Hall–Petch Behavior in Ultra-Fine-Grained AISI 301LNStainless Steel

S. RAJASEKHARA, P.J. FERREIRA, L.P. KARJALAINEN, and A. KYROLAINEN

An ultra-fine-grained AISI 301LN austenitic stainless steel has been achieved by heavy coldrolling, to induce the formation of martensite, and subsequent annealing at 800 �C, 900 �C, and1000 �C, from 1 to 100 seconds. The microstructural evolution was analyzed using transmissionelectron microscopy and the yield strength determined by tension testing. Ultra-fine austenitegrains, as small as ~0.54 lm, were obtained in samples annealed at 800 �C for 1 second. Forthese samples, tensile tests revealed a very high yield strength of ~700 MPa, which is twice thetypical yield strength of conventional fully annealed AISI 301LN stainless steels. An analysis ofthe relationship between yield strength and grain size in these submicron-grained stainless steelsindicates a classical Hall–Petch behavior. Furthermore, when the yield dependence on annealingtemperature is considered, the results show that the Hall–Petch relation is due to an interplaybetween fine-grained austenite, solid solution strengthening, precipitate hardening, and strainhardening.

DOI: 10.1007/s11661-007-9143-4� The Minerals, Metals & Materials Society and ASM International 2007

I. INTRODUCTION

AUSTENITIC stainless steels (SS) are commonlychosen for applications where good corrosion proper-ties, moderate strength, and aesthetic appearance areimportant. However, austenitic SS are less suitable forstructural applications due to their relatively low yieldstrength (230 to 350 MPa).[1] Although the yieldstrength can be improved up to 1500 MPa by coldrolling due to the formation of stress-induced martens-ite, these high-strength SS have reduced ductility andpoor formability properties. In this context, research hasbeen conducted to identify alternative routes to producehigh-strength SS.[2–5] One of these methods involvesheavy cold rolling of metastable SS to induce theformation of stress-induced martensite, followed by anannealing treatment to revert the martensite into ultra-fine-grained austenite. The ultra-fine-grained austeniteproduced in this fashion could provide both significantstrengthening and enhanced formability properties.

Formation of ultra-fine-grained austenite has beenfirst demonstrated in special noncommercial metastableFe-Cr-Ni alloys with negligible C, N, and Mn con-tents.[2–4] More recently, a commercial AISI 304 SS hasalso been investigated;[5] however, because the austenitephase is rather stable in this alloy, the formation ofstress-induced martensite and subsequent austenitereversion is highly inefficient. Thus, using more meta-

stable SS, such as AISI 301LN SS could presumablylead to higher volume fractions of martensite duringcold rolling and, consequently, smaller austenite grainsupon annealing. Preliminary results obtained by thepresent authors on AISI 301LN SS have already shownconsiderable success.[6–9] In fact, transmission electronmicroscopy (TEM) analysis and tensile testing hasconfirmed the presence of fine austenite grains withdesirable mechanical properties.[10]

In order to better understand the interplay betweenfine austenite grain size and the mechanical propertiesobtained, it is thus important to determine the Hall–Petch relation in these ultra-fine-grained SS. Shinoet al.[5,11] has reported a Hall–Petch type behavior forAISI 304 SS and AISI 301 SS down to 0.8- and 3-lmgrain size, respectively. According to Shino et al.,[11] theHall–Petch relation seemed to break down below 3-lmgrain size for AISI 301 SS. However, these investiga-tions[5,11] did not seem to consider the fact thatmetastable austenitic SS do not fully convert thestress-induced martensite to reverted austenite duringannealing, particularly at low annealing temperatures.Hence, the presence of martensite in annealed sampleswill influence the yield strength, which consequently willaffect the Hall–Petch behavior. Furthermore, no resultshave been reported for the nitrogen-bearing AISI301LN SS, which is the focus of this work.In this context, the objective of this work was to

examine the relationship between the ultra-fine austenitegrain size, formed using the method aforementioned,and the yield strength obtained in AISI 301LN SS. Inour approach, we have first considered the case wherethe Hall–Petch relationship is independent of tempera-ture. However, during annealing at different tempera-tures, the microstructure is likely to change, inparticular, due to the formation of precipitates andchanges in dislocation density. Thus, we have further

S. RAJASEKHARA, Doctoral Student, and P.J. FERREIRA,Assistant Professor, are with the Materials Science and EngineeringProgram, The University of Texas at Austin, Texas 78712,USA. L.P. KARJALAINEN, Professor, is with the Department ofMechanical Engineering, The University of Oulu, 90014, Oulu, Fin-land. A. KYROLAINEN, Senior Researcher, is with the OutokumpuStainless Oy, 95400, Tornio, Finland. Contact e-mail: ferreira@mail.utexas.eduManuscript submitted May 20, 2006.Article published online June 14, 2007.

