metals

Article Prediction of Static Recrystallization Nucleation Sites in Tensile Deformed Single Pure Iron through a Combination of In-Situ EBSD and CP-FEM

Zichao Luo 1,*, Masahiko Yoshino 1, Motoki Terano 2 and Akinori Yamanaka 3 1 Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan; [email protected] 2 Department of Mechanical Systems Engineering, Okayama University of Science, Okayama 700-0005, Japan; [email protected] 3 Department of Mechanical Systems Engineering, Tokyo University of Agriculture and Technology, Tokyo 183-8538, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-080-1120-7027

 Received: 18 September 2018; Accepted: 17 October 2018; Published: 20 October 2018 

Abstract: Microstructure control is of vital importance in tailoring physical properties of metallic materials. Despite the enormous efforts devoted to the study of microstructure evolution during recrystallization, most previous research has been conducted under non-simple conditions, either applying complex deforming boundary conditions or employing specimens with sophisticated crystalline structure. These complexities hinder comprehensive understanding of the fundamental aspects in texture evolution and make it even harder to penetrate the already intricate recrystallization behaviors. The present study aims at a detailed evaluation of widely used phenomenological model in reproducing experimentally observed deformation characteristics under simple crystalline structure and deformation condition, as well as the prediction of nucleation sites during static recrystallization. In situ electron back-scattering diffusion (EBSD) observations were performed to record texture change during static recrystallization of single crystal pure iron specimens after tensile deformation. CP-FEM (crystal plasticity finite element method) method was employed to simulate deformed texture. Deformation heterogeneity characterized by kernel average misorientation maps derived from EBSD data and numerical calculations were compared. The former data shows deformation heterogeneity sensitive to localized microstrain while the later delivers an effective meso-scale deformation distribution. Observed approximate nucleation sites have shown a qualitative coincidence with highly distorted regions in numerical calculations.

Keywords: in situ EBSD scan; CP-FEM; single crystal iron; static recrystallization; nucleation site

1. Introduction In metallic materials, atoms are orderly arranged into the form of . The agglomeration of crystals and crystalline defects makes up the microstructure of metals. A large number of material properties are related to the distribution of microstructural elements over the volume of the material. By controlling the microstructure, materials with improved material properties, such as strength, toughness, ductility, hardness, corrosion resistance, or wear resistance can be attained without adding high price rare elements [1,2]. One of the well-accepted methods in texture control is through the combination of plastic deforming and annealing [3,4]. When plastically deformed metal materials are subject to heat treatment under sufficiently high temperature, new and relatively defect-free grains will emerge from deformed material matrix and expand until the deformation microstructure becomes fully consumed. These two processes,

Metals 2018, 8, 858; doi:10.3390/met8100858 www.mdpi.com/journal/metals Metals 2018, 8, 858 2 of 15 referred to as “nucleation” and “growth”, form the microstructural evolution mechanism known as recrystallization [5]. In the past years, microstructure evolution during plastic deformation and recrystallization has piqued the interest of many researchers. Despite efforts devoted to in-situ/ex-situ observations and simulations of texture evolution during plastic deforming and static recrystallization in various scales, previous research works are still short in several aspects: Firstly, despite wide industrial application of body centered cubic metals, texture evolution observation of BCC metal with the simplest crystalline structure—single crystal BCC iron is astonishingly rare. Due to the deficiency in available observation results, some recent advanced modellings of texture change during plastic deforming and recrystallization of single crystal iron were either compare with materials of similar microstructure such as low IF steel [6], ARMCO Fe [7], or datasets derived up to 30 years ago [8,9], long before modern microstructural-crystallographic characterization techniques, like electron back-scattering diffusion (EBSD) and dark field X-Ray microscopy get involved. Moreover, most investigations of texture evolution during plastic deformation and following recrystallization have been conducted under non-simple conditions—extra complexities would have been introduced into experiments due to the use of metals with complex crystalline structures as well as the employment of deforming techniques with sophisticated boundary conditions. Most widely adopted materials in experimental observations of such studies have been particle-containing alloys [10–12] and polycrystalline pure metals [13,14] with intricate crystal structures. The complexity in initial microstructure would lead to interaction between migrating boundaries and static ones, hard particles, as well as other texture components during grain growth. Even for studies carried out on single crystal materials, like the ones on plastically deformed single crystal by Zaafarania et al. [15] and on single-crystal nickel-base super alloy by Zambaldi et al. [16], as they employed indentation to introduce plastic deformation into the specimens the straining condition of deformed matrix was quite complex and straining level could not be well controlled. Models able to reproduce kink bands occurred during tensile tests on single crystal tubes were developed by researchers from Ecole des Mines de Paris [17,18]. Without available microstructure data of deformed specimen, comparison between simulation models and experimental measurements were limited to only load-displacement and shape of slipping band on the tube. The coupling between intricacy in experimental conditions and inevitable randomness rooting in the nature of recrystallization hinders comprehensive understanding of the fundamental aspects in texture evolution and puts extra obstacles in the interpretation of observed results. Other investigations employing rolling (e.g., [19–22]) channel die compression (e.g., [23,24]), and micro-pillar compression (e.g., [25,26]) would suffer from similar problems. To sum up, for revealing the relationship between initial texture and deformed texture, and that between deformed matrix and recrystallized structure, study of texture evolution during plastic deforming and recrystallization under conditions with minimized complexity is demanded. The present study aims at a detailed evaluation of widely used phenomenological model in reproducing experimentally observed deformation characteristics under simple crystalline structure and deformation condition, as well as the prediction of nucleation sites during static recrystallization. In situ EBSD observations were performed to record texture change during static recrystallization of single crystal pure iron specimens after tensile deformation. Meanwhile, crystal plasticity finite element method (CP-FEM) was employed to simulate deformed texture and strain/stress distribution after tensile test. Deformation heterogeneities characterized by kernel average misorientation (KAM) map derived from EBSD data and numerical calculation were compared. The former data shows deformation heterogeneity sensitive to localized microstrain while the later delivers an effective meso-scale deformation distribution. Observed approximate nucleation sites have shown a qualitative coincidence with highly distorted regions in numerical calculations. Metals 2018, 8, 858 3 of 15

Metals 2018, 8, x FOR PEER REVIEW 3 of 15 2. Methodology 2. Methodology 2.1. Experimental Setting 2.1. Experimental Setting Single-crystal 99.994+% pure iron (from MaTecK, Juelich, Germany) was chosen for studying texture evolutionSingle-crystal in this99.994 experiment.+% pure iron To (from avoid MaTecK, extra strain Juelich introduced, Germany) during was chosen specimen for studying fabrication, specimenstexture evolution were cut in with this experiment. wire electrical To avoid discharging extra strain machine introduced into during the shape specimen shown fabrication, in Figure 1. specimens were cut with wire electrical discharging machine into the shape shown in Figure 1. The The profile deliberately introduces strain concentration to ensure that recrystallized region falls into the profile deliberately introduces strain concentration to ensure that recrystallized region falls into the neck of the specimen, thus an area of interest can be determined prior to observations. Six specimens neck of the specimen, thus an area of interest can be determined prior to observations. Six specimens withwith three three different different initial initial orientations orientations were were fabricated fabricated from from two two single single crystal crystal rods (specimen rods (specimen 1-1, 1- 1-1, 1-2 were2 were cut cut out out from from one one rodrod andand the other four four specimens specimens from from another). another). Initial Initial crystal crystal orientations orientations are givenare given in Tablein Table1 in 1 Eulerin Euler angles angles following following Bunge’s Bunge’s convention [27 [27].].

