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Reverse bending fatigue of shot peened 7075-T651 aluminium alloy: The roleof residual stress relaxation

M. Benedetti a,*, V. Fontanari a, P. Scardi a, C.L.A. Ricardo a, M. Bandini b

a Department of Materials Engineering and Industrial Technologies, University of Trento, Via Mesiano 77, 38100 Trento, Italyb Peen Service, Via A. Pollastri 7, 40138 Bologna, Italy

a r t i c l e i n f o

Article history:Received 5 August 2008Received in revised form 10 November 2008Accepted 26 November 2008Available online 10 December 2008

Keywords:Aluminium alloysShot peeningFatigue strengthResidual stress relaxation

a b s t r a c t

The effect of different shot peening treatments on the reverse bending fatigue behaviour of Al-7075-T651was studied. The fatigue improvements with respect to the unpeened condition and the influence of thepeening intensity on fatigue were discussed accounting for the effects of surface modifications (rough-ness and strain hardening) and of residual stresses. In particular the extent of the residual stress redistri-bution during loading was investigated by means of X-ray diffraction (XRD) measurements. Nosignificant residual stress relaxation was observed in samples tested to a load level corresponding tothe fatigue endurance at 5 � 106 cycles. Residual stress relaxation was observed only when the materialplastic flow stress was achieved during the compressive part of the fatigue load cycle. Accordingly, shotpeened samples with deep sub-superficial compressive residual stress peak showed a fatigue endurancelevel corresponding to the condition of incipient plastic flow. This phenomenon was also accompanied bysub-superficial fatigue crack initiation. On the contrary, samples tested at shorter fatigue lives showedcrack initiation close to the surface. The initial and the stabilized residual stress profiles were consideredfor discussing the improvement in the fatigue behaviour due to peening. For this purpose, a multiaxialfatigue criterion was adopted to account for the biaxial residual stress field. The fatigue life was quiteaccurately predicted as long as fatigue initiation occurs on the surface.

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1. Introduction

High-strength aluminium alloys are widely used in aerospaceapplications due to a very favourable strength-to-weight ratio.Strengthened aluminium alloys, such as those of the 7xxx series,exhibit, despite high tensile strength values (greater than500 MPa), a relatively low fatigue resistance: the fatigue endurancein the high-cycle fatigue regime (>5 millions cycle) is about140 MPa [1]. Since the majority of fatigue cracks initiate on thesurface, the conditioning of the surface to resist crack initiationand earlier crack growth is an attractive method of improving fati-gue performance. For this reason, aluminium alloys are frequentlysubjected to surface treatments. For instance, shot peening has al-ways received particular attention, allowing for noticeable incre-ments in the fatigue life of mechanical components [2–6]. In theliterature, the major part of this improvement has been almostunanimously attributed to the introduction of compressive resid-ual stresses in the surface region, which very often overcompen-sates the worsening of surface morphology and microstructurecaused by shot impacts [3–8]. Some investigations, however,pointed out that, owing to compressive surface residual stresses,

the crack initiation site may move from the surface to the interiorof the sample or even into the tensile residual stress region be-neath the surface hardened layer, especially in the high-cycle fati-gue regime [9,10].

In some cases, the shot peening treatment is responsible forbeneficial microstructural transformations such as stress inducedmartensitic transformation of the retained austenite in carbu-rized steels [11]. The microstructural effect of shot peening inaluminium alloys is ambiguous. On one side, work hardening isresponsible for enhanced resistance to crack initiation, on theother side it causes lower crack growth resistance due to mate-rial embrittlement [12]. Taking into account the controversial ef-fects exerted by the peening treatment on the surface layers,some indications about the process parameters have been identi-fied in order to maximize the fatigue performance. For instance,peening of soft materials, like aluminium alloys, with steel shot,widely used for high-strength steel and titanium alloys, is knownto be quite detrimental to fatigue performance. Luo et al. [13]showed that the rough peened surface of 7075-T6 aluminiumspecimens significantly lowered the beneficial effect on the fati-gue behaviour with only a net increase of 7% in fatigue life. Onthe contrary, peening with lighter media such as glass or ceramicbeads improves the fatigue resistance due to the decreased sur-face roughness [4]. In addition, aluminium alloys for aerospace

0142-1123/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijfatigue.2008.11.017

* Corresponding author. Tel.: +39 0461882457; fax: +39 0461881977.E-mail address: matteo.benedetti@ing.unitn.it (M. Benedetti).

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applications, such as those of the 7xxx series, are preferably shotpeened using ceramic beads rather than steel shots in order toprevent the surface from ferrous contaminations that induceundesired galvanic effects.

