerning multi-component phase equilibrium diagrams, therefore on their basis the exact temperatures of transformations occurring in multi-component alloys cannot be determined. At present these temperatures are determined through transformation of multi-component phase equilibrium diagrams into twocomponent ones and by means of that phase equilibrium temperatures are calculated. Recently in the CAE systems there have been implemented expert systems and systems using tools of artificial intelligence for casting processes operation. In order to determine various physical and metallurgical parameters of solidified aluminum alloys (e.g. number of fractions of solid in any solidification time, degree of cooling of liquid, solidification front velocity and microstructures) it is necessary to find out the precise the solidus and liquidus temperature of solidified alloys of certain chemical content. As it has been proved by many research centres, the temperatures change not only along with the change of chemical content but also with the change of thermodynamic conditions of solidified alloys. The findings of research presented in articles [1-5] show that the increasing of cooling rate results in decreasing of the solidus temperature of the examined alloy. That leads to widening of range of temperatures in which alloy undergoes solidification, therefore to change in proportion of solid fraction and liquid occurring while commencing successive phase transformations, which triggers directly change of alloy microstructure. There are not sufficient publications on mathematical and functional relation between the liquidus temperature, solidus temperature, chemical content and cooling rate for multicomponent aluminum alloys, the effect of which is that the temperature must be each time defined experimentally in exact conditions accounting for suitable cooling rate. Such a procedure results in increasing design cost and time of cast aluminum alloy constructions. However, extensively-developing methods of artificial intelligence, especially artificial neural networks, enable new possibilities of modelling of such complex cases. Artificial neural networks are very sophisticated modelling techniques capable of modelling extremely complex functions. At present, neural networks are nonlinear, which allows free and easy (it is unnecessary to formulate complex hypotheses) construction of nonlinear describing features of examined objects. An enormous advantage of neural networks is the ability to search for models of little known phenomena and processes; furthermore, it is not required from the user to assume any form of desired model or to be sure of any mathematical relation (algorithm) between the modelled objects. The main characteristic of artificial neural networks is the ability to generalize knowledge for new data not yet provided during learning process. It is not necessary for artificial neural networks to gather data and have access to entire database containing knowledge on predicted issue. They also show tolerance to discontinuity, random disturbances or shortage in learning set. Such characteristics allow their application where there are problems with data transformation, analysis, sorting and classification along with prediction or controlling on their basis of a certain process. Research carried out by Prof. L. A. Dobrzanski s team [6-9, 10] has shown that artificial neural networks is a useful tool to predict materials engineering phenomena. They have facilitated formation of numerical models describing kinetic

3 transformations in working steel under creep conditions. Results obtained from artificial neural networks turned out more precise than the ones obtained from empirical calculations. 2. Materials and experimental procedure 2.1. Materials for training Artificial Neutron Networks Formation of numerical model that allows calculation of the solidus temperature depending on chemical content and cooling rate has been determined by working out a suitable set of empirical data. The set of representative data including mass concentration of elements, the liquidus solidus temperature, solidification time, has been gathered through own research, the results made available by Dr. W. Kierkus [8] and specialist publications. The range of concentration of alloy elements and cooling rates have been presented in Table 1. Table 1 Range of mass concentration of elements and cooling rates (CR) in investigated Al-Si hypoeutectic alloys Si Fe Cu Mn Mg Zn Ti min 5 0,08 0, , ,03 max 11,9 1,35 4,64 0,6 1,28 2,9 11,9 2,5 Range Mass concentration of elements, % CR. ºC /s %Sr+%Ni+%Sn+%Pb+%Na%Ca 0,3 The gathered set of data designed for formation of a numerical model determining the liquidus and solidus temperature in relation to chemical content and cooling rate has been divided into two subsets: the learning set and the validation set. The data have been divided in proportion of 75% for the learning set and 25% for the validation set. The division into the sets has been made at random and the arithmetic mean and standard deviation from the assumed value have been observed. In order to control the learning correctness of artificial neural networks data obtained from a metallurgical experiment have been used. The results of the experiment have been used to make a testverification set. The data used in the process of learning and testing have been normalized by means of the minimax function that transforms the domains of variables to range 0, Materials for testing Artificial Neutron Networks The data obtained from the metallurgical experiment have been used for testing artificial neural networks. For the sake of research in the metallurgical laboratory of the University of Windsor there had been made six Al-Si experimental hypoeutectic alloys based on the