FigureFigure 1. Dimensions1. Dimensions of of the the specimen: specimen: ( aa)) f frontront view view;; and and (b ()b s)ide side view view (unit (unitss are in are mm) in mm)..

TableTable 1. 1.Neck Neck elongation elongation andand initial crystal crystal orientation orientation of ofeach each specimen. specimen.

Orientation Specimen Neck Orientation No. Specimen No. Neck ElongationInitial (%) Crystal Initial Orientation Crystal Orientation (In Bunge’s (In Bunge’s Convention) Convention) No. No. Elongation (%) 1-1 15.6 Orientation 1 1-1 15.6 146.7, 133.1, 329.2 Orientation 1 1-2 31.1 146.7, 133.1, 329.2 1-2 31.1 2-1 17.9 Orientation 2 2-1 17.9 272.5, 95.7, 347.8 Orientation 2 2-2 27.3 272.5, 95.7, 347.8 2-2 27.3 3-1 27.66 Orientation 3 3-1 27.66 60.9, 11.5, 33.8 Orientation 3 3-2 26.86 60.9, 11.5, 33.8 3-2 26.86

To provideTo provide driving driving force force for for recrystallization, recrystallization, plastic plastic deformation deformation was was applied applied to the to specimens the specimens by slowlyby slowly stretching stretching with with a a uniaxial uniaxial tensiletensile machine shown shown inin Figure Figure 2a2 ata atroom room temperature temperature until until neckneck elongation elongation had had reached reached 15–30%. 15–30%. Specimens Specimens were were fixed fixed into into position position by insertingby inserting pins pins of diameter of 0.79diameter mm through 0.79 mm the through two pinholes. the two Tensilepinholes direction. Tensile direction was aligned was aligned with the with centerline the centerline of specimen. of Tensilespecimen. loading Tensile speed was loading set to speed a constant was set0.2 mm/min to a constant to guarantee 0.2 mm/min quasi-static to guarantee deformation quasi-static condition. Neckdeformation elongation condition. and initial Neck crystal elongation orientation and initial of each crystal specimen orientation are of listed each specimen in Table1 are. Cold listed worked in Table 1. Cold worked specimens were sent to mechanical polishing with SiC2400. Then the surface specimens were sent to mechanical polishing with SiC2400. Then the surface of specimen was of specimen was sequentially polished with 6, 2 and 0.25 μm diamond suspensions. Finally, the sequentially polished with 6, 2 and 0.25 µm diamond suspensions. Finally, the surface was finished surface was finished by chemical-mechanical polishing using colloidal silica solution. Surfaces free by chemical-mechanicalof detectable polishing polishing damages were using generated colloidal from silica the solution. surface preparation Surfaces free procedures. of detectable polishing damagesIn were-situ annealing generated and from EBSD the observation surface preparation was carried procedures. out using a heating stage (Type HSEA-1000, TSLIn-situ Solutions annealing Ltd., Sagamihara and EBSD, observation Japan) with heating was carried range outfrom using room atemperature heating stage to 1000 (Type °C . HSEA-1000, Figure ◦ TSL2 Solutionsb depicts Ltd., heating Sagamihara, stage used Japan) in in situ with observation. heating range After from deformed room temperature specimen was to1000 mountedC. Figure on 2b depictsheating heating stage, stage two pairs used of in thermocouples in situ observation. were attached After deformed to both the specimen observed specimen was mounted surface on an heatingd stage, two pairs of thermocouples were attached to both the observed specimen surface and the heating basis to precisely control the temperature of specimen. The specimens were heated to 600 ◦C to initiate Metals 2018, 8, x FOR PEER REVIEW 4 of 15 Metals 2018, 8, 858 4 of 15 the heating basis to precisely control the temperature of specimen. The specimens were heated to 600 °C to initiate recrystallization and kept at the temperature for a certain time span. In order to recrystallization and kept at the temperature for a certain time span. In order to determine when determine when to stop for a scan, field emission scanning electron microscope (FE-SEM) was to stop for a scan, field emission scanning electron microscope (FE-SEM) was employed to monitor employed to monitor grain growth (JSM 7001F, JEOL, Tokyo, Japan). Temperature variation was grainconstrained growth (JSM to be 7001F, within JEOL, ± 0.2 °C Tokyo, during Japan). annealing. Temperature Then specimen variation temperature was constrained was reduced to to be 200 within ◦ ◦ ±0.2°CC and during EBSD annealing. scanning was Then performed specimen with temperature a step size of was2 μm reduced over an area to 200 of approximateC and EBSD 900 scanning μm was performed× 500 μm. High with vacuum a step level size of 29.µ5m× 10 over−5 Pa an was area kept of approximatethroughout the 900 in-µsitum observation× 500 µm. Highto prevent vacuum − leveloxidization. of 9.5 × 10 5 Pa was kept throughout the in-situ observation to prevent oxidization.

FigureFigure 2. (a 2.) Device(a) Device employed employed for for tensile tensile test; test; ((bb)) deformeddeformed specimen specimen set set on on in insitu situ heating heating stage. stage.

