Materials Science & Engineering A 568 (2013) 160–170

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Materials Science & Engineering A

0921-50

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E-m1 Cu

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journal homepage: www.elsevier.com/locate/msea

On the interactions between strain path reversal and dynamicrecrystallisation in 316L stainless steel studied by hot torsion

L. Sun a,n,1, K. Muszka a,b, B.P. Wynne a, E.J. Palmiere a

a Department of Materials Science and Engineering, The University of Sheffield, Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD, UKb Faculty of Metals Engineering and Industrial Computer Science, AGH University of Science and Technology, Mickiewicza 30, 30-059 Krakow, Poland

a r t i c l e i n f o

Article history:

Received 9 January 2013

Accepted 18 January 2013Available online 4 February 2013

Keywords:

Austenite

Stainless Steel

Dynamic recrystallisation

Microstructure

Dislocation boundaries

Electron backscattering diffraction (EBSD)

93/$ - see front matter & 2013 Elsevier B.V. A

x.doi.org/10.1016/j.msea.2013.01.045

esponding author. Tel.: þ44 141 534 5240.

ail address: lin.sun@strath.ac.uk (L. Sun).

rrent address: Advanced Forming Research

yde, 85 Inchinnan Drive, Inchinnan, Renfrew

a b s t r a c t

A 316L austenitic stainless steel was subjected to hot cyclic torsion tests to the same total accumulative

von Mises equivalent strain of 2.0 with different amounts of reversals in order to study the effect of

strain path on dynamic recrystallisation (DRX) behaviour. Both the macroscopic flow stress and

corresponding microstructural analyses revealed that there is a strong influence of applied strain path

on the DRX kinetics. In the case of higher deformation per pass and less strain path reversals, the

combination of three effects, i.e. higher stored energy, enhanced grain boundary serration and bulging

through increased grain boundary area and more developed strain-induced high angle boundaries

together facilitated DRX. On the contrary, deformation of more strain path reversals combined with

lower strain per pass lead to a complete suppression of DRX even at the high accumulative strain of 2.0.

Proper understanding of the strain path effects on hot deformation behaviour of steels is a key factor in

control and optimisation of the microstructure and properties of semi-final and final products.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Process optimisation and control of industrial thermomecha-nical processing of steels is becoming increasingly dependent onsophisticated scientific computational modelling [1]. Such models[2–4], developed and improved by understanding the fundamen-tal physics behind the microstructural changes and assisted byever increasing computing power, are now critical for both offlineoptimisation and online control for thermomechanical processing.

One area, however, where modelling produces inadequatepredictions is when the stock material is subjected to complexdeformation histories with non-linear strain paths. This is notsurprising given that most of the current microstructural modelshave been developed and validated based on studies of micro-structure evolution under simplified laboratory conditions usingmonotonic deformation tests, i.e. linear strain paths, without anyconsideration of strain path changes. For example, models basedon the von Mises equivalent strain evm as the microstructuralstate variable produce adequate predictions of microstructureafter monotonic compression in rolling, i.e. at the centre of theplate but fail to predict the variation of microstructure throughthe thickness, i.e. where the strain path history is non-linear dueto the shear deformation caused by the friction between the rolls

ll rights reserved.

Centre, The University of

shire, PA4 9LJ, UK.

and the stock material [1,5]. These discrepancies clearly suggestthe need to develop a new generation of models which arecapable of predicting local variations in microstructure evolutionduring rolling and forging when there are major changes in strainpaths [1]. To incorporate strain path into future microstructuremodels, first it is necessary to study the microstructure evolutionunder deformation conditions with non-linear strain path historyto develop an understanding of the basic physics which there isstill a limited knowledge base.

During thermomechanical processing, a number of metallurgi-cal phenomena could occur simultaneously with hot deformation,such as work hardening, dynamic recovery and dynamic recrys-tallisation (DRX) [3]. The last one is of profound importance forprocessing metals and alloys with low stacking fault energies (SFE),such as austenitic stainless steels. The initiation of DRX bringsabout changes to both mechanical and microstructural behavioursof the stock materials by reductions of deformation resistance(hence roll force) as well as considerable grain refinement [6,7].DRX tend to take place under low Z deformation conditions, i.e.high temperature and slow strain rate (Z is the Zener–Hollomonparameter defined as Z ¼ _Eexp ðQdef =RTÞ where _E is the strain rate,R is the gas constant, T is the instantaneous absolute temperatureand Qdef is the activation energy for deformation [8]). Furthermore,the occurrence of DRX could increase at higher strains through theaccumulation of retained work hardening during multi-pass roll-ing [9]. Therefore, to improve the accuracy of computer models forthermomechanical processing, DRX behaviours have be under-stood and described appropriately.

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170 161

The aim of the present work is to study the effect of strain pathreversals on the mechanical behaviour and microstructural evo-lution in austenitic stainless steel 316L, especially through thepromotion or retardation of DRX, when deformed to large strainsby hot cyclical torsion. It is hoped that some insights could begained on the microstructure level to understand better theunderlying mechanism for the interactions between strain pathreversal and DRX during hot deformation.

