effect of phase contiguity and morphology on the evolution of...

Effect of Phase Contiguity and Morphology on theEvolution of Deformation Texture in Two-PhaseAlloys

N.P. GURAO and SATYAM SUWAS

Deformation texture evolution in two-phase xFe-yNi-(100-x-y)Cr model alloys andTi-13Nb-13Zr alloy was studied during rolling to develop an understanding of micro-mech-anisms of deformation in industrially relevant two-phase FCC-BCC steels and HCP-BCCtitanium alloys, respectively. It was found that volume fraction and contiguity of phases lead tosystematic changes in texture, while morphology affects the strength of texture. There was acharacteristic change in texture from typical Brass-type to a weaker Copper-type texture in theaustenite phase accompanied with a change from alpha fiber to gamma fiber in ferrite phase forFe-Ni-Cr alloys with increase in fraction of harder ferrite phase. However, similar characteristictexture evolution was noted in both a and b phase irrespective of the different initialmorphologies in Ti-13Nb-13Zr alloy. Viscoplastic self-consistent simulations with two-phasescheme were able to qualitatively predict texture evolution in individual phases. It is proposedthat the transition from iso-strain-type behavior for equiaxed microstructure at low strain toiso-stress-type behavior at higher strain is aided by the presence of higher volume fraction of thesecond phase and increasing aspect ratio of individual phases in two-phase alloys.

DOI: 10.1007/s11661-016-3856-1� The Minerals, Metals & Materials Society and ASM International 2016

I. INTRODUCTION

MANY engineering alloys like steels, alloys ofaluminum, titanium, and zirconium consist of twoconstituent phases with distinct mechanical and physicalproperties. It is assumed that the response of two-phasematerials to an external stimulus will be an average ofthe constituent phases. This is, however, not the caseand in addition to the properties of individual phases,the response of two-phase materials depends on volumefraction, morphological and crystallographic orienta-tion as well as contiguity of individual phases. Theevolution of texture and microstructure during process-ing of two-phase alloys is of paramount importance indetermining the in-service performance of various com-ponents.[1-5] This aspect is particularly important fortwo-phase alloys due to the inherent complexitiesinvolved in the deformation of two-phase materialswherein the properties of individual phases interact todecide the overall behavior. Two-phase alloys can beclassified into various types depending on the amountand type of the constituent phases.[4] The variouspossible combinations are an interpenetrating hard/duc-tile phase or a matrix and inclusion-type microstructure.In addition, in-situ composites like Cu-Ag. Cu-Nb alloys

with a ductile eutectic phase and multi-layers of differentpure metals and alloys at the nano-length scale consti-tute special cases of two-phase systems that have beeninvestigated in great detail.[6,7]

The mechanism of plastic deformation in two-phasecomposites is complicated due to the interactionbetween the two phases. As a general rule, in thepresence of a hard and soft phase, it is expected that thesofter phase carries more strain, while the harder onetakes more stress. Therefore, it may be rationalized thatthe evolution of deformation texture in the softer phaseis accelerated, while that in the harder phase is retardedat a given macroscopic strain compared to the sin-gle-phase counterparts. However, the above hypothesispresents an oversimplified scenario during the deforma-tion of two phases and various other microstructuralparameters like contiguity, shape, and size as well ascrystallographic relationship between the phases influ-ence the texture evolution in the individual phases. Theelasto-plastic behavior of such systems has been stud-ied,[2-5] but the large strain plastic deformation hasreceived little attention. Most of the studies havefocused on conventional alloys like dual phase mostlyferrite-martensite steels[8-10] and Ti alloys[11-14] as thesesystems have tremendous industrial applications.Various investigations[15-26] have employed character-

ization tools like X-ray, neutron, synchrotron, andelectron backscatter diffraction (EBSD) to study textureand microstructure evolution in the individual phases oftwo-phase materials. Finite element methods andself-consistent simulations[8,13-19] have been used toelucidate the deformation behavior of these materials.Lebensohn et al.[16] modeled the rolling texture

N.P. GURAO, Assistant Professor, is with the Department ofMaterials Science and Engineering, Indian Institute of TechnologyKanpur, Kanpur 208 016, India. Contact e-mail: [email protected] SUWAS, Professor, is with the Department of MaterialsEngineering, Indian Institute of Science, Bangalore 560 012, India.

Manuscript submitted July 10, 2016.Article published online November 4, 2016

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 48A, FEBRUARY 2017—809

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evolution in two-phase (a+ b) titanium alloys using a2-site VPSC formulation that consisted of solving a twoinclusion problems as against a single inclusion problemfor 1-site VPSC simulations. Titanium (a+ b) alloys arethe classical examples of correlated microstructures witha specific crystallographic orientation relationshipbetween a and b phase and the effect of morphologyof individual phases still remain unexplored.

In addition, recent investigations have focused onstudying deformation of two ductile phases from afundamental point of view to study slip transfer andcoupling of microstructure and texture evolution inindividual phases of multi-layers of pure metals at thenano-length scale and in-situ nano-composites.[6,7,27-36]

Novel findings like extensive slip and twin transfer,non-crystallographic shear banding, interface amor-phous phase formation as well as co-rotation have beenfound to be relevant in these materials. Thus, techno-logical necessity and a desire to develop fundamentalunderstanding have led to many studies at the extremelength scales. However, fundamental understanding ofmicro-mechanisms of deformation as developed formulti-layers is still missing for bulk two-phase systems.The effect of contiguity and morphology of individualphases on deformation microstructure and textureevolution has received less attention till date. This isparticularly important for two-phase steels and alu-minum alloys wherein the volume fraction and contigu-ity of individual phase play an important role indetermining the overall response of the alloy. Similarly,the morphology of the alpha and beta phase plays animportant role in titanium alloys with engineeringapplications. The present investigation aims to explorexFe-yNi-(100-x-y)Cr alloys and Ti-13Nb-13Zr as modelsystems to study the effect of contiguity and morphologyof the second phase, respectively using electronbackscatter and X-ray diffraction as well as crystalplasticity simulations.

