Effect of kinematic stability of the austenite phase on phase transformation behavior and deformation heterogeneity in duplex stainless steel using the crystal plasticity finite element method

Accepted Manuscript Effect of kinematic stability of the austenite phase on phase transformation behavior and deformation heterogeneity in duplex stainless steel using the crystal plasticity finite element method Eun-Young Kim, WanChuck Woo, Yoon-Uk Huh, BaekSeok Seong, JeomYong Choi, Shi-Hoon Choi PII:

S0749-6419(15)00208-9

DOI:

10.1016/j.ijplas.2015.12.009

Reference:

INTPLA 1999

To appear in:

International Journal of Plasticity

Received Date: 7 August 2015 Revised Date:

11 December 2015

Accepted Date: 12 December 2015

Please cite this article as: Kim, E.-Y., Woo, W., Huh, Y.-U., Seong, B., Choi, J., Choi, S.-H., Effect of kinematic stability of the austenite phase on phase transformation behavior and deformation heterogeneity in duplex stainless steel using the crystal plasticity finite element method, International Journal of Plasticity (2016), doi: 10.1016/j.ijplas.2015.12.009. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Effect of kinematic stability of the austenite phase on phase

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transformation behavior and deformation heterogeneity in duplex stainless steel using the crystal plasticity finite element method Eun-Young Kim1, WanChuck Woo2, Yoon-Uk Huh3, BaekSeok Seong2, JeomYong Choi4 and Shi-Hoon Choi1*

Department of Printed Electronics Engineering, Sunchon National University,

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1

315 Maegok, Sunchon, Jeonnam 540-950, Republic of Korea

Neutron Science Division, Korea Atomic Energy Research Institute, Daejeon, 305-535, Republic of Korea 3

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2

Graduate Institute of Ferrous Technology, POSTECH, Pohang, 790-784, Republic of Korea 4

POSCO Technical Research Laboratories, Pohang 790-785, Republic of Korea

Abstract

The crystal plasticity finite element method (CPFEM) was applied to determine the

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influence that the kinematic stability of the austenite (γ) phase exerts on the phasetransformation behavior and deformation heterogeneity of duplex stainless steel (DSS) showing γ to martensite (α΄) transformation during uniaxial tension. A phase-

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transformation model was implemented in the CPFEM to consider the effect of transformation-induced plasticity (TRIP) on micromechanical behaviors in DSS. The

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individual flow curves of the ferrite (α), γ and α΄ phases in DSS were determined via insitu neutron diffraction in combination with the CPFEM. The effect of the kinematic stability of the γ phase on phase-transformation behavior and deformation heterogeneity in DSS during uniaxial tension was demonstrated using the CPFEM based on the representative volume elements (RVEs) of a unit cell for DSS. Keywords: Neutron diffraction; Duplex stainless steel; Phase transformation; Crystal plasticity; Kinematic stability 1

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1. Introduction

Duplex stainless steels (DSS) consisting of ferrite (α) and austenite (γ) phases were developed for application in desalination plants, heat exchangers, and marine parts where

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greater strength and a higher resistance to stress-corrosion cracking are required (Gunn

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1997). Recently, cost-effective lean alloy systems that replace expensive Ni and Mo with Mn and N have been developed to expand the application of this favorable combination of mechanical properties and corrosion resistance. The mechanical properties of Mn-Nbearing lean DSS are closely related to the deformation modes of constituent phases such as

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α (BCC), γ (FCC) and martensite (α′: BCT or ε: HCP), and the spatial distribution of constituent phases (Choi et al., 2011; Choi et al., 2012a,b; Herrera et al., 2011). Many

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microstructure characterizations have revealed how, as stacking fault energy (SFE)

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increases, the deformation mechanisms of the γ phase in DSS changes from transformationinduced plasticity (TRIP, i.e. formation of ε or α΄) to twinning-induced plasticity (TWIP, formation of twin) and to a planar glide of dislocations (Herrera et al., 2011; Remy and Pineau, 1977; Byun, 2003; Humphery and Hatherly, 2004; Park et al., 2010). In particular, microstructure analysis using transmission electron microscopy (TEM) has indicated that

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the α΄ phase is mainly nucleated at the shear band intersections that develop in the

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deformed γ phase. The shear bands consist of stacking faults (SFs), twins, and an ε phase, as well as bundles of overlapping SFs, twins, and ε-phase mixtures (Choi et al., 2012b;

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Herrera et al., 2011). Although the exact atomic mechanisms explaining the TRIP phenomenon of the γ phase are still disputed, several models for mechanically induced

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martensitic transformation have been proposed to explain the nucleation of the α′ phase in the retained γ phase (Bogers et al., 1964; Olson and Cohen, 1972,1975,1976a,1976b,1982; Roitburd and Temkin, 1986; Kaganova and Roitburd, 1987,1989; Stringfellow et al., 1992;

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Fischer et al., 1996; Cherkaoui et al., 1998; Cherkaoui and Berveiller, 2000; Fisher et al., 2000; Levitas, 2000; Han et al., 2004; Humber et al., 2007; Kundu and Bhadeshia, 2007;

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Lee et al., 2013). These models were successfully implemented in the finite element analysis to establish a correlation between the external loading conditions (strain rate,

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loading direction) and the mechanical behaviors of TRIP steels (Leblond et al., 1989; Marketz and Fisher, 1995; Levitas et al., 1998; Tjahjanto et al., 2006, 2007; Lee et al., 2009,2010). FEM studies have been performed to explain the phase transformation at the shear-band intersection (Levitas et al., 1999; Diani et al., 1998; Ma and Harmaier, 2015). The inheritance of a dislocation structure during phase transformation was considered as

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one of the key problems in the interaction between the phase transformation and plasticity

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(Brainin et al., 1981; Levitas, 1998; Lovey and Torra, 1999; Idesman et al., 2000; Lovey et al., 2004; Javanbakht et al., 2015; Levitas and Javanbakht, 2015).

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The deformation behavior of the γ phase in DSS (hereafter referred to as TR-DSS), in

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which direct γ-to-α′ transformation mainly occurs, is relatively easy to explain. In order to simulate the micromechanical behaviors of the constituent phases in TR-DSS during plastic deformation, an accurate evaluation of the mechanical properties of the constituent phases and a physical model for the γ-to-α′ transformation should be considered in the modeling

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scheme. The mechanical properties of the constituent phases of DSS (hereafter referred to as NTR-DSS), in which phase transformation does not occur, have been evaluated using in-

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situ neutron or high energy X-ray diffraction techniques in combination with either self-

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consistent (SC) polycrystal models (Baczmański and Braham, 2004; Jia et al., 2006; Jia et al., 2008a,b) or the crystal plasticity finite element method (CPFEM) (Hedström et al., 2010; Jeong et al., 2014, 2015). In the in-situ diffraction techniques for NTR-DSS (Jeong et al., 2014, 2015), the lattice strains developed in the constituent phases were measured along the loading direction as a function of macroscopic stress with no consideration of phase

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transformation. The micromechanical hardening parameters of the constituent phases were

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successfully determined from the fitting of lattice strains and macroscopic flow curve. However, as far as we could ascertain, the microscopic hardening parameters of the

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constituent phases in TR-DSS have not been determined using diffraction techniques in combination with polycrystalline models that consider phase transformation.