4 319 alloy. The alloys of chemical content shown in Table 2 were cast in an electrical resistance furnace with a ceramic melting crucible. The process of melting proceed in the nitrogen protective atmosphere to prevent the liquid metal from the diffusion of oxygen and hydrogen. Directly before casting of ingots, melted metal was degassed for 20 minutes in order to eliminate from the alloy hydrogen atoms as one of the learning vectors which influenced the liquidus and solidus temperatures and was undesirable in the investigated alloys. The melting and soaking temperature of the alloy was 850 ºC. Ingots of 45 mm in diameter and 50 mm in height were cast into thin-walled cups made of hot-work tool steel. The ingot mass was 330 g ±10 g. 2.3 Thermal analysis procedure In order to determine exactly the solidus and liquidus temperatures of the investigated alloys thermoanalysis has been made by means of the UMSA device equipped with data-measuring and recording system made by National Instruments company, attached to a PC computer Table 2 Chemical content, liquids temperature, solidus temperature and cooling rate of alloys used for artificial neural networks testing Alloy label Mass concentration of elements, %, Si Fe Cu Mn Mg Zn Ti 7-1 7,17 0,14 0,99 0,11 0,27 0,05 0, ,98 0,17 1,91 0,01 0,26 0,43 0, ,45 0,34 3,60 0,25 0,28 0,05 0, ,09 0,72 1,05 0,36 0,27 0,14 0, ,03 0,19 2,25 0,01 0,19 0,45 0, ,27 0,17 4,64 0,01 0,28 0,05 0,09 T LIQ, ºC %Sr+%Ni+%Sn+%Pb+%Na%Ca 0,95 T SOL, ºC Solidification Time, s CR, ºC /s 609,8 482,3 724,73 0,17 614,4 476,1 374,00 0,45 622,1 464,4 164,66 0,95 603,8 479,1 778,80 0,16 605,4 472,2 399,70 0,33 612,6 469,2 201,9 0,71 599,2 465,3 842,48 0,12 604,9 441,3 326,00 0,36 610,9 427,9 169,46 0,72 587,6 468,5 764,73 0,16 599,9 456,7 297,07 0,48 608,3 450,7 151,93 1,04 585, ,60 0,13 591,9 465,6 299,87 0,42 603,4 469,8 159,40 0,84 580,6 477,3 791,00 0,13 586,8 464,5 300,47 0,41 593,9 461,2 149,13 0,89. The device has been calibrated according to American Regulations of National Institute of Standards and Technology. Holes of 2 mm in diameter and 25 mm in length from the top of the ingot have been centrally made in the samples in order to install thermocouple. The thermocouple of the K type made by OMEGA company has been installed for measuring of the temperature. The samples have been placed in the heating cooling system and the lower and upper parts of the crucible have been isolated by means of ceramics in order to enforce the direction of solidification process from the cup walls towards the centre. To ensure exact measurement of temperature changes in time during the cooling process, the investigated alloys have again been melted and held in the temperature of 850 ºC for 15 minutes. The samples have been cooled at appropriate rate by means of compressed air provided through nozzles of the heating cooling system. In the experiment three types of cooling rates

