Materials Science & Engineering A

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1 Mterils Science & Engineering A 588 (2013) Contents lists vilble t ScienceDirect Mterils Science & Engineering A journl homepge: Slip trnsmission in bcc FeCr polycrystl Luc Ptrirc,n, Wel Abuzid b, Huseyin Sehitoglu b,1, Hns J. Mier c Politecnico di Milno, Deprtment of Mechnicl Engineering, Vi L Ms 34, I Milno, Itly b Deprtment of Mechnicl Science nd Engineering, University of Illinois t Urbn-Chmpign, 1206W. Green St., Urbn, IL 61801, USA c Institut für Werkstoffkunde, Leibniz Universität Hnnover, An der Universität 2, D Grbsen, Germny rticle info Article history: Received 27 Mrch 2013 Received in revised form 31 July 2013 Accepted 26 August 2013 Avilble online 2 September 2013 Keywords: Bcc polycrystl Slip trnsmission EBSD Digitl imge correltion bstrct Grin boundries induce heterogeneities in the deformtion response of polycrystls. Studying these locl vritions in response, mesured through high resolution strin mesurement techniques, is importnt nd cn improve our understnding of ftigue dmge initition in the vicinity of grin boundries nd mteril hrdening. In this work, strin fields cross grin boundries were mesured using dvnced digitl imge correltion techniques. In conjunction with strin mesurements, grin orienttions from electron bck-scttered diffrction were used to estblish the disloction rections t ech boundry, providing the corresponding residul Burgers vectors due to slip trnsmission cross the interfces. A close correltion ws found between the mgnitude of the residul Burgers vector nd the locl strin chnge cross the boundry. When the residul Burgers vector mgnitude (with respect to the lttice spcing) exceeds 1.0, the high strins on one side of the boundry re pired with low strins cross the boundry, indicting the difficulties for slip disloctions to penetrte the grin interfces. When the residul Burgers vector pproches zero, the strin fields vry smoothly cross the boundry due to limited resistnce to slip trnsmission. The results suggest tht the residul Burgers vector mgnitude, which reltes to the GB (Grin Boundry) resistnce to slip trnsmission, enbles quntittive nlysis of the ccumultion of strin t the microstructurl level nd the development of strin heterogeneities cross grin boundries. The results re presented for FeCr bcc lloy which exhibits single slip per grin mking the mesurements nd disloction rections rther strightforwrd. The work points to the need to incorporte detils of slip disloction grin boundry interction (slip trnsmission) in modeling reserch. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Understnding the interction between slip disloctions nd grin boundries (GBs) hs prmount importnce on the mechnicl response of metls [1,2]. Extensive reserch hs been reported during the lst decdes on the strengthening effect introduced by blockge of prtil or full slip disloctions t GBs. In prticulr, much interest hs been devoted to the specific slip disloction GB rections nd the resultingsliptrnsmissionprocesscrossthegb.inthisregrd,erly reserch focused on the detils of these rections t GBs utilized trnsmission electron microscopy (TEM) [3,4]. In prticulr Clrk et l. [3] nd Lee t l. [4] utilized in situ TEM imges nd chrcterized the possible outcomes of the disloction rections occurring t GB. Severl insights into the trnsmission of the incoming disloction, nd incorportion into the GB creting extrinsic (residul) disloctions were gined s result of these studies. n Corresponding uthor. Tel.: þ ; fx: þ E-mil ddress: luc.ptrirc@polimi.it (L. Ptrirc). 1 Tel.: þ ; fx: þ Further experimentl efforts re required to overcome the difficulties in correlting the results of these disloction rections with the ssocited strin fields cross the GBs (on the meso-scle). A mesure of the strengthening ssocited with GB is decided bsed on whether disloction strin fields undergo continuous vrition (full disloction trnsmission), or whether lrge strins ccumulte on one side of the GB (disloction blockge). The level of strin heterogeneity mesured cross the GBs represents mesure of the cpbility of GB to block or trnsmit disloctions. Therefore, focused study on the experimentl determintion of the loclized strin grdients cross GBs is importnt nd will provide considerble insight into disloction trnsmission nd GB contribution to hrdening. In this pper, with specil imge correltion techniques, we study the locl strin fields t the meso-length scles covering multiple grins in Fe Cr lloy. The strin mesurements re used to estblish the possible outcome of slip-gb interction nd cpture the importnce of the residul disloction medited plsticity. We extend the combintion of locl strin nd grin orienttion mesurements on fcc lloys [5,6] introduced in erly work to bcc metl where single slip system per grin is ctivted llowing cler exmintion of the strin fields /$ - see front mtter & 2013 Elsevier B.V. All rights reserved.