1202—VOLUME 38A, JUNE 2007 METALLURGICAL AND MATERIALS TRANSACTIONS A

considered the case where the Hall–Petch relation will beaffected by the annealing temperature. The studydescribed herein will be an additional step towardunderstanding the effect of annealing conditions and thevarious strengthening mechanisms on the mechanicalproperties of reversion-annealed SS.

II. EXPERIMENTAL

A. Materials

An AISI 301LN SS sheet with the composition shownin Table I was prepared by Outokumpu Stainless Oy.The Md30 and Ms values for this material were calcu-lated to be 35 �C and –127 �C, respectively.[12] The Md30

value above room temperature indicates that stress-induced martensite will form in samples deformed atambient temperature. Samples from a 1.5-mm-thicksheet were then subjected to 63 pct cold reduction in alaboratory rolling mill at Outokumpu Stainless Oy.

B. Methods

After cold rolling, the samples were annealed on aGleeble 1500 thermomechanical simulator at the Uni-versity of Oulu. The samples were heated at a rate of200 �C/s and held at 800 �C, 900 �C, or 1000 �C for 1,10, or 100 seconds, respectively. Subsequently, thesamples were forced-air-cooled at a cooling rate ofapproximately 200 �C/s. Annealed specimens withdimensions ~85 · 10 mm2, with a heated zone of15 · 10 mm2, were subjected to further studies. Threesets of samples were prepared. The first set was used forSQUID measurements to determine the volume fractionof reverted austenite. These results were publishedelsewhere.[8] The second set was used for TEM analysis,and the third set for testing the mechanical properties.

1. Transmission electron microscopyFor the TEM observations, the samples were first

thinned to ~100 lm by mechanical polishing. Thereaf-ter, these samples were thinned to electron transparencyin a jet-polishing apparatus (Struers Tenupol-5). Amixture of 59 vol pct methanol, 35 vol pct m-butanol,and 6 vol pct perchloric acid was used as the electrolyte.The thinning procedure took place at –10 �C, at avoltage of ~32 V and a current of 50 to 60 mA. Electrontransparent samples were analyzed in a JEOL* 2010F

transmission electron microscope operating at 200 kV.

2. Grain size measurements—average grain sizeNegatives obtained from the TEM were used to

estimate the austenitic average grain size. The negativeswere first scanned and the digitized images weresubsequently analyzed using the Image J software. Foreach sample, 100 grains were measured to determine themean linear intercept grain size, �d.

3. Grain size measurements—weighted average grainsizeAs a preliminary examination of the TEM micro-

graphs indicated, the presence of a significant grain sizedistribution a weighted average grain size, �dw, was alsocalculated for all annealed samples. For this calculation,100 individually measured grains were distributed inbins 0.25 lm in size, for a given sample. A bin size of0.25 lm was selected to optimize the statistical results. Asmaller bin size leads to poor statistical accuracy,whereas a larger bin size masks the effect of smallgrains. After evaluating the range of grain sizes present,the bins were defined as B = (b1,b2,…,bN), whereb1 = 0 to 0.25 lm, b2 = 0.25 lm to 0.50 lm,…,bN = 19.75 lm to 20.00 lm. Subsequently, the numberof grains belonging to each of the ith bin is counted froma sample of 100 grains. Denoting the number of grainsin the ith bin as ni and dividing it by the total number ofgrains, N, the weight of the ith bin can written as

wi ¼niN

½1�

Additionally, the square root of the areal mean of nigrains in the ith bin gives the average grain size, �di, forthe ith bin. Knowing �di and wi, the weighted averagegrain size of the sample is calculated by

�dw ¼XN

i¼1wi

�di ½2�

4. Tensile testingAnnealed samples from the Gleeble 1500 thermome-

chanical simulator were used for testing mechanicalproperties. Coupons of dimensions 150 · 15 · 0.9 mm3

were tensile tested under a strain rate of 3 · 10–3 s–1 ona Zwick Z250 testing machine at Outokumpu StainlessOy. This nonstandard geometry was used, because theuniform annealed zone in the coupon was small(~15 mm).

