1

Engineering Fracture Mechanics 76 (2009) 134–148

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Engineering Fracture Mechanics

journal homepage: www.elsevier .com/locate /engfracmech

Fatigue life predictions using fracture mechanics methods

T. Ghidini a,*,1, C. Dalle Donne b

a ESA, European Space Agency, Product Assurance and Safety Department, Materials and Processes Division, P.O. Box 299, NL-2200AG Noordwijk, The Netherlandsb EADS Deutschland GmbH, Innovation Works, Munich, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Available online 5 August 2008

This paper is dedicated to the memory ofArij de Koning who passed away the 6th ofFebruary 2007.

Keywords:Fracture mechanicsFatigue life predictionPre-corrosionFriction stir weldingVariable amplitude loadingCold expansionAFGROWNASGRO

0013-7944/$ - see front matter � 2008 Elsevier Ltddoi:10.1016/j.engfracmech.2008.07.008

* Corresponding author.E-mail address: [email protected] (T. Ghi

1 The work has been performed during the author

In the present work, a simple engineering approach which is based on a relatively solidbackground and which is checked against fatigue test data for various test conditionswas developed: it may provide a practical and reliable basis for the analysis of structuresunder in-service loading conditions, in the presence of previous corrosion attack, or in thepresence of a residual stress field, by using widespread fracture mechanics software. In par-ticular, the approach was checked against an experimental program which consists of thefollowing fatigue tests: base and friction stir welded (FSW) material under constant ampli-tude loading at different loading ratios (R = 0.1, 0.5, �1); pre-corroded base and FSW mate-rial under constant amplitude loading at load ratio R = 0.1; centre hole FSW specimensunder the standardised variable amplitude loading spectrum FALSTAFF. Moreover, fromthe literature fatigue experiments under FALSTAFF of cold expanded as well as not coldexpended holes were also used to validate the approach. The predictions were performedwith the last version of AFGROW and NASGRO 3.0 software.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

In general, structures contain micro structural defects such as porosity, voids, discontinuities which can lead to the for-mation of cracks if the service loading exceed a certain level. Once a crack is present, it may grow in a stable manner and aftera certain time results in an unstable crack growth and eventually in the ultimate failure of the structure. Fatigue is one of themost difficult, and insidious, design issues to resolve. Experience has shown that the majority of structural failures occur as aresult of fatigue: the percentage of such failures in mechanical components is set around the order of 90%. In the aerospaceindustry, the introduction of damage tolerance requirements has been a milestone in the design of fatigue resistant struc-tures and it was possible only thanks to the level of maturity that linear elastic fracture mechanics has reached. Many crackgrowth prediction models have been proposed and used by the industrial and scientific community [1,2]. The calculations ofthis work were performed with AFGROW [3], ESACRACK 4 [4], and NASGRO 3.0 [5]. More recent versions, NASGRO 5.2, exist,NASGRO 3.0 was the version available at the time the work has been performed. AFGROW is a computer program developedby the US Air Force and is available on line. ESACRACK 4 was written by ESA and NASA and NASGRO 3.0 was created by NASA.Since NASGRO 3.0 is also part of the ESACRACK 4 software package, in the following just AFGROW and NASGRO 3.0 will becompared. Both software need the same initial data to perform the crack growth analysis: the crack geometry, the loadingconditions, the da/dN � DK crack propagation curve of the material as well as static and fracture toughness properties(which can be found in a large database of the software or can be implemented by the user). The programs then useimplemented K-factors solutions and crack growth concepts to propagate the crack until failure occurs. During the last three

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dini).’s stay at the Institute of Materials Research of the DLR in Cologne, Germany.

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T. Ghidini, C. Dalle Donne / Engineering Fracture Mechanics 76 (2009) 134–148 135

decades considerable work has been devoted to understand the fatigue crack propagation under constant amplitude loading.However, the basic problem is to predict fatigue crack growth in real structures of complex geometry under in-service load-ing conditions. Fatigue loads in-service generally imply a randomly variable amplitude, rather than constant amplitude load-ing. Different types of load sequences are known to induce a number of different load interaction effects [6,7], which canresult in significant variation on the crack growth rate. Moreover, it is well known that corrosion unfavourably affects thestructural integrity since fatigue cracks nucleate from corrosion pits [8,9], drastically reducing the fatigue life of the compo-nent. The computation effort is more complex for structures which are affected from the presence of a residual stress field.Residual stresses are, in many cases, an undesired consequence of the manufacturing and joining technologies adopted(welding, cold forming) or, in other cases, are intentionally produced by means of proper techniques (e.g. shot peening, coldworking) with the aim of improving strength. All these effects should be included in the predictions as they can affect struc-tural health of structures. For practical applications, industrial designers require reliable prediction models, easy to handle,without too many empirical constants (derived from specific tests) and, lastly, capable of running in a reasonably short timeon personal computers. In previous works the authors have successfully demonstrated the capability of the previously men-tioned software to predict the crack growth life of pristine and welded specimens, both under constant and amplitude load-ing spectra [10–12].