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In the present study, the in-situ neutron diffraction technique in combination with CPFEM was used to evaluate the stress-strain relationships of the constituent phases (α, γ and α′) in TR-DSS, which mainly involves a direct γ-to-α′ transformation. The phase

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transformation model has been implemented into the user subroutine in the commercial finite element software, ABAQUS (2008). The lattice strains for constituent phases were

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determined by fitting the diffraction peaks of α, γ and α΄ phases with independent symmetric Gaussian functions during in-situ tensile loading. A CPFEM based on

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representative volume elements (RVEs) was used to simulate the phase transformation of the metastable γ phase and the micromechanical behaviors of constituent phases in TR-DSS during uniaxial tension. The microscopic hardening parameters of the constituent phases were determined by fitting the measured macroscopic flow stress and the response of lattice strains for each phase under uniaxial loading. Moreover, the determined microscopic

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hardening parameters for the constituent phases were used to explain the influence of the

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heterogeneity of the RVEs for TR-DSS during uniaxial tension.

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kinematic stability of the γ phase on the phase-transformation behavior and deformation

2. Experimental

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The TR-DSS used in the present study was 1 mm in thickness with a nominal chemical composition of 0.03C-0.6Si-1.8Mn-22.8Cr-2.5Ni-0.6Mo-0.5Cu-0.22N (wt %). The initial crystallographic texture of the constituent phases in TR-DSS was analyzed using an EBSD

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technique (Dingley, 2004). The EBSD measurements were conducted in the three sections (RD (rolling direction), TD (transverse direction), and ND (normal direction)) in the center

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parts through the thickness direction. The dimensions of the step size and the scanned area were 0.5 µm and 300 µm × 300 µm, respectively. Figs. 1(a) and (b) show the ND inverse

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pole figure (ND-IPF) and phase maps, respectively, for the three orthogonal sections of TRDSS. The microstructure of the as-received TR-DSS was characterized as a discrete bamboo structure consisting of α and γ phases along the RD. The average volume fractions of the α and γ phases in the three sections were about 64.7 and 35.3%, respectively. The average grain sizes of the α and γ phases in the three sections were 16.13 and 4.84 µm, 6

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respectively. Fig. 2(a) shows ϕ2=45° sections of the 3-D orientation distribution function

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(ODF) for the α and γ phases, as measured on the ND section. TSL software was used for the ODF calculation under the assumption that the crystal-sample symmetries were cubic-

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orthorhombic. The major and minor texture components developed in the α phase can be characterized as Rotated Cube (RC) ( {001} < 1 1 0 > ) and Goss ( {110} < 001 > ) orientations,

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respectively. The major texture components developed in the γ phase can be identified as two orientations of Copper ( {112} < 11 1 > ) and Brass ( {110} < 1 1 2 > ). Figs. 2(b) and (c) show the ϕ2=45° sections of 3-D ODF for the α and γ phases, as measured on the TD and

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RD sections, respectively. A Goss orientation was developed in the γ phase as a minor texture component. The microtexture analysis indicated that the three orthogonal sections

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had a similar crystallographic orientation while the initial morphological anisotropy was strong. Transmission electron microscopy (TEM) specimens were prepared by electro-

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chemical polishing in a 12% perchloric acid + 90% acetic acid solution maintained at room temperature and a constant voltage of 50 V. TEM analysis on the deformed specimens was carried out in a 200 kV field-emission transmission electron microscope (JEOL JEM2100F). Neutron diffraction has become a well-established method to determine the mesoscopic properties in polycrystalline metals and alloys. Neutron diffraction experiments

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were performed in-situ during uniaxial tension in order to measure the evolution of lattice

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strains in (hkl) planes developed in the constituent phases of TR-DSS. These experiments were conducted using a Residual Stress Instrument (RSI) at the Korea Atomic Energy

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Research Institute (KAERI) (Woo et al., 2011; Woo et al., 2012). First, the tensile specimens were prepared using electrical discharge machining (EDM) with a total length of

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100 mm and a gauge length of 25 mm. It was installed on the load flame of the neutron diffractometer with the gauge length parallel to the loading direction (Q-vector//loading direction) to measure the longitudinal strain component of the specimen. A bent perfect

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crystal monochromator Si (220) at a take-off angle of 45° provided a neutron beam with a wavelength of 1.46 Å. Diffraction angles (2θ) of 60.7° and 76.2° were selected for the

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(200) and (211) diffraction peaks of the α phase, respectively. For the γ phase, the 2θ was 41.0°, 47.0° and 83.6° for the (111), (200) and (311) diffraction peaks, respectively. The

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scattering gauge volume of a neutron beam was defined by a cadmium slit in the incident beam that was 5 mm wide and 4 mm high, and by a cadmium slit that was 2 mm wide. Thus, the diffraction conditions provided reflections from each set of grains in the gauge volume of the TR-DSS specimen. The micromechanical response of each constituent phase in the TR-DSS was characterized in the unique volume-averaged bulk-measurement

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manner, which is the nature of a neutron scattering beam (Hutchings et al, 2005). A total of

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nine static loading stages were used to measure the neutron diffraction peaks. The displacement of the tensile loading was controlled by a load cell at a strain rate of 1.0×10−3

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s−1. The measured diffraction peaks were analyzed using symmetric Gaussian functions. The analyzed peak location in terms of the intensity as a function of the diffraction angle

phase according to Bragg’s law:

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(2θ) was used to determine the interplanar spacing (d-spacing) in a crystalline constituent

λ = 2d hkl sin θ

(1)

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where λ is the wavelength of the neutron, dhkl is the d-spacing of atomic planes characterized by Miller indices {hkl}, and 2θ is the diffraction angle of the peak being

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measured. As the external loading increases, the initial location (do) of the diffraction peak shifts continuously. Thus, the elastic lattice strains (εhkl) were calculated using the following

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formula:

(2)

where the do is the d-spacing of the spelled hkl plane in the initial stress-free state and 2θo is the diffraction angle for the stress-free state. To quantitatively determine the evolution of the volume fraction of the constituent phases in TR-DSS during uniaxial tension, the

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Rietveld’s refinement method for whole- neutron profile with preferred orientation

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corrections was used (Seong et al., 2014). The diffraction patterns were measured using a high-resolution powder diffractometer in the HANARO reactor at the KAERI. The

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wavelength of the neutron beam used was 1.84 Å. The data were collected at intervals of

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0.05° between 10° and 155° in 2θ with a sample rotation.

