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Scripta Materialia 64 (2011) 65–68

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In situ damage assessment in a cast magnesium alloy during veryhigh cycle fatigue

Anish Kumar,a,b,⇑ Raghavendra R Adharapurapu,a J. Wayne Jonesa andTresa M. Pollockc

aDepartment of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109, USAbMetallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, 603102 Tamil Nadu, India

cUniversity of California, Santa Barbara, CA 93106, USA

Received 8 June 2010; revised 24 August 2010; accepted 3 September 2010Available online 15 September 2010

Damage evolution during very high cycle fatigue (VHCF) in AXJ530 die-cast magnesium alloy was studied in situ using nonlin-ear ultrasonic measurements via analysis of the feedback signal of a closed-loop ultrasonic fatigue system. Variations in acousticnonlinearity with fatigue cycles revealed cyclic hardening/softening during early fatigue life (<108 cycles) as well as the initiationand growth of a dominant fatigue crack in the VHCF regime (Nf = 0.82 � 109 cycles).� 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Very high cycle fatigue, Fatigue damage; Cast Mg alloy; Fatigue crack initiation; Nonlinear ultrasonics

Magnesium alloys offer a variety of opportunitiesfor structural applications in automotive and aerospaceindustries due to their low density, high strength/weight ra-tio, good castability and high damping properties. Auto-motive components are often subjected to cyclic stressesfor more than 108 cycles during their lifetime. Hence, a bet-ter understanding of the response of cast magnesium alloysto fatigue loading, especially at lifetimes in the very high cy-cle fatigue (VHCF) regime (Nf > 108), is of great impor-tance. In order to study the fatigue properties ofmaterials in this regime, accelerated testing methods viaultrasonic instrumentation are often utilized. The ultra-sonic (�20 kHz) fatigue technique has been extensivelyused in the past two decades for investigation of the VHCFbehavior of various materials under different testing condi-tions, e.g. single-crystal Ni-base superalloys at tempera-tures up to 1273 K [1], cast Al alloys in differentenvironments [2,3], Mg alloys [4,5] and thin sections ofthe Ni-base single-crystal superalloy CMSX-4 [6]. Ultra-sonic fatigue has also been used for fatigue crack growthstudies [7,8]. In conventional ultrasonic fatigue studies,the only data obtained at the end of a test is the numberof cycles to failure (Nf) for the case of an S–N type endur-ance test, and number of cycles (N) and crack length (a)

1359-6462/$ - see front matter � 2010 Acta Materialia Inc. Published by Eldoi:10.1016/j.scriptamat.2010.09.008

⇑Corresponding author at: Metallurgy and Materials Group, IndiraGandhi Centre for Atomic Research, Kalpakkam, 603102 TamilNadu, India; e-mail: anish@igcar.gov.in

measured by other techniques (i.e. optical, replica and po-tential drop) for the case of crack growth studies.

In a typical ultrasonic fatigue testing setup, very highamplitude sound waves are injected from the ultrasonictransducer into one end of the load train consisting ofan amplification horn, a lambda (k) rod and the specimen[7,9]. The sound waves travel along the amplification hornand the lambda rod, enter the fatigue specimen and arethen reflected from the end of the specimen. When the fre-quency of the sound wave is equal to the resonant fre-quency of the mechanical system, the incoming andreflected waves superimpose to form a resonant vibration.A displacement transducer, working on induction princi-ples, measures the displacement of the load train at one ofthe nodes, which is used as the feedback signal to controlthe vibration amplitude during a fatigue test. The evolu-tion of fatigue damage in terms of cyclic hardening/soft-ening and initiation/growth of a fatigue crack changesthe resonance behavior of the mechanical system. Hence,the feedback signal obtained from the displacement trans-ducer is expected to provide information about the cur-rent damage state of the specimen. Based on this idea,we have recently reported a new nonlinear ultrasonicmethodology for in situ detection of the initiation of afatigue crack in a material by monitoring the increase inthe amplitude of the higher harmonics in the feedbacksignal with the successive accumulation of fatigue damage[3,9]. In a cast Al alloy [3], this nonlinear ultrasonic meth-

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Figure 1. (a) Typical feedback signal and (b) its amplitude spectrumshowing a fundamental resonance peak at 20 kHz and its harmonics at40 and 60 kHz. A single resonance cycle is also shown in the inset in (a).

66 A. Kumar et al. / Scripta Materialia 64 (2011) 65–68

odology was used to study the fraction of life consumed incrack initiation and propagation as functions of the ap-plied stress amplitude and the pore size from which thelife-limiting fatigue crack initiated, and also for under-standing the fatigue crack growth behavior.