II. EXPERIMENTAL

A. Materials and Processing

Four compositions of Fe-Ni-Cr alloys (Table I) weremelted using a vacuum arc furnace. Different volumefractions of BCC ferrite phase were obtained in the FCCaustenite matrix by varying the content of austenitestabilizer Ni and ferrite stabilizer Cr. The cast structureof the alloys was broken by hot forging at 1373 K(1100 �C) to 50 pct reduction in thickness. The so-ob-tained wrought alloys were subjected to long-termannealing as described in Table I to obtain equiaxedmicrostructures. The composition of the alloys ensureddifferent kinds of microstructures from inclusion-type tointerpenetrating network-type in addition to differentvolume fractions of the harder ferrite phase in the softaustenite matrix. Ti-13Nb-13Zr alloy was prepared byvacuum arc melting. The cast material was hot-rolled at1173 K (900 �C) in the b phase field to break the as-castmicrostructure. Following this, two distinct thermo-me-chanical treatments were carried out to obtain two

different morphologies: (a) annealing in the b field at1173 K (900 �C) to obtain a colony microstructure and(b) cold rolling to 50 pct reduction at room temperaturefollowed with annealing at 938 K (665 �C) for 24 hoursto obtain an equiaxed microstructure of a and b phase.Samples with dimensions 15 9 10 9 5 mm were

machined from the heat-treated materials and subjectedto cold rolling using a Buhler laboratory-scale twohigh-rolling mills to a final 90 pct reduction (e = 2.3)for xFe-yNi-(100-x-y)Cr alloys, while a reduction of50 pct (e = 0.69) and 65 pct (e = 1.0) for colony andequiaxed microstructures of Ti-13Nb-13Zr alloy, respec-tively. It is to be mentioned here that Ti-13Nb-13Zrsamples showed extensive edge cracking beyond afore-mentioned reduction even for deformation in steps of5 pct rolling reduction per pass.

B. X-Ray and Electron Back Scatter Diffraction

Bulk texture measurement using Schulz reflectiongeometry was carried out using Bruker D8 Discoverdiffractometer using Co Ka radiation. Incomplete (111),(200), (220), and (113) pole figures of austenite andincomplete (110), (200), and (112) pole figures of ferritewere measured. Similarly incomplete (0002), ð10�10Þ,ð10�11Þ, ð10�12Þ, ð10�13Þ, ð10�20Þ, and ð10�22Þ pole fig-ures were measured for the HCP a phase and (200) and(112) incomplete pole figures were measured for theBCC b phase in Ti-13Nb-13Zr alloy. Sufficient care wastaken to avoid overlapping of peaks during individualpole figure measurement by using a narrow slit andpoint detector. A detailed analysis of texture wasperformed by calculating the three-dimensional Orien-tation Distribution Function (ODF) from the experi-mental incomplete pole figures by commerciallyavailable LaboTex software using the Arbitrary DefinedCells algorithm.[37] Microstructural characterization wascarried out using a Field Emission Gun ScanningElectron Microscope (FEG-SEM) Sirion equipped withTSL-OIM Electron Backscatter Diffraction (EBSD)system. TSL-OIM software version 5.2 was used fordata acquisition and analysis. Different step sizes wereused to capture the microstructural details of thedeformed samples. It is to be mentioned here that allX-ray investigations were carried out at the midthickness of the ND plane, while EBSD was carriedout on the center of the TD plane of the rolled samples.

III. VISCOPLASTIC SELF-CONSISTENTSIMULATIONS

Crystal plasticity simulations were carried out usingthe VPSC-7 package including the two-phase sub-rou-tine. The VPSC model is described in detail in Reference38 and the Predominant Twin Reorientation (PTR)scheme is elaborated in Reference 39. For two-phasematerials, a two-site viscoplastic self-consistent modelthat is an extension of Eshelby problem to two inter-acting ellipsoidal inclusions was employed.[40] Thetwo-phase model calculates one-site Eshelby tensors

810—VOLUME 48A, FEBRUARY 2017 METALLURGICAL AND MATERIALS TRANSACTIONS A

for the individual phases as well as two-site Eshelbytensor for each phase that acts as coupling factorsbetween the eigenstrain in one inclusion and localdeviation in strain of other phase. Consider twoinclusions (#1 and #2) with eigenstrains e1� and e2�,respectively, embedded in a matrix subjected to macro-scopic stress–strain state ðR;EÞ. The microscopicstress–strain state in both the inclusions will be differentand can be given by (r1, e1) and (r2, e2). The stress andstrain deviations are as follows:

~r1 ¼ r1 � R ½i�

~r2 ¼ r2 � R ½ii�

~e1 ¼ e1 � E ½iii�

~e2 ¼ e2 � E ½iv�

and the Eshelby relations are

~e1 ¼ S11e1� þ S12e2� ½v�

~e2 ¼ S21e1� þ S22e2� ½vi�

where S11 and S22 are ordinary Eshelby tensors forinclusions #1 and #2, respectively, and depend on theproperties of the homogeneous medium and shape ofellipsoid. S12 and S21 represent two-site Eshelby’stensors that act as coupling factors between eigenstrainof one inclusion and local deviation in strain of the otherinclusion. The two-phase scheme developed above isthen incorporated in conventional viscoplastic self-con-sistent model. The two-site model can incorporate thevolume fraction and morphology of the individualphases as well as crystallographic relationship betweenthe two phases. The measured bulk texture was dis-cretized to obtain 2000 single orientations for individualphases that were used as input to the model. An aspectratio of one was used for both the phases as themicrostructures showed equiaxed grains for both thephases in all four alloys. An intermediate affine-basedlinearization procedure that gives a response betweenthe iso-stress and iso-strain that constitute the lower andupper bounds was adopted to carry out the simulations.

