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Materials Science and Engineering A 527 (2010) 4092–4102

Contents lists available at ScienceDirect

Materials Science and Engineering A

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ffects of low-cycle fatigue on static mechanical properties, microstructuresnd fracture behavior of 304 stainless steel

uyi Ye ∗, Yuandong Xu, Lei Xiao, Haibo Chanstitute for Process Equipments, Zhejiang University, Hangzhou 310027, China

r t i c l e i n f o

rticle history:eceived 27 September 2009eceived in revised form 3 March 2010ccepted 8 March 2010

eywords:tatic mechanical propertiesow-cycle fatigueicrostructures

a b s t r a c t

A series of experiments, including constant amplitude low-cycle fatigue tests, post-fatigue tension tofailure tests, LOM (TEM) observations, and SEM examinations, were performed at room-temperature toinvestigate the effects of low-cycle fatigue damage on the static mechanical properties, microstructuresand fracture behavior of 304 austenitic stainless steel. The changing characteristics of various staticmechanical property parameters, including the strength parameters (�ys and �ult), stiffness parameter(E), ductility parameters (ı and ϕf) and strain hardening exponent (n) during fatigue damage process of thestainless steel were obtained experimentally and their micromechanisms were discussed by analyzingboth the deformation microstructures and the fracture features of cyclically pre-deformed specimens. Itwas shown that the austenite/martensite transformation resulting from the accumulation of cyclic plastic

racture behaviorartensitic transformation

strain was mostly responsible for the variation in the strength, ductility and strain hardening ability ofthe stainless steel during fatigue damage process. The depletion of the inherent ductility in the materialdue to fatigue damage evolution led to the ductile-to-brittle transition (DBT) in the fracture modes.Based on the macro/micro-experiments regarding the exhaustion of the ductility during fatigue damage,the ductility parameter was suggested as a damage indicating parameter for the present stainless steelin further studying the fatigue damage mechanics model as well as the residual fatigue life prediction

method.

. Introduction

Static mechanical properties of a material, such as the elasticodulus, yield strength, ultimate tensile strength, elongation and

eduction in area provide the most fundamental parameters for thetructural design, particularly in the stress calculation and strengthnalysis of structural components and elements. It has been indi-ated [1,2] that these material properties not only depend onarious metallurgical factors, such as grain size, alloying element,uenching, aging, and annealing, but also are intensively influ-nced by service conditions including the loading history, state oftress imposed, environment, temperature, etc. In the case of engi-eering structures operating under dynamic or alternating loadingonditions, a notable character is that their service properties, espe-ially the mechanical properties, deteriorates progressively with

he service times. This degradation in material properties due tolternating loading, also called fatigue damage, seriously affects theervice safety of engineering structures or components and thus isn important consideration in their designing against fatigue fail-

∗ Corresponding author at: Institute for Process Equipments, 38 Zheda Road,angzhou 310027, Zhejiang, China. Tel.: +86 571 88869213; fax: +86 571 88869213.

E-mail address: duyi ye@zju.edu.cn (D. Ye).

921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2010.03.027

© 2010 Elsevier B.V. All rights reserved.

ure. On the other hand, the residual fatigue life studies of existingengineering structures in service conditions, generally, involve theevaluation of fatigue damage. Such evaluation is frequently per-formed by quantitatively measuring the mechanical deteriorationof a material, such as the elastic modulus, ultimate tensile strength,hardness, reduction in area and toughness [3–6], in the frameworkof continuous damage mechanics (CDM). It is accordingly of greatpractical meaning to investigate the effects of fatigue damage onthe static mechanical properties of structural materials as well asthe damage evaluation method based on the degradation of mate-rial mechanical properties during fatigue damage process.

Austenitic stainless steel 304 is an extremely important com-mercial alloy in engineering applications due to its excellentcorrosion resistance, high strength, good ductility and toughness.This alloy is currently being used in industrial installations, such aspetrochemical plants, electric-power generating stations and pro-cess plants as piping and structural material. In these applications,the components of the structures are often subjected to dynamicor alternating stresses as a result of temperature gradients, which

occur on heating and cooling during startups and shutdowns, orduring variations in operating conditions. For this reason, eval-uation of fatigue damage and the residual fatigue life becomesan important content in their safe designing against fatigue fail-ure. Despite the fact that fatigue mechanical behavior of type 304

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ing twins and small elongated delta-ferrite. Fig. 2 shows a TEMmicrograph of the virgin material, indicating that the initial disloca-tion structures have in general low density and consist of primarydislocations having predominantly screw character (either com-pletely straight or with bowed segments) and small loops. Both