Nonlinear ultrasonic studies are based on the genera-tion of second (2x0) and higher harmonics (nx0) of thefundamental frequency (x0) due to the distortion of thesinusoidal ultrasonic waves as they propagate through anonlinear or anharmonic solid. In a typical experimentalsetup for nonlinear ultrasonic measurement, a longitudi-nal ultrasonic wave with a tone burst of amplitude, a0, atfrequency, x0, is launched on one side of the specimenbeing examined. If a0 is sufficiently large, the wave de-tected on the other side of the specimen will containmany harmonic components, i.e. the detected wave pos-sesses a component of amplitude a1 at the fundamentalfrequency x0 along with a component of amplitude a2 atthe second-harmonic frequency 2x0, etc. The ultrasonicnonlinearity parameter (b) is determined experimentallyby measuring the absolute amplitudes of the fundamen-tal (a1) and the second-harmonic (a2) displacement sig-nals, and is defined as [10–14]:

b ¼ 8v2a2

x20za2

1

; ð1Þ

where v and z are the ultrasonic phase velocity and thepropagation distance, respectively. The acoustic nonlinear-ity in a material increases with the introduction of latticedefects such as dislocations and structural defects such asmicrocracks [11]. Based on this, the potential of nonlinearultrasonics to quantitatively detect and characterize fatiguedamage has been demonstrated in several recent studies invarious metals and alloys including Cu-base alloys [10], Ni-base alloys [11], Al alloys [12], Ti alloys [13] and steels [14].However, all the studies were focused on the low-cyclefatigue (Nf < 104–105 cycles) [10–14] regime where the plas-tic strain amplitude is quite high. No study has been re-ported so far for the evaluation of fatigue damage in aMg alloy using nonlinear ultrasonic measurements.

In the present paper, we show that the nonlinear ultra-sonic measurements via the analysis of the feedback signalof an ultrasonic fatigue system can be used for a morecomprehensive characterization of the fatigue behaviorin a cast Mg alloy, i.e. to characterize the hardening/soft-ening behavior during initial cycles (<108), to detect theinitiation of a life-limiting fatigue crack and also for fati-gue crack growth study in the gigacycle fatigue regime.

The composition (wt.%) of the die-cast Mg alloy(AXJ530) used in the present study is 4.81Al–3.02Ca–0.3Mn–0.17Sr (<0.01Zn, Sn) and balance Mg [15]. Themicrostructure of the alloy consisted of cells of primarya-Mg surrounded by eutectic phases in the interdendritic re-gions with a grain size of 19 lm; more details are given else-where [15]. Cylindrical fatigue specimens were tested at aload ratio of R = �1 and stress amplitudes of 55, 65 and75 MPa. The stress amplitudes were suitably selected toinvestigate the fatigue behavior of the alloy near its fatiguestrength at 109 cycles, which was between 60 and 65 MPabased on ultrasonic fatigue tests of several specimens at dif-ferent stress amplitudes. The value of Young’s modulus wastaken as 44 GPa for calculating the stress from the strainmeasured at the center of the specimens using foil strain

gauges. A specimen was considered to be “run-out” if itdid not fail at or before 109 cycles. The fractured surfaceswere observed by scanning electron microscopy (SEM).Transmission electron microscopy (TEM) analysis was con-ducted on 3 mm diameter foil specimens extracted from thegauge portion of the failed or run-out specimens.

The experimental setup for ultrasonic fatigue and thenonlinear ultrasonic measurements is presented in detailelsewhere [3,9]. In order to avoid heating of the specimensduring the fatigue cycling, a pulse–pause cycle of 100:1000 ms was used and compressed air was blown on thespecimen gage section continuously. The only modifica-tion to the standard ultrasonic fatigue system for the non-linear ultrasonic analysis is the use of a personal computerfor online acquisition of the feedback signal from theoscilloscope through a USB port. Software was developedin LabVIEW for acquisition and frequency analysis of thefeedback signal for in situ monitoring of the fatigue dam-age during ultrasonic fatigue. In a pulse of 100 ms, thefeedback signal of 10 ms length (Fig. 1a; 2500 data pointsat a digitization rate of 250 kHz) is stored at a start delayof 35 ms. A typical feedback signal and its amplitude spec-trum are shown in Figure 1. The fundamental frequencypeak at 20 kHz and its second harmonic at 40 kHz areclearly resolved in the amplitude spectrum. The amplitudeis plotted on a dB scale to resolve the presence of higherharmonics of even lower amplitudes. Rearranging Eq.(1), we obtain:

logðbÞ ¼ logðkÞ þ logða2Þ � 2 logða1Þ20 logðbÞ ¼ 20 logðkÞ þ 20 logða2Þ � 2� 20 logða1Þ20 logðbÞ ¼ K þ A2 � 2A1 ð2Þ

In order to analyze the variations in the nonlinearitywith respect to the undamaged specimen, brelative (=b/b0,where b0 indicates the undamaged material condition) isused as a parameter to study the accumulation of fatiguedamage, as it requires measurement of amplitudes atfundamental and second-harmonic frequencies only inthe damaged and undamaged conditions [10–14]. Fur-ther extending Eq. (2), we can obtain:

20 logðb=b0Þ ¼ ðA2 � 2A1Þ � ðA2 � 2A1Þ0: ð3ÞThe parameter (A2 � 2A1) � (A2 � 2A1)0, henceforth

referred to as brel, is used to correlate with the fatiguedamage in the present study.