A similar approach was followed for Ti-13Nb-13Zr,albeit with different aspect ratios of the individual phaseas well as two different morphological orientations wereconsidered in the simulations. In addition, it was found

that the best match of texture was obtained by adoptingthe neff = 10 approximation in VPSC-7 code. Thus, thefollowing three sets of simulations were carried out onTi-13Nb-13Zr alloy:

(i) Aspect ratio and no morphological orientation(ishape = 2, where ishape is the grain mor-phology index used in VPSC simulation tocalculate the Eshelby’s tensor. If ishape = 2,individual grain ellipsoids are used to calculateEshelby’s tensor).

(ii) Aspect ratio and similar morphological orien-tation of both the phases, ishape = 4 (initialgrain ellipsoid information is read from a fileand used to calculate Eshelby’s tensor).

(iii) Aspect ratio and different morphological ori-entations of individual phases, ishape = 4

Different morphological orientations were obtainedby generating random Euler angles to mimic randomorientation of grains in the actual microstructure. Sameset of Euler angles was used for both the phases inscheme (ii), while different sets of Euler angles were usedfor the two phases for scheme (iii).

IV. RESULTS

A. Microstructural Features of the Starting Materials

1. Fe-Ni-Cr alloysThe optical micrographs of the starting materials for

the four different Fe-Ni-Cr alloys are shown inFigure 1(a). The single-phase austenite alloy I is char-acterized by an equiaxed microstructure with numerousrecrystallization twins, a common feature in annealedlow stacking fault energy (SFE) FCC metals and alloys.The microstructures of the remaining three alloys namedas alloys II, III, and IV consists of two phases with 15,35, and 65 pct of the ferrite (dark phase) and balanceaustenite phase, respectively. The austenite phase inthese alloys exhibits recrystallization twins, while theferrite phase is devoid of twins. In addition to thedifferent volume fractions, microstructures of the alloysII, III, and IV represent (i) matrix/inclusion, (ii) perco-lating microstructure, and (iii) inclusion/matrix-typemorphology. Thus, the three alloys correspond tosub-critical, critical, and super-critical percolating sys-tem for the ferrite phase. The initial texture of theaustenite (c) and ferrite (a) phases in the startingmaterial indicates the presence of Kurdjumov–Sachs

Table I. Chemical Composition of the Four Different Fe-Ni-Cr Alloys

Alloy Ni (Wt Pct) Cr (Wt Pct) Fe (Wt Pct) Ferrite (Pct) Heat Treatment

I 17 21 62 0 1293 K (1020 �C) for 2 hII 15 23 62 15 1398 K (1125 �C) for 12 hIII 14 24 62 35 1448 K (1175 �C) for 5 hIV 10 28 62 65 1343 K (1070 �C) for 12 h

The respective ferrite volume fraction and the heat treatment followed are also presented.


orientation relationship[41] wherein f111gc k f101gaandh101ic k h111ia (Figure 2(a)).

2. Ti-13Nb-13Zr alloyThe microstructure of the Ti-13Nb-13Zr alloy in two

morphologies is shown in Figure 1(b). The material inthe b worked, cold-worked and recrystallized conditionexhibited equiaxed morphology for both a and b phases.The microstructure after b working and air cooling ischaracterized by a-lath structure in the b matrix. Thevolume fraction of a and b phases in the equiaxedmicrostructure as determined by EBSD was 60 and

40 pct, while that in colony microstructure was 80 and20 pct, respectively. The pole figures of the two phasesindicate the presence of f101gb k f0002ga and

h111ib k h11�20ia Burgers orientation relationship[42] for

Ti-13Nb-13Zr alloy (Figure 2(b)).

B. Evolution of Deformation Texture

1. The FCC-BCC case: effect of volume fraction andcontiguityThe (111) pole figures of Fe-Ni-Cr alloys deformed to

the strain level e = 2.3 are shown in Figure 3(a). The

(a)

(b)

100 µm

100 µm 50 µm

50 µm

I II

III IV

Fig. 1—(a) Optical micrographs for the starting material of Fe-Ni-Cr alloys and (b) SEM micrograph of equiaxed Ti-13Nb-13Zr sample (left)and image quality map of Ti-13Nb-13Zr sample with colony morphology (right).


pole figure of alloy I displayed a typical Brass-typetexture, as exhibited by low SFE FCC materials. Similarevolution of texture was observed in the austenite phaseof the other three alloys showing decrease in the textureintensity with increase in ferrite content. The u2 sectionsof the ODF for the samples rolled to the strain levele = 2.3 (Figure 3(b)) corroborated the above observa-tion. The volume fraction of important FCC rollingtexture components[1] like Bs f1�10g 112h i, Cuf11�2g 111h i, and S f12�3g 634h i reduced as the ferritecontent increased. However, a direct comparison oftexture by considering the volume fraction of differentdeformation texture components is not likely to givecomplete information about the texture evolution in thepresence of varying fraction of individual phases.Therefore, the ratio of volume fractions of the individ-ual texture component was obtained (Figure 3(c)) at 50

and 90 pct rolling reduction. The Cu/Bs ratio reducedcontinuously along with Cu/S and S/Bs ratios withincrease in ferrite content. Therefore, it can be inferredthat there was an increase in the Cu component followedby the S component at the expense of the Bs componentwith increase in ferrite content.The (101) pole figures (Figure 4(a)) for the ferrite

phase of the three alloys showed a typical BCC rollingtexture that strengthened with increase in the ferritecontent. The u2 sections of the ODF for the ferrite phaseof the two-phase samples rolled to the strain levele = 2.3 are shown in Figure 4(b). The important rollingtexture components and fibers in BCC metals andalloys, namely, the a fiber ranging from {001}h110i tof1�11g 110h iand the c fiber ranging from f1�11g 110h i tof1�11g 112h i are clearly seen in the ODF section. A closerlook of the ODF u2 = 45 deg section showed the

(a)

(b)

I II III IV

111 FCC

101 BCC

RD

TD

RD

TD

RD

TD

RD

TD

RD

TD

RD

TD

RD

TD

Fig. 2—(a) Initial texture in terms of (111) pole figure of the austenite phase and (101) pole figure of the ferrite phase for the starting material ofFe-Ni-Cr alloys and (b) initial texture in terms of (0002) pole figure of the a phase and (101) pole figure of the b phase for the starting materialof Ti-13Nb-13Zr alloy.


discontinuous nature of the a fiber with higher intensityat orientations close to the {001}h110i component foralloy IV.

