On the evolution and modelling of lattice strains during the cyclic loading of TWIP steel

Transcription

1 Univerity of Wollongong Reearch Online Faculty of Engineering and Information Science - Paper: Part A Faculty of Engineering and Information Science 213 On the evolution and modelling of lattice train during the cyclic loading of TWIP teel Ahmed A. Saleh Univerity of Wollongong, aaleh@uow.edu.au Elena V. Pereloma Univerity of Wollongong, elenap@uow.edu.au Bjorn Clauen Lo Alamo National Laboratory Donald W. Brown Lo Alamo National Laboratory Carlo N. Tome Lo Alamo National Laboratory See next page for additional author Publication Detail Saleh, A. A., Pereloma, E. V., Clauen, B., Brown, D. W., Tome, C. N. & Gazder, A. A. (213). On the evolution and modelling of lattice train during the cyclic loading of TWIP teel. Acta Materialia, 61 (14), Reearch Online i the open acce intitutional repoitory for the Univerity of Wollongong. For further information contact the UOW Library: reearch-pub@uow.edu.au

2 On the evolution and modelling of lattice train during the cyclic loading of TWIP teel Abtract The evolution of lattice train in fully annealed Fe 24Mn 3Al 2Si 1Ni.6C twinning-induced platicity (TWIP) teel i invetigated via in itu neutron diffraction during cyclic (tenion compreion) loading between train limit of ±1%. The pronounced Bauchinger effect oberved upon load reveral i accounted for by a combination of the intergranular reidual tree and the intragranular ource of back tre, uch a dilocation pile-up at the interection of tacking fault. The recently modified elato-platic elf-conitent (EPSC) model which empirically account for both intergranular and intragranular back tree ha been uccefully ued to imulate the macrocopic tre train repone and the evolution of the lattice train. The EPSC model capture the experimentally oberved tenion compreion aymmetry a it account for the directionality of twinning a well a Schmid factor conideration. For the train limit ued in thi tudy, the EPSC model alo predict that the lower flow tre on revere hear loading reported in earlier Bauchinger-type experiment on TWIP teel i a geometrical or loading path effect. Keyword loading, cyclic, during, train, lattice, modelling, evolution, twip, teel Dicipline Engineering Science and Technology Studie Publication Detail Saleh, A. A., Pereloma, E. V., Clauen, B., Brown, D. W., Tome, C. N. & Gazder, A. A. (213). On the evolution and modelling of lattice train during the cyclic loading of TWIP teel. Acta Materialia, 61 (14), Author Ahmed A. Saleh, Elena V. Pereloma, Bjorn Clauen, Donald W. Brown, Carlo N. Tome, and Azdiar A. Gazder Thi journal article i available at Reearch Online:

3 ON THE EVOLUTION AND MODELLING OF LATTICE STRAINS DURING THE CYCLIC LOADING OF TWIP STEEL Ahmed A. Saleh 1 *, Elena V. Pereloma 1,2, Bjørn Clauen 3, Donald W. Brown 4, Carlo N. Tomé 4, Azdiar A. Gazder 1,2 1School of Mechanical, Material and Mechatronic Engineering, Univerity of Wollongong, New South Wale 2522, Autralia 2Electron Microcopy Centre, Univerity of Wollongong, New South Wale 2519, Autralia 3Lo Alamo Neutron Science Center, Lo Alamo National Laboratory, New Mexico 87545, United State 4Material Science and Technology Diviion, Lo Alamo National Laboratory, New Mexico 87545, United State Abtract The evolution of lattice train in fully annealed Fe 24Mn 3Al 2Si 1Ni.6C TWinning Induced Platicity (TWIP) teel i invetigated via in itu neutron diffraction during cyclic (tenioncompreion) loading between train limit of ±1%. The pronounced Bauchinger effect oberved upon load reveral i accounted for by a combination of the intergranular reidual tree and the intragranular ource of back tre uch a dilocation pile up at the interection of tacking fault. The recently modified Elato Platic Self Conitent (EPSC) model which empirically account for both intergranular and intragranular back tree ha been uccefully ued to imulate the macrocopic tre train repone and the evolution of the lattice train. The EPSC model capture the experimentally oberved tenion compreion aymmetry a it account for the directionality of twinning a well a Schmid factor conideration. For the train limit ued in thi tudy, the EPSC model alo predict that the lower flow tre on revere hear loading reported in earlier Bauchinger type experiment on TWIP teel i a geometrical or loading path effect. Keyword: TWIP teel, Neutron diffraction, lattice train, Bauchinger effect, EPSC. * Correponding author: Ahmed A. Saleh School of Mechanical, Material and Mechatronic Engineering Univerity of Wollongong, New South Wale 2522, Autralia Phone: Fax: e mail: aaleh@uow.edu.au 1