It shouldIt should be recognizedbe recognized that that the the conducted conducted observationsobservations extracted extracted microstructure microstructure information information onlyonly from from the thesample sample surface. surface. Given Given the the fact fact that both specimen specimen deformation deformation and and grain grain growth growth actuallyactually happen happen in three-dimensionalin three-dimensional space, space, it it is important to to thoroughly thoroughly consider consider the the effect effect of of characterizingcharacterizing 3D phenomenon 3D phenomenon with with 2D observations. 2D observations. As for As evaluating for evaluating strain strain and and deformation deformation energy energy distribution with 2D EBSD scans, Calcagnotto et al. compared 2D EBSD scan results with 3D distribution with 2D EBSD scans, Calcagnotto et al. compared 2D EBSD scan results with 3D ones ones on compressed dual-phase steels and concluded distribution estimation from 2D on compressed dual-phase steels and concluded dislocation distribution estimation from 2D EBSD EBSD scans has a reasonable precision [28]. In terms of texture evolution realized by nucleation and scansgrowth, has a reasonable although surface precision effects [28 ].such In termsas thermal of texture groovi evolutionng would realizedalso contribute by nucleation to the observed and growth, althoughresults surface [29], grain effects formation such as and thermal expansion grooving similar would to those also presentedcontribute in to 2D the scanning observed were results also [29], grainreported formation in 3D and observations expansion [30 similar]. Thus to, sufficient those presented information in can 2D scanningbe obtained were from also 2D observation reported in 3D observationsfor investigating [30]. Thus, non- sufficientspecific texture information evolution can in plastic be obtained deformation from 2Dand observation static recrystallization. for investigating non-specific texture evolution in plastic deformation and static recrystallization. 2.2. CP-FEM Simulation Setting 2.2. CP-FEM Simulation Setting In addition to in situ EBSD observations in which microstructure on observed surface can be analyzedIn addition with to in high situ spatial EBSD observationsresolution, numerical in which microstructure simulations of on tensile observed deforming surface process can be were analyzed withemployed high spatial for resolution,a comprehensive numerical understanding simulations of straining of tensile in the deforming whole bulk. process Crystal were plasticity employed finitefor a comprehensiveelement method understanding was implemented of straining in the in user the subroutine whole bulk. UMAT Crystal using plasticity commercial finite software element package method was ABAQUS (version 6.14-1, Dassault Systèmes Simulia, Johnston, RI, USA) as the boundary problem implemented in the user subroutine UMAT using commercial software package ABAQUS (version 6.14-1, solver. Dassault Systèmes Simulia, Johnston, RI, USA) as the boundary problem solver. Constitutive model used in this work follows the continuum mechanical framework of elastoplasticityConstitutive modelat finite used strain in established this work by follows Asaro et the al. [31,32 continuum]. At quasi mechanical-static strain framework rates, the of elastoplasticitylocalized obstacles at finite to dislocation strain established glide are mainly by Asaro overcome et al. by [thermal31,32]. activation. At quasi-static Shear strain strain rate rates, the localizedof each slip obstacles system can to dislocationbe described glidewith a are power mainly law model overcome as follows: by thermal activation. Shear strain rate of each slip system can be described with a power1 law model as follows: |τα| m γ̇ α = γ̇ [ ] sign(τα) (1)  0 ατ  1 . α . |τ |c m α γ = γ0 sign(τ ) (1) τc

. where γ0 is the reference shear rate, τc the shear stress required to overcome the athermal barrier to dislocation motion on the α-th slip system, τα the resolved shear stress on the α-slip system, and m the strain-rate sensitivity. Metals 2018, 8, x FOR PEER REVIEW 5 of 15 where γ̇ 0 is the reference shear rate, τc the shear stress required to overcome the athermal barrier to dislocation motion on the α-th slip system, τα the resolved shear stress on the α-slip system, and m Metalsthe strain2018,-8rate, 858 sensitivity. 5 of 15 An isotropic hardening system following the hardening-recovery format proposed by Kocks and MeckingAn isotropic [33] was hardeningemployed systemin this study following. All theslip hardening-recoverysystems were assumed format to harden proposed at the by Kockssame rate, and Meckingresulting [in33 the] was following employed evolutio in thisn study.equation All of slip slipping systems system were assumedcritical shear to harden stress [ at34 the]: same rate, － resulting in the following evolution equation of slippingτs τc systemα critical shear stress [34]: τ̇ c = h0 ( ) ∑|γ̇ | (2) τs－ τ0 α .  τ − τ  . τ = s c |γα| τ c h0τ ∑ h (2) where 0 is the initial critical shear stress, s τthes − saturationτ0 α critical shear stress, and 0 stands for the initial hardening rate. whereInτ the0 is current the initial work, critical {110} shear <–111> stress, and 12τs {112}the saturation <11–1> slip critical families shear were stress, taken and intoh 0accountstands during for the initialCP-FEM hardening calculation. rate. Glide of on these slipping systems have been reported to govern mechanicalIn the current response work, and {110} accommodate <–111> and plastic 12 {112} deformation <11–1> slip families of BCC were metals taken at into room account temperatur duringe CP-FEM[35,36]. By calculation. fitting load Glide-stroke of dislocations curves derived on these from slipping numerical systems calculations have been to reported those attained to govern in mechanicalexperiments, response hardening and accommodate parameters can plastic be deformation determined,of as BCC listed metals in at Table room 2 temperature. Elastic constants[35,36].

Byc11,c fitting12,c44 were load-stroke taken fro curvesm [37 derived]. from numerical calculations to those attained in experiments, hardening parameters can be determined, as listed in Table2. Elastic constants c11, c12, c44 were taken from [37]. Table 2. Material constants and parameters in current CP-FEM model.

Category Parameter Meaning Value Table 2. Material constants and parameters in current CP-FEM model. Elastic c11,c12,c44 Elastic coefficient 229, 134, 115 (GPa) <110>Category systems m Parameter Strain rate sensitivity Meaning factor Value0.05 γ̇ Elastic c110 , c12, c44 ReferenceElastic shear coefficient rate 229, 134,0.01 115 (GPa) h <110> systems0 mInitial Strain hardening rate sensitivity rate factor150.5 0.05 (MPa) τ . 0 γ0 Initial criticalReference shear shear stress rate 40.0 0.01 (MPa) τs h0 SaturationInitial shear hardening stress rate 250.875 150.5 (MPa) (MPa) <112> systems m τ0 Strain Initialrate sensitivity critical shear factor stress 40.00.05 (MPa) τs Saturation shear stress 250.875 (MPa) γ̇ 0 Reference shear rate 0.01 <112> systems m Strain rate sensitivity factor 0.05 h0 . Initial hardening rate 67.5 (MPa) γ0 Reference shear rate 0.01 τ0 Initial critical shear stress 58 (MPa) h0 Initial hardening rate 67.5 (MPa) τs Saturation shear stress 250.0 (MPa) τ0 Initial critical shear stress 58 (MPa) τs Saturation shear stress 250.0 (MPa) Specimen dimensions in CP-FEM simulation were in accordance with the design shown in FigureSpecimen 1. The minor dimensions dimension in CP-FEM deviation simulation introduced were in during accordance specimen with thefabrication design shown was ignored in Figure in1. Thenumerical minor dimension study. Each deviation specimen introduced was divided during into specimen 12,606 fabricationnodes and was 9865 ignored C3D8R in numerical mesh elements study. Each(three specimen-dimensional was quadrilateral divided into mesh 12,606 with nodes one and reduced 9865 C3D8Rintegration mesh point). elements Five (three-dimensionallayers of elements quadrilateralwere used along mesh thickness with one direction. reduced integration Boundary point). conditions Five layersof the ofsimulation elements wereis illustrated used along in Fig thicknessure 3. direction.Uniaxial tensile Boundary deformation conditions was of theapplied simulation as displacement is illustrated boundary in Figure 3condition. Uniaxial on tensile the upper deformation half of wasthe top applied pin hole as displacement along y-axis boundary such that condition a constant on loading the upper speed half ofsame the as top experiment pin hole along wasy -axisobtained. such thatLower a constant half of the loading bottom speed pin same hole aswas experiment fully constrained was obtained. and other Lower part half of of the the specimen bottom pin was hole free was to fullydeform. constrained and other part of the specimen was free to deform.

Figure 3. Boundary condition of CP-FEM simulation model. Upper half of the top pin hole was coupled with a reference point subject to displacement along vertical direction. Lower half of the bottom pin hole was fully constraint through the coupling with another reference point.