Since the larger contribution of shot peening to enhance fati-gue performance is given by compressive residual stresses, it isof paramount importance to understand whether the initial resid-ual stress field remains stable throughout the service life. For thispurpose, relaxation and redistribution of residual stresses occurwhen the summation of the residual stress and applied stressdue to subsequent mechanical loading exceeds the yield condi-tion of the material [14,15]. In addition, repeated fatigue cyclingmay induce residual stress relaxation, even when the mechanicalload cycles do not cause macroscopic plastic deformation [16].The extent of cyclic stress relaxation depends on applied loadsas well as on the tendency of many materials to exhibit cycle-dependent softening in the surface layer because of the intensecold working introduced by the treatment. This topic has receivedextensive attention in the literature, especially for conventionaland stainless steels as well as titanium alloys [17]. More limitedis the amount of information available on relaxation of residualstresses in shot peened aluminium alloys: moderate relaxationhas been reported for 2024 and 6082 aluminium alloys[6,18,19], relaxation in lesser extent was found in bending fatigueof 7075 alloys, especially at higher load levels [20,21]. Notably,most changes in the residual stress profile occurred on the firstcycles, like a static effect [22]. Moreover, no discernable relaxa-tion was found in this alloy at load levels approaching the high-cycle fatigue endurance [23].

In the present work, these aspects are considered for studyingthe fatigue behaviour of the Al-7075-T651 alloy, subjected to threedifferent controlled shot peening treatments. Peening intensitywas varied to have different initial residual stress profiles and sur-face microstructural conditions. An extensive analysis of the resid-ual stress field was carried out by measuring with the X-raydiffraction (XRD) technique the residual stress profile before andat the end of the fatigue tests, so as to investigate the onset of a sta-bilized residual stress field. The dependence of the residual stressrelaxation on the material’s work hardening as well as on the ap-plied cyclic load was studied. Fatigue crack initiation sites havebeen investigated through scanning electron microscopy (SEM)fractography and the role of surface roughness on fatigue resis-tance has been analyzed. The initial and the stabilized residualstress profiles were used to discuss the improvement in the fatigueresponse in the hypothesis of crack initiation and early crack prop-agation as fatigue controlling parameters. For this purpose, a mul-tiaxial fatigue criterion was adopted to account for the residualstress field.

2. Experimental procedure

2.1. Material and mechanical testing

The experimentation was performed on the Al 7075 alloy,widely used for aeronautical applications, supplied in the form of4 mm thick rolled plate. The material received the T651 thermo-mechanical treatment, consisting in a solution heat treatment for30 min at 748 K, a water quenching, a stress relief by stretchingto give a permanent elongation strain of 2.5% and a final aging at394 K for 6 h. The resulting microstructure, shown in Fig. 1, con-sists of a fine dispersion of Cr2Mg3Al18 and (Fe,Mn)Al6 intermetallicprecipitates, responsible for the high mechanical properties of thematerial. Equiaxial pancake grains were observed on the rollingplane (Fig. 1a). The grain size varies from 50 lm to 100 lm. Theaverage grain size is approximately 70 lm. On the cross sectionthrough the plate thickness (Fig. 1b), highly elongated grains wereobserved as a consequence of the intense cold rolling. The averagethickness of grains is approximately 10 lm.

Monotonic tensile tests (initial strain rate of 1 � 10�3s�1) wereperformed in the longitudinal (L) orientation using plane hourglassspecimens (Fig. 2a). The results, summarized in Table 1, show ayield stress higher than 500 MPa, combined with a good materialductility (total elongation of 18%).

To evaluate the cyclic stress–strain behaviour, reverse strain ax-ial testing was performed in the L-orientation by single-step onplane hourglass specimens similar to those used to determinethe monotonic tensile properties. Specifically, the tests were per-formed at a strain rate of 1 � 10�4s�1 and at strain amplitudes rang-ing from 0.006 to 0.014. The tests were started in compression andcarried out up to saturation of the tension and compression peakstresses (after about 15–20 cycles). The results thereof will be pre-sented in Section 3.4.

The fatigue characterization was performed on prismatic spec-imens whose geometry, according to the standard ISO 3928, isillustrated in Fig. 2b. The microstructure was tested with the stressaxis parallel to the L-direction. The fillet radius is large enough tomake any notch fatigue effects negligible.

Part of the fatigue specimens was subjected to different con-trolled shot peening treatments. Fused ceramic beads were em-ployed, which were found to induce a higher fatigue strengthimprovement as compared to steel shots without introducingundesired galvanic effects. The ceramic material composition andits mechanical properties are listed in Table 2. An air-blast ma-chine, whose parameters are reported in Table 3, was utilized toperform three types of shot peening treatments, illustrated in Table4. The basic idea was to apply a widely used commercial peeningtreatment, termed CE-Z425, employing beads of medium size

Nomenclature

Dp mean spacing of adjacent roughness peaksf�1 alternate fatigue strengthf0 pulsating fatigue strengthHV0.1 Vickers microhardness (1 N load)k slope of the Wöhler curveKt stress concentration factorN number of cyclespm hydrostatic pressureR stress ratioRa average roughnessRq root mean square roughnessRt mean value of the peak-valley distance determined on a

specific measurement length

Tr scatter of fatigue resultsa, b parameters of the equation representing the Sines crite-

rionrP50 fatigue endurance with a failure probability of 50%r0P50, k parameters of the S–N curver1,2,3 principal stress componentsr5�106 fatigue endurance corresponding to 5 � 106 cyclesrY cyclic yield stressra stress amplituderm mean stressrRS residual stressreq equivalent stress