3. Crystal plasticity finite element method (CPFEM) considering the TRIP effect The micromechanical behaviors of TR-DSS were simulated using the commercial finite

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element code, ABAQUS (2008), with the programming for the user material model based on continuum crystal plasticity theory. A more detailed description of the constitutive

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model can be found in previous papers (Choi, 2003; Choi et al., 2007,2009). The plastic

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velocity gradient, Lp , is defined by the following equation.

(3)

The plastic velocity gradient is decomposed further into symmetric and antisymmetric parts (

)

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(4)

where D p is the plastic part of the rate of deformation tensor and

is the plastic spin.

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The Jaumann rate of the Kirchhoff stress can be expressed as follows:(Peirce et al., 1983)

(5)

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where K is a fourth-order tensor based on the anisotropic elastic modulus, D is the rate of the deformation tensor (symmetric part of the velocity gradient), and R α = is a tensor that is dependent on the current slip plane normal and

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direction, the symmetric Kirchhoff stress (ττ) and the elastic modulus. For cubic crystal symmetric materials, three independent elastic constants for each phase were used in the

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present study (Table 1) (Fréour et al., 2003). We assumed the elastic constants of constituent phases in TR-DSS were the same as the elastic constants of the pure state for

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each phase. Assuming a rate-dependent material, the relationship between the slip rate and the resolved shear stress on the active slip systems can be related by the power law as follows (Hutchinson, 1976; Asaro and Needleman, 1985):

γ& α = γ& oα

τα τ oα

1/ m

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sign ( τ α )

(6)

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The evolution of the τ αo values was evaluated by the following simple micromechanical

n

τ& αo = ∑ Q αβ γ& β

α, β = 1...n

β

Q

αβ

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hardening law (Kalidindi et al, 1992):  τα  = q h o 1 − o   τ sat  ij

a

(7)

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where Q αβ is a (n×n) hardening matrix, which is a term that considers the interaction

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between slip systems in the constituent phases. Here n represents the total number of slip systems in each phase. In the hardening matrix, the diagonal and off-diagonal portions of

q αβ accounted for the self-hardening and latent-hardening terms, but we assumed that the terms were equal to one in the present study. Although the hardening matrix for pure metals

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is relatively well defined, the actual hardening matrix for multi-components metals remains an open question (Khadyko et al., 2016) The calibration of the hardening matrix is not a

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trivial task, and is beyond the scope of the present paper, because of a lack of experimental

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data that could be measured for different loading directions. The macroscopic stress and lattice strains measured by uniaxial tension were used to determine the micromechanical hardening parameters (a, ho and τ sat ) of the constituent phases. In the present study, 24 slip systems (12 × {110}<111>, 12 × {112}<111>) were considered for the α and α′ phases and 12 slip systems (12 × {111}<110>) were considered for the γ phase.

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To consider the effect of TRIP on micromechanical behaviors, a phase-transformation

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model was implemented in the CPFEM. The shape deformation due to martensitic transformation is an invariant plane strain on a plane with a unit normal ( ; γ*)=(p1p2p3),

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and a displacement in the unit direction [γ; ]=[d1d2d3] of magnitude η. The notation used here is due to Bowles and MacKenzie (Bowles and MacKenzie, 1954; Kundu and

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Bhadeshia, 2007). The terms γ and γ* define the real and reciprocal bases of the austenite.

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The deformation can be represented by a matrix P for austenite as follows:

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The interaction energy term was evaluated to consider the interaction between the stress

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and the shape deformation of the γ phase during mechanically induced martensitic

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transformation. Considering the phase transformation of γ to α′, the crystallographic set includes the habit plane, shape deformation and coordinate transformation (Bhadeshia, 2001). Symmetry operation generated 24 crystallographic sets corresponding to the 24 variants of the α′ phase possible in each γ phase. The interaction energy suggested by Patel and Cohen (Patel and Cohen, 1953; Kundu and Bhadeshia, 2007) was used for variant

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selection during phase transformation.

(9)

where σN is the normal stress on the invariant plane, δ is the dilatational strain along the

strain along the unit vector

direction, and s is the shear

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direction, τ is the shear stress on the invariant plane in the

. For a given crystal coordinate system, the traction,

, can

3(a) (Kundu and Bhadeshia, 2007),

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be resolved along with the normal and shear stresses on the invariant plane, as shown in Fig.

(10)

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As a result, the interaction energy for the specific variant, m can be expressed as follows,

(11)

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A variant with the highest interaction energy was activated for the calculation of the γ-toα′ transformation. The relationship between a plastic deformation and a phase transformation was proposed by Olson and Cohen (1972; 1982). Based on this relationship, a fault-band intersect will produce a martensite nucleus, as shown in Fig. 3(b).

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In the present paper, we assumed that the fault-band intersect acts as a site for a martensite

directions,

, and slip

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nucleation. At first, the shear rates on FCC slip planes with normals,

were projected to the fault-band systems (Table 2) to evaluate the shear rate

(12)

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of the fault bands as follows,

To determine the matrix X αβ , we assumed that 3 FCC slip systems on one slip plane can only be projected to 3 fault band systems with the same slip plane. By summing the fault-

(13)

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follows

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band systems in each element, the accumulated shear amount, Γacc, was determined as

At each increment, the amount accumulated in the individual fault-band systems is

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compared against a threshold shear amount, Γth, defined as follows

(14)

The threshold values, Cth1 and Cth2 are fitting parameters that determine the evolution of the volume fraction of the α′ phase during plastic deformation. After each deformation increment, if at least two fault-band systems were greater than the threshold shear amount,

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Γth, the element was allowed for phase transformation. The algorithm prevented

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reorientation by phase transformation until a threshold value, which was mostly determined by Cth1, was attained. Cth2 is a parameter for the mechanical stabilization of the γ phase

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during plastic deformation. When the strain in the γ phase becomes sufficiently large, the transformation will not occur as a result of the inhibition of the motion of the glissile

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interfaces (Chatterjee et al., 2006). Here, we assumed that the mechanical stabilization increased as the effective strain increased. Therefore, the critical value of Cth1 determines the initiation of γ-to-α′ transformation and Cth2 determines the evolution of the volume

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fraction of the α′ phase during plastic deformation. The optimal values of Cth1 and Cth2 should be determined by considering the evolution of the real microstructure during

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uniaxial tension. During the γ-to-α′ transformation, the whole part of the corresponding element changed to the α′ phase and the evolution of volume fraction of the α′ phase was

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not required. Since the present scheme for TRIP does not account for the inheritance of a dislocation structure during the γ-to-α′ transformation (Brainin et al., 1981; Levitas, 1998; Levitas and Javanbakht, 2015), the activated variant is geometrically admissible and the orientation of the α′ phase can be updated based on the interaction energy suggested by Patel and Cohen, as explained from Eqs. (11) to (14). After the γ-to-α′ transformation, the 16