D. Ye et al. / Materials Science and

ustenitic stainless steel, such as the cyclic stress response, cyclictress–strain curves (CSSCs) and Coffin–Manson curves have beennvestigated extensively in the past decades [7–14], relatively fewtudies, however, have focused on the changing characteristics ofhe static mechanical properties of this steel during fatigue dam-ge process. As it has been pointed out, the latter would be of greatmportance for the safe designing against fatigue failure, especiallyor the prediction of the residual fatigue life of existing structuresr components operating under alternating service conditions. Thiss the motivation of the present study to investigate the effectsf low-cycle fatigue damage on the static mechanical properties,eformation microstructures and fractural behavior of type 304tainless steel. The main purpose of this study, on the one hand,s to gain a more complete understanding of fatigue mechanicalroperties of this stainless steel so as to use it more effectively inngineering practical applications, on the other hand, to provide anxperimental basis for further study of the reliable residual fatigueife prediction method.

. Experimental details

The material used in this investigation is an austenitic 304 stain-ess steel supplied in the form of a plate, 18 mm in thickness. Thelates were hot rolled at 1040 ◦C for 0.2 h, followed by quenching inater. The chemical composition of the steel in percentage weight

s listed in Table 1. The 18 mm plates were then machined intoonventional push–pull cylindrical specimens with the tensile axisarallel to the final rolling direction. The nominal dimensions ofhe specimen in the gauge section were 14.0 mm (length) × 6.0 mmdiameter). Prior to testing, the surface of each specimen was

echanically polished to a final roughness of ∼0.4 �m.Tests for the present investigation purpose consist mainly of

i) constant amplitude low-cycle fatigue tests to produce speci-ens with various amounts of cyclic pre-deformation or fatigue

amage, and (ii) uniaxial tension to fracture tests to measure theost-fatigue static mechanical property parameters. Details of test-

ng procedures are described as follows.Fully reversed, push–pull, total strain amplitude controlled

atigue tests were performed at room temperature in an ambi-nt air using a 250 kN closed-loop servohydraulic testing system.triangular strain waveform with zero mean strain (R = −1) at a

onstant total strain rate (ε) of 5 × 10−3 S−1 was used. The strainmplitudes (εa) chosen for the present fatigue testing were 0.6%nd 1.0%, resulting in the fatigue life (Nf5) 184 and 2280, respec-ively. In this study, the fatigue life (Nf5) was defined as the cyclesorresponding to 5% drop in the maximum stress amplitude, whichas related to the growth of the macro cracks. Cyclic tests were

nterrupted at various chosen fatigue life fractions (N/Nf5) at eachf strain amplitudes before fracture to produce specimens witharious amounts of cyclic pre-deformation. At each strain ampli-ude, fatigue tests were conducted at least with 15–20 differentyclic fractions. During testing, the load was continuously moni-ored and hysteresis loops were recorded at appropriate intervals.fter the cycling, the specimens were returned to the state of zerotress and zero strain and then loaded in monotonic tension to frac-

ure with a strain rate of 3.0 × 10−5 S−1. Cyclically pre-deformedpecimens were first pulled to a certain strain level in a strainontrol mode to measure the modulus of elasticity (E) and 0.2 pctroof stress (�ys), and then tensioned up to fracture in a dis-

able 1hemical composition of 304 stainless steel in wt.%.

C Si Mn S P Cr Ni Mo N

0.015 0.53 1.64 0.0048 0.03 18.27 8.16 0.02 0.049

eering A 527 (2010) 4092–4102 4093

placement control mode to measure the ultimate tensile strength(�ult), the elongation (ı) and the reduction in area (ϕf), respec-tively. The strain hardening exponent (n) was determined fromthe power-law that relates stress and plastic strain [15], � = Kεn

p ,where K is the strength coefficient, together with the measureddata. During tension, the load–displacement plots were recordedcontinuously.

Microstructural changes during low-cycle fatigue process wereexamined using a light optical microscopy (LOM) and a trans-mission electron microscopy (TEM). In the case of LOM, thedeformation microstructures formed at various stages of the fatiguedamage process were examined, while in the case of TEM onlythe fatigue fracture microstructures were observed. Samples forthe microstructural examinations were prepared below the frac-tured surface in the fatigue failure specimens and taken from thegauge portions in the cyclically pre-deformed specimens by cuttingperpendicular to the tensile axils. LOM samples were first mechani-cally polished using emery papers of various grinds from 230 to 600grit and then using 1.5 �m diamond paste to a final roughness of∼0.1 �m. To reveal the grains, etching for 30 s was used in a mixedsolution of 16 vol% of HNO3, 32 vol% of HCl and 50 vol% of glyc-erol at 313 K. TEM samples were mechanically thinned to 30 �m orless from the initial thickness of about 0.3 mm, and then thinnedto perforation by a twin-jet electrochemical polisher. The TEMfoils were examined in a HITACH H9000NA transmission electronmicroscope.