2 309 Fig. 1. Schemtic of the disloction grin boundry interction geometry. For both the incoming nd outgoing slip plnes re indicted the norml to the slip plnes (n 1 nd n 2 ) nd the Burgers vectors of the disloctions (b 1 nd b 2 ). ϑ indictes the ngle between the lines of intersection between the two slip plnes nd the GB plne. The Burgers vector of the residul disloction left t the GB is determined from the eqution b 1 ¼ b 2 þ b r. As emphsized bove, severl importnt studies exmining disloction GB interctions hve been undertken in the pst [7 10]. Recently, dvnced simultion tools lso provided further insight into energetics of the disloction glide ner grin boundries [11 13] nd corroborted the experimentl findings. On the other hnd, n experimentl quntifiction of the role of GBs on the locl strin fields, e.g. the strin grdients following specific slip GB interction, hs received less ttention. In this work, we combine microstructure chrcteriztion vi electron bck sctter diffrction (EBSD) nd high resolution strin mesurements from DIC [5,6,14,15]. By combining these two techniques, we im to shed further light into the locliztion of plstic strins due to disloction GB interctions. Before introducing the experimentl results, we provide brief overview of the slip GB geometry nd the interctions. A schemtic of GB is shown in Fig. 1. Grin 1 contins the incoming slip system, while Grin 2 contins the outgoing slip system. In this schemtic, the disloctions leve the GB in the second crystl (outgoing slip plne) s result of the disloction GB interction. Of prticulr importnce is the residul Burgers vector of the disloction left t the GB [16 18]. Bsed on the geometry of the incoming nd outgoing slip systems, different possible rections cn occur [2]: () trnsmission by cross-slip: the slip plnes intersect the GB plne on common line (ϑ ¼ 0 where ϑ is the intersecting ngle), b 1 nd b 2 re prllel to the intersection line, no residul disloction is left on the GB; (b) direct trnsmission: ϑ ¼ 0, in this cse b 1 nd b 2 re not prllel, prtil residul disloction is left on the GB; (c) indirect trnsmission: ϑ0, b 1 nd b 2 re not prllel, prtil residul disloction is left on the GB; (d) no trnsmission, the disloctions do not cross the GB nd remin in the GB. For these cses the residul Burgers vector mgnitude vries from zero for the cse () to higher vlues in cse (b) nd (c) [4], nd to mximum for (d). The residul Burgers vector mgnitude, j b rj, cn be evluted from b 1 ¼ b 2 þ b r )jb rj¼jb 1 b 2j ð1þ where b 1 (incoming) nd b 2 (outgoing) re determined on the sme coordinte bsis. We clculte j b rj using the slip directions of the incoming nd outgoing slip systems in order to chrcterize the verge slip disloction GB rection tht hd occurred t the GB. The estimted j b rj is then used to link the rection occurring t the tomistic scle with the strins induced by disloction slip on the mesoscopic scle. For the GBs nlyzed with smll residul Burgers vector mgnitude the strins re trnsmitted lmost unltered. For the cse of high residul Burgers vector mgnitudes, the slip ccumultes on one side of the interfce. A cler chrcteriztion of the strin ccumultion cross GBs is chieved s result of this experimentl study. In the present work the selected mteril is body-centered cubic Fe 47.8 t% Cr lloy. We confined the experiments to smll deformtions in compression with externl strins less thn 2%. We indexed the slip systems using grin orienttions determined by EBSD. The dvntge of choosing the FeCr lloy is tht predominntly single slip system ws observed per grin. This mkes the Burgers vector conservtion nlysis rther simple, nd voids complex interctions ssocited with multiple slip systems. Successively, we focus the nlysis on the strin grdients generted t the GBs. Our high resolution DIC pinpointed the locl strins with high sptil resolution. The fine speckles dopted in the experiments enbled to cpture imges from the opticl microscope with resolution up to 0.18 mm/pixel. The usge of the residul Burgers vector for predicting the level of strin heterogeneities t GB is not common yet, since these experimentl cpbilities hve only become vilble recently. The correltion between the strin grdients cross the GBs with the mgnitude of the residul Burgers vector provides n excellent tool to quntify the cpbility of strin trnsmission t GB. This result suggests tht the residul Burgers vector mgnitude cn be used to improve future modeling efforts for polycrystl mterils. 2. Mteril nd methods 2.1. Microstructure chrcteriztion A FeCr lloy with composition of 47.8 t% Cr ws sectioned into 4 mm 4 mm 10 mm compression smple by electrodischrge mchining (EDM). The mteril ws solution nneled t 900 1C for 1 h followed by wter quench. For EBSD, the surfce ws polished using SiC pper (from P800 up to P4000), nd finl surfce finish which is suitble for EBSD dt cquisition ws obtined using vibro-polishing with colloidl silic (0.05 μm).

