Artificial neural network approach to predict the flow stress in the isothermal compression of as-cast TC21 titanium alloy
Introduction
A generic class of titanium-based materials has been developed over the past years. At present, titanium and its alloys are being extensively applied in the field of aviation and aerospace industries because of their superior combination of properties, including their low densities, excellent corrosion and erosion resistance in various kinds of environments and high temperature capability [1], [2]. It is well known that the hot deformation behavior of titanium alloys is sensitive to the hot processing parameters such as strain, strain rate and deformation temperature, and is highly non-linear during hot deformation. The constitutive relationship, which describes the correlation of material properties with hot processing parameters in the forming process, therefore is significant to explore and understand the hot deformation behavior and optimize the deformation process of material [3], [4]. Over the past few decades, many researchers have taken used of the regression method to conduct the constitutive relationships, including typical Arrhenius constitutive equations based on exponential law, power exponential law and hyperbolic sine law, respectively. However, these empirical and semi-empirical constitutive relationships are not quite satisfied because the non-linear relationships, which may exist between flow stress, microstructural evolution and processing parameters, are difficult to be described accurately with a mathematical expression by the regression method. In addition, the regression constants need to be recalculated whether the new experimental data are added or experimental data cross the different phase regions [5], [6].
Fortunately, the artificial neural network (ANN) method unlike the regression method possesses the abilities of adjustment, memorisation and anticipation and its better performances than regression equations is simply because interpolation and extrapolation within the specific data ranges and nearby while the empirical analytical equations are designed for wider data ranges. This approach provides a novel way of using examples of a target function to find the coefficients that makes a certain mapping function approximate the target function as closely as possible [7], [8]. Moreover, it is in particular suitable for treating complex and non-linear relationships and has been successfully applied to the prediction of constitutive relationships for some alloys. Lin et al. [9] predicted the flow stress of 42CrMo steel in isothermal interrupted hot compression tests using ANN and pointed out that the experimental and predicted results showed a very good correlation. Pernot and Lamarque [10] successfully developed the constitutive laws with the help of ANN and considered that the neural network could cope with the experimental data uncertainties better than the conventional constitutive laws. Sun et al. [11] constructed the constitutive relationship of Ti–22Al–25Nb alloy using artificial neural network and suggested that the ANN model had a strong ability to predict the flow stress value across the whole deformation mechanisms domains while the regression method only predicted the flow stress value in the single phase region. Han et al. [12] modeled the constitutive relationship in isothermal compression of Ti–25V–15Cr–0.2Si alloy using an artificial neural network coupled with a fuzzy set. Reddy et al. [13] developed a back-propagation neural network model to predict the flow stress of Ti–6Al–4V alloy for given processing conditions and pointed out that the network can be successfully trained across different phase regions.
Ti–6Al–2Sn–2Zr–3Mo–1Cr–1Nb (TC21) titanium alloy, which is a newly developed alpha–beta damage tolerance titanium alloy characterized by excellent fracture toughness and high strength and mainly used in aircraft structural applications, has attracted great attentions recently [14], [15], [16], [17], [18], [19]. Zhao et al. [14], [15] introduced a newly high strength, toughness and damage-tolerant TC21 titanium alloy in 2004 and improved its processing performance using thermo-hydrogen treatment process in 2007. Feng et al. [16] obtained that the smallest activation energy for deformation in the α + β and β regions of TC21 alloy in isothermal compression at the deformation temperatures of 900–1100 °C and strain rates of 0.01–50.0 s−1 were 330.57 kJ mol−1 and 176.49 kJ mol−1, respectively. Qu et al. [17] studied the relationship among forging technology and microstructure as well as mechanical properties of TC21 alloy bars and pointed out that basket-weave microstructure was obtained by beta finish-forging method, while duplex or tri-modal microstructure appeared in TC21 alloy bars manufactured by near-beta forging technology. Chen et al. [18] analyzed the effect of microstructure on impact toughness of TC21 alloy and pointed out that heat treatment at 915 °C for 1 h followed by air-cooling can achieve the highest impact toughness. Wang et al. [19], [20] investigated the kinetics of hydrogen absorption/desorption in TC21 alloy under different initial hydrogen pressure at the temperature range of 575–850 °C and the dehydrogenation kinetics of TC21 alloy. Therefore it is great significant to further research the TC21 alloy. In the present investigation, an artificial neural network (ANN) model with an error back-propagation learning algorithm has been applied to predict the flow stress in isothermal compression of as-cast TC21 titanium alloy. Furthermore, the predicted flow stress values based on the ANN model is compared with those calculated by the regression method.
Section snippets
Materials and experimental procedures
The nominal composition (wt.%) of the alloy used in this investigation is as follows: 6Al, 2Sn, 2Zr, 3Mo, 1Cr, 1Nb, 0.1Si and the balance Ti. The beta-transus temperature of the alloy was approximately 950 °C. The as-cast TC21 titanium alloy used in present work was an ingot of 155 mm in diameter with large β grains in diameter of 0.83–2.78 mm, as shown in Fig. 1. The specimens for isothermal compression tests were machined into cylinder with 10 mm in diameter and 15 mm in height.
The isothermal
Modeling constitutive relationship using artificial neural network
An artificial neural network (ANN), which is a mathematical model or computational model of a biological neuron, is able to understand, memorise and generalise the underlying rules of the material behavior, and is a quite efficient computing tool at the same time [21]. A typical ANN topology consists of an input layer, an output layer and a hidden layer. The fundamental unit of ANN is the processing element, also called an artificial neuron or simply a neuron. The various process elements are
Modeling constitutive relationship of as-cast TC21 alloy using regression method
The typical flow stress–strain curves of as-cast TC21 titanium alloy deformed in the deformation temperature range of 1000–1150 °C and strain rate of 0.01–10.0 s−1 are shown in Fig. 3. As seen in Fig. 3, the flow stress increases significantly with the decreasing of temperature and increasing of strain rate. Fig. 4 shows that the microstructures of the specimens deformed at strain rate of 0.1 s−1 and different deformation temperatures of 1100 °C and 1150 °C. It is clearly seen that discontinuous
Conclusions
The isothermal compression test of as-cast TC21 alloy was conducted at deformation temperatures of 1000, 1050, 1100 and 1150 °C, strain rates of 0.01, 0.1, 1.0 and 10.0 s−1, and height reduction of 60%, and hot deformation behavior was studied. It is found that the flow stress of as-cast TC21 alloy decreases with the increasing deformation temperature and decreasing strain rate in isothermal compression. On the basis of the data obtained from the compression experiment, a back-propagation neural
Acknowledgements
This work was supported by the National Natural Science Foundation of China with Grant No. 51075333, 973 Project of China with No. 2007CB613807, and the fund of the State Key Laboratory of Solidification Processing in NWPU with No. 35-TP-2009.
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