Figure 2a shows the variations in brel with the fatiguecycle until 1.2 � 108 cycles for specimens tested at stressamplitudes of 55, 65 and 75 MPa. The brel parameterincreased continuously until about 5 � 107 cycles,

A. Kumar et al. / Scripta Materialia 64 (2011) 65–68 67

followed by a plateau for the specimen tested at 75 MPa.However, the two specimens tested at 65 MPa exhibitedan increase in brel until about 3 � 107 cycles followed bya decrease. One of the two specimens tested at 65 MPafailed at 4 � 107 cycles away from the gage region dueto a large pore and exhibited a sudden increase in brel

prior to failure. However, before failure of the specimen,the similarity in the variation in the brel with fatigue cy-cles for the two specimens tested at a stress amplitude of65 MPa demonstrates the excellent repeatability of thetest and the applicability of the technique for the detec-tion of cyclic hardening/softening behavior. In the otherspecimen tested at 65 MPa, brel decreased with fatiguecycles until 1.2 � 108 cycles followed by a plateau until109 cycles, at which point the specimen was consideredto be a run-out and the test terminated. The specimentested at 55 MPa exhibited a slight increase in brel duringthe initial few pulses, followed by a continuous decreaseuntil 5 � 107 cycles, beyond which a plateau is observeduntil 109 cycles. The effect of the stress amplitude on therate of change in brel is shown in Figure 2b by analyzingthe change in dbrel/dN with fatigue cycles. The maxi-mum rate of change in brel with the fatigue cycles is ob-served at �2 � 107 cycles and was found to be almostdouble for the specimen fatigued at 75 MPa stressamplitude as compared to that at 65 MPa.

An increase in the ultrasonic nonlinearity during cyc-lic hardening has been observed in the past by severalinvestigators in different materials via conventionalnonlinear ultrasonic measurements [10–14]. However, adecrease in brel with fatigue cycles has not been reportedsince the previous studies were carried out in the low-cy-cle fatigue regime where significant cyclic hardening andan increase in the dislocation density was observed withcycling. The stress field associated with the presence ofdislocations results in a local nonlinearity in elastic prop-erties, and increasing dislocation density increases the

Figure 2. Variations in (a) nonlinear ultrasonic parameter (brel) and (b)dbrel/dN with fatigue cycles during tests at 55, 65 and 75 MPa stressamplitudes.

acoustic nonlinearity of the material [11]. Recently,Cantrell [11] has derived the contributions of dislocationmonopoles and dipoles to the nonlinear parameter of afatigued material. The nonlinearity due to dislocationmonopoles (bmp) and dipoles (bdp) is given by [11]:

bmp ¼ 24

5

XKmpL4R3ðAe2Þ

2

G3b2jr0j ð4Þ

bdp ¼ 16p2XR2Kdph3ð1� mÞ2ðAe2Þ

2

G2bð5Þ

where X is the conversion factor from shear to longitu-dinal strain, Kmp and Kdp are the density of isolated sin-gle dislocations and dislocation dipoles, respectively, Lis the average dislocation half loop length, R is the Sch-mid factor from longitudinal to shear wave propagation,Ae

2 is the second-order Huang coefficient of the polycrys-talline material, |r0| is the magnitude of the initial (resid-ual or internal) longitudinal stress in the material, G isthe shear modulus, b is the amplitude of the Burger’svector, m is the Poisson’s ratio and h is the dipole height(distance between parallel slip planes of a dislocation di-pole). It is apparent from Eqs. (4) and (5) that the non-linearity due to both monopoles and dipoles increaseswith increasing dislocation density.

Negligible (initial) hardening followed by a continuoussoftening in the specimen tested at a stress amplitude of55 MPa indicates that the stress is not high enough to gen-erate a significant population of additional dislocationsduring cycling. This is consistent with the fatigue strengthof the alloy (60–65 MPa); no failure was observed in anyof the specimens tested for 109 cycles at 60 MPa or at lowerstress amplitudes. The cyclic hardening/softening observedat various stress amplitudes is also corroborated by theTEM analysis of the specimens. Figure 3a–d are TEMimages showing the dislocation structures in the a-Mgphase in an as-cast specimen as well as in the specimens fa-tigued at 55 MPa (run-out at 1 � 109 cycles), 65 MPa (run-out at 1 � 109 cycles) and 75 MPa (failure at 8.19� 108

