J. Cent. South Univ. Technol. (2010) 17: 715-719

DOI: 10.1007/s11771-010-0545-x

Effects of aging parameters on hardness and electrical conductivity of Cu-Cr-Sn-Zn alloy by artificial neural network

SU Juan-hua(苏娟华), JIA Shu-guo(贾淑果), REN Feng-zhang(任凤章)

College of Materials Science and Engineering, Henan University of Science and Technology, Luoyang 471003, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2010

Abstract: In order to predict and control the properties of Cu-Cr-Sn-Zn alloy, a model of aging processes via an artificial neural network (ANN) method to map the non-linear relationship between parameters of aging process and the hardness and electrical conductivity properties of the Cu-Cr-Sn-Zn alloy was set up. The results show that the ANN model is a very useful and accurate tool for the property analysis and prediction of aging Cu-Cr-Sn-Zn alloy. Aged at 470-510 ℃ for 4-1 h, the optimal combinations of hardness 110-117 (HV) and electrical conductivity 40.6-37.7 S/m are available respectively.

Key words: Cu-Cr-Sn-Zn alloy; aging parameter; hardness; electrical conductivity; artificial neural network

1 Introduction

In plastic packaging application of integrated circuit, copper alloys are the most popular lead frame alloys due to their high thermal and electrical conductivity as well as high strength [1-3]. The functions of lead frame in electronic packing are providing channels for electronic signals between devices and circuits, and fixing devices on circuit boards. The aging hardening process in the fabrication of lead frame copper alloy makes it possible to get better mechanical and electrical properties. XIE  et al [4] studied the microstructure and solidification behavior of Cu-Ni-Si alloys with four different Cu contents systematically under near-equilibrium solidification conditions. HUANG and MA [5] researched the precipitation in Cu-Ni-Si-Zn alloy for lead frame. WANG et al [6] analyzed the influence of DC electric current on the hardness of thermally aged Cu-Cr-Zr alloy. HUANG and MA [7] analyzed the phases in Cu-Cr-Zr alloy. Cu-Cr-Sn-Zn alloy is a material for lead frames with excellent soften resistivity, press formability, electroplatability, bondability and solderability [8-9]. The aging precipitating process is an effective way to get high performance for lead frame Cu-Cr-Sn-Zn alloy [10]. The process has been mainly studied empirically by trial-and-error method so far. It is important and desirable to simulate the effects of aging treatment processes by numerical methods in order to analyze them. Artificial neural network (ANN) attempts to achieve good performance via dense interconnection of simple computational elements. The models are composed of many non-linear computational elements operating in parallel and arranged in a pattern of a biological neural network. ANN can be used for the mapping of input to output data without knowing the relationship between those data and can be applied in optimum design, classification and prediction problems [11-12]. SU and LI [13] made use of the ANN model and improved the Levenberg-Marquardt algorithm to analyze the hardness of a lead frame Cu-Cr-Zr copper alloy. LI et al [14] adopted a full-factorial design method to collect sample datasets. In Ref.[15], martensite and austenite start temperatures of Fe-based shape memory alloys were predicted by using a back- propagation (BP) ANN that used gradient descent learning algorithm. MOHAMMED et al [16] studied the potential of using neural network in prediction of wear loss quantity of some aluminum-copper-silicon carbide composite materials. In this work, a universal ANN program was designed on the basis of BP training algorithms to map the correlation between aging process parameters and properties and to predict the aging properties in the fabrication of high performance Cu-0.36Cr-0.23Sn- 0.15Zn (mass fraction, %) alloy.

2 Input and output variables of ANN

The input and output variables of ANN are based on the background of a process. The followings are used as input variables: the aging temperature (θ) and the aging time (t). Output variables are determined by the properties acquirement of hardness and electrical conductivity. The knowledge of a specific field is implicated in the existing training samples, so an appropriate dataset with good distribution is significant for reliable training and performance of neural networks. To ensure reasonable distribution and enough information containing in the dataset, aging processes are covered with different parameters. The aging temperatures are 400, 430, 450, 470, 500, 530, 550, 580 and 600 ℃, respectively; and the aging times are 0, 5, 15, 30, 60, 90, 120, 150, 180, 240, 300, and 360 min, respectively.

