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Materials Science and Engineering A 457 (2007) 139–147

Temperature effect on the low-cycle fatigue behavior of type316L stainless steel: Cyclic non-stabilization and

an invariable fatigue parameter

Seong-Gu Hong a,b,∗, Soon-Bok Lee b, Thak-Sang Byun a

a Materials Science and Technology Division, Oak Ridge National Laboratory, P.O. Box 2008, MS-6151, Oak Ridge, TN 37831, USAb Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology,

373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea

Received 11 September 2006; received in revised form 1 December 2006; accepted 8 December 2006

bstract

The temperature effect on the cyclic non-stabilization of cold-worked 316L stainless steel during low-cycle fatigue deformation was investigated.he material underwent additional cyclic hardening at room temperature and in the temperature range of 250–600 ◦C; the hardening at room

emperature came from plasticity-induced martensite transformation and the hardening in the temperature range of 250–600 ◦C was attributedo dynamic strain aging. These hardening mechanisms competed with the cyclic softening induced by dynamic recovery, which is generally

redominant in cold-worked materials, and this led to the cyclic non-stabilization of the material. Three fatigue parameters: the stress amplitude,lastic strain amplitude and plastic strain energy density, were evaluated to find an invariable fatigue parameter. The results revealed that the plastictrain energy density was stabilized at the early stage of fatigue life and nearly invariant through the entire life. 2006 Elsevier B.V. All rights reserved.

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eywords: Cyclic non-stabilization; Dynamic strain aging; Plasticity-induced m

. Introduction

Type 316L stainless steel is a prospective material for theeactor vessels and piping systems in nuclear power plants ands also the major structural material for the international ther-

onuclear experimental reactor (ITER) fusion device that willoon begin construction [1–6]. The choice of this material isrimarily based on a good combination of high-temperature ten-ile and creep strength and corrosion resistance, coupled withnhanced resistance to sensitization and associated intergranularracking. In liquid metal cooled fast breeder reactor (LMFBR)pplications, for example, the components are exposed to

igh temperature ranging from 300 to 600 ◦C and undergoemperature-gradient induced cyclic thermal stresses as a resultf start-ups and shut-downs. Therefore, low-cycle fatigue (LCF)

∗ Corresponding author at: Materials Science and Technology Division, Oakidge National Laboratory, P.O. Box 2008, MS-6151, Oak Ridge, TN 37831,SA. Tel.: +1 865 241 9493; fax: +1 865 574 0641.

E-mail addresses: hongsg@ornl.gov, hsg@kaist.ac.kr (S.-G. Hong).

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921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2006.12.035

site transformation; Dynamic recovery; Fatigue parameter; 316L stainless steel

s recognized as one of the main degradation mechanisms affect-ng the integrity of the reactor vessels and piping systems inMFBR [1–6], and specific attention on LCF is required in theesign and life assessment of these components.

Our previous studies [4–6] on the same material, in this study,evealed that cold-worked (CW) 316L austenitic stainless steels not stabilized during fatigue deformation. Its cyclic stressesponse (CSR) continuously changes with the number of cyclesnd the characteristic of CSR depends on temperature. Theidely used life prediction models, such as the Coffin–Mansonodel [7], S–N curve-related models and energy-based models

8] were developed on the basic assumption that the behavior ofaterial experiencing cyclic loading is stabilized (or saturated)

uring the initial stage, at least within several tens of cycles.n many materials, however, such a stabilized state is hardlychieved because the cyclic stress response of a material resultsrom the interaction between competing mechanisms of hard-

ning and softening, and the activated mechanisms for cyclicardening or softening depend on test conditions, such as tem-erature, load amplitude, loading rate and so on. Hence, materialehavior under cyclic loading becomes very complicated and

1 and Engineering A 457 (2007) 139–147

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electing a proper fatigue parameter, which represents the statef material during a whole life, is recognized to be significantn reliability evaluation of structures.

