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Rare Metals

, Volume 38, Issue 12, pp 1124–1130 | Cite as

Microstructure quantification of Cu–4.7Sn alloys prepared by two-phase zone continuous casting and a BP artificial neural network model for microstructure prediction

  • Ji-Hui Luo
  • Xue-Feng LiuEmail author
  • Zhang-Zhi Shi
  • Yi-Fei Liu
Article
  • 113 Downloads

Abstract

Microstructures of Cu–4.7Sn (%) alloys prepared by two-phase zone continuous casting (TZCC) technology contain large columnar grains and small grains. A compound grain structure, composed of a large columnar grain and at least one small grain within it, is observed and called as grain-covered grains (GCGs). Distribution of small grains, their numbers and sizes as well as numbers and sizes of columnar grains were characterized quantitatively by metallographic microscope. Back propagation (BP) artificial neural network was employed to build a model to predict microstructures produced by different processing parameters. Inputs of the model are five processing parameters, which are temperatures of melt, mold and cooling water, speed of TZCC, and cooling distance. Outputs of the model are nine microstructure quantities, which are numbers of small grains within columnar grains, at the boundaries of the columnar grains, or at the surface of the alloy, the maximum and the minimum numbers of small grains within a columnar grain, numbers of columnar grains with or without small grains, and sizes of small grains and columnar grains. The model yields precise prediction, which lays foundation for controlling microstructures of alloys prepared by TZCC.

Keywords

Two-phase zone continuous casting Cu–Sn alloy Grains-covered grains Microstructure quantification Back propagation artificial neural network 

1 Introduction

Grain size, number, and shape are important for quantifying microstructures of as-cast alloys [1, 2, 3, 4, 5, 6]. According to grain size, microstructures can be divided into those of coarse, fine, or ultrafine grains. According to grain shape, microstructures can be divided into those of equiaxed, spherical, or columnar grains. Yvell et al. [7] studied the microstructural changes during the deformation of 316L stainless steel through measuring grain size and number. Tseng et al. [8] studied the stress–strain behavior of FeMnAlNi alloys and quantified the grain size and number using electron back-scattered diffraction (EBSD) method. Tiley et al. [9] measured grain size and number using the linear intercept method. Conventionally, grain size and shape in an alloy are relatively uniform, with a variation not very huge.

However, a Cu–4.7Sn (in wt% as default) alloy prepared by two-phase zone continuous casting (TZCC) is composed of large columnar grains and small grains. Small grains possibly distribute at the boundaries of the columnar grains, at the surface of the alloy, or within columnar grains. A compound grain structure, composed of a large columnar grain and at least one small grain within it, is observed and called as grain-covered grains (GCGs) [10, 11]. A proper way to quantify such a microstructure with a huge variation of grain size and shape is necessary to be developed in order to better control the microstructure.

Artificial neural network simulates human brain, and its key characteristic is the capability of self-organization or self-learning [12, 13, 14, 15, 16]. It is especially suitable for treating nonlinear phenomena and complex relationships with a high calculation efficiency, and it is an artificial intelligence technique for establishing an implicit model [17, 18, 19, 20]. It has been successfully applied to establish models relating microstructures with processing parameters. Zhou et al. [21, 22] developed an efficient artificial neural network model to establish the relation between strain rate, strain, temperature, and stress in plastic deformation. Luo and Li [23] developed an empirical model for the relation between α phase size and processing parameters of hot deformation of Ti–6Al–4V alloy. Jiang et al. [24] used artificial neural network method to establish a model for predicting parameters of continuous casting and cooling rate of spring steel slab.

In this paper, microstructures of Cu–4.7Sn alloys prepared by TZCC were characterized and quantified. Back propagation (BP) artificial neural network was used to establish a reliable model for predicting microstructure with processing parameters as inputs.

