Procedia Engineering 81 ( 2014 ) 1366 – 1371

1877-7058 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University doi: 10.1016/j.proeng.2014.10.158

ScienceDirectAvailable online at www.sciencedirect.com

11th International Conference on Technology of Plasticity, ICTP 2014, 19-24 October 2014, Nagoya Congress Center, Nagoya, Japan

Microstructure based description of deformation behavior of dual phase steel sheets

Thipwipa Sirinakorna,*, Vitoon Uthaisangsuka, Sompong Srimanosawapalb aDepartment of Mechanical Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, 126, Pracha Uthit Road,

Bang Mod, Thung Khru, Bangkok 10140, Thailand bNational Metal and Materials Technology Center, National Science and Technology Development Agency, 114 Paholyotin Road, Klong 1,

Khlong Luang, Pathumtani 12120, Thailand

Abstract

Dual Phase (DP) steels are Advanced High Strength (AHS) steels that have been widely used in the automotive industries. Generally, DP steels exhibit high strength as well as good formability. Their microstructures consist of hard martensitic islands embedded in soft ferritic matrix. Formability description of this steel grade is challenged, as its damage mechanism was very complex on the micro-scale. The aim of this work was to investigate deformation and fracture behavior of the DP steel grade 1000 by means of a microstructure based Finite Element modelling. Representative Volume Elements (RVEs) were applied to consider effects of various microstructure constituents and characteristics. Individual stress-strain curves were provided for ferrite, martensite as well as transformation induced Geometrically Necessary Dislocations (GNDs) including in the RVEs. The flow curves were based on dislocation theory and partitioning of local chemical composition. Furthermore, the Gurson-Tvergaard-Needleman (GTN) model was used to represent ductile damage evolution in the microstructure. Occurrences of void initiation were observed and damage parameters for RVE simulations were identified. Then, influences of the GNDs, local stress and strain distributions and interactions between phases on crack initiation in the DP microstructure were studied and correlated with experimental results. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of Nagoya University and Toyohashi University of Technology.

Keywords: Dual phase steel; Transformation-induced geometrically necessary dislocations; Gurson Tvergaard Needleman damage model; Local crack initiation

* Corresponding author. Tel.: +6-624-709-133; fax: +6-624-709-111. E-mail address: vitoon.uth@kmutt.ac.th

© 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Department of Materials Science and Engineering, Nagoya University

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1. Introduction

In modern automotive industries, materials are most considerate to support topical demands, in which weight reduction of vehicles has been aimed in order to minimize fuel consumption and emissions. To fulfil this purpose various steel grades have been continuously developed. The DP steels have been applied for automotive main components of around 75% of car body weight. Beneficial mechanical properties of DP steels for forming processes are continuous yielding behaviour and high work hardening rate. Usually, microstructure of DP steels consists of hard martensite islands dispersed in soft ferritic matrix, in which strength and ductility of both phases is appropriately combined. Effects of microstructure constituents on mechanical properties of the DP steels have been discussed in numerous investigations. Recently, phase transformation from austenite to martensite during quenching by production of DP steel was studied by Ramazani et al. (2013). Hereby, Geometrically Necessary Dislocations (GNDs) due to the transformation occurred around interfaces between ferrite and martensite. To describe strain hardening of DP steels, individual stress strain responses were defined for ferrite, martensite and GND zone in micro-scale simulations done by Sodjit et al. (2012). In addition, fracture modelling for high strength multiphase steels has been extensively developed. For example, ductile fracture models were widely used to predict failure behavior of DP steels, by which damage occurred according to void initiation, void growth and void coalescence mechanisms. The classical Gurson-Tvergaard-Needleman (GTN) model was applied by Uthaisangsuk et al. (2009) to investigate local crack initiation in high strength steel sheets during forming processes. Sun et al. (2009) indeed introduced plastic strain localization as fracture criterion for DP steels. The strain localization was resulted from incompatibility deformation between ferrite and martensite. It was also found that state of stress during deformation strongly affected local fracture mode took place such as shear, split and necking.

The present work aimed to investigate and characterize crack initiation mechanism of a DP steel grade 1000, which contained about 50% martensite phase fraction. Tensile tests and fractography were carried out for determining local void initiation. 2D representative volume elements based on real micrographs were used to analyse local deformation between phases. Flow curves for singles phases were given with regard to dislocation theory and alloying partitioning. Furthermore, GNDs at interphases were taken into account by an additional strengthening. The GTN model was applied to represent damage initiation driven by interface cracking of the DP steel. Model parameters and calculated results were then correlated with experimental results.

