Effect of initiation feature on microstructure-scale fatigue crack propagation in Al–Zn–Mg–Cu

International Journal of Fatigue 42 (2012) 104–121

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International Journal of Fatigue

journal homepage: www.elsevier .com/locate / i j fa t igue

Effect of initiation feature on microstructure-scale fatigue crackpropagation in Al–Zn–Mg–Cu

James T. Burns a,b,⇑, James M. Larsen a, Richard P. Gangloff b

a Air Force Research Laboratory Materials and Manufacturing Directorate (AFRL/RX), Wright Patterson Air Force Base, OH 45433, USAb Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904, USA

a r t i c l e i n f o

Article history:Available online 16 August 2011

Keywords:FatigueAluminumSmall crackFracture mechanicsCorrosion

0142-1123/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijfatigue.2011.08.001

⇑ Corresponding author. Address: 395 McCormic22903, USA. Tel.: +1 434 243 1939; fax: +1 434 982 5

E-mail address: [email protected] (J.T. Burns).

a b s t r a c t

High fidelity measurements of constituent particle or corrosion topography nucleated fatigue crackgrowth rates (da/dN) are established for 7075-T651 in humid air. Values of microstructure-scale da/dNare determined by microscopy of programmed load-induced crack surface markers, rather than sur-face-only measurements. Both pristine and corroded specimen da/dN from various applied stress levelsare successfully correlated using continuum-elastic stress intensity (DK or DK and Kmax) or dislocation-based (Bilby–Cottrell–Swindon) crack tip opening displacement (cyclic / and /max), with the formeraccounting for the gradient of elastic stress concentration due to the initiating feature. Values of da/dNvary by an order of magnitude at each fixed driving force due to microstructural influences that resultin a locally irregular crack front. Grain-scale models using stress intensity closure or slip-based crystalplasticity do not capture experimental da/dN variability. Due to an inadequate mechanistic basis,mechanics-inspired models of da/dN do not predict multiple growth regimes that are typical of environ-ment enhanced cracking. An elastic DK-based description of long crack da/dN data for a given alloy-envi-ronment can be transformed to a continuum elastic–plastic /c basis to provide a mean crack growth ratedescription. Coupling mean rates with a statistical description of microstructure sensitive variability, anddislocation or crystal plasticity-finite element modeling of component /c for non-continuum cracking,will enhance prognosis in the MSC regime.

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1. Introduction

Next-generation prognosis methods aim to increase the safetyand reliability of aircraft structures by coupling real-time stateawareness and realistic loading/environmental spectra with envi-ronment-sensitive fatigue properties predicted from an under-standing of microstructure and damage physics [1,2]. Emphasishas been placed on understanding the mechanical driving forcesand material response for fatigue crack formation and growth inhigh strength aluminum alloys; as governed by distributions of ini-tiation feature, microstructure, fatigue environment, and timedependence [3–8]. Additionally, the deleterious effect of localizedcorrosion (pitting, exfoliation, intergranular attack, etc.) on fatigueformation and early growth must be integrated into a realistic air-craft prognosis capability [9–17]. Fatigue crack growth rate (da/dN) measurement and modeling focused on elastic stress intensityrange (DK = Kmax � Kmin) similitude is well established in the dam-age tolerant fracture mechanics framework [7,18–21]. However,the corrosion–fatigue interaction requires consideration of the

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microstructurally small crack (MSC) problem. While much pro-gress has been reported in MSC propagation measurement andmodeling [22–24] challenges remain.