4 1. Introduction TWinning Induced Platicity (TWIP) teel containing wt.% Mn with mall addition of Al and Si have been developed a a promiing material for automotive application due to their characteritically extended period of work hardening under applied macrocopic (or type I) tre [1]. TWIP teel comprie a table face centred cubic (fcc) autenite phae with low tacking fault energy between 18 4 mj/m 2. Thi low tacking fault energy initiate twinning along with dilocation glide during room temperature deformation. Twinning affect the high work hardening rate through either of two predominant mechanim: (i) iotropic hardening or the Dynamic Hall Petch effect or, (ii) kinematic hardening or the Bauchinger effect. In addition to lattice friction and foret hardening effect, iotropic hardening in TWIP teel ha been acribed to reduction in the mean free path of dilocation caued by the twin boundarie acting a obtacle to further glide [2 4]. On the other hand, kinematic hardening ha been attributed to the preence of an internal forward tre on the twin and an internal back tre on the matrix [2, 4]. In thi regard, while everal experimental and theoretical invetigation have correlated the train hardening behaviour of low tacking fault energy material with their twinning activity in term of the iotropic hardening effect [3, 5, 6], limited detail are available on the contribution of kinematic hardening or the Bauchinger effect to the overall train hardening [2, 4]. The Bauchinger effect i generally manifeted by a lowering of the yield tre upon load reveral and an extended elato platic tranition region. The phenomenon i generally explained through internal tre and/or dilocation baed theorie [7]. The Bauchinger effect wa initially acribed to internal tree and macrocopic reidual tree ariing from the inhomogeneou deformation of individual grain [8] due to the aniotropy in their elatic moduli and yield trength with orientation and/or different phae [9]. Such internal tree that elf equilibrate at length cale comparable to the grain ize are known a intergranular or type II tree [1]. Thereafter, dilocation baed theorie introduced by Mott [11] and Seeger et al. [12] attributed the Bauchinger effect to long range back tree generated by the pile up of dilocation at microtructural barrier uch a grain boundarie, eile dilocation and econd phae particle during forward loading. Thee tree aid revere dilocation motion when the lip direction i changed during revere loading. In ummary both, internal tre and dilocation theorie (or intergranular and intragranular effect) are relevant when explaining the Bauchinger effect in polycrytalline material. To thi end, the magnitude of the Bauchinger effect in ingle phae alloy i generally dependent on the tacking fault energy uch that a greater lowering in yield trength upon revere loading i aociated with lower tacking fault energy value [13]. The ignificant Bauchinger effect in low tacking fault energy material i related to the planar nature of their lip and the conequent 2

5 reveribility of their dilocation. Moreover, in Hadfield teel ingle crytal [14], TWIP teel [2] and bra [15], deformation twinning i uually accompanied by a prominent Bauchinger effect. Karaman et al. [14] acribed the twin related Bauchinger effect to the long range back tree generated by the dilocation pile up at twin boundarie. Gil Sevillano [4] attributed the generation of back tree to the high trength of the nanometer ized twin thicknee. In agreement with [4], a tranmiion electron microcopy (TEM) tudy on TWIP teel further clarified that the high trength of the twin i due to the exitence of eile dilocation (the denity of which depend on the alloying content) within the twin lamellae [16]. Thu, the above explanation for the oberved back tre attribute the enhanced work hardening in TWIP teel to the compoite trengthening provided by the harder twin and the ofter autenite matrix. While the role of the above intragranular ource to the back tre can be analyed by TEM baed local area diffraction experiment, no uch work ha been undertaken to date. On the other hand, the evolution of intergranular tree during the uniaxial loading of Fe 25Mn 3Si 3Al ha been characteried by in itu ynchrotron X ray diffraction [17]. However, the contribution of thee intergranular ource to the back tre can only be quantified by in itu diffraction meaurement during cyclic loading (for example tenion compreion, compreion tenion or forward revere torion tet). The internal train evolution during cyclic loading allow aement of the contribution of intergranular and intragranular tree to the Bauchinger effect. The coupling of neutron diffraction (ND) with an in itu cyclic teting apparatu enable the imultaneou tracking of the change in the internal train along with the bulk repone. While everal in itu ND experiment during uniaxial cyclic loading were performed on hexagonal cloe packed material (e.g.: [18, 19]), the very limited tudie undertaken on ingle phae fcc material have only focued on autenitic tainle teel which deform olely by lip [2, 21]. Conequently, there are no report of imilar experiment on low tacking fault energy fcc material uch a TWIP teel that deform via concurrent lip and twinning. The in itu ND meaurement in turn can be further interpreted uing an Elato Platic Self Conitent (EPSC) [22] polycrytal platicity model. The EPSC model imulate both, the macrocopic tre train behaviour a well a the average repone of the variou grain orientation. While the original EPSC model implement a Voce law and inherently account for the intergranular contribution to the back tre, a recent modification incorporating a non linear kinematic hardening rule applied to the hardening of lip ytem capture the effect of intragranular ource on the back tre [21]. In thi regard, while the EPSC model ha not been applied previouly to the revere loading of TWIP teel, Favier and Barbier [23] have recently attempted to imulate a revere imple hear deformation via a tranlated field model. However, the model failed to capture the Bauchinger effect uch that the flow tre wa overetimated upon load reveral a the model accounted only for intergranular tree but not for the intragranular tree. 3