2. Experimental

The 316L stainless steel, chemical composition of 0.02C–17.1Cr–11.2Ni–2.12Mo–1.78Mn–0.37Si–0.048P–0.009S (wt%), used in thisstudy was received as 50 mm diameter bar from Outokumpu. Itwas then solution heat treated at 1250 1C for 1 h in an inert atmo-sphere followed by immediate water quenching resulting in amicrostructure consisting of deformation-free equiaxed grains witha mean size of �150 mm. Solid bar torsion specimens of 20 mmgauge length and 10 mm diameter were then machined according tothe geometry described elsewhere [10].

Hot torsion tests with single and multiple strain path reversalswere performed using the servo-hydraulic Arbitrary Strain Path(ASP) testing rig at The University of Sheffield. Specimens wererapidly heated up by an induction method at 12 1C s�1 to thedeformation temperature of 950 1C, which corresponded toapproximately 0.7 of the absolute melting point (Tm). A two-pass and an eight-pass cyclical torsion test were conductedisothermally at a constant angular speed which produced aconstant strain rate of 1 s�1 at the effective radius, i.e. �72.4% ofthe gauge radius, as schematically shown in Fig. 1(a). The conceptof effective radius was proposed by Barraclough et al. [11] tominimise the complexity of calculating shear stress (hence von

Fig. 1. (a) The position of the effective plane for microstructural observations within th

shown as percentages of the von Mises equivalent strain level along the vertical centr

Mises equivalent stress) from recorded machine torque data fortorsion tests.

Generally, the total torque G can be expressed as the integra-tion of shear stresses tðrÞ along radial direction r by the followingequation:

G¼Z R

0dG¼ 2p

Z R

0r2tðrÞdr ð1Þ

where R is the maximum gauge radius. However, the shear stresstðrÞ at a radial location r is not just a function of the shear strain g,but also depends on shear strain rate _g. Therefore, assuming thematerial flow behaviour obeys the simple power-law relationshipas follows [12]:

tðrÞ ¼ Kgn _gmð2Þ

where K, m and n are considered as material constants. K is thestrength index, n is the strain hardening exponent and m is thestrain rate sensitivity exponent. Based on the above assumption,Fields and Backofen [13] showed that the shear stress tðrÞ at theradius of r in the gauge section can be calculated from the totaltorque G by the following equation:

tðrÞ ¼ðmþnþ3Þ rmþnG

2pRmþnþ3ð3Þ

For the Fields–Backofen method, the m and n values have to bedetermined experimentally by multiple tests and the calculationis still tedious. However, by applying the concept of an effective

radius introduced by Barraclough et al. [11], the calculation can besignificantly simplified.

As tðrÞ is a continuous function on the closed interval rA ½0,R�,according to the first mean value theorem for integration, there

e gauge section of a torsion specimen; (b) the strain gradient on the effective plane

al line of the plane. Dashed lines indicate increments of 2.5% in strain.

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170162

exists a number xAð0,RÞ such that:Z R

0r2tðrÞdr¼ tðxÞ

Z R

0r2dr ð4Þ

Combining Eq. (4) with (1) gives:

t xð Þ ¼G

2pR R

0 r2dr¼

3G2pR3

ð5Þ

Clearly, the calculation of the shear stress t at a position r¼x ismuch easier as it is independent of m and n. Combing Eqs. (3) and (5):

tðxÞtðrÞ¼ðmþnþ3Þ

3

r

R

� �mþn

ð6Þ

The ratios of tðxÞ=tðrÞ as a function of r=R as described by Eq. (6)for various mþn values are plotted in Fig. 2. It can be clearly seenthat there exists an effective radius re � 0:724%R , at whichposition the shear stress tðrÞ is equal to the integration averageshear stress tðxÞ (as tðxÞ=tðrÞ ¼ 1), regardless of the mþn values. Thevariation of shear stress with ðmþnÞA ½�0:5, þ0:5� is less than0.5% at the effective radius. The distinctive advantages of thisapproach over the Fields–Backofen method are twofold: first thecalculation of the shear stress, hence von Mises equivalent stress,is significantly simplified; secondly microstructure observationsmade at the effective radius are consistent, therefore comparablefrom test to test.

Finally, the von Mises equivalent stress svm and strain evm canbe calculated as follows:

svm ¼ffiffiffi3p

tðxÞ ¼3ffiffiffi3p

G2pR3

ð7Þ

evm ¼gðxÞffiffiffi

3p ¼

0:724Ryffiffiffi3p

lð8Þ

where y is the twist angle (in radians), R is the maximum gaugeradius, l is the gauge length. The above two equations will be usedthroughout this research for calculating von Mises equivalentstress–strain from torque-angle data from torsion tests. However,as the surface at the effective radius is cylindrical, it is notpractical to make microstructure observations on such a surface.Therefore, all microstructure and crystallographic observationswere made along the intersection line of the plane tangential tothe effective radius, as schematically illustrated in Fig. 1(a), onwhich a strain gradient exists. As shown in Fig. 1(b), for the

Fig. 2. Plot of t(x)/t(r) as a function of r/R for various mþn values indicates the

position of the effective radius at around 72.4% of the total radius R.

torsion specimen geometry used in this study, within a range of71 mm around the central vertical axis, the strain increasesabout 2.5%. Therefore, in order to avoid inconsistency, all micro-structure observations were made within this 71 mm range.