III. RESULTS

A. Microstructure

The TEM images from the cold-rolled sample revealthat the sample is primarily comprised of martensite(Figure 1). Selected area diffraction patterns (SADPs)from two different regions of the sample indicate thepresence of different types of martensite: the lath-typemartensite, which is comprised of elongated grains ofmartensite and characterized by the spotlike SADP

Table I. Chemical Composition (Weight Percent) of AISI

301LN SS Used in This Investigation

C N Ni Cr Mn Si Cu Mo

301LN 0.017 0.15 6.5 17.3 1.29 0.52 0.2 0.15

*JEOL is a trademark of Japan Electron Optics Ltd., Tokyo.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 38A, JUNE 2007—1203

(Figure 1(b)), and the dislocation-cell-type martensite,which was formed due to the heavy deformation of lath-type martensite and characterized by the ringlike SADP(Figure 1(c)).

Upon annealing the cold-rolled samples at the tem-peratures of 800 �C, 900 �C, and 1000 �C, there is analmost complete martensite (a¢) fi austenite (c) rever-sion. As discussed elsewhere,[8] these samples exhibitapproximately the same amount of austenite, which isaround 93 pct. The remaining 7 pct is attributed tomartensite, which was identified in all annealed samples.An example of the presence of martensite in theannealed samples is shown in Figure 2.

A careful TEM examination of the microstructures ofthe various annealed samples shows distinct features(Figure 3). The samples annealed at 800 �C for 1 and10 seconds (Figures 3(a) and (b)) exhibit a mixture oflarge equiaxed austenitic grains, small newly nucleatedgrains of austenite, and secondary-phase precipitates,namely, CrN nitrides, which were identified by electronnanodiffraction analysis (Figure 4). As the annealingduration is further increased to 100 seconds, a dramaticincrease in grain size is observed (Figure 3(c)).

The TEM images for the samples annealed at 900 �Cand 1000 �C are also shown in Figure 3. After 1-secondannealing time, larger defect-free austenitic grains areformed at both annealing temperatures. These austenitic

Fig. 1—(a) TEM image of cold-rolled AISI 301LN SS, (b) SADP of lath-type martensite, and (c) SADP of dislocation-cell type martensite.

Fig. 2—TEM image of a martensitic region in the AISI 301LN SSsample annealed at 800 �C for 10 s. The insert shows the SADP ofthe martensitic region within the black circle.

1204—VOLUME 38A, JUNE 2007 METALLURGICAL AND MATERIALS TRANSACTIONS A

grains rapidly grow in size with further annealing for 10and 100 seconds. Finally, when compared with thesamples annealed at 800 �C, there is a marked reductionin the number of CrN nitrides formed for the samplesannealed at 900 �C. At 1000 �C, the nitrides dissolve dueto the high solubility of nitrogen in austenite.[24]

B. Grain Size Measurements

Results obtained from average grain size �d werecompared with weighted average grain size, �dw. Asexpected, the �dw values differ by at least 10 pct from �d,for the samples annealed at 800 �C for 1 second,demonstrating the presence of a significant grain sizedistribution. However, for the samples annealed at900 �C and 1000 �C, the difference between �dw and �d is

less than 1 pct. This result indicates that for higherannealing times and temperatures, the weight due tolarge grains becomes more significant in calculating �dw.In general, because the weighted average grain sizeprovides a more realistic representation of grain size forall annealing temperatures, we have chosen to use �dwthroughout this work.The weighted average grain size as a function of

annealing conditions is shown in Figure 5. As ex-pected, samples annealed at 800 �C for 1 second showthe smallest average grain size of ~0.54 lm. When theannealing duration is increased from 1 to 100 seconds,these samples show an increase in grain size from~0.54 to ~2.4 lm. Similar trends are observed for thesamples annealed at 900 �C, which exhibit an increasein grain size from ~1.2 to ~6.1 lm, and the 1000 �C

Fig. 3—TEM images of cold-rolled AISI 301LN SS samples annealed at (a) through (c) 800 �C, (d) through (f) 900 �C, and (g) through (i)1000 �C for different times.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 38A, JUNE 2007—1205

samples, which show a drastic increase from ~1.5 to~10 lm.