In this study, the mechanisms of cyclic hardening or softeningt each temperature and their effects on material behavior werenvestigated by analyzing cyclic stress responses and microstruc-ures of CW 316L stainless steel undergoing LCF deformation.t was also attempted to find out a suitable fatigue parameter byxamining the evolutions of several fatigue parameters with theumber of cycles.

. Experimental details

.1. Material and specimen

The material used in this study was CW 316L stainlessteel having the following chemical compositions in wt%:-0.025, Si-0.41, Mn-1.41, P-0.025, S-0.025, Ni-10.22, Cr-6.16, Mo-2.09, N-0.043 and Fe-balance. The test material wasolution-annealed at 1100 ◦C for 40 min, water-quenched andold-drawn to a round bar having a diameter of 16 mm. Thisold-drawing introduced a tensile prestrain of 17%, and thisreatment yielded an average intercept grain size of ∼44 �m. The

icrostructures of the material are presented in Fig. 1. �-Ferritecc structure precipitation, which appears as irregular bands dis-ributed along the drawing direction, is noticed in Fig. 1(a). Thereas no remarkable grain elongation along the cold-drawingirection. The cold-drawing induced uniformly distributed butartially tangled dislocation substructure, as shown in Fig. 1(b).he as-received material was fabricated into dog-bone typeylindrical fatigue specimens having a gauge length of 36 mmnd a gauge diameter of 8 mm in accordance with ASTM stan-ard E606-92.

.2. Test equipment and procedure

A closed-loop servo-hydraulic test system with 5-tonnesapacity was used to carry out LCF tests. A three-zone resis-ance type furnace, which controls temperature within a rangef ±1 ◦C at steady state, was used for temperature control. Aigh temperature extensometer with a gauge length of 25 mmMTS model no.: 632-13F-20) was used to control and measuretrain. Low-cycle fatigue tests were performed in laboratory airnder fully reversed total axial strain control mode using a trian-ular waveform at room temperature (RT), 200, 400, 550, 600nd 650 ◦C. The strain amplitude varied from 0.3 to 0.8% and atrain rate was fixed at 1 × 10−3 s−1. Strain rate dependency testsere also carried out by changing the strain rate from 3.2 × 10−5

o 1 × 10−2 s−1 in the temperature range of 400–650 ◦C, wherehe strain amplitude was fixed at 0.5%.

The changes of dislocation substructure and the precipitationf secondary-phase particles during LCF testing were studiedsing a JEOL 2000FX transmission electron microscope (TEM).

amples for TEM were obtained from a thin slice cut at a distancef 1 mm away from the fracture surface and then electropolishedn a solution containing 5% perchloric acid and 95% acetic acidt 70 V and 10 ◦C.

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ig. 1. The microstructures of the as-received material: (a) optical micrographnd (b) TEM micrograph.

. Results

.1. Cyclic stress response

The cyclic stress response of a material represents an evo-ution of tensile peak stress with the number of cycles duringatigue deformation and is the consequence of the interactionetween competing mechanisms of hardening and softening.ence, it is important to figure out which mechanisms are

ctivated for cyclic hardening or softening at each temper-ture in order to analyze CSR of a material. The CSRs ofW 316L stainless steel at each temperature with a fixed

train rate of 1 × 10−3 s−1 are depicted in Fig. 2. The CSRf the steel strongly depended on temperature and was char-cterized by cyclic softening at all test temperatures exceptor room temperature. At RT CSR changed with strain ampli-ude and could be categorized by two distinct regions. Aboveεt/2 = 0.4% gradual softening was observed up to some

umber of cycles, followed by secondary hardening until fail-

re. Below �εt/2 = 0.4%, on the other hand, cyclic softeningominated the room temperature CSR as at higher tempera-ures.

S.-G. Hong et al. / Materials Science and Engineering A 457 (2007) 139–147 141

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The variations of cyclic stress response with strain rate at twoemperatures are depicted in Fig. 3. The strain rate dependencef CSR depended on temperature; a negative strain rate sensitiv-ty (SRS) in the temperature range of 250–600 ◦C, transitionalehavior at about 600 ◦C and a positive SRS above 600 ◦C weredentified.