3 310 Fig. 2. () Grin orienttions in the lod direction obtined vi EBSD for 2 mm 2 mm region on the smple's surfce. (b) Grin orienttions in the lod direction (see Fig. 2) re shown in the stereogrphic tringle long with the slip systems for bcc mterils displying the lrgest SFs. Tble 1 Euler ngles obtined from EBSD for ech grin in the selected re of the smple's surfce. Grin φ 1 [1] Φ [1] φ 2 [1] A2mm 2 mm region on the smple's surfce ws mrked using Vickers indenttion mrks (the procedure is discussed in [19], lso used in [5,6]). The underlying microstructure in the mrked region of interest ws chrcterized using EBSD. Fig. 2 shows the grin orienttions for the nlyzed region nd Tble 1 lists the mgnitudes of the Euler ngles in Bunge convention (φ 1, Φ, φ 2 ) for ech detected grin. A totl of nine grins were observed in the selected re, with n pproximtely men grin size of bout 1 mm. In Fig. 2b, the stereogrphic tringle long with the crystl orienttions of ech grin in the lod direction re reported. The stereogrphic tringle is subdivided into five regions [20] tht indicte the slip systems with the lrgest Schmid Fctors (SFs) for bcc mterils. In determining the slip system with the lrgest SFs in Fig. 2b, ll of the {112}, {011} nd {123} slip plnes were considered with 111 slip directions Experimentl set-up nd strin mesurements The experiment ws conducted t room temperture using servo hydrulic lod frme. The smple ws deformed in displcement control t men strin rte of s 1. We used the strin dt from in situ DIC [21 24] to construct the stress strin curve using DIC field verges. The imges were cptured using n IMI model IMB-202 FT CCD cmer ( pixels) with Nvitr opticl lens, providing resolution of 3.0 μm/pixel. The speckle pttern for DIC ws obtined using blck pint nd n Iwt Micron B irbrush. We cptured reference imge of the smple surfce t zero lod, nd deformed imges of the sme re every 2 s during loding. We lso used ex situ high resolution DIC for cquiring higher resolution strin mesurements. In tht cse, the reference nd

4 deformed imges were cquired out of the lod frme (see detils for this procedure in [19]) using n opticl microscope which enbles cpturing higher mgnifiction imges thn the in situ set-up (0.18 nd 0.87 μm/pixel for ex situ imges, s opposed to in situ imges which were obtined t 3.0 μm/pixel). A speckle pttern suitble for high resolution DIC ws pplied on the smple's surfce fter the initil EBSD scn. A set of 140 imges covering the nlyzed region ws cptured before the experiment (reference condition) nd fter loding the smple (deformed condition). The correltions were implemented on ech pir of imges (reference nd deformed) nd the results were successively stitched together. We overlid the grin mp (from EBSD) Fig. 3. Stress strin curve nd DIC strin mesurements for the compression smple. The strin fields re obtined using ex-situ DIC mesurements for two lod steps, Ai nd Bi. The two rectngles drwn in the inset imges (Ai nd Bi) mrk regions 1A B nd 2A B which show slip trnsmission through the GB nd slip ccumultion on one side of the GB, respectively. 311 with the strin fields (from DIC) using the Vickers indenttion mrks which re visible in the EBSD grin orienttion mp nd the opticl microscope imges. We note tht the reported strin fields using ex situ DIC refer to the residul plstic strins (un-loded smple). 3. Results 3.1. Stress strin curve nd DIC strin mesurements We provide the results of the stress strin curve nd the strin contours in this section. Fig. 3 shows the stress strin curve for the smple deformed in compression. The reported strins (x xis) were obtined using DIC field verges (in situ). The insets in Fig. 3 show strin contour plots of the xil strin εyy in the lod direction. The inset imges, mrked Ai nd Bi, represent the residul xil strin fields for the 2 mm 2 mm region obtined vi ex-situ DIC t two different levels of strin. Ech strin field is composition of 9 imges (resolution 0.87 μm/pixel) cptured outside the lod frme nd fter unloding from points A nd B on the stress strin curve. Strin heterogeneities develop s consequence of the locl grin orienttion. The contour plots lso show cler strin bnds tht re ssocited with slip system ctivtion, we then identified the observed slip systems using the grin orienttions from EBSD nd SF nlysis. The ctivted slip plnes were determined by observing the possible trces of ll the slip plnes on the well-known {112}, {110}, {123} plne fmilies for bcc mterils. The slip direction, which is required to define the slip system, ws determined using Schmid fctor nlysis for ech observed slip. The slip systems with lrgest Schmid fctors re successively selected compring the projected lines with the slip trces on the smple's surfce. Two regions re selected from the globl strin fields: 1A nd 2A fter lod step Ai, nd 1B nd 2B fter lod step Bi (Fig. 3). In Fig. 4 the sme regions re pired with the schemtic of the slip plne geometries. The GB plne is drwn using the GB trce from the EBSD mp ssuming tht the norml Fig. 4. Geometric nlysis of the slip systems for the selected grin boundries from Fig. 3. On the top slip trnsmission cse is described, the residul disloction left t the GB hs low j b r j o 1 nd slip is trnsmitted cross the GB leding to high strins on both sides of the grin boundry. For the second cse shown strins ccumulte preferentilly on one side of the GB nd the ssocited j b r j 41 is high indicting the difficulty for the slip to propgte through the grin boundry.