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microscopic hardening parameters of the α′ phase were mapped into the corresponding

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element with an updated crystal structure and orientation. The present study assumed that the independent microscopic hardening parameters of the α′ phase could replace the

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inheritance of dislocation structure during the γ-to-α′ transformation. The microscopic hardening parameters for α′ phase were determined via in situ neutron diffraction in

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combination with the CPFEM, as will be explained in section 4-2. A numerical integration scheme of the stress rate (Eq. (5)) with the unknown,

, was explained in the previous

paper (Choi et al., 2011). A material Jacobian ( ∂∆τˆ / ∂∆ε ) for the implicit method can be

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obtained using Eq. (5). The stress vector in the UMAT subroutine can be updated by multiplying the material Jacobian by the strain increment. All state variables were saved

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and returned to the main subroutine of ABAQUS. Fig. 3(c) shows an example in which the orientation of α′ was modeled from the initial orientation of the γ phase after phase

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transformation, assuming that a variant with the highest interaction energy was activated. Fig. 4 shows simplified RVEs for the uniaxial tension simulation of TR-DDS under the prescribed displacement boundary conditions. The micromechanical behavior of the α, γ and α΄ phases in TR-DSS was simulated in a 3-D mesh (15×15×15=3375 elements).

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To effectively conduct the fitting of the microscopic hardening parameters, the spatial

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distribution of the undeformed α and γ phases was assumed to be random in a 3-D mesh. EBSD data measured on the three orthogonal sections were used to calculate the individual

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ODFs for each phase using a Gaussian standard function (Matthies et al., 1987). A set of 3,375-grain orientations with the same weight factor was generated from the calculated

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ODFs using orientation repartition functions (Francois et al, 1991). The generated discrete orientations for each phase then were randomly imposed on the integration points of elements corresponding to each phase. Displacement (Ui: i=X,Y,Z) boundary conditions

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were applied to the four planes of the RVEs that are comprised of a 3-D solid element, C3D8R (ABAQUS 2008), with 8 nodes and 1 integration point. A prescribed displacement

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in the X-direction was imposed on the 4-3-7-8 face for uniaxial tension along the RD, as shown in Fig. 4(a). Free surface boundary conditions were imposed on the 1-2-3-4 and 2-3-

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7-8 faces while conducting the simulation to model uniaxial tension. To calculate the lattice strains in TR-DSS, the average lattice strain for a crystallographic family along the diffraction direction was calculated for each phase in TR-DSS at every time step. A more detailed explanation can be found in a previous paper (Jeong et al., 2014)

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4. Results and Discussion

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4.1. Analysis of microstructure and deformation mechanisms The evolution of the neutron diffraction patterns of the TR-DSS during uniaxial tension

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is shown in Fig. 5. The Rietveld’s refinement method for a complete neutron profile revealed that the ε phase does not appear in the TR-DSS during uniaxial tension. It is clear

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that the peak intensity corresponding to the γ phase gradually decreases during uniaxial tension. In order to characterize the deformed structure during uniaxial tension, the deformed γ phase in TR-DSS after uniaxial tension of ε=0.2 was analyzed via TEM. Well-

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developed line contrasts were observed as shown in Fig. 6(a). The crisscrossed patterns of those line contrasts were also detected (Fig. 6(b)). Those line contrasts were identified as

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SFs, as shown in Fig. 6(c). The high-resolution image in Fig. 6(d) shows a crisscrossed pattern for the SFs. Fig. 7(a) shows the TEM bright field (BF) and electron diffraction

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pattern (EDP) insets of a deformed γ phase in TR-DSS after uniaxial tension of ε=0.4. In a γ matrix, the areas where γ is transformed to α΄ by tensile deformation are aligned by direction. The magnified image in Fig. 7(b) shows the α΄ embedded in the γ matrix. The high-resolution image on the left side in Fig. 7(b) reveals the remaining SFs in the γ matrix (Fig. 7(c)). This means that the γ to α΄ transformation is related to the crisscrossed SFs in 19

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the proposed model (Bogers et al., 1964; Olson and Cohen 1976b). The orientation

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relationship between the transformed α΄ and γ matrix was investigated via electrondiffraction pattern, as shown in Fig. 7(d). α΄and γ shows the Kurdjumov-Sachs (K-S)

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(Kurdjumov and Sachs, 1930) relationship, i. e.,

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4.2. Determination of microscopic hardening parameters

Fig. 8 shows the neutron diffraction peaks of (211) for the α phase (blue color in the schematic microstructure) in TR-DSS under loadings of 0 and 1,053 MPa. The diffraction

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peak of the α΄ phase (red color in the schematic microstructure) was broadened and shifted to a lower diffraction angle as the load increased, while the diffraction peak of the α phase

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was not broadened significantly but shifted to a lower diffraction angle as the load increased. The diffraction peaks were successfully fitted with the two symmetric Gaussian

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functions. The lattice strains developed in the constituent phases were determined by analyzing the peak position (2θhkl) of each hkl plane. When the external load was absent (0 MPa), the (211) peak position for the α phase was located at a scattering angle of 77.147°, as shown in Fig. 8. When the external load was increased to 1,053 MPa, the (211) peak positions for the α and α΄ phases were shifted to scattering angles of 76.732° and 76.412°, 20

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respectively. Fig. 9 shows the neutron diffraction peaks of (100) for the γ phase (green color

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in the schematic microstructure) in TR-DSS under loading of 0 and 1,053 MPa. The diffraction peak was broadened and shifted to a lower diffraction angle as the load

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increased. The diffraction peak can be successfully fitted with a symmetric Gaussian function. When the external load was absent (0 MPa), the (100) peak position of the γ phase

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was located at a scattering angle of 47.655°, as shown in Fig. 9. When the external load was increased to 1,053 MPa, the (100) peak position for the γ phase was shifted to a scattering angle of 47.240°. Such peak shifts enabled us to evaluate the evolution of the elastic lattice

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strains in the constituent phases during uniaxial loading using Eq. (2). Fig. 10(a) compares the measured and simulated lattice strains of the α (F) and α΄ (M) phases along the loading

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direction as a function of macroscopically applied strains. CPFEM successfully simulated the evolution of the (211) lattice strain in the α phase during uniaxial tension, while the

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(200) lattice strain in the α phase slightly underestimated the experimental results. With an applied strain level of more than 0.1, the measured lattice strains in the α phase were increased in a linear fashion, which indicated that plastic deformation did not significantly affect the slope of the applied strain vs. the lattice strain in the α phase. It should be noted that CPFEM also successfully simulated the evolution of the (200) and (211) lattice strains

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in the α΄ phase after the phase transformation of γ-to-α′ had begun. Fig. 10(b) compares the

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measured and simulated lattice strains of the γ (A) phases along the loading direction as a function of the macroscopically applied strain. The CPFEM successfully simulated the

