Elsevier

Materials & Design

Volume 35, March 2012, Pages 557-562
Materials & Design

Application of artificial neural network and constitutive equations to describe the hot compressive behavior of 28CrMnMoV steel

https://doi.org/10.1016/j.matdes.2011.08.049Get rights and content

Abstract

Isothermal hot compression of 28CrMnMoV steel was conducted on a Gleeble-3500 thermo-mechanical simulator in the temperature range of 1173–1473 K with the strain rate of 0.01–10 s−1 and the height reduction of 60%. Based on the experimental results, constitutive equations and an artificial neural network (ANN) model with a back-propagation learning algorithm were developed for the description and prediction of the hot compressive behavior of 28CrMnMoV steel. Then a comparative evaluation of the constitutive equations and the trained ANN model was carried out. It was obtained that the relative errors based on the ANN model varied from −3.66% to 3.46% and those were in the range from −13.60% to 10.89% by the constitutive equations, and the average absolute relative errors were 0.99% and 4.09% corresponding to the ANN model and the constitutive equations, respectively. Furthermore, the average root mean square errors of the ANN model and the constitutive equations were obtained as 1.43 MPa and 5.60 MPa respectively. These results indicated that the trained ANN model was more efficient and accurate in predicting the hot compressive behavior of 28CrMnMoV steel than the constitutive equations.

Highlights

► The hot compressive behavior of 28CrMnMoV steel was investigated over a wide range of temperatures and strain rates. ► The material shows strain hardening, strain rate hardening and thermal softening. ► A BP ANN model and constitutive equations were employed to predict the flow stress. ► It was found that the ANN model has a better prediction precision.

Introduction

High grade steel tube is widely used for petroleum exploitation owing to its excellent mechanical properties. However, with the increasing severity and complexity of service environment, it puts forward higher requirements for the properties of steel tubes. Therefore, it is of great importance to improve the mechanical properties of the steels used for the tubes correspondingly. 28CrMnMoV steel is a new kind of low-carbon micro-alloyed steel designed to manufacture V150 grade seamless tube with high strength and high toughness.

The understanding of hot deformation behaviors of materials is quite important for the determination of the thermo-mechanical process parameters which directly affects the microstructure evolution of the materials and the mechanical properties of the formed product [1], [2]. Constitutive equation is often used to represent flow behaviors of materials in a form that is suitable to feed in computer code to model the materials response under the specified loading conditions [3]. For the past few years, in order to describe the hot deformation behaviors of materials and thus optimize the thermo-mechanical process parameters, many research groups have made use of the regression methods to develop constitutive equations from the experimental data [4], [5], [6], [7]. Li et al. [4] fitted established Zener–Hollomon equation against the experiments to find material parameters and predict high temperature flow stress of Al–14Cu–7Ce alloy. Cai et al. [6] developed the constitutive equation of different phase regimes to study the workability of Ti–6Al–4V alloy. However, the response of the deformation behaviors of materials under elevated temperatures and strain rates is highly nonlinear, and the effects of many factors on the flow stress are also often nonlinear, which reduce the accuracy of prediction by the regression methods and limit the applicable range. Moreover, development of such constitutive equations is always time consuming.

Fortunately, artificial neural networks (ANN) are best suited to solve the problems that are the most difficult to solve by traditional computational methods [8]. Unlike the regression methods, an artificial neural network does not need to postulate a mathematical model or identify its parameters [9]. The ANN learns from training data and recognizes patterns in a series of input and output values without any prior assumptions about their nature and interrelations [10]. The ANN possesses the abilities of adjustment, memorization and anticipation, and better performances than constitutive equation. Therefore, artificial neural networks can provide a novel approach to materials modeling especially for complex and nonlinear relationships, and they have been successfully applied in the prediction of constitutive relationships for some metals and alloys over the last few years. Lin et al. [11] predicted the flow stress of 42CrMo steel in isothermal interrupted hot compression tests by using ANN and pointed out that the experimental and predicted results showed a very good correlation. Reddy et al. [12] developed a back-propagation neural network model to predict the flow stress of Ti–6Al–4V alloy and pointed out that the network can be successfully trained across different phase regions. Sun et al. [13] developed the constitutive relationship model for Ti40 alloy and indicated predicted flow stress by artificial neural network model was in good agreement with experimental results.

However, there are few reports about the application of ANN and constitutive equations to describe the flow behavior of 28CrMnMoV steel. In present investigation, a three-layer feed-forward artificial neural network with a back-propagation learning algorithm was established to explore and predict the flow behavior of 28CrMnMoV steel during hot compression. The strain, strain rate and deformation temperature were taken as input vectors, and the flow stress as output vector. Also, constitutive equations were developed to predict the flow stress of 28CrMnMoV steel. Furthermore, a comparative evaluation of the constitutive equations and the trained ANN model was carried out.

Section snippets

Materials and experimental procedures

The chemical composition (in wt.%) of 28CrMnMoV steel used in the present investigation is 0.28C–0.90Cr–0.80Mn–0.50Mo–0.05V–(bal.)Fe. The specimens for isothermal compression tests were machined into cylinder with 12 mm in height and 8 mm in diameter. In order to reduce the friction between the anvil and the specimens during hot compression, flat-bottomed grooves with a depth of 0.2 mm were machined in the undersurface to entrap the lubricant of graphite mixed with machine oil. The isothermal hot

True stress–strain curves

The true stress–strain curves obtained from the hot compression tests of 28CrMnMoV steel are shown in Fig. 1. It can be seen that the stress increases rapidly as increasing the strain in the initial stage of deformation, and then keeps unchanged or decrease to a plateau until high strains under different deformation conditions. At the lower strain rate of 0.01 s−1, all the true stress–strain curves exhibit a peak stress, after which the stress decreases gradually until it reaches a steady state,

Conclusions

The deformation behavior of 28CrMnMoV steel has been investigated over a practical range of temperatures (1173–1473 K) and strain rates (0.01–10 s−1) by isothermal hot compression tests. It is found that the flow stress of 28CrMnMoV steel increases with the increase of strain rate and the decrease of deformation temperature in isothermal hot compression. Based on the experimental data, constitutive equations and a feed forward back-propagation artificial neural network model were used to describe

Acknowledgement

The authors are very much grateful to Tubular Goods Research Center of CNPC, Xi’an, China, for technical assistance.

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