The two-pass test consisted of forward torsion to a von Misesequivalent strain of 1.0 (evm¼1.0 at the effect radius), followed byimmediate reverse torsion of evm¼1.0 to a total accumulativestrain of 2.0 but a net strain of 0. The delay due to reversing wasless than 0.2 s. The eight-pass test consisted of four cycles offorward–reverse torsion with each pass of evm¼0.25, producingthe same total strain of 2.0 and a net strain of 0. Delays of similarduration existed between each pass of the eight-pass tests due toreversing the strain direction. It should be noted that at 950 1Cstatic recrystallisation (SRX) of 316L can occur during prolongedinter-pass holding, especially after large strains, however, it isunlikely to have occurred during these tests with their very shortinter-pass times, as 316L has fairly slow SRX kinetics [14]especially for coarse-grained ones.

After deformation, specimens were water quenched to pre-serve the as-deformed microstructures. The delay between strain-ing and quenching was less than 0.2 s. The recorded averagequenching rate from deformation temperature of 950 1C to 200 1Cwas in excess of 120 1C s�1. The very rapid quenching is believedto eliminate the phenomena of ‘‘metadynamic’’ recrystallisationwhich could occur during cooling after deformation [15].

The as-quenched specimens were sectioned to reveal thetangential plane which is normal to the radius direction (r) atthe effective radius and contains the axial (Z) and shear (y)directions of the torsion test as outlined in Fig. 1(a). The speci-mens were then mechanically ground using SiC papers. This wasfollowed by mechanical polishing with diamond suspensiondown to 1 mm. Finally, the specimens were polished for 15 minusing a colloidal silica suspension with a nominal particle size of0.04 mm. EBSD maps were obtained on the tangential plane of thespecimens in a FEI Quanta 250 FEG SEM operating at 20 kV usingan Oxford Instruments HKL Nordlys Fþ camera with Channel5 software. A step size of 0.4 mm was chosen to cover typical areasof 1000 mm (in Z direction) by 800 mm (in y direction) which werelocated very close to the central axis of the tangential plane, wellwithin the 71 mm range. As EBSD maps are commonly not 100%indexed a post-acquisition noise reduction procedure whichproduces consistent quantitative metallography measurementswas applied [16].

3. Results

3.1. Flow stress–strain behaviour

The recorded torque-angle data from both the two-pass and theeight-pass tests were converted to von Mises equivalent stress–strain curves according to Eqs. (7) and (8). The calculated flowcurves are presented in Fig. 3. It can be seen that the macroscopicflow stress–strain curves from the two tests are distinctivelydifferent. For the two-pass test, continuous work hardening wasobserved in the initial part of the forward torsion until a peakstress of sp (242 MPa) was reached at the peak strain of ep (0.62).A significant amount of dynamic softening was observed beyond ep

which indicates DRX [17]. The flow stress then continued todecrease until the end of the first pass. However, in the two-passtest after the strain path reversal, unlike previous studies [18,19]where significant drop of flow stress known as Bauschingerbehaviour was observed, the flow stress of 316L increased veryrapidly to the pre-interruption level, then remained almost con-stant throughout the second pass. Conversely, in the eight-passtest, strong Bauchinger effects were observed with significant

Fig. 3. von Mises equivalent stress–strain curves from eight-pass and two-pass

torsion tests.

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170 163

drops of flow stress each time after the straining direction wasreversed. Nevertheless, the flow stress of the eight-pass test onlyshowed continuous work hardening during each deformation pass,i.e. no dynamic softening was observed. The maximum stressvalues before each strain reversal were almost constant at around214 MPa (0.88sp). Work by Ryan and McQueen on both as-cast andwrought 316 stainless steel deformed by hot monotonic torsiontests at various temperature and strain rate showed that thecritical stress (sc) associated with the initiation of DRX is about0.98sp [20]. Apparently, the maximum flow stress during theeight-pass test is still considerably lower than the critical stressfor DRX under current deformation condition. The critical condi-tions for DRX are analysed and discussed further in Section 4.1.Nevertheless, the observations from the macroscopic flow beha-viour suggest that during the forward torsion in the two-pass test,the monotonic strain of evm¼1.0 was large enough to produceconsiderable amounts of DRX, whereas in the eight-pass test theforward strain of evm¼0.25 before each strain path reversal wasnot high enough to initiate DRX.

