J M A T E R S C I 4 1 (2 0 0 6 ) 2 4 4 9 –2 4 5 5

Stress relaxation in bending of AISI 316 at 773 K

F. POVOLOUnidad de Actividad Materiales CAC–CNEA, Av. Gral Paz 1499, 1650 San Martın, Argentina;CONICET, Av. Rivadavia 1917, 1033, Buenos Aires, Argentina

G.A. MANSILLA ∗UTN – Facultad Regional San Nicolas, Colon 332, 2900 San Nicolas, ArgentinaE-mail: gmansilla@frsn.utn.edu.ar

E . B. HERMIDAUnidad de Actividad Materiales CAC–CNEA, Av. Gral Paz 1499, 1650 San Martın, Argentina;CONICET, Av. Rivadavia 1917, 1033, Buenos Aires, Argentina

Published online: 3 March 2006

In this article, stress relaxation in bending of AISI 316 stainless steel at 773 K during 490 hoursis characterized. Samples were cut either parallel or transverse to the rolling direction andtreated at different temperatures prior to the bending tests. The mechanical behavior shown bythe longitudinal samples is quite different from that of the transverse samples and so weconclude there must be differences at the level of their microstructures. However, the presenceof sigma phase precipitates in both cases is the consequence of a stress-assisted process.Besides, intragranular carbide density in either sample proved to be a function of the relaxationtime. C© 2006 Springer Science + Business Media, Inc.

1. IntroductionRecently, Nabarro [1] added a worthy contribution to thediscussion around the mechanisms concerned with creepat very low strain rates (less than 10−11 s−1). He proposedthat deformation occurs by the migration of vacanciesrather than by a dislocation glide. Earlier Lifshitz [2]suggested, in a continuous model for diffusional creep,that grain boundary sliding should necessarily occur. Healso pointed out that two simultaneous sliding processesshould be considered, i.e. a grain boundary sliding pro-moted by diffusional processes and another that wouldaccommodate these diffusional processes. On the otherhand, Langdon [3] demonstrates that in the region of lowstresses the Harper-Dorn creep and grain boundary slidingare operative creep mechanisms.

It is well known that during creep tests dislocationsdo move inside the grains and that also grain boundariesmigrate. Precipitation in practical engineering materialsrepresents an important mechanism for anchoring grainboundaries and thus decreasing plastic deformation. How-ever, individual polycrystalline grains may become dis-placed during high temperature creep. Mechanisms suchas dynamic strain ageing cause an increased rate of dis-location multiplication, which delays the recovery of thedislocation structure. At 773 K, stainless steel type AISI

∗Author to whom all correspondence should be addressed.

316 shows dynamic strain ageing due to the presence ofsubstitutional solutes. Nowadays a complete descriptionand interpretation of dynamic strain ageing phenomenacan be found in [4].

We believe that although AISI 316 has been widelyinvestigated already, in these last years there have beenvery few papers concerning its stress relaxation behav-ior. Some papers do establish relationships between itsmechanical properties and its microstructure, but neithertemperature nor stress dependence have been consideredup to now. Most papers are devoted to tertiary creep [5]and to the discussion of proper methods for calculatingthe Monkman-Grant parameters.

Thus, the aim of this paper is to achieve a better under-standing of the stress relaxation behavior of AISI 316 Lat 773 K, at very low strain rates, and its dependence ontexture and on the thermal treatments received.

2. Theoretical backgroundTwo of the most useful theoretical expressions consid-ered when relating the stress-relaxation or creep data toelementary dislocation models, are the Johnston-Gilmanand Hart equations. On the one hand Johnston and Gilmandescribed the plastic strain rate ε produced by dislocationsthat move with a mean velocity v, when the applied stress

0022-2461 C© 2006 Springer Science + Business Media, Inc.DOI: 10.1007/s10853-006-5152-8 2449

σ is greater than the minimum stress required to move dis-locations, σ i. The model is summarized by the followingconstitutive equation [7 ]:

ε = φρbv = φρbvo

σ m0

(σ − σi )m ≡ εJ G

σ m0

(σ − σi )m

= ε0 (σ − σi )m (1)

where φ is the orientation factor of the slip system, ρ is thedensity of mobile dislocations that move with the meanvelocity v, b is the Burgers vector and ν0, σ0 and m arematerial constants.