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(diameter �500 lm), which introduces some surface roughnessand a deep cold worked layer (depth�300 lm), to explore an inno-vative peening treatment, called CE-B120, with small ceramicbeads leading to a gentle and superficial effect, which was foundto promote a remarkable improvement of the fatigue response

and finally to investigate a double peening consisting in the CE-Z425 followed by the CE-B120 treatment with the aim of combin-ing the advantages of both treatments. All the treatments were ap-plied with 100% coverage, estimated according to the standard SAEJ2277, since it is widely requested by the aerospace industry. TheAlmen intensities were measured for each shot peening surfacetreatment according to the standard SAE J442. The CE-B120 Almenintensity was 4.5 scale N, the CE-Z425 Almen intensity wasremarkably higher, amounting to 4.5 scale A, and the combinedshot peening treatment showed the same intensity as the more se-vere CE-Z425 treatment.

Reverse (zero mean stress, R = �1) plane bending displacement-controlled fatigue tests were carried out, both for the unpeenedmaterial and for the three peened conditions, at different stresslevels corresponding to fatigue lives in the range between nearly5 � 104 and 5 � 106 cycles. Tests were conducted in room tempera-ture air at a nominal frequency of 30 Hz. The fatigue curves corre-sponding to 50% of failure probability, represented by the S–Ncurve

rP50 ¼ r0P50 � N�1k ð1Þ

were determined, following the standard procedure [24], by fittingthe log(N) vs. log(r) results. The uncertainty range was assumed tobe constant and approximated by its centroid value. As a represen-tative value of the scatter, the following expression was used:

Tr ¼ 1 : rP90=rP10 ð2Þ

P90, P10 denote the 90% and 10% levels of failure probability,respectively. The fatigue endurance corresponding to a fatigue lifeof 5 � 106 cycles was obtained by a staircase procedure, employing12–15 samples.

2.2. Characterization of the surface layers of shot peened samples

The modifications of the surface layers of the shot peened sam-ples were investigated through microhardness, surface roughnessand residual stress profile measurements. To this regard, microh-ardness profiles were measured to characterize the material’s workhardening. A diamond Vickers indenter was used applying a max-imum force of 1 N. The load was applied gradually at a constant0.1 N/s rate with a dwell time of 10 s. Three measurements were

Fig. 1. Optical micrographs of the microstructure of Al-7075-T651. (a) Microstructure on the rolling plane. (b) Microstructure on the plate thickness. L: longitudinal, T: longtransverse, ST: short transverse direction.

Fig. 2. Geometry of specimens used in this study. (a) Hourglass tensile testspecimen for determining the monotonic and cyclic stress–strain curve. (b) Planebending fatigue specimen. All dimensions are given in mm.

Table 1Monotonic tensile properties of the Al-7075-T651 alloy.

E (GPa) rY0.2 (MPa) UTS (MPa) rF (MPa) T.E. (%) R.A. (%)

73 (±1) 515 (±5) 565 (±5) 760 (±10) 18 (±2) 24 (±2)

E: elastic modulus; rY0.2: 0.2% yield stress; UTS: ultimate tensile strength; rF: truefracture stress; T.E.: total elongation; R.A.: reduction in area.

Table 2Material properties of the bead’s material used for shot peening.

Composition Hardness (HV1) Bulk density (g/cm3) Elastic modulus (GPa)

ZrO2 67% 700 2.3 300SiO2 31%

Table 3Characteristics of the air-blast machine for shot peening.

Nozzle Angle ofimpingement

Working distance(mm)

Flow rate(kg/min)

Tetra 12 mm diameter 90� 100 5

Table 4Parameters of the three shot peening treatments considered in this study.

Treatment Bead size(mm)

Air pressure(bar)

Bead speed(m/s)

Coverage(%)

Almenintensity

CE-B120 63–125 1.0 57 100 4.5NCE-Z425 425–600 1.3 26 4.5ACE-Comb CE-Z425 followed by CE-B120

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performed at each depth and averaged in order to account formaterial’s heterogeneity and measurement errors.

The surface roughness was determined by the centreline aver-age and peak height distributions resulting from a profilometerscan of the specimen surface. The profilometer provides the posi-tion of all irregularities having a crest spacing of less than a presetcut-off value.

The analysis of the residual stress field induced by the peeningtreatments was carried out by measuring the stress profile by XRDtechnique. The measures are based on the sin2w method [25]. Thecrystallographic direction h422i was chosen with CuKa reflectionin order to obtain high angle measurements with higher stress sen-

sitivity. The elastic properties of the alloy were used in the calcu-lation by means of Neerfeld-Hill method [25–27]. A specificprocedure of chemical etching for the progressive thinning of thespecimen was employed [6]. The correction accounting for the ef-fect of the removed layer on the residual stress field was performedfollowing the indications reported in [25] and using an appropriatealgorithm proposed in [28]. Several measurements were also car-ried out for comparison by using the hole-drilling techniqueobtaining quite similar results.