3.2. Microstructure analyses

3.2.1. Microstructure after the eight-pass deformation

The microstructure after the eight-pass test is shown inFig. 4(a) as an inverse pole figure (IPF) coloured map. Thepresented area is only about 1/3 of the total data obtained.It can be seen that after the eight-pass cyclical deformation toevm¼2.0, the original grain shape is maintained. However, there isa considerable fraction of the original grain boundaries (GBs)showing serrations and bulging, as indicated by the arrows inFig. 4(a), which are believed to be the main nucleation mechan-isms for DRX [21]. Nevertheless, no DRX was observed in the as-deformed microstructure which is consistent with the indicationfrom its flow stress–strain curve. Conversely, a previous study on316SS by Ryan and McQueen using monotonic torsion at the samestrain rate of 1 s�1 showed extensive DRX after a strain ofevm¼2.0 [20]. The reason for the observed difference is believedto be the small amplitude of forward strain evm¼0.25 in the eight-pass test is not sufficient to initiate DRX. Although GB serrationscan be developed due to the growing fluctuations of GB shapewith straining; the critical strain level which could cause enoughbulging of prior GBs to form new DRX grains was never reached ineach forward torsion pass in the eight-pass test. Because theforward strain evm of 0.25 can only increase the GB area by �4%according to Zhu et al. assuming the grains are in the form of

14-faced space-filling kelvin tetradecahedron [22]. Consequently,after the reverse torsion of evm¼�0.25, as the original equiaxedgrain shape was restored, the GB area was reduced, thus probablylimiting further GB bulging, and hence, suppressing DRX. Theeffect of deformation on the increment of grain boundary area isfurther discussed in Section 4.2.2.

Fig. 4(b) is the band contrast map of the same microstructuresuperimposed on the boundary map with LABs of 51oyo151represented by red lines and HABs (yZ151) as black lines and S3twin boundaries (within 51 of 6019/111S) as blue lines. Somenewly generated HABs were found within the original grainsindicating that they are formed by austenite grain subdivision.The generation of new HABs could be attributed to two majormechanisms: (1) microstructure/strain accumulation and (2) tex-ture/subgrain rotation [23].

One interesting example indicating a possible microstructure/strain accumulation mechanism is highlighted by the whitearrows in Fig. 4(b). It can been seen that the pair of nearly paralleldislocation boundaries across the grain consists mainly of LABs(as red lines) with the middle part of the upper boundary showingdisorientation characteristics of HABs (as black lines). The natureof these boundaries are believed to be GNBs, as there is clearlylattice rotation of the subgrain relative to the rest of the originalgrain indicated by the orientation (colour) variations within theIPF map (Fig. 4a). These features are evidence of the evolution ofLABs to form new HABs with straining through grain subdivision[23]. It was suggested that the microstructure/strain accumula-tion mechanism could be activated at a relatively early stage ofdeformation as blocks of materials within the austenite grainwere deformed by different active slip systems, generating a GNBtype of LABs to accommodate lattice rotations. During furtherstraining, the disorientation angles across these GNBs increasethrough accumulation of dislocations, therefore, producing HABsof disorientation mainly up to 15–301. Similar grain subdivisionbehaviour was also observed in a model austenitic Fe–30 wt%Nialloy deformed under a very similar deformation schedule [24].

Some of the HABs also show evidence of grain subdivision viatexture/subgrain rotation mechanisms, i.e. HABs separatinglamellar subgrains of alternating orientations with one set ofsuch subgrains orientated close to one of the ideal shear texturecomponent. One such example can be seen in the enlarged subsetshown in Fig. 4(c). The alternating IPF colours of subgrainsbetween pink and green suggest their alternating orientations.Furthermore, as indicated by the /111S pole figure of the greencoloured subgrain shown in Fig. 4(e), the orientations of this set ofsubgrains are very close to the orientation of the ideal sheartexture component A1n[25], i.e. (11�1) [2–11] for Z�y, which isgiven by its corresponding /111S pole figure in Fig. 4(d).As noted by a previous investigation [23], the texture/subgrainrotation mechanism could only be activated at higher strainswhen the end stable orientations were well developed. Thesubdivided blocks within a grain, acting as individual crystallite,could rotate to different preferred orientations and/or to the sameend orientation but at different speeds, therefore, HABs areproduced in-between.

However, the disorientation line scan from A to B as shown inFig. 4(f) indicates some of the HABs have the rotation angles/axesof 301–401 around /232S axes which could be reasonabledeviations from the ideal S3 twin boundaries (6019/111S) afterlarge amounts of deformation. Therefore, it is difficult to identifywhether these HABs are due to the evolution of original S3 twinboundaries with straining or produced by grain subdivision.Nevertheless, there are still a considerable number of S3 twinboundaries (blue lines) maintaining their disorientation charac-teristics within 51 of 6019/111S through the eight-pass cyclicaldeformation.

Fig. 4. EBSD analysis of eight-pass tested 316L specimen: (a) IPF map (black lines represent boundary disorientation Z151); (b) band contrast map superimposed on

boundary map with LABs of 51oyo151 as red lines, HABs (yZ151) as black lines and S3 twin boundaries (within 51 of 6019/111S) as blue lines; (c) IPF map of the subset;

(d) /111S pole figure of ideal shear texture component A1*; (e) /111S pole figure of the subgrain marked with arrow; (f) disorientation angle/axis characteristics of some

HABs along the scan line AB. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170164

3.2.2. Microstructure after the two-pass deformation

A selected area of typical microstructure after the two-passtest is shown in Fig. 5(a) as IPF-coloured map and in Fig. 5(b) asband contrast map superimposed on boundary map, respectively.