Fracture surfaces of both the fatigue failure specimens and thepost-fatigue tension to fracture specimens were observed using ascanning electron microscope (SEM). SEM examinations were per-formed with a SIRION-100 scanning electron microscopy operatingat 25 kV.

3. Experimental results

3.1. Initial microstructures and tensile properties

The optical microscopy of 304 stainless steel in the as-receivedcondition, as shown in Fig. 1, reveals that the initial grain structureconsists of equiaxed austenitic grains with a few straight anneal-

Fig. 1. Optical micrograph of 304 austenitic stainless steel in the as-received con-dition.

4094 D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102

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ig. 2. TEM micrograph of 304 austenitic stainless steel in the as-received condition.

OM and TEM observations display no metallographic evidencef martensitic transformation in the initial state of the stainlessteel.

According to Schaeffler diagram [16], steels with compositionsn the range where austenite, delta-ferrite and martensite aren equilibrium can be expected to become unstable during plas-ic deformation by nucleation of martensite. The susceptibility to

artensitc transformation for the present stainless steel was esti-ated using Schaeffler diagram by calculating its chromium and

ickel equivalents, as illustrated in Fig. 3. It appears in this figurehat the stabilized grade of 304 stainless steel is located in the two-hase region of martensite + austenite, indicating thereby that theartensitic transformation may take place in the present materialhen the other factors, such as temperature, strain, strain rate and

tress state are satisfied.Table 2 lists the monotonic tensile properties of the virgin 304

tainless steel at room-temperature. The results reported are the

ean values based on multiple (three) tests. The yield strength

�ys) defined as the stress corresponding to a plastic strain of 0.2%s 259.8 MPa. The ultimate tensile strength (�ult) is 750.3 MPa. Thearge difference between the yield strength and the ultimate ten-ile strength indicates a significant amount of work hardening in

ig. 3. Position of 304 austenitic stainless steel grade in the Schaeffler diagram.

Fig. 4. Typical cyclic stress response of 304 stainless steel.

the virgin material during monotonic deformation. The elongationto failure and reduction in area were 69.1% and 65.1%, respectively,indicative of a high ductility in the initial state of the austeniticstainless steel.

3.2. Stress response during low-cycle fatigue

The stress response curves of 304 stainless steel, cycled at twostrain amplitudes investigated, are shown in Fig. 4. It is visible in thisfigure that during fatigue damage process, the material exhibits aninitial small hardening followed by a great hardening up to finalfailure. The period of the second great hardening leads even toan inflexion on the stress response curves. This inflexion occurslater with a small applied strain amplitude. The above-presenttwo-stage cyclic hardening characters provide useful informationpertaining to the mechanical stability of the stainless steel duringlow-cycle fatigue and will help to understand the micromech-

anisms responsible for the variation of the static mechanicalproperties during fatigue damage process, which will be presentsubsequently.

Fig. 5. Typical post-fatigue tensile plots of stress vs. strain of 304 stainless steel.

D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102 4095

Table 2Mechanical properties of the virgin 304 stainless steel.

Pa)

3s

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FN

0.2% proof stress, �ys (MPa) Ultimate tensile strength, �ult (M

259.8 750.3

.3. Static mechanical properties at various fatigue damagetages

Typical post-fatigue tensile plots of stress vs. strain, obtainedrom 304 stainless steel specimens subjected to various numbers

f precycles at the constant strain amplitude εa = 1.0%, followedy monotonic tension to fracture, are shown in Fig. 5, where theensile plot of the virgin specimen is also present for compara-ive purposes. Fig. 6 gives out a set of these tension to fracturepecimens.

ig. 6. Post-fatigue tensile fracture specimens: (1) N = 0; (2) N = 10; (3) N = 20; (4)= 30; (5) N = 50; (6) N = 100; (7) N = 150; (8) N = 184.

Fig. 7. Variation of the strength parameters (�ys and �ult) with straining cycl

Elongation, ı (%) Reduction of area, ϕf (%)

69.1 65.1

It is obvious in Fig. 5 that for the present austenitic stainless steelthe prior cyclic straining history remarkably influences its subse-quent tensile stress–strain behavior. The applied previous strainingcycles results in an intensive increase in the tensile stress response,but a distinct decrease in the total elongations to failure. As theprecycles increased, the slope in the rising portion of the tensileplots that is a measure of the strain hardening appears progressivedecrease and the tensile plots become relative flat beyond the yieldstrength. The reduction in the total elongation to failure resultingfrom cyclic pre-deformation can also be inferred from the obser-vation of the tension to fracture specimens shown in Fig. 6, wherethe final length of the fractured specimens tends to decrease andthe necking phenomenon of the specimens becomes unapparent asthe precycles increased.