2. The HCP-BCC case: effect of morphologyFigure 5 shows the (0002) pole figures of the

deformed samples depicting RD split 0002 pole figure for

equiaxed morphology, while a TD split 0002 polefigure was observed for colony microstructure ofTi-13Nb-13Zr alloy. The ODF sections (Figure 6(a))of the sample with equiaxed morphology showed thepresence of characteristic deformation texture compo-nents like the B 0001f g 10�10

� �tilted from ND toward

TD component (u1 = 0, F = 40, u2 = 0) deg and the

(a)

Alloy IIAlloy I

Alloy IVAlloy III

RD

TD

RD

TD

RD

TD

RD

TD

(b)

Alloy I Alloy II

Alloy III Alloy IV

1=0-90

=0-90Bs

Cu

S

Fig. 3—(a) 111 pole figure and (b) u2 ODF sections of the austenite phase in the Fe-Ni-Cr samples deformed to strain e = 2.3 and (c) ratio ofvolume fraction of important deformation texture components in rolled Fe-Ni-Cr alloy in austenite phase.


E component 0001f g 11�20� �

tilted from ND toward TD(u1 = 0, F = 40, u2 = 30) deg. There is no character-istic change in deformation texture of a phase for boththe morphologies; however, the deformation texture ofcolony morphology becomes stronger with strain, whilethat for equiaxed weakens at higher strain.

The (101) pole figures for the b phase of the deformedsamples corresponding to two morphologies of theTi-13Nb-13Zr alloy are shown in Figure 5. A charac-teristic rolling texture of BCC metals and alloys is seenin both the cases. The u2 = 45 deg section of the ODF(Figure 6(b)) was plotted to get a clearer idea of thetexture evolution. The rolling texture of b phase wascharacterized by the presence of a and c fibers. Therewas an initial increase in the strength of overall texturewith deformation that gradually reduced at the higheststrain for both the morphologies.

C. Evolution of Microstructure and Micro-texture

1. The FCC-BCC caseThe representative Inverse Pole Figure (IPF) map for

the individual phases of the samples rolled to 50 pctreduction (strain e = 0.69) shows elongated grains forboth the phases (Figure 7(a)). The IPF map of thesingle-phase austenite alloy (alloy I) displayed extensivetwinning. A decrease in the fraction of the

twin-boundary fraction is observed with increase infraction of ferrite. The austenite phase in alloy I andferrite phase in alloy IV showed gradual conversion oflow-angle grain boundaries (LAGB) to high-angle grainboundaries (HAGB) with increase in strain, while theaustenite phase in alloy IV showed a monotonic increasein LAGB. The EBSD data also revealed that theintragranular misorientation analyzed in terms of theGrain Average Misorientation (GAM) increased withthe deformation for both the phases (Table II) till 50 pctrolling reduction and then decreased or saturated. Thedifference in GAM values between the two phasesreduced with increasing strain in a given alloy andsimilar observation was made for higher fraction offerrite phase at given strain. The austenite phase wascharacterized by deformation twinning which becameless dominant with increase in ferrite volume fraction inthe two-phase alloy systems. The Sigma 3 (60 degmisorientation about h111i axis) twin-boundary fractioncalculated from the EBSD maps clearly (Figure 7(b))show a decrease in twin fraction with increase in strainand ferrite volume fraction in Fe-Ni-Cr alloys.

2. The HCP-BCC caseThe morphology of both the phases was modified on

rolling. Elongated features are clearly seen in both themicrostructures (Figure 7(c)). Significant intragranular

(c)

Fig. 3—continued.


misorientation was observed in a phase of the equiaxedas well as colony microstructure. Strong intragranularmisorientation developed in the a and b phases for boththe initial microstructures. This was manifested in termsof the continuous increase in the GAM value withincrease in strain. The intragranular misorientation in bphase was higher for the colony sample, despite thelower volume fraction compared to the equiaxed

microstructure (Table III), while a phase showed higherGAM for equiaxed morphology.

D. Simulations

Texture results obtained from viscoplastic self-consis-tent simulations show a qualitative match with theexperimental findings. It is to be mentioned here that the

(b)

(a)

Alloy II Alloy III

Alloy IV

1=0-90

=0-90

{001}<110>{111}<112>{554}<225>{111}<110>{112}<110>

2.01.71.51.31.0

Fig. 4—(a) 101 pole figures and (b) u2 section of the ODF for the ferrite phase in the three different Fe-Ni-Cr alloys deformed to strain e = 2.3.


simulation results offer better insight into the operativemicro-mechanisms of deformation and are comparedwith experimental findings like twin fraction, to developconfidence. Detailed results of the simulations areenumerated below.