Extensive research has delineated the unique features of MSCbehavior, particularly for aluminum alloys, which include: crackingbelow the apparent long crack threshold level of DK, oscillating-in-creased da/dN with retardation by grain boundaries, high da/dNvariability associated with microstructure and measurement inac-curacy, and slip band cracking character dictated by grain-levelplasticity [25–28]. Researchers have proposed elastic DK [6,7,29–36] and elastic–plastic dislocation based crack tip opening dis-placement (/) [22,37–49] approaches to describe MSC da/dN.While this phenomenology is extensive, quantitative-predictivemodels of MSC propagation kinetics must be better developed.Deficiencies are associated with: (a) uncertain crack tip damagemechanisms lacking both direct validation of quantitative featurecrystallography and local-failure criteria that capture the interac-tion between plastic strain accumulation, tensile stress, and envi-ronmental factors, (b) the data used to analyze MSC growth aregenerally obtained via surface measurement techniques that donot describe the two-dimensional character of crack growth withmicrostructural interactions [29–32,50–53], (c) MSC growth ratemodels contain one or more adjustable parameters, and (d) MSC

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J.T. Burns et al. / International Journal of Fatigue 42 (2012) 104–121 105

parameters based on / have not been developed for complex com-ponent stress states and geometries. Most models for MSC da/dNare based on a plasticity perspective. However, the data used to as-sess such models and constants have been obtained for fatigue inmoist environments; environmental effects have not been explic-itly factored into existing MSC models. Accordingly, validationsare suspect pending comparisons with MSC data obtained for highvacuum or inert gas environments.

Given these uncertainties the present work focuses on MSCpropagation in Al–Zn–Cu–Mg. Companion studies investigated fa-tigue crack formation from a single-pit in pre-corroded specimensat various stresses [54], and the role of stressing environment oncrack formation and MSC propagation [55]. Coupling quantitativecharacterization of corrosion damage, associated fatigue crack for-mation sites, and underlying microstructure with solid mechanicsanalysis of local driving forces provided an experimental basis tomodel crack formation [54]. At an engineering level, this work val-idated the linear-elastic fracture mechanics (LEFM) assumptionthat formation life (Ni) is nil at moderate-applied stress levelsand demonstrated that empirical modeling reasonably predictscrack formation life at lower stresses [54]. A science-based founda-tion for prognosis of corrosion initiated fatigue requires couplingthis work with a similar analysis of microstructure-scale crack pro-gression. Once the governing mechanics are established for humidair crack formation and MSC growth, then the important effects ofcyclic loading in realistic operating environments (e.g., salt waterspray at lower altitudes and low-temperature high altitude flight)can be quantified and analyzed. The sum of these observations caninform and justify the assumptions inherent in modeling of crackformation and microstructure-scale crack growth (1–1300 lm),thus extending current damage tolerant prognosis techniques intothe small crack regime.

The goals of the current work are threefold. First, obtain quan-titative (da/dN versus crack length, da/dN variability) and qualita-tive (crack shape progression, fracture surface morphology)descriptions of MSC growth from realistic crack formation sitesand over the 1–1300 lm size scale and at various stress levels.Crack formation sites include: constituent particles, controlledellipsoidal corrosion pits, and a broadly corroded alloy surface. Sec-ond, quantitatively evaluate various mechanical driving force mod-els used to correlate small crack growth from engineering andmechanistic viewpoints. Third, extend the method for predictingcorrosion nucleated fatigue crack growth below a typical airframedamage tolerant flaw size (�1300 lm) [56,57]. The approach uti-lizes programmed loading to produce crack surface marker-bandsat set cycle intervals, allowing comprehensive analysis of crackgrowth relative to the underlying microstructure.

2. Experimental methods

A 50.8 mm thick, rolled plate of 7075-T651 (Al-5.7 Zn-2.53 Mg-1.66 Cu-0.263 Fe-0.06 Si-0.026 Mn-0.19 Cr-0.02 Ti; wt%) from theDARPA Structural Integrity Prognosis System (SIPS) program heatwas investigated [2]. The average grain size ranges were 1–2 mm, 50–74 lm and 8–19 lm, in the longitudinal (L), transverse(T) and short-transverse (S) directions, respectively, with a par-tially recrystallized microstructure [2]. The monotonic tensile yieldstrength (rys) was 508 MPa (L-oriented), ultimate tensile strength(rUTS) was 598 MPa, and plane strain fracture toughness was33 MPa