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evolution of the (111), (200) and (311) lattice strains in the γ phase considering the experimental errors. Fig. 11(a) compares the measured (Neutron) and simulated (CPFEM)

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volume fractions of constituent phases in TR-DSS as a function of macroscopic strain. It is shown that the evolution of the simulated volume fractions was similar to the experimental data. Fig. 11(b) compares the measured and simulated macroscopic stresses of TR-DSS as a

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function of the macroscopic strain. The stress-strain relationships of the constituent phases in TR-DSS were also simulated as a function of the macroscopic strain. The simulated

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macroscopic stress of TR-DSS was in good agreement with the experimentally measured macroscopic stress of TR-DSS. It should be noted that CPFEM successfully simulated the

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sigmoidal shape induced by the phase transformation during uniaxial tension. The microscopic hardening parameters for the constituent phases of TR-DSS are summarized in Table 3. The optimal values for Cth1 and Cth2 were determined as 0.083 and 0.116, respectively. The identified material parameters for TR-DSS are significantly different than the set for NTR-DSS (Jeong et al., 2014, 2015). It seems that the different partitioning of

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chemical components and the appearance of the γ-to-α′ transformation induce a significant

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change in the material parameters for the constituent phases of TR-DSS. The validity of the identified material parameters was not checked under more complex deformation

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conditions. The γ-to-α′ transformation is sensitive to non-proportional loadings, showing

separate study in the near future.

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phenomena like tension-compression asymmetries. The validity test will be conducted as a

4.3. Simulation of micromechanical behaviors

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A CPFEM that was based on the RVEs of the unit cell revealed that the kinematic stability of the constituent phases of NTR-DSS strongly affected the micromechanical

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behaviors during plastic deformation (Jeong et al., 2014). In the present study, a CPFEM that was based on the RVEs of the unit cell, as shown in Fig. 12(a), was also used to

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investigate the extent that crystallographic orientation had contributed to the micromechanical behaviors of TR-DSS in which a phase transformation of γ-to-α′ had occurred. A regular bamboo structure was assumed to represent the typical microstructure of TR-DSS, as shown in Fig. 1. The relative size of the constituent phases in the RVEs of a unit cell was determined from the corresponding average values of the constituent phases

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measured by the EBSD technique, as explained in section 2. The RVEs of the unit cell were

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made up of one grain for the α phase (α) and two grains for the γ phase (γ1 and γ2). One and three orientations for the α and γ phases were selected by considering the initial texture of

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TR-DSS: RC for the α phase; and, Copper, Brass, and Goss for the γ phase. Three RVEs of the unit cell were used to construct the initial configuration: [RVEs1] α(RC)-γ1 (Copper)-

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γ2(Brass); [RVEs2] α(RC)-γ1(Copper)-γ2(Goss); and, [RVEs3] α(RC)-γ1(Goss)- γ2(Brass). The periodic boundary conditions (PBCs) for a uniaxial tension of ε=0.3 were applied to the six planes of the initial mesh, as shown in Fig. 12(b) (Kanjarla et al., 2010;

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Kadkhodapour et al., 2011; Choi et al., 2013; Jeong et al., 2014).

According to the calculation results on the kinematic stability of the initial orientations

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(Jeong et al., 2014), the RC, Copper and Goss orientations were predicted to be relatively stable under uniaxial tension, but the Brass orientation was predicted to be relatively

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unstable under uniaxial tension. Therefore, the RVEs1 and RVEs3, in which the Brass orientation was included as the γ phase (γ2 grain), were expected to exhibit relatively heterogeneous deformation behavior during uniaxial tension, while RVEs2, which consisted of relatively stable orientations, was expected to exhibit a relatively homogeneous deformation behavior during uniaxial tension. Fig. 13 shows the evolution of the phase map

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for the three RVEs of the unit cell during uniaxial tension of ε=0.3. A comparison of Figs.

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13(a) and 13(b) shows how the orientations (Brass or Goss) of the γ2 grain affected the transformed region in the γ1 grain (Copper). A comparison of Figs. 13(a) and 13(c) also

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shows how the orientations (Copper or Goss) of the γ1 grain affected the transformed region in the γ2 grain (Brass). This result indicates that the initial orientation stability of the γ

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grains in TR-DSS did not significantly affect the kinetics of phase transformation inside the grain under uniaxial tension. The orientation relationship between the γ and α′ phases can be characterized by the K-S ., (111)γ (110)α′ and [1 01]γ [111]α′,(Kurdjumov and Sachs, and Nishiyama-Wassermann (N-W) relationships, i.e., (111)γ (011)α′ and

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1930), i.e.,

[112]γ [011]α′ (Nishiyama, 1934-35; Wassermann, 1933; Kim et al., 2007).

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Fig. 14 shows the orientation relationship between the γ and α′ phases in the deformed RVEs of the unit cell during uniaxial tension. The phase boundaries between the two phases

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were identified as either a K-S or a N-W relationship. The selection of a specific orientation relationship was achieved by considering the closest theoretical orientation within the range of the tolerance angle (5°). Fig. 15 shows the ND-IPF map for the three RVEs that contained a partially transformed region in the γ grains during uniaxial tension. The crystallographic orientations for the transformed regions and the activated α′-variants 25

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among 24 possible variants (red dots) are shown in the (001) pole figure. Phase

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transformation drastically changed the crystallographic orientation in each phase during uniaxial tension. It was clear that the number of activated α′-variants in TR-DSS was not

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closely related to the kinematic stability of the initial orientation in a partially transformed state. Relatively stable Copper (γ1 in RVEs1 and RVEs2) under uniaxial tension exhibited

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two activated α′-variants. Relatively unstable Brass (γ2 in RVEs3) also exhibited two activated α′-variants. Fig. 16(a) shows the ND-IPF and α′-variants maps for the RVEs1 after a uniaxial tension of ε=0.3. Figs. 16(b) and (c) show the orientations of regions (α′1

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and α′2) transformed from γ grains (γ1 and γ2) and the activated α′-variants in the transformed regions. After uniaxial tension of ε=0.3, the two initial Copper (γ1) and Brass

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(γ2) grains were completely covered by the transformed regions of α′1 and α′2, respectively. The transformed regions did not show a significant orientation spread. However, the

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number of activated α′-variants strongly depended on the kinematic stability of the γ grain under uniaxial tension. The relatively unstable Brass (γ2) under uniaxial tension showed four activated α′-variants, as shown in Fig. 16(c), while the relatively stable Copper (γ1) showed two activated α′-variants, as shown in Fig. 16(b). If we neglect the difference in the crystal structure between the α and α′ phases, the minor α′-variants (1 in α′1 and 2, 6, 13 in 26

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α′2) were mostly activated at the near region of the triple junction. Fig. 17 shows the ND-