Both initial and stabilized residual stress fields were measured.For this purpose, measurements were performed on tested speci-mens after failure in a region far enough from the fracture surface

Fig. 3. Optical micrographs of the microstructure of the surface layers of the fatigue samples. (a) As-received condition, (b) CE-B120, (c) CE-Z425 and (d) CE-Comb peeningtreatment. L: longitudinal, ST: short transverse direction.

Fig. 4. SEM micrograph illustrating the morphology of the peened surfaces. (a) CE-B120, (b) CE-Z425 and (c) CE-Comb peening treatment.

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(about 2 mm) so that the material rupture was supposed not tohave altered the residual stress field. Residual stress profiles mea-sured on run-out specimens were found to be very similar to thosedetermined on failed samples, thus confirming this assumption.

3. Results and discussion

3.1. Material characterization: surface layers of shot peened samples

The effect of the different shot peening treatments on themicrostructure of the surface layers is illustrated in Fig. 3. It canbe noted that neither the gentle treatment CE-B120 (Fig. 3b) nor

the more intense peening treatments, i.e. CE-Z425 (Fig. 3c) andCE-Comb (Fig. 3d), appreciably modified the microstructure ofthe surface layers as compared with the as-received condition(Fig. 3a). Accordingly, the grain size is of the same order of magni-tude in all the material variants investigated.

The surface morphology of the peened samples was investi-gated by SEM analysis as well. Notably, the large shots used inthe more intense peening treatments, i.e. CE-Z425 (Fig. 4b) andCE-Comb (Fig. 4c), created large and deep impact craters responsi-ble for the wavy surface profiles illustrated in Fig. 3c (CE-Z425) andd (CE-Comb). Dimples of smaller size are visible on the surface andthe surface profile of the CE-B120 (Figs. 3b and 4a) and CE-Combconditions (Figs. 3d and 4c).

The effect on the surface roughness exerted by the shot peeningtreatments is quantified in Table 5, where the results of profilom-eter measurements are summarized. Accordingly, the estimatedpeak-to-peak distance Dp was in good agreement with the opticaland SEM micrographs depicted in Fig. 3 and 4, respectively. Themean value, within an assessment length of 2 mm, of the maxi-mum peak to valley height (Rt) and the mean spacing of adjacentlocal peaks (Dp) were used to estimate the notch effect exertedby the surface dimples according to the following expression pro-posed by [29]:

Kt ¼ 1þ 4Rt

Dp

� �1:3

ð3Þ

The values of the estimated Kt for the conditions considered arelisted in Table 5. It can be noted that the shot peening treatmentsintroduce a limited-to-moderate stress concentration effect, rang-ing from 1.08 (CE-B120) to 1.17 (CE-Z425 and CE-Comb).

A comparison among the microhardness profiles measured forthe peening treatments considered is illustrated in Fig. 5. Notice-able differences, which are directly correlated to the surface workhardening experienced by the material as well as to the depth of

Table 5Surface roughness properties.

Condition Ra (mm) Rq (mm) Rt (mm) Dp (mm) Kt (Eq. (3)

As-received 0.25 0.30 0.9 – –CE-B120 1.35 1.67 6.1 120 1.08CE-Z425 3.39 4.36 15.2 175 1.17CE-Comb 3.41 4.37 16.4 190 1.17

Fig. 5. Microhardness profiles of the as-received and peened variants, obtained byaveraging the results of three tests.

Fig. 6. Initial residual stress profiles of the as-received and peened variantsmeasured by XRD technique.

Fig. 7. Reverse bending fatigue curves of the as-received and peened conditions.Run-out tests are marked by arrows.

Table 6Principal results of fatigue tests

Condition Endurance limit Low cycle fatigue

r5�106 (MPa) St Dev (MPa) k r0P50 (MPa) Tr

As-received 145 8 4.68 2605 1:1.20CE-B120 213 4 7.38 1400 1:1.11CE-Z425 164 12 6.12 1885 1:1.15CE-Comb 189 12 9.05 980 1:1.14

k: Slope of the Wöhler curve according to Eq. (1).

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the surface layer interested by the plastic deformation, can be ob-served: the CE-B120 treatment is very superficial, the maximumhardness is reached on the surface, the surface layer interestedby a change in the microhardness with respect to the base materialis about 0.15 mm. On the contrary, the CE-Z425 treatment inducesa sub-superficial microhardness peak, where the Hertzian pressureis nearly maximal [30]; the effect of shot peening vanishes atapproximately 0.3 mm below the surface. In the combined treat-ment, the second peening increased the microhardness within adepth of about 0.15 mm, that is exactly the depth of the light treat-

ment, while the sub-superficial peak and the treatment depthresemble those of the CE-Z425 treatment.

