Constitutive modelling for high temperature behavior of 1Cr12Ni3Mo2VNbN martensitic steel

doi:10.1016/j.msea.2011.03.050

Materials Science and Engineering: A

Volume 528, Issue 15, 15 June 2011, Pages 5081-5087

https://doi.org/10.1016/j.msea.2011.03.050 Get rights and content

Abstract

The deformation behavior of 1Cr12Ni3Mo2VNbN martensitic steel in the temperature range of 1253 and 1453 K and the strain rate range of 0.01 and 10 s⁻¹ are investigated by isothermal compression tests on a Gleeble 1500 thermal–mechanics simulator. Most of the stress–strain curves exhibit a single peak stress, after which the stress gradually decreases until a steady state stress occurs, indicating a typical dynamic recrystallization (DRX) behavior of the steel under the deformation conditions. The experimental data are employed to develop constitutive equations on the basis of the Arrhenius-type equation. In the constitutive equations, the effect of the strain on the deformation behavior is incorporated and the effects of the deformation temperature and strain rate are represented by the Zener–Holloman parameter. The flow stress predicted by the constitutive equations shows good agreement with the experimental stress, which validates the efficiency of the constitutive equations in describing the deformation behavior of the material.

Highlights

► The hot compression tests were conducted in the temperature range of 1253–1453 K and the strain rate range of 0.01–10 s⁻¹. ► The constitutive equations of 1Cr12Ni3Mo2VNbN martensitic steel considering the effect of strain were proposed. ► The developed constitutive equations can accurately reproduce the experimental flow stress and DRX behaviors. ► The constitutive equations were appropriate and reliable for the analysis of the hot deformation process of this material.

Introduction

Numerical methods such as Finite Element (FE) have been successfully used for analysis of various metal-forming processes and optimization of the hot formation process parameters [1], [2], [3]. The constitutive equation, which is the mathematical representation of the flow behavior of materials, is used as input to the FE code for simulating the response of the material under specified loading conditions [4], [5], [6]. Therefore, the accuracy of the numerical simulation largely depends on how accurately the deformation behavior of the material is represented by the constitutive equation [7]. Recently, various empirical, semi-empirical, phenomenological and physically based constitutive models have been proposed to predict the constitutive behaviors of a wide range of metals and alloys [8], [9], [10], [11], [12]. Ideally, a constitutive equation should involve a reasonable number of material constants, which can be evaluated by using a limited number of experimental data [3]. The equation should represent the flow behavior of the material accurately and easily, such that it can be used in practice. For this goal, a phenomenological approach is proposed by Jonas et al. [13], in which the flow stress is expressed by the hyperbolic laws in an Arrhenius-type equation. Then, attempts have been made to revise this phenomenological model by incorporating the effect of the strain. A strain-dependent parameter is introduced by Sloof et al. [14] into the hyperbolic sine constitutive equation to predict the flow stress in a wrought magnesium alloy. A hyperbolic sine constitutive equation revised by considering the strain and strain rate compensation has been adopted to predict high temperature flow behavior in 42CrMo steel and alloy D9 [15], [16].

Turbine blades are often operated in harsh environments such as high temperature, high pressure, high speed rotation and wet steam, which require that the blade material should have the characteristics of good vibration and corrosion resistance. In China, the blades for the supercritical and ultra-supercritical steam turbines are usually made of imported materials, which are high-cost and difficult to meet specific requirements. 1Cr12Ni3Mo2VNbN, an advanced martensitic stainless steel developed indigenously in China, has the advantage of low cost. This material shows a good balance between strength and toughness and a property of excellent corrosion and wear resistance in an extreme working environment. This material has been widely applied as the material for the last-stage blades in China. The 1Cr12Ni3Mo2VNbN blade is manufactured by the hot forging process. However, since the shape of the blade is complex and the high-temperature flow behavior of 1Cr12Ni3Mo2VNbN steel is unknown, there are still a large number of difficulties in the determination of process parameters and the choice of the suitable forging technique. It is, therefore, of vital importance to understand the hot deformation behavior of this steel.

In this paper, isothermal compression tests of 1Cr12Ni3Mo2VNbN martensitic steel are conducted at different temperatures and strain rates to characterize the flow behavior of the steel in hot deformation. Based on the experimental data, a set of constitutive equations incorporating the effects of the strain, strain rate and deformation temperature are derived to describe the plastic flow property. The reliability of the constitutive equations is also evaluated by the mean error of the predicted flow stress.

Section snippets

Experiments

The material used in this investigation is 1Cr12Ni3Mo2VNbN martensitic steel. Its chemical composition is given in Table 1. Cylindrical specimens with 12 mm in length and 8 mm in diameter (Fig. 1) are prepared from the homogenized ingot for the compression tests. Isothermal hot compression tests are conducted on a Gleeble 1500 thermal–mechanics simulator with a maximum load capacity of 100 kN. The stimulator is equipped with a control system to impose exponential decay of the actuator speed to

Constitutive equations

The correlation between the flow stress, temperature and strain rate, particularly at high temperatures, can be expressed by an Arrhenius-type equation [17]. The combined effects of the temperature and strain rate on the deformation behavior can be represented by the Zener–Hollomon parameter (Z) in an exponent-type equation [18]. The two equations are mathematically expressed as $Z = \dot{ε} \exp (\frac{Q}{R T})$ $\dot{ε} = A F (σ) \exp (- \frac{Q}{R T})$ where $F (σ) = = \{\begin{array}{c} σ^{n} & α σ < 0.8 \\ \exp (β σ) & α σ > 1.2 \\ {[\sinh (α σ)]}^{n} & for all σ \end{array}$ , $\dot{ε}$ is the strain rate (s⁻¹), R is the

Model verification

A comparison between the experimental and predicted results is carried out to evaluate the accuracy of the developed constitutive equations in predicting the hot deformation behavior of 1Cr12Ni3Mo2VNbN martensitic steel. The predicted values of the flow stress in the strain rate range of 0.01 and 10 s⁻¹ and the temperature range of 1253 and 1453 K are determined by substituting the calculated material constants into the deformation constitutive equations. In both the experiments and the

Conclusions

(1)
The deformation characteristics of 1Cr12Ni3Mo2VNbN martensitic steel have been investigated over a range of temperatures and strain rates by means of the hot compression tests. The results indicate that the flow stress of this steel increases with the increasing of the strain rate and the decreasing of the deformation temperature; 1Cr12Ni3Mo2VNbN martensitic steel exhibits typical DRX behaviors at lower strain rates.
(2)
The constitutive equations of 1Cr12Ni3Mo2VNbN martensitic steel are obtained by

Acknowledgements

The present investigation has been carried out with the support from Dongfang Turbine Co., Ltd., Deyang, China. The authors gratefully acknowledge the assistance of Dr. Jie Zhong for development of the new blade material 1Cr12Ni3Mo2VNbN martensitic stainless steel (Patent Number 200710049980).

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Constitutive modelling for high temperature behavior of 1Cr12Ni3Mo2VNbN martensitic steel

Abstract

Highlights

Introduction

Section snippets

Experiments

Constitutive equations

Model verification

Conclusions

Acknowledgements

Comput. Mater. Sci.

Comput. Mater. Sci.

Comput. Mater. Sci.

Comput. Mater. Sci.

Mater. Sci. Eng. A

Comput. Mater. Sci.

Int. J. Plast.

Exp. Syst. Appl.

Comput. Mater. Sci.