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IPF and α′-variants maps for the RVEs2 after uniaxial tension of ε=0.3. Figs. 17(b) and (c) show the orientations of the transformed regions (α′1 and α′2) in the RVEs2, and the

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activated α′-variants for the transformed regions. The grain of the initial Goss (γ2) was partially occupied by the transformed α′2 region, while the grain of the initial Copper (γ1)

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was completely occupied by the transformed α′1 region. This result indicated that the kinematic stability of the γ grain was not closely related to the kinetics of the phase transformation of γ-to-α′. Copper (γ1) and Goss (γ2) showed one and two activated α′-

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variants, respectively. This result indicated that the γ grains with a relatively stable orientation in RVEs2 exhibited a small number of activated α′-variants in the transformed

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region. The minor α′-variant (13 in α′2) was also activated at the near region of the triple junction. Fig. 18 shows the ND-IPF and α′-variants maps for the RVEs3 after a uniaxial

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tension of ε=0.3. Figs. 18(b) and (c) show the orientations of the transformed regions in RVEs3, and the activated α′-variants for the transformed regions. The grain of the initial Goss (γ1) was almost occupied by the transformed α′1 region, while the grain of the initial Brass (γ2) was completely occupied by the transformed α′2 region. Goss (γ1) and Brass (γ2) showed four and two activated α′-variants, respectively. Contrary to the RVEs1 and RVEs2, 27

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the minor α′-variants (4, 6, 13 in α′1 and 16 in α′2) were mostly activated at the phase

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boundaries between the γ and α grains. These results indicated that heterogeneous stress states were developed in the phase boundaries between the γ and α grains in the RVEs3

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during uniaxial tension. Comparing Figs. 16 and 18 indicates that the activated α′-variants in the Brass orientation were dependent on the neighboring γ grains. Comparing Figs. 17

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and 18 also shows that the activated α′-variants in the Goss orientation were strongly dependent on the orientation of the neighboring γ grains.

A CPFEM based on the RVEs of the unit cell revealed that the kinematic stability of

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initial orientations significantly affected the heterogeneity of the kernel average misorientation (KAM) and ductile failure in the constituent phases of NTR-DSS during

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uniaxial tension (Jeong et al., 2014). Also, the KAM was equivalently partitioned to the constituent phases regardless of the kinematic stability of the initial orientations. In the

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present study, a KAM was also used for quantitative analysis of the deformation heterogeneity in the RVEs of the unit cell for TR-DSS during uniaxial tension. The data acquisition procedure can be used to obtain the KAM from the CPFEM results (Jeong el al., 2014). The 3rd nearest neighbors were considered in order to calculate the average misorientation. To avoid high KAM values at the grain boundaries, misorientations

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exceeding a tolerance angle of 5° were excluded from the calculation of the average

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misorientation. CPFEM results for NTR-DSS revealed that the RVEs1 and RVEs3 exhibited a relatively heterogeneous KAM distribution compared with that of the RVEs2

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(Jeong et al., 2014). The Brass orientation, which was kinematically unstable under uniaxial tension, contributed to the heterogeneous distribution of KAM in the RVEs1 and RVEs3.

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Fig. 19 shows the distribution of the KAM in the deformed RVEs of the unit cell for TRDSS after a uniaxial tension of ε=0.3. These results show that the three RVEs exhibited significantly different distributions of the KAM in the constituent phases after uniaxial

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tension. The RVEs3 exhibited a relatively heterogeneous distribution of the KAM compared with the RVEs1 and RVEs2. It seemed that the scattered distribution of minor α′-

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variants (16 in α′2) in RVEs3, as shown in Fig. 18(a), induced the enhancement of deformation heterogeneity in all constituent phases. A comparison of the KAM distribution

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in the α′1 of Figs. 19(a) and 19(b) shows how deformation heterogeneity in the γ1 grain (Copper) was influenced by the micromechanical behaviors in the neighboring γ2 grains (Brass and Goss). A comparison of the KAM distribution in the α′2 for Figs. 19(a) and Fig. 19(c) also shows how the deformation heterogeneity in the γ2 grain (Brass) was influenced by the micromechanical behaviors in the neighboring γ1 grains (Copper and Goss). These 29

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results show how the kinematic stability of γ grains as well as the neighboring γ grains

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should be simultaneously considered in order to understand the deformation heterogeneity

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in TR-DSS during uniaxial tension.

5. Conclusions

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The effect of the kinematic stability of the initial orientation of the γ phase on phasetransformation behavior and deformation heterogeneity in TR-DSS was investigated using in-situ neutron diffraction and the crystal plasticity finite element method (CPFEM).

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1. The evolution of lattice strains in the constituent phases in TR-DSS along the loading direction as a function of macroscopically applied strains was calculated by fitting the

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diffraction peaks using independent symmetric Gaussian functions with different widths and positions.

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2. A phase-transformation model was implemented in the CPFEM to consider the effect of TRIP in TR-DSS. The microscopic hardening parameters of the constituent phases were determined by fitting the measured macroscopic stress and lattice strains along the loading direction as a function of macroscopically applied strain using a CPFEM based on RVEs.

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3. The determined microscopic hardening parameters for each phase were used to explain

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the influence of the kinematic stability of the initial orientation for the γ phase on the phase transformation behavior and deformation heterogeneity of the constituent phases

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in the RVEs of unit cells with a regular bamboo structure of TR-DSS during uniaxial tension.

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4. The kinematic stability of the initial orientation for the γ phase did not significantly affect the kinetics of phase transformation and deformation heterogeneity in TR-DSS under uniaxial tension. However, the number of activated α′-variants strongly depended

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on the kinematic stability of the γ grain and the orientation of the neighboring γ grains under uniaxial tension. A specific combination of the Brass orientation (a relatively low

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stability) with the neighboring Goss orientation (a relatively high stability) induced a scattered distribution of minor α′-variants along the phase boundaries and enhanced the

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deformation heterogeneity in all constituent phases during uniaxial tension.

Acknowledgments

This study was supported by the Nuclear Research & Development Program of the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government

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(MEST) (NRF-2013M2A2A2A6029106), and by the Basic Science Research Program

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through the National Research Foundation of Korea (NRF) funded by the Ministry of

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Education (NRF-2014R1A6A1030419).

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Wassermann, G., 1933. Influence of the transformation of an irreversible Ni steel onto crystal orientation and tensile strength. Arch Eisenhüttenwes. 16, 647.

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Woo, W., Em, V., Seong, B.S., Shin, E., Mikula, P., Joo, J., Kang, K., 2011. Effect of wavelentgh-dependent attenuation on neutron diffraction stress measurerments at depth in steel. J. Appl. Cryst. 44, 747-754. Woo, W., Em, V.T., Kim, E.-Y., Han, S.H., Han, Y.S., Choi, S.-H., 2012. Stress–strain relationship between ferrite and martensite in a dual-phase steel studied by in situ neutron diffraction and crystal plasticity theories. Acta Mater. 60, 6972-6981.