5 have been applied: 0,2 ºC /s, 0,5 ºC /s and 1 ºC /s. The cooling rates have been calculated according to equation 2. The exact liquidus and solidus temperatures for each investigated alloy and the solidification time have been calculated on the basis of the derivative curves and precise thermal analysis has been presented in Table Evaluate of the Artificial Neural Networks Variety of artificial neural networks used in the experiment makes it necessary to apply number indicators, which allow the evaluation of the learning process. The following indicators have been regarded as the essential ones: mean network error, standard deviation quotient for errors and data, standard deviation for the error and the Pearson correlation coefficient. The mean network error has been calculated according to the following: E 1 = n n ( X mi X pi ) i= 1 Where: E mean network error, n number of data in test set, X mi i-times calculated value, X pi i-times calculated value by neural network. Standard deviation quotient for errors and data has been adopted as a quality quotient of a numerical model made by artificial neural networks. The numerical model of relationship between the liquidus and solidus temperature in relation to chemical content and cooling rate calculated by artificial neural networks can be accepted as a correct one provided that the output values given by the network contain smaller errors than a simple calculation of unknown output value. The simplest method for calculation of output value is still assumption of an average value of output values for he learning and testing sets. In that case, mean error is equal of standard deviation for output value in the learning set, whereas standard deviation quotient equals one. The smaller network error is, the smaller values for the standard deviation quotient become, finally reaching zero for the ideal forecast [ 6, 7]. 3. Results and discussion The presented in this paper method of the liquidus and solidus temperature calculation that is functionally depending on cooling rate and chemical content, allows to determine the liquidus and solidus temperature easily and quickly for any chemical content and cooling conditions. To find a solution to the problem, three types of artificial neural networks have been applied: - MLP neural networks multilayer perceptron with Beck Propagation and Conjugate Gradient Descent (CG) learning algorithms, - RBL neural networks Radial Base Function with K-Means (KM), K-Nearest Neighbour (KN) and Pseudo inversion (PI) learning algorithms, - Generalized Regression Neural Networks (GRNN) with sub-sample learning algorithms. For the MLP and GRNN networks a learning process has taken place for one and two hidden layers; however, for the RBL type a network has been trained for one hidden layer. Structures of trained networks have been presented along with learning algorithms in Table 4. (1)

6 Table 4 Structure and parameters of neural network learning Network type Network Structure Neurons in the 1 st hidden layer Neurons in the 2 nd hidden layer Learning algorithm GRNN 6: : SS MPL 6: : BP, CG RBF 6:6-70-2: KM, PI The networks have been trained on the learning set containing 73 learning vectors, while the validation set allowing to modify weights contained 20 learning vectors, in which the variables were the cooling rate (CR) and chemical content limited to the following elements: Si, Fe, Mn, Mg, Cu. In Table 5 there have been compared quality quotients of best trained networks belonging to each of the following groups. Table 5 Quality of neural networks researched in experiment Quality indicator Network type GRNN MPL RBF T Liq T Sol T Liq T Sol T Liq T Sol Mean 606, , , , , ,359 Standard Deviation 13,864 7,495 13,864 7,495 13,865 7,495 Average Error -0,8081 0,000-6,897-26,457 0,000 0,000 Error Standard Deviation 13,856 5,968 16,078 6,523 2,943 3,443 Mean absolute error. 10,848 4,944 14,219 26,457 2,214 2,820 Standard Deviation Quotient 0,999 0,796 1,1597 0,870 0,212 0,459 Pearson Correlation 0,035 0,605 0,789 0,591 0,977 0,888 As a result of the calculations made, it has been established that the smallest error committed in forecasting of the solidus temperature depending on chemical content and cooling rate occurs in the RBF network while applying the KM, KN and Pa learning algorithms, and the greatest error occurs in the GRNN network while applying sub-sample learning algorithm. Comparisons of the actual solidus temperature and the temperature calculated for the best network that has been produced in the experiment, are shown in Figure 1.

7 a) b) Figure 1. Comparison of actual liquidus and solidus temperature and temperature calculated by means of RBF network. The prepared model of artificial neural networks has been applied in a computer simulation of the influence of chemical content and cooling rate on the liquidus and solidus temperature of hypoeutectic aluminum alloys. Figures 2, 3 present the influence of chemical content on the solidus temperature of the modelled alloy at cooling rate of 0,2 K/s. These elements have considerable influence on mechanical and fatigue properties of Al-Si cast alloys after heat treatment, which consists in Al, Cu and Mg, Si phase emissions that become solidified as the last ones in the solidification process of the 3XX group. The greatest influence on the increase of the solidus temperature is exerted by Mn in more than 0,7% concentration and by Mg. Figure 2 Influence of alloy elements on the solidus temperature of the silumin of the other element concentration: 5% Si, 1% Cu, 0,01% Ti and cooling rate at 0,2 K/s Figure 3 Influence of alloy elements on the solidus temperature of the silumin of the other element concentration: 0,1% Mn, 0,5% Mg, 0,01% Ti and cooling rate at 0,2 K/s