The aim of the present work is to demonstrate the possibility of applying fracture mechanics methods to perform fatiguelife predictions. The calculations were compared with experimental results. The following experimental test program wascarried out:

� Constant amplitude loading fatigue tests of base and FSW material of un-notched specimens at different loading ratios(R = 0.1,0.5,�1).

� Constant amplitude loading tests of pre-corroded base and FSW material at load ratio R = 0.1.� Variable amplitude loading fatigue tests of centre holed FSW specimens under FALSTAFF.� Variable amplitude loading fatigue tests of centre holed cold expanded specimens under FALSTAFF.

In predicting the fatigue life of base and friction stir welded structures a basic assumption was done: the crack is startingfrom constituent particles and particle clusters; moreover, in order to apply to fatigue the fracture mechanics statements, itwas also assumed that the cracks formed immediately at the particles and the entire fatigue life was comprised of crackpropagation.

The pre-corroded base as well as friction stir welded materials were simulated by identifying and quantifying the wide-spread corrosion damage by many metallographic sections. A model was then developed which creates a single surface crackhaving the deepest and largest corrosion attack as dimension. In the model no distinction was done between the two ob-served corrosion types, i. e. pitting and inter-granular corrosion. In predicting the fatigue life of the centre holed FSW spec-imens under FALSTAFF the same assumptions regarding the starting cracks as the un-notched specimens were adopted, andthe load sequence effects were taken into account by using the Willenborg retardation model [13]. Because of the small sizeof the specimens, the very low transverse residual stresses were not considered.

In the calculations for the cold expanded holes, since the residual stresses were too high to be neglected, the Willenborgmodel was used in combination with a residual stress profile in specimen thickness as well as width direction obtained byfitting the X-ray diffraction measurements.

2. Experimental program

2.1. Friction stir welding and specimen geometry

Four millimeter thick AA 2024-T3 material was provided from Pechiney, in the form of sheets. Table 1 gives a survey ofthe chemical and mechanical properties of the alloy investigated in the experimental procedure. The FSW butt joints wereproduced at the DLR, the German Aerospace Centre following the TWI patent [14]. All the welds were performed parallel tothe rolling direction of the sheets. The material was welded in T3 condition and no additional heat treatment was carried outafter the welding procedure. The welding speed was 300 mm per minute, the rotating speed of the tool was 850 revolutionsper minute and the tilt angle was kept constant at 0�. The welding parameters used to produce the joints are summarised in

Table 1Chemical composition and mechanical properties of the alloys investigated

Alloy Si Fe Cu Mn Mg Cr Zn Ti Zr

Chemical composition of the alloys in wt%AA 2024-T3 0.50 0.50 3.8–4.9 0.3–0.9 1.2–1.8 0.1 0.25 0.15 –

Material Rp0 (MPa) Rm (MPa) E Elongation (%)

Mechanical propertiesAA2024-T3 329 476 72000 25.7

Table 2Welding parameters and static properties of AA2024-T3 T(L)

Alloy Rotational speed (rpm) Weld speed (mm/min) Rp0.2 (MPa) Rm (MPa) RmRm, Base (%)

AA 2024-T3 850 300 316 460 96.6

-25 -20 -15 -10 -5 0 5 10 15 20 2580

100

120

140

160

HV

1

Position [mm]

AA 2024-T3 FSW

Base Material

1 2 2 3 3 4 4

1= DXZ 2= TMAZ 3= HAZ 4= Base Material

Fig. 1. Hardness profile of the AA 2024-T3 friction stir welded material.

136 T. Ghidini, C. Dalle Donne / Engineering Fracture Mechanics 76 (2009) 134–148

Table 2, where a comparison between the ultimate strength of the FSW and the base material is also given. The hardnessprofile of the butt joints is presented in Fig. 1: all the measurements were taken in the midsection of the FSW joints.

The hardness of AA 2024-T3 base metal is also presented in the diagram of Fig. 1. The diagram shows the same generaltrend which has been observed in previous works, [15,16]: the hardness distribution results in an ‘‘M” like form with twominima almost 5 mm out of the centre of the weld. The typical different areas of a FSW weld, described in detail in [17],can be identified here. Parent plates, dash bands in the diagram, hardness values were at more than 10 mm from the centreof the weld. The 0 position in the diagram corresponds to the centre of the weld nugget. The hardness distribution in thejoints was consistent with the tensile strength. The centre hole friction stir welding fatigue specimens used for the variableamplitude loading testing, Fig. 2, were machined taking the hardness profile into account. The hole was machined in theweakest area of the sample, as shown in [15,16]: The centre of the weld was placed in the middle of the coupon, and thehole was produced 5 mm out of the weld centre in the TMAZ of the retreating side, in correspondence of the hardness min-imum. Particular care was devoted to the realisation of the hole, to avoid the presence of residual stress due to the machiningprocess. Un-notched base material and friction stir welding fatigue specimens were machined for the constant amplitudeloading part of the testing activity, Fig. 3. All the coupons used for the experimental program, both open-hole and un-notched, were machined in T–L orientation. The loading axis was perpendicular to the rolling direction and to the weldingdirection. The weld nugget was in the middle of the specimen.