pm (L–T) [58]. Fatigue experiments with pre-corrosion

were performed on flat-uniform gauge specimens machined withspecimen thickness (parallel to S) centered 7.0 mm from the platesurface and tensile axis parallel to L. Gauge length was 30.5 mm,thickness was 7.6 mm and width was 19.1 mm. Also used weretwo-holed specimens (machined in the same orientation) with

specimen thickness centered 19 mm from the plate surface. Thespecimens were 47.4 mm wide and 5.7 mm thick, with two4.8 mm diameter holes aligned perpendicular to the tensile direc-tion, 0.13 mm from either L–S surface [2]. The hole surfaces wereelectro-polished and not pre-corroded.

Prior to fatigue testing, isolated-controlled pitting and EXCO-solution exposures were used to corrode the L–S uniform-gaugesurface at the mid-length position along L. Specimens were maskedusing solvent resistant polyvinylchloride and rubber electro-plat-ing tape (3M-470) and peelable butyl rubber lacquer (Miccro-superXP 2000). Three equally spaced 370 lm diameter holes weredrilled through the electro-plating tape to allow solution contactwith the metal surface. The corroding solution consisted of 0.1 MAlCl3 + 0.86 M NaCl to which HCl was added to lower the pH to2. A potentiostat provided a constant current of 4.5 mA for15 min to the three holes simultaneously, and equal current(1.5 mA) at each hole was assumed. This protocol was applied atabout 23 �C to both L–S surfaces of the fatigue specimen to producesix semi-ellipsoidal pits; each approximately 230 lm deep (TP inthe T direction), 630 lm in surface length (SP) along S, and630 lm height (LP) along L. To mimic pit heights on broadly cor-roded surfaces, controlled pits with either elongated (SP/LP < 0.8)or short (SP/LP > 1.2) LP-dimensions were formed by varying thehole size in the electroplating tape and adjusting current. The spec-imen and relevant orientations are shown in Ref. [54]. For selectspecimens, one L–S surface (no corner exposure) was exposed toEXCO solution for 3 h in accordance with ASTM G-34 [59]. This cor-rosion protocol was chosen based on prior work showing thatEXCO corrosion was repeatable, produced consistent fatigue livesat various severities, and mimicked 7075-T6511 corrosion seenin sea-coast aircraft operating environments [9,10,60,61]. Aftercorrosion, all specimens were rinsed and ultrasonically cleanedfor 15 min in methanol, dried with nitrogen, then stored at ambi-ent temperature in a desiccator with anhydrous calcium sulfate.Post-test energy-dispersive X-ray spectroscopy (EDX) was per-formed on four pits and an EXCO specimen. Only trace amountsof Cl (K – a = 2.622 keV) were present, with the spectra otherwiseconsistent with the composition of 7075 [55].

Constant amplitude uniaxial fatigue testing was performed onpre-corroded specimens in accordance with ASTM E466 [62]. Amicrometer was used to center the specimen in a hydraulicallyactuated grip equipped with 90� diamond serrated wedges. Bend-ing calibrations, performed in accordance with ASTM E1012, re-sulted in acceptable measured-maximum bending strains of 2.6%and 3.1% of the total applied strain for the top and bottom grips,respectively [63]. For baseline loading, maximum applied tensilestress (rmax) was either 100, 200 or 300 MPa, stress ratio(R = rmin/rmax where rmin is minimum-applied tensile stress)was 0.5, and frequency (f) was 30 Hz. Testing was performed atroom temperature (23 �C) in water vapor saturated N2 (RH > 85%)maintained in a plexiglass chamber O-ring sealed to the specimen.Two-holed specimens (tested by Northrop Grumman [2]) were fa-tigued at 23 �C in laboratory air (RH � 55%) at rmax = 276 MPa,R = 0.5 and f = 5 Hz. The test matrix is shown in Table 1.