3.2. Residual stress analysis

XRD measurements were carried out on the fatigue samples inorder to characterize the residual stress field prior to fatigue test-ing. The obtained stress profiles are illustrated in Fig. 6. Notably,the residual stresses introduced by thermo-mechanical treatmentas well as by the machining in the as-received condition are one or-der of magnitude smaller than those measured in the peened sam-ples and will be therefore neglected.

The specimens subjected to the more intense peening treat-ments (CE-Z425 and CE-Comb) were characterized by deeper com-pressive residual stress profiles and by higher sub-superficialcompressive peaks with respect to the CE-B120 treatment. In thislatter case, the surface layer affected by compressive residual stres-ses is very thin and the peak is located on the surface. The CE-Z425and the CE-Comb treatments differ slightly in terms of the surfaceresidual stress and sub-superficial peak values, whereas the depthof the compressive peak is nearly the same (0.075–0.080 mm). Thedifference between the two treatments tends to fade out nearly200 lm beneath the surface. For all the peening conditions, thepeak stress levels reached a considerable value ranging from 0.56to 0.72 of the material monotonic yield stress.

Table 7Effect of residual stresses, microhardness and surface roughness on fatigueendurance.

Condition Surfaceresidualstress(MPa)

Compressivepeak residualstress (MPa)

Leff

(mm)Surfacemicrohardness(HV0.1)

Kf r5�106

(MPa)Gain(%)

CE-B120 �285 �285 0.08 191 1.08 213 47CE-Z425 �286 �344 0.28 182 1.17 164 13CE-Comb �335 �366 0.28 196 1.17 189 30

Leff: depth of the surface layer interested by compressive residual stresses; Kf: notchstress concentration factor due to surface dimples calculated according to Eq. (3);Gain: increment of the fatigue endurance of the shot peened samples as comparedwith the as-received condition.

Fig. 8. Comparison between initial and stabilized residual stress profiles measured on the fatigue samples subjected to (a) CE-B120, (b) CE-Z425, and (c) CE-Comb shotpeening. Stabilized residual stress profiles were measured after specimen failure about 2 mm far from the fracture surface.

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3.3. Fatigue curves

The results of the reverse bending fatigue tests as well as the P50

fatigue lines are compared in Fig. 7 for the different material vari-ants considered. The parameters representing the fatigue curvescorresponding to 50% of failure probability, according to Eq. (1),the results scatter, according to Eq. (2), and the fatigue enduranceat 5 � 106 cycles are listed in Table 6. All the peening treatmentsconsidered were effective in prolonging the fatigue life of thematerial. This improvement depends on the applied load, beingmore remarkable for load levels corresponding to longer fatiguelives, leading however to lower values of the slope in the P50 fati-gue line. It can also be observed that the more intense peeningtreatments (CE-Z425 and CE-Comb) did not result in a furtherimprovement of the fatigue behaviour as compared to the CE-B120 treatment, but, on the contrary, gave a less positive effecton the endurance limit at 5 � 106 cycles.

Table 7 summarizes the main material’s modifications inducedby the peening treatments, quantified in terms of residual stresses,microhardness as well as surface roughness, and the correspondingfatigue endurance values. It can be observed that the CE-B120treatment leads to the highest fatigue endurance increment (al-most 50%) with respect to the base material, despite the lowerresidual stresses and microhardness values as compared with themore intense peening treatments. Not even the slightly higherstress concentration effect exerted by the larger surface dimplesof the CE-Z425 and CE-Comb conditions (calculated according toEq. (3) and listed in Table 7) can explain their lower fatigue endur-ance. In order to shed light on this apparently anomalous result, anexperimental campaign was carried out with the aim of investigat-ing the evolution of the residual stress field during the fatigue life.

3.4. Residual stress evolution and fatigue endurance

Fig. 8a, b, and c illustrates the evolution of the residual stressfield at different loading levels for the CE-B120, CE-Z425 and CE-Comb treatment, respectively. It can be noted that some relaxationof the residual stress field occurred at load levels higher than thefatigue endurance, the more pronounced the higher the load levels,whereas the residual stress profiles measured in the specimenstested in correspondence of the fatigue endurance did not showappreciable evolution with respect to the initial residual stressfield: the residual stress modification is of the same order of mag-nitude of the uncertainty band of the XRD measure. This evidencesuggests the hypothesis that the relaxation is more like a ‘‘quasi-static” effect, due to the achievement of the material’s plastic flowregime [14,22], rather than cyclic relaxation, which should be evi-dent in the high-cycle fatigue regime as well. Accordingly, the factthat the specimens were tested under reverse bending configura-tion implies the possibility of material’s plasticization when thecompressive bending stresses are superimposed to the compres-sive surface residual stress field. Moreover, it is well known thatthe Al-7075-T651 alloy, as a consequence of the stretching treat-ment prior to aging, displays an asymmetric cyclic behaviour, i.e.a cyclic yield stress in compression lower than that in tension,especially when the initial loading direction is in compression[31]. Accordingly, the stabilized strain–stress cycles measured atstrain amplitudes ranging between 0.006 and 0.014 are shown inFig. 9. The asymmetric cyclic behaviour of the material is evidentfor all the strain amplitudes tested.