110

5

12.5

12.5

∅ 5

110

FSW Weld

Fig. 2. Dimensions of the centre hole FSW fatigue specimens used for testing under FALSTAFF.

80

220

20

R50

12.5

5119

FSW Weld

Fig. 3. Dimensions of the un-notched FSW fatigue specimens.


2.2. Corrosion treatments

Prior to fatigue testing, the 2024-T3 un-notched test samples were corroded with an alternate immersion technique inaccordance with ASTM G44-99 standard [18]. All specimens were prepared by manual polishing and by covering the edgeswith a protective mask (TURCO 5580G), leaving just the centre of the specimen exposed to the corrosion attack, Fig. 4. Thiswas done to avoid any ‘‘edge effect” and to analyse only the propagation of cracks starting from the corroded surfaces. Thespecimens were cyclic immerse during 10 min in a 3.5% NaCl aqueous solution and they remained 50 min in air (1 h per cy-cle). 100, 250 and 1000 h were the corrosion times chosen in this research. Air temperature and relative humidity were keptconstant (27 �C and 45%). After the corrosion procedure the protective TURCO masking was removed. The specimens werefatigue tested without any further treatments. On the other hand, the specimens used for metallographic characterisation ofthe corrosion attack were cleaned in 50% HNO3 aqueous solution for 15 min, in order to eliminate the residual corrosionproducts. The characterisation of the corrosion attack on the 2024-T3 base metal and the friction stir welded joints was car-ried out using light microscopy techniques.

In the case of the base metals, depth and width of the corrosion attack of about 200 corroded areas (pitting and inter-granular corrosion) were measured for the different exposure times. For the pre-corroded FSW-joints consecutive metallo-graphic preparation was necessary to depict the corrosion attack on the different zones of the weld joint (i.e. weld nugget,HAZ, etc). The FSW specimens were polished and metallographic sections were prepared parallel to weld nugget each0.5 mm beginning at the centre of the weld nugget and finishing when the unaffected base metal was reached (about12 mm from the joint centre line).

2.3. Constant amplitude loading

The entire SN fatigue testing was conducted using an Amsler resonance machine of 100 kN capability equipped with aTestExpert control software. All the fatigue experiments were performed under constant amplitude loading and 60 Hz atroom temperature (21 + �2 �C). The 2024-T3 base material specimens were tested in lab environment at load ratio Fmin/Fmax

of R = 0.1, R = 0.5 and R = �1 in order to obtain reference curves to check the fracture mechanics software. The diagram re-ported in Fig. 5 shows the results of the fatigue life tests of 2024-T3 base material and the effect of the load ratio R: decreas-ing the value of R will result in a shorter fatigue life, especially when the results are plotted in function of the maximumapplied stress. The same type of un-notched specimens of 2024-T3 base material and FSW joints were pre-corroded by alter-nate immersion in 3.5% NaCl solution and they were subsequently tested under constant amplitude loading and lab environ-ment at load ratio Fmin/Fmax of R = 0.1 (loading direction perpendicular to the weld).

a

b

A

A

Loading Direction

Fig. 4. (a) Schematic of a corroded FSW specimen, and (b) appearance of the pits on the exposed surface.

104 105 106 10750

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Laboratory air

R=0.1 R=0.5 R=-1

AA 2024-T3 T(L)t=4mm

Max

imum

Str

ess

[MPa

]

Cycles

Fig. 5. Comparison between fatigue life of base material 2024-T3 specimens under constant amplitude loading at load ratio Fmin/Fmax of R = 0.1, R = 0.5 andR = �1.

104 105 106 10750

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60 HzLaboratory air

Base Material Not-Corroded FSW Material Not-Corroded

Base Material 100h Corroded Base Material 250h Corroded Base Material 1000h Corroded

FSW Material 100h Corroded FSW Material 250h Corroded FSW Material 1000h Corroded

Max

imum

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ess

[MPa

]

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Fig. 6. Comparison between not corroded and 100, 250 and 1000 h corroded polished base and FSW material.


The diagram in Fig. 6 shows the effect of corrosion time on the fatigue life of 2024-T3 friction stir welded joints and basematerial. Also a comparison between base and FSW not corroded material is given. In general, no significant difference infatigue life between the 2024-T3 base metal and FSW-joints can be observed. Most of the un-corroded FSW-specimens failedeither in the unaffected base metal (62%) or at the advancing side of the weld nugget (12.5%). Generally, the origin of thefailure was found to be a cluster of the second phases present in the microstructure of the 2024-T3 aluminium alloy. Thebase material has a shorter fatigue life as the FSW material at least on the threshold region: At first glance, this could becontradictory to the normal fatigue behaviour of FSW structures [19–21]: a preliminary explanation of the experimentalobservation could be that the surfaces of the sheets have been milled before to produce the weld. This could results in asmoother surface, with smaller clusters, and therefore in a better polishing procedure which leads to better fatigue proper-ties. This effect disappears when considering the corroded specimens where practically no difference exists between thepristine and the FSW specimens. In fact the fracture mechanism is now governed by the corrosion pits, whose dimensionsare bigger than the clusters and the constituent particles. Moreover, referring to Fig. 6, corrosion has obviously a detrimentaleffect producing a dramatic drop of the fatigue life of both types of specimens (base metal and friction stir welded joints).The FSW joints show a similar drop in fatigue strength as the base material, which seems to be virtually independent of thecorrosion time, also due to the logarithmic scale of the plot. Although the test results of 100, 250 and 1000 h pre-corrosionspecimens fall in the same scatter band, the trend is in general consistent (increase exposure leads to reduced fatigue life).