2. Experiment

A cold rolled DP steel sheet grade 1000 (DP1000) with a thickness of 1.4 was used in this work. The chemical composition of the investigated DP steel was shown in Table 1. First, samples were prepared for metallography examination, by which 2% Nital was used as etchant. In the micrograph the bright zones were ferrite and the dark distributed areas were martensite, as depicted in Fig. 1. The microstructure of the DP steel exhibited about 50% martensite phase fraction which were characterized by means of a MSQ image analysis. Table 1. Chemical composition of investigated DP steels (in wt.%).

Material C Si Mn P S Cr Cu Al DP1000 0.147 1.424 2.072 0.015 0.004 0.010 0.005 0.029

Uniaxial tensile tests of the investigated DP steel were performed. Tensile specimens were prepared according

to standard DIN EN 10002. The sheet samples had a gauge length of 25 mm and a nominal width of 5 mm. The tensile samples were elongated under uniaxial deformation at a strain rate of 0.002 s-1. In addition, fracture surfaces of the samples were examined by SEM. All obtained results were correlated and subsequently used to define damage model parameters for further representative volume elements simulations.

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Fig. 1. (a) Light optical micrograph and (b) SEM image of as-received DP steel sheet with 50% martensite.

3. Micromechanical modeling

3.1. Representative Volume Element model

A 2D representative volume element model was generated based on real microstructures of the DP steel taken from light optical microscopy. Here, a micrograph with a size of 25 25 μm was considered. A constant element size of 0.25 μm was used. Furthermore, elements along interfaces between ferrite and martensite in the representative volume elements were defined and included in the ferritic phase area as GND regions. Thickness of the GND zone was assumed to be 0.25 μm and constant everywhere. The representative volume elements investigated in this work were generated in two types, namely, representative volume elements with and without GND zone, as demonstrated in Fig. 2.

Fig. 2. (a) Micrograph of the investigated DP microstructure with about 50% martensite and 2D representative volume elements model of the investigated steels (b) without GNDs zone and (c) with GNDs zone.

3.2. Flow curve modeling of single phases

True stress-true strain behavior for each single phases, ferrite and martensite were defined on the basis of the dislocation theory and carbon partitioning, whereby its details were provided in Ramazani et al. (2013). Additionally, local dislocation strengthening according to the GNDs could be described by dislocation storage and back stresses. In order to take into account strengthening effects of the GNDs a kinematic term proposed by Sodjit et al. (2012) was included to the standard Kock-Mecking hardening approach. The modeled stress-strain curves of ferritic, martensitic phase and phase boundaries of the investigated DP steel were depicted in Fig. 3.

3.3. GTN damage model and parameter identification

The Gurson-Tvergaard-Needleman (GTN) damage model was applied for ferrite and GNDs regions in the representative volume elements model for describing ductile fracture mechanism. Constitutive equations of the GTN model were provided by West et al. (2012). In this work, the initial void volume fraction (f0) of 0.00029 was determined. For the secondary void volume fraction (fN), amount of triple junctions between ferrite and martensite observed in the microstructures were considered and a value of 0.0015 was defined. The plastic strain for void initiation ( N) of 0.19 was obtained by tensile testing in combination with the digital image correlation technique, which could be generally used to characterize local strain in a formed specimen. The values of q1, q2 and q3 as suggested in Min et al. (2011) were used.

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Fig. 3. Modelled flow curves for individual phases and GNDs zone of the investigated DP steel.

4. Results and discussions

4.1. Experimental results

Experimentally determined stress-strain curve of the DP steel were shown in Fig. 4. Local plastic strains along the middle section of the samples were examined and a critical local strain was then identified by a Digital Image Correlation technique. The local failure strain of about 0.091 was obtained for the DP1000 steel. In Ramazani et al. (2013) it was shown that this strain could be well correlated with effective failure strain, at which micro crack appeared in an in situ test on the mesoscale. Therefore, the observed fracture strain was used to determine a critical strain for crack initiation at triple junctions between ferrite and martensite. Note that in this work, primary crack initiations in the microstructure were presumed to be generally induced by void initiation at the triple junctions. This consideration was confirmed by SEM observations of the microstructures of the DP steel after tensile loading, as seen in Fig. 5. Representative volume elements simulation was performed until macroscopic failure initiation state and average equivalent plastic strain of the triple junctions was calculated. This average critical strain was taken as the plastic strain for void initiation ( N).