Metals 2018, 8, x FOR PEER REVIEW 6 of 15

Figure 3. Boundary condition of CP-FEM simulation model. Upper half of the top pin hole was coupled with a reference point subject to displacement along vertical direction. Lower half of the Metals 2018, 8, x FOR PEER REVIEW 6 of 15 Metalsbottom2018, 8, 858pin hole was fully constraint through the coupling with another reference point. 6 of 15

Figure 3. Boundary condition of CP-FEM simulation model. Upper half of the top pin hole was 3. Results and Discussions coupled with a reference point subject to displacement along vertical direction. Lower half of the 3. Results and Discussions bottom pin hole was fully constraint through the coupling with another reference point. 3.1. Deformation Characteristics 3.1. Deformation Characteristics 3.To Results validate and Discussions CP-FEM simulation results, deformation characteristics including deformed specimenTo validate profile, CP-FEM load-stroke simulation curve results,and microstructure deformation characteristicsderived from observations including deformed and simulations specimen 3.1. Deformation Characteristics profile,were compared load-stroke in detail. curve and microstructure derived from observations and simulations were comparedExperimentallyTo in validate detail. CP measured-FEM simulation and nume results,rically deformation calculated characteristics specimen including profiles deformed after tensile deformationspecimenExperimentally have profile, been measuredload shown-stroke andin curve Figure numerically and 4 microstructure. For space calculated-saving derived specimen purpose, from profilesobservations only specimen after and tensile withsimulations deformation the largest were compared in detail. haveneck elongation, been shown i.e. in Figure, specimen4. For 3- space-saving1, has been presented. purpose, onlySimilarity specimen in general with the shape largest is obvious neck elongation, between Experimentally measured and numerically calculated specimen profiles after tensile i.e.,mea specimensured and 3-1, simulated has been results, presented. except Similarity for that shrinkage in general in shape neck iswidth obvious is a betweenlittle bit more measured severe and in deformation have been shown in Figure 4. For space-saving purpose, only specimen with the largest simulated results, except for that shrinkage in neck width is a little bit more severe in experiment. experiment.neck elongation, i.e., specimen 3-1, has been presented. Similarity in general shape is obvious between measured and simulated results, except for that shrinkage in neck width is a little bit more severe in experiment.

Figure 4. Specimen profileprofile of specimen 3-13-1 after deformation ( a) measured by SEM; and (b) derivedderived fromFigure CP-FEMCP-FEM 4. Specimen simulation profile (units(unit ofs specimen areare inin mm).mm). 3-1 after deformation (a) measured by SEM; and (b) derived from CP-FEM simulation (units are in mm). With aforementioned set of parameters,parameters, fittingfitting results on experimentallyexperimentally derived load-strokeload-stroke With aforementioned set of parameters, fitting results on experimentally derived load-stroke curves of of three three different different initial initial crystal crystal orientations orientations are presented are presented in Figure in5. AsFigure previously 5. As mentioned, previously curves of three different initial crystal orientations are presented in Figure 5. As previously formentioned, each of thefor threeeach differentof the three initial different orientations, initial orientations, two repetitions two of repetitions tensile tests of were tensile conducted tests were to evaluatementioned, the statistical for each scatterof the three in measured different load-strokeinitial orientations, curves. two As repetitions presented of in tensile Figure tests5, satisfying were conductedconducted to e tovaluate evaluate the the statistical statistical scatter scatter inin measuredmeasured load load-stroke-stroke curves curves. As. Aspresented presented in Figure in Figure reproducibility was found in separated experiments with same initial crystal orientation, confirming 5, satisfying5, satisfying reproducibility reproducibility was was found found in in separated separated experimentsexperiments with with same same initial initial crystal crystal orientation, orientation, the reliability of experimental results. confirmingconfirming the threliabilitye reliability of ofexperimental experimental results. results. GoodGoodGood fittings fittings fittings were were were observed observed observed on on orientation orientation orientation 1 and 1 and 2.2. For For 2. simulation simulation For simulation with with orientation orientation with orientation 3 in 3Figure in Figure 3 in Figure5c, yielding5c5, c,yielding yielding point point point in in simulated in simulated simulated load load load-stroke-stroke-stroke curve curve was was was lower lower lower than than than that thatthat in in experimental in experimental experimental data data.. data . Nevertheless,NeverthelessNevertheless, thethe, the hardening hardening tendencytendency tendency coincidedcoincide coincided withwith experiments experimentsexperiments as asas indicated indicatedindicated by bybya same aa same slope slope in in load-strokeloadload-stroke-stroke curves.curves. curves.

Figure 5. Measured and simulated load stroke curves of (a) initial orientation 1; (b) orientation 2; and (c) orientation 3. Crystal lattices before tensile loading were given with black lines highlighting <111> slipping directions. Loading direction was given with red arrow. Metals 2018, 8, x FOR PEER REVIEW 7 of 15

Figure 5. Measured and simulated load stroke curves of (a) initial orientation 1; (b) orientation 2; and

Metals(c2018) orientation, 8, 858 3. Crystal lattices before tensile loading were given with black lines highlighting <111>7 of 15 slipping directions. Loading direction was given with red arrow.

Deformed microstructure of specimen neck region was extracted and visualized with inverse pole figuresfigures (IPF) using the open open-source-source MATLAB toolbox MTEX 5.1.1 [3838]. The comparison between EBSD observed microstructures and numerically simulated ones after tensile deformation is given in Figure6 6.. To To save save space, space, only only the the results results of specimens of specimens with with larger larger neck elongation neck elongation in each in initial each crystal initial crystalorientation orientation are presented. are presented. As shown As in shown Figure in6, goodFigure agreement 6, good agreement between measured between and measured simulated and simulatedtexture can texture be found can for be all found three for initial all three crystal initial orientations. crystal orientations. The capability The of capability current CP-FEM of current setting CP- FEMin characterizing setting in characterizing texture evolution texture during evolution tensile during deforming tensile can deforming be confirmed. can be confirmed.

Figure 6. ComparisonComparison between between EBSD EBSD observed observed microstructures microstructures in in the the specimen neck region and numerically calculated calculated results results after after tensile tensile deformation. deformation. Only the Only specimens the specimens with larger with neck larger elongation neck elongationin each initial in each orientation initial orientation were presented were to presented save space. to save space.