5 312 lies on the plne of the smple surfce. For the region mrked 1 A B (Fig. 4 nd b), the observed incoming slip system is ½111Šð231Þ, while the outgoing slip system is ½111Šð321Þ. In tht cse, the residul Burgers vector mgnitude is low j b rjo1: 2 ½111Š Grin2-2 ½111Š Grin4 þ b r )jb rj¼ 0:38 The strin fields 1 A nd 1 B clerly show n ccumultion of strins on both sides of the GB which cn be ssocited with slip trnsmission cross the interfce. For the second cse, 2 A B (Fig. 4c nd d), we selected GB for which the rection occurring between the incoming nd the outgoing slip systems leds to high residul Burgers vector mgnitude j b rj41: 2 ½111Š Grin2-2 ½111Š Grin7 þ b r )jb rj ¼ 1:28 The incoming slip system is ½111Šð231Þ, while the outgoing slip system is ½111Šð211Þ. In this cse the strins preferentilly ccumulte on one side of the GB, indicting the difficulty for the incoming disloctions to be trnsmitted through the GB. The ccumultion of strins on the GB side of the incoming slip system is observed for both the loding steps (Fig. 4c nd d). More detils on the slip GB interction for the cses nlyzed in Eqs. (2) nd (3) re given in Fig. 5. All the ctive slip systems hve high SF vlues close to 0.5. The ngle ϑ nd the residul Burgers vector mgnitude j b rj re higher for the second cse (j b rj¼1:28, ϑ ¼ 48:51) compred to the first cse (ϑ ¼ 17:61 nd j b rj¼0:38) which showed esy slip trnsmission nd strin ccumultion cross both sides of the GB High resolution DIC strin mesurements In this section we provide ex situ strin fields obtined cpturing ex situ imges t higher resolutions thn reported in the previous section. Higher imge resolutions re required in ð2þ ð3þ order to index ll the slip systems ctivted in the selected EBSD region (Fig. 2) nd thus clculte the disloction rections. Fig. 6 displys the strin field obtined using imges t high resolution (0.18 μm/pixel). A totl of 140 imges were cptured before the experiment. As described in the previous section, fter loding the smple (point A i in Fig. 3), slip systems were indexed using grin orienttions from EBSD. In Tble 2 the slip systems for ech grin long with the SFs re reported. For grins 2, 3, 4, 5, 7 nd 8 only single slip system is observed, while for grins 1 nd 6 trces of secondry slip systems re visulized. In the schemtic of Fig. 6b the j b rj vlues for ech GB re lso reported. We then mrked the GBs on the DIC strin field with T in cse of slip trnsmission visulized s strin continuity long the slip trces, while B indictes the GBs for which no strin continuity is observed. For GBs 1 2, 2 4, 2 6, 7 8, 7 6 it is evident how the strins induced by slip continued lmost unltered through the interfces, while for GBs 2 3, 3 4, 4 5, 5 6, 2 7, 2 8, 6 4 the strins ccumulte on one side of the GB. Strin ccumultion is prticulrly evident for GBs 4 5 nd 2 7. Ech GB cn be lso chrcterized by the estimtion of the j b rj mgnitude due to slip trnsmission (see schemtic in Fig. 6b). Tble 3 gives summry of the observed outcomes due to slip GB interction in the vicinity of GBs (T: slip trnsmission, B: slip ccumultion) nd the correltion with the j b rj mgnitudes nd the misorienttion ngles. From Tble 3 it is cler tht low j b rj is ssocited with the slip trnsmission cses (geometriclly smooth strin pthwys), while slip ccumultion is observed for the rections resulting in high j b rj mgnitudes (high strins on one side of the grin boundry). From Tble 3 it is lso evident tht considering only the misorienttion ngle is not sufficient to explin the observed slip trnsmission nd ccumultion cses Strin mesurements cross grin boundries In order to quntify the mgnitude of the strin chnge cross the GB sides, we provide two sets of strin mesurements for low nd high j b rj mgnitudes. The inset imge () in Fig. 7 shows the strin contour plot for specific region consisting of grins 1 nd 2 (see lso Fig. 6). In this cse cler strin continuity ssocited with the incoming slip system ½111Šð123Þ nd outgoing slip system ½111Šð231Þ is observed cross the GB, nd the residul Burgers vector mgnitude is low (j b rjo1): 2 ½111Š Grin1-2 ½111Š Grin2 þ b r )jb rj ¼ 0:16 ð4þ Fig. 5. SFs for the incoming nd outgoing slip systems, j b rj mgnitudes nd ngle ϑ for the slip GB interction cses shown in Figs. 3 nd 4. For both the nlyzed cses the SF vlues of the ctivted slip plnes re close to the mximum resolved sher stress plne. In cse of slip trnsmission (Fig. 4 nd b) both the residul Burgers vector mgnitude j b rj¼0:38 nd the ngle ϑ ¼ 17:61 re low compred to the blockge cse (j b rj¼1:28, ϑ ¼ 48:51, Fig. 4c nd d). In Fig. 7b we lso report the strin mesurements clculted cross the grin boundry reported in Fig. 7 nd