In order to identify the maximum bending stress level, whichthe peened material can sustain without reaching the compressionyield stress with consequent quasi-static residual stress relaxation,the knowledge of the local compression cyclic yield stress of thematerial is necessary. To this purpose, the microhardness mea-sured at different depths in the peened samples were correlatedto the microhardness measured on the plane hourglass specimensutilized in the cyclic axial tests: the cyclic yield stress correspond-ing to 0.1% plastic deformation was determined for each strainamplitude tested (and therefore for several microhardness values),as schematically shown in Fig. 9: a kinematic hardening rule wasassumed in order to account for the Bauschinger effect displayedby the 7075-T651 aluminium alloy [31,32]. The obtained resultsare listed in Table 8: since the maximum plastic strain introducedin the specimen with the same hardness of the as-received condi-tion, which was tested at a strain amplitude of 0.006, was less than0.1%, the compression peak stress was taken as cyclic yield stress ofthe virgin material. Notably, the cyclic axial tests were performedup to 0.014 strain amplitude that corresponded to the highestmicrohardness value measured on the shot peened samples (about200 HV0.1).

The maximum uniaxial compressive stress that can be appliedwithout material plasticization may be expressed using the VonMises yield criterion. This gives, in the case of a plane residualstress field and uniaxial external load stress

1ffiffiffi2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðrlim

1 þ rRS1 Þ � rRS

2

� �2 þ rlim1 þ rRS

1

� �2 þ rRS2

� �2q

¼ rY ð4Þ

Under the assumptions of an equibiaxial residual stress field(rRS

1 ¼ rRS2 ¼ rRS), Eq. (4) yields the following expression of the lim-

it uniaxial stress:

rlim1 ¼

�rRS �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4r2

Y � 3ðrRSÞ2q

2; rY ¼ f ðHV0:1Þ ð5Þ

where the yield stress is a function of the microhardness value andtherefore varies along specimen’s depth.

Table 8Correlation between compression cyclic yield stress and microhardness.

Strain amplitude,ea

MicrohardnessHV0.1

Compression cyclicyield stress, rY,c (MPa)

0.006 179 (as-received) 435a

0.008 192 4550.010 197 4700.012 201 4750.014 204 480

a Compression peak stress.

Fig. 9. Hysteresis loops for the Al-7075-T651 tested at strain amplitudes rangingfrom 0.006 to 0.014. Tests were started in compression to highlight the cyclicasymmetric behaviour displayed by the alloy. A kinematic hardening rule wasassumed to estimate the cyclic yield strength.

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Fig. 10a, b, and c illustrates the comparison between the depthprofiles of the applied bending stress corresponding to the fatigueendurance and of the maximum applicable uniaxial compressivestress expressed by Eq. (5) for the CE-B120, CE-Z425 and CE-Combconditions, respectively. It can be noted that the fatigue enduranceof the two more intense peening treatments (Fig. 10b and c) corre-sponds to the condition of incipient material plasticization: in or-der to preserve the stability of the initial residual stress field,which was experimentally observed in the specimens tested atthe fatigue endurance stress, the applied bending stress may notovercome this limit condition. On the contrary, there is still somemargin before material plasticization for the specimens subjectedto the CE-B120 treatment (Fig. 10a). This evidence might also ex-plain the lower fatigue endurance manifested by the more intensepeening treatments, despite higher compressive residual stressesand microhardness values. Apparently, in these high-strength alu-minium alloys, the material plasticization and the consequentresidual stress relaxation exert a detrimental effect on the high-cy-cle fatigue resistance.

SEM analysis carried out on the fracture surfaces of the speci-mens tested at load levels close to the fatigue endurance revealedsub-superficial fatigue crack initiation for the CE-Z425 (Fig. 11c)and CE-Comb (Fig. 11d) conditions, in a region comprised be-tween 200 and 300 lm below the surface. On the contrary, the

crack nucleation was found to occur on the surface of the speci-mens in the as-received (Fig. 11a) or close to the surface(�20 lm below the surface) in the CE-B120 (Fig. 11b) conditions.At load levels corresponding to the fatigue endurance, the stressamplitude is low enough to keep the initial residual stress fieldunchanged, so that the crack cannot be initiated at or close tothe surface where the CE-Z425 and CE-Comb treatments intro-duced high compressive residual stresses. Similar observationswere also reported in [9,10]. The shallow residual stress profileof the CE-B120 process combined with the higher stress ampli-tude corresponding to the fatigue endurance allowed the crackto initiate close to the surface. It is worth noticing that, in thepresent work the peened condition characterized by superficialcrack onset led to the highest fatigue endurance as compared withpeening treatments characterized by sub-superficial crack initia-tion, in contrast with the observation of Wang et al. [10] thatthe best increment of the fatigue limit is obtained when cracksource is under the hardened layer.