8 Figure 4 The influence of cooling rate on the liquidus temperature of silumin of the following chemical content: 5% Si, 0,1% Fe, 0,1% Mn, 0,5% Mg, 0,1%Ti at various cooling rates and Al concentrations Figure 5 The influence of cooling rate on the solidus temperature of silumin of the following chemical content: 5% Si, 0,1% Fe, 0,1% Mn, 0,5% Mg, 0,1%Ti at various cooling rates and Cu concentrations The influence of cooling rate on the start of solidification liquidus temperature at different Cu and Si concentration is presented in Figure 4. In this experiment was used fallowing combination of concentrations of Cu: 1, 2, 4% with 7, 9% Si. For the better visualization of influence adding element on the start of solidifications axis X is expressed in content of Al. Very interesting is the influence of cooling rate on the start of solidification temperature liquidus temperature during continues cooling. The increase of the cooling rate affected on the increase of the solidification start temperature. The phenomena of an increase in the solidification start temperature with an increase in the cooling rate depends on the mobility of the clusters of atoms in the melt. The influence of cooling rate on the solidus temperature at different Cu concentration is presented in Figure 6. The decrease of the solidus temperature is generally determined by the increase of cooling rate. The effect is intensified only by Cu, Fe and Mn up to the 0,7% concentration or moderated by Mg and Mn up to the 0,7% concentration. 4. Conclusion As it has been shown in research, artificial neural networks are excellent for technological parameters forecast on the solidus temperature of cast aluminum alloys. The neural network error can be compared with the error produced while measuring of temperature by means of the UMSA device. The application of artificial neural networks allows to replace partially expensive and timeconsuming experimental research. Due to design of a suitable calculation model it is possible to determine the influence of not only a single element but also a couple of alloy elements at freely set value of other ingredients within the accepted range. The model obtained from artificial neural networks can be applied as an ingredient of the CAE systems that facilitate cast process control. Reference [1] L.A. Dobrzański, and etc.: Ocena metodą analizy termicznej wpływu szybkości krystalizacji na strukturę odlewniczego stopu aluminium AC AlSi7Cu, Materiały

9 konferencyjne II Polsko Ukraińskiej Konferencji Naukowej, Techniczno-Ekonomiczne Uwarunkowania Rozwoju Przedsiębiorczości, Kraków [2] R.MacKay, M. Durdjevic, J. Sokolowski: The effect of cooling rate on the fraction solid of the metallurgical reaction in the 319 alloy, AFS Transaction, [3] J.M. Boileau, J.W. Zindel and J.E. Allison: The effect of solidification time on the mechanical properties in a cast A356-T6 aluminum alloy, Society of Automotive Engineers, Inc., [4] L. Backerud, E. Król, J. Tamminen: Solidification characteristics of aluminum alloys, Vol. 1, Universitetsforlaget, Oslo [5] L. Backerud, G. Chai J. Tamminen: Solidification characteristics of aluminum alloys, Vol. 2. AFS [6] J. Trzaska, L.A. Dobrzański: Application of neural networks for designing the chemical composition of steel with the assumed hardness after cooling from the austenitising temperature, 13 th International Scientific Conference AMME 2005, Gliwice [7] J. Trzaska, L.A. Dobrzański: Modeling of transformations occurring during quenching in engineering steels, 3 rd International Scientific Conference MMME 2005, Gliwice [8] ProCAST The Leading Finite Element Solution for Casting Process Simulation, ProCast the user guide, ESI Gropu, [9] W.T. Kierkus, and etc.: Analysis of the Solidification of the 3XX Family of Aluminium Alloys, Data not published, [10] L.A. Dobrzański, J Trzaska, K. Pozimska: Zastosowanie sztucznych sieci neuronowych do wyznaczania temperatur Ac 1 Ac 3 stali konstrukcyjnych, Proceedings of the Iinternational Conference, Achievements in the Mechanical and Materials Engineering, AMME [11] R.MacKay, M. Durdjevic, J. Sokolowski: The effect of cooling rate on the fraction solid of the metallurgical reaction in the 319 alloy, AFS Transaction, [12] J.M. Boileau, J.W. Zindel and J.E. Allison: The effect of solidification time on the mechanical properties in a cast A356-T6 aluminum alloy, Society of Automotive Engineers, Inc., [13] L. Backerud, E. Król, J. Tamminen: Solidification characteristics of aluminum alloys, Vol. 1, Universitetsforlaget, Oslo [14] L. Backerud, G. Chai J. Tamminen: Solidification characteristics of aluminum alloys, Vol. 2. AFS [15] L. Backerud, G. Chai: Solidification characteristics of aluminum alloys, Vol. 3, AFS 1992.