chrcterized by the disloction rection in Eq. (4). Fig. 7b reports the verged strins pproching the grin boundry sides. The difference of the strins mesured cross the GB provides direct quntifiction of the slip ccumulted on one side of the grin boundry. Ech point on the strin plot in Fig. 7b is clculted verging selection of strin vlues cptured from the DIC strin field (Fig. 7). The selected strin vlues re contined in rectngulr selection oriented long the GB side with n pproximte size of 40 μm 400 μm. The coordinte x is the distnce between the center of the rectngulr selection nd the GB. For the grin boundry between grins 1 nd 2 (Fig. 5) the disloction rection (Eq. (4)) indictes low residul Burgers vector mgnitude j b rj¼0:16, nd the difference of the strin mgnitudes pproching the GB is equl to jδε GB1 2 j¼0:09%. The grin boundry between grins 2 nd 6 is nlyzed in Fig. 8 (see lso Fig. 6). Strin bnds ssocited with the incoming slip system ½111Šð231Þ nd the outgoing slip system ½111Šð123Þ re still observed to propgte continuously cross the GB. The DIC strin

6 313 Fig. 6. () High resolution ex situ DIC strin field mesurements. A totl number of 140 reference imges nd 140 deformed imges were cptured outside the lod frme (ex-situ), correlted nd successively stitched. Slip systems were indexed using crystl orienttions from EBSD selecting the systems with slip trces displying the lrgest SFs. (b) Schemtic displying grin numbers nd residul Burgers vector mgnitudes. Depending on the mgnitude of the residul Burgers vector, disloctions gliding on the ctive slip system in one grin cn be trnsmitted through the GB or cn ccumulte t the GB. Different strin fields in the proximity of the GBs result from different disloction grin boundry interctions. Strins re trnsmitted in cse of low j b r j o 1, leding to high strin vlues mesured t both sides of the GBs. In cse of slip ccumultion (high j b r j4 1), high locl strins cn be observed on one side of the GB (see for exmple GB 2 7). Tble 2 Activted slip systems nd SFs. Grin 1 Slip ½111 ð011þ 0.46 ½111 ð123þ ½111 ð231þ 0.48 ½111 ð110þ 0.49 ½111 ð321þ 0.47 ½111 ð121þ ½111 ð211þ 0.42 ½111 ð123þ ½111 ð211þ 0.49 ½111 ð211þ 0.49

7 314 Tble 3 Comprison between the observtions on the DIC strin field on the slip mechnism (T: slip trnsmission, B: slip ccumultion) with the residul Burgers vector mgnitude j b rj nd misorienttion ngle [1]. GB Slip mechnism T B B T B B T B B T T B j b rj (divided by ) Misorienttion ngle [1] Fig. 7. Strin mesurements cross grin boundry in cse of low j b rj¼0:16. For this cse slip trnsmits lmost unltered through the GB (). The strins mesured cross the interfce (b) disply the smll strin chnge cross the grin boundry. Fig. 8. Strin mesurements cross grin boundry in cse of low j b rj¼0:28. For this cse smll step on the strin field (b) is observed which represents preferentil slip ccumultion on the left side of the GB (). The residul Burgers vector mgnitude clculted is slightly higher thn in the previous cse shown in Fig. 7. field displys lso intermedite mgnitudes of strin bnds (green color) between the incoming slip bnds on the left side of the GB. These dditionl strin bnds developing in proximity of the GB cn be ssocited with the prtil disloctions left in the GB hving residul Burgers vector mgnitude of 2 ½111Š Grin2-2 ½111Š Grin6 þ b r )jb rj ¼ 0:28 In the ssocited strin plot (Fig. 8b) the verged strin vlues increse pproching the left side of the GB. For this grin ð5þ boundry (j b rj¼0:28, Eq. (5)) the difference in the strin mgnitudes pproching the GB is higher thn the previous cse (j b rj¼0:16, Eq. (4)) nd equl to jδε GB2 6 j¼0:22%. The higher strin chnge mesured in this cse is pired with higher residul Burgers vector mgnitude. In Figs. 9 nd 10 two cses of grin boundries displying high j b rj41 mgnitudes re shown. The first cse refers to the strin mesurements cross grins 4 nd 5 (see lso Fig. 6). The incoming disloctions glide on the ½111Šð121Þ slip system, while the outgoing disloctions glide on the ½111Šð321Þ slip system. In this cse, the slip trnsmission process is chrcterized by disloction