ThusThus,, it can be concluded that CP-FEMCP-FEM simulations were reliable in reproducing deformation characteristics of single crystal iron specimen with distinct initial crystalcrystal orientations.orientations. 3.2. Deformation Heterogeneity 3.2. Deformation Heterogeneity Plastic deformation rarely happens in a homogeneous manner in microscale. Especially for a single Plastic deformation rarely happens in a homogeneous manner in microscale. Especially for a crystal specimen in which the activation of slipping systems is largely determined by its initial crystal single crystal specimen in which the activation of slipping systems is largely determined by its initial orientation, deformation heterogeneity is commonly presented in forms like deformation and transition crystal orientation, deformation heterogeneity is commonly presented in forms like deformation and bands. These band regions contain a larger quantity of dislocations, as well as larger variations in transition bands. These band regions contain a larger quantity of dislocations, as well as larger crystalline orientation and higher local deformation energy. Nucleation, especially nucleation by the variations in crystalline orientation and higher local deformation energy. Nucleation, especially migration of low angle boundaries which are formed by a collection of dislocations, tends to locate in nucleation by the migration of low angle boundaries which are formed by a collection of dislocations, these heterogeneities since concentration of lattice defects provides potential nucleation sites for the tends to locate in these heterogeneities since concentration of lattice defects provides potential following generation of high angle grain boundaries separating this area with surrounding [39]. nucleation sites for the following generation of high angle grain boundaries separating this area with Kernel average misorientation mapping gives a representation of pointwise heterogeneity inside surrounding [39]. selected kernel by calculating and averaging the misorientations between the center point of the Kernel average misorientation mapping gives a representation of pointwise heterogeneity inside kernel and all neighboring points in the kernel. In this study, only the points at the perimeter of the selected kernel by calculating and averaging the misorientations between the center point of the kernel were used for the calculation of KAM value. For EBSD observations, kernel size was selected kernel and all neighboring points in the kernel. In this study, only the points at the perimeter of the so that only first order neighbors of selected points were included, as demonstrated in Figure7a. kernel were used for the calculation of KAM value. For EBSD observations, kernel size was selected For numerical calculated results, the surface layer of elements were extracted and first order neighbors so that only first order neighbors of selected points were included, as demonstrated in Figure 7a. For were decided based on connectivity of mesh elements, as depicted in Figure7b. Then KAM values numerical calculated results, the surface layer of elements were extracted and first order neighbors were calculated based on the local variation in misorientation as: were decided based on connectivity of mesh elements, as depicted in Figure 7b. Then KAM values were calculated based on the local variation in misorientation1 as: θ = ∆θ (3) KAM N ∑ i i Metals 2018, 8, x FOR PEER REVIEW 8 of 15

1 Metals 2018, 8, 858 1 8 of 15 θKAM = ∑ ∆θ푖 (3) KAM 푁 푖 (3) 푖 where N is the number of neighboring points inside the kernel, ∆θ is the misorientation between wherewhere NN isis thethe numbernumber ofof neighboringneighboring pointspoints insideinside the kernel,kernel, ∆∆θi푖 isis thethe misorientationmisorientation betweenbetween selectedselected pointpoint andand thethe ii-th-th neighbor.neighbor.

FigureFigure 7.7. PrinciplePrinciple ofof KAMKAM calculationcalculation performed on (aa)) EBSDEBSD data;data; ((bb)) simulationsimulation results;results; PP standsstands forfor thethe selectedselected point.point. RedRed blocksblocks indicateindicate firstfirst orderorder neighborsneighbors ofof thethe selectedselected point.point.

KAMKAM maps measured with EBSD on specimens after tensile deformation are shown in Figure 88.. InIn thisthis work as well other research works on plastic heterogeneity (e.g.,(e.g., [[4040,,4411]),]), KAMKAM mapsmaps areare usedused toto show show the the heterogeneity heterogeneity in indeformation deformation and and stored stored energy energy on observed on observed surface surface as high as KAM high regions KAM indicateregions highlyindicate distorted highly distorted regions. By regions. comparing By comparing between groups between (a–b), gro (c–d),ups (a and–b), (e–f), (c–d) deformation, and (e–f), heterogeneitydeformation heterogeneity patterns were patterns found towere be found dependent to be ondependent initial crystal on initial orientation crystal orientation of the specimen. of the Forspecimen. specimens For specimens with the same with initial the same texture, initial the texture, same heterogeneity the same heterogeneity pattern persisted pattern when persisted specimens when werespecimens deformed were to deformed different degrees.to different However, degrees. as Howev applieder, plastic as applied deformation plastic deformation grew larger, deformationgrew larger, heterogeneitydeformation heterogeneity patterns were patterns strengthened were strengthened for the storage for the of morestorage deformation of more deformation energy, as energy, can be concludedas can be concluded by comparing by comparing Figure8a,b, Figure as well 8a as,b, Figureas well8 c,d.as Figure 8c,d.

Figure 8. Kernel average misorientation maps derived from EBSD after tensile deformation of (a) spe. Figure 8. Kernel average misorientation maps derived from EBSD after tensile deformation of (a) spe. 1-1; (b) spe. 1-2; (c) spe. 2-1; (d) spe. 2-2; (e) spe. 3-1; and (f) spe. 3-2. Dashed lines were used to 1-1; (b) spe. 1-2; (c) spe. 2-1; (d) spe. 2-2; (e) spe. 3-1; and (f) spe. 3-2. Dashed lines were used to separate separate specimens with different initial orientations. specimens with different initial orientations. With the principle shown in Figure7b, KAM values can be calculated from CP-FEM results in a With the principle shown in Figure 7b, KAM values can be calculated from CP-FEM results in a comparableWith the definition principle to shown EBSD measurements.in Figure 7b, KAM Contour values plots can of be derived calculated KAM from values CP are-FEM demonstrated results in a comparable definition to EBSD measurements. Contour plots of derived KAM values are incomparable Figure9. Similar definition to the to results EBSD derived measurements. from EBSD Contour data, deformation plots of heterogeneity derived KAM patterns values were are demonstrated in Figure 9. Similar to the results derived from EBSD data, deformation heterogeneity dependentdemonstrated of initialin Figure crystal 9. Similar orientations. to the results The same derived pattern from persists EBSD fordata, specimens deformation of the heterogeneity same initial patterns were dependent of initial crystal orientations. The same pattern persists for specimens of the crystalpatterns orientation were dependent but undergone of initial differentcrystal orientations. degrees of plasticThe same deformation. pattern persists for specimens of the same initial crystal orientation but undergone different degrees of plastic deformation.