2 Experimental

Cu–4.7Sn (wt%) alloys with wide two-phase zone (920–1050 °C) were prepared by a self-developed TZCC technology. The principle of TZCC technology can be found in Refs. [10, 11]. Five critical processing parameters include melt temperature of 1080–1200 °C, mold temperature of 1005–1050 °C, continuous casting speed of 5–35 mm·min−1, cooling water temperature of 15–30 °C, and cooling distance of 5–20 mm. The L16(45) orthogonal tests were designed to study the influence of the processing parameters on microstructure, as shown in Table 1. Samples for microstructure observation were cut from the Cu–4.7Sn alloys. After polishing, the samples were etched by a solution of FeCl3 (5 g) and alcohol (80 ml). Optical microscope (OM, Nikon Coolpix 995) was used to observe the microstructure.
Table 1

Nos. 1–16 samples designed for training BP artificial neural network and No. 17 sample for testing trained BP artificial neural network

Nos.

Melt temperature/°C

Mold temperature/°C

Continuous casting speed/(mm·min−1)

Cooling water temperature/°C

Cooling distance/mm

1

1080

1005

5

15

5

2

1080

1020

15

20

10

3

1080

1035

25

25

15

4

1080

1050

35

30

20

5

1120

1005

15

25

20

6

1120

1020

5

30

15

7

1120

1035

35

15

10

8

1120

1050

25

20

5

9

1160

1005

25

30

10

10

1160

1020

35

25

5

11

1160

1035

5

20

20

12

1160

1050

15

15

15

13

1200

1005

35

20

15

14

1200

1020

25

15

20

15

1200

1035

15

30

5

16

1200

1050

5

25

10

17

1200

1050

20

20

5

BP artificial neural network was used to establish a model for predicting microstructures under different processing parameters. In general, the network has input, hidden, and output layers, as shown in Fig. 1. The input layer consists of five processing parameters, which are melt temperature (Ta), mold temperature (Tm), continuous casting speed (v), cooling water temperature (Tw), and cooling distance (lw). The output layer consists of nine microstructure quantities, including numbers of small grains within columnar grains (n1), at the boundaries of the columnar grains (n2) or at the surface of the alloy (n3), the number of columnar grains (N1), the number of columnar grains containing small grains (N2), the minimum (L1) and the maximum (L2) numbers of small grains within a columnar grain, sizes of small grains (d), and large columnar grains (D). MATLAB software was used to establish the BP artificial neural network [25, 26, 27, 28, 29].
Fig. 1

Structure of a BP neural network correlating five processing parameters in Table 1 as input layer neutrons and nine microstructure quantities in Table 2 as output layer neutrons

3 Results and discussion

3.1 Microstructure and its quantification

The microstructures of Nos. 1–17 samples were observed and quantified. Take the microstructure of No. 2 sample for example. Figure 2a shows its longitudinal microstructure, which mainly contains large columnar grains. A local region in Fig. 2a is enlarged in Fig. 2b, in which there are two small grains within a large columnar grain, as pointed out by red arrows. The two small grains and their host columnar grain form a compound GCG grain structure. There also exists a small grain at a boundary of the columnar grains, as pointed out by a green arrow. Figure 2c shows the transverse microstructure of No. 2 sample, which contains 28 uniformly distributed columnar grains with an average diameter of about 1889.8 μm. A local region in Fig. 2c is enlarged in Fig. 2d, in which there exist two small grains within a columnar grain (pointed out by red arrows) and a small grain at a boundary of the columnar grains (pointed by a green arrow).
Fig. 2

OM images of No. 2 sample: a longitudinal section, b an enlarged region in a, c transverse section, and d an enlarged region in c

Figure 3 shows all the 19 small grains in Fig. 2c. Sixteen small grains within columnar grains are pointed out by red arrows, as shown in Fig. 3a–j. Two small grains at the boundaries of the columnar grains are pointed out by green arrows, as shown in Fig. 3j, k. One small grain locates at the surface of the alloy, which is pointed out by a green arrow in Fig. 3l. The average size of the 19 small grains is about 50.8 μm. Six columnar grains contain small grains. The minimum and the maximum numbers of small grains in a columnar grain in Fig. 3 are 1 and 9, respectively. Analogously, the microstructures of the other samples in Table 1 are quantified, as listed in Table 2.
Fig. 3

OM images of all 19 small grains in Fig. 2c of No. 2 sample: ai small grains within columnar grains, j two small grains within a columnar grain and one small grain at a boundary of columnar grains, k a small grain at a boundary of columnar grains, and l a small grain at surface of alloy

Table 2

Microstructure quantification of Nos. 1–17 samples

Nos.