8 315 Fig. 9. Strin mesurements cross grin boundry in cse of high j b r j ¼ 1:14. In this cse the strin plot (b) shows n high strin discontinuity mesured cross the grin boundry. Fig. 10. Strin mesurements cross grin boundry in cse of high j b r j ¼ 1:28. In this cse the strin plot (b) shows n high strin discontinuity mesured cross the grin boundry. rection tht results in high residul Burgers vector mgnitude (1.14): 4. Discussion ½111 Grin4 - ½111 Grin5 þ b r ) j b r j ¼ 1: Considerble reserch efforts hve been devoted to incorporting disloction slip t the crystl level to predict the overll response of metls. Substntil progress hs been gined in predicting crystl orienttion effects, strin hrdening of the slip systems [25], slip twin interctions [26], nd chnge in crystllogrphic texture [27,28] upon deformtion. Grin boundries hve been treted s contributor to geometric hrdening nd the obstcle length hs been incorported in the crystl plsticity models [26]. These models typiclly llow for predicting the overll mcroscopic stress strin response upon use of vrious homogeniztion schemes. Further dvnces in these models should encompss developments on grin boundry specifics. The grin boundries represent different levels of strengthening depending on the incoming nd outgoing slip becuse of the different residul Burgers vectors tht remin t the boundry. The level of strengthening ssocited with the grin boundries cn be quntified by mesuring the energetics of the slip trnsfer process. Using moleculr dynmics simultions, Sngid et l. estblished the energy brrier levels for different grin boundries ð6þ From the DIC strin plot (Fig. 9b) it is cler tht s consequence of the high j b r j, strins ccumulte on the right side of the GB leding to n high strin grdient equl to jδεgb4 5 j ¼ 0:47% which is higher thn the cses previously reported in Eqs. (4) nd (5). The lst cse nlyzed (Fig. 10) hs been lredy introduced in Fig. 4c nd d (strin field 2A B) using lower imge resolution (0.87 versus 0.18 μm/pixel). The disloction rection between the incoming ½111 ð231þ nd the outgoing ½111 ð211þ slip systems (see Eq. (2)) indictes residul Burgers vector mgnitude of j b r j ¼ 1:28. From the strin mesurements obtined, the strin chnge cross the GB is prticulrly high jδεgb2 7 j ¼ 1:29%. The results presented clerly indicte tht the level of strin heterogeneity (mesured s the difference between the verged strins pproching the GB sides) increses with the residul Burgers vector mgnitude j b r j.

9 316 [12] in fcc metls. In prticulr, nlyzing different twin nd grin boundries, the uthors show tht high energy brriers for slip trnsmission correspond to high residul Burgers vector mgnitudes. The influence of the grin boundry specifics on the slip disloction GB interctions cn lso be experimentlly studied on the mesoscopic scle, since the slip trnsmission process influences the locl deformtion behvior t the grin boundries. In tht regrd, the results reported in this work present unique chrcteriztion of the locl strin fields cross grin boundries. The high strin discontinuities mesured for certin grin boundries derive from the difficulty for slip to propgte through the grin boundries. In these cses, the ctivtion of the slip system on the second grin (outgoing slip system) is pired with n high residul Burgers vector mgnitude of the disloction tht remins on the grin boundry. The lrgest contribution to the strengthening is then provided by the grin boundries tht disply high strin discontinuities, concomitnt with the high energy brriers tht re mesured for slip disloction GB rections nd high residul Burgers vector mgnitudes [12]. The locl strin heterogeneities cross the grin boundries hve lso prmount importnce in dmge nucletion. Dmge nucletion hs been observed mostly t grin boundries where imperfect slip trnsfer tkes plce nd strin heterogeneities rise, then in loctions where high locl strins re mesured [29,30]. It is therefore worthwhile to recognize the correltion between the grin boundry specifics with the mesured locl strin heterogeneities, nd thus identify the potentil dmge initition sites. As shown long the present work, grin boundries re chrcterized with the ssocited residul Burgers vector following slip disloction grin boundry interction. The concept of residul Burgers vector hs been estblished in erlier works nd its importnce is well known in the mterils science community [2,31]. In prticulr, in mny experimentl studies different uthors lredy recognize the importnce of the residul Burgers vector in chrcterizing the slip process through grin boundries [4,5,12,32]. Wht hs been lcking is quntittive illustrtion of the link between the residul Burgers vector nd the locl strin fields, prticulrly for bcc mteril. This becme possible with the development of digitl imge correltion techniques, nd specil codes in this study, written for the purpose of nlyzing the strins long the slip lines s the slip pproches the boundry, nd emntes or gets blocked t the boundry. Using this methodology, in Section 3 we provided different types of strin fields cross selected GBs which disply different residul Burgers vector mgnitudes. Along the work we mke the fundmentl ssumption tht the strin fields re directly