6 Throughout the paper and following the notation ued in [21], the term iotropic hardening refer to the Voce law impoing a non directional, monotonically increaing hardening of deformation ytem. It i emphaied that unlike the claical definition of iotropic hardening, the ue of the term iotropic from here on doe not refer to a proportional expanion of the ingle crytal yield urface while retaining it hape. While uch proportional expanion of the yield urface require that the rate of increae in the critical reolved hear tre i the ame for all deformation ytem, it i not enforced here during EPSC modelling. Rather, a Voce law with different parameter for each deformation mode will be ued. The claical mechanic definition of kinematic hardening i ynonymou with a rigid tranlation (or diplacement) of the entire yield urface and doe not enable the prediction of general train path change. In the modified EPSC cheme, only the active facet and it oppoite facet in the ingle crytal yield urface are diplaced in the ame direction, while the inactive facet are not diplaced. Thi approach i more repreentative of the real material behaviour ince it correlate with the reveral of dilocation on a given lip plane [2]. Conequently, the non linear kinematic hardening rule empirically account for the aforementioned directional planar mechanim. Latly, it hould be tated that a univeral phyical decription of hardening during cyclic loading (or kinematic hardening in general) hould alo take into account the influence of deformationinduced dilocation microtructure on the intragranular back tre (for example, the compoite cheme uggeted in [24, 25] when evaluating material repone at large train, or more complex train path change, or for numerou cycle. However, the preent experiment along with the modified EPSC model trictly deal with uniaxial load reveral at mall train; where the Bauchinger effect i motly related to the reveral of dilocation motion [21]. With the above outlook in mind, the preent tudy i the firt to characterie the Bauchinger effect in TWIP teel uing neutron diffraction. It i alo the firt time that the modified EPSC model i applied on an fcc material that deform via concurrent lip and twinning. Hence the ND experimental data et further validate the performance of the modified EPSC model. The effect of the initial uniaxial loading direction and the influence of the loading path on the revere flow tre for the train level ued in the preent tudy are alo dicued. 2. Experimental procedure The nominal compoition of the preent TWIP teel i 24Mn 3Al 2Si 1Ni.6C wt.%. The cat lab wa 52% hot rolled and then 42% cold rolled followed by iochronal annealing. The heat treatment included 24 of heating to table temperature followed by 3 of oaking time and immediate water quenching. Full recrytalliation wa attained after annealing at 85 C with a recrytallied grain ize of ~7 µm [26]. A round tenion/compreion ample of 7.62 mm (.3") gage length and

7 mm (.1") diameter wa machined from the fully recrytallied material with it gage length parallel to the rolling direction. In itu neutron diffraction meaurement were performed at the Spectrometer for Material Reearch at Temperature and Stre (SMARTS) diffractometer at the Manuel Lujan Jr. Neutron Scattering Center, LANSCE, Lo Alamo National Laboratory [27]. A chematic of the ample and the diffraction geometry i hown in Fig. 1a. The ample i oriented at 45 relative to the incident beam. The two detector bank on either ide of the ample are at ±9 relative to the incident beam and imultaneouly record data with diffraction vector parallel (Q ) and perpendicular (Q ) to the applied load. The incident neutron beam wa defined by 3 3 mm 2 boron nitride aperture and each diffraction pattern took ~3 to record. Cyclic uniaxial tenion compreion loading between train limit of ±1 % were performed uing train control on a purpoe built horizontal Intron load frame [27]. Five complete tenioncompreion cycle were performed followed by a ixth tenion half cycle. For the firt three complete tenion compreion cycle, diffraction pattern were acquired at predetermined train level. Thereafter, diffraction pattern were meaured at the maximum tenion, maximum compreion and zero unload point for the fourth complete and ixth half cycle. The fifth cycle wa kipped due to beam time contraint. Throughout the experiment, an extenometer that panned the irradiated region remained attached to the ample in order to negate load frame compliance error. Data analyi involved ingle peak fitting uing the General Structure Analyi Software (GSAS) [28]. Single peak fitting enable following the repone of individual lattice reflection {hkl} to deformation and thu directly provide information on intergranular effect. The change in the individual peak poition during deformation a returned from ingle peak fitting were ued to calculate the {hkl} pecific lattice train ( hkl ) uing: d d hkl hkl hkl dhkl Eq. (1) where, d hkl i the intantaneou lattice pacing at any train tep and d hkl i the untrained interatomic pacing. Throughout the paper the lattice train i preented in unit of micro train (µε) where 1 µε = It i emphaied here that the lattice train are a meaure of the average elatic normal train in the direction of the cattering vector in the grain whoe {hkl} lattice plane normal i parallel to the cattering vector. In other word, they do not repreent the tate within a ingle grain but are an average over a family of grain which fulfil the Bragg cattering condition for a given reflection. A typical axial diffraction pattern collected before the tart of cycling i given in Fig. 1b with the invere pole figure (IPF) obtained from Rietveld refinement given in Fig. 1c. 5

8 3. Elato platic elf conitent modelling In the original EPSC model developed by Turner and Tomé [22], a ingle grain (or crytallographic orientation) i aociated with a volume fraction and i repreented a an ellipoidal incluion embedded in and interacting with an infinite homogeneou effective medium that correpond to the polycrytalline aggregate. While the elatic repone of the individual grain i decribed by the ingle crytal elatic contant, the platic repone of the individual grain i decribed by activating the variou deformation ytem () at predetermined value of the critical reolved hear tre (CRSS, cr ). While the incluion formalim predict uniform tre and train within an ellipoidal domain, the value are different for each grain. A a conequence, the incluion formalim can inherently capture the effect of the intergranular tre but not the intragranular tre. Conequently, without the incorporation of an intragranular back tre during revere loading, the original EPSC model only account for the contribution of intergranular tre to the Bauchinger effect [22]. Recently, a nonlinear kinematic hardening law wa implemented by Wollmerhauer et al. [21] into the EPSC framework in order to account for the intragranular effect upon revere loading at low train level. The modified EPSC model uccefully imulated the macrocopic tre train repone and the evolution of the lattice train during the cyclic loading (tenion compreion between train level of ±2%) of 317L autenitic tainle teel which deform olely by lip. The EPSC model formulation ha been detailed in previou publication [21, 22, 29] and only a brief decription i given here. In order to initiate activity on a particular deformation ytem in the original c EPSC model, the reolved hear tre ( m : ) ha to firt reach it CRSS. Thereafter, the deformation c ytem activity i utained a long a the reolved hear tre rate ( m : ) meet the CRSS rate ( c ) a it harden upon training [22]. Here ( ) i the tre rate and ( m ) i Schmid tenor. In the cr modified EPSC model, the intragranular back tre effect i captured by updating the activation condition to include a back tre term ( b ) uch that: The c m : Eq. (2) for b c m : Eq. (3) for b b term account for kinematic hardening in individual lip ytem a it reduce the reolved applied tre by the directional back tre ariing from the pile up of dilocation at variou barrier. On the other hand, for (originally denoted a the CRSS, ) i the iotropic hardening term which i aociated with the non directional accumulation of obtacle uch a foret dilocation and/or deformation twin boundarie. Thu, with the accumulation of train, the evolution of the for term account for the reduction in the mean lip path and the increaed reitance to further dilocation cr 6