39

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C11(GPa)

C12(GPa)

α

231.4

134.7

γ

197.5

124.5

C44(GPa) 116.4

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SC

Phase

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Table 1. Single crystal elastic constants for each phase.

Table 2. Fault-band systems of the FCC crystal structure.

3 4 5

[1121] ⊗ (11 1) / 18 [1 12] ⊗ (11 1) / 18

[2 1 1] ⊗ (1 1 1) / 18 [12 1] ⊗ (1 1 1) / 18

AC C

6

[12 1] ⊗ (11 1) / 18

7

8

TE D

2

Fault-band systems

EP

α 1

[112] ⊗ (1 1 1) / 18

9

10 11

12

40

[2 11] ⊗ (1 11) / 18 [112] ⊗ (1 11) / 18 [2 11] ⊗ (1 11) / 18 [211] ⊗ (111) / 18 [12 1] ⊗ (111) / 18 [112] ⊗ (111) / 18

122

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Table 3. Material parameters in the constitutive relations for TRIP.

Physical Meaning

Values

Reference shear rate m

0.001

Rate sensitivity coefficient

τ αo (γ)

173

Initial slip resistance for γ phase (MPa)

102

Initial slip resistance for α′ phase (MPa)

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τ oα (α′)

0.05

Initial slip resistance for α phase (MPa)

SC

τ αo (α)

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Parameters

τ oα (α)×1.5

ho(α)

Hardening parameter for α phase (MPa)

1,980

ho(γ)

Hardening parameter for γ phase (MPa)

2,500

ho(α′)

Hardening parameter for α′ phase (MPa)

ho (α)×1.4

Saturated value of slip resistance for α phase (MPa)

430

Saturated value of slip resistance for γ phase (MPa)

360

τ sat (α)

TE D

τ sat (γ)

Saturated value of slip resistance for α′ phase (MPa)

τ sat (α′)

δ s

Shear strain along the unit vector

Cth2

4 0.00143 0.22797

A critical value for the initiation of γ-to-α′ transformation

0.083

A parameter for the mechanical stabilization of the γ phase

0.116

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C

th1

Hardening coefficient for constituent phases Dilatational strain along the direction

EP

a

τ sat (α)×2.5

Figure Captions

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Fig. 1. (a) Inverse pole figure map; and, (b) phase map of TR-DSS measured on three orthogonal sections (ND, TD and RD) in the center regions in the thickness direction.

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Fig. 2. ϕ2=45° sections of the orientation distribution function (ODF) for the constituent phases measured on (a) the ND section; (b) the TD section; and, (c) the RD section.

Fig. 3. (a) Stress state on the invariant plane; (b) a schematic diagram showing a martensite

SC

nucleation at a fault band intersect; and, (c) the orientation of α′ predicted by the model.

Fig. 4. Fig. 4. Simplified RVEs for uniaxial tension simulation of TR-DSS: (a) the

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prescribed displacement boundary conditions, (b) undeformed, (c) ε= 0.22 and (d) ε=0.4. Fig. 5. Neutron diffraction patterns of the TR-DSS measured at different strain levels. Fig. 6. Deformed γ phase in TR-DSS after uniaxial tension of ε=0.2; (a) TEM bright field

TE D

(BF) image of γ phase, (b) crisscrossed patterns of line contrasts, (c) a high resolution (HR) image of stacking faults (SFs) and corresponding fast Fourier transform (FFT) pattern, (d) a crisscross pattern of the primary and secondary SF and its FFT pattern.

EP

Fig. 7. Deformed structures of TR-DSS after uniaxial tension of ε=0.4; (a) TEM BF image

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in γ-on axis condition, (b) magnified image of the selected area in (a), (c) the remained SFs in a γ matrix, and (d) EDP of the circled area in (b). Fig. 8. Neutron diffraction peaks in TR-DSS under loadings of 0 and 1053 MPa: (211) for the α and α΄ phases.

Fig. 9. Neutron diffraction peaks in TR-DSS under loadings of 0 and 1053 MPa: (200) for the γ phase.

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Fig. 10. Measured and simulated lattice strains of the constituent phases in the loading

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direction as a function of the macroscopically applied strain: (a) the α and α΄ phases; and, (b) the γ phase.

Fig. 11. (a) Comparison of experimentally measured and theoretically simulated volume fraction of constituent phases in DSS; and, (b) simulated stress-strain relationship of the α,

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γ and α΄ phases and the measured macroscopic stress of TR-DSS as a function of the macroscopic strain.

boundary conditions.

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Fig. 12. (a) RVEs of the unit cell with a regular bamboo structure; and, (b) periodic

Fig. 13. Evolution of the phase map in the RVEs of the unit cell during uniaxial tension: (a) RVEs1; (b) RVEs2; and, (c) RVEs3.

TE D

Fig. 14. Evolution of the orientation relationship in the RVEs of the unit cell during uniaxial tension: (a) RVEs1; (b) RVEs2; and, (c) RVEs3. Fig. 15. ND-IPF map for the RVEs that contain a partially transformed region in γ grains: (a)

EP

RVEs1; (b) RVEs2; and, (c) RVEs3.

Fig. 16. (a) ND-IPF and α′-variants maps for the RVEs1 after uniaxial tension of ε=0.3.

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The orientations of transformed regions from γ grains and the activated α′-variants: (b) α′1; and, (c) α′2.

Fig. 17. (a) ND-IPF and α′-variants maps for the RVEs2 after uniaxial tension of ε=0.3. The orientations of transformed regions from γ grains and the activated α′-variants: (b) α′1; and, (c) α′2. Fig. 18. (a) ND-IPF and α′-variants maps for the RVEs3 after uniaxial tension of ε=0.3.

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The orientations of transformed regions from γ grains and the activated α′-variants; (b) α′1;

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and, (c) α′2. Fig. 19. Distribution of the KAM in the deformed RVEs of the unit cell after uniaxial

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EP

TE D

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tension of ε=0.3: (a) RVEs1; (b) RVEs2; and, (c) RVEs3.

