Modeling hot deformation behavior of low-cost Ti-2Al-9.2Mo-2Fe beta titanium alloy using a deep neural network

doi:10.1016/j.jmst.2018.11.018

Abstract

Abstract:

Ti-2Al-9.2Mo-2Fe is a low-cost β titanium alloy with well-balanced strength and ductility, but hot working of this alloy is complex and unfamiliar. Understanding the nonlinear relationships among the strain, strain rate, temperature, and flow stress of this alloy is essential to optimize the hot working process. In this study, a deep neural network (DNN) model was developed to correlate flow stress with a wide range of strains (0.025-0.6), strain rates (0.01-10 s^-1) and temperatures (750-1000 °C). The model, which was tested with 96 unseen datasets, showed better performance than existing models, with a correlation coefficient of 0.999. The processing map constructed using the DNN model was effective in predicting the microstructural evolution of the alloy. Moreover, it led to the optimization of hot-working conditions to avoid the formation of brittle precipitates (temperatures of 820-1000 °C and strain rates of 0.01-0.1 s^-1).

Key words: Deep neural networks, Back propagation, Processing map, Recrystallization, Beta titanium

Cheng-Lin Li, P.L. Narayana, N.S. Reddy, Seong-Woo Choi, Jong-Taek Yeom, Jae-Keun Hong, Chan Hee Park. Modeling hot deformation behavior of low-cost Ti-2Al-9.2Mo-2Fe beta titanium alloy using a deep neural network[J]. J. Mater. Sci. Technol., 2019, 35(5): 907-916.

Figures/Tables 13

Fig. 1 Initial microstructure of the Ti-2Al-9.2Mo-2Fe alloy: (a) low and (b) high magnification.

Fig. 2 Schematic illustration of the present DNN architecture.

Table 1 Statistics of the database used in the present study.

Variable		Minimum	Maximum	Standard deviation
Inputs	Temperature (°C)	748	1000.24	81.102
	Strain rate (s^-1)	0.01	10	4.1915
	Strain	0.025	0.6	0.1732
Output	Stress (MPa)	19.63	296.08	66.4198

Fig. 3 Instantaneous temperature of the alloy deformed at temperatures of 750?°C (a), 800?°C (b), 850?°C (c), 900?°C (d), 950?°C (e), and 1000?°C (f).

Fig. 4 Experimental flow curves of the alloy deformed at temperatures of 750?°C (a), 800?°C (b), 850?°C (c), 900?°C (d), 950?°C (e), and1000?°C (f).

Fig. 5 Average error with variation of (a) the number of hidden neurons, (b) number of iterations, (c) learning rate, and (d) momentum term for conventional ANN and present DNN models. The arrows indicate the minimum average error for each plot.

Fig. 6 Average error during optimization using the conventional ANN and present DNN models.

Fig. 7 Comparison of predicted and experimental flow stress during training (a) and (b) testing of the present DNN model.

Fig. 8 Comparison of experimental (solid line) and predicted (dashed line for ANN and dotted line for DNN) flow behaviors of the alloy deformed at temperatures of 750?°C (a), 800?°C (b), 850?°C (c), 900?°C (d), 950?°C (e), and 1000?°C (f).

Fig. 9 Processing maps for Ti-2Al-9.2Mo-2Fe alloy at a strain of 0.6 predicted by ANN (a) and DNN (b). The shaded areas, contour lines, and dotted rectangles represent the unstable domains, the efficiency of power dissipation, and optimum hot working conditions, respectively.

Fig. 10 Microstructures of alloys formed under different deformation conditions to validate unstable regions: (a)(b) 800?°C, (c)(d) 850?°C, (e)(f) 1000?°C; (a)(c)(e) 1 s-1, (b)(d)(f) 10 s-1.

Fig. 11 Inverse pole figure (IPF) maps for the β phase of the alloy deformed at a strain rate of 0.1 s-1 and temperatures of 800?°C (a), 900?°C (b), and 1000?°C (c). Black and white lines indicate high-angle (≥15°) and low-angle (2°-15°) grain boundaries, respectively. The arrows indicate typical DRXed grains. The inset in Fig. 11(a) shows an IPF map for the α phase.

Fig. 12 IPF maps for the β phase of the alloy deformed at a strain rate of 10 s-1 and temperatures of 800?°C (a), 900?°C (b), and 1000?°C (c), respectively. Black and white lines indicate high-angle (≥15°) and low-angle (2°-15°) grain boundaries, respectively. Maps were taken from areas outside the flow-localized band.

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