9 motion. The hardening of the form [3]: for for each deformation mode follow an extended Voce hardening rule of, for for 1, for 1, for1 exp 1, for An analogou relationhip i employed to decribe the evolution of the back tre [21]:, b b 1, b x 1, b 1 exp 1, b x Eq. (4) Eq. (5) and 1 are the initial and back extrapolated critical reolved hear tree and and 1 are the initial and final aymptotic hardening rate for the foret hardening (for in Eq. (4)) and back tre (b in Eq. (5)) formulation. i the total accumulated hear train on all deformation ytem in a grain. The and x term are the train and tre memory parameter and are both initially et to zero during the firt forward half cycle. In what follow, a lip ytem that i active during the forward loading i referred to a a forward lip ytem (). If the load i revered, the lip direction of the forward lip ytem i revered and the lip ytem i denoted a a revere lip ytem ( ). Upon load reveral, the above memory parameter are updated uch that: (i) the value of the revere lip ytem at the tart of the revere half cycle i equal to the total accumulated hear ( ) of the forward lip ytem at the end of the forward half cycle. Thu account for the high initial hardening rate of the revere lip ytem. (ii) The x value of the revere lip ytem at the tart of the revere half cycle i equal to the poitive reolved back tre ( b ) of the forward ytem at the end of the forward half cycle. Hence x reduce the CRSS of the revere lip ytem by b. It i emphaied that both of the aforementioned memory parameter are computed a a function of the train path and are not fitting parameter 1. In the abence of intergranular contribution to the back tre, the combined memory effect extend the elato platic tranition upon lip direction reveral and are a manifetation of the dilocation baed mechanim governing the Bauchinger effect [21]. A uggeted by Lorentzen et al. [2], the rate of increae of the reolved back tre of the active lip ytem i equal to the rate of decreae of the reolved back tre of the revere lip ytem uch that: tot 1 It hould be noted that: (i) the evolution of the CRSS (Eq. 4) depend on the total grain hear ( ) wherea the evolution of the back tre (Eq. 5) i a function of ingle lip ytem hear ( ). (ii) Eq. 5 doe not involve an initial CRSS a it i accounted for in Eq. 4. Pleae ee Ref. [21] for further detail. 7

10 (if ) Eq. (6) b b The kinematic hardening rule denoted by Eq. (5 and 6) are trictly valid for lip ytem only a dilocation can revere their lip direction upon load reveral. It follow that Eq. (5 and 6) are inapplicable to twinning due to it unidirectional nature. Latly, the activitie on the variou lip and twinning ytem harden other each other according to: ' ' Vh Eq. (7) ' where, depending on the hardening law V d d or d d and ' h i the latent hardening matrix. The hardening matrix ha diagonal value (or the elf hardening) of one. In the current work, the off diagonal value were alo et to one uch that all deformation ytem are aumed to contribute equally to the hardening of each other, i.e. equal latent hardening i aumed 2. While in the original EPSC model [22] twinning i treated a a directional lip mechanim, the preent tudy utilie the twinning cheme which ha been incorporated into the EPSC model by Clauen et al. [29]. Thi cheme account for: (i) the volume effect of twinning on texture evolution and, (ii) the tre relaxation aociated with the twin formation. With regard to the volume effect, the reorientation by twinning for the low train level employed in thi tudy i rather limited. Conequently, the volume effect of twinning on the texture evolution at thee train level can be preumed to be inignificant. In fact, the volume effect of twinning in fcc polycrytal i generally limited even at higher train [31, 32]. Alternatively, the tre relaxation effect i achieved via the o called finite initial fraction approach; wherein the twin i aumed to grow to a fixed volume fraction of it parent grain at the nucleation tage. In thi cheme, the localied hear tranformation aociated with the twinning ytem generate a back hear tre on the twin due to the contraint of the urrounding grain. Due to thi effect, the hear in the parent grain i omewhat relaxed while the hear in the newly created twin domain i revered. In the preent imulation, 24 { 111}11 perfect lip ytem (counting both forward and revere lip direction) and 12 { 111}112 forward twinning ytem (a twinning i only operative in one direction) were introduced into the EPSC model. Additionally, the kinematic hardening parameter for twinning were et to zero. Further EPSC model input include the initial ample texture and the ingle crytal elatic contant. The orientation ditribution function (ODF) obtained from X ray diffraction in [26] wa dicretied into 5 ingle orientation with varying volume fraction choen to reproduce the initial texture. Since the ingle crytal elatic contant of the preent TWIP teel are not known, interpolated value (C 11 = GPa, C 12 = 11.3 GPa and C 44 = GPa, leading to an elatic aniotropy factor (A) 2 ' We have alo verified that uppreing latent hardening for coplanar ytem ( h ) reduce the flow tre but doe not lead to qualitative change in the predicted tre train repone during unloading. 8