The variation of the various static mechanical property param-eters of 304 stainless steel during fatigue damage process at twostrain amplitudes investigated, is exhibited in Figs. 7–10, where thesolid and dashed lines present, respectively, the changing trends

of the individual mechanical property at each strain amplitude.Table 3 summarizes a set of typical post-fatigue static mechani-cal property parameters of the stainless steel specimens, in whichthe monotonic tensile properties of the virgin specimen were alsolisted for comparison purpose.

Table 3Typical measured data of post-fatigue static mechanical property parameters of 304stainless steel specimens (εa = 1.0%).

N (cycles) E (GPa) �0.2 (MPa) �ult (MPa) n ı (%) ϕf (%)

0 200.3 259.8 750.3 0.23 69.1 65.13 196.7 276.2 764.5 0.22 68.3 61.9

10 192.4 326.8 791.1 0.23 69.1 61.720 191.6 366.4 791.1 0.2 60.3 59.530 175.1 451.5 819.9 0.19 57 61.050 188.1 550.8 856.5 0.18 55.8 59.270 161.0 617.7 894.0 0.15 52.5 53.4

100 177.3 685.2 933.2 0.14 47.1 46.7120 174.8 721.3 970.1 0.13 45.8 41.0150 180.1 749.9 957.2 0.08 42.1 40.2184 156.9 740.8 935.9 0.007 15.3 16.2

es. (a) 0.2 pct proof stress (�ys) and (b) Ultimate tensile strength (�ult).

4096 D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102

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Fig. 8. Variation of the modulus of elasticity (E) with straining cycles.

Note in Fig. 7 that under cyclic straining both �ys and �ult exhibitnitial slight increase followed by strong increase almost with-ut reaching their saturated values. This changing character in thetrength parameters well corresponds to the two-stage cyclic hard-ning behavior in Fig. 4. Data analyse, in Table 3, further indicateshat the straining cycles to failure enhance �ys and �ult by around

and 1.2 times, respectively, as compared to those of the virginpecimen. This means that for 304 austenitic stainless steel thetrength is a sensitive mechanical property to the cyclic strainingistory. The modulus of elasticity (E) that is a measure of the stiff-ess property of a material appears a progressive decrease, as ahole, with the increase of straining cycles (Fig. 8). In contrast to

he two-stage increasing character in the strength parameters, theuctile parameters (ı and ϕf) exhibit two-stage descending behav-

or in the course of fatigue failure, as shown in Fig. 9. In this figuren initial slight decrease followed by a drastic decrease up to final

xhaustion in both ı and ϕf is clearly visible. Such inverse correla-ion between the strength parameters and the ductility parametersbserved in the present stainless steel has also been reported forther metastable steels subjected to fatigue loading [17–20]. Its also obtained in Fig. 9 that the ductility parameters are sensi-

Fig. 9. Variation of the ductility parameters (ı and ϕf) with strain

Fig. 10. Variation of the strain hardening exponent (n) with straining cycles.

tive to the fatigue damage evolution process. As shown in Fig. 10,the strain hardening exponent (n) displays a two-stage descend-ing character as well during fatigue damage process. Thus thecyclic pre-deformation can deplete significantly the ability to strainhardening of the stainless steel. The above-present changing char-acteristics of the static mechanical properties of 304 stainless steelduring low-cycle fatigue were also obtained in studies of the effectsof cyclic pre-deformation on tensile properties of other metallicmaterials, such as structural steels and nickel-based superalloys[21–24].

3.4. Microstructures at various fatigue damage stages

The microstructure formed in 304 stainless steel at variousstages of fatigue damage process has been examined using LOM.Figs. 11–13 show typical optical micrographs of the stainless steel

specimens subjected to 5%, 25% and 100% of the fatigue fracturelife, respectively, at a total strain amplitude of 1.0%.

It is obvious in Fig. 11a that, after 5% of the fatigue fracturelife, the grains generally contained a few slip bands and slip is

ing cycles. (a) elongation (ı) and (b) reduction in area (ϕf).

D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102 4097

Fig. 11. Optical micrograph of the specimen subjected to 5% of the fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.

Fig. 12. Optical micrograph of the specimen subjected to 50% of the fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.

Fig. 13. Optical micrograph of the specimen cycled to the end of fatigue life at εa = 1.0%: (a) slip band features and (b) different morphologies of martensite.