cycles), respectively. A low density of long, curved disloca-tion segments is observed in the as-cast condition (Fig. 3a).During fatigue cycling at 55 MPa, these grown-in disloca-tions are most likely annihilated in the early stages of cy-cling. As the acoustic nonlinearity is proportional to thefourth power of the length of the dislocation monopoles(Eq. (4)), the annihilation of the long dislocations is consis-tent with the large decrease observed inbrel. Further cyclingto 109 cycles at 55 MPa does result in a modest increase indislocation density (Fig. 3b). Additionally, an increase indislocation density with increasing fatigue stress amplitudeis clearly evident (Fig. 3b–d). The higher overall densities inthe samples cycled at 65 and 75 MPa, respectively, are con-sistent with a more rapid increase in brel. This is in agree-ment with the observations of Koike et al. [16] inAZ91Mg alloy that the cyclic hardening increases substan-tially just above the fatigue limit.The specimen tested at astress amplitude of 75 MPa failed after 8.19� 108 cycles.An SEM image of the fractured surface showing an inter-nal initiation of the fatigue crack is shown in Figure 4. Afterthe initial increase with fatigue cycles, brel remained almostconstant until 8.12� 108 cycles, at which point it sharplyincreased until failure of the specimen at 8.19 � 108 cycles.A magnified view of the variation in brel with fatigue cycles

Figure 3. TEM images showing dislocation structures in the a-phase in(a) an as-cast specimen, (b) the specimen fatigued at 55 MPa for1 � 109 cycles, (c) the specimen fatigued at 65 MPa for 1 � 109 cyclesand (d) the specimen failed at 8.19 � 108 cycles at 75 MPa.

68 A. Kumar et al. / Scripta Materialia 64 (2011) 65–68

during crack propagation is shown in the inset in Figure 4.The start of the increase in brel was observed at 8.12 � 108

cycles, indicating that the fatigue crack growth life is�7 � 106 cycles. Taking the Paris law ðda

dN ¼ CðDKn

�DKnthÞÞ constants for a die-cast Mg alloy as C = 2.0 �

10�10 mcycle�1, m = 3.0, DKth = 1.3 MPa m�1/2 [17] andDK ¼ 2

p rmax

ffiffiffiffiffiffi

pap

for an internal crack with 2a diameter,the fatigue life spent in the long-fatigue-crack growth re-gime from the calculated threshold crack length ai =0.24 mm (for 75 MPa stress amplitude) to af = 1.64 mm(Fig. 4) is determined to be 2.1 � 106 cycles. The experi-mentally observed fatigue crack growth life is �3.5 timeslarger than that predicted from this analysis, indicatingthat the nonlinear ultrasonic-based methodology used inthe present investigation is able to detect the initiation ofan internal fatigue crack at a size much smaller than thelong-crack threshold crack size. Further, by establishinga correlation between brel and fatigue crack size it shouldalso be possible to quantitatively monitor fatigue crackgrowth behavior.

The nonlinear ultrasonic-based methodology devel-oped in the present study can be used to study the VHCFbehavior for a wide range of materials in order to betterunderstand the cyclic hardening/softening as well as initi-ation and growth of fatigue cracks for both internal and

Figure 4. Variations in nonlinear ultrasonic parameter (brel) withfatigue cycles during a test at 75 MPa stress amplitude. The magnifiedview of the data during the growth of the fatigue crack and the SEMimage of the fractured surface are also shown.

surface-initiated cracks. The variation in acoustic nonlin-earity with accumulation of fatigue damage, as studied bythe present methodology, can be used as a basis for devel-oping nonlinear ultrasonics-based nondestructive evalua-tion methodology for in-service detection of fatiguedamage accumulation in structures and components.

In summary, the present study demonstrates the appli-cability of a new nonlinear ultrasonic methodology forcomprehensive in situ characterization of the accumulationof fatigue damage during VHCF, i.e. initial hardening/softening, crack initiation and fatigue crack growth canall be studied via the developed methodology. In theAXJ530 die-cast Mg alloy examined in this study continu-ous cyclic hardening occurred prior to failure at the higheststress amplitude (75 MPa) while softening was observed atthe lowest stress amplitude of 55 MPa, which is below theobserved 109 cycle endurance limit for the alloy. A fatiguecrack growth life�3.5 times longer than that predicted forlife attributable to growth of a large fatigue crack from thethreshold crack size was observed, which indicates thatsmall crack growth can also be monitored using the meth-odology discussed in the present study.

This work was sponsored by an AFOSR-MURIprogram, Award No. FA9550-05-0416. One of theauthors (A.K.) is thankful to Dr. Baldev Raj, Director,Indira Gandhi Centre for Atomic Research, Kalpakkam,for continuous encouragement and support.

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