The alloy investigated was prepared by solution treatment at 920 ℃ for 1 h in argon atmosphere and water quenching. The aging treatments were carried out in a tube electric resistance furnace under a fluid atmosphere of argon with temperature accuracy of ±5 ℃. The electrical resistivity was determined by measuring the resistance of sample in a length of 100 mm using a ZY9987 digit-showed ohmmeter. The microhardness was measured on an HVS-1000 hardness tester under a load of 100 g and holding for 10 s. Every sample was tested five times with an accuracy of ±5%. The samples for transmission electronic microscope (TEM) analysis were prepared by conventional electro- polishing method using an electrolyte of V(HNO₃):V(CH₂OH)=1:3. The electron microscope measurement was carried out by using an H-800 TEM at 200 kV.

3 Hidden layers and neurons

Hidden layers perform abstract functions, namely, they can extract characteristic knowledge implicated in input data. So it is the hidden layers that give neural networks the ability to robustly deal with nonlinear and complex problems. However, different algorithms of BP networks have different limitations in practice. For instance, it is difficult for a single-hidden-layer network to improve its closeness-of-fit if it has too few hidden nodes; while excessive many hidden nodes enable it to memorize (over-fit) the training dataset, which produces poor generalization performance. At present there is not a valid analysis formula for designing hidden layers and it is an art to decide the quantity of nodes per hidden layer, so a trade-off exists between generalization performance and the complexity of training procedure when designing the topology of a neural network.

In this work a lot of computational instances show that two-hidden-layer neural networks are suitable. N (not too great) is the dimension of input layers, N₁ and N₂ are the quantities of nodes in the first and the second hidden layers, respectively. Set N₁= N, and adjust N₂ to ensure that both the generalization performance and the rate of the convergence are satisfactory. After many times of trial-and-error computation by the ANN program, perfect topologies ({2, 4, 9, 2}) of the hardness and electrical conductivity outputs are founded for lead frame Cu-Cr-Sn-Zn alloy.

4 BP neural networks

BP, which is one of the most famous training algorithms for multi-layer perception, is a gradient descent technique to minimize the error for particular training pattern. The weights of the neurons are iteratively adjusted in accordance with the error correction rule until the output for a specific network is close to the desired output [17-19].

Each input unit of the input layer receives input signal x_j and broadcasts this signal to all units in the hidden layer. Each hidden unit y_i sums its weighted input signal and applies its activation function to compute output signal.

                            (1)

where w_ij is the weight from input unit x_j to hidden unit y_i. The output signal of hidden unit y_i is sent to all units in the output layer. Each output unit o_l sums its weighted input signal and uses its activation function to compute its output signal.

                          (2)

where ω_il is the weight from hidden unit y_i to output unit o_l . The activation function used in this work is a logistic sigmoid function defined as

                                (3)

The BP training algorithm is an iterative gradient descent algorithm, which is designed to minimize the sum of square error (E) and averages all patterns, is calculated as follows:

                        (4)

where t_l  is the desired or actual output; and o_l is the predicted output for the lth pattern.

The training procedure is shown in Fig.1. It reveals that the training error is always reduced during the training procedure. The training error is hardly changed after the epochs are up to 500 times.

Fig.1 Training procedure of neural network mode (Performance is 0.051 220 2)

5 Results and discussion

Fig.2 reveals the relationship between the predicted values from the trained neural network and the tested data to test the generalization performance of the trained networks. Very good agreements between them are achieved, which indicates that the trained networks are of optimal generalization performance. This also demonstrates that, as a typical data mining technique, neural network can find the basic pattern information implied in a great number of experimental data, extract useful rules and then use these rules for obtaining reasonable predicted results.

Fig.2 Results of validating generalization: (a) Electrical conductivity; (b) Hardness

By using the domain information stored in the trained networks, three-dimensional graph is drawn in Fig.3, which presents much more professional information about the relationship between hardness and aging properties.