C. Mechanical Properties

1. Yield strength and tensile strengthThe yield strength for all annealed samples is shown

in Figure 6(a). All samples annealed at 800 �C, andthe sample annealed for 1 second at 900 �C exhibithigh yield strength values. In fact, samples annealed at800 �C for 1 second demonstrate a yield strengththat is almost twice that of conventionally processedAISI 301LN (~350 MPa). However, as the anneal-ing duration is increased for the 900 �C samples, orthe annealing temperature is increased to 1000 �C,the yield strength decreases considerably. The tensilestrength of all annealed samples is shown in

Figure 6(b). These values are at least 50 pct higherwhen compared with conventionally processed AISI301LN.

Fig. 4—(a) Secondary phase precipitates observed in AISI 301LN SS annealed at 800 �C and 900 �C are shown within the black circle. (b)Electron nanodiffraction analysis of the precipitates shown in (a) reveal the presence of CrN nitrides with a face-centered cubic structure and alattice parameter of 4.14 A.

Fig. 5—Weighted average grain size of AISI 301LN SS samplessubjected to different annealing conditions.

Fig. 6—(a) Yield strength and (b) tensile strength obtained for AISI301LN SS samples for different annealing conditions.

1206—VOLUME 38A, JUNE 2007 METALLURGICAL AND MATERIALS TRANSACTIONS A

2. Uniform elongationAs shown in Figure 7, the uniform elongation of

practically all annealed samples is comparable to thoseof conventionally processed AISI 301LN SS. Addi-tionally, using the Considere criterion,[15] the workhardening exponent (n) can be related to the uniformelongation strain (eu ), as n = eu at the onset ofnecking. Thus, from Figure 7, it can be inferred thatthe samples have a high work hardening exponent (n)of at least 0.40 for the annealing temperatures of900 �C and 1000 �C. Because the work hardeningexponent measures the formability characteristic of analloy, we can deduce that ultra-fine-grained samplesobtained in this work have formability characteristicsthat are similar to those of conventionally processedAISI 301LN SS.

For samples annealed at 800 �C for 1 and 10 seconds,the uniform elongation is slightly less than convention-ally processed AISI 301LN SS, as expected due to a finergrain size.

IV. DISCUSSION

In order to understand the origin of the high yieldstrength obtained for all annealed samples, we assumethe yield strength to be correlated with the grain sizeobtained, according to the Hall–Petch relationship:[5,16]

ryield ¼ ro þ k �d� ��1

2 ½3�

where ro is the lattice friction stress, �d the average au-stenitic grain size, and k a constant. However, thisequation assumes a single phase and an average grainsize. Therefore, Eq. [3] needs to be modified to takeinto account (1) the presence of both austenite andmartensite phases in the annealed samples and (2) alarge grain size distribution for certain samples.

The presence of both austenite and martensite can beresolved by using the classical rule of mixtures,ryield ¼ Va0ra0 þ Vcrc, where ra0 is the yield strength ofmartensite (a¢), Va0 the volume fraction of martensite, rc

the yield strength of austenite, and Vc is the volumefraction of austenite. Assuming ra0 ~ 1500 MPa,[14] wecan extract from Figure 6(a) the yield strength due onlyto the presence of austenite. In addition, as cold rollingleads to the formation of approximately 97 pct stress-induced martensite and 3 pct retained austenite,[8] uponannealing, the total austenite content is a mixture ofreverted austenite, which nucleated from stress-inducedmartensite, and retained austenite, which has likelyrecrystallized.The presence of a broad grain size distribution in

certain samples can be considered by replacing theaverage grain size �d with a weighted average grain sizeterm, �dw, which can be calculated according to Eq. [2].

Fig. 7—Uniform elongation obtained for AISI 301LN SS samplesfor different annealing conditions.