1. The FCC-BCC alloysThe simulated (111) pole figure of the austenite phase

and (101) pole figures of ferrite phase of the Fe-Ni-Cralloys with different austenite contents are presented inFigures 8(a) and (b). The simulated pole figures show aqualitative match with the experimental pole figures forboth the phases. The Voce hardening parameters of theaustenite and the ferrite phases used for modeling thedeformation texture are given in Table IV. Latenthardening coefficient of one was used for slip–slipinteraction, while that for slip–twin interaction, a valueof 0.9 was used. The pole figures indicated a decrease inBs component with the increase in ferrite phase.However, the simulated pole figures cannot be directlycompared with the experimental pole figures as there is adecrease in the overall intensity of the experimentaltexture due to X-ray fluorescence. The ratio of volumefraction of the deformation texture components is likelyto remain same, for the experimental texture andsimulated texture, provided the simulations are appro-priate. The simulated Cu/Bs ratio for all the four alloysclosely matched with the experiments (Figure 3(c)).Thus, there is a gradual deviation from the Brass-typetexture in low SFE austenite (alloy I) to Copper-typetexture due to the presence of harder ferrite phase.

2. The HCP-BCC alloySimulations were carried out by activating the pris-

matic, basal, and pyramidal slip system in the a phaseand the {110}h111i slip system in the b phase. For theequiaxed morphology, an aspect ratio of 1.0:1.0:1.0 wasused for both the phases, while for the colony morphol-ogy, an aspect ratio of 2.0:1.0:0.5 was used for a phase

and an aspect ratio of 2.0:1.0:0.05 was used for the bphase. Twinning was not incorporated as a deformationmechanism as the microstructural examination showedthat it was not dominant in this alloy. The Vocehardening parameters used for various slip systems in aphase and the b phase are given in Table V. Three sets ofsimulations were carried out by incorporating nomorphological information and including two sets ofmorphological orientation of the individual phases. Inone case, random orientations (u1 F u2) were generatedfor the 2000 orientations of individual phase andincorporated in the simulations. In the latter case, sameorientation (u1 F u2) was used for a pair of grainsbelonging to each phase and incorporated in thesimulations. The details of different schemes are givenin Table VI. Figures 8(c) and (d) shows the simulated(0002) a pole figures and the (101) b pole figures for therolled Ti-13Nb-13Zr alloy with equiaxed and colonymorphology for different schemes. The texture of aphase is qualitatively similar for all the three schemes forequiaxed and colony microstructure. The texture of bphase shows better prediction with the experimentaltexture once the morphology of the individual phase isconsidered. There is no significant difference betweenthe uncoupled and coupled morphology of both thephases as followed in scheme (ii) and (iii), respectively.However, results from scheme (ii) will be discussed inthe subsequent sections as initial texture showed anorientation relationship between the two phases. Areasonable match between the experimental texture andthe simulation results by incorporating aspect ratio aswell as morphological orientation of individual phasewas obtained for both the schemes.

V. DISCUSSION

The results of the present investigation indicate asignificant role of the second ductile phase on thedeformation behavior of two-phase Fe-Ni-Cr andTi-13Nb-13Zr alloys. The initial textures of the austeniteand ferrite phases in the starting material indicate thepresence of Kurdjumov–Sachs orientation relation-ship,[41] while Burgers relationship[42] is valid for a andb phases of Ti-13Nb-13Zr alloy. However, there is adeviation from the individual relationship with defor-mation and the orientation relationship is practicallynon-existent in the heavily rolled samples. Therefore, thetwo-phase alloys in the present investigation do notdeform by co-rotation of individual phases. Neverthe-less, elasto-plastic properties, volume fraction, contigu-ity, and morphological orientation of the individualphases play an important role in the evolution ofmicrostructure and texture by controlling strain parti-tioning in the individual phases and are discussed below.

A. Influence of Strain Partitioning on Two-PhaseDeformation

The evolution of crystallographic texture andmicrostructure of individual phases is directly linked tothe strain partitioning between the individual phases.

Equiaxed Colony

RD

TD

RD

TD

RD

TD

RD

TD

0002 HCP

101 BCC

Fig. 5—0002 pole figures for the a phase and 101 pole figures for theb phase of the Ti-13Nb-13Zr alloys in equiaxed and colony mor-phology at the highest strain of 1 and 0.69, respectively.


For both the alloy systems, the constituent phases havedifferent initial strengths; however, the extent of strainhardening is lower for the softer b phase inTi-13Nb-13Zr compared to softer austenite phase inxFe-yNi-(100-x-y)Cr alloys. Strain partitioning can beestimated from the evolution of intragranular misorien-tation in individual phases. Thus, the results of thepresent investigation indicate that the softer austenitephase carries most of the strain in xFe-yNi-(100-x-y)Cralloys at different strain levels, similar to softer b phase incolony Ti-13Nb-13Zr, while the harder a phase carriesmore strain in equiaxed morphology. During initialstages of deformation, the softer phase carries most ofthe strain and undergoes strain hardening and a stage isreached at high plastic strains that the strength of thesofter phase becomes comparable to that of harder

phase. This is manifested in terms of higher misorienta-tion development in the harder ferrite phase in xFe-y-Ni-(100-x-y)Cr alloys at higher strain and a phase inequiaxed Ti-13Nb-13Zr alloy. Thus, an iso-stress condi-tion is achieved in the moderately deformed two-phasemicrostructure which is manifested in terms of theso-called bamboo structure of elongated grains of boththe phases in rolling direction. Experimental observa-tions indicate that the alignment of both the phases isvery dominant for all the xFe-yNi-(100-x-y)Cr alloysand Ti-13Nb-13Zr alloy with equiaxed morphology. ForTi-13Nb-13Zr alloy with colony morphology, the align-ment is not complete which can explain the lack ofductility for this morphology. Thus, there is a deviationfrom general assumption of softer phase carrying morestrain and the real situation is closer to iso-stress

(a)

(b)

ColonyEquiaxed1=0-90

=0-90

φ2 = 45°

Colony1=0-90

=0-90Equiaxed

φ2 = 0°

φ2 = 30°

Fig. 6—ODF sections for (a) a and (b) b phase of the Ti-13Nb-13Zr alloys in equiaxed and colony morphology at the highest strain of 1 and0.69, respectively.


condition. Better understanding of such a phenomenonis obtained from crystal plasticity simulations which shedlight on the detailed consequence and reasons of strain

partitioning and are elaborated in the subsequent sec-tions for xFe-yNi-(100-x-y)Cr alloys and different mor-phologies of Ti-13Nb-13Zr.