The parameter, “softening ratio”, is introduced to quantify themount of cyclic softening during LCF deformation and to studyts temperature and strain rate dependence more systematically.oftening ratio is defined in Eq. (1), where σmax and σmax|Nf/2re the maximum tensile peak stress and a tensile peak stress atalf-life, respectively:

oftening ratio = σmax − σmax|Nf/2

σmax(1)

The variation of softening ratio with temperature and strainate is presented in Fig. 4. Regarding the change of softeningatio with temperature in Fig. 4(a), the softening ratio increasedith temperature until it reached a maximum value at 250 ◦C.owever, in the temperature range of 250–600 ◦C, it decreasedith temperature and increased again above 600 ◦C. Also, the

oftening ratio tended to be lower at higher strain amplitudes. It isoted that, below 550 ◦C, the softening ratio increases with strainmplitude and has a maximum value at strain amplitude rangesf 0.4–0.5% and after the maximum it decreases. As shown inig. 4(b), the strain rate dependence of softening ratio variedith temperature. At 250–550 ◦C the softening ratio decreasedith a decrease in strain rate, but increased again beyond 600 ◦C.

It is noticed that cyclic hardening was observed at all test

onditions during the initial few cycles. This is believed to comerom the static recovery which was introduced during the heatingf a specimen up to test temperature.

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× 10−3 s−1: (a) RT, (b) 200 ◦C, (c) 400 ◦C and (d) 650 ◦C.

.2. Microstructures

Our previous study on the dislocation substructures of LCF-ailed specimens at �εt/2 = 0.5% revealed that the dislocationtructure changes from an elongated cellular structure at tem-eratures below 250 ◦C to a planar structure in the temperatureange of 250–600 ◦C (the regime of dynamic strain aging (DSA),hich will be discussed in Section 4.1.2), and back to an equi-

xed cell at high strain rates or a subgrain structure at low strainates beyond 600 ◦C, as shown in Fig. 5 [6]. This indicates thathe mechanism of plastic deformation changes from a wavy slip

ode in the non-DSA regime to a planar slip mode in the regimef DSA. Wavy slip structures characterized by cells and sub-rains are the low energy dislocation substructures, induced byynamic recovery. Therefore, it can be inferred that dynamicecovery becomes important in RT-250 ◦C and above 600 ◦C.

TEM micrographs depicting the grain boundaries of LCF-ailed specimens at �εt/2 = 0.5% are presented in Fig. 6. At highemperatures (≥600 ◦C) and low strain rates (≤1 × 10−4 s−1),

23C6 type chromium-rich carbides precipitated along the grainoundaries, but the amount of precipitates was relatively small.

. Discussion

.1. The temperature dependence of cyclic hardening andoftening

The cyclic stress behavior of a material results from the

eneration and annihilation of dislocations. In cold-workedaterials, the softening effect by dynamic recovery surpassesork hardening and cyclic softening is predominant during

atigue deformation. Dynamic recovery in cold-worked mate-

142 S.-G. Hong et al. / Materials Science and Engineering A 457 (2007) 139–147

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ig. 3. Strain rate dependence of cyclic stress response at �εt/2 = 0.5%: (a)00 ◦C and (b) 650 ◦C.

ials can occur in the following cases [4–5,9–10]: (1) when thennihilation rate of dislocations is greater than the generationate, causing a net decrease in dislocation density; (2) when aearrangement of previously formed dislocation structure takeslace with the number of cycles, resulting in an increase in theean free path of dislocations. A previous study on the sameaterial revealed that the strain amplitude should be larger thancritical value (∼0.3%) to observe cyclic softening [11]; a plas-

ic strain larger than the threshold is required to remove andearrange the initial dislocation substructures induced by cold-orking [12]. When applied strain amplitude is less than 0.3%,owever, there is no remarkable change in CSR through thehole life [11].The effect of dynamic recovery will be enhanced as temper-

ture increases or strain rate decreases since dynamic recoverys a thermally activated process, which is induced by the cross-lip of screw dislocations and the climb of edge dislocations.f there are no additional mechanisms contributing to CSR ofmaterial, the cyclic softening will be more pronounced with

n increase in temperature or with a decrease in strain rate andonsequently a positive SRS will be observed. As mentioned inection 3.1, however, several anomalous features in the mate-ial behaviors, such as: (1) the secondary hardening in CSR at

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ig. 4. The variation of softening ratio with (a) temperature and (b) strain rate.