correlted with the mechnism of interction. Other potentil sources of strins cross GBs re then neglected. For exmple, elstic grin nisotropy induces the genertion of comptibility stresses which cn ctivte dditionl slip systems in the proximity of the GBs [1]. In some cses these contributions hve to be considered in the nlysis. In the present study, however, we only refer to the strin heterogeneities induced by prtil disloction trnsmission (including blockge nd full trnsmission cses), since for the mteril considered only one single slip system ws ctive cross ech nlyzed GB. In the present tretment we observe tht the ccumultion of residul disloctions t the grin boundry induce strin discontinuity cross the interfce tht is proportionl to the j b rj mgnitude. In cse of full trnsmission, the Burgers vector conservtion implies tht no residul disloctions re left t the GBs [2], for this cse no substntil strin grdients re expected to occur cross the grin interfce. In our experiments, for GBs displying low j b rj-0 we observed tht the mesured strins vry lmost unltered cross the interfce (Fig. 7, j b rj¼0:16). Low j b rj-0 GBs re then expected to provide the lowest strengthening contributions. In the generl cse of prtil trnsmission of disloctions, residul disloction is left on the grin boundry, nd nother disloction glides in the other grin. The presence of residul disloction t GBs cretes disloction impingements on the side of the incoming disloctions. In this cse, higher locl strins re expected on tht side of the GB, generting generl discontinuity in the strin field. For these common cses chrcterized by intermedite residul Burgers vector mgnitudes j b rj¼0:2 to 1, the mesured strins ccumulte on one side of the grin boundry depending on the j b rj mgnitude (Fig. 8, j b rj¼0:28). The highest vlues of strin chnge cross GBs re then mesured for the lrgest residul Burgers vector mgnitudes j b rj41 (Fig. 9, j b rj¼1:14, nd Fig. 10, j b rj¼1:28). These results cn be utilized to illustrte the significnt role tht grin boundries ply in the slip trnsfer process, in prticulr they cn be useful in further modeling efforts. The j b rj cn then be used s prmeter to (i) provide n indiction of the level of strin heterogeneity t the grin boundry which indictes the possibility to ccumulte dmge nd (ii) quntify the level of strengthening due to the single grin boundry. We note the judicil choice of FeCr polycrystls with reltively lrge grin sizes, nd most importntly the ctivtion of single slip system in ech grin fcilitted such observtions. In the presence of two or more ctivted slip systems nd lso twinning, the interprettion of DIC strin fields becomes more complex. Multiple slip nd twin systems lso introduce dditionl strengthening effects. Our previous experiments conducted on single crystls of the sme mteril nd conditions (smple geometry, het tretment nd strin rte) indicte tht very low hrdening is observed (for low deformtions εo3%) when only one or two slip systems re ctivted [33]. It follows tht the contribution to the hrdening observed in the present cse (h ¼ 0:014E, see Fig. 3) is provided by prtil or full blockge of the disloctions t the grin boundries. Therefore, the isolted single slip system results for the present polycrystl smple shed light into the mechnism very clerly, hence represent unique findings in this work. The strin resolution dopted by mens of the DIC ex situ setup offers the possibility to cpture the strin heterogeneities introduced by the single slip trce. Experimentlly, these results were chieved by the utiliztion of very fine speckles (which enbled to cquire imges t resolutions up to 0.18 mm/pixel) nd using polycrystl mteril with lrge verge grin size (bout 1 mm). The dopted experimentl set-up cn lso be used for mterils with smller grin sizes. Further dvncements cn lso be chieved for mterils tht plsticlly deform by twinning. Twin GB nd twin slip interctions, which provide dditionl strengthening contributions, cn be quntittively nlyzed through the sme methodology bsed on the mesure of strin heterogeneities cross twin or grin boundries. An importnt issue to be ddressed is the improvement of the strin resolution for in situ strin mesurements, since for now ll the strin fields reported re obtined cquiring imges with the opticl microscope in the un-loded condition (ex-situ). The chllenge is to rech the sme strin resolutions dopted in the ex situ DIC set up (0.18 mm/pixel) lso for the in-situ set-up. Such high resolution rel-time strin mesurements potentilly llow to cpture the dynmics of slip nd twinning during deformtion, nd thus provide further insight into vlidity of the present results t lrger deformtion levels when multiple slip/twin systems ctivte simultneously. In summry, we illustrted the considerble promise of the digitl imge correltion method when utilized in conjunction with EBSD in gining insight on the strin fields t the grin boundries. Other techniques such s TEM cn be used in conjunction with these results presented here s well. These present results llow nlysis t the mesoscle llowing rpid

