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Materials Science and Engineering A 520 (2009) 49–55

Contents lists available at ScienceDirect

Materials Science and Engineering A

journa l homepage: www.e lsev ier .com/ locate /msea

ltrasonic back reflection evaluation of crack growth from PSBs in low-cycleatigue of stainless steel under constant load amplitude

d. Nurul Islam, Yoshio Arai ∗

epartment of Mechanical Engineering, Graduate School of Science and Engineering, Saitama University, 255 Shimo-ohkubo, Sakura-ku, Saitama 338-8570, Japan

r t i c l e i n f o

rticle history:eceived 25 December 2008eceived in revised form 1 May 2009ccepted 8 May 2009

a b s t r a c t

The objective of this study is to develop a method for evaluating crack growth from persistent slip bands(PSBs) in low-cycle fatigue of stainless steel, using an ultrasonic back reflection wave during the earlystages of its fatigue life. Changes in the back reflection intensity from surface of the material undercyclic loading are measured. Back reflection intensity decreased due to the evolution of PSBs before the

eywords:ow-cycle fatigueltrasonic methodack reflection intensitymall crackrack growth

start of fatigue crack growth from the crack initiated along PSBs with increase in the number of cyclicloads. The average dislocation density in a grain including PSBs corresponds to the attenuation changemeasured during the fatigue test, from the initial state to the nucleation and growth of the fatigue crack.The attenuation is caused by the movement of dislocation due to ultrasonic waves, whose mechanismwas considered quantitatively. In this study, micromechanical modeling was conducted as a predictionmethod for remaining fatigue life to start crack growth from PSBs based on the changes in ultrasonic back

reflection intensity.

. Introduction

It is useful to devise a non-destructive technology to detect theevelopment process of fatigue damage before initiation of fatigueracks in metallic materials subjected to cyclic loadings [1–3]. Inoderate lifetime regime (larger than 10,000 cycles), fatigue life

s dominated by the crack initiation stage, while the life is domi-ated by crack propagation stages at high applied strain amplitude

n a very short lifetime regime [4]. In cyclically loaded materials,he plastic strain is localized in intensive slip bands, called persis-ent slip bands (PSBs). The evolution of PSBs and the initiation ofrack at the PSBs are important behaviors of polycrystalline materi-ls strained cyclically. Comprehensive studies have been conductedn the internal dislocation structures in face-centered cubic crys-als and polycrystals [5,6]. A number of fatigue damage detection

ethods, using laser speckle, X-ray, electrochemical, and ultra-onic detection methods were proposed [7–10]. Numerous studiesased on the dislocation vibration models of Koehler, Granato andücke have been performed for detecting fatigue damage [11–13],nd to explain the acoustic attenuation and velocity change with

espect to dislocation mobility. The behavior of the attenuationoefficient and velocity change as a function of fatigue cycles,sing electromagnetic acoustic resonance, during the fatigue pro-ess in aluminum alloys, steel, and polycrystalline copper have been

∗ Corresponding author. Tel.: +81 48 858 3438; fax: +81 48 856 2577.E-mail address: yarai@mech.saitama-u.ac.jp (Y. Arai).

921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2009.05.016

© 2009 Elsevier B.V. All rights reserved.

reported recently [2,14–19]. Experiments were performed usingultrasonic wave velocity and attenuation [2,20], or ultrasonic veloc-ities having three different frequencies [21], to evaluate the averagedislocation density and loop length over the volume which corre-sponds to the ultrasonic wave path. These studies used an averagemeasurement over an extremely large volume, instead of a singlecrystal grain, allowing PSBs to evolve into cracks, since ultrasonicwaves could not be focused on a specific position in several tensmicro-meter length scale.

In this research, we propose a method of evaluating the low-cycle fatigue crack growth from the crack initiated along PSBs (asurface crack length of about 50 �m) using a local ultrasonic mea-surement. The ability to detect the start of crack growth from thecrack along PSB is proven by the experiment. A method of modelingthe change in ultrasonic back reflection intensity, correspondingto fatigue damage due to cyclic loading, based on the dislocationvibration model and the crystal grain boundary reflection modelis also proposed. The remaining life to start fatigue crack growthfrom PSBs is predicted by this method and its effectiveness is shownexperimentally.

2. Experimental methods

The material used in this experiment was an austenite stainlesssteel (JIS-SUS304) [22]; its chemical compositions and mechani-cal properties are listed in Tables 1 and 2, respectively. The shapeof the test piece is shown in Fig. 1. To observe the slip bands andcracks using an optical microscope, fine polishing and buffing on

50 Md.N. Islam, Y. Arai / Materials Science an

Table 1Chemical compositions (wt.%).