4098 D. Ye et al. / Materials Science and Engi

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ig. 14. TEM micrograph of the specimen cycled to the end of fatigue life at εa = 1.0%.

ostly restricted to one system. In some austenitic grains, marten-itic phase with different morphologies has already been observed,s shown in Fig. 11b. It is also visible in this figure that at thenitial stages of cyclic deformation the distribution of martensitichase is highly inhomogeneous in austenitic matrix. The aboveicrostructural observation indicates that for the present inves-

igated stainless steel even a small number of straining cycles or amall amount of cumulative plastic strain has resulted in a phaseransformation from austenite to martensite. When the specimenubjected to 50% of the fatigue life, in addition to the localized singlelip bands, multiple slip modes with intersecting bands on differentlanes, penetrating the whole austenitic grains, are found com-only in the cyclically deformed specimen (Fig. 12a). Meanwhile,

he nucleation of martensite has frequently been observed overeveral austenitic grains, as seen in Fig. 12b. From this microstruc-ural observation, it can be recognized that with increasing numberf straining cycles, not only the density of slip band, but also theolume fraction of the strain-induced martensite increases con-iderably in the cycled specimen. Similar microstructural featuresith those presented in Fig. 12 are also observed in the fatigue fail-re specimen, as shown in Fig. 13, in which the further increase

n the slip band density characterized by more activated slip sys-ems and smaller interband spacing of the slip band and the furtherncrease in the amount of the strain-induced martensite are, morer less, visible.

The substructure formed in the fatigue failure specimens of 304tainless steel has also been characterized by TEM in this study.ig. 14 shows the representative dislocation structure presented inhe specimens cycled to the end of fatigue life at a strain amplitudef 1.0%. In this figure, in addition to some dislocation pile-ups andicrotwins observed, a well-developed cellular dislocation net-ork is found to be dominant in the austenite matrix. As suggested

y Jin et al. [25], these well-developed cells must be the result ofislocations from different slip systems interacting and trappingach other at intersecting regions. The cellular structure penetratedy individual striations with parallel orientation in the austen-

te matrix indicates the strain-induced martensite transformationrom grain to grain.

.5. Fracture features at various fatigue damage stages

Fig. 15 shows typical SEM observations on the fracture surfacef 304 stainless steel specimens subjected to various numbers of

neering A 527 (2010) 4092–4102

precycles followed by monotonic tension to fracture, where thefractography of uncycled specimen was also presented as a com-parison. It is seen in Fig. 15a that in the case of the uncycledspecimen the tension fracture surface comprises a high popula-tion of micro-voids with wide range of sizes and large and deepdimples, indicative of a high-ductile nature in the virgin mate-rial. When the specimen undergone 25% of the fatigue fracturelife, an embryonic cleavage-like feature characterized by the for-mation of crystallographic facets connected with ductile bridge is,more or less, visible on the fracture surface, although the dim-pled or microvoid coalescence appearance is still dominant (seeFig. 15b). For the specimen subjected to 50% of the fatigue frac-ture life, a multitude of quasi-cleavage facets with isolated stepsin grain interior and small amount of ductile dimples at grainboundaries, are clearly observed on the fracture surface (Fig. 15c).These features basically indicate occurrence of brittle modes offracture at local regions probably originating from presence ofbrittle phase in the cyclically pre-deformed specimen [19]. Suchmixed brittle/ductile fracture feature becomes more pronouncedfor the specimen undergone 80% of the total number of cycles tofracture, as seen in Fig. 15d. The fatigue fracture surface exhibitsextensive micro-cracks with a typical transgranular appearance onwell-defined striations, as seen in Fig. 15e. Some isolated planarfacets are also observed in the crack propagation region (Fig. 15f).Crack propagation occurred by a striation-forming mechanismindicates some cyclic cleavage fracture feature. The above micro-scopic fracture observations thus indicate that, with increasingnumber of precycles, the fracture mode in 304 stainless steel speci-mens takes place distinct ductile-to-brittle transition (DBT), whichwell accords with the progressive loss in the ductility during fatiguedamage process of the stainless steel presented in the previoussection.

4. Discussions

The variation in the static mechanical property parameters of304 stainless steel during low-cycle fatigue, as presented in theprevious section, essentially comes from the complex submicro-scopic and microscopic evolution in the structure in the course offatigue failure. In the initial state of the stainless steel, the grainstructure displays complete austenite without martensitic trans-formation product (Fig. 1), and the dislocation substructures exhibita low-dislocation density (Fig. 2). While the specimen is subjectedto cyclic straining, the unpinning and multiplication of dislocationsas well as the mutual interactions of dislocations and the interac-tions of dislocations with grain and twin boundaries increases theresistance to plastic deformation, which may be responsible for theinitial increase in the strength parameters (�ys and �ult), as shownin Fig. 7. The nucleation of the localized slip bands (see Fig. 11a)can be considered as an indication of this early evolution of thedeformation microstructures. The repeated plastic straining alsoresults in the depletion of the inherent ductility in the materialthat gives rise to the decrease in the ductile parameters (ı and ϕf),as shown in Fig. 9. According to the Schaeffler diagram in Fig. 3,the stainless steel under investigation is structurally metastableat room-temperature and may undergo a partial phase transfor-mation from austenite to martensite during cyclic deformation. Ithas been indicated by numerous investigations [8–12] that, duringcycling of metastable steels, the deformation-induced phase trans-formation not only depends on the plastic strain amplitude, but

also relies on its accumulative value. For a given strain amplitude,there exists a critical value of the cumulative plastic strain nec-essary to initiate the martensitic transformation in the austeniticmatrix [11,12]. Investigation of the influence of the martensitictransformation on the fatigue mechanical behavior of metastable