10 317 ssessment of the microstructure. The methodology forwrded in this study cn be utilized to check the confidence of crystl plsticity clcultions s well s the simultions conducted with moleculr dynmics methods which provide better description of grin boundries. 5. Conclusions In this study we investigted disloction grin boundry interctions for FeCr lloy using strin fields determined by digitl imge correltion. Strin fields cross GBs provide direct quntifiction of the GB cpbility to trnsmit or block slip disloctions. The study elucidtes the role of the residul Burgers vector mgnitude in predicting full/prtil slip trnsmission, or slip blockge. We provide the strin fields cross GBs displying different residul Burgers vector mgnitudes. In prticulr, for low j b rj-0 slip is observed to trnsmit unltered cross the interfce, the resulting strin field is continuous nd the GBs re then expected to provide low strengthening contributions. For intermedite j b rjo1, step on the strin field is observed on the interfce depending on the j b rj mgnitude. The strin chnge represents the slip ccumultion on the GB side of the incoming slip system. Finlly, for high j b rj41, slip ccumultes t the grin boundry, nd high strins re mesured on one side of the grin. The results clerly show direct correltion of the strin chnge cross the interfces with the j b rj mgnitude thus indicting the possibility to use the j b rj s prmeter for predicting the slip trnsmission cpbility of the grin boundries in polycrystl mteril. Acknowledgments The work ws supported by the Ntionl Science Foundtion, NSF CMMI This support is grtefully cknowledged. References [1] J. Hirth, Metll. Mter. Trns. B 3 (1972) [2] A.P. Sutton, R.W. Blluffi, Interfces in crystlline mterils, Clrendon Press, Oxford, [3] W.A.T. Clrk, C.E. Wise, Z. Shen, R.H. Wgoner, Ultrmicroscopy 30 (1989) 76. [4] T. Lee, I. Robertson, H. Birnbum, Metll. Mter. Trns. B 21 (1990) [5] W.Z. Abuzid, M.D. Sngid, J.D. Crroll, H. Sehitoglu, J. Lmbros, J. Mech. Phys. Solids 60 (2012) [6] W. Abuzid, M.D. Sngid, H. Sehitoglu, J. Crroll, J. Lmbros, Procedi IUTAM, vol. 4, p [7] R.E. Hook, J.P. Hirth, Act Metll. 15 (1967) 535. [8] R.E. Hook, J.P. Hirth, Act Metll. 15 (1967) [9] P. Šittner, V. Novák, J. Brádler, Scr. Metll. Mter. 27 (1992) 705. [10] P. Šittner, V. Pidr, Act Metll. 37 (1989) [11] T. Ezz, M.D. Sngid, H. Sehitoglu, Philos. Mg. 91 (2011) [12] M.D. Sngid, T. Ezz, H. Sehitoglu, I.M. Robertson, Act Mter. 59 (2011) [13] M. de Koning, R.J. Kurtz, V.V. Bultov, C.H. Henger, R.G. Hoglnd, W. Ci, M. Nomur, J. Nucl. Mter. 323 (2003) 281. [14] C. Efstthiou, H. Sehitoglu, J. Lmbros, Int. J. Plsticity 26 (2010) [15] M. Schtleber, Z. Zho, D. Rbe, Mter. Sci. Eng. A 336 (2002) 81. [16] L.C. Lim, Scr. Metll. 18 (1984) [17] L.C. Lim, R. Rj, Act Metll. 33 (1985) [18] L.C. Lim, R. Rj, Act Metll. 33 (1985) [19] J. Crroll, W. Abuzid, J. Lmbros, H. Sehitoglu, Rev. Sci. Instrum. 81 (2010). [20] A. Seeger, Phys. Sttus Solidi A 201 (2004) R21. [21] M. Sutton, J. Turner, H. Bruck, T. Che, Exp. Mech. 31 (1991) 168. [22] M.A. Sutton, C. Mingqi, W.H. Peters, Y.J. Cho, S.R. McNeill, Imge Vision Comput. 4 (1986) 143. [23] M.A. Sutton, J.-J. Orteu, H.W. Schreier, Imge Correltion for Shpe, Motion nd Deformtion Mesurements: Bsic Concepts, Theory nd Applictions, [24] M.A. Sutton, W.J. Wolters, W.H. Peters, W.F. Rnson, S.R. McNeill, Imge Vision Comput. 1 (1983) 133. [25] K.K. Mthur, P.R. Dwson, Int. J. Plsticity 5 (1989) 67. [26] I. Krmn, H. Sehitoglu, A.J. Beudoin, Y.I. Chumlykov, H.J. Mier, C.N. Tomé, Act Mter. 48 (2000) [27] S.R. Klidindi, C.A. Bronkhorst, L. Annd, J. Mech. Phys. Solids 40 (1992) 537. [28] R.A. Lebensohn, C.N. Tomé, Act Metll. Mter. 41 (1993) [29] T.R. Bieler, P. Eisenlohr, F. Roters, D. Kumr, D.E. Mson, M.A. Crimp, D. Rbe, Int. J. Plsticity 25 (2009) [30] W. Abuzid, A. Orl, H. Sehitoglu, J. Lmbros, H.J. Mier, Ftigue Frct. Eng. Mter. Struct. 36 (2013) [31] J. Hirth, J. Lothe, Theory of Disloctions, Second ed., John Wiley nd Sons, Inc., New York, [32] C.T Lee, M.I Robertson, K.H Birnbum, Prediction of Slip Trnsfer Mechnisms cross Grin Boundries, Pergmon Press, Elmsford, NY, ETATS-UNIS, [33] L. Ptrirc, W. Abuzid, H. Sehitoglu, H.J. Mier, Y. Chumlykov, Mter. Chrct. 75 (2013)