On the other hand, Hart interpreted the relaxationcurves in terms of a state variable approach. At high ho-mologous temperatures the log σ − log ε curves can berepresented by [8 ]:

ε = εH ln( σ

σ ∗)−1/λ

(2)

where σ ∗ is a hardness parameter, λ is a temperatureindependent parameter and εH depends on temperature,heat treatment and deformation. Furthermore, the internalstress can be calculated as [9 ]

σi = σ − σ0[ln

(σ ∗/σ

)]−1/λm(3)

If relationships (1) and (2) are plotted in a log σ − log ε

diagram, two distinct curvatures are found: one of themconcave upwards, equation (1) and the other one concavedownwards, equation (2). When the log σ − log ε curveof experimental data presents a double curvature, bothmodels are applied [9]. The characteristic parameters ofthe Johnston-Gilman equation, m, εJ−G = φρbvo,σ0 andσ i, or those of the Hart model, λ, εH and σ ∗, determinedby a proper fit of relaxation data will be correlated withthe respective microstructure of AISI 316 L samples.

3. Experimental procedure3.1. Sample preparationThe original material was supplied by a Finish company inthe form of a 0.6 mm thick sheet and in a mildly annealedcondition. Table I gives the typical composition of theAISI 316 L alloy.

Two sets of specimens were cut. The first one was cutwith its axis parallel to (that is, longitudinal to) the rollingdirection and the second was cut with its axis perpendic-ular to (that is, transverse to) the rolling direction. Eachsample was 100 mm long and 10 mm wide. Samples

T AB L E I : Composition of AISI 316 L alloy

C Cr Ni Mo Mn P S N Si Fe

.032 17.2 10.7 2.57 1.50 .032 .01 .044 .65 balance

T AB L E I I . Thermal treatments prior to the bending tests

Type Temperature (K) Time (hours) Cooling mediaAR As received

A 1172 1 waterB 1203 1 waterC 1253 1 water

were carefully cleaned with detergent, rinsed with water,immersed in isopropyl alcohol and blow-dried. Both thelongitudinal and the transverse samples were separated infour groups of ten samples. Each group of samples wassealed into fused silica tubes with an argon atmosphere inorder to avoid oxidation during heating. Table II presentsthe temperatures of the heat treatments chosen to dissolvethe different precipitates.

It is worth mentioning that after each thermal treatmentall specimens (including those named as received) wereheated and cooled in air for 1 hour at 823 K, in order torelease internal stresses.

3.2. Stress relaxation in bendingBending is a very useful technique to determine qua-sistatic mechanical properties, in particular the elemen-tary dislocation involved in plastic deformation. In fact,the influence of a broad set of variables such as com-position, thermo mechanical treatments, etc, can beevaluated simultaneously through this technique. Fur-thermore experimental data are obtained up to timesof the order of those reached in creep. The proce-dure consists of locating flat specimens in a holderwith a specific curvature [10]. This curvature will de-termine the initial stress applied to the outer sur-face; hence the holder is usually labeled by the holderstress �.

In our tests we consider three different holders char-acterized by the following initial stresses: 210 MPa,171 MPa and 137 MPa. In each holder we dispose twosamples corresponding to each heat treatment (AR, A, Band C). In all, we put eight specimens per holder, insertedinto a furnace at the selected temperature (773 ± 1) Kand controlled with thermocouples attached to the hold-ers. Periodically we extract the samples out of the holdersto measure the remnant curvature using a profile projec-tor; duplicate specimens helped us evaluate the dispersionbetween the curvatures corresponding to samples with thesame thermal treatment.

The stress at the surface of a sample bent inside theholder is [11]:

σb = Eh

2

(1

R− 1

Ri

)(4)

where E = 166 GPa is the elastic modulus of the AISI316 at 773 K [12], R the radius of the holder, h thethickness of the specimen and Ri the curvature of the

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sample when released from the holders after a relaxationtime ti.

The stress at the surface of the bent specimen beforeunloading, σ b, can be correlated with the homogeneousstress of a sample submitted to an uniaxial test, σ , by therelationship [11]:

σ = 2

3σb + �

3

dσb

d�(5)

where � = Eh/2R is the stress imposed by the holder atthe surface of the bent specimen. For evaluating dσb/d�

holders with different radii were employed.