102 103 104 105200

250

300

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450

30 Hz

Laboratory air

FALSTAFF

AA 2024-T3 FSWt=4 mm

Max

imum

Str

ess

[MPa

]

Flights

FSW Weld

Fig. 7. Experimental results of the centre hole FSW specimen under FALSTAFF spectrum loading.


2.4. Variable amplitude loading

The centre hole FSW specimens were tested under a standardised flight simulation load history, FALSTAFF [22]. FALSTAFFis a standard load sequence considered representative for the load time history in the lower wing skin near the wing root of afighter aircraft.

The different specimens were tested at different values of rmax. Fatigue testing under flight simulation loading were car-ried out on a servo-hydraulic machine of 400 kN capability controlled by Fast Track software. The specimens were enclosedin anti-buckling guides to allow compressive loads during the tests. The tests were carried out in a laboratory air environ-ment at room temperature and at a frequency of 30 Hz. In Fig. 7, the experimental results are plotted in a diagram showingthe different levels of rmax plotted against the number of flights at failure. In order to reduce testing time, the tests werecarried out at high stress levels.

3. Experimental program from the literature

3.1. Cold expanded holes

A very well documented experimental program was taken from the open literature [23] in order to check the developedmethod under variable amplitude loading and in the presence of a pre-existent residual stress field. Low-load transfer jointspecimens and open-hole specimens of similar geometry were machined of aluminium alloy 2024-T351. The description ofthe entire test program is given in [23], for brevity purpose only the open-hole testing activity will be presented here. Thegeneral dimension of the specimens were 6.35 mm hole diameter, 6.0 mm thickness and 25 mm width. The test programincludes non-cold expanded (NCx or plane hole) tests and cold expansion on production (Cx, or 0% Cx). The FTI split sleevecold expansion method was used. The expansion process consists of pulling an oversized tapered mandrel through the hole,causing extremely high radial pressures on the hole, thus expanding the hole well behind the yield strength of the material.This procedure produces a zone of residual compressive stress that extends approximately one radius from the edge of thehole. The specimens were expanded to a nominal rate of 4.0–4.4%, resulting in a retained expansion of 2.8–2.9%. All the spec-imens, NCx and Cx, were than fatigue cycled under FALSTAFF spectrum. All tests were conducted with a peak net stress of300 MPa. Crack lengths were measured through the use of acetate replicas, which were examined with an optical micro-scope. The crack lengths were tracked on both sides of the specimen as well as within the bores of the holes.

4. Fatigue life predictions

4.1. Base and FSW material

In modelling the fatigue life of the base material specimens a basic assumption was done: the crack is starting from con-stituent particles and particle clusters. It was assumed that the cracks formed immediately at the particles and the entirefatigue life was comprised of crack propagation. Previous work has demonstrated that cracks form primarily at single par-ticles or holes, indicating that coalescence is not an issue, at least in the LS direction of propagation [24,25]. In the literature


fatigue cracks were observed to start at slip lines around large inclusion clusters containing iron and silicon in 2024-T3 [26]and the cyclic straining was observed to weak and to deteriorate the particle matrix interface, increasing the susceptibility todebonding [27]. In [28,29] it has been pointed out that cracks formed at inclusions and inclusion clusters in thin sheet 2024-T3 aluminium and the nucleation site was observed to quickly form a semi-elliptical surface crack approximately the size ofthe inclusion. The idea of using fracture mechanics for predicting the fatigue life of components by starting from the micro-structural features of the materials was first proposed in [30]. Fig. 8 shows the semi-elliptic crack modelled over a constit-uent particle observed in a post-mortem failure surface analysis carried out with the scanning electron microscope. Thefigure is just a schematic, therefore the presented inclusion does not exactly match the crack front since the reported crackfront is a mean value measured of the constituent particles. The microstructure of the base metal used in this study consistsin flattened grains, the so called ‘‘pancake shape”, which mayor axe was parallel to the rolling direction. The constituent par-ticles were aligned at the grain boundaries forming clusters. The maximal sizes of the second phases were to be 38–42 lm.SEM–EDX analysis has mainly shown the presence of two kinds of constituent particles containing AlCu and AlCuMg. Themeasured dimension have been used in AFGROW and NASGRO 3.0 as initial crack dimensions for the implemented modelsemi-elliptical surface crack, which is shown in Fig. 9. The model implemented in both codes utilises a stress intensity factorsolution developed by Newman and Raju. The dimensions of the modelled semi-elliptical crack were approximatelya = 40 lm and c = 80 lm, referring to the biggest constituent particles also reported in [24,25]: the fatigue strength was as-sumed to be governed by one critical inclusion and not by the presence of many critical clusters. The assumption was also inagreement with [31]. The dimensions W and t in the model of Fig. 9 are the specimen width and thickness respectively. Inmodelling the fatigue tests the base material data stored in the NASGRO database was used.