11 = 2 C 44/(C 11 C 12) = 5.2) were etimated from the ab initio calculation of the elatic propertie of Fe Mn Al/Si alloy [33]. 4. Experimental reult 4.1. Macrocopic behaviour during cyclic loading The macrocopic tre train repone obtained during cyclic loading i hown in Fig. 2a wherea the maximum tre ( max ) at the end of each tenion and compreion half cycle i extracted from Fig. 2a and hown in Fig. 2b a a function of the number of half cycle. All macrocopic tree and train are hown uing their true value. The tre relaxation oberved in Fig. 2a correpond to the period of neutron data collection where the ample wa hold at contant train. From Fig. 2a and b, it i clearly evident that the increae in the macrocopic flow tre upon multiple tenion compreion cycling approache aturation by the ixth cycle. It i alo noted that the maximum tre during the compreion half cycle i ~7% higher than the maximum tre during tenion half cycle throughout the experiment. In Fig. 2a, the relatively harper elato platic tranition during macro yielding (~29 MPa) in the firt tenile half cycle i markedly different from the more gradual elato platic tranition recorded when multiple cycling between tenion compreion or compreion tenion i undertaken. More importantly, the maximum tre at the end of the firt tenion half cycle i ~32 MPa. Upon load reveral, yielding occur during the unloading and before the macrocopic tre croe the abcia at ~+1 MPa. Thi i alo aociated with an anelatic train ( anelatic ) of ~.4% during unloading from either tenion or compreion half cycle (illutrated in Fig. 2a uing a dahed line when unloading from tenion to compreion). All of the above obervation are manifetation of a pronounced Bauchinger effect. A more quantitative etimation of the Bauchinger effect i obtained by the method originally uggeted by Cottrell [34] and implemented by Kuhlmann Wildorf and Laird [35]. Here the cyclic flow tre i divided into a friction tre and a back tre. The friction tre i independent of the direction of loading and i decribed a the tre aociated with hort range interaction uch a lattice friction and foret hardening effect. On the other hand, the back tre arie from the intragranular and intergranular tre contribution and aid yielding upon revere loading. In thi approach, the hyterei loop i conidered to be ymmetrical uch that the mall difference in the tre level between forward and revere loading half cycle are neglected. Friction ( ) and back ( B ) tree are determined a follow: F max F B Eq. (8) 9

12 where, R F B Eq. (9) max i the maximum tre at the forward loading half cycle and R i the yield tre after load reveral taken a the point of deviation from elaticity. Conequently, B i defined a: 2 For example, applying Eq. (1) after the firt tenion half cycle with max R B Eq. (1) = 32 MPa and max R = 1 MPa reult in a back tre of 21 MPa. Thi value of back tre i ~65% of the maximum tre at the firt tenion half cycle. The evolution of the back tre with further cycling i alo hown in Fig. 2b. The back tre to maximum tre ratio decreae lightly from ~65% to ~62% after the ixth cycle The evolution of lattice train The evolution of the lattice train during the firt tenion half cycle i given in Fig. 3a for variou grain familie. A linear fit wa applied to the initial elatic repone (up to σ <15 MPa) of each grain family in both, axial and radial direction in order to obtain the material diffraction elatic contant lited in Table 1. Typical of aniotropic fcc crytal, the {111} and the {2} grain familie bound the repone of other grain familie a the {111} orientation are the tiffet orientation while the {2} are the mot elatically compliant orientation [36]. Conequently, the {111} grain family exhibit the lowet tenile lattice train in the axial direction during the elatic regime, wherea the {2} orientation record the highet tenile lattice train (Fig. 3a). In other word, the evolution of the lattice train in the elatic regime i dictated by the elatic aniotropy uch that it follow the relative magnitude of the directional elatic modulu [37]. In agreement with the earlier obervation on autenitic tainle teel [36], the axial lattice train repone of the {2} grain family appear to exhibit the double inflection behaviour (blue curly bracket in Fig. 3a) compriing the three deformation tage of linear elatic loading, gradual tranition to platicity and a econd linear tage following complete yielding. In other general obervation related to Fig. 3a, the maller negative lattice train that develop in the radial direction (perpendicular to the load axi) are due to Poion effect. Additionally, the larger catter recorded for the {22} orientation i aociated with their mall volume fraction in the initial texture (refer to the IPF in Fig. 1c). The change in the lattice train of the variou grain familie in the axial direction a a function of the total macrocopic train for the firt three cycle i hown in Fig. 3b. Since the diffraction technique detect only change in the elatic lattice train, the meaured lattice train i necearily proportional to the um of the type I and type II tree on a particular grain family [19]. A uch, the 1

13 repreentation in Fig. 3b i alo an approximation of the load partitioning between the variou grain familie baed on axial direction data. While the {111} orientation are the firt to ceae accommodating elatic train, the {2} orientation exhibit the larget increae in elatic lattice train through all tenion and compreion half cycle (cf. Section 6.1). It i emphaied that the above approximation of the load partitioning between the variou grain familie doe not account for the lattice train in the radial direction. In thi regard, the radial lattice train are not traightforward to interpret ince they comprie grain familie with different plane normal parallel to the direction of loading [36] Reidual train The reidual lattice train meaured at zero macrocopic tre while unloading from each tenion and compreion half cycle are hown in Fig. 4a and b, repectively. It i recognied that the anelatic effect aociated with the early yielding during load reveral and the time relaxation effect during diffraction meaurement (cf. Fig. 2a) influence the lattice train meaurement at the zero unload point. However, the demarcation of the reidual train provide an etimate of the intergranular ource of back tre to the overall Bauchinger effect. In the following paragraph, the poitive and negative ign denote tenile (+) and compreive ( ) reidual train or tree. A een in Fig. 4a and b, the {2} grain family ha the highet axial tenile and compreive train after unloading from the tenion and compreion half cycle, repectively. Irrepective of the loading direction, thee reidual train tend to aturate after the third half cycle (at approximately +8 µε and 9 µε). The axial {111} grain family exhibit the mallet reidual train after unloading from both tenion and compreion half cycle 3. The {22} grain family develop limited compreive train (~12 µε) after unloading from the tenion half cycle but ha higher tenile train (~4 µε) upon unloading from the compreion half cycle. To erve a an example, the reidual tenile (+) train in the {22} family (Fig. 4b) after a compreion half cycle will promote early yielding in a ubequent tenion half cycle. On the other hand, the reidual train developed in the {2} and {311} grain familie follow the ign of the applied macrocopic tre uch that they do not ait in early yielding upon ubequent load reveral. The recorded reidual train need to be converted to tree in order to determine the exact contribution of intergranular tre to the oberved back tre. If radial data i ignored, an approximate etimation of the magnitude of intergranular tree can be obtained when the axial reidual train i converted to tre via the meaured diffraction elatic contant (Table 1). For 3 After unloading from the fourth compreion half cycle, the axial reidual train in Fig. 4b for the {111} grain family i compreive; which i oppoite to the trend een in the firt three cycle. Since additional data point were not acquired beyond the fourth compreion cycle, it i not poible to verify whether thi change in the ign of the reidual train will perit with further cycling or i aociated with data uncertainty. 11