Finally, superficial fatigue crack onset was detected in the sam-ples tested at stress levels leading to failure within 4 � 105 cycles,even in the samples subjected to the CE-Z425 (Fig. 12a) and CE-Comb (Fig. 12b) conditions. Evidently, in the low cycle fatigue re-gime, the stress amplitude is high enough to induce a large amountof residual stress relaxation at the surface layer. As a result, the

Fig. 10. Comparison between bending stress profile applied at the fatigue endurance and the limit stress for incipient compression yielding. The equibiaxial residual stressfield and the cyclic compression yield stress (derived from the correlation between microhardness and reverse strain axial tests) are incorporated in the limit stress accordingto Eq. (4).

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stress concentration effect exerted by the surface dimples movedthe crack initiation site from the interior to the specimens’ surface.

3.5. Simulation of the fatigue response

A numerical model was developed in order to account for boththe surface roughness and the residual stresses on the fatiguebehaviour. The effect of the surface roughness was taken into ac-count by incorporating into a fatigue criterion the stress concentra-tion factor determined in Section 3.1. Residual stresses weretreated as mean stresses superimposed to the oscillating stressesintroduced by the external cyclic load [33,34]. Because of the equi-biaxiality of the residual stress field, a multiaxial fatigue criterionwas employed. Therefore, the Sines criterion was adopted for mod-elling the stress conditions as discussed in [34]. Two main assump-tions were made: (i) the material’s work hardening introduced bythe shot peening exerts a negligible influence on the fatigue resis-tance; therefore, the intrinsic fatigue resistance of the peenedmaterial was assumed to be the same as that of the base materialand (ii) the fatigue crack initiation occurs on or close to the speci-men surface. This was confirmed by experimental investigations,

except for the specimens subjected to the two more intense treat-ments in the high-cycle fatigue regime. This fact will be discussedin the following.

The Sines criterion includes the octahedral shear stress ampli-tude, or equivalently the Von Mises equivalent stress amplitudereq,a, and the mean hydrostatic pressure pm in a linear equationof the form:

req;a þ a � pm ¼ b ð6Þ

The equivalent stress amplitude is expressed in terms of theprincipal stresses’ amplitude by

req;a ¼1ffiffiffi2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðr1;a � r2;aÞ2 þ ðr2;a � r3;aÞ2 þ ðr3;a � r1;aÞ2

qð7Þ

The mean hydrostatic pressure is given by

pm ¼ðr1;m þ r2;m þ r3;mÞ þ ðrRS

1 þ rRS2 þ rRS

3 Þ3

ð8Þ

The a and b material’s parameters refer to the unpeened condi-tions (according to the first assumption) and can be identified fromtwo independent fatigue tests. In this work, they were determined

Fig. 11. SEM micrographs of the fracture surfaces around the fatigue crack initiation sites for specimens tested at the fatigue endurance stress. (a) As-received (ra = 144 MPa,N = 4.24 � 106 cycles), (b) CE-B120 (ra = 221 MPa, N = 2.87 � 106 cycles), (c) CE-Z425 (ra = 155 MPa, N = 3.30 � 106 cycles), and (d) CE-Comb (ra = 188 MPa, N = 3.86 � 106 cycles)conditions. Crack initiation sites are marked by arrows.

Fig. 12. SEM micrographs of the fracture surfaces around the surface crack initiation sites for specimens tested in the low cycle regime. (a) CE-Z425 (ra = 230 MPa,N = 511000 cycles) and (b) CE-Comb (ra = 230 MPa, N = 420000 cycles) conditions. Crack initiation sites are marked by arrows.

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from the fully reversed bending tests performed on the as-receivedcondition (R = �1) and from pulsating fatigue tests (R = 0) pre-sented in [35]

a ¼ 3f�1

f0� 1

� �; b ¼ f�1 ð9Þ

where f�1 and f0 are fully reversed and pulsating fatigue strength fora given number of cycles to failure, respectively.

The initial and the stabilized values of residual stresses on thesurface (according to the second assumption) were consideredfor evaluating the fatigue response in the hypothesis that the initi-ation life takes a preponderant part of the total fatigue life. It isworth noting that the XRD surface measurements of the residualstresses represent the mean value over a 20 lm thick surface layer.It is therefore reasonable the assumption that the fatigue crack issubjected to these values of residual stresses during the initiationand early propagation stages. The stress concentration factor Kt

due to the surface dimples was used to reduce the fatigue strengthpredicted by Eq. (7).

The comparison between the experimental data and the calcu-lated mean fatigue curve is illustrated in Fig. 13a, b, and c for theCE-B120, CE-Z425 and CE-Comb conditions, respectively. It canbe noted that the low cycle fatigue regime (up to about 4 � 105 cy-cles) is well represented by the Sines criterion, particularly whenthe stabilized residual stresses (SRS) are considered. Conversely,

a slight overestimation of the fatigue strength, especially at thehigher load levels, is obtained when the initial residual stresses(IRS) are incorporated into the fatigue criterion. Apparently, thebeneficial effect of the residual stresses on the fatigue response ispartly reduced by the residual stress relaxation.