Fig.3 Hardness of Cu-Cr-Sn-Zn alloy with regard to temperature and time

Fig.3 reveals that the time to reach the peak hardness decreases with increasing temperature. With the enhancement of the temperature, the initial kinetic of the precipitation is higher, which leads to shorter time to reach the peak hardness [20]. For example, aging at 470-  510 ℃ for 4-1 h the maximum hardness can be obtained from 110 to 117 (HV). At the peak hardness the full precipitation is available and the hardening effect is optimum.

The TEM image of the precipitates is shown in Fig.4. The microstructures of Cu-Cr-Sn-Zn alloy are the finely dispersed precipitates in Cu matrix, having a size of 10-40 nm, as shown in Fig.4. These fine precipitates together with Cu matrix give rise to peak hardness. The hardness increase follows the empirical Orowan relationship:

                                (5)

where ?τ is the increase in shear stress; k is the constant; f is the volume fraction of precipitates; and R denotes the diameter of precipitates. By means of the TEM analysis of Fig.4, the volume fraction of precipitates is 30%- 40%. The higher the volume fraction of precipitates, the smaller the size of the precipitates, the greater the Δτ, the greater the hardness of the alloy.

Fig.4 TEM image of Cu-Cr-Sn-Zn alloy aged at 500 ℃ for  15 min

The electrical conductivity increases with the increase of time and temperature, as shown in Fig.5. Aged at 510 ℃ for 1 h the electrical conductivity is 37.7 S/m. The highest conductivity reaches 40.8 S/m at 600 ℃ for 6 h. The higher temperature and longer time bring about more precipitates, which leads to the conductivity almost reaching 40.6 S/m, as shown in Fig.5. The growth of precipitates reduces the contents of solute atom in matrix and results in a continuous increase in electrical conductivity during the aging process. So, the electrical conductivity in Cu-Cr-Sn-Zn lead frame alloy remains a higher level at a higher temperature and longer time aging process.

Fig.5 Electrical conductivity of Cu-Cr-Sn-Zn alloy with regard to temperature and time

Upon aging the solidified Cu-Cr-Sn-Zn alloy first underwent the precipitation process due to its extended super-saturation limit and much more crystal defects. It is the precipitation of supersaturated solid solution that results in the initial sharp increase of conductivity. The precipitation proceeds through diffusing the solute atoms with the aid of vacancies. The vacancies with higher concentration in the solidified alloy shift rapidly at the initial stage of aging process, and the decay of them can be expressed by the following equation [21]:

N₀exp(-ant)                              (6)

where  is the quantity of vacancy; n is the number of vacancy sites that keep constant upon aging; a is the constant at a definite aging temperature; t is the aging time; and N₀ is the vacancy quantity of supersaturated solid solution. It is noted that the decay of vacancies conforms to the variation of resistivity at a definite aging temperature. The longer the aging time, the less the number of the supersaturated vacancies, the more slowly the precipitation process.

6 Conclusions

(1) A neural network model of aging processes is built for Cu-0.36Cr-0.23Sn-0.15Zn alloy. High precision as well as good generalization performance of the model is demonstrated.

(2) By the domain knowledge stored in the trained networks, three-dimensional graph is obtained. With the help of the knowledge repository stored in the trained network, important foundation is laid for the optimally controlling and predicting the aging properties of Cu-0.36Cr-0.23Sn-0.15Zn alloy.

(3) Aging at 470-510 ℃ for 4-1 h, the optimal combinations of hardness and conductivity of the alloy are 110-117 (HV) and 40.6-37.7 S/m, respectively.

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Foundation item: Project(2006AA03Z528) supported by the National High-Tech Research and Development Program of China; Project(102102210174) supported by the Science and Technology Research Project of Henan Province, China; Project(2008ZDYY005) supported by Special Fund for Important Forepart Research in Henan University of Science and Technology

Received date: 2009-10-20; Accepted date: 2010-03-05

Corresponding author: SU Juan-hua, PhD, Professor; Tel: +86-379-64276860; E-mail: sujh@mail.haust.edu.cn

(Edited by CHEN Wei-ping)