A comparative study on constitutive equations and artificial neural network model to predict high-temperature deformatio

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Shiqiang Lu,a) Kelu Wang, and Guifa Li School of Material Science and Engineering, Nanchang Hangkong University, Jiangxi 330063, China (Received 10 September 2014; accepted 28 April 2015)

The present study was conducted to predict the hot deformation behavior of the as-forged Nitinol 60 shape memory alloy by using the Arrhenius type, multiple-linear, and artificial neural network (ANN) models. The acquired flow stress data from isothermal hot compression tests in a temperature range of 650–850 °C under strain rate range of 0.01–1 s1 were used to calculate the material constants for establishing the corresponding constitutive equations. Furthermore, a comparative study has been made on the capability of the aforementioned models to predict the high-temperature deformation behavior by comparing the prediction relative errors, average absolute relative error, and correlation coefficient. The results show that multiple-linear model predicts the flow behavior more accurately than the Arrhenius type model. The ANN model is much more efficient and has a better prediction power for the as-forged Nitinol 60 alloy than both the Arrhenius type and multiple-linear models.

Contributing Editor: Yang-T. Cheng a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.144

materials under specified loading condition,7,9 which will have a significant effect on the accuracy of the numerical simulation. Over the past few years, various analytical, phenomenological, and empirical models have been constructed to predict constitutive behavior. A comprehensive review on constitutive analysis in hot working of austenitic stainless steel, carbon and alloy steels, ferritic steel, and Al alloy could be found in Ref. 10. An internal state variable-based self-consistent constitutive model was proposed for Ti–6Al–4V alloy. 11 Among the phenomenological models, Arrhenius type equations and their modified forms were extensively applied to describe the hot deformation behavior of materials. A strain-dependent parameter into the sine hyperbolic constitutive equation was introduced by Sloof et al.12 The constitutive equations for pure titanium at temperature ranges of 350–500 °C13 and 400–700 °C14 were proposed by using Arrhenius type equation, and the influence of strain was incorporated in the constitutive equation by considering the effects of strain on material constants (i.e., A, b, and activation energy Q). A modified sine hyperbolic constitutive equation was adopted by incorporating strain and strain rate to predict the elevated temperature flow behavior in D9 alloy and TC4-DT alloy.15,16 On the other hand,

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Ó Materials Research Society 2015

I. INTRODUCTION

The Nitinol 60 shape memory alloy (60 wt% Ni, 40 wt% Ti), which is first developed by US Navy in the early 1960s, has been a primary candidate material for aircraft due to its good mechanical and chemical properties,1–3 for example, hardness up to 62RC, nonmagnetic, excellent corrosion resistance, high-yield strength, and lower density. Thermomechanical proce