C Si Mn P S Ni Cr Fe

0.05 0.66 1.81 0.03 0.03 8.76 18.34 Bal.

Table 2Mechanical properties.

E (GPa) � �0.2 (MPa) �B (MPa)

195 0.25 331 662

tarcb1smsmPt[iw

as well as propagated on the surface. The back reflected wave wasreceived by the transducer. The propagation direction in horizontalplane is along the stress direction. The typical waveform of a wavereflected backward by grain boundaries of un-fatigued specimensurface is shown in Fig. 4. The maximum amplitude of the back

Fig. 1. Specimen configuration (unit: mm).

he center portion of the test piece were done finally with 0.1 �mlumina powders. An optical microscope image of the tested mate-ial microstructure is shown in Fig. 2. The average diameter of therystal grain was about 30 �m. Fatigue testing was done using planeending loading; the stress ratio was −1, the cyclic frequency wasHz, and the testing was performed at room temperature. Con-

tant nominal bending stress amplitude of 450 MPa with a constantoment amplitude control was the cyclic loading condition. The

lip bands and surface fatigue cracks were observed with an opticalicroscope (magnification of 1000). The damage development in a

SB, crack initiation along the PSB, and beginning of growth from

he crack are considered to be a continuous transition phenomenon4,5]. In this research, we are focusing on acoustic responses dur-ng the fatigue process before and after a number of cyclic loads

hen the increase in surface length of the observed black line

Fig. 2. Optical microscope image of microstructure of tested material.

d Engineering A 520 (2009) 49–55

(PSBs with or without crack) on optical microscope begins. Thelength scale of ‘increase’ is several micro-meters which character-ize the length scale of the definition of ‘beginning of crack growth’in this study. The development of the PSBs and the beginning offatigue crack growth from the crack initiated along PSBs were evalu-ated by ultrasonic back reflection intensity. Immersion method wasused to attain high spatial resolution with a single high frequency(100 MHz) point-focused transducer for evaluation with ultrasonicwaves. Fig. 3(a) and (b) shows the outline of the measurement sys-tem, and the propagation route of the ultrasonic wave, respectively.The focal length was 12.5 mm in water, the scan pitch 5 �m, and theangle of incidence 30◦ which is large enough compared with thecritical angle to generate surface wave. The induced surface waveis reflected backward by grain boundaries located on the surface

Fig. 3. Ultrasonic back reflection method. (a) Ultrasonic scanning system. (b) Illus-tration of ultrasonic back reflection wave path.

Md.N. Islam, Y. Arai / Materials Science an

rdaAeupcm

3

(pccilawotctcuosashiTttw(ttsf

A /A ) which is 0.715 is shown as a 2-dot dash line in Fig. 8 with

Fig. 4. Typical waveform of back reflected wave from initial surface.

eflection wave shown in Fig. 4 (voltage of the peak magnitude) isefined as A. The transducer was moved in a horizontal plane, par-llel to the specimen surface, so that A reaches the maximum, andat this time was denoted by Amax. To normalize this value, a ref-

rence value A0 (measured at initial state of the fatigue test) wassed. The observed area is 5 mm × 5 mm. In this research the cycliclastic strain amplitude was about 400 �-strain, and the effect ofyclic creep and martensitic transformation caused by plastic defor-ation of the material was not considered.

. Experimental results and discussions

Fig. 5 shows a back reflection ultrasonic microscope imageupper) and corresponding optical microscope image (lower). Thearts indicated by each white rectangular mark in ultrasonic imagesorrespond to the location where PSBs are located in the opti-al images indicated by the arrows. In the ultrasonic microscopemages, the inhomogeneous brightness distribution denotes theocation dependence of back reflection intensity from grain bound-ries. The brightness of the ultrasonic image in the location markedith a rectangle, when N/Nf = 0.45–0.58 (Nf = 22,011 is the number

f cycles to fracture), decreased due to fatigue damage accumula-ion. Later, at N/Nf = 0.60 the brightness increased with the start ofrack growth. In the optical microscope image, at N/Nf = 0.45–0.58,he length of the black line (PSBs with or without crack) remainedonstant, but at N/Nf = 0.60, the length started increasing and theltrasonic back reflection intensity increased correspondingly. Therientation of the PSBs on the surface was almost normal to thetress direction. The PSBs were formed mainly in the grains, rarelylong the grain boundaries. Fig. 6 shows changes in ultrasonic inten-ity due to fatigue, in form of a set of line distributions along theorizontal white line with arrow of the ultrasonic image in Fig. 5

ncluding the intensity from left edge to right edge of the image.he origin of the co-ordinate in Fig. 6 is set at a specific loca-ion, and is the same for each number of cycles. Fig. 6 shows thathe peak of back reflection intensity indicated by ‘PSB1’ decreasesith an increase in cyclic loading before beginning of crack growth