The high-cycle fatigue response of the CE-B120 (Fig. 13a) condi-tion is quite well simulated by the proposed approach, which takesadequately into account the superficial initiation of fatigue cracksobserved in this material condition. Conversely, the proposed ap-proach cannot describe the high-cycle fatigue behaviour of thetwo intense peening treatments (Fig. 13b and c), whose 5 � 106 cy-cles fatigue endurance was found to correspond to the condition ofsub-superficial incipient plasticization. This phenomenon cannotbe captured by the multiaxial fatigue criterion. Noteworthy, thetwo material conditions subjected to the more intense peeningconditions did not display a change in the slope of the fatiguecurves observed around 1 � 106 cycles for both the as-receivedmaterial and the CE-B120 condition. Hence, the proposedapproach, which is based on the fatigue properties of the basematerial, is not capable to reproduce, for these two material condi-tions, the intermediate fatigue regime comprised between 4 � 105

and 5 � 106 cycles, which is characterized by the same slope ofthe low cycle fatigue curve. SEM investigations revealed sub-superficial fatigue crack nucleation in the region that underwentplastic flow and therefore residual stress relaxation; this indicates

Fig. 13. Comparison between experimental and calculated P50 fatigue curves of the peened conditions. (a) CE-B120, (b) CE-Z425, and (c) CE-Comb peening treatment. IRS:initial residual stresses, SRS: stabilized residual stresses. The fatigue regimes leading to sub-superficial crack initiation and to compression plasticization are indicated as well.

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that material damaging, due to plasticization of a highly work-hardened microstructure might exert a detrimental effect on thehigh-cycle fatigue strength: the intense plastic deformation ofthe surface layer caused by the shot peening causes the build upof a dislocation structure, leading to a diffused damage in thematerial when the lattice distortion is too much intense and thusto an easier micro-crack initiation [5,12].

These findings highlight the importance of a well designed shotpeening treatment, especially when high-strength aluminium al-loys are subjected to in-service alternate cyclic stresses: theachievement of compression yielding conditions, with consequentresidual stress relaxation, must be avoided in high-cycle fatigueapplications. In these sense, graphs similar to those depicted inFig. 10 yield a useful tool for the choice of an optimal shot peeningtreatment.

4. Conclusions

The role of residual stress relaxation on the reverse bending fa-tigue resistance of shot peened 7075-T651 aluminium alloy wasinvestigated. Experiments were conducted on specimens subjectedto three different shot peening treatments. Surface roughness wasmeasured to characterize the impact of the peening treatmentupon the fatigue response. XRD measurements were carried outto determine the initial and the stabilized residual stress field. Con-ditions for compression plasticization of the material during the fa-tigue life, leading to quasi-static residual stress relaxation, wereidentified. SEM investigations on the fracture surfaces were per-formed to identify fatigue crack initiation sites. An analytical mod-el was built up for predicting the fatigue resistance taking intoaccount the effect of both residual stresses and surface roughness.The following conclusions can be drawn:

(1) Controlled shot peening employing ceramic beads deter-mines a remarkable increment of the high-cycle fatigueresistance of high-strength aluminium alloys, rangingbetween 15% and 50%. Such improvement can be essentiallyattributed to the compressive residual stress field intro-duced by the treatment in the surface layers.

(2) No significant residual stress relaxation was observed atstress levels close to the 5 � 106 cycles fatigue endurance.Therefore, cyclic residual stress relaxation seems to be mar-ginal in the tested high-strength aluminium alloy.

(3) The 7075-T651 aluminium alloy, owing to the stretch treat-ment prior to aging, possesses an asymmetric cyclic behav-iour: the cyclic yield stress in compression is lower thanthat in tension, especially when the cyclic test is started incompression. Therefore the shot peened alloy is prone toplasticization if tested under reverse bending condition.The fatigue endurance of the two variants subjected to themore intense peening treatments corresponds to the condi-tion of incipient material plastic flow.

(4) Sub-superficial crack initiation was found in the two vari-ants subjected to the more intense peening treatmentstested in the intermediate and high-cycle fatigue regimes(>4 � 105 cycles). The preferential crack initiation sites arelocated close to the material layers that undergo plasticiza-tion in compression in the former case, and �200–300 lmbelow the surface, in the latter case.

(5) The fatigue resistance of the peened conditions can be satis-factorily predicted by a multiaxial fatigue criterion incorpo-rating the residual stress field and the stress concentrationeffect exerted by the surface dimples, provided that fatiguecrack initiation occurs on the specimen surface. In this case,a better estimation of the fatigue curve is obtained consider-

ing the stabilized residual stresses (SRS) instead of the initialresidual stresses. The long-life fatigue resistance implyingsub-superficial plastic flow might be interpreted by a dam-age model incorporating the microstructural modificationsinduced by shot peening as well as the occurrence of mate-rial plasticization.

Acknowledgement

Mr. Luca Benedetti is gratefully acknowledged for conductingthe scanning electron microscope observations.

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