D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102 4099

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ig. 15. Fractographies of specimens subjected to various cyclic fractions (N/Nf5) ac) N/Nf5 = 50%; (d) N/Nf5 = 80%; (e) and (f) N/Nf5 = 1.0.

tainless steels also revealed that the formation of the martensiteed to a substantial cyclic hardening in the materials [10,11,17].

direct correlation between the martensitic transformation and

ardening was established by measurements of the volume frac-ion of the martensite during fatigue tests of 300 series stainlessteels [10,11,19,20]. In the present study, a well-defined marten-itic structure has been observed in austenitic grains after thepecimen undergone 5% of the fatigue fracture life (see Fig. 11b).

strain amplitude followed by tensioning to fracture: (a) N/Nf5 = 0; (b) N/Nf5 = 25%;

This microstructural observation thus suggests that for 304 stain-less steel investigated, only a small amount of cumulative plasticstrain might induce the martensitic transformation during cyclic

deformation. To verify this suggestion, the degree of cyclic harden-ing defined by (�a − �ys) is plotted as a function of the accumulatedplastic strain (4

∑εpa) in Fig. 16, where �a is the stress ampli-

tude, and �ys is the yield stress. It is visible in this figure thatwhen the accumulated plastic strain reaches a value found to be

4100 D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102

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ig. 16. Dependence of the degree of cyclic hardening on the accumulated plastictrain.

bout 0.5 for 1.0% strain amplitude and 1.0 for 0.6% strain ampli-ude, the secondary strong hardening takes place. These valuesf the cumulative plastic strain, dependent on the applied strainmplitude, mostly correspond to the formation of the martensiten the present stainless steel in accordance with the investigationy Smaga et al. [12]. In order to discern the relative differences ofhe local mechanical properties between austenite and martensite,he depth-sensing indentation (DSI) testing has been performed inhis study. In doing so, an instrumented indentation with a Vick-rs indenter was utilized under a load of 500 mN to measure thendentation hardness (HV) as well as the residual depth of penetra-ion after complete unloading (hr) for each constitutive phase. TheSI tests were carried out according to ISO 14577-1. The indenta-

ion hardness (HV) is defined as the ratio between the maximumorce (Pmax) and the surface area of indentation (A) in accordanceith ISO 6507-1. As it is indicated [26], HV represents the resistance

o plastic deformation and hr characterizes the ability of plasticityn a material. Table 4 summarizes the measured values of HV andr as well as their mean values of two constitutive phases. Fig. 17hows typical indentation load–penetration depth (P–h) curves foroth austenitic and martensitic structures. For the sake of clarity,nly one curve for each phase is presented in this figure. It fol-ows from Table 4 that the deformation resistance of the martensites almost two times greater than that of the austenite, while thelasticity of the martensite is obviously less than that of the austen-

te. From the indentation load–penetration depth (P–h) curves, thetrain hardening exponent (n) of two constitutive phases can also

e estimated approximately by using the approach suggested byao et al. [27], which has also been listed in Table 4. The estimatedalues of n in Table 4 indicate that the martensitic phase possessesless strain hardening ability in comparison with the austenitic

able 4ummary of the measured values from the DSI tests.

Measurement Austenite Martensite

HV 0.05 hr (�m) n HV 0.05 hr (�m) n

1 261.2 2.7 0.365 430.8 1.91 0.3212 226.1 2.72 0.364 443.1 1.87 0.3213 244.2 2.47 0.366 430.2 2.11 0.3224 269.7 2.39 0.366 442.7 1.96 0.3215 253.9 2.48 0.366 456.4 1.88 0.32

Mean value 253.9 2.48 0.366 456.4 1.88 0.321

Fig. 17. Typical indentation load–penetration depth (P–h) curves for austenitic andmartensitic phases.