10,000–12,800 cycles) significantly compared with other peaks;

he intensity increases sharply (13,200 and 13,400 cycles) afterhe start of crack growth. The increase of average dislocation den-ity in the grain including PSBs due to the increase in number ofatigue cycles before beginning of crack growth is considered to be

d Engineering A 520 (2009) 49–55 51

the mechanism of the intensity decrease. The evolution of PSBs,crack initiation along PSBs and start of crack growth from PSBsincluding the change in average dislocation density of the grain,are phenomena occurring in the crystal grain located on the mate-rial surface. The present ultrasonic method induces surface wavemotion of the crystal grain, and the change in damping coefficient ofthe crystal grain due to cyclic load can be detected by measuring theultrasonic back reflection intensity non-destructively. Figs. 5 and 6show the possibility of detecting grains where cracks will startthe growth from the PSBs in future using the present ultrasonicback reflection method. Optical methods, however, are not able todistinguish the crack-initiating PSBs from the stable one until thegrowth occurs. Fig. 7 shows the change in ultrasonic back reflectionintensity from boundaries of the crystal grain due to cyclic loads,corresponding to the change in peak top values in Fig. 6. Solid sym-bols represent the reflected wave intensity from the boundaries ofgrain including PSBs at which the crack growth from the PSBs isobserved optically. Also, the open symbols represent the averageintensity change over an area (600 �m × 600 �m) subjected to thesame cyclic deformation, but where no crack growth is observed.In this figure the experimental data for PSB1 and the open symbolshave the same origin of Amax/A0; while for PSB2, 3, and 4 their ori-gins are shifted to allow a clear illustration. A large number of slipbands (observed as black lines optically) were generated in the earlystage of cyclic loading (from beginning to N = 9000, the final den-sity is about 9.2 line/mm2). The length of the black lines remainedunchanged until about N = 13,000 cycle (60% of the number of cyclesto fracture), when some of them commenced elongation. The rangeof the number of cyclic loads is shown as “start of crack growth”in Fig. 7. Fig. 7 shows that the ultrasonic back reflection intensitydecreases slightly due to uniform plastic deformation in the earlystage of cyclic loading. When the slip band emerged at the measure-ment location, the intensity increased slightly (arrow 1 in Fig. 7)and decreased subsequently due to dislocation damping in PSBs(arrow 2 in Fig. 7, at about 60% of the number of cycles to begincrack growth). The intensity showed a decrease of up to a 30% inthe beginning of crack growth, however the decrements in averageintensity observed in the area where no crack growth occurred wereless than 15%, as shown by the open symbols. The relations betweenAmax/A0 and N were almost linear in the range from the cycle indi-cated by arrow 2 to the one at start of crack growth, though thedetails of the behavior differed among PSBs and may depend on thecrystal orientation. The back reflection intensity increased rapidly,after the beginning of crack growth, due to reflections on the cracksurface instead of that on the grain boundary. Assume N* is thenumber of fatigue cycles from which a decrease in back reflectionintensity was detected immediately after its increase (arrow 2 inFig. 7), and N∗

+1 is the number of cycles during the decrease in backreflection intensity (considered the next evaluation cycle after N*).Growth from the crack initiated along PSBs starts when the decreasein ultrasonic back reflection intensity reaches a specific thresholdvalue, as shown in Fig. 7. By using the decrease in reflection intensity�A = Amax(N∗

+1) − Amax(N∗), and the linear relationship betweenAmax/A0 and N, the remaining life (NS − N∗

+1) to the start of fatiguecrack growth can be predicted by the following equation:

Ns − N∗+1 = �As − �A

�A(N∗

+1 − N∗), (1)

where �As is the amount of decrease in back reflection intensitytill the start of crack growth. The experimentally measured aver-age value of Amax/A0 at start of crack growth (the critical value of

max 0linearly approximated relationships between Amax/A0 and N (Eq.(1)), and the experimental results of Amax/A0 (solid symbols). TheN∗

+1 is assumed to be 5%, 7%, and 9% larger than N* as shown inFig. 8, respectively. The cross-points between the linear relation

52 Md.N. Islam, Y. Arai / Materials Science and Engineering A 520 (2009) 49–55

Fig. 5. Ultrasonic and optical micrograph of slip bands, (a)–(c) and growing crack from the crack initiated along the slip bands (d) for PSB 1. Nf = 22,011 is the number of cyclesto fracture. The horizontal direction corresponds to the loading direction.