(b)

(a)

(c)

Fig. 7—(a) Inverse pole figure map of austenite (left) and ferrite phase (right) for Fe-Ni-Cr alloys rolled to strain 2.3 with (b) twin fraction interms of R3 boundary fraction and (c) inverse pole figure map for equiaxed and colony Ti-13Nb-13Zr sample deformed to strain e = 1 and0.69, respectively.

Table II. Evolution of Intragranular Misorientation Parameter Grain Average Misorientation (GAM�) in Fe-Ni-Cr Alloys withDeformation in Austenite and Ferrite Phases

Alloy

e = 0.29 e = 0.69 e = 1.2 e = 2.3

Austenite Ferrite Austenite Ferrite Austenite Ferrite Austenite Ferrite

I 1.6 — 2.0 — 2.0 — 2.1 —II 2.0 1.7 2.5 2.4 2.0 2.0 2.1 1.9III 2.4 2.5 2.6 2.6 2.0 2.1 2.2 2.1IV 1.8 1.8 2.2 2.2 2.1 2.1 2.1 2.2


Table III. Evolution of Intragranular Misorientation Parameter Grain Average Misorientation (GAM�) in a and b Phases of

Ti-13Nb-13Zr with Different Morphologies

Morphology

e = 0 e = 0.29 e = 1.0

a b a b a b

Equiaxed 0.8 0.8 1.3 1.4 2.3 2.0

Colony

e = 0 e = 0.69 e = 0.69

a b a b a b

0.7 0.6 1.5 1.6 1.6 1.8

Fig. 8—(a) 111 pole figures of the austenite phase (b) 101 pole figures of the ferrite phase for the four Fe-Ni-Cr alloys deformed to straine = 2.3 and (c) 0002 pole figures of the a phase and (d) 101 pole figures of the b phase in two morphologies of the Ti-13Nb-13Zr alloy for dif-ferent simulation schemes.


B. Role of Volume Fraction and Contiguity

There is a characteristic change in texture fromBrass-type to Copper-type in the FCC austenite phaseof Fe-Ni-Cr alloy. The evolution of Brass-type texture inlow SFE FCC materials can be attributed to

deformation twinning, shear banding, and planarslip.[43-49] Leffers and Juul Jensen[50] have shown thatthere is limited slip on the {111} planes in grainsundergoing twinning. This is tantamount to iso-stressSachs model (single slip) unlike the iso-strain Taylor

Fig. 8—continued.


model (multiple slip) in grains without twins. Theinhomogeneous deformation can also lead to the for-mation of shear bands that can further contribute to Bscomponent. The formation of shear bands can erode thetwinned microstructure, thereby leading to the reductionin the fraction of the twin-boundary fraction asobserved in the present investigation. Nevertheless, asynergistic effect of twining by contributing to shearbanding or planar slip is expected to lead to Brass-typetexture in Fe-Ni-Cr alloy I. For the remaining alloys, thereduced propensity of twinning contributes to lower Bscomponent in the austenite phase.

A quantitative estimate of strain partitioning isobtained from simulations. There is an increase in thecontribution to strain from the ferrite phase with increasein ferrite content in the two-phase xFe-yNi-(100-x-y)Cralloys (Figure 9(a)) along with a qualitative matchbetween experimental and simulated twin activity(Figure 9(b)). In addition, the ferrite phase carries morestrain (Figure 9(c)) with increase in ferrite content but haslower number of average active slip systems than theaustenite phase irrespective of the volume fraction of theferrite phase. The continuous increase in the contributionto overall strain of theBCC ferrite phase indicates that theferrite phase accommodated deformation and carriedmore strain with increasing ferrite content. Once theferrite phase became contiguous, it carriedmajority of thestrain despite of the higher hardness and showed strongertexture while the austenite phase showed the weakesttexture despite showing a highly refined sub-structure.The grain reference orientation deviation map for alloy II

and III samples deformed to strain of 0.29 shows highermisorientation in the percolating austenite and ferritephases, respectively (Figure 10(a)). Propensity of twin-ning in the austenite phase is also compromised due toactivation of slip in the harder ferrite phase. The exactreasons for the reduced twin activity will be discussedlater. Thus, percolation plays an important role in strainpartitioning compared to initial hardness and initialtexture and determines the evolution of deformationmicrostructure and texture in two-phase ductile compos-ites. The sub-structure evolution and texture evolutionare decoupled for the non-contiguous soft austenitephase. A schematic depicting the effect of alpha phaseon the micro-mechanisms of deformation of austenitephase is depicted in Figure 10(b) andwill be discussed in alatter section.

C. Role of Morphology of Individual Phases

The effect of morphology on texture evolution inindividual phases is not very drastic in Ti-13Nb-13Zralloy compared to the effect of volume fraction of ferritephase in Fe-Ni-Cr alloys. Simulation results indicatethat during initial stages of deformation, the activity of{101}h111i slip system in the b phase is dominant, whilea phase is deformed by prismatic and basal slip(Figure 11(a)). There was negligible activity of pyrami-dal slip for both the morphologies. The activity of basalslip became dominant over the prismatic slip in a phaseduring further deformation. Thus, another importantobservation was that the deformation in the a phasecould be accommodated by the activation of onlyprismatic and basal slip systems without the activationof pyramidal slip system and extension or contractiontwinning which are essential to accommodate strainalong c-axis in HCP materials. The strain partitioningplot (Figure 11(b)) shows that the harder a phase carrieshigher strain at higher rolling reduction. This effect ismore dominant for the colony microstructure and thiscan explain the lower ductility in colony microstructurecompared to equiaxed microstructure. The number ofaverage active slip systems in the hard HCP phaseremains constant, while that in the BCC phase increaseswith strain (Figure 11(c)) indicating that the imposedstrain is accommodated mostly in the softer phase. It isto be mentioned here that the extent of reorientation ofboth the phases during rolling is significantly differentwith the equiaxed morphology showing all the elongatedgrains aligned along rolling direction. However, this isnot true for the colony morphology which leads todeviation from iso-stress condition that is observed forbamboo microstructure as shown in Figure 12.