T and (2) the negative SRS and decrease in softening ratioith an increase in temperature or with a decrease in strain

ate in 250–600 ◦C, were observed. This implies that, besidesork-hardening and dynamic recovery, additional hardening or

oftening mechanisms are activated during cyclic deformationnd the activated mechanisms vary with temperature. The acti-ated mechanisms for cyclic hardening at each temperature areiscussed below.

.1.1. Plasticity-induced martensite transformationAs shown in Fig. 2(a), it is noted that the secondary harden-

ng in CSR took place at RT when the applied strain amplitudeas larger than a critical value (∼0.4%). It is well known that

ustenitic steels are meta-stable and their � → �′ phase trans-ormations are strongly promoted by mechanical deformation inhe temperature range of Ms–Md, where Ms is the temperatureor spontaneous martensitic transformation on cooling and Mds the maximum temperature at which the transformation can benduced by mechanical loading [13,14]. The formation of �′-

artensite leads to a substantial cyclic hardening of a materialuring fatigue deformation. According to Baudry and Pineau14], plasticity-induced martensite transformation in austenitictainless steels under cyclic deformation is proceeded by � → �-

S.-G. Hong et al. / Materials Science and Engineering A 457 (2007) 139–147 143

Fig. 5. TEM micrographs depicting the dislocation substructures after LCF test-ing at �εt/2 = 0.5%: (a) RT, ε̇ = 1 × 10−3 s−1, (b) 400 ◦C, ε̇ = 1 × 10−2 s−1 [6],(c) 400 ◦C, ε̇ = 1 × 10−4 s−1 [6] and (d) 650 ◦C, ε̇ = 3.2 × 10−5 s−1.

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ig. 6. TEM micrographs depicting the grain boundaries after LCF testing atεt/2 = 0.5%: (a) 400 ◦C, ε̇ = 1 × 10−4 s−1, (b) 650 ◦C, ε̇ = 1 × 10−2 s−1 and

c) 650 ◦C, ε̇ = 3.2 × 10−5 s−1.

artensite → �′-martensite and Md is about 100 ◦C. It is noticedhat there is a critical value of the cumulative plastic strainor the � → �′ phase transformation to take place. This criticalumulative strain (2NT �εp) to nucleate �′-martensite increasesxponentially as strain amplitude decreases, where NT is theumber of cycles necessary to initiate the � → �′ phase trans-ormation and �εp is the plastic strain range at each cycle. Thetrain amplitude dependence of the critical cumulative strain cane explained as follows: the intersections of shear bands formedy �-martensite platelets, deformation twins or slip bands, serve

s effective plasticity-induced nucleation sites for the transfor-ation. Hence, the more applied strain amplitude decreases, the

ower the density of defects and shear bands in austenite. Thiseads to a reduced number of nucleation sites for the � → �′

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44 S.-G. Hong et al. / Materials Science

hase transformation. It is believed that the physical meaning ofcritical cumulative strain necessary to initiate the phase trans-

ormation is attainment of some critical value of nucleation sitesn austenite. These facts are also reflected in this study. As shownn Fig. 2(a), NT increases with a decrease in strain amplitude.t low strain amplitudes (<0.4%), however, the accumulated

train through the whole life is too small in comparison with theritical value required to initiate the martensitic transformationnd, thus, there is no significant change in CSR. Therefore, it iselieved that the secondary hardening observed at RT is associ-ted with the plasticity-induced martensite transformation.