Md.N. Islam, Y. Arai / Materials Science and Engineering A 520 (2009) 49–55 53

F

acils

aAirttrr

Fc

ig. 6. Ultrasonic back reflection distribution along horizontal co-ordinate for PSB1.

nd the critical value of Amax/A0 give the predicted life to startrack growth from PSBs based on linear approximation. The exper-mentally measured Nss are indicated by arrows in Fig. 8 where theinearly approximated relationship predicts the remaining life totart crack growth with an error of 3–10% conservatively.

Fig. 9 illustrates the model for ultrasonic wave reflections ofngle beam incidence on the surface and the grain boundary. Area0 represents water, A1 is a grain on which the ultrasonic wave 1

mpinges, and A2 is the material surrounding this grain. In the backeflection intensity measurements, as the incident angle is larger

han the critical angle for refraction of longitudinal and shear waveshe surface wave is induced (wave 5), reflected (wave 6) and theefracted wave 3 from the grain to water is measured. The surfaceoughness due to PSBs does not generate backward reflection sig-

ig. 7. Relation between ultrasonic back reflection intensity, Amax/A0 and number ofycles, N. For PSB4 arrows 1 and 2 coincide each other.

Fig. 8. Comparison between linear approximation results and experimental resultsof back reflection intensity and number of cycles.

nificantly because the roughness is about 1 �m, which is too smallcompared with the wave length (50 �m). Considering a PSB in alarge grain and assuming that the crystal grain size of SUS304 is50 �m, the time difference between forward reflected wave 2 bythe real surface and back reflected wave 3 by the grain boundariesis about 0.017 �s (the surface wave speed in SUS304 is assumed tobe 2900 m/s). The forward reflected wave 2 on the real surface andthe backward reflected wave 3 on the grain boundary are insep-arable when the normal incidence/reflection method is used. Thebackward reflected wave 3 on the grain boundary can be measuredseparately as back reflection intensity with large incident angle.Amax/A0 is expressed as follows:

Amax

A0= exp [−(˛1 − ˛0)H] , (2)

where ˛0 and ˛1 are the attenuation coefficient in the initial and

fatigued states (the propagation length is assumed to be the graindiameter, H). According to the Granato and Lücke model of vibratingdislocation [11–13]:

˛ = C1f 2�L4, (3)

Fig. 9. Model for back reflection ultrasonic wave of oblique incidence, propagationas surface wave and reflection on the boundary of grains.

54 Md.N. Islam, Y. Arai / Materials Science an

Table 3Condition of simulation.

Diameter of crystal grain, H (�m) 50Dislocation loop length, L (m) 75-125 × 10−9

Proportional factor, C1 (s/m2) 9000Initial dislocation density, �0 (m−2) 7 × 1013

Dislocation density at start of crack growth, �s (m−2) 95 × 1013

SND

wd(udacNat

�

wctictf

�

r˛tglp

tarting cycle of damage evolution, N* [cycle] 11,000umber of cycle for start of crack growth, Ns (cycle) 13,000ecrease in reflection intensity up to start of crack growth,Amax/A0

0.715

here f is the frequency of the stress wave, � the dislocationensity, L the dislocation loop length, and C1 a material constantdescribed in detail in Appendix A). When the material is loadednder cyclic plastic deformation of constant amplitude, fatigueamage develops in crystal grains having large grain size and prefer-ble crystal orientation. Also, the average dislocation density overrystal grain increases rapidly at a threshold number of cyclic loads* [5], corresponding to the evolution of PSBs. In such case, the aver-ge dislocation density over a crystal grain is assumed proportionalo the cumulative plastic strain amplitude ��εp [23–25]:

= K∑

�εp, (4)

here K is a material constant. Under the present experimentalonditions, the cumulative plastic strain amplitude is proportionalo the number of cycles N − N*. Therefore, considering �0 as thenitial dislocation density, �s the dislocation density at start ofrack growth, Ns the number of cycles for start of crack growth, andhe change of dislocation density is proportional to the number ofatigue cycles:

= �0 + (�s − �0)N − N∗

Ns − N∗ . (5)

Assuming a constant dislocation loop length, we can predict theemaining life to start of crack growth, using Eqs. (2), (3) and (5).

