Elsevier

Materials & Design

Volume 106, 15 September 2016, Pages 420-427
Materials & Design

Physically-based constitutive modelling of hot deformation behavior in a LDX 2101 duplex stainless steel

https://doi.org/10.1016/j.matdes.2016.05.118Get rights and content

Highlights

  • Hot deformation and work hardening behavior of LDX 2101 was studied

  • Saturated stresses were measured using hyperbolic-sine equation

  • Work hardening-dynamic recovery regime was modelled by Estrin–Mecking equation

  • Avrami equation was coupled to the Estrin–Mecking to model the DRX region

Abstract

A detailed understanding of the hot deformation and work hardening behavior of LDX 2101 dual phase steel has been obtained through a wide range of hot compression tests with strain rates from 0.01 to 50 s 1 and temperatures from 900 to 1250 °C. In most of the cases, the material showed typical dynamic recrystallization (DRX) behavior i.e., a peak followed by a gradual decrease to a steady state stress. The work hardening rate showed a two stage behavior i.e., a transient sharp drop at low stress values followed by a gradual decrease at higher stresses. Using the work hardening rate behavior at the latter stage, the saturation stress was calculated for different hot working conditions. Regression methods were used to develop a hyperbolic-sine equation linking the saturated stress to the deformation conditions. A physically-based Estrin–Mecking (EM) constitutive equation was then employed to model the flow behavior in the work hardening (WH)-dynamic recovery (DRV) regime. Finally, the Avrami equation to describe the evolution of the softening fraction was coupled to the EM model to extend the model to the dynamic recrystallization region. The results show that the model which is based on the stress-strain and work hardening behavior accurately predicts the flow behavior of this microstructurally complex steel.

Introduction

Duplex stainless steels with a microstructure composed of austenite and ferrite offer an attractive combination of strength and toughness as well as high corrosion resistance. This is why a significant metallurgical research over the past few years has been devoted to design and study of physical and mechanical properties of this grade of steels. LDX 2101 (EN 1.4162, UNS S32101) is a relatively new duplex stainless steel with mechanical characteristics and corrosion resistance comparable to standard single and dual phase stainless steels [1]. A low alloying element content, particularly Ni, makes this grade more economical over other common duplex stainless steels. Also the low alloying element content makes this grade less prone to the formation of undesirable precipitates and intermetallics [2]. Accordingly, LDX 2101 would be a cost-effective potential candidate to be used in diversified applications such as structural members and reinforcement bars as well as chemical process vessels, piping and heat exchangers.

Hot working is an important step in producing dual phase steel sheet and plate. In comparison to single phase steels, the deformation of dual phase steels is much more complicated where due to the different co-existing crystal structures and stacking fault energy values; ferrite and austenite show very different responses to external loading at high temperatures [3], [4]. This necessitates a detailed study of hot deformation of these steels. Advanced analysis of the hot working behavior relies on knowledge of the flow of the material under different thermomechanical conditions. This is typically performed through constitutive analysis where a series of mathematical equations describe the instantaneous response of the material to loading as a function of the process variables and material structure [5], [6]. The development of accurate but simple constitutive equations for deformation behavior of materials has driven a significant amount of research over the past few decades.

In the literature there is a wide range of constitutive equations employed for different materials. In general, however, these equations could be classified into three main groups i.e., empirical, semi-empirical and physically-based models [5]. The two former categories are based on regression methods and are often straightforward [7], [8], [9]. Nevertheless, they lack any physical meaning. On the other hand, physically-based models offer an equation which takes the structure of the material and micromechanisms of deformation into account, although they are more complicated [10]. Kocks [11] and later Estrin and Mecking [12] have proposed a physical model in which the material resistance to flow was considered as a transient process from an initial state to a stationary final state. In a simple way this could be described as σ=σSε̇T where dS=σSε̇T in which σ is the flow stress, S is the structural parameter representing the physical state of the material, ε̇ is strain rate and T is the temperature. The structural parameter was then related to the dislocation density as the internal variable. Incorporation of dislocation density is important as it is the dislocation evolution and movement that causes both the deformation and strain hardening [13]. The related parameters for considering the dislocation evolution in the model are obtained through analysis of the work hardening behavior of the material.

Based on the Estrin–Mecking (EM) analysis, in the absence of dynamic recrystallization (DRX), the flow characteristics of the materials is dictated by the hardening effect of dislocation generation and tangles and softening effects of recovery during which dislocations rearrange and annihilate [14]. This will then result in a typical stress-strain behavior with convergence to a steady state at a saturation stress without any stress decrease. Many metals, however, dynamically recrystallize during hot deformation. The most widely adopted approach to incorporate the softening induced by DRX in the constitutive equation is to employ the Avrami equation [15]. Based on this approach, the softening induced by DRX is calculated and incorporated to the EM saturation stress values for any strain value beyond εc (the critical strain for DRX).

Taking all the above into account, the objective of this work is to establish an appropriate constitutive relationship between the flow stress and deformation parameters to predict the hot deformation behavior of LDX 2101 dual phase steel. To achieve this, a wide range of hot compression tests were carried out. Using stress strain and the corresponding work hardening curves, the relationship between structural and deformation parameters and characteristic stress and strain values were determined. Finally the modified EM constitutive equation coupled with the Avrami equation was used to model the flow stress of the duplex stainless steel.

Section snippets

Experimental procedure

Production LDX 2101 steel with the chemical composition of 21.5Cr, 1.5Ni, 0.03C, 5Mn, 0.22 N, 0.3Mo, 0.7Si, 0.35Cu, and remainder Fe (wt.%) was received as hot rolled transfer bar, approximately 26 mm thick. Cylindrical compression samples were prepared from this material in size of Φ10 × H15. The hot uniaxial compression tests were conducted in the temperature range of 900–1250 °C under the strain rates of 0.01, 0.1, 1, 10 and 50 s 1. Compression tests were done using a Gleeble® 3800 Hydrawedge

Hot compression behavior

The true stress-strain curves obtained during hot compression of the experimental material at different temperatures under various strain rates are given in Fig. 1 (a–e). The curves show the classical DRX-accompanied flow shape i.e., initial work hardening and a peak followed by softening beyond the peak. More detailed observation shows that a yield point like phenomenon is observed at the working temperature of 1250 °C (see Fig. 1). Dehghan-Manshadi et al. [16], and Duprez et al. [17] also

Conclusion

A detailed study of the hot compression and work hardening behavior of duplex stainless steel LDX 2101 was carried out over a wide temperature and strain rate range. The stress-strain curves showed typical dynamic recrystallization (DRX) behavior i.e., a peak followed by a gradual decrease to a steady state stress. The work hardening rate evolution consisted of two stages: a transient sharp drop at low stress values followed by a gradual decrease at higher stresses. It was shown that the peak

Acknowledgements

This paper is dedicated to the memory of Dr. Jan-Olof Andersson, who made a significant contribution to the computational thermodynamics and physical metallurgy of stainless steels and the metals industry in Sweden, and who instigated and supported the research from which this paper stems. Parts of this work were performed and funded under the auspices of the Swedish National Action for Metallic Materials funded “Profroll” project. The authors would also like to acknowledge the support of

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This paper is dedicated to the late Dr. Jan-Olof Andersson.

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