A programmed loading sequence created resolvable bands on thefatigue crack surface [9,10,60,61,64–66]. The example shown inFig. 1 for a corroded specimen is typical of all stress levels investi-gated. The rmax for marker-band loading equaled the baseline rmax,but with R = 0.1 and f = 10 Hz; such cycles were applied after every5000, 10,000, or 300,000 baseline (R = 0.5) cycles for rmax = 300,200 and 100 MPa, respectively. For short and elongated L-dimensionpits, marker loads were applied every 20,000 cycles. A full descrip-tion of the corroded specimen marker sequence is given in Ref.[54]. Marker loading for the uncorroded two-hole specimens con-sisted of up to 40 repetitions of: 1000 baseline loads (rmax = 276MPa, R = 0.5) followed by 10 marker cycles at rmax = 276 MPa

Table 1Test matrix for 7075-T651 in water saturated N2 or ambient air at 23 �C.

Specimen Description Characteristics rmax (MPa) b (da/dN � ab) Max kt�ea # of Pits examined

Prepitted Controlled 0.8 < Sp/Lp < 1.2 100 0.52 1.94 12200 0.61 1.94 62300 0.54 1.94 12

Controlled Baked 200 0.40 1.94 3

Prepitted Controlled Short Sp/Lp > 1.2 200 0.39 2.23 5Prepitted Controlled Long Sp/Lp < 0.8 200 0.40 1.74 11Prepitted EXCO Broadly Corroded 200 0.55 1.71 2 Specimens2-Holed Pristine 276 0.79 (1.1)b 3 1 Specimen

a The crack forming pit is used to determine the maximum kt�e along the longitudinal center-line of the controlled pits [54]. For EXCO specimens, pit height (LP) is assumedto equal surface length (SP). The 2-holed data assume no stress field interaction between the holes.

b Data analysis was validated independently for a separate specimen [2].

Fig. 1. Scanning electron fractographs of the T–S fracture plane of pitted 7075-T651stressed in humid N2 where small arrows point to fracture surface marks fromprogrammed loading. The pit perimeter is located at the bottom-left of (a), withcrack growth progressing as a ‘‘bump’’ along the indicated-large arrow.

106 J.T. Burns et al. / International Journal of Fatigue 42 (2012) 104–121

and R = 0.1. In principle baseline cracking directly following theR = 0.1 marker sequence could display a load history effect dueto increased cyclic plastic zone size, however long crack con-stant-maximum K (Kmax) tests [30] demonstrate that changes inminimum stress intensity factor (Kmin) do not cause da/dN tran-sients provided that the Kmax is constant. Others have confirmedthat manipulating Dr (rmax � rmin) in lieu of rmax avoids over-load retardation [67]. Data presented elsewhere show that themarker sequence has a second order impact on specimen life,suggesting that transient crack growth associated with the lowR-higher stress intensity range (DK = Kmax � Kmin) part of the se-quence is inconsequential compared to crack extension duringthe base loading at R = 0.5 [10,60].

Scanning Electron Microscopy (SEM) analysis of marker-bandsprovided the precise crack formation location, Ni to �20 lm [54],and characterization of local crack growth rates. The fracture sur-face marks are typically <1 lm wide and are of variable qualityacross the crack front. For propagation analysis, crack length andband spacing were measured along a vector approximately per-pendicular to the local perimeter of the crack formation site. Assuch, the measurement vector varied for different sites. In some in-stances growth rates were isolated in a single grain; however, themajority of data represent cracking across multiple grains in 2-dimensions. Crack length measurements were used to determinelocal Da (the distance between two adjacent marker-bands), whichwas coupled with the known applied cycles between marker-bands to determine a local da/dN. These growth rates are associ-ated with the mean of the two crack lengths used to calculateDa. This da/dN varied substantially due to crack perimeter tortuos-

ity through the microstructure; curve fitting was not used to estab-lish an average crack front. As such, these rates are trulymicrostructure sensitive and subject to substantial variabilitywhich is physically real.

