Failure Initiation in Dual-Phase Steel A. Ramazani 1,a, A. Schwedt 2,b, A. Aretz 2,c and U. Prahl 1,d

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1 Key Engineering Materials Vol. 586 (2014) pp Online available since 2013/Sep/10 at (2014) Trans Tech Publications, Switzerland doi: / Failure Initiation in Dual-Phase Steel A. Ramazani 1,a, A. Schwedt 2,b, A. Aretz 2,c and U. Prahl 1,d 1 Department of Ferrous Metallurgy, RWTH Aachen University, Germany 2 Central Facility for Electron Microscopy, RWTH Aachen University, Germany a ali.ramazani@iehk.rwth-aachen.de, b schwedt@gfe.rwth-aachen.de, c aretz@gfe.rwth-aachen.de, d ulrich.prahl@iehk.rwth-aachen.de Keywords: dual phase (DP) steel, in-situ bending test, digital image correlation (DIC), kernel average misorientation (KAM) map, EBSD, representative volume element (RVE), extended finite element method (XFEM) Abstract. This research work aims to model the failure initiation in dual-phase (DP) steel. A microstructure based approach by means of representative volume elements (RVE) is employed to evaluate the microstructure deformation and the failure initiation on the mesoscale. In order to determine cohesive parameters for martensite cracking, a two level approach has been performed experimentally. First, in-situ bending test in SEM with EBSD measurements before and after the test showed that the crack initiation occurs in martensite islands. Then, mini tensile tests with DIC technique were carried out to identify macroscopic failure initiation strain values. RVE modeling combined with extended finite element method (XFEM) was utilized to model martensite cracking on mesoscale. The identified parameters were validated by comparing the predictions with the experimental results. Introduction Since DP steels offer an outstanding combination of strength and ductility due to their microstructure, in which a hard martensitic phase is dispersed in a soft ferrite phase, these steel grades are demanded extensively for the automotive industry [1-3]. Based on many researchers reports dual-phase steels fail in a ductile manner [4-10]. These research works have described that the void initiation takes place around or inside martensite grains. Afterwards, growth and coalescence of voids occurs due to ferrite failure. Ahmed et al. [5] showed that at high V m void formation occurred mainly by particle cracking and decohesion of martensite-ferrite. Maire et al. [6] investigated the failure behavior of DP steels using in situ tensile tests and nondestructively in three dimensions X-ray tomography. They concluded that damage is never observed in the ferrite phase. They also observed both martensite cracking and ferrite/martensite interface debonding during the test. Calcagnotto et al. [7] investigated failure behavior of DP steels with different grain sizes using mini tensile test with DIC technique and showed that while in classical DP steels (of coarse grain and high impurity) the cleavage fracture and grain split cause failure, in modern DP steels (of fine grain and low impurity) grain boundaries play the significant role. Ramazani et al. [8,9] have studied the failure of DP steels macroscopically using GTN model and microscopically utilizing XFEM. Vajragupta et al. [10] have also investigated the failure behavior of DP steel using XFEM and damage model. This research work aims to model the failure initiation in DP600 steel with 46% martensite utilizing XFEM with traction-separation. 2D RVEs were defined based on real microstructures. Experimental procedure DP microstructure was produced through laboratory heat treatment from a DP600 steel composition that was delivered in a cold-rolled, ferrite-pearlite state with a thickness of 1 mm. The chemical composition is given in Table 1. Sheet samples were annealed in a salt bath at 780 C temperature with a holding time of 5 minutes and quenched in water to generate dual phase ferrite-martensite All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: , University of Michigan Library, Media Union Library, Ann Arbor, United States of America-13/11/13,07:28:16)