0 and ˛1 in Eq. (2) are assumed to be ˛ in Eq. (3) which means

he dislocation density � in Eq. (3) is the average density over therain including PSBs. The change in back reflection intensity calcu-ated using this method is shown in Fig. 10 by lines. Table 3 lists thearameters used in the calculation. It has been reported from TEM

Fig. 10. Comparison between simulated results and experimental results.

d Engineering A 520 (2009) 49–55

observations that the dislocation loop length for stainless steel is inthe range of 25–164 nm [26–28]. A range of loop length L from 75to 125 nm gives the simulation results which show good agreementwith the experimental results of decreasing back reflection inten-sity during the fatigue damage development (solid symbols). Thisagreement implies that, the micromechanical modeling presentedin this study is reasonable for evaluating fatigue damage evolutionusing the present ultrasonic back reflection method. In Fig. 10, thethin and thick arrows indicate the number of cycle to start crackgrowth of experimental and simulation results, respectively. Theerror in measurement of Amax/A0 is about 5% due to fluctuations ofAmax in the ultrasonic measurements. The remaining life before thebeginning of fatigue cracks growth can be predicted by the linearapproximation method with an accuracy of 2–7% due to the errorof Amax/A0. The life to start crack growth from PSBs predicted by thedislocation damping model for a loop length of 125 nm varies fromthe linear approximation estimation with an error of 3–9%. Thisagreement implies that the linear approximation method for pre-dicting life to start fatigue crack growth is supported quantitativelyby the dislocation damping model. Although the effectiveness of themethod for detecting fatigue damage by ultrasonic back reflectionunder the test conditions (polished JIS-SUS304 stainless steel sur-face, a frequency of 100 MHz, and low-cycle fatigue under constantload amplitude) of this research was examined quantitatively, it willbe necessary to examine the effectiveness of ultrasonic back reflec-tion intensity method for fatigue damage evaluation under otherconditions (materials, surface roughness, and load conditions).

4. Conclusion

In this research, a method for evaluating low-cycle fatigue crackgrowth from the crack initiated along PSBs (about 50 �m in surfacecrack length) using ultrasonic back reflection intensity caused bychanges in the dislocation density was proposed, and the start ofcrack growth from the crack along PSBs was detected experimen-tally. The utility of the method in predicting life to start fatigue crackgrowth was proven by the experiment. In addition, this researchproposed a method of modeling the change in back reflection inten-sity during cyclic loading, using the dislocation vibration modeland the crystal grain boundary reflection model. Their accuracyin estimating the remaining life to start cracks growth from PSBswas evaluated, and their effectiveness demonstrated. The resultsobtained are summarized as follows:

1. Back reflection intensity from the boundary of grains where aPSB is formed decreases before the beginning of crack growth (atabout 60% of the number of cycles to start crack growth), untila large decrease (about 30%) occurs at the beginning of crackgrowth.

2. The proposed model can simulate the decrease behavior ofback reflection intensity indicating the development of fatiguedamage in the experiment. Under the test conditions of thisresearch, (finely polished surface of stainless steel, a frequency of100 MHz, and low-cycle fatigue under constant load amplitude),the remaining life to start fatigue crack growth from the crackinitiated along PSBs could be predicted (using a linear approx-imation method from the change in ultrasonic back reflectionintensity) with an accuracy of 7%.

Acknowledgements

The authors express gratitude to the Ministry of Education, Sci-ence, Sports, and Culture, of the Government of Japan for providingfinancial support during this research work.

Md.N. Islam, Y. Arai / Materials Science an

Table A1Constants used to calculate C1 (material constant).

Parameter Description Value

a Lattice constant 0.3571 nmb Burger’s vector 0.2526 nmCCDl

A

i

C

wdt

B

w

ˇ

atl

R

[

[[[[[

[

[

[

[

[[[[[[[28] A. Wolfenden, Scr. Metall. 17 (3) (1983) 321–325.[29] J.D. Eshelby, Proc. Roy. Soc. London A197 (1949) 396–416.

p Specific heat at constant pressure 500 J/kg Kv Specific heat at constant volume 418 J/kg K2 Thermal diffusivity 0.0391 cm2/s

“Cut-off” length 10−7 cm

ppendix A.

In Eq. (3) the material constant C1 [13] can be calculated assum-ng a long wavelength approximation as follows:

1 = 4B(1 − �)2

�2Gb2, (A.1)

here G is the shear modulus, � the Poisson’s ratio, B the specificamping constant, and b the Burgers vector magnitude. Accordingo Eshelby’s theory [29], the value of B is given by:

= ˇGa2, (A.2)

here a is the lattice constant,

= 110D2

Cp − Cv

Cplog

D2

ωl2, (A.3)

where D2 the thermal diffusivity, Cp and Cv are the specific heats,nd l the “cut-off” length, ω the angular frequency. The values ofhese material constants for stainless steel SUS304 [30–32] are

isted in Table A1.

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[[[

d Engineering A 520 (2009) 49–55 55

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