14 example, the axial reidual train of the {22} grain family after unloading from compreion half cycle i ~+4 µε. Thi reult in an intergranular tre of ~+8 MPa that aid yielding upon ubequent tenion. Clearly, the effect of thi tre on the overall repone will be weighted by the volume fraction of the grain contributing to a correponding peak. 5. EPSC imulation Due to the load relaxation exhibited during the diffraction meaurement, the EPSC model wa fitted to the tre train time averaged value over the period of data collection (hown a olid blue dot in Fig. 5a). The iotropic and kinematic hardening parameter were adjuted until optimal correpondence with the experimental macrocopic tre train wa achieved. The parameter utilied in the preent imulation are lited in Table 2. It hould be noted that ince the ample had a round cro ection, the poition of the rolling normal (ND) and tranvere (TD) direction (contained in the ection) i unknown. Conequently, while the experimental neutron data comprie one et of radial train, the EPSC reult perpendicular to the load axi are given in the two orthogonal direction that correpond to the cold rolling ND and TD and bound all radial direction. The difference between the ND and TD prediction give alo an indication of the enitivity of the radial lattice train to the exact population of the grain probed in the radial direction The elatic regime The EPSC imulated bulk elatic modulu correpond very well with the meaured macrocopic value (Table 1). The predicted axial and radial (given in two orthogonal direction, E ND and E TD) elatic moduli of the variou grain familie are alo lited in Table 1. The model i generally in good agreement with the experimental diffraction elatic contant. However, dicrepancie were found for the {111} grain family uch that more compliant (lower) and tiffer (higher) value were predicted in the axial and radial direction, repectively. Thi diparity can be attributed to the imprecie knowledge of the ingle crytal elatic contant. For all grain familie, the difference between the two orthogonal elatic moduli E ND and E TD i le than 5%; with the exception of the {22} orientation which returned a 13% difference (cf. Fig. 6d). In 39 tainle teel, Pang et al. [38] reported a 3% difference in the lope of the {22} orientation between the tranvere and the normal direction. Oliver et al. [39] demontrated that the elatic repone of the tranvere {11} grain family in aniotropic cubic crytal i very uceptible to crytallographic texture a it i controlled by the grain orientation perpendicular to it (i.e. along the axial loading direction). Thee grain comprie orientation ditributed between 1 and 11 direction. Grain cloe to 1 are more uceptible to contraction while thoe cloe to 11 are 12

15 more prone to expanion. Therefore, the reultant repone will be dictated by the exact ditribution of the orientation along the load axi which make up the radial {11} grain family The platic regime The EPSC imulated macrocopic tre train behaviour i in very good agreement with the bulk experimental data a hown in Fig. 5a. The experimental flow curve i plotted a a dahed line while the olid dot are the time averaged tre and train value during the collection of the diffraction pattern. The EPSC prediction cloely follow the experimental hyterei loop uch that the modelled macrocopic flow tre alo tend to aturate with further cycling. The gradual elato platic tranition upon load reveral i generally well captured. In agreement with the experimental evidence, the EPSC model predict the oberved tenion compreion aymmetry (Fig. 5b) with higher maximum tree during compreion half cycle (ee Section 6.4). The difference between the combined iotropic and kinematic hardening law and the original ingle iotropic hardening law 4 [22] i hown in Fig. 5c. An EPSC imulation performed uing only the latter approach predict a harper elato platic tranition and only a light Bauchinger effect. The poor agreement of the EPSC imulation with the experimental data upon load reveral i becaue the original EPSC formulation only capture the effect of the intergranular tre and not the intragranular tre. The lattice train prediction from the EPSC model are hown in Fig. 6 and 7. The lattice train of the variou grain familie during the firt tenion half cycle are given in Fig. 6. The model reaonably capture the hape, magnitude and width of the lattice train hyterei loop of the variou grain familie during the firt three cycle in both the axial and radial direction (Fig. 7). Conidering that the elatic effect in autenitic teel are dictated by the evolution of the internal train at low train level (~<2%) [4] and that there i uncertainty in the value of the ingle crytal elatic contant of the preent TWIP teel, the EPSC model till return atifactory lattice train prediction for the firt tenion half cycle (Fig. 6). For example, in pite of the dicrepancie between the meaured and imulated diffraction elatic contant for the {111} orientation (Table 1), better correpondence between the experimental and imulated lattice train i obtained beyond 15 MPa in both the axial and radial direction (Fig. 6a and b). Here the effect of the above dicrepancy i highlighted by the mall deviation in the lope of the radial {111} hyterei loop (Fig. 7a). The evolution of the lattice train of the {311} grain family i very well captured throughout the loading cycle in both the axial and radial direction a een in Fig. 6a, b, and 7d. 4 The Voce parameter (in MPa) ued with the ingle iotropic hardening law (Eq. (4)) are τ = 85, τ 1,for = 2, θ,for = 1, θ 1,for = 1 for lip ytem and τ = 15, τ 1,for = 2, θ,for = 1, θ 1,for = 1 for twinning ytem. 13