3.3. Metallographic characterizationMicrostructural analyses were preformed before bend-ing tests with the aim of controlling precipitatesdevelopment during heat treatments. After the relaxationtests the microstructure of the samples was observed againusing metallographic and scanning electron microscopes.Samples were polished carefully and then etched in or-der to reveal the general structure and the precipitates.Because its crystalline structure is tetragonal, the sigmaphase responded to crossed polarized light blinking and,when observed under this kind of light, looks like light-blue lagoons. Also we found titanium carbides whichshine with crossed polarized light, but do not sparkle.

The semi-quantitative chemical composition of the pre-cipitates was determined by means of Energy DisperseSpectra (EDS) analyzer attached to the scanning electronmicroscope.

4. Results4.1. Relaxation testsFigures 1 and 2 show the stress relaxation curves for thedifferent heat treatments for longitudinal and transversesamples. In order to fit these data with the phenomeno-logical equations (1) or (2) these data should be plotted ina log σ − log ε diagram. This can be easily done on con-sidering that the plastic strain rate is ε = − σ

E , where Eis the elastic modulus and the dot indicates the derivativewith respect to the relaxation time [9].

4.1.1. Longitudinal samplesFigures 3 (a) and (b) illustrate the relaxation behaviorof the longitudinal samples exposed to different heattreatments before the bending tests. Relaxation curvesshow clearly two different types of curvatures. Thoseconcave upwards were fitted by the Johnston-Gilmanequation [9, 12], while the branch of the Hart equationfor high homologous temperatures was used to fit theconcave downwards curves. For the case of the doublecurvature, observed in the relaxation of longitudinalsamples with thermal treatment C disposed in the holders

Figure 1. (a) - Stress – time curves for the longitudinal samples as received(full symbols) and with the heat treatment A (open symbols) (b) Stress -time curves corresponding to the longitudinal samples subjected to the heattreatment B (full symbols) and those corresponding to treatment C (opensymbols). The labels in curves indicate the holder stress

with the lowest stresses, both equations were used to geta proper fit (see Table III).

Stress relaxation of the samples as received, exposed tostresses of 137 MPa and 171 MPa were quite linear whenplotted in a log σ − log ε diagram. Thus, these curves canbe fitted by equation (1) on assuming that σ � σi, whichwould mean we are at the beginning of the relaxationprocess [13 ]. Then, if we neglect the contribution ofthe internal stress, for those curves we can determine theparameter m and the factor εJ−G/σ m

0 .

4.1.2. Transverse samplesA quite different mechanical response was obtained fromtransverse samples, as shown in Figs. 2(a) and (b). Therelaxation begins at higher stresses than those observed forthe longitudinal samples, certainly due to the differencesin texture.

Figure 4(a) shows clearly the anomalous relaxation be-havior of the material (as received) bent under an ini-tial stress of 137 MPa. The relaxation curve is linear, so

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Figure 2. (a) Stress – time curves for the transverse samples as received(full symbols) and with the heat treatment A (open symbols); (b) Stress -time curves corresponding to the transverse samples exposed to the heattreatment B (full symbols) and those corresponding to treatment C (opensymbols). The labels in curves indicate the holder stress

equation (1) does fit the experimental data if we neglectthe internal stress. From these data it is impossible for usto specify whether the movements of the dislocations heldduring the relaxation directly involve interactions with theprecipitates present in these samples.

Figure 3. (a) - Relaxation curves for longitudinal samples as received (fullline) and with the heat treatment A (dashed line); (b) Relaxation curvescorresponding to the longitudinal samples subjected to the heat treatmentsB (full line) and C (dashed line). The labels in curves indicate the holderstress

All other curves are concave upwards, and so theJohnston-Gilman equation is employed to fit the data,yielding the parameters shown in Table IV.

Relaxation of the transversal samples can be dividedinto two groups, according to the stress exponent: onegroup includes samples with m = 3 and the other in-cludes samples with m = 2, independently of the ther-mal treatment received by the samples. The relaxation of

T A B L E I I I . Fitting parameters for the relaxation of the longitudinal samples

Johnston-Gilman HartType � m εJ−G /σm

0 σ i λ ε∗ σ∗[MPa]

[x 10−11 s−1.MPa−m]

[MPa]

[s−1]

[MPa]