It can be seen that a considerable amount (�20% based onimage analysis) of recrystallised grains containing LABs (as redlines) and S3 twin boundaries (as blue lines) are observed nearprior GBs and twin boundaries. The very short delays (o0.2 s)during strain reversal and before applying quenching after defor-mation suggest that static recrystallisation (SRX) was very unli-kely to occur as 316 steels exhibit slow SRX kinetics caused bysolute elements such as Mo segregated at GBs reducing GBmobility, and hence, retarding SRX [26]. Furthermore, the LABswithin the recrystallised grains also suggest lattice curvature dueto further straining once they were formed. Therefore, it is

believed that the majority of these newly formed grains are theresult of dynamic recrystallisation (DRX).

By separating the small DRX grains (grain diameter o20 mm)from the large deformed grains, the textures of the DRX grainsand remaining deformed matrix are plotted in Fig. 5(c) and (d),respectively, by /111S pole figures. The textures are based on thewhole EBSD data set, which covers a much bigger area (about3 times) than the maps presented in Fig. 5. The texture of thesmall DRX grains is close to random (shown in Fig. 5d) comparedto the strong texture of the deformed matrix (shown in Fig. 5c).Work by Ponge and Gottstein [21] showed that the orientations ofthe first generation DRX grains are close to that of their parentgrain. However, as DRX progresses, the orientation coherencyrapidly diminishes leading to a relatively random texture of DRXgrains. This is attributed to rotation and multiple twinning of DRX

Fig. 5. EBSD analysis of two-pass tested 316L specimen: (a) band contrast map superimposed on boundary map with LABs of 51oyo151 as red lines, HABs (yZ151) as

black lines and S3 twin boundaries (within 51 of 6019o1114) as blue lines; (b) IPF map with black lines represent boundary disorientation4151; (c) o1114 pole figure

of deformed grains; (c) o1114 pole figure of DRX gains. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of

this article.)

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170 165

grains during further deformation which randomises orientation[21]. Therefore, the above observations on microstructure andmicrotexture suggest that in the two-pass test, DRX occurredduring forward torsion deformation to evm¼1.0 which is consis-tent with the macroscopic flow stress–strain analysis.

New HABs generated by grain subdivision through the texturemechanism are also observed in the 316L stainless steel subjectedto the two-pass deformation. One such example is given inFig. 6(a); the disorientation line scan from C to D (shown inFig. 6b) reveals the angle/axis characteristics of these HABs. Thetwo planar HABs of subgrain 3 have similar disorientation angles,i.e. �301 and rotation axes of the same family but oppositedirections, i.e. [31�4] and [�3�14]. The orientations of sub-grains 1 to 4 along the scan line CD are shown by their /111Spole figures in Fig. 6(c). It can be seen that these subgrains arealternating between two orientations: subgrains 1 and 3 share thesame orientation which is also close to that of A1n ideal sheartexture component [25] as shown in Fig. 6(e) whilst subgrains2 and 4 are aligned very close to each other. Very similarobservations, i.e. lamellar subgrains with alternating orientationsseparated by HABs, were also made in a Fe–30%wtNi modelaustenitic alloy subjected to a similar two-pass deformation testdeformed at a lower homologous temperature (�0.65Tm) [24].

These are the typical features of HABs generated by grainsubdivision via the texture/subgrain rotation mechanism. How-ever, the strain induced HABs in 316L show more serrations andbulging with even a small number of DRX grains formed nearthese HABs, as shown in Fig. 6(a). This is most likely due to thehigher mobility of HABs at higher homologous temperature(0.7Tm). Furthermore, comparing to Fe–30%wtNi model alloy,the much lower SFE of 316L could lead to rapid accumulationof stored energy facilitating DRX which was not observed inFe–30 wt%Ni deformed by the similar two-pass test.

3.2.3. Comparison of disorientation angle distributions

Based on the large area EBSD maps, quantitative analysis of thedisorientation angle distributions after the two tests is shown ashistograms in Fig. 7, for both LABs and HABs with disorientationangles ranging from 21 to 62.81 and in Fig. 8 for HABs(151ryr62.81) only. It has to be pointed out that the disorienta-tion angle densities (the absolute number of disorientation anglesper unit area) is used in this analysis instead of the relativefrequency distribution of the disorientation angles. The reason forthis choice is that the latter one is inadequate to quantify the

Fig. 6. (a) IPF map showing HABs generated by texture mechanism, (b) disorientation line scan from subgrains 1–4 showing angle/axis characteristics of the new HABs, (c)

o1114pole figures of subgrains 1–4, (d) histograms showing the absolute frequency of disorientation angles per unit area after two- and eight-pass tests.

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170166

interfacial area per unit volume (Sv) associated with the deforma-tion microstructures.

The absolute number of LABs per square millimetre is on the orderof 105–106 mm�2 in both specimens after either the two-pass oreight-pass tests. These levels of LABs in 316L are comparable to whatwere observed in Fe–30 wt%Ni from early work [24]. The levels ofHABs frequency in 316L are in the order of 104–105 mm�2 comparedto less than 103 mm�2 in Fe–30%wtNi. The higher levels of HABsfrequency in 316L are partly due to its smaller initial grain size(�150 mm) than Fe–30%wtNi (�400 mm) as there are less GBs henceHABs per unit area for a coarser microstructure.