2 68 Local Mechanical Properties IX microstructure. Metallography shows ferrite grain size of 3.21 µm and martensite fraction of 46% [11]. Using Thermocalc TCFE6.7, carbon content in ferrite and austenite was calculated as % and 0.151%, respectively. In-situ SEM bending test were carried out to identify and quantify the failure initiation. The test procedure and the sample geometry are schematically shown in Fig. 1. Rolling direction was considered parallel to the major stress direction. During loading, the applied force was increased incrementally and displacement (deflection of specimen) and load were recorded automatically. At each stepwise holding the surface images of the samples have been recorded by SEM. Additionally, EBSD measurements were made before and after the test in order to identify failure initiation sites. In order to identify the crack initiation and the correspondent local strain, there parallel mini tensile tests with digital image correlation (DIC) technique were carried out parallel to the rolling direction. The geometry and dimensions of tensile test specimen is illustrated in Fig. 2. During the tests, images were taken from the surface in every second. So, strain distributions can be captured in different deformation steps in the evaluated zone. The microstructure evolution by means of SEM was investigated in the center line along loading direction in order to observe where the crack initiates and to identify the responsible strain (Fig. 2 ). Fig. 1. Bending test procedure and Sample geometry Table 1 Chemical composition of the investigated DP steels (in wt%) C Si Mn P S Cr Ni Al Cu V Micromechanical modelling Fig. 2. Geometry and dimensions of the mini geometry in situ tensile test specimens and positions of SEM analysis in center line of broken specimen A 2D RVE from the EBSD microstructure was developed using a microstructural meshing program known as OOF (see Fig. 3) [12]. In a former study, the acceptable size of the RVE was considered as a minimum of 24 μm while it should include at least 19 martensite particles. Quadratic elements with the size of 0.25 µm were used. Periodic boundary conditions were imposed on the RVE. The elastic modulus for ferrite and martensite is assumed to be 210 GPa. The flow curve of individual phases for ferrite and martensite is quantified based on a dislocation density based strain hardening model. The full approach has been given in a former study [11,13]. Fig. 3 EBSD map and the selected RVE with different phases

3 Key Engineering Materials Vol In order to model the failure initiation in DP steels, XFEM with cohesive zone (traction-separation) law was utilized. The onset and propagation of cracking in quasi-static problems were studied using the XFEM since it allows describing crack growth along an arbitrary, solution-dependent path without remeshing the FE model. The maximum principle stress criterion (MAXPS) is used for describing damage initiation. Martensite is assumed to lose its stiffness as soon as the damage initiation criterion is reached and linear degradation behaviour with steep slope is assigned as local damage evolution law on mesoscale [9,10]. 2D RVE generated based on real micrographs can involve all microstructural features, but it is not able to predict the 3D material flow precisely. The predicted flow curves of 2D modelling 2D has to be correlated to the 3Ds 3D by introducing a correlation factor (Eq. 1), which was developed by Ramazani et al. [11]: σ 3D /σ 2D = (ε p eq) 2 V 3 m (ε p eq) V 3 m V 3 m (ε p eq) 2 V 2 m (ε p eq) V 2 m V 2 m (ε p eq) 2 V m (ε p eq) V m V m (ε p eq) (1) Results and discussions Fig. 4 shows the load deflection curve during bending test. Small drops in the curve correspond to a pausing of the experiment in order to capture SEM images at displacements 3, 4, 5, 6, and 7 mm. SEM images at start and after test deflection are also shown. Comparing KAM map before and after the bending test (Fig. 4 ) shows that the crack initiation occurs in martensite islands. Calculated single phase flow curves of ferrite and martensite are shown in Fig. 5. For XFEM parameters identification for martensite in the studied DP600 steel, the maximum principle stress criterion was defined with respect to the fracture strain of martensite. To identify the equivalent crack initiation strain in martensite, 2D RVE micromechanical modelling was performed until macroscopic state of failure initiation (ε f = 0.065). Then, using first order homogenization strategy [14], the corresponding average equivalent plastic strain in martensite was estimated to be ε f m = The correspondent stress for this strain can be considered as critical stress for martensite cracking in DP steels and it was calculated from the flow curve of martensite (e.g. σ c = 1370 MPa). According to J integral theory [15], cohesive energy for martensite failure was considered as the area of behind martensite stress-strain curve and calculated as J/m 2. The developed cohesive zone model will be utilized in XFEM in order to simulate the crack initiation in DP steel. Fig. 4 Load-Deflection curve of bending experiment with SEM picture at start and after loading, and KAM analysis of failure initiation in P600 steel; before (upper image), and after (lower image) loading After implementing XFEM on the martensite particles, numerical tensile tests were carried out on the generated 2D RVEs of DP600 steel. Fig. 6 shows the contour plot of von Mises stress and damage evolution on microscale for the global martensite failure initiation strain ε f = A comparison between experimental and RVE calculated true stress-true strain curves is demonstrated in Fig. 6. Also, the corrected 2D flow curve to 3D flow curve is shown using correlation factor