AR 210 0.2 1.5 10−16 111171 115 10−233 —137 92 10−177 —

A 210 1.8 4 75171 0.13 2 10−15 93137 1.9 4 61

B 210 2.0 3 73171 1.9 5 68137 1.6 8 58

C 210 4.9 2. 10−3 84171 4.4 5. 10−5 54 0.2 6 10−15 91137 3.4 0.2 58 0.18 4 10−16 73

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T AB L E I V. Johnston–Gilman parameters for transverse samples, ther-mal treatments are indicated

Type � [MPa]εJ−G /σm

0 [x 10−11

s−1.MPa−m] m σ i [MPa]

AR 210 1 3 119171 4 2 99

A 210 0.2 3 120171 0.5 3 78137 2 2 63

B 210 4 2 94171 4 2 78137 5 2 51

C 210 4 2 78171 0.4 3 77137 0.7 3 64

the transverse samples (as received), tested at 137 MPa,was fairly linear and therefore no internal stress could bedetermined.

4.2. Metallographic observationsThe comparison of the microstructure observed beforeand after each heat treatment allows us to say that themicrostructure is free of precipitates before the bendingtests. Furthermore, it is characterized by two grain sizes(22 and 32 µm) and some grains exhibit twins. After thestress relief treatment (performed to all samples includingthose named as received) before bending the microstruc-ture shows a remarkable grain enlargement, and no pre-cipitates. Keeping in mind that this last treatment wasperformed at 823 K during 1 hour and air cooled, fromthe transformation alloy curves no precipitates are ex-pected. This agrees with the metallographic observationsas shown in Fig. 5.

Besides, carbide density grows as the relaxationtime increases which can be proved comparingmicrostructures before and after relaxation tests. This factcan be explained if we consider that dislocations createdduring relaxation act as carbides nucleation sites.

Figure 4. Relaxation curves for transversal samples: (a) material as re-ceived (full line) and treatment B (dashed line); (b) samples exposed to heattreatments B (full line) and C (dashed line). The labels indicate the holderstress

Figure 5. Secondary electron micrograph of longitudinal samples corre-sponding to as received samples, the microstructure is characterized by twograin sizes and twins inside the grains

Figure 6. Secondary electron micrograph depicting small (particle’s sizesless than 1 micron) dispersion of M23C6 carbides inside the grains and atgrain boundaries for longitudinal sample subjected to thermal treatment Cbent at 171 MPa

4.2.1. Longitudinal samplesAccording to the alloy time-temperature-composition di-agram [14], in AISI 316 heated at 773 K during 490 honly M23C6 particles are expected to appear as precipi-tates. Nevertheless, recent studies [15] show the existenceof four distinct precipitation stages in 316 L between673 K and 773 K, which involve sigma phase precipita-tion and the formation of M23C6 carbides after a 24 houraging. This agrees with the microstructure of our sam-ples; titanium carbides at grain boundaries, and Cr andMo carbides of the type M23C6 are mainly found insidethe grains, as seen in Fig. 6. Besides these precipitates, inthe samples as received bent at holder stress of 210 MPaand in those subjected to the heat treatment A tested intothe holder of 171 MPa we found sigma phase particles(with a size greater than 3 µm) both inside the grains andat grain boundaries as shown in Fig. 7.

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Figure 7. Scanning micrograph showing coarse sigma phase precipitates atgrain boundaries as well as inside them associated to longitudinal samplesrelaxed at 171 MPa after heat treatment A

The presence of sigma phase can be explained as atemperature/stress assisted phenomena, where the tem-perature used during the stress relaxation is the maincause of the generation of this microstructure. Besides,the presence of silicon in the chemical composition alsopromotes the formation of sigma phase.

4.2.2. Transverse samplesFrom a microstructural analysis we can consider twoperfectly different groups of samples: one character-ized by very fine dispersions of Titanium carbides and(Cr,Mo)23C6 mainly located inside the grains, as illus-trated in Fig. 8, and a second group which includes sam-ples with very small sigma phase precipitates (1 micron)not expected, as explained above, nucleated preferentlyat grain boundaries even when some particles were foundinside the grains, exhibited in Fig. 9.