Comparing microstructures from the two-pass and eight-passtest, the levels of disorientation angles densities of LABs

(21oyo151) are higher in the former. Nevertheless, these differ-ences are relatively small compared to the difference of frequencydensities of HABs (151ryr551) between the deformation micro-structures from the two tests. It can be seen in Fig. 8 that the two-pass test produced a much higher frequency of HABs densitiesfrom 151 to 551 than that of the eight-pass test. This differenceshould mainly come from the new GBs of DRX grains in the two-pass tested 316L.

It is believed that the frequency of density peaks at 601disorientation angle mainly come from S3 twin boundaries. Forthe eight-pass test, a considerable amount of the disorientationangles from the original twin boundaries were maintained dueto the small amplitude of forward strain 0.25. Whilst for the

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170 167

two-pass test, newly formed DRX grains made a substantialcontribution to its higher level of twin boundaries.

Fig. 7. Histogram showing the absolute frequency of the magnitude of disorienta-

tion angles per unit area (square mm) in 316L samples after two-pass and eight-

pass test including both LABs and HABs from 21 to 62.81.

Fig. 8. Histogram showing the absolute frequency of the magnitude of HABs

(yZ151) per unit area (square mm) in 316L samples subjected two-pass and

eight-pass tests.

Fig. 9. Work hardening rate during forward torsion to evm¼1.0 from

4. Discussion

4.1. The critical conditions for the initiation of DRX

DRX is commonly observed in low SFE FCC systems during hotdeformation due to slow dynamic recovery leading to high storedenergies [1]. Note, however, the actual initiation of DRX takesplace prior to the peak strain (ep) corresponding to the character-istic peak stress (sp) on the flow stress–strain curves as shown inFig. 3 [17,27]. In fact the DRX behaviour can be seen more clearlywhen the work hardening rate (Y¼ @s=@E) is plotted againststress and strain as shown in Fig. 9(a) and (b), respectively. As therestoration process of DRX would change the work hardening rateby introducing new strain free grains to deformed matrix, theinitiation of DRX is reflected by the appearance of an inflectionpoint on the work hardening-flow stress (Y-s) curve, which isalso known as Kocks–Mecking plot [28] as this analysis techniquewas firstly developed by Mecking and Kocks [29] to determine thecritical stress sc for initiation of DRX. The corresponding thresh-old strain is known as the critical strain (ec) for DRX [30]. It hasbeen successfully employed for subsequent studies on variousaustenitic stainless steels to determine the onset of DRX duringmonotonic hot deformation tests [31–34]. Therefore, for the 316Lstainless steel under the current deformation conditions, thecritical stress of scE230 MPa and critical strain of ecE0.40 canbe determined from the strain curves during the forward torsionpass of the two-pass test as shown in Fig. 9.

However, the precise determination of the inflection point onthe Kock–Mecking plot can sometimes be difficult to establish.More recently, Poliak and Jonas [35] derived the conditions for theonset of DRX from the principles of irreversible thermodynamics.They showed that the initiation of DRX is governed by bothenergetic and kinetic critical conditions. The former requires thatthe local stored energy during a given deformation attain amaximum value, whilst the latter requires the dissipative pro-cesses associated with deformation to decelerate to a minimumlevel [35]. This kinetic critical condition, which is defined by aminimum value in the rate of decrease in strain hardening rate(i.e. �@Y=@s) and can be regarded as the instant when DRX isinitiated. Therefore, the minimum of �@Y=@s can be usedto determine the onset of DRX from the macroscopic flow

two-pass test plotted against (a) flow stress and (b) flow strain.

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170168

stress–strain curves by the following expression:

@

@s �@Y@s

� �¼ 0 ð9Þ

where the initiation of DRX is identified by the appearance of astationary point on the ð@Y=@sÞ-s curve. This second-derivativemethod proposed by Poliak and Jonas has been successfully usedby other researchers to determine the critical strains of DRXduring the hot deformation of a wide range of materials, includingaustenitic stainless steels such as 304 [7,34,36], 316 [37], 321[38]and 800H [39], as well as plain carbon [38,40–42] and Nbbearing steels [38,43]. By applying this method to the Y-s curvegiven in Fig. 9(a), the precise value of the critical stress for DRX(sc,DRX) can be determined to be 231 MPa as shown in Fig. 10.

Furthermore, the relationship between the peak strain andcritical strain, ec¼0.65ep, is in good agreement with previouswork by Ryan and McQueen using both cast (ec¼0.66ep) andwrought (ec¼0.64ep) 316 stainless steel studied by hot torsiondeformed at the same strain rate of 1 s-1 [20]. The above analysesshowed that the monotonic strain of evm¼1.0 during forwardtorsion of the two-pass test far exceeded the critical strain forinitiating DRX (ec,DRX¼0.4). Therefore, it is not surprising thatconsiderable DRX was observed in the two-pass deformed speci-men. On the other hand, the monotonic strain of evm¼0.25 duringthe forward torsion of the eight-pass test was much smaller thanthe ec,DRX. As a result, little DRX was observed in the latter case.