D. Effect of Second Phase on Micro-mechanisms ofDeformation

Experimental results clearly indicate that there is achange in operating micro-mechanisms in individualphase due to the presence of the other phase. The moststriking is the reduction in twin activity in austenitephase of Fe-Ni-Cr alloys as well as the absence ofextension twinning in a phase and increase in basal slip

Table V. Voce Hardening Parameters for Simulations of

Ti-13Nb-13Zr Alloys

Slip/Twin System s0 s1 h0 h1

{0002}h1120i a prism 45 40 1000 500{1010}h1120i a basal 90 50 200 100{1011}h1123i a pyramidal 395 10 2000 1100{110}h111i b 25 0 50 50

Table VI. Different Simulation Schemes Opted in the

Present Investigation

AspectRatio Morphological Orientation

a b a b

Scheme (i) yes yes no noScheme (ii) yes yes yes (u1 F u2) yes (u1

* F* u2*)

Scheme (iii) yes yes yes (u1 F u2) yes (u1 F u2)

Table IV. Voce Hardening Parameters for Simulations for

Austenite and Ferrite Phases of Fe-Ni-Cr Alloys

Slip/Twin System s0 s1 h0 h1

{111}h110i austenite 35 38.3 65 2{111}h112i twin austenite 42.5 20 30 1.25{110}h111i ferrite 90 0 0 0


of Ti-13Nb-13Zr alloy. The effect of various materialvariables like purity, grain size, strain rate, temperature,and pre-strain is well understood.[51] However, the effect

of second phase on the propensity of twinning is not wellunderstood. It has been reported that aging in Ti-Zralloys leads to suppression of twinning. This isattributed to the difficulty in propagating a twin acrossa coherent or incoherent boundary. In addition, thecomplex dislocation structure that is expected to evolveduring the deformation of a composite could also leadto suppression of twinning. Twinning involves co-oper-ative movement of partial dislocations on parallel planesthat may be hindered in the presence of the second phaseas the major criterion is to maintain cohesion betweenthe two phases. It is also known that twin nucleation canbe either homogenous or defect assisted. In most cases,twinning is defect assisted and homogenous twin occursonly in perfect crystals. However, the stress required tonucleate a twin is quite high compared to the stressrequired for twin propagation. It is well known that insingle-phase materials, the localized value of stress attriple junction or grain boundary may exceed the stressrequired to nucleate a twin. However, in case oftwo-phase composites, the localized stresses may leadto propagation of slip in the second phase if the CRSSof the slip system of the second phase is lower than thenucleation stress for twinning in the first phase. It can beeasily understood that with increase in fraction of ferritecontent, the higher probability of heterogeneous inter-faces can contribute in reducing twin nucleation in theaustenite phase drastically. A schematic depicting such ascenario is presented in Figure 10(b). The operation oftwinning in the austenite phase is governed by not onlythe critical resolved stress for twinning and the resolvedshear stress but also the resolved shear stress in theferrite phase. The continuous decrease in twinningactivity with increase in ferrite content indicates thatthere is an increase in the activity of slip in ferrite at theexpense of twinning in austenite.Similar argument can be proposed for Ti-13Nb-13Zr

alloy for suppression of extension and contractiontwinning as well as pyramidal hc+ ai slip; however,morphology also plays a role in suppressing twinning.The interaction stress is expected to be higher for thelamellar microstructure, but the smaller size of a grains/lamellas ensures that the twin propensity is reduced.Therefore, twinning is not observed in a phase ofTi-13Nb-13Zr alloy irrespective of the different mor-phology and volume fraction of the b phase. Anotherimportant observation is that the activity of pyramidalhc+ ai is suppressed in a phase of Ti-13Nb-13Zr alloyin the presence of b phase. It is to be mentioned herethat in the absence of extension and contractiontwinning, hc+ ai pyramidal slip is the only mechanismthat can accommodate strain along c-axis of the HCP aphase. The higher stress concentration for the colonysample explains the reduced formability of the samplewith respect to the equiaxed microstructure.An important observation from viscoplastic self-con-

sistent simulations is that strain partitioning between thephases is accompanied with significant difference innumber of active slip systems in the two phases. Thesofter phase not only carries more strain but also hasmore slip systems active than the harder phase. Thus,the von Mises criterion of having five independent shear

0.00

0.25

0.50

0.75

1.00 Slip I Twin I Slip II Twin II Slip III Twin III Slip IV Twin IV

Con

trib

utio

n to

she

ar s

trai

n

Strain(a)

4

5

6

7

8

9

10

11

EBSD data

Twin

act

ivity

from

sim

ulat

ions

Twin

bou

ndar

ies

from

EB

SD (%

)

Ferrite content (%)

0.20

0.25

0.30

0.35

0.40

Simulations

ε = 1.6

(b)

0.0 0.5 1.0 1.5 2.0 2.5

0 15 30 45 60 75

0.0 0.5 1.0 1.5 2.0 2.50.0

0.2

0.4

0.6

0.8

1.0

Aus I Aus II Fer II Aus III Fer III Aus IV Fer IV

Stra

in p

artit

ioni

ng

Strain(c)

Fig. 9—(a) Activity of {111} h110i slip system and {112} h110i twinsystem in the austenite phase and (b) comparison of twin activityfrom EBSD with simulations. (c) Strain partitioning in the austeniteand ferrite phase for four different Fe-Ni-Cr alloys.