Figure 8. Secondary electron micrograph depicting (Cr, Mo)23C6 particles(dark) and sigma phase precipitates (white) at grain and twin boundaries aswell as inside the grains – transverse sample relaxed 210 MPa after heattreatment A

Figure 9. Secondary electron micrograph developed by transverse samplessubjected to heat treatment B and bent at 210 MPa: 1 - M23C6 chromiumrich carbides, 2 - sigma phase precipitates and 3 - titanium carbides

5. Discussion5.1. Longitudinal samplesAccording to the mechanical behaviour and the mi-crostructure presented in the previous section, we proposethe following model:

The main relaxation mechanism of AISI 316 L is themovement of dislocations. The driving forces of thismechanism are the testing temperature, the applied stress,and the obstacles to be surmounted (precipitates inside thegrains and at grain boundaries). When the energy barrierset by the obstacles is greater than the energy provided bythe driving forces, we then say that the obstacles anchorthe movement of the dislocations. The relaxation dueto this mechanism can be well described by Johnston-Gilman’s equation. At any given time all the intragranularprecipitates—either in longitudinal or transversesamples—delay or impede the dislocation movements,disregarding which thermal treatment was previously ap-plied. At low applied stresses there are not enough mobiledislocations for us to appreciate a measurable relaxation,as shown for samples type AR 137 MPa in Fig. 1(a).However, when the applied stress and consequently thenumber of unpinned dislocations increases, a certainstress relaxation is observed, as illustrated in Figs. 1(a)and (b).

The driving forces can act through another defor-mation mechanism [2, 3]: sliding at grain boundaries.Relaxation through this mechanism usually appears athigh homologous temperatures and is well fitted by thehigh-homologous temperature branch of Hart’s equation.It should be pointed out that, even when tests were notperformed at high temperatures, grain boundary slidingis the only possible mechanism of deformation when theprecipitates inside the grains anchor dislocations. Thisis clearly seen in the relaxation of samples subjectedto the heat treatment at the lowest temperature andbent under intermediate stresses, Fig. 3(a), and at thebeginning of the relaxation curves with double curvature

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as illustrated in the relaxation of samples type C inFig. 3(b). We therefore conclude that the changes in theinternal stress are due to the precipitate-matrix interface.This fact is more comprehensible if we consider theminima free energy and contact angle of the secondphase.

5.2. Transverse samplesBy simple observation we could determine that the relax-ation curves were concave upwards figures 4(a) and (b),and so the Johnston-Gilman model is the appropriate forfitting data in this particular case (this model has alreadybeen explained in a previous paragraph). Considering thecharacteristic m parameter of this model, relaxation curvesmay be arranged into two groups, each one of them char-acterized by a different m value.

The first group, with m = 3, has a microstructure con-sisting of very fine precipitates of titanium, (Cr,Mo) car-bides and a sigma phase. Precipitates were found bothinside the grains and at their boundaries, as shown infigure 8.

The second group, represented by the stress parameterm = 2, presents M23C6 and MC precipitates as well assigma phase precipitates, as depicted in Fig. 9. The latterwere extremely small (in the order of a micron) and werepresent at a much lower density than in the m = 3 sam-ples. In all of the cases studied the interior of the grainsrepresents the favourite nucleation site. Although a fewprecipitates were found at grain boundaries, these did notrepresent an obstacle for the movement of dislocations.Consequently, the deformation speed is greater than inthe m = 3 case, because the dislocations can slide easilyand their movement is not affected by the presence of theprecipitates.

That the existance of an effective precipitates size thatdoes not interfere with the sliding of dislocations is clear;even when they coarse slowly, if they are to adopt a largersize, they can become walls for the dislocations to climb-this is in fact the case of the titanium and (Cr, Mo) carbidespresent in the m = 3 samples.

We can finally conclude that the m parameter seems tobe in some way related to the amount of second phaseprecipitates found at grain boundaries. At the same time,this parameter shows no dependence on the tension ap-plied by the holders- this last being the main parameter ofthe tests of our analysis.

6. ConclusionsTwo phenomenological models, developed by Johnston-Gilman and Hart, are suitable to explain the stress relax-ation in bending of AISI 316 L at 773 K. Our proposal putsforward that the Johnston-Gilmanes model is useful whenthe relaxation mechanism consists in the movement of dis-locations controlled by precipitates inside the grains. Onthe other hand, Hart’s model applies when the obstaclesto overcome to observe relaxation of the microstructureare precipitates at grain boundaries.

AknowledgmentsAuthors wish to thanks authorities of Instituto Argentinode Siderurgia, in which the researchers developed partof this investigation, through the agreement with Fac-ultad Regional San Nicolas – Universidad TecnologicaNacional

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Received 18 May 2004and accepted 7 July 2005

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