4.2. Effect of strain path reversal on DRX

4.2.1. Stored energy from deformation

Recrystallisation is a process primarily driven by the storedenergy from the deformation process [44]. The stored energy ofplastic deformation is retained in the form of dislocations, both assubgrain dislocation boundaries and those randomly distributedwithin the deformed austenite microstructure. These two para-meters can be related by the following equation [45]:

Es ¼ rEel ð10Þ

where Es is the stored energy per volume in the deformedmicrostructure; r is the overall dislocation density of thedeformed austenite; and Eel is the energy per unit length ofdislocation line. The last term can be expressed as

Eel ¼ KG9b92ð11Þ

Fig. 10. The critical stress for DRX determined by the ‘‘double-differentiation’’

method, e.g. the stationary point on the curve of the derivative of work hardening

rate with respect to flow stress.

where G is the shear modulus, b is the Burgers vector and K is aconstant with an approximate value of 0.5 [46]. Substituting Eq.(11) into Eq. (10) yields the following relationship:

Es ¼1

2rG9b92

ð12Þ

An empirical relationship exists between the flow stress anddislocation density for many metals and alloys subjected to low tomedium strains, and is given as [45,47]

s�s0 ¼MaG9b9ffiffiffiffirp

ð13Þ

where s is the flow stress, s0 is the friction stress, M is theTaylor factor, and a is a constant with a value in the range of0.2 to 0.3 [48]. By combining Eqs. (12) and (13), the stored energyEs can be expressed as a function of the flow stress s:

Es ¼1

2G

s�s0

Ma

h i2ð14Þ

Taking the values M¼2.86 for FCC crystals strained in torsion[49], a¼0.24 [50], G¼4�104 MPa at high temperatures [51] andassuming s*s0, from the flow data shown Fig. 3, it can beestimated that at the peak stress (sp) of 242 MPa during thetwo-pass deformation, the stored energy of 316L is1.55�106 J m�3 (�11.2 J mol�1). For the eight-pass test, at themaximum flow stress of 219 MPa, the stored energy is1.27�106 J m�3 (�9.2 J mol�1). These values are comparable tothe measured stored energy of aluminium (99.99%) colddeformed to similar von Mises strains [45]. The reduction in thestored energy after multiple strain path reversals in the eight-pass test could be attributed to the repeated annihilation ofopposite dislocations produced by the same sources after eachstrain reversal [52]. Therefore, the maximum difference of storedenergies between the two tests is only 2.8�105 J m�3

(�2.0 J mol�1). Albeit small in term of value, it still constitutesan 18% reduction which is significant considering the storedenergy of deformation is the main driving force for any recrys-tallisation process.

4.2.2. Increment of prior-grain boundary area

Furthermore, the spatial distribution of the stored energyusually is not uniform in deformed microstructure. Inhomoge-neous deformation tends to occur at GBs and triple junctions (TJs)where compatibility strain is required to accommodate theincompatible shape changes of grains at their common grainboundaries leading to greater local strain gradient hence higherstored energy, therefore, making GBs and TJs the preferential sitesfor nucleation of DRX [53,54].

However, in addition to the reduction of dislocations density/stored energy caused by multiple strain path reversals after theeight-pass test, the increment of grain boundary surface area perunit volume (Sv) due to the shape change of austenite grainswould be much smaller after the monotonic forward torsion ofevm¼0.25 compared to the large forward strain of evm¼1.0 in thetwo-pass test.

Zhu et al. [22] calculated the effect of plastic deformation onthe increase of Sv under different deformation modes assumingrandomly orientated grains in the shape of tetrakaidecahedronwhich is a space-filling polyhedron with 14 faces including8 hexagonal ones and 6 square ones. The advantage of usingtetrakaidecahedron is that whilst maintaining space filling it givesgood representation of the grain shapes observed by metallogra-phy. Furthermore, the angles between the tetrakaidecahedronsurfaces represent more accurately the angles between grainboundaries for balancing the interfacial tensions at grain boundaryjunctions, requiring only minor surface curvatures [22].

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170 169

Applying the same method, the ratio between Sv and its initialvalue at zero strain Sv0 is plotted as a function of the von Misesequivalent strain during monotonic torsion (shear) in Fig. 11.However, in this case, only one specific orientation of the grainrelative to the deformation axes is calculated which was used in aprevious study [55] for the convenience of calculation. Admit-tedly, this simplification omits other orientated tetrakaidecahe-drons, which may lead to different Sv/Sv0 ratios at the same strainvalue. Nevertheless, work by Zhu et al. [22] showed that at smallto medium shear strains (e.g. go4) the spread of Sv/Sv0 as a resultof randomly orientated tetrakaidecahedron is very limited.

It can be seen in Fig. 11 that the maximum increase of the GBarea, which is the primary nucleation site for DRX, introduced bythe small amplitude of forward strain evm¼0.25 in the eight-passtest is only �4%. In comparison, in the two-pass test, the GBincreases by �10% at ec¼0.40 during forward torsion and reaches�35% increment (if assuming no DRX) when strained to max-imum value of evm¼1 before the strain reversal. Therefore, thelarge amplitude of forward strain could produce a much highernumber of potential nucleation sites for DRX as well as causingmore extensive GB serrations and bulging.