4.2. Representative Volume Element simulation results

Fig. 4 showed stress-strain curves from the experiment in comparison with those from the representative volume element simulations with and without GND zones. Obviously, flow stresses from the model with GNDs were somewhat higher than those from the model without GNDs in the early state of plastic deformation because of the strengthening effect of the GNDs at the phase boundaries. Equivalent stress and strain distributions of the DP microstructure calculated by the representative volume element models were presented for a uniaxial strain of 0.3% in Fig. 5. It could be found that local stresses and strains of ferrite and martensite in both representative volume elements models were similar, but local stresses of phase boundary zones of the representative volume element model including GNDs were definitely higher than those of the representative volume element model without GNDs.

Representative volume elements simulations with and without GNDs were carried out in combination with the GTN model. The representative volume elements simulations were terminated when the void volume fraction ff calculated by the GTN model was reached, in which a mesocrack was predicted. Note that the critical void volume fraction fc was not yet taken into account in this work. This state of the representative volume elements was used to predict crack initiation occurred in the DP microstructure. The state of crack initiation and evolutions of void volume fraction of ferrite-martensite triple junction at the most critical areas in both representative volume elements were determined and compared in Fig. 4 and 6, respectively. From the results, the failure states calculated by both representative volume elements with and without GNDs were close to each other. Nevertheless, increase of void volume fraction of the critical element in the representative volume elements model including GNDs slightly higher than that of the representative volume elements model without GNDs. Obviously, higher stresses in the GNDs zones were observed, but higher strain incompatibilities were observed in the representative volume elements including GNDs zone, as seen in Fig. 5. By SEM results it could be observed that crack initiation mainly

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occurred through martensite islands and at triple junctions between ferrite and martensite. Nevertheless, areas of the triple junctions were the most frequently initiation sites, as shown in Fig. 7. Crack or void initiation could be significantly induced by these incompatibilities. In addition, distributions of total void volume fraction in both representative volume elements under consideration of the GTN model at an early state of plastic deformation were presented in Fig. 8. The void volume fractions were generally higher in the representative volume elements model with GNDs zone. Higher damage values mostly occurred on the interconnecting areas between ferrite and martensite which was correlated with experiment.

Fig.4. Experimentally determined and calculated stress-strain curves and states of crack initiation of the investigated DP steel predicted by using the GTN model.

Fig. 5. Calculated local stress and strain distribution in representative volume elements (a) without GNDs and (b) with GNDs at a uniaxial tensile strain of 0.3%.

Fig. 6. Void evolutions of the most critical areas of ferrite-martensite triple junction in the representative volume elements. Fig. 7. Characteristics of initial crack of the investigated DP steels.

Fig. 8. Calculated void volume fractions in both representative volume elements (a) without GNDs and (b) with GNDs taking into account GTN damage model at a uniaxial tensile strain of 0.3%.

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5. Conclusions

FE simulations using 2D representative volume elements based on real micrograph was applied to investigate crack initiation at phase boundaries in the DP microstructure. The representative volume elements models were defined with and without consideration of the GNDs induced by austenite-martensite transformation. Representative volume elements simulations were performed under uniaxial tensile loading, by which flow curves for ferrite, martensite and GNDs region were individually given in the representative volume elements model. The GNDs occurred by the volume expansion due to the martensitic transformation during quenching process were taken into account as a local strengthening of the interfaces. Calculated stress-strain curves were well in agreement with the experimentally determined curves. It was found that stress-strain response and/or strain hardening rate predicted by the model with GNDs was higher at the early state of plastic deformation. Local stresses and strains in the representative volume elements with GNDs were higher than those in the representative volume elements without GNDs when comparing at the same overall equivalent plastic strain. In addition, the GTN model was defined for the ferritic phase and interfaces representing GNDs zone in order to describe ductile failure development in the DP microstructure. By this manner, state of crack initiation in the microstructure could be identified. It was observed that damage evolution in the model with GNDs was somewhat higher. Additionally, the highest stress concentration occurred at martensite triple junctions, which were corresponded to the crack initiation in the microstructure.

Acknowledgements

The authors would like to acknowledge Office of the Higher Education Commission, Thailand Research Fund (TRF) and King Mongkut’s University of Technology Thonburi (KMUTT) for financial supports and Thai Summit Group for supporting the material.

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