Elsevier

Computational Materials Science

Volume 63, October 2012, Pages 66-74
Computational Materials Science

Micromechanics based modeling to predict flow behavior and plastic strain localization of dual phase steels

https://doi.org/10.1016/j.commatsci.2012.05.061Get rights and content

Abstract

The current work aims to predict the flow behavior, plastic strain localization and plastic instability of dual phase (DP) steels. A microstructure based approach by means of representative volume element (RVE) is employed for this purpose. Dislocation based model is implemented to predict the flow behavior of the single phases. Ductile failure of DP steel is predicted in the form of plastic strain localization which arises due to incompatible deformation between the hard martensite and soft ferrite phases. Different failures modes arise from plastic strain localization in two DP steels are investigated on the actual microstructure by finite element method.

Highlights

► Strain partitioning among ferrite and martensite during deformation. ► Strain localization arises due to incompatible deformation between martensite and ferrite. ► Material inhomogeneity causes to triggering instability. ► Different failure modes observed in different stress state.

Introduction

The advanced high strength steels (AHSS) are increasingly used in the next generation automobile to reduce vehicle weight, fuel consumption and emissions without sacrificing its safety. Among AHSS, dual phase (DP) steels are increasingly used due to its low yield strength, high work hardening rate and superior formability [1], [2], [3]. In general, DP steels are produced by the intercritical heat treatment of low carbon steel, and they consist of composite microstructure of soft ferrite matrix and hard martensite. Its flow behavior not only depends on the properties of ferrite and martensite, but also on their volume fraction, morphology of the martensite islands [3], [4], [5], and the partitioning of stress–strain between the two phases during deformation [6], [7], [8], [9]. For a constant volume fraction of martensite, a microstructure of finely dispersed martensite has a better combination of strength and ductility.

The strength of ferrite in general is determined by its composition and grain size [3], [4], [9]. In DP steel, ferrite gets additional strength from the initial dislocation density, i.e. strain field, created due to the compatibility stresses and strains when austenite transforms into martensite during cooling [10], [11]. The strength of martensite depends primarily on its carbon content [5], [12].

The failure/fracture modes can be broadly categorized into (i) cleavage and (ii) ductile failure/fracture. In simple tension, cleavage fracture is generally caused by separation of weak grain boundaries and decohesion of weak surfaces, whereas ductile fracture is normally caused by plastic instability (necking) of materials. Plastic instability can be further classified into three categories: (a) initial geometrical imperfections: the classical Marciniak–Kuczynski (‘M–K’) model [13] in predicting localized necking can be considered as initial geometrical imperfections in triggering instability [14], [15], (b) damage and void-growth: the popular Gurson–Tvergaard–Needleman model [16], [17], [18] can be analytically formulated as material instability on the constitutive level [19], (c) material microstructure-level inhomogeneity [20], [21], [22], [23], [24].

Different damage mechanisms are active in DP steels, therefore damage mechanism of particular DP steels are also related to their chemical compositions, heat treatment history and differences in their final microstructure [3], [4]. Stevenson [25] reported that cracks initiate first in martensite under low strain and then propagate into ferrite. The fracture mechanism in a fine and coarse martensite morphology having 0.09% carbon and 17% martensite was studied by He et al. [26]. They reported that in the coarse structures the initial void formation occurs due to cracking of the martensite at very low strain levels, and is followed by the formation of a second type of void by interfacial decohesion at ferrite/martensite interfaces at higher strain level. However, in the structures with fine martensite morphology, the majority of voids are formed by decohesion at the ferrite/martensite interface. On the other hand, significant plastic deformation of martensite occurs when its strength is reduced either by carbon content or by tempering.

Recently, Sun et al. [21], [22] developed a microstructure-based modeling procedure in which the failure mode and ultimate ductility of DP steels are predicted under different loading conditions using the plastic strain localization theory. Ductile failure is predicted as the natural outcome of the plastic strain localization due to the incompatible deformation between the hard martensite phase and the soft ferrite phase. Similar microstructure-based finite element analysis was used by Choi et al. [23] in predicting the ductility and failure modes of transformation induced plasticity (TRIP) steel. Sun et al. [21] also reported that when the volume fraction of martensite is above 15%, the pre-existing voids in the ferrite matrix does not significantly reduce the overall ductility of the DP steels, and the overall ductility is more influenced by the mechanical property disparity between the two phases. Strain localization is the earliest stage of fracture process. Strain localization normally leads to localized increase of stress–strain in a particular zone and reduction (i.e. unloading) in the remaining zone. Once strain localization is initiated, final fracture (i.e. initiation and separation of surfaces) occurs quickly in that localized zone by initiation, growth and coalition of voids or decohesion of ferrite–martensite interface. By knowing the importance of strain localization in fracture process, many researchers studied strain localization on different steels; namely DP steels [21], [22], TWIP steels [23], ferrite–pearlite steel [27], etc. In this work, flow behavior and plastic strain localization of DP590 and DP780 steels are investigated.

Section snippets

Materials used

DP 590 and DP 780 steels used in this investigation are obtained from USA source in the form of cold rolled strips of 1 mm thickness. The chemical compositions of the two DP steels are listed in Table 1.

Tensile specimens of 50 mm gauge length and 12.5 mm gauge width (ASTM E8) were machined parallel to the rolling direction from the as-received steel sheets. All samples were tested at room temperature using an electro-mechanical tensile testing machine at a crosshead speed of 1 mm min−1 which roughly

Constitutive description

Effective mechanical properties using von Mises elastic–plastic material law were assumed for each single phase. To define the isotropic flow behavior of each individual phase in the calculations, a model based on dislocation theory [28], [29], [30] was used. The stress–strain relation is given by:σ=σy+αMGb1-exp(-MKrε)KrLwhere σ is the flow stress at true strain of ε. The explanations of each term are given below and the values used were obtained from a previous study [29].

The second term takes

Conclusions

In this study, flow behaviors, plastic strain localization and plastic instability of dual phase steels are successfully predicted by the micromechanics based approach. Strain localization can be considered as the early stage of failure/fracture. Determination of strain localization is very much helpful to understand fracture modes in this dual phase steels. The ductile failure of dual phase steels is predicted in the form of plastic strain localization resulting from the incompatible

Acknowledgements

Author likes to acknowledge Dr. Arunansu Haldar and Dr. Monideepa Mukherjee, R&D, Tata Steel Limited, Jamshedpur, India and Dr. Soumitra Tarafder, National Metallurgical Laboratory, Jamshedpur, India for their valuable suggestions.

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