44

RD

EP

TD

100㎛ ㎛

100㎛ ㎛


Scan Area : 300 x 300 [µ µm ]
Step Size : 0.5 [µ µm ]

AC C

ND

TE D

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SC

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(a)

Ferrite

64.7%

Austenite

35.3%

(b) Fig. 1

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ϕ1

90°° (001)[ 1 1 0]

Φ (111)[1 21]

(111)[0 1 1]

(111)[1 1 0]

(111)[ 1 1 2]

(554)[ 2 25]

(332)[ 1 1 3]

90°°

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γ − fiber

0°°

SC

(112)[1 1 0]

(110)[001]

ϕ1

90°°

Φ

EP

(112)[1 1 1]

TE D

α − fiber

90°°

(110)[1 1 2]

(a)

AC C

α-phase

(001)[1 1 0]

γ-phase

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0°°

(110)[001]

(b) Fig. 2

(c)

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σt

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σN (|| p)

(001)

Martensite nucleus

τmax

TE D

τ (|| e)

Austenite matrix

(a)

AC C

EP

: Initial Orientation : Orientation after P-T

(b)

Fig. 3

(c)

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2 1

6 7

5 Z (ND)

8 X (RD)

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Y (TD)

(1-2-6-5) : UX= 0 (1-4-8-5) : UY= 0 (5-6-7-8) : UZ= 0 (4-3-7-8) : UX(εε) = 0.4

SC

4

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3

(b)

AC C

EP

TE D

(a)

Martensite Austenite Ferrite

(d)

(c) Fig. 4

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(110)

SC

(211)

(200)

(220)

ε=0.4

EP

ε=0.2

TE D

ε=0.3

ε=0.1

AC C

(111)

M AN U

(200)

ε=0.0

Fig. 5

(220)

(311) (222)

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(b)

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SC

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(a)

BF

(d)

TE D

111 - 111 002

B=[110]

EP

γ

AC C

(c)

Fig. 6

111 - 111 002

γ

B=[110]

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(b)

(a)

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γ

γ DP1

α΄ α΄

α΄

γ

γ

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γ

γ-on axis condition 111 002

(d)

B=[110]

γ SF

AC C

EP

γ

- 111

TE D

(c)

DP1

- 101 111

110

- 111

002

α΄ γ B=[110] α΄ B=[111]

Fig. 7

011

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Scattering vector, Q

Ferrite

Scattering vector, Q

SC

Ferrite

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Martensite

(211) : 1053 MPa

Combined Martensite Ferrite

AC C

Ferrite

EP

TE D

(211) : 0 MPa

Fig. 8

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Scattering vector, Q

Austenite

Scattering vector, Q

EP

Austenite

AC C

(100) : 0 MPa

TE D

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SC

Austenite

Fig. 9

(100) : 1053 MPa

Austenite

AC C

EP

TE D

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SC

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(b)

(a)

Fig. 10

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EP

TE D

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(b)

(a)

Fig. 11

(RC)- 1 (Copper)- 2(Brass)

RVEs2:

(RC)- 1(Copper)- 2(Goss)

RVEs3:

(RC)- 1(Goss)-

2(Brass)

4 8

γ1

(1-2-3-4)/(5-6-7-8) : PBCs (1-2-6-5)/(4-3-7-8) : PBCs (1-4-8-5)/(2-3-7-6) : PBCs(εε=0.3)

2

1 6

5 3

AC C

X (RD)

EP

α

Y (TD)

Z (ND)

γ2

TE D

γ1

7

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α

3

SC

RVEs1:

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(a)

(b)

Fig. 12

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RD

ε=0.0

α γ1

Brass

Copper

Copper

Copper

Goss

α+α′ α′-phase α′ γ - phase

α

α′1

α′1 γ1

γ1

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α

α

α (a)

α′1

γ1

γ2

TE D EP

α α′2

γ1

Brass

Goss

α ε=0.269

α′1

α γ1

α′1 α′2

γ2

α′2 α′1

γ1

γ1 α′ γ1 1

α α′2

α

α

(b)

(c)

Fig. 13

α′2

ε=0.3

ε=0.3

α

γ2

α′2

α

α

ε=0.3

α′1

γ2

ε=0.277

α γ2

Goss

α

ε=0.246

γ1 α′1

γ1

γ1

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Copper

γ2

γ1

γ2

SC

γ1

α

α

AC C

TD

ε=0.0

ε=0.0

α′1

γ1 γ1

ε=0.246

α γ2

α α′1 γ1

α′1

γ1

α

(a)

α′1

EP

α′1

AC C

α

α′1

γ1

α′2

γ2

α′2

α′2

α

γ2

α′2

α

α′1

ε=0.3

γ1 α′1

γ1

α α′2

Fig. 14

α′1

γ1 γ1

α α+α′ α′-phase α′ γ - phase

(b)

γ1

α

ε=0.3

TE D

α α′2

γ1

α

ε=0.3

α′1

γ2

α

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γ1 α′1

ε=0.269

ε=0.277

SC

RD

TD

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(c)

K-S N-W G.B

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ε=0.246

α

α

α α′1 γ1

γ2

α′1

γ1

γ1

γ2

α

α′1

γ1

α′2

γ2

α′2

M AN U

●

●

γ1

●

●

γ1

●

γ2

●

●

●

TE D

●

●

(5)

EP

(1, 5)

(4, 16)

AC C

TD

γ1

α

SC

α

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γ1 α′1

ε=0.269

ε=0.277

TD

TD

RD

RD

RD

(a)

(b)

(c)

Fig. 15

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RVEs1 α α′2

α′1

α′1

α′2

α′1

α′1

RI PT

(a)

α

α

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SC

α

(1, 5)

●

●

γ1

(b)

RD

EP

TE D

●

TD

●

(c)

(2, 4, 6, 13)

AC C

γ2

●

TD

●

●

RD

Fig. 16

α′2 α′1

2 4 1

6

5

13

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RVEs2 α α′1

α′2

γ2

α′2

α′1

α′1

α

α′2

γ2

α′2

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(a)

α α′1

α′1

α

(b)

TE D

●

(5)

TD

RD

EP

γ2

●

AC C

(c)

●

(4, 13)

●

TD

●

RD

Fig. 17

4 5

SC ●

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●

γ1

α′2 13

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RVEs3 γ1 α′1

γ1 α′1

α′2

γ1

γ1 α′1

α′2

γ1

γ1

α′1

α

●

●

(2, 4, 6, 13) TD

RD

EP

●

TE D

●

M AN U

γ1

SC

α

(b)

γ1

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(a)

α

α

●

AC C

γ2

(4, 16)

●

(c)

TD

●

●

RD

Fig. 18

γ1

α′1 2 4

α′2

6

4

13

16

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RVEs1

RVEs2

RVEs3

α α′1

α′1

α′2

α

γ2

α′1

α′2 α

EP

TE D

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SC

α

α′2

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α′2

γ1 α′1 γ1

AC C

α′1

α

α

(a)

(b)

Fig. 19

(c)

γ1 α′1 γ1

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Highlights

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CPFEM revealed the effect of the kinematic stability of the γ phase on the phasetransformation behaviors of DSSs.
A phase-transformation model was implemented in the CPFEM to consider the effect of TRIP on micromechanical behaviors in DSS
TEM analysis revealed that α΄and γ in the deformed sample shows the KurdjumovSachs (K-S) relationship.

AC C

EP

TE D

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SC


The individual flow curves of the α, γ and α΄ phases in DSS were determined via insitu neutron diffraction in combination with the CPFEM.
CPFEM revealed the effect of the kinematic stability of γ on the number of activated α΄-variants.