Fig. 8—Hall–Petch relationship between austenite grain size andyield strength, assuming (a) temperature-independent and (b) temper-ature-dependent conditions. The R-square values are given forcomparison.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 38A, JUNE 2007—1207

Thus, the modified Hall–Petch equation can now bewritten as

rcyield ¼ ro þ k �dw

� ��12 ½4�

where all the terms have been previously defined.Based on the values for rc

yield and �dw� ��1

2 for variousannealing parameters, a linear curve can be fit to thesedata, so that the constant k and the off-set stress ro

can be estimated (Figure 8(a)). In this fashion, a k va-lue of ~274 MPa lm1/2 and an offset stress of~252 MPa were calculated. These values differ consid-erably from those obtained by Schino et al.[5,11] forAISI 301 SS and AISI 304 SS. In particular, theseinvestigations reported higher k values (~400 MPalm1/2) for both SS and a deviation from the Hall–Petch relationship for AISI 301 SS below a grain sizeof 3 lm. In this regard, one might be tempted to thinkthat the use of �dw, instead of �d, could explain the dis-crepancy. However, calculations using �d yields a valueof k ~ 290 MPa lm1/2 that is still significantly less thanthose reported in the literature.[5,11] Thus, we believethat there may be fundamental reasons, other thangrain size, that may be responsible for a low k value.Possible reasons may include (1) the presence of re-tained tempered martensite after annealing, which wasnot considered by Schino et al.;[5,11] (2) the presence ofnitrogen in AISI 301LN SS, which has a differentstrengthening effect from that of carbon, which is pres-ent in AISI 301 SS and AISI 304 SS; and (3) the for-mation of CrN nitrides in AISI 301LN SS, instead ofcarbides, that may be present in AISI 301 SS and AISI304 SS.

Another important aspect in establishing the correla-tion between the yield strength and grain size is the factthat the microstructure of AISI 301 LN SS is dependenton the annealing temperatures used in this work. Thus,it is relevant to consider the Hall–Petch behaviorseparately for each temperature. This analysis is shownin Figure 8(b), where a marked influence of the anneal-ing temperature on the off-set stress ro (intercept withthe y-axis) is observed. On the other hand, it seems thatthere is no significant effect of the annealing temperatureon the Hall–Petch coefficient k. The nondependence of kon the annealing temperature has also been demon-strated in a different alloy system by Conrad et al.[17]

However, it should be kept in mind that, in the currentwork, precipitates formed in AISI 301LN SS uponannealing, which has been claimed to affect the value ofk.[18] Plausible explanations for this apparent discrep-ancy may be that the parameter k is neither stronglyinfluenced by precipitates below a certain size, nor byprecipitates which are not located predominantly at thegrain boundaries. In fact, Mangen and Nembach[18]

have shown that for precipitates below 10 nm, disloca-tion pileups were readily formed. In addition, they alsoshowed that the parameter k could be affected byprecipitates at grain boundaries due to the creation of aprecipitation-free zone along grain boundaries.

In the case of AISI 301LN SS, the average size rangeof nitride precipitates is typically below 10 nm and no

precipitates were observed at the grain boundaries.Thus, although nanosized precipitates were present inAISI 301 LNSS, particularly at 800 �C, they seem nothave a strong influence on the critical stress required tounlock dislocations and on the number of dislocations nin a pileup, which is related to the parameter k throughthe expressions[17]

k ¼M2:2plbð2� tÞsc

4ð1� tÞ

� �½5�

nse ¼ sc ½6�

where M is the Schmidt factor, l the shear modulus, bthe Burgers vector, m the Poisson’s ratio, se the appliedresolved shear stress, and sc the critical shear stress toinitiate dislocation movement in the adjacent grain.In order to better understand the temperature effects

on the Hall–Petch equation, we should consider that theoff-set stress can be written, in general, as the sum ofseveral strengthening mechanisms: (1) precipitatestrengthening, (2) strain hardening, and (3) solid solu-tion strengthening. This can be expressed as follows:

ro ¼ rd þ rppt þ rss ½7�

where rd = 2 lb�q is the strengthening contributiondue to dislocation-dislocation interaction (strain hard-ening), l is the shear modulus, b is the Burgers vector,and q is the dislocation density; rppt = (0.84spptlb)/LCu[19] is the strengthening contribution due to thepresence of precipitates, sppt is the critical resolvedshear stress required to move dislocations past a ran-dom array of precipitates, L is the distance betweenthe precipitates, and C/ is the Schmid factor. Finally,rss is the strengthening contribution due to solid solu-tion.Thus, to assess the off-set stress, we need to determine

the contributions by each strengthening mechanism as afunction of temperature. For the calculations, thevarious errors associated with the measurements wereconsidered, in particular the residual errors associatedwith determining the off-set stress (intercept with the y-axis) and the errors in measuring the distances betweenprecipitates. The errors were then calculated and con-verted to MPa values. Finally, the geometric mean oferrors was considered due to additions or subtractionsperformed during calculations.In assessing the contributions of the various

strengthening mechanisms to the off-set stress, webegin with the calculation of rss at 1000 �C. Assumingthe samples annealed at this temperature exhibitcharacteristics of a fully annealed material, i.e., theabsence of secondary phase precipitates (rppt = 0) anda typical equilibrium dislocation density of 1012 m–2,Eq. [7] can be simplified and rearranged in the formrss = ro – rd. Thus, for a dislocation density q ~1012 m–2,[20] a shear modulus, l = 77 GPa,[19] and aBurgers vector, b = 2.51 A, rd can be calculated as~39 MPa. Because ro ~ 252 MPa at 1000 �C (obtainedfrom Figure 8b), the solid solution strengthening rss

1208—VOLUME 38A, JUNE 2007 METALLURGICAL AND MATERIALS TRANSACTIONS A

can be calculated as ~213 MPa for the sample annealedat 1000 �C (Figure 9).

For the 800 �C and 900 �C samples, the calculation ofrss is not as trivial, because CrN nitrides are present atthese temperatures (Figure 3), leading to a depletion ofchromium and nitrogen from the austenitic matrix. Aloss of nitrogen from the austenite matrix, due to nitrideformation, will thus affect the strengthening due to solidsolution.[22–25] Hence, it is necessary to quantify theamount of nitrogen present in the precipitates to be ableto assess rss. This can be done by estimating the volumefraction of nitrides in a given sample, according to theexisting number and size of nitrides per unit volume,determined through TEM analysis. The volume ofmaterial considered for the calculation was estimatedby measuring (1) the area of the TEM micrographthrough image-analysis software, and (2) the foil thick-ness by analyzing the Kossel–Mollenstedt fringes in aconvergent beam electron diffraction pattern(CBED).[26] This analysis shows that ~0.010 wt pct Nand ~0.009 wt pct N are present in the form of nitridesfor the samples annealed at 800 �C and 900 �C, respec-tively. As the strength of austenitic stainless steel isdependent on nitrogen content, according to the empir-ical expression Dr ~ 1014 · [DN] (in MPa),[22–25] where[DN] is the change in wt pct N, the reduction in rss forthe samples annealed at 800 �C and 900 �C can becalculated as ~15 MPa and ~11 MPa, respectively.Subtracting these values from the calculated rss, forthe fully annealed alloy (~225 MPa), yields the rss valuesfor the samples annealed at 800 �C and 900 �C(Figure 9).

Consider now the strengthening contribution rppt dueto the presence of CrN nitrides. Nabarro has shown thatthe critical resolved stress required to move dislocationspast a random array of precipitates can be expressed assppt ~ 0.84 lb/(LCu).[19] Because sppt = rpptCu andassuming (1) a random orientation of grains with respectto the applied stress axis and (2) a maximum stressdirection on the slip plane, we can write rppt = 3sppt.