phase. From the above investigations, it can thus be deduced thatfor the present stainless steel, accompanied by the formation ofthe martensite in austenitic matrix, the strength parameters (�ys

and �ult) will increase considerably due to the strengthening effectof the martensite, while the ductility parameters (ı and ϕf) aswell as the strain hardening exponent (n) will decrease substan-tially as a result of fact that the martensitic phase possess a lessplasticity and strain hardening ability compared to the austeniticphase. This behavior is expected to further develop with increas-ing amount of martensite in the austenitic matrix by increasingthe number of straining cycles. Therefore, in accordance with thenumerous investigation conclusions [10,11,19,20], the formationof the martensite will be responsible for the two-stage changingbehavior observed in the strength, ductility and strain hardeningability of the present austenitic stainless steel (Figs. 7, 9 and 10). Inaddition to the strengthening effect of the martensitic transforma-tion, the increase of the slip band density with straining cycles, asseen in Figs.11a through 13a, will also contribute to the increasingbehavior of the strength property during cyclic deformation accord-ing to Ashby’s model [28], �f = �y0 + (1 − �/d)(K1/d) + (�/d)(K2�−1/2),where �f is the flow stress, �y0 the friction stress, � the slip length,d the grain diameter, and K1 and K2 are constants. From this modelan inverse proportional relation between the flow stress (�f) andslip length (�) can be deduced when the slip band density becomevery large and the slip length approaches zero. Since the martensiticphase possesses a high strength, when the initiated micro-cracksencounter the hard martensitic phase, it is liable to progress ina brittle manner exhibiting the quasi-cleavage facets as observedon the fracture surface of the cyclically pre-deformed specimens(see Fig. 15c and d). In other words, brittle behavior is promoteddue to the formation of the martensite in the austenitic stainlesssteel. Therefore, the tension fracture of the cyclically pre-deformedspecimens tends to occurring ductile-to-brittle transition (DBT)features with increasing number of precycles and hence greaterdeformation-induced martensite, as shown in Fig. 15. The physicsof metals [2] points out that the modulus of elasticity (E) is onlydetermined by the binding force between atoms and cannot bechanged without changing the basic nature of the material. Theprogressive decrease in E during cycling, as shown in Fig. 8, is thus

attributed to the destruction of local ordered atomic arrangementin the material as well as the formation of point defects such asvacancies and interstices, and the formation of new free surfacesuch as voids and cracks internal and external the specimens in the

D. Ye et al. / Materials Science and Engineering A 527 (2010) 4092–4102 4101

cpst

aptcdfuddtse([etUsce

U

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sIafisiip

it

Fig. 18. Variation of the static toughness (Ut) with straining cycles.

ourse of fatigue failure [4–6]. The above fatigue damage evolutionrocess reduces the load-carrying area of the cyclically deformedpecimen that results in the reduction in the stiffness property ofhe stainless steel.

The inverse correlation between the strength parameters (�ys

nd �ult) and ductility parameters (ı and ϕf) during fatigue damagerocess, as observed in the present study, has also been reportedo be characteristic for the metastable stainless steels subjected toyclic loading [17–20]. The austenitic/martensitic transformationuring cyclic deformation would be responsible for this inverse per-ormance [19,20]. In the case of engineering structures operatingnder alternating loading, the increase in the strength is beneficialue to its strengthening the material and hence reducing the plasticeformation, while the progressive loss in the ductility is detrimen-al due to its promoting the brittle behavior in the material. Thisynthetical effect of the strength and ductility on the material prop-rty can also be represented by a single parameter, static toughnessUt) defined as the total area under the tensile stress–strain plot2]. This parameter characterizes the ability of a material to absorbnergy in the process of deformation and fracture and is an impor-ant property of a material in the resistance to fracture. Generally,t can be determined directly by integrating the area of the tensiletress–strain plot. For the purpose of engineering approximativealculation, it can also be determined by the following simplifiedxpression [1]:

t = �ys + �ult

2· ı (1)

It follows from the above equation that the static toughness iscomposite mechanical property relating both the strength and

uctility.Fig. 18 shows Ut, determined by integrating the tensile

tress–strain plots, as a function of the number of straining cycles.t is seen in this figure that for the majority of fatigue life Ut exhibitsn insignificant decreasing behavior, and only by the end of fatigueailure, it displays sharp decrease up to final exhaustion. This resultndicates that for 304 stainless steel investigated, although both thetrength and ductility parameters are sensitive to the cyclic strain-ng history, their composite parameter, the static toughness, is an

nsensitive mechanical property to the fatigue damage evolutionrocess.

The mechanical properties of a material in monotonic load-ng are of interest in fatigue damage analysis and evaluation ashey can be measured in relatively simple, fast and cheap ways

Fig. 19. Synthetical comparison of the normalized static mechanical propertyparameters (εa = 1.0%; Nf5 = 184).