n1

n2

n3

d/μm

N1

D/μm

N2

L1

L2

1

19

6

1

67.8

26

1961.1

8

1

3

2

16

2

1

50.8

28

1889.8

6

1

9

3

17

8

1

39.6

31

1796.1

7

1

8

4

9

3

1

31.2

33

1740.7

5

1

3

5

15

4

2

48.3

22

2130.0

6

1

4

6

16

7

3

61.1

20

2236.1

6

1

5

7

9

1

2

36.3

35

1690.3

5

1

3

8

10

5

0

37.6

30

1825.7

5

1

4

9

14

1

2

43.8

33

1740.8

8

1

3

10

9

2

0

40.1

35

1690.3

7

1

2

11

17

4

2

62.7

24

2041.2

4

1

8

12

9

5

0

37.5

29

1856.9

5

1

4

13

11

2

2

38.4

37

1643.8

9

1

2

14

13

3

1

44.7

31

1796.0

7

1

4

15

15

2

0

49.5

27

1924.5

6

1

4

16

12

2

3

56.3

19

2294.1

7

1

3

17

13

7

0

44.1

26

1975.5

8

1

3

3.2 BP artificial neural network modeling

Before training a BP artificial neural network, experimental data are normalized to improve learning rate. The normalization equation is:
$$X^{'} = {x \mathord{\left/ {\vphantom {x {x_{ \hbox{max} } }}} \right. \kern-0pt} {x_{ \hbox{max} } }},$$
(1)
where x is a value of an experimentally measured microstructure quantity, and xmax is its maximum value. It is well known that the number of hidden layer neurons significantly affects prediction accuracy [24, 30]. If the number of hidden layer neurons is small, a BP artificial neural network may not yield a precise prediction. However, the larger the number of hidden layer neurons is, the more time-consuming the training process is. A proper number of hidden layer neurons should balance prediction accuracy and training time. An empirical formula for the number “l” of hidden layer neurons is [24, 30]
$$l \approx \sqrt {n + m} + a,$$
(2)
where l is an integer number, n is the number of input layer neurons, m is the number of output layer neurons, and a is an integer from 1 to 10. In the present work, n = 5, m = 9, a is set to be 8, and then it can be calculated that l = 12. Processing parameters and microstructure quantities of Nos. 1–16 samples were used to train the BP artificial neural network, while those of No. 17 sample were used to test the prediction accuracy of the trained BP artificial neural network. Figure 4 shows that mean square error reaches the best value of 1 × 10−4 after 124,081 training epochs.
Fig. 4

Variation of training error in BP neural network

The trained results and their deviations from the experimental results are shown in Table 3. For microstructure quantities n2, n3, N2, L1, L2, perfect training results are achieved with no error. For the other microstructure quantities, training errors are within ± 7.7%, of which the majorities are within ± 5%. Overall, the trained BP artificial neural network reaches a high precision. It successfully establishes a reliable relationship between the five processing parameters and the nine microstructure quantities. No. 17 sample was used to test its prediction accuracy. Table 4 shows the predicted microstructure quantities. For microstructure quantities n1, n2, n3, N2, L1, L2, perfect predicted results are obtained with no error. For the other microstructure quantities, prediction errors are within ± 7.7%. Overall, the trained BP artificial neural network yields a precise prediction.
Table 3

Trained results of Nos. 1–16 samples and their relative errors (%) with respect to experimental results (Exp.) of nonzero values, i.e., relative error = (Exp. − Trained)/Exp. × 100% (as to experimental results of zero value, absolute errors being calculated, indicated by *)

Nos.

n1

n2

n3

d/μm

N1

D/μm

N2

L1

L2

 