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Figure 9. Kernel average misorientation maps derived from CP-FEM simulation after tensile Figure 9. Kernel average misorientation maps derived from CP-FEM simulation after tensile deformation of (a) spe. 1-1; (b) spe. 1-2; (c) spe. 2-1; (d) spe. 2-2; (e) spe. 3-1; and (f) spe. 3-2. deformation of (a) spe. 1-1; (b) spe. 1-2; (c) spe. 2-1; (d) spe. 2-2; (e) spe. 3-1; and (f) spe. 3-2. Dashed Dashed lines were used to separate specimens with different initial orientations. lines were used to separate specimens with different initial orientations. By comparing KAM maps derived from EBSD scans (Figure8) and CP-FEM simulations (Figure9), it canBy be comparing seen that theKAM results maps derived derived fromfrom CP-FEMEBSD scans would (Figure capture 8) and more CP-FEM macroscopic simulations features (Figure of plastic9), it can deformation. be seen thatAround the results specimen derived edges, from highCP-FEM KAM would value capture regions more were macroscopic observed both features in EBSD of dataplastic and deformation. simulations; Around contour specimen lines in edges, Figure 9high have KAM shown value similar regions shapes were with observed their counterpartsboth in EBSD indata Figure and 8simulations;—horizontal contour lines were lines bothin Figure found 9 have in Figures shown8a similar and9a, shapes contour with lines their forming counterparts similar in inclinedFigure 8— rectangularhorizontal shapes lines were can be both seen found in Figures in Figure8c–fs and8a 9andc–f. 9 Ina, thecontour central lines area forming of specimen similar inclined rectangular shapes can be seen in Figures 8c–f and 9c–f. In the central area of specimen neck, neck, low KAM areas indicated by large region colored in blue were found in numerical calculations, whilelow KAM miniature areas indicated deformation by large heterogeneity region colored formed in blue clear were slipping found bands in numerical under EBSD calculations observations., while miniature deformation heterogeneity formed clear slipping bands under EBSD observations. Additionally, in areas where local variation in misorientation is large, simulated KAM values are generallyAdditionally larger, in thanareas the where ones l derivedocal variation from experiments in misorientation since clearly is large, more simulated of regions KAM colored values in redare generally larger than the ones derived from experiments since clearly more of regions colored in red can be identified from Figure9. can be identified from Figure 9. The reasons accounting for these differences may be that simulated deformation heterogeneity The reasons accounting for these differences may be that simulated deformation heterogeneity differs from experimental observations in mainly two aspects: firstly, due to resolution difference(in differs from experimental observations in mainly two aspects: firstly, due to resolution difference(in current study, each EBSD scan contains over 200,000 data points while CP-FEM calculations were current study, each EBSD scan contains over 200,000 data points while CP-FEM calculations were conducted on less than 10,000 elements), local distortions cannot be fully expressed in simulations; conducted on less than 10,000 elements), local distortions cannot be fully expressed in simulations; Secondly, the convergence of FEM simulation results is built on continuum theory in which large local Secondly, the convergence of FEM simulation results is built on continuum theory in which large distortion which can cause the divergence of to-be-solved partial differential equations is not allowed. local distortion which can cause the divergence of to-be-solved partial differential equations is not Therefore, significant local fluctuations in lattice rotation and large relative nodal displacement were allowed. Therefore, significant local fluctuations in lattice rotation and large relative nodal eliminated, leading to a more averaged and macroscopic result in CP-FEM simulations; Moreover, displacement were eliminated, leading to a more averaged and macroscopic result in CP-FEM the rudimentary model employed in current work may be incapable of capturing the immediate simulations; Moreover, the rudimentary model employed in current work may be incapable of partitioning of a discrete structure evolving inside the material bulk. More sophisticated crystal capturing the immediate partitioning of a discrete structure evolving inside the material bulk. More plasticity models taking account of intrinsic features of BCC plasticity such as non-Schmidt effects sophisticated crystal plasticity models taking account of intrinsic features of BCC plasticity such as and dislocation climbing [42] as well as models which are able to characterize interaction between non-Schmidt effects and dislocation climbing [42] as well as models which are able to characterize dislocations with arbitrary grid resolution [43] may be helpful in reproducing such microscale interaction between dislocations with arbitrary grid resolution [43] may be helpful in reproducing deformation heterogeneity. such microscale deformation heterogeneity. 3.3. Nucleation Sites—Observation and Prediction 3.3. Nucleation Sites—Observation and Prediction Full recrystallization process was recorded with in-situ EBSD system. Microstructure evolutions of specimenFull recrystallization 1-2, 2-2, 3-1 andprocess 3-2 duringwas recorded annealing with at in 600-situ◦ CEBSD till 1 system h are presented. Microstructure in Figures evolutions 10–13. Asof specimen for specimen 1-2, 1-12-2, and3-1 and 2-1, the3-2 during applied annealing deformation at 600 seemed °C till not 1 h enough are presented to trigger in Figure textures evolution10–13. As andfor specimen no newly 1 formed-1 and grain2-1, th wase applied found deformation even after heated seemed for not 1 h. enough to trigger texture evolution and noTwo newly different formed types grain of was nucleation found even can beafter observed heated infor the 1 h. presented texture evolution records: at theTwo early different stage of types annealing, of nucleation new grains can be emerged observed from in the presented edge regions texture where evolution large deformation records: at heterogeneitythe early stage wasof annealin characterizedg, new bygrains high emerged KAM value, from asthe canedge be regions seen in where Figure large 10b, deformation Figure 11b, Figureheterogeneity 12b, and was Figure characterized 13b. According by high KAM to Cahn-Cottrellvalue, as can be model, seen in the Figure formations 10b, 11 ofb, 1 these2b, and grains 13b. mayAccording consist to ofCahn two-Cottrell steps—first model, sub-grain the formation boundaries of these took grains shape may by consist polygonization of two step ofs— condensedfirst sub- grain boundaries took shape by polygonization of condensed dislocations and then embryos expanded in area at the cost of absorbing and rearranging neighboring microstructural defects [44–

MetalsMetals 20182018,, 88,, x 858 FOR PEER REVIEW 1010 of of 15 15 Metals 2018, 8, x FOR PEER REVIEW 10 of 15 4Metals6]; the 2018 second, 8, x FOR type PEER of REVIEW nucleation started from already-formed high angle grain boundaries, as10 ofcan 15 dislocations and then embryos expanded in area at the cost of absorbing and rearranging neighboring 4be6]; noticed the second in Figure type sof 1 0nucleationc,d and 11 startedc,d and from other already recorded-formed microstructure high angle after grain annealing boundaries, for longeras can 4microstructural6]; the second type defects of nucleation [44–46]; the started second from type already of nucleation-formed started high fromangle already-formed grain boundaries, high as angle can bethan noticed 15 min. in Figure As beens 1 0 suggestedc,d and 1 1 byc,d Beck,and other the mechanismrecorded microstructure of such nucleation after annealing may be duefor longer to the begrain noticed boundaries, in Figure ass can 10c be,d noticedand 11c in,dFigure and other 10c,d recorded and Figure microstructure 11c,d and other after recorded annealing microstructure for longer thanmigration 15 min. of pre As- existin been suggestedg high angle by grain Beck, boundaries the mechanism toward of more such nucleationhighly-deformed may be area dues [ 47 to ,4 the8]. thanafter annealing15 min. As for been longer suggested than 15 min. by Beck, As been the suggested mechanism by of Beck, such the nucleation mechanism may of such be due nucleation to the migrationThe later mechanism of pre-existin is gcommonly high angle accompanied grain boundaries by high toward angle more grain highly boundary-deformed serration area ands [47 is,4 not8]. migrationmay be due of to pre the-existin migrationg high of pre-existingangle grain highboundaries angle grain toward boundaries more highly toward-deformed more highly-deformed areas [47,48]. Theonly later related mechanism to local deformation is commonly heterogeneity accompanied but by also high grain angle boundary curvature serration [49]. In thisand paper,is not Theareas later [47, 48mechanism]. The later is mechanism commonly isaccompanied commonly accompanied by high angle by grain high angleboundary grain serration boundary and serration is not onlyfocus related will be to put local on deformation the first kind heterogeneity of nucleation but in alsowhich grain deformation boundary heterogeneitycurvature [49]. has In thisa decisive paper, onlyand isrelated not only to local related deformation to local deformationheterogeneity heterogeneity but also grain but boundary also grain curvature boundary [49]. curvature In this paper, [49]. focusimpact will on nucleationbe put on the site. first kind of nucleation in which deformation heterogeneity has a decisive impactfocusIn this will paper,on nucleationbe put focus on will thesite. befirst put kind on the of nucleation first kind of in nucleation which deformation in which deformation heterogeneity heterogeneity has a decisive has impacta decisive on nucleation impact on nucleationsite. site.