.1.2. Dynamic strain agingIn the temperature range of 250–600 ◦C cyclic softening was

ignificantly reduced in comparison with those at other temper-tures, as shown in Figs. 2–4. This implies that additional cyclicardening mechanisms are activated in this temperature range.emperature-dependent hardening mechanisms, precipitation ofecondary-phase particles and/or dynamic strain aging, are con-idered as responsible mechanisms. Microstructural study onCF failed specimens revealed that chromium-rich carbides of

ype M23C6 precipitate along the grain boundary beyond 600 ◦Cnly when applied strain rate is less than 1 × 10−4 s−1 (Fig. 6).ur previous study [5] on the same material, in this study,

howed that the regime of DSA under LCF loading is in the tem-erature range of 250–550 ◦C at a strain rate of 1 × 10−4 s−1,n the temperature range of 250–600 ◦C at 1 × 10−3 s−1, and inhe temperature range of 250–650 ◦C at 1 × 10−2 s−1. Hence,ynamic strain aging and precipitation of type M23C6 carbideso not occur simultaneously, and the reduction of cyclic soft-ning in the temperature range of 250–600 ◦C is attributed toSA-induced hardening.Dynamic strain aging is the phenomenon of interaction

etween diffusing solute atoms and mobile dislocations duringlastic deformation. It depends on deformation rate and tem-erature, which govern the velocities of mobile dislocations andiffusing solute atoms, respectively. The occurrence of DSA can

able 1ctivated mechanisms for cyclic hardening or softening with temperature

emperature (◦C) Activated mechanisms for

Cyclic hardening

20 Strain hardeningMartensite phase transformat

00 Strain hardening

00 Strain hardeningDynamic strain aging

50 Strain hardeningDynamic strain aging

00 Strain hardeningDynamic strain aging (≥1 ×Precipitation hardening (≤1 ×

50 Strain hardeningDynamic strain aging (≥1 ×Precipitation hardening (≤1 ×

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ngineering A 457 (2007) 139–147

e manifested by DSA-induced anomalous features of materialehavior. Hong and Lee [5] reported that the anomalies associ-ted with DSA during LCF loading are different from those inensile loading. The dynamic strain aging under LCF loading inype 316L stainless steel can be manifested in the forms of theegative temperature dependence of cyclic peak stress, negativeemperature dependence of plastic strain amplitude or soften-ng ratio, negative SRS and negative strain rate dependence oflastic strain amplitude or softening ratio.

The mechanisms responsible for DSA have been identifiedy evaluating activation energies [6]. There were three differentctivation energies in the regime of DSA indicating that morehan one mechanism is responsible for the phenomenon andhe mechanism changes with temperature. The activation ener-ies were about 0.57–0.74 times those for lattice diffusion andhese relatively low values of activation energy for DSA could bechieved by pipe diffusion. In type 316L stainless steel, at lowemperatures, DSA occurs by pinning of dislocations throughhe pipe diffusion of the interstitial atoms, such as C or N alonghe dislocation core and, at high temperatures, the pipe diffusionf substitutional Cr along the dislocation core is responsible forSA.DSA-induced hardening comes from the following two

echanisms. The first mechanism is based on the impurity pin-ing model [15], where DSA is a consequence of the pinning andegeneration of dislocations. The pinning of dislocations duringeformation could result from the formation of either Snoek orottrell atmospheres. As the dislocations are immobilized byinning, more dislocations have to be generated to maintain themposed strain rate. The enhancement in dislocation density asresult of such a process increases the flow stress required to

mpose the same strain during subsequent cycles. The secondechanism is a strain partitioning mechanism, as indicated in

Cyclic softening

Dynamic recovery (>0.2%)ion (≥0.4%)

Dynamic recovery (>0.2%)

Dynamic recovery (>0.2%)

Dynamic recovery (>0.2%)

Dynamic recovery (>0.2%)10−3 s−1)

10−4 s−1)

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10−4 s−1)

ig. 5(b and c). DSA enhances the degree of inhomogeneityf deformation by the solute locking of slow moving disloca-ions between slip bands; the dislocation velocities inside thelip bands are too high for solute atmospheres to lock mobile

ce and Engineering A 457 (2007) 139–147 145

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S.-G. Hong et al. / Materials Scien

islocations, and consequently DSA enhances the partitioningf cyclic strain into separate regions characterized by high andow amplitudes of dislocation movement [16]. This mechanismestricts the cross-slip of screw dislocations and consequentlyeduces the dynamic recovery, resulting in the reduction of cyclicoftening.