4 70 Local Mechanical Properties IX as explained in Section 3.4. It can be seen, that the corrected 3D flow curve is in excellent agreement with the experimental flow curve. Comparison between Fig. 6 and reveals that the simulations show roughly the same cracked positions as experiments. Fig. 5 Calculated von Mises stress equivalent plastic strain responses of ferrite and martensite for studied DP steel Fig. 6 damage evolution (microcrack formation in martensite), and Comparison between experimental and simulated true stress-true strain curves for DP steel Summary Martensite cracking has been identified to be the main failure initiation mechanisms for the investigated DP steel. A two level experimental approach based on mini tensile test and in-situ SEM bending test offers the quantification of martensite failure initiation as function of macroscopic loading. Quantitative identification of parameters for XFEM modeling of martensite cracking has been performed and validated by numerical versus experimental tensile test comparison. Acknowledgments This research was carried out under Project number MC in the framework of the Research Program of the Materials Innovation Institute M2i ( References [1] D. Cornette, T. Hourman, O. Hudin, J.P. Laurent, A. Reynaert, SAE Transactions Journal of Materials & Manufacturing 110 (2001) [2] J.R. Shaw, B.K. Zuidema, SAE Transactions Journal of Materials & Manufacturing 110 (2001) [3] A. Ramazani, B. Berme, U. Prahl, Steel and Iron Based Alloys, in: Structural Materials and Processes in: D. Lehmhus, M. Busse, A.S. Herrmann, K. Kayvantash (Eds.), Transportation, Wiley- VCH, 2013, [4] Y. L. Su, J. Gurland, Mater. Sci. Eng. 95 (1987)

5 Key Engineering Materials Vol [5] E. Ahmed, M. Tanvir, L.A. Kanwar, J.I. Akhtar, Journal of Materials Engineering and Performance, 9(3) (2000) [6] E. Maire, O. Bouaziz, M.D. Michiel, C. Verdu, Acta Materialia 18 (2008) [7] M. Calcagnotto, Y. Adachi, D. Ponge, D. Raabe, Acta Materialia 59 (2) (2011) [8] A. Ramazani, M. Abbasi, U. Prahl, W. Bleck, Comp. Mater. Sci. 64 (2012) [9] A. Ramazani, A. Schwedt, A. Aretz, U. Prahl, W. Bleck, Comp. Mater. Sci. (2013), DOI: doi.org/ /j.co mmatsci [10] N. Vajragupta, V. Uthaisangsuk, B. Schmaling, S. Münstermann, A. Hartmaier, W. Bleck, Computational Materials Science 54 (2012) [11] A. Ramazani, K. Mukherjee, H. Quade, U. Prahl, W. Bleck, Materials Science and Engineering A 560 (2013) [12] Information on [13] A. Ramazani, K. Mukherjee, U. Prahl, W. Bleck, Comp. Mater. Sci. 52 (2012) [14] V.G., Kouznetsova, Computational homogenization for the multi-scale analysis of multiphase materials, PhD thesis, Technical University Eindhoven, The Netherlands, [15] G.E. Dieter, Mechanical Metallurgy, 2nd ed., McGraw-Hill, 1976.

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