Figure 10. Microstructure evolution of specimen 1-2 at annealing time (a) 0 min; (b) 5 min; (c) 15 min; Figure 10. Microstructure evolution of specimen 1-2 at annealing time (a) 0 min; (b) 5 min; (c) 15 min; andFigure (d) 10.60 minMicrostructure. Grain boundaries evolution were of specimenhighlighted 1-2 with at annealing white lines. time (a) 0 min; (b) 5 min; (c) 15 min; andFigure (d) 1 600. Microstructuremin. Grain boundaries evolution were of specimen highlighted 1-2 with at annealing white lines. time (a) 0 min; (b) 5 min; (c) 15 min; andand ( (dd)) 60 60 min min.. Grain Grain boundaries boundaries were were highlighted with white lines.

Figure 11. Microstructure evolution of specimen 2-2 at annealing time (a) 0 min; (b) 5 min; (c) 30 min; Figure 11. Microstructure evolution of specimen 2-2 at annealing time (a) 0 min; (b) 5 min; (c) 30 min; Figureand (d) 1 601. Microstructuremin. Grain boundaries evolution were of specimen highlighted 2-2 with at annealing white lines. time (a) 0 min; (b) 5 min; (c) 30 min; andFigureand ( (dd) )1 60 601. Microstructuremin min.. Grain Grain boundaries boundaries evolution were were of specimen highlighted highlighted 2-2 with withat annealing white lines. time (a) 0 min; (b) 5 min; (c) 30 min; and (d) 60 min. Grain boundaries were highlighted with white lines.

Figure 12. Microstructure evolution of specimen 3-1 at annealing time (a) 0 min; (b) 12.83 min; ( c) Figure 12. Microstructure evolution of specimen 3-1 at annealing time (a) 0 min; (b) 12.83 min; (c) 15 15 min; and (d) 60 min. Grain boundaries were highlighted with white lines. Figuremin; and 12 .( dMicrostructure) 60 min. Grain evolution boundaries of specimenwere highlighted 3-1 at annealing with white time lines. (a) 0 min; (b) 12.83 min; (c) 15 min;Figure and 12 (. dMicrostructure) 60 min. Grain evolution boundaries of werespecimen highlighted 3-1 at annealing with white time lines. (a) 0 min; (b) 12.83 min; (c) 15 min; and (d) 60 min. Grain boundaries were highlighted with white lines.

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Figure 13. Microstructure evolution of specimen 3-2 at annealing time (a) 0 min; (b) 10 min; (c) 20 min; FigureFigure 1 13.3. MicrostructureMicrostructure evolution evolution of of specimen specimen 3 3-2-2 at at annealing annealing time time ( (aa)) 0 0 min min;; ( (bb)) 10 10 min; min; ( (cc)) 20 20 min; min; and (d) 60 min. Grain boundaries were highlighted with white lines. andand ( (dd)) 60 60 min min.. Grain Grain boundaries boundaries were were highlighted highlighted with with white white lines. lines. In Figure 14, inverse pole mappings of specimens at the time point when newly-formed grains InIn Figure Figure 1 144, ,inverse inverse pole pole mappings mappings of of specimens specimens at at the the time time point point when when newly newly--formedformed grains grains were first observed were given and nucleation sites were pointed out with yellow circles. For specimen werewere first first observed observed were were given given and and nucleation nucleation sites sites were were pointed pointed out out with with yellowyellow circles. circles. For For 1-1, and 2-1, since no recrystallization was observed, no circle was plotted on the corresponding figures. specimenspecimen 1 1--1,1, and and 2 2--1,1, since since no no recrystallization recrystallization was was observed, observed, no no circle circle was was plotted plotted on on the the As previously mentioned, most newly formed grains at early stage of static recrystallization originated correspondingcorresponding figures. figures. As As previously previously mentioned, mentioned, most most newly newly formed formed grains grains at at early early stage stage of of static static from specimen edges in this study. recrystallizationrecrystallization originated originated from from specimen specimen ed edgesges in in this this study. study.

FigureFigure 14.14. EBSDEBSD measured measured inverse inverse pole pole mapping mapping of of (a ()a 1)- 1-11 annealed annealed for for 60 60min min;; (b) ( b1-)2 1-2annealed annealed for Figure 14. EBSD measured inverse pole mapping of (a) 1-1 annealed for 60 min; (b) 1-2 annealed for for5 min 5 min;; (c) 2 (-c1) annealed 2-1 annealed for 60 for min 60; min; (d) 2 (-d2 )annealed 2-2 annealed for 30 for min 30; min;(e) 3-1 (e annealed) 3-1 annealed for 15 formin 15; and min; (f) and 3-2 5( fmin) 3-2; ( annealedc) 2-1 annealed for 10 for min. 60 Grainmin; (d boundaries) 2-2 annealed were for labeled 30 min with; (e) 3 -1 annealed black lines. for 15 These min; and mappings (f) 3-2 annealed for 10 min. Grain boundaries were labeled with solid black lines. These mappings have annealedhave indicated for 10 approximatemin. Grain boundaries locations of were nucleation labeled sites. with Yellow solid black circles lines. pointed These out mappings nucleation have sites indicated approximate locations of nucleation sites. Yellow circles pointed out nucleation sites at the indicatedat the first approximate stage of recrystallization. locations of nucleation Dashed sites. lines Yellow were used circles to separatepointed out specimens nucleation with sites different at the first stage of recrystallization. Dashed lines were used to separate specimens with different initial firstinitial stage orientations. of recrystallization. Dashed lines were used to separate specimens with different initial orientations. orientations. The same nucleation sites were labeled on top 20% KAM value regions of all specimens as The same nucleation sites were labeled on top 20% KAM value regions of all specimens as demonstratedThe same in nucleation Figure 15 . sites As can were be labeled noticed, on although top 20% nuclei KAM did value appear regions from highof all KAM specimens locations as demonstrated in Figure 15. As can be noticed, although nuclei did appear from high KAM locations demonstrated(among top 20% in Figure on observed 15. As surface),can be noticed, it was although impossible nuclei to determine did appear exact from locations high KAM merely locations from (among top 20% on observed surface), it was impossible to determine exact locations merely from (amongKAM values. top 20% Especially on observed in Figure surface), 15d–f, it despitewas impossible high KAM to concentrationdetermine exact in thelocations central merely of specimen from KAM values. Especially in Figure 15d–f, despite high KAM concentration in the central of specimen KAMneck, values. first grains Especially emerged in Figure from the 15d edges.–f, despite The mainhigh KAM reason concentration might be that in KAM the central map, of in specimen its nature, neck, first grains emerged from the edges. The main reason might be that KAM map, in its nature, neck,would first be largelygrains emerged influenced from by localthe edges. deformation The main features, reason suchmight as be stress that concentration KAM map, in due its nature, to local would be largely influenced by local deformation features, such as stress concentration due to local wouldzig-zags be around largely specimen influenced edge, by local surface deformation unevenness features, and impurity such as contained stress concentration in specimens. due These to local local zig-zags around specimen edge, surface unevenness and impurity contained in specimens. These zigfeatures-zags addedaround “noise” specimen into edge, KAM surface mapping unevenness and impeded and theimpurity expression contained of mesoscale in specimens. distribution These of local features added “noise” into KAM mapping and impeded the expression of mesoscale localdeformation features heterogeneity. added “noise” As a into result, KAM it is challenging mapping and to make impeded precise the predictions expression of nucleation of mesoscale sites distribution of deformation heterogeneity. As a result, it is challenging to make precise predictions distributionwith EBSD observedof deformation deformation heterogeneity. heterogeneity As a result, alone. it is challenging to make precise predictions ofof nucleation nucleation sites sites with with EBSD EBSD observed observed deformation deformation heterogeneity heterogeneity alone. alone.