In the regime of DSA, slip planarity is enhanced with aecrease in strain rate (Fig. 5(b and c)). This is attributed to thextension of the temporary arrest time of moving dislocations atorest dislocations, tw, which is inversely related to strain rate,ith a decrease in strain rate [17]. The enhanced-DSA effectith a decrease in strain rate gives a reasonable explanation fornegative SRS, one of the most important manifestations ofSA.

.1.3. Precipitation hardeningAs shown in Fig. 6, M23C6 type chromium-rich carbides pre-

ipitated along the grain boundaries only when temperature waseyond 600 ◦C and the strain rate was less than 1 × 10−4 s−1.he previous study on the precipitation of secondary-phase par-

icles in type 316L stainless steel during aging treatment showedhat M23C6 type carbides nucleate along the grain boundariesbove 600 ◦C as the material is aged over 50 h [18]. Consider-ng the number of cycles to failure at the onset of precipitation600 ◦C, ε̇ = 1 × 10−4 s−1 and �εt/2 = 0.5%) is 600 cycles, itakes about 33.3 h for precipitates to nucleate. This indicates thathe precipitation of M23C6 type carbides was promoted by theyclic loading. When the precipitates nucleate and grow, theyntersect slip planes in a random fashion and serve as obstaclesgainst the motion of dislocations. This mechanism induces anncrease in flow stress during plastic deformation (precipitationardening). However, as shown in Fig. 4(b), the cyclic soften-ng increases with a decrease in strain rate at 600 and 650 ◦C,ven though precipitation hardening takes place at these temper-tures. The number of precipitates, which nucleated along therain boundaries during LCF deformation, is relatively small,o the hardening from precipitation seems to be not enough toompensate the softening effect induced by dynamic recovery,hich becomes pronounced at low strain rates.Based on above results, the activated mechanisms for cyclic

ardening or softening during LCF deformation at each temper-ture in type 316L stainless steel are summarized in Table 1.

.2. Fatigue parameters

All of the widely used fatigue life prediction models, such ashe Coffin–Manson relation [7], S–N curves, and energy-based

odels [8], are based on the assumption that the behavior ofaterials undergoing cyclic loading is stabilized (or saturated)

t an early stage of life. In these models, the damage accumulateder each cycle is assumed to be identical through the whole life.s mentioned in the previous sections, however, the cyclic stress

esponses of CW 316L stainless steel were not stabilized during

atigue deformation, but continuously changed with the numberf cycles. Hence, it is important to find a proper fatigue param-ter, which satisfies the required features as a fatigue parameter,n order to provide a reasonable prediction of fatigue life. Three

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ig. 7. Evolution of fatigue parameters at RT and ε̇ = 1 × 10−3 s−1: (a) stressmplitude, (b) plastic strain amplitude and (c) plastic strain energy density.

atigue parameters, the stress amplitude, plastic strain amplitudend plastic strain energy density, were selected and evaluatedy examining the evolution of each property with the numberf cycles. The characteristics of cyclic non-stabilization duringatigue deformation are closely related to the activated mecha-isms for cyclic hardening or softening, and thus the temperatureange showing the similar tendency of CSR was consistent with

he results in Table 1. The results at three important tempera-ures are presented in Figs. 7–9, where the term, “normalized”,

eans that property at each cycle is divided by that at half-life.he variations in stress amplitude and plastic strain amplitude

146 S.-G. Hong et al. / Materials Science and Engineering A 457 (2007) 139–147

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aslocations and the cyclic stress is related to the resistance against

ig. 8. Evolution of fatigue parameters at 200 ◦C and ε̇ = 1 × 10−3 s−1: (a)tress amplitude, (b) plastic strain amplitude and (c) plastic strain energy density.