Fig. 10—(a) Grain reference orientation deviation maps in alloy II (left) and alloy III (right) deformed to strain of 0.29 show higher misorienta-tion in the contiguous austenite phase and ferrite phase, respectively. (b) Schematic showing the possible operative micro-mechanisms in two-phase austenite-ferrite alloy.


(slip/twinning) systems which is pre-requisite for theTaylor iso-strain approximation is not valid fortwo-phase deformation. From a mechanistic point ofview, classical iso-strain Taylor approximation and thelower bound iso-stress Sachs approximation constitutethe two extremes of polycrystal deformation in sin-gle-phase materials. It is also agreed that most materialsfollow the Taylor approximation either strictly or in arelaxed way at large strain. The aforementioned crite-rion is very stringent and viscoplastic self-consistent

simulation imposes the same in an average way.However, the presence of second phase puts a stringentcriterion for the validity of the iso-strain approximationdue to drastically different elasto-plastic properties ofthe individual phases at low strain. In case of ductiletwo-phase systems, it appears that the softer phasecompensates for the lack of sufficient shear systems (slipor twining) in the harder phase. Similar situation isencountered during deformation of a polycrystal withhigh aspect ratio of both the phases at a lower strain

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8 HCP Prismatic HCP Basal BCC {101}<111>

Con

trib

utio

n to

she

ar s

trai

n

Strain0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8 HCP Prismatic HCP Basal BCC {101}<111>

Con

trib

utio

n to

she

ar s

trai

n

Strain(a)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0 HCP BCC

Stra

in p

artit

ioni

ng

Strain0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0 HCP BCC

Stra

in p

artit

ioni

ng

Strain(b)

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

8 HCP BCC

Avr

age

Act

ive

Slip

Sys

tem

s

Strain0.0 0.2 0.4 0.6 0.8 1.0

0

1

2

3

4

5

6

7

8

9 HCP BCC

Ave

rage

Act

ive

slip

Sys

tem

s

Strain(c)

Fig. 11—(a) Slip activity, (b) strain partitioning and (c) average active slip systems in HCP a and BCC b phase in Ti-13Nb-13Zr alloy forequiaxed (left) and colony (right) morphology.


compared to a polycrystal with equiaxed phase mor-phology. Thus, higher volume fraction of second phaseor higher aspect ratio of individual phase can lead to adeviation from iso-strain condition which demandsminimum five independent slip systems. Therefore, itcan be concluded that iso-stress condition in individualphases is favored during two-phase deformation at largestrain.

VI. SUMMARY AND CONCLUSIONS

In the present investigation, a series of xFe-y-Ni-(100-x-y)Cr alloys and Ti-13Nb-13Zr were used asa model system to study the evolution of deformationtexture and sub-structure in the individual phases ofFCC-BCC and HCP-BCC two-phase materials, respec-tively, as a function of contiguity and morphology. Acombinatorial approach comprising of state-of-the-artexperimental techniques and crystal plasticity simula-tions was used to understand deformation behavior oftwo-phase systems. The major findings of the presentinvestigation are as follows:

1. In xFe-yNi-(100-x-y)Cr alloys, an increase in thevolume fraction of the harder BCC ferrite phase ledto transition of deformation micro-mechanism fromcontiguous austenite to ferrite phase. It is foundthat contiguity leads to strain partitioning in thephases, which affects the operative micro-mecha-nisms in individual phases. This leads to decrease intwinning in the FCC austenite phase which con-tributed to weakening of Bs component in theaustenite phase with increasing ferrite content. Onthe contrary, texture in BCC ferrite phase becamestronger with increased contiguity of the ferritephase.

2. The effect of morphology in Ti-13Nb-13Zr alloys ismore subdued as there is no characteristic change intexture with change in morphology. However, thestrength of texture evolution in individual phases isaltered with the colony morphology showing weak-er texture for the softer beta phase.

3. Viscoplastic self-consistent simulations were able tocorrectly predict texture and microstructural fea-tures in terms of twin and slip activity in individualphases of two-phase alloys. A quantitative estimate

Fig. 12—Schematic showing evolution of microstructure for different morphologies. Equiaxed morphology shows both the phases oriented todirection of rolling, while the extent of reorientation is not complete for colony microstructure. Microstructure in equiaxed phase promotes iso-s-tress condition, while that in colony is not suitable for iso-stress condition. This explains higher ductility of equiaxed morphology compared tocolony morphology in Ti-13Nb-13Zr.


of strain partitioning due to contiguity and mor-phology which affects deformation micro-mecha-nisms is successfully achieved using simulations.

4. Deformation behavior of two-phase aggregates athigher strain is closer to the lower bound Sachsapproximation than the upper bound Taylorapproximation. The transition from Taylor- toSachs-type behavior is aided by increasing volumefraction of the second phase and higher aspect ratioof individual phases in two-phase alloys.

ACKNOWLEDGMENTS

The authors would like to acknowledge Dr. S. K.Bhaumik of National Aeronautical Laboratory, Banga-lore, India, for providing the assistance in melting thealloys used in the present study. The authors are grate-ful to Dr. C. N. Tome and Dr. R. A. Lebensohn (LosAlamos National Laboratory, USA) for providingVPSC-7 code. NPG had useful discussions with Dr. K.S. Suresh. The authors thank the Department of Scienceand Technology, Government of India, for providingcharacterization facilities at the Institute X-ray facilityand Advanced Facility for Microscopy and Microanaly-sis at Indian Institute of Science, Bangalore, India.

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