[29]. According to the continuum damage mechanics (CDM) basedon the thermodynamics [4], any physical parameter developingmonotonously from initial state to the expiration of fatigue life canbe used as a scale for the degree of fatigue damage. This physi-cal parameter is called ‘damage indicating parameter’. In terms ofthe CDM, for the present investigated stainless steel, the stiffnessparameter (E), ductility parameters (ı and ϕf) and strain harden-ing exponent (n) as well as the composite mechanical parameter,the static toughness (Ut), can be chosen as the damage indicat-ing parameters, since they decrease monotonously with strainingcycles, as obtained experimentally in this study. Generally, anappropriate damage indicator parameter should further satisfy thefollowing features, i.e., it is consistent with the fatigue damagemechanisms, sensitive to fatigue damage process, and can be mea-sured by a simple experimental procedure [4]. In order to comparethe sensitivity of the above-mentioned damage indicating parame-ters to the fatigue damage evolution process, the static mechanicalproperty parameters (E, ı, ϕf, n and Ut) were expressed by dimen-sionless ratios with respect to their original values and then plottedagainst the cyclic fraction in Fig. 19. It follows in this figure thatas the cyclic fractions (N/Nf5) increase, the ductility parameters(ı, ϕf) and strain hardening exponent (n) display more sensitivechanging characteristics than the stiffness parameter (E) and thecomposite mechanical parameter, the static toughness (Ut). Sincethe depletion of the ductility during fatigue failure process revealsthe deterioration of the inherent material property due to fatiguedamage evolution, and according to the ‘exhaustion of ductility’model [29], the depletion of the ductility can be further related tothe summation of cyclic plastic strain that is ultimately responsi-ble for fatigue damage [29], it is then suggested from the presentinvestigation that for 304 stainless steel, it would be a promisingway to study the fatigue damage mechanics model as well as theresidual fatigue life prediction method on the basis of the depletionof the ductility during fatigue damage process. Such investigationis being carried out and will be presented elsewhere.

5. Conclusions

The investigation regarding the effects of low-cycle fatigue dam-age on the static mechanical properties, deformation microstruc-tures and fracture behavior of 304 austenitic stainless steel atroom-temperature leads to the following conclusions:

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102 D. Ye et al. / Materials Science an

. During low-cycle fatigue process, the strength parameters (�ys

and �ult) exhibit initial slight increase followed by strongincrease without reaching their saturated values, which wellcorresponds to the two-stage cyclic hardening behavior, whilethe ductile parameters (ı and ϕf) as well as the strain harden-ing exponent (n) present two-stage descending characteristicfeatures. The modulus of elasticity (E) displays a progressivedecrease, as a whole, with the increase of precycles.

. The synthetical effect of the strength and ductility on the mate-rial property can be represented by a single parameter, statictoughness (Ut). It is shown that during fatigue damage process Ut

exhibits an insignificant decrease for the majority of fatigue life,and only by the end of fatigue failure it displays a sharp decreaseup to exhaustion. This means that the composite parameter ofthe strength and ductility, the static toughness, is an insen-sitive mechanical property to the fatigue damage evolutionprocess.

. With increasing number of straining cycles, both the number ofgrains containing slip bands and the slip band density withinthe grains tend to increase, and the amount of the deformation-induced austenisite/martensite transformation also exhibitsincrease. The critical value of the cumulative plastic strain toinitiate the martensite in austenitic matrix is found to be about0.5 for 1.0% strain amplitude and 1.0 for 0.6% strain ampli-tude. It is shown by the depth-sensing indentation (DSI) teststhat the deformation resistance of the martensite is almost twotimes greater than that of the austenite, while the plasticityof the martensite is obviously less than that of the austenite.The strain hardening exponent (n) estimated from the inden-tation load–penetration depth (P–h) curves also indicates thatthe martensitic phase possesses a less strain hardening ability incomparison with the austenitic phase.

. As the number of precycles increases, the tension fractureexhibits distinct ductile-to-brittle transition (DBT) feature. Thischange in the fracture mode is mostly attributed to the evolutionof deformation microstructures, especially the deformation-induced martensitic transformation, during low-cycle fatigueprocess.

. It is shown that the ductility parameters exhibit a sensitivechanging character to the fatigue damage evolution process and

can thus be chosen as the damage indicating parameter. Basedon the macro/micro-experimental results of the present inves-tigation, it is suggested that for 304 stainless steel it would be apromising way to study the fatigue damage mechanics modelas well as the residual fatigue life prediction method on the

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neering A 527 (2010) 4092–4102

basis of the depletion of the ductility during fatigue damageprocess.

Acknowledgements

The authors would like to express their sincere thanks for thefinancial support of ‘National Natural Science Foundation of China(NSFC)’ under Grant 50975254 and 10572126 as well as ‘NationalHigh-Tech Research Development Project (863) of China’ underGrant 2006AA04Z419 and 2009AA044801 in completion of thisresearch work. The first author also wishes to thank Dr. ZhiyingHe for her valuable discussions in preparing this manuscript.

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