hrough a whole life were considerable and could not be negli-ible. It seems to be reasonable to rule out these two parametersrom a fatigue parameter. However, as shown in Figs. 7–9(c),lastic strain energy density showed the desirable features as aatigue parameter; it was stabilized at an early stage of life inomparison with other two parameters and this stabilized stateas maintained until N/N ≈ 0.8, where macrocracks initiate and

fropagate. Plastic strain energy density is a combination of stressnd plastic strain, which are inversely related, and thus its vari-tion during fatigue deformation becomes relatively small even

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ig. 9. Evolution of fatigue parameters at 600 ◦C and ε̇ = 1 × 10−3 s−1: (a)tress amplitude, (b) plastic strain amplitude and (c) plastic strain energy density.

hough there are considerable changes in CRS with the numberf cycles (Figs. 7(a) and 8(a)). These results suggested that thelastic strain energy density is a suitable fatigue parameter foryclically non-stabilized materials under fatigue loading.

The plastic strain energy density per cycle can be regarded ascomposite measure of an amount of fatigue damage per cycle

ince the cyclic plastic strain is related to the movement of dis-

heir motion [8]. Hence, the fatigue resistance of a metal cane characterized in terms of its capacity to absorb and dissipatelastic strain energy. Life prediction based on the plastic strain

S.-G. Hong et al. / Materials Science and

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ig. 10. Fatigue life–plastic strain energy density (Nf–�Wp) curves [19].

nergy density has been investigated on the same material in thistudy [19]. As shown in Fig. 10 [19], the results revealed thathe Morrow model employing the plastic strain energy densitys a fatigue parameter provided a reasonable representation ofatigue behavior under isothermal condition.

. Conclusions

1) The stress response of CW 316L stainless steel to cyclicloading strongly depended on temperature since the acti-vated mechanism for cyclic hardening or softening variedwith temperature. The stainless steel underwent additionalhardening at room temperature and in the temperature rangeof 250–600 ◦C; the hardening at room temperature resultedfrom the plasticity-induced martensite transformation, andthe hardening in the temperature range of 250–600 ◦C wasattributed to the dynamic strain aging. These hardeningmechanisms competed with softening induced by dynamicrecovery, which is generally predominant in cold-workedmaterials, resulting in the cyclic non-stabilization of thematerial. M23C6 type carbides precipitated along the grainboundaries above 600 ◦C when a strain rate was less than1 × 10−4 s−1, however, its hardening effect was too small

to make a contribution to the CSR of the material.

2) It was also found that plastic strain energy density shows thedesirable features for a fatigue parameter; it was stabilizedat the early stage of fatigue life and nearly invariant through

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Engineering A 457 (2007) 139–147 147

the whole life. Therefore, the plastic strain energy density isrecommended as a suitable fatigue parameter for cyclicallynon-stabilized materials under fatigue loading.

cknowledgements

This work was supported by Ministry of Science and Tech-ology in Korea through “Development of Reliability Designechnique and Life Prediction Model for Electronic Com-onents”, and the Korea Research Foundation Grant fundedy Korea Government (MOEHRD, Basic Research Promotionund) (No. M01-2005-000-10267-0). This study was also spon-ored by the Offices of Fusion Energy Sciences, U.S. Departmentf Energy, under Contract DE-AC05-00OR22725 with UT-attelle, LLC. The authors express special thanks to Drs. S.J.inkle, M. Grossbeck, and M. Li for their technical reviews and

houghtful comments.

eferences

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[2] K. Kanazawa, K. Yamaguchi, S. Nishijima, in: H.D. Solomon, G.R. Hal-ford, L.R. Kaisand, B.N. Leis (Eds.), Low Cycle Fatigue, ASTM STP 942,American Society for Testing and Materials, Philadelphia, 1988, p. 519.

[3] J. Bressers, Proceedings of International Conference on High Tempera-ture Alloys and Their Exploitable Potential, Elsevier Applied Science,Amsterdam, 1987, p. 385.

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