The material constants used are those of the AA 2024-T3 orientation T(L). In case the calculated DK was below the prop-agation threshold, the NASGRO equation (used in AFGROW as well) is taking the small-crack effect into account by allowingto linearly extrapolating the crack growth values below threshold [4]. This approach was adopted in this work.

The constants are listed in Table 3. The fit obtained by the constants includes ‘‘small-crack effect” [32,33] correction in thenear threshold region of the da/dN � DK curve. The same dimensions of the inclusion particles were used in predicting the

a 2c

Fig. 8. Schematic of the semi-elliptical surface crack modelled over a constituent particle observed in a post-mortem failure surface analysis carried outwith the scanning electron microscope.

W t

2c a

Fig. 9. Semi-elliptical surface crack model implemented in AFGROW and in NASGRO 3.0.

Table 3Material parameters given in the material database of NASGRO for the material AA2024-T3 T(L)

UTS (MPa) YS (MPa) KIC (N/mm3/2) DK0 (N/mm3/2) C n p q a

448.16 330.95 1007.7 100.77 6.08 � 10�11 2.6 0.5 1.0 1.5

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Experimental Data NASGRO 3.0 AFGROW

AA 2024-T3t=4mmR=0.1

Max

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[MPa

]

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AA 2024-T3t=4mmR=0.5

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AA 2024-T3 FSWt=4mmR=0.1

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Fig. 10. Comparison between base and FSW material experimental results and computer simulations.


life of the FSW joints. Moreover, the observation of the fatigue failed polished FSW specimens demonstrated that all the cou-pons broke in the base material away from the weld nugget.

Neglecting the generally very low transverse residual stresses [34] allows the prediction to use the base material datastored in the NASGRO database also for the friction stir welded material. Therefore, the two predictions referring to baseand FSW material are identical. Fig. 10 represents the comparison between base and FSW material experimental data andcomputer simulations. Both NASGRO 3.0 and AFGROW results are in good agreement with the experimental observation.The small differences between NASGRO 3.0 and AFGROW results are probably due to different integration routines.

Both computer programs showed to predict well also the R ratio effect which is implemented in the NASGRO equationeven for compressive loads. Concerning the FSW coupons, the difference between the simulated fatigue lives and the exper-imental ones is higher than in the case of base material ones. Apparently the FSW specimens seem to have a higher fatiguelife then the base material (since the simulation was performed with the same basic assumptions, the NASGRO and AFGROWlives are the same in both comparisons).

4.2. Pre-corroded material

In all cases (2024-T3 FSW and base metal corroded during 100, 250 and 1000 h), the corrosion type found on the metal-lographic coupons was a mixture of pitting and inter-granular corrosion (IGC), Fig. 11a. In some cases two or more pits wereconnected through IGC ramification forming a bigger corroded damaged zone. Seventy-seven percent of the pre-corrodedFSW-joint specimens failed at the fine grained region on the advancing side of the weld nugget. At first glance, this couldbe contradictory to the corrosion findings, since it would be then expected that the failure should occur at TMAZ wherethe greater corrosion damage was found. A detailed study of the fatigued fracture surfaces of different pre-corroded FSW-specimens showed the presence of several pits at the crack initiation site, as it can be seen in Fig. 11b.

Fig. 11. Typical corrosion damage zone found in a 250 h pre-corroded 2024-T3 base metal section.


These pits were interconnected by IGC generating a greater corrosion zone, with similar dimensions of the maximal cor-rosion attack zones found in the TMAZ. Therefore, it is assumed that between defects with similar overall geometry, the crackwould start from the material with a greater quantity of corrosion damage areas, in this case, from the fine grained region ofthe pre-corroded FSW-specimens. In modelling the fatigue tests of the pre-corroded base material and friction stir weldedspecimens some basic assumptions and simplifications were done in order to create a general approach to the corrosion-fa-tigue of welded structures. On the basis of the results published in [20] the effect of the different weld microstructures on da/dN � DK was neglected. Again residual stresses were not considered. This assumption allowed using the base material datastored in the NASGRO database, as in the previous simulations. The second important simplifying assumption is about thedimensions of the initial defects.

The widespread corrosion damage identified and quantified by many metallographic sections such as the one in Fig. 11a,was modelled by a single surface crack having the deepest and largest corrosion attack as dimension.