[18]

In addition, as the material studied herein is a polycrys-talline material, an average value rppt

� �due to the

presence of CrN nitrides in multiple grains should beestimated. This was done by measuring rppt in 100grains for samples annealed at 800 �C and 900 �C andthen calculating their average. Calculated rppt

� �average

values for the samples annealed at 800 �C and 900 �Care shown in Figure 9. The results indicate a dramaticdecrease in precipitate strengthening as the annealingtemperature is increased from 800 �C to 900 �C due tothe absence of nitrides at higher temperatures.[27]

Finally, the strain hardening rd can be calculated bysubtracting the values of rss and rppt from the off-setstresses ro obtained for each annealing temperature(Figure 9). The results show that the strain hardeningcontribution obtained for the 800 �C and 900 �C sam-ples is ~40 MPa and decreases slightly for higherannealing temperature. Based on this value, an approx-imate dislocation density was estimated to be~1 · 1012 m–2 for both samples, which compares wellwith that of a fully annealed polycrystalline alloy. Thisindicates that the retained austenite, which may have

failed to recrystallize does not seem to play an importantrole in strain hardening.In general, it is clear that for samples annealed at

800 �C, a large off-set stress primarily due to solidsolution and precipitate strengthening can be observed.However, as the annealing temperature is increased, thecontribution of precipitate strengthening to the off-setstress is reduced and solid solution strengthening,mainly due to the presence of nitrogen, becomes thepredominant effect.We are now left with the task of considering the sole

effect of grain-boundary strengthening rgbs as a functionof annealing temperature. As the value of k remainsapproximately constant with annealing temperature(Figure 8(b)), the effect of grain boundary strengtheningis shown in Figure 10. On this basis, comments on theimportance of each strengthening mechanism (strainhardening, precipitate strengthening, grain boundarystrengthening, and solid solution strengthening) to theyield strength at different annealing temperatures can bemade.As shown in Figure 9, strain hardening has a minor

influence on the yield strength at all annealing temper-atures considered. Attention is thus focused on theremaining three strengthening mechanisms. At thelowest annealing temperature of 800 �C and shortestannealing time of 1 second, the presence of ultra-fineaustenitic grains contributes the most to the yieldstrength via grain boundary strengthening (Figures 9and 10). However, as temperature increases or timeprogresses, grain growth occurs. Thus, grain boundarystrengthening is diminished (Figure 10), while solidsolution strengthening becomes the predominant factor(Figure 9). Furthermore, at the annealing temperatureof 800 �C, the presence of nitrides contributes substantiallyto the yield strength through precipitate strengthening.

Fig. 9—Strengthening mechanisms operating in AISI 301LN SSsamples annealed at various temperatures. The solid lines are bestfits to the calculated data.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 38A, JUNE 2007—1209

This contribution decreases at the annealing tempera-ture of 900 �C, and eventually plays no role at 1000 �C,the highest annealing temperature tested (Figure 9).From this discussion, one can see that different strength-ening mechanisms gain prominence at different anneal-ing times and temperatures.

V. CONCLUSIONS

Stress-induced martensite in commercial AISI 301LNSS was successfully reverted to ultrafine-grained austen-ite during annealing at 800 �C for 1 second. The samplesannealed at this temperature exhibited the highest yieldstrength compared with that of conventional processedSS. Annealing the samples at 900 �C and 1000 �Ccaused significant grain growth, but the yield stresswas still higher than in conventionally processed SS.

Overall, the yield strength obtained for all annealedsamples was evaluated with respect to the two termspresent in the Hall–Petch relationship: the off-setstrength (ro) and grain boundary strengthening (rgbs).The off-set strength was subdivided into three contribu-tions: precipitate strengthening (rppt), solid solutionstrengthening (rss), and strain hardening (rd), and theeffect of the annealing parameters on these contributionswas analyzed.

For samples annealed at 800 �C, the high yieldstrength was primarily due to the presence of (1) ultra-fine grains leading to significant grain boundarystrengthening, (2) solid solution strengthening, and (3)secondary-phase nitrides leading to substantial precip-itate strengthening. As the annealing temperature wasincreased to 900 �C and 1000 �C, the dominantstrengthening mechanism to yield strength was due tosolid solution strengthening. On the other hand, strainhardening was not an important mechanism in increas-ing the yield strength for any of the annealed samples.

ACKNOWLEDGMENTS

The authors at the University of Texas at Austinacknowledge the financial support from the NationalScience Foundation (NSF), Award No. DMR-0355234.The authors at the University of Oulu acknowledge thefinancial support from TEKES, Helsinki, Finland.

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Fig. 10—Grain boundary strengthening as a function of annealingconditions in AISI 301LN SS samples.

1210—VOLUME 38A, JUNE 2007 METALLURGICAL AND MATERIALS TRANSACTIONS A