Trained

Error

Trained

Error

Trained

Error

Trained

Error

Trained

Error

Trained

Error

Trained

Error

Trained

Error

Trained

Error

1

19

0

6

0

1

0

67.4

0.6

26

0

1962.2

− 0.1

8

0

1

0

3

0

2

16

0

2

0

1

0

50.6

0.4

28

0

1876.3

0.7

6

0

1

0

9

0

3

17

0

8

0

1

0

39.8

− 0.5

31

0

1801.5

− 0.3

7

0

1

0

8

0

4

9

0

3

0

1

0

30.7

1.6

33

0

1758.4

− 1.0

5

0

1

0

3

0

5

14

6.7

4

0

2

0

49.0

− 1.4

22

0

2047.4

4.0

6

0

1

0

4

0

6

16

0

7

0

3

0

60.4

1.1

20

0

2265.2

− 1.3

6

0

1

0

5

0

7

9

0

1

0

2

0

36.7

− 1.1

36

− 2.9

1691.5

− 0.1

5

0

1

0

3

0

8

10

0

5

0

0

0*

37.5

0.3

30

0

1807.8

1.0

5

0

1

0

4

0

9

14

0

1

0

2

0

43.1

1.6

33

0

1761.3

− 1.2

8

0

1

0

3

0

10

9

0

2

0

0

0*

39.7

1.0

35

0

1705.5

− 0.9

7

0

1

0

2

0

11

17

0

4

0

2

0

62.0

1.1

24

0

2092.7

− 2.5

4

0

1

0

8

0

12

9

0

5

0

0

0*

37.5

0.0

29

0

1862.1

− 0.3

5

0

1

0

4

0

13

11

0

2

0

2

0

38.7

− 0.7

37

0

1624.5

1.2

9

0

1

0

2

0

14

14

− 7.7

3

0

1

0

44.6

0.2

31

0

1813.4

− 1.0

7

0

1

0

4

0

15

15

0

2

0

0

0*

50.6

− 2.2

27

0

1913.8

0.6

6

0

1

0

4

0

16

12

0

2

0

3

0

56.6

− 0.5

19

0

2260.2

1.5

7

0

1

0

3

0

Table 4

Predicted results (Pred.) of No. 17 sample and their relative errors (%) with respect to experimental results of nonzero values, i.e., relative error = (Exp. − Pred.)/Exp. × 100% (as to experimental results of zero value, absolute errors being calculated, indicated by *)

n1

n2

n3

d/μm

N1

D/μm

N2

L1

L2

Pred.

Error

Pred.

Error

Pred.

Error

Pred.

Error

Pred.

Error

Pred.

Error

Pred.

Error

Pred.

Error

Pred.

Error

13

0

7

0

0

0*

41.1

6.8

28

− 7.7

1941.4

1.7

8

0

1

0

3

0

4 Conclusions

Cu–4.7Sn alloys prepared by two-phase zone continuous casting (TZCC) technology consist of large columnar grains and small grains. Seventeen Cu–4.7Sn alloy samples (Nos. 1–17 samples) were prepared by 17 combinations of five processing parameters, which are temperatures of melt, mold and cooling water, speed of TZCC, and cooling distance. Their microstructures were characterized by nine quantities, which are numbers of small grains within columnar grains (n1), at the boundaries of the columnar grains (n2) or at the surface of the alloy (n3), the minimum (L1) and the maximum (L2) numbers of small grains within a columnar grain, numbers of columnar grains with (N2) or without (N1 − N2) small grains, and sizes of small grains (d) and columnar grains (D).

BP artificial neural network was used to build a model for predicting the nine microstructure quantities with the five processing parameters as inputs. Nos. 1–6 samples were designed to train the BP artificial neural network. For microstructure quantities n2, n3, N2, L1, L2, perfect training results are achieved with no error. For the other microstructure quantities, training errors are within ± 7.7%, of which the majorities are within ± 5%. Overall, the trained BP artificial neural network reaches a high precision. No. 17 sample was used to test the prediction accuracy of the trained BP artificial neural network. For microstructure quantities n1, n2, n3, N2, L1, L2, perfect predicted results are obtained with no error. For the other microstructure quantities, prediction errors are within ± 7.7%. Overall, the trained BP artificial neural network yields a precise prediction.

Notes

Acknowledgements

This work was financially supported by the National Key Research and Development Plan of China (No. 2016YFB0301300), the National Natural Science Foundation of China (Nos. 51374025, 51674027 and U1703131), and the Beijing Municipal Natural Science Foundation (No. 2152020).

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Copyright information

© The Nonferrous Metals Society of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringUniversity of Science and Technology BeijingBeijingChina
  2. 2.Beijing Laboratory of Metallic Materials and Processing for Modern TransportationUniversity of Science and Technology BeijingBeijingChina

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