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Figure 15.15. KAM mapsmaps showingshowing locations locations with with top top 20% 20% KAM KAM values values for for specimen specimen (a) ( 1-1;a) 1 (-b1); 1-2;(b) 1 (-c2); 2-1; (c) (d) 2-2; (e) 3-1; and (f) 3-2 before annealing. Yellow circles pointed out nucleation sites same as those in 2-1; (d) 2-2; (e) 3-1; and (f) 3-2 before annealing. Yellow circles pointed out nucleation sites same as the previous figure. Dashed lines were used to separate specimens with different initial orientations. those in the previous figure. Dashed lines were used to separate specimens with different initial Byorientations. comparing approximate nucleation sites depicted in Figure 15 and high KAM regions in numerical calculation, qualitative coincidence can be found, indicating a potential correlation between By comparing approximate nucleation sites depicted in Figure 15 and high KAM regions in nucleation and mesoscale distortion in calculation. This substantiates the use of microstructure numerical calculation, qualitative coincidence can be found, indicating a potential correlation simulation algorithms such as cellular automaton, phase field method and Monte Carol model on between nucleation and mesoscale distortion in calculation. This substantiates the use of energy/distortion distribution derived from CP-FEM for nucleation prediction. Yet direct quantitative microstructure simulation algorithms such as cellular automaton, phase field method and Monte comparison between concentration of dislocations in CP-FEM and observed nucleation sites is Carol model on energy/distortion distribution derived from CP-FEM for nucleation prediction. Yet difficult due to the following obstacles: firstly, with two-dimensional microstructure characterization direct quantitative comparison between concentration of dislocations in CP-FEM and observed methods, it is challenging to capture the true nucleation sites as nuclei may actually occur beneath the nucleation sites is difficult due to the following obstacles: firstly, with two-dimensional observed plane and emerge into the observed scope during growth; secondly, numerically calculated microstructure characterization methods, it is challenging to capture the true nucleation sites as specimens can hardly have exactly the same macroscopic deformation as derived in experiments. nuclei may actually occur beneath the observed plane and emerge into the observed scope during Thus, a perfect overlay of the mesh grid in simulation and the measured points would be of great growth; secondly, numerically calculated specimens can hardly have exactly the same macroscopic difficulty. Quantitative analysis like cross-correlation which is sensitive to such overlapping can hardly deformation as derived in experiments. Thus, a perfect overlay of the mesh grid in simulation and be performed. the measured points would be of great difficulty. Quantitative analysis like cross-correlation which 4.is sensitive Conclusions to such overlapping can hardly be performed.

4. ConclusionsIn the present study, CP-FEM combined with in situ EBSD observations were used to characterize deformation heterogeneity on tensile deformed single crystal pure iron specimens of three different initialIn crystal the present orientations. study, CP Texture-FEM evolution combined during with in annealing situ EBSD under observations 600 ◦C was were traced used and to approximatecharacterize deformation nucleation sites heterogeneit were comparedy on tensile with deformed high KAM single areas crystal derived pure from iron EBSD specimens data and of simulations.three different The initial following crystal conclusions orientations. can Texturebe drawn: evolution during annealing under 600 °C was traced and approximate nucleation sites were compared with high KAM areas derived from EBSD 1.data aReal-worldnd simulations scale. The CP-FEM following calculations conclusions on single can be crystal drawn: iron tensile test were compared with experimental observations in four aspects: macroscopic deformation of specimen, load-stroke 1. Real-world scale CP-FEM calculations on single crystal iron tensile test were compared with curve, deformed texture and kernel average misorientation maps. The capability of widely used experimental observations in four aspects: macroscopic deformation of specimen, load-stroke phenomenological model in reproducing experimentally observed deformation characteristics curve, deformed texture and kernel average misorientation maps. The capability of widely used was evaluated. phenomenological model in reproducing experimentally observed deformation characteristics 2. Comparison was made between deformation heterogeneities expressed by KAM derived was evaluated. from EBSD observations and numerical simulations. Around the edges, high deformation 2. Comparison was made between deformation heterogeneities expressed by KAM derived from heterogeneities were both found in experiments and simulations, while in the central of specimen EBSD observations and numerical simulations. Around the edges, high deformation neck, KAM maps contained more local deformation information than numerically calculated heterogeneities were both found in experiments and simulations, while in the central of results. Failure in capturing microscale deformation heterogeneity in simulations may be specimen neck, KAM maps contained more local deformation information than numerically attributed to relatively low grid resolution and incapability of employed constitutive equations calculated results. Failure in capturing microscale deformation heterogeneity in simulations may in accounting for evolving of discrete dislocation structures inside the material. be attributed to relatively low grid resolution and incapability of employed constitutive 3. Areas with large distortion concentration in simulation has a qualitative coincidence with equations in accounting for evolving of discrete dislocation structures inside the material. approximate nucleation sites in the first stage of recrystallization. This observation justifies 3. Areas with large distortion concentration in simulation has a qualitative coincidence with the direct application of microstructure simulation methods such as cellular automaton model on approximate nucleation sites in the first stage of recrystallization. This observation justifies the energy/distortion distribution derived from CP-FEM for nucleation prediction. direct application of microstructure simulation methods such as cellular automaton model on energy/distortion distribution derived from CP-FEM for nucleation prediction.

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4. Experimentally-derived KAM maps have shown similar level of heterogeneity in a large portion of specimen edges. Experimentally observed KAM map is sensitive to local miniature features like zig-zags along edge curvature, surface unevenness, and impurity in specimen.

Author Contributions: Z.L. performed the experiments and simulations, analyzed results and composed the manuscript; M.Y. supervised throughout experiments, reviewed, and edited the manuscript; M.T. contributed to the design of experiment, material preparation, and specimen fabrication; and A.Y. contributed to the CPFEM simulation techniques. Funding: This research was funded by AMADA Foundation, grant number AF-2016035. Conflicts of Interest: The authors declare no conflict of interest.

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