Post-mortem failure surface analysis provided the justification for this assumption. Fig. 11b clearly demonstrates that thefatigue crack started from the semi-elliptical corrosion pit. The SEM pictures were taken perpendicular to the loading direc-tions (section A–A in Fig. 4b). As already mentioned not only pitting but also inter-granular corrosion within the pits wasfound, Fig. 11b. In the model no distinction was made between the two corrosion types, which are therefore referred toas corrosion damage in the following. The schematic view of Fig. 12 clarifies the fracture mechanical treatment of the cor-rosion damaged area, which was simulated by a semi-elliptical surface crack. This surface crack comprehended the damagedue to pitting and inter-granular corrosion. Since the real surface of the corroded specimen presented several corrosion dam-aged areas, the dimensions of depth, a, and width, c, of final single semi-elliptical surface crack of the model were taken sep-arately from the deepest and the widest corrosion damage found in the metallographic sections, Fig. 13. Fig. 14 clarifies how

Fig. 12. Damage due to pitting and inter granular corrosion is simulated by a surface crack which comprehends the total corrosion damaged area.

2c2c2c

a a

2c

Fig. 13. The definitive model surface crack has the dimension of the deepest (a) and widest (2c) corrosion damages.

2c

a

2c 2c

a

2c

a

2c2ca

2c 2c

a

Fig. 14. The definitive model surface crack has the dimension of the deepest (a) and widest (2c) corrosion damages also in the case of coalescence of severalpits.

Table 4Corrosion damage dimensions in AA 2024-T3 specimens

Exposure time Maximum depth a (lm) Maximum width c (lm) a/c

BM FSW BM FSW BM FSW

100 203.7 104 600.3 220 0.339 0.47250 170.2 165 370.6 606 0.459 0.181000 536.6 308 762.4 864 0.356 0.356


the model could also take into account the presence of coalescence of several pits. The effect of exposure time on the cor-rosion damage dimensions are listed in Table 4.

The measurements of the base material were taken from a metallographic section parallel to the rolling direction (T(L)).About 200 randomly selected pits for each exposure time were analysed. Regarding the FSW material, the maximal widthand depth of the pits were measured in the T–L direction of the specimens (parallel to the weld nugget). The degree of cor-rosion was evaluated in the different zones of the joint (DXZ, TMAZ, HAZ and unaffected base material). The specimens wereiteratively cut, metallographic prepared and measured each 0.5 mm: the measurements began at the centre of the weld nug-get and finished until the unaffected metal was reached (about 12 mm from the joint line). Referring to Table 4, the expla-nation for the un-expected drop of the dimension of the corrosion zone after 250 h alternate immersion of the base materialis the following: the corrosion process on the aluminium alloy has a volumetric nature. It means that the pit grows in thethree dimensions, not only in depth. At certain period of time the extension of inter-granular corrosion attack led to a coa-lescence of 2 (or more) contiguous pits. Finally, this coalescence resulted in the separation of a corroded layer (exfoliationcorrosion), exposing smaller pits. Moreover, it should be noted once comparing the values of Table 4 to the correspondingfatigue lives of Fig. 6, that the measurements are obtained separately using the model described in Figs. 12–16, and not de-rived from the failed samples. The dimensions reported in Table 4 were used in AFGROW and in NASGRO 3.0 as initial crackdimensions for the implemented model semi-elliptical surface crack, which is shown in Fig. 9. The dimension W and t of themodel are the specimen width and the specimen thickness, respectively. No remarkable differences were found between themaximum corrosion damage area (from metallographic studies for the same corrosion time exposition) and the post-mor-tem findings, displaying similar fatigue life results. Both, the corrosion damage and post-mortem geometry simulation re-sults, are in good agreement with the experimental results, which validate the assumptions made for the implementationof this model. The simulations results for the polished 100, 250 and 1000 h pre-corroded base and FSW material are pre-sented in Fig. 15. All the simulation results both from NASGRO 3.0 and AFGROW showed a good agreement with the exper-imental observation.

4.3. Variable amplitude loading

In modelling the fatigue life of the open-hole FSW specimens the same basic assumptions as for the base and FSW un-notched simulations were done. Namely, the crack is considered as starting from the same constituent particles and particleclusters, and the entire fatigue life is treated as comprised of crack propagation. Moreover, also here the residual stresseswere neglected. The same dimensions of particle inclusions as for the base and FSW un-notched simulations were used.The AA2024-T3 T(L) stored in the NASGRO database, whose constants are listed in Table 3, and the double corner crack athole model was used for performing the calculations. The model implemented in AFGROW has a stress intensity factor solu-tion developed from Newman and Raju [35]. The sketch of the model is presented in Fig. 16. D is the hole diameter, t is thespecimen thickness and W the width. a and c are the crack length in depth and width direction, respectively. The variableamplitude loading spectrum used in the test, introduces the problem of the interaction effects.

There are currently six choices of load interaction models in AFGROW: the Closure Model, FASTRAN, the Hsu Model, theWheeler and the Generalised Willbenborg Model. As also presented in [17], for loading histories with single overloads orwith a predominance of overloading, the Generalized Willenborg retardation model showed very good agreement with

104 105 106 107

100

150

200

250

300

350

60 HzLaboratory air

100h Corroded Experimental Data NASGRO 3.0 AFGROW

AA 2024-T3t=4mmR=0.1

Max

imum

Str

ess

[MPa

]

Cycles104 105 106 107

100

150

200

250

300

350

60 HzLaboratory air


AA 2024-T3t=4mmR=0.1

Max

imum

Str

ess

[MPa

]

Cycles

104 105 106 107

100

150

200

250

300

350

60 HzLaboratory air


AA 2024-T3t=4mmR=0.1

Max

imum

Str

ess

[MPa

]

Cycles104 105 106 107

50

100

150

200

250

300

350

60 HzLaboratory air



Max

imum

Str

ess

[MPa

]

Cycles

104 105 106 10750

100

150

200

250

300

350

60 HzLaboratory air



Max

imum

Str

ess

[MPa

]

Cycles104 105 106 107

50

100

150

200

250

300

350

60 HzLaboratory air



Max

imum

Str

ess

[MPa

]

Cycles

Fig. 15. Comparison between base and FSW pre-corroded material experimental results and computer simulations.