16 A a further point of difference between the EPSC imulation and the experimental data, the prediction of the lattice train for the {2} orientation how greater diparitie in both the axial and radial direction (Fig. 6c and d). In the axial direction, the EPSC model predict three inflection with four tage (indicated by arrow in Fig. 6c) rather than the two inflection repone een in Fig. 3a. The third inflection and the ubequent fourth tage i accompanied by a ignificant overetimate of the predicted axial train for the {2} grain family. Thi deviation could be attributed to the greater influence of load relaxation on compliant orientation uch a {2}. Another diparity in the EPSC model prediction i noted for the {22} grain family in the axial direction (Fig. 6c and 7c). Slight under prediction of the axial lattice train i een in Fig. 6c along with a leftward hift in the lattice train hyterei loop (Fig. 7c). Here the imulated loop are of the correct width but are hifted toward lower lattice train value uch that under and over prediction are obtained for the tenion and compreion half cycle, repectively. In the EPSC imulated lattice train, the hift i lightly le during the tenion half cycle than the compreion half cycle. 6. Dicuion 6.1. Diffraction elatic contant, lattice train and reidual lattice train Fe Mn Al Si TWIP teel tend to have lower C 11 and C 12 value (cf. Section 3) compared to Fe Cr Ni autenitic tainle teel (C 11 = GPa and C 12 = GPa) [41, 42]. Thi difference i attributed to the o called magneto volume effect; i.e. the coupling of the magnetic energy to the elatic energy of a material [43]. Both Mn and Al have a lattice oftening effect due to the trong dependence of local magnetic moment on the lattice parameter (or volume) [43]. While uch an effect i le pronounced in hear type elatic contant (C 44 and ½(C 11 C 12)), it i more prominent in dilation type elatic contant (C 11 and C 12) [44]. The lattice oftening effect i aociated with a ignificant elatic aniotropy (A) uch that the preent TWIP teel returned a value of 5.2; which i ignificantly higher than the average A value of for autenitic tainle teel [41, 42]. Accordingly, the difference in the meaured elatic contant between the tiffet {111} and mot compliant {2} orientation i ~9% (Table 1) a oppoed to the lower value of 6 68% reported previouly for autenitic tainle teel [36, 38]. While the elatic aniotropy dictate the evolution of lattice train in the elatic regime, their evolution in the elatic platic tranition region i governed by a combination of the elatic and platic aniotropy of the material. Here grain with a high directional trength to tiffne ratio will yield later than grain with a low directional trength to tiffne ratio leading to higher lattice train in the former grain [37]. Defining (i) the directional trength of a particular crytallographic orientation or fibre a the Taylor factor calculated in the fully developed platicity regime, and (ii) the directional tiffne a the elatic modulu of that fibre in the elatic regime, Wong and Dawon [37] 14

17 demontrated that for fcc polycrytal with high elatic aniotropy (A 2), the {2} and {111} grain have the highet and lowet directional trength to tiffne ratio, repectively. It follow that the {111} grain are the firt to yield wherea the {2} grain yield lat. Conequently, ince the {111} grain family yield firt, it will exhibit an increae in lope becaue they no longer accumulate elatic train at the ame rate; a ome of their total train i now platic train. Alternatively, the {2} grain that tay elatic the longet record the larget increae in elatic lattice train and exhibit a decreae in lope a they have to carry the load hed by the other yielding grain. Thereafter, in the platic regime the lattice train of variou grain familie tend to aturate (with mall incremental change compared to the elatic regime, ee alo Fig. 3b), uch that the relative trend developed during the elatic platic tranition region perit with further training. A hown in Fig. 4a and b, the reidual lattice train in the {2} grain family tend to aturate after the third tenion/compreion half cycle. Pang et al. [38] made a imilar obervation during the multiple tenion loading unloading of autenitic tainle teel. In that tudy, relatively large reidual axial train (~+6 µε) were found in the {2} grain family after the firt tenion loading unloading cycle at ~2% train. Thereafter, only mall increae were detected upon multiple tenion loadingunloading uch that a final reidual train of ~+8 µε wa reached after unloading at 7.2% train. The near plateauing of reidual train value wa acribed to the aturation of elaticity uch that the ubequent evolution of lattice train i controlled by platic deformation The modified EPSC model prediction Since the modified EPSC model atifactorily capture the baic experimental feature, it emphaie the adequacy of the hardening decription via the combined iotropic kinematic law. Thu the EPSC model can be ued to gain further inight into the underlying deformation mechanim. The relative lip/twinning activitie a a function of total macrocopic train (up to the maximum load point of the third compreion half cycle) are hown in Fig. 8a. Note that the overlap between the tenion (T) and compreion (C) line at the top of Fig. 8a i due to the decreae and ubequent increae in total macrocopic train during unloading and loading. The EPSC model return higher twinning activity during the tenion half cycle and very limited twinning during the compreion half cycle. Thi i acribed to the directionality of twinning and Schmid factor conideration wherein not all the twinning ytem activated during tenion are activated during compreion [45]. Decreaing twinning activity i alo predicted upon multiple cycling. A imilar experimental obervation wa reported in ferritic tainle teel where twinning activity wa found to reduce after a few cycle [46]. The model attribute uch behaviour to the increaing lip ytem activity with greater accumulated train. Since the oppoite ytem of thoe newly activated lip ytem get ofter, they are eaier to activate upon load reveral than activating new twinning ytem. Only ~8% twin volume fraction i predicted at the end of the ixth cycle; which correpond to ~18% total macrocopic train (Fig. 8b). 15