An investigation on a steel microalloyed with Nb subject totorsion [56] showed that when deforming at the austeniterecrystallisation temperature, the strain reversal delayed theDRX of austenite as indicated by a postponed flow stress peakto higher accumulative strains, which was also confirmed by theoptical observations of the austenite microstructures. The authorsattributed this mainly to the reduction of Sv as nucleation sites forrecrystallisation due to the reverse torsion.

However, previous work on Fe–30%wtNi showed that althoughGB serrations can be developed due to the growing fluctuations ofaustenite GB shape with straining in both tests, the extent of GBserrations was found to be much higher after the two-pass testthan after the eight-pass test [24]. Therefore, the suppressing ofDRX during the eight-pass test in the current study could also beattributed to the amount of GB serration and bulging affected bystrain reversal as follows: as determined by the macroscopic flowstress analysis, the critical strain of DRX (ec,DRX) is around 0.4,which is about 60% higher than the amplitude (evm¼0.25) of theforward torsion in the eight-pass test. Therefore, it is likely thatduring each forward-torsion pass in the eight-pass test the criticalstrain level (ec,DRX) which could cause enough bulging of prior-GBs to facilitate the nucleation of new DRX grains is neverreached. The subsequent reverse strain of evm¼�0.25 wouldrestore the original grain shape and reduce the GB area thereforeeliminating further GB serration and bulging. As a result, DRX was

Fig. 11. Calculated increment of grain boundary area per unit volume (Sv/Sv0) as a

function of von Mises equivalent strains during shear deformation.

suppressed by the unique strain path of the eight-pass test, i.e. acombination of multiple strain reversals with small strain ampli-tude of each pass. Conversely, the large amplitude of forwardstrain evm¼1.0 in the 2-pass test well exceeded the ec,DRX of 0.4.Therefore, it could introduce enough GB bulging to initiate DRXduring the forward straining.

4.2.3. Development of subgrain dislocation boundaries

As mentioned above, subgrain dislocation boundary (bothGNBs and IDBs) could be formed through grain subdivision byboth dislocation accumulation/microstructure mechanism andsubgrain rotation/texture mechanism during deformation[23,57,58]. These intragranular planar defects could also act aspotent sites for DRX nucleation during deformation [59], espe-cially GNBs of high energies, i.e. higher disorientations. However,the generation of GNBs with higher disorientations, especially theHABs (y4151), could be significantly retarded by the repeatedstrain path reversals in the eight-pass test which was observed inan early study using Fe–30 wt%Ni austenitic alloy [24]. It has beenestablished that there is a threshold strain level for the activationof the subgrain rotation/texture mechanism to generate HABsduring monotonic deformation only when preferred stable orien-tations are well-developed. Thus, below this threshold strain, noor only very limited amount of HABs can be produced by thetexture/subgrain rotation mechanism [23]. The small amplitudeof forward strain (evm¼0.25) in the eight-pass test was probablybelow this threshold strain. Hence, the repeated strain pathreversals suppressed the formation of HABs via grain subdivisionby the texture mechanism. On the other hand, the large forwardmonotonic strain of evm¼1.0 in the two-pass test could easilyexceed the threshold strain for activating the texture mechanism,subsequently promoting HABs to be developed within the originalgrains. Consequently, during the two-pass test, a higher numberof intragranular nucleation sites could be available for DRX, inaddition to the greater increase of original grain boundary area aspreferred intergranular nucleation sites for DRX associated withthe shape change of grains.

5. Conclusions

Based on the above analyses of flow behaviour and micro-structure evolution of the 316L stainless steel subjected to a two-pass and an eight-pass cyclical torsion deformation, it is believedthat the significantly higher amount of DRX grains observed afterthe two-pass test can be attributed to the combination of severaleffects, i.e. higher driving force from stored energy, increasednucleation sites from both GB area and more developed straininduced HABs.

The following concluding remarks can be made:

�

The critical strain for dynamic recrystallisation (DRX),ec,DRX¼0.4, was determined by the double differentiationmethod. � The 2-pass deformation with single strain path reversal lead to

substantial DRX (�20%) compared to no perceivable DRX afterthe 8-pass deformation with multiple strain path reversals.

� During the forward torsion in the two-pass test, the monotonic

strain (evm¼1.0) exceeded the critical strain (ec¼0.40). Theaustenite GB area, which is the primary nucleation site forDRX, increases by �10% at ec¼0.40 and reaches �35% incre-ment when strained to evm¼1.0. Therefore, the forward tor-sion caused sufficient GB serration and bulging to initiate DRX.

� In comparison, in the eight-pass test, the small strain ampli-

tude in each passes suppressed DRX of 316L stainless steel.

L. Sun et al. / Materials Science & Engineering A 568 (2013) 160–170170

The maximum increment of GB area is only �4% after forwardtorsion to evm¼0.25, which was insufficient to initiate DRX.

� Grain subdivisions by a texture mechanism were observed in

both tests of 316L. However, it appears that grain subdivisionis competing with DRX during monotonic deformation of thelow SFE 316L at higher temperatures.

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