Wt

t

D c

a

Fig. 16. Semi-elliptical surface crack model implemented in AFGROW.


102 103 104 105200

250

300

350

400

450

60 Hz

Laboratory air

Experimental DataAFGROW Willenborg R

SO=3

AA 2024-T3 FSWt=4 mmFALSTAFF

Max

imum

Str

ess

[MPa

]

Flights

Fig. 17. Comparison between FSW open-hole specimens experimental results under FALSTAFF and computer simulations.


experimental data: this model was used for the present investigation with a shutoff value of the stress ratio,RSO = KOL

max=Kmax = 3.0 (which is the suggested value for aluminium). Moreover the option of taking the effect of compressivestresses into account was switched off. This means, that the original version of the Willenborg Model was used, with no pos-sibility of reducing the retarding effect after an underload reducing the plastic zone ahead of the crack tip. Fig. 17 gives thecomparison between the experimental results of the FSW open-hole specimens and the computer simulations. Also here, thecalculations are in very good agreement with the fatigue test.

4.4. Cold expanded holes

The predictions were performed with the code AFGROW. The base material data stored in the NASGRO database (alsopresent in AFGROW) were used. The material constants are those for the AA 2024-T351 orientation T(L). The material con-stants are summarised in Table 5. In the predictions of the experimental activity presented in [36] a slightly different ap-proach was adopted: the initial crack size was set at 0.5 mm to correlate with the test data. The double corner crack athole model [35] was used and corner crack aspect ratio was set at 1. To initiate a 0.5 mm crack, approximately 7370 and11340 flights were needed for the NCx and Cx holes, respectively. Therefore, these flights were assumed as the lives for ini-tiating a crack of 0.5 mm and added to the AFGROW results. Since the experimental procedure was conducted under FAL-STAFF, also here the Generalised Willbenborg Model [13] was employed to account for the overload retardation effect.The shutoff value of the stress ratio, RSO = KOL

max=Kmax, was set at 3.0. In Fig. 18 the prediction (smooth line) obtained withAFGROW is plotted together with the experimental data (scatter symbols) for the AA 2024-T351 NCx specimens in the formof an a�N diagram. The calculations show a very good agreement with the measured values. Symbols L and R signify the left-and right-hand sides of the hole when viewed from the front in the test machine, while F and B represent the front and backside of the specimen. The diagram contains four experimental tests.

The determination of the residual stress distribution around a cold-worked hole is needed in order to be able to perform arealistic life prediction. The residual tangential stress distribution introduced by cold expansion technique is the main reasonfor fatigue life extension of the part considered. Various techniques have been developed and used to determine the residualstress distribution; these could be divided into three group: experimental, numerical and analytical approaches. Closed-formsolutions are usually obtained by analytical techniques. Compared with the numerical or experimental methods, the closed-form theory often provides a simpler and faster method to acquire the residual stress distribution. With the development ofcold expansion, a number of such models have been developed, such as those of Hsu and Forman [37], Rich and Impellizzeri[38], Chang [39], Ball [40,41] and many others [42,43]. In [36], the cold work-induced tangential stresses were calculatedwith closed-form methods as well as measured with X-ray diffraction technique. The residual stress distribution is presentedin Fig. 19, [36]. The tangential stress is compressive near the hole’s edge within the distance of 1–2 times of the hole radius.

Table 5Material parameters given in the material database of NASGRO for the material 2024-T351 T(L)

UTS (MPa) YS (MPa) KIC (N/mm3/2) DK0 (N/mm3/2) C n p q a

468.84 358.52 1424.68 90.34 1.59 � 10�12 3.3 0.5 1.0 1.5

0 2000 4000 6000 8000 100000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5Not cold Expanded FALSTAFF

Specimen 2 LFSpecimen 2 RFSpecimen 2 LBSpecimen 2 RB




AFGROW Willenborg RSO

=3

Cra

ck L

engt

h [m

m]

Flights

Fig. 18. Comparison between NCx specimens experimental results under FALSTAFF and computer simulations.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

-700

-600

-500

-400

-300

-200

-100

0

100

200

X-Ray Entrance FaceX-Ray Exit FaceBallChangHsu-FormanRich-ImpellizzeriLinear Fit Entrance FaceLinear Fit Exit Face

σ res [

MPa

]

Normalized Distance from Hole Edge r/R

Fig. 19. Residual stress distributions determined by different closed-form models, compared with X-ray diffraction tests.