18 Thi i in agreement with the limited twinning (no value given) oberved after cyclic fatigue experiment on TWIP teel [47]. The above limited twin volume fraction i alo cloe to our Vico Platic Self Conitent model prediction of ~6% (at 18% tenile train) following the imulation of the monotonic tenile loading of the ame TWIP teel [32]. A final remark on Fig. 8a i that the lip ytem remain active during unloading indicating that no real elatic unloading occur. Thi utained deformation ytem activity can be acribed to two factor: (i) the incorporation of a back tre in the modified EPSC model which activate lip very early on during unloading and/or, (ii) the tre relaxation effect of the twinning cheme [29]. In order to further examine thee factor, a imulation wa performed by treating twinning a a directional lip mechanim 5 uch that the tre relaxation effect of the twinning cheme i uppreed. While the imulation reult are not hown here, two main difference between the above directional lip approach and the twinning cheme of thi tudy are noted: (i) in the directional lip cae, an interval with zero deformation ytem activity i predicted during unloading and, (ii) the twinning cheme imulation follow the experimental macrocopic tre train curve more cloely than the directional lip cae during unloading. It follow that the utained deformation ytem activity i more attributable to the tre relaxation effect of the twinning cheme and the aociated back tre that i enforced upon twin creation The Bauchinger effect While the calculation of the R value following the Cottrell cheme (Eq. (1)) i baed on the deviation from elaticity upon unloading, an alternative approach calculate the R value at a particular offet revere train (for example, at.1 or.2%). Bouaziz et al. [2] ued an offet revere train of.2% to evaluate the back tre contribution during the revere hear teting of Fe 22Mn.6C TWIP teel. Gutierrez Urrutia et al. [48] applied the ame approach to compare their reult in an analogou experiment. Although the offet revere train method i very enitive to the value of the choen revere train [49], applying a.2% offet revere train to the current reult returned a back tre contribution which wa ~2% of the maximum tre at the end of the firt tenion half cycle. Alternatively, if the reult in [2, 48] are extrapolated to the train level employed in the preent work, a lower back tre contribution of ~1% i deduced. The Bauchinger effect oberved in [2] wa attributed to the high back tre generated by the dilocation pile up at twin boundarie. Accordingly, Gil Sevillano [4] uggeted a compoite type deformation pattern uch that back tree proliferate a the thin twin lamellae reinforce the parent autenite matrix. For the firt tenion half cycle, the low train limit (1%) implie limited twinning. 5 Thi approach follow the treatment of twinning in the original EPSC model uch that while a twin ytem require a CRSS to be activated, it i only operative in one direction. 16

19 Hence twinning alone cannot be reponible for the rather pronounced Bauchinger effect oberved upon load reveral. Moreover, the magnitude of the intergranular tree i inufficient to account for the large oberved back tre a verified by the failure of the original EPSC model (which only capture intergranular tre) to predict the macrocopic flow tre upon load reveral (Section 4.3 and Fig. 5c). Conequently, other intragranular ource of back tre hould be preent in the matrix. The above tatement i upported by TEM invetigation conducted at the early tage of deformation. During the monotonic tenile loading of Fe 3Mn 3Al 3Si TWIP teel, deformation wa dominated by tacking fault and dilocation array at.19% train [5]. Thereafter, limited deformation twinning wa oberved at 3% train along with predominant planar and wavy dilocation. Planar dilocation tructure compriing pile up and tacking fault are alo the characteritic feature in 316L autenitic tainle teel at tenile train <1.5% [51]. During the uniaxial cyclic loading (between ±.4% train) of low tacking fault energy Co bae uperalloy, TEM obervation revealed extenive tacking fault and tacking fault interection at the end of the third cycle [52]. Rajan and Vanderande [53] pointed out that the tacking fault interection can act a effective barrier to dilocation motion in low tacking fault energy material a dilocation pile up were detected at thee interection. Accordingly, tacking fault interection were uggeted a a major ource of the back tree encountered in low tacking fault energy ingle phae alloy [54]. A imilar rationale can be applied to the pronounced Bauchinger effect in the current TWIP teel. An additional ource of the back tre aociated with low tacking fault energy material i the energy torage from the tre induced eparation of partial dilocation [13]. It i argued that while partial dilocation are pulled apart during forward loading, they tend to retore their equilibrium eparation ditance upon unloading. In turn, the tored energy releae and the change in lip direction during load reveral can both contribute to the train relaxation effect (ee the anelatic repone during unloading in Fig. 2a) Tenion compreion aymmetry A een in Fig. 2a, b and reported previouly during the cyclic deformation of Cu [55], Cu Al [56] and Cu Zn alloy [57], aymmetry in the flow tre between tenion and compreion exit regardle of the initial loading direction. Although a definitive explanation for the exitence of tenion compreion aymmetry i till lacking in the literature, the phenomenon i expected in material that deform by twinning due to their inherently lower yield tre in uniaxial tenion compared to compreion [58]. Uing Bihop and Hill type analyi, Hoford and Allen [58] concluded that the yield tre hould be 28% higher in compreion compared to tenion for randomly oriented fcc polycrytal. Chin et al. [59] returned a 25% difference between compreion and tenion uing Taylor type analyi. 17