The diagram summarizes the results obtained with the plane stress closed-form models proposed by Ball, Chang, Hsu-For-man and Rich-Impellizzeri.

The scatter symbols refer to the X-ray measurements, both for the entrance and exit face of the cold-worked hole. A linearfit of the both experimental results is also present in the diagram of Fig. 19. The diagram shows the stresses versus the nor-malized distance from the hole’s edge.

Since the experimental results show the most conservative values in the area of interest for the calculations, i. e. between0.5 mm and 3.6 mm from the edge of the hole, those values were used for performing the predictions. The AFGROW com-puter code was used for performing the calculations, since it allows accounting for the existence of residual stresses by cal-culating additive residual stress intensities, Kres, at user defined crack length increments. The linear fit of the entrance face(which shows the highest residual stresses and therefore has the highest probability of initiating a crack) was used for theresidual stress values in width direction (correcting the c length of the crack in Fig. 16), while a linear interpolation betweenthe entrance and exit face residual stresses was adopted for the residual stresses in depth direction (correcting the a length ofthe crack in Fig. 16). It should be noted that the linear fit is not self-equilibrated. However, the fit was able to match theexperimental data much better than the other models, therefore it has been considered as a reasonable approximation. AF-GROW utilizes than the Gaussian integration method, which uses the point load stress intensity solution from the Tada, Parisand Irwin Stress Intensity Handbook [44]. The stress intensities factors are than merely added to the maximum and mini-mum stress intensities caused by the applied load: this causes a variation of the true R ratio, Rtr, while DK remains unaf-fected. The true load ratio of the specimens affected from residual stresses is now defined as

10000 20000 30000 40000

0.00.51.01.52.02.53.03.54.04.55.05.56.06.5

Willenborg RSO

=3Residual Stresses

Willenborg RSO

=3No Residual Stresses

Specimen 1 LF Specimen 1 RF Specimen 1 LB Specimen 1 RB Specimen 2 LF Specimen 2 RF Specimen 2 LB Specimen 2 RB Specimen 3 LF Specimen 3 RF Specimen 3 LB Specimen 3 RB AFGROW 1 AFGROW 2

Cold Expanded FALSTAFF

Cra

ck L

engt

h [m

m]

Flights

Fig. 20. Comparison between Cx specimens experimental results under FALSTAFF and computer simulations.


Rtr ¼Ktr;min

Ktr;max¼

Kmin;app þ Kres� �

Kmax;app þ Kres� � ð1Þ

where Kmax,app and Kmin,app are the maximum and minimum values of the K applied. The presence of the residual stressesis therefore influencing the da/dN value, by meaning of the Rtr ratio. With this approach and the base material data, theda/dN � DK behavior of welded structures can be predicted, as elsewhere published [11,12,17]. Since in [12] and in [11]the authors have successfully shown the potential of the model with constant amplitude and with simpler variableamplitude loading history, the present calculation was considered as a further validation of the model in the presence ofan in-service load spectrum.

Therefore also here, in the prediction of the Cx specimens the Generalised Willbenborg Model with a shutoff value of 3.0was used.

In Fig. 20 the predictions obtained with AFGROW are plotted together with the experimental data for the AA 2024-T352Cx specimens in an a-nr. of Flights diagram. The calculations show a very good agreement with the measured values. Theexperimental data of three specimens (scatter symbols) are compared with two predictions: the calculations obtained takingthe residual stresses into account, referred as AFGROW 1 and simulations without the implementation of the rres in the soft-ware, AFGROW 2. The predictions obtained without using the residual stress distribution are extremely conservative, whilethe calculations performed taking into account the presence of a residual stress field in width and depth direction extremelyimprove the agreement with experimental results, while remaining conservative.

5. Conclusions

In the present investigation it was successfully demonstrated the possibility of using fracture mechanics to predict thefatigue life of structures. In particular the fatigue lives of pristine and pre-corroded base and friction stir welded specimens,even in the presence of residual stresses and under variable amplitude loading conditions, can be predicted with widespreadaerospace fracture mechanics based packages. The calculations are in very good agreement with the experimental resultsonce the following basic assumptions have been done:

� The weld material is treated as base material and the very low transverse residual stresses are neglected.� The cracks in the base as well as the FSW material are assumed to form at particle inclusions and the entire fatigue life is

comprised of crack propagation.� Pitting and inter-granular corrosion are treated as a single corrosion damage source and the model surface crack compre-

hends this damage.� The several corrosion damaged areas of the specimen surface are simulated with a single semi-elliptical surface crack hav-

ing the dimensions of the deepest and the widest corrosion damage area.� The Generalised Willenborg retardation model with a shutoff value of the stress ratio, RSO = 3.0 is used for the variable

amplitude loading predictions.� A residual stress profile in specimen thickness as well as width direction obtained by fitting the X-ray diffraction measure-

ments is used in combination with the Generalised Willenborg retardation model for the predictions of the cold expandedholes specimens under variable amplitude loading.


Acknowledgement

The Authors wish to acknowledge the work of Mr. Ulises Alfaro related to the corrosion testing and characterisation.

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