3. Results

3.1. Crack formation characteristics

The same specimens were used to characterize both crack for-mation and MSC propagation from either a pristine (constituentparticles) or corrosion damaged 7075-T651 surface; formationbehavior reported elsewhere is summarized here [2,54]. For thepre-corrosion case, the 3-dimensional pit macro-topography(150–750 lm size) provides global-elastic stress concentrationand micro-topography (5–50 lm) about the pit surface elevates lo-cal plastic strain, to govern crack formation location and load cy-cles to form a 20 lm deep crack (Ni). An average of less than twocracks formed per pit, enabling characterization of MSC propaga-tion apart from crack interaction effects. Crack formation locationswere distributed over the pit surface and along the loading direc-tion. Fatigue cracks progressed as concentric ‘‘bumps’’ on the sur-face of the pit before transitioning to a full-periphery crack(Fig. 2) [54].

For pristine specimens, multiple fatigue cracks formed fromconstituent particle clusters (5–60 lm) on hole surfaces, were ori-ented 90� from the loading axis, and propagated as Mode I crackson T–S planes [55]. The hole provides global-macro stress concen-tration and constituent particles are microscopic crack formationsites due to plastic strain localization [2], as illustrated in Fig. 3a.On average, eight cracks formed per hole side and cracking also oc-curred on multiple T–S planes along the loading direction [2,54].Two fatigue crack size-classes are present: small-individual crackssurrounded by ductile fracture (Fig. 3a; A), and multiply-initiatedfatigue cracks that coalesce to form larger Mode I cracks, includingthose leading to specimen failure (Fig. 3b; B–D). Selected-high-lighted marker-bands in Fig. 3b illustrate coalescence from multi-ple initiation sites into a single crack front at the 200 lm depthscale; on average coalescence occurred at �300 lm. Six of thesemany cracks are analyzed, including both multiple-grain cracksand single-grain cracks.

3.2. Pristine two-hole crack growth kinetics

Cracks form in 7075-T651 from constituent particles (typicallyFe-bearing) [2,58,68–70], grow within a single or a few grains (S-direction grain size �10 lm), and generally coalesce into a singlecrack front by 75 lm penetration, as illustrated in Figs. 4a and b.Fig. 5 presents quantitative marker-band da/dN versus crack lengthdata from both single and multi-grain pristine specimen cases,

Fig. 2. Scanning electron fractographs of the T–S fracture plane of 7075-T651 stressed in water vapor saturated N2. The highlighted marker-bands delineate crack progressionfrom a controlled pit (bottom). The dashed box shows the formation location magnified in (b) and the arrow shows the vector along which growth rates were determined.

Fig. 3. Fractographs of the T–S fracture plane of a pristine two-hole specimenstressed in laboratory air (55% relative humidity), showing fatigue crack formationat locations A–E. The delineated marker-bands in (b) illustrate coalescence of the B–D cracks in (a) to form a single crack front. The dashed lines in (a) show the onset ofductile rupture. In each image, crack growth is from bottom-to-top.


including data obtained within a few micrometers of the formationsite perimeter to depths between 100 and 200 lm.1 These da/dNvalues are consistent for multiple cracks. A trend line of the formda/dN � ab reasonably describes the data from a single-applied rmax

of 276 MPa (Fig. 5), with b = 0.79 given in Table 1. The mean da/dN(lm/cycle) for crack lengths between 7–10 lm is 3.2 � 10�3 lm/cy-cle and standard deviation (SD) is 2.1 � 10�3 lm/cycle; for cracklengths between 40 and 60 lm the mean and SD are1.7 � 10�2 lm/cycle and 7.9 � 10�3 lm/cycle, respectively. It is as-sumed that growth rates are normally distributed for a given cracksize; as such, the da/dN variability (bounding 95% of the data) aboutthe mean is plus or minus twice the SD to mean ratio. The maximumda/dN variation of ±130% in Fig. 5 occurs between 7 and 10 lm. Thisvariability is characteristic of the crack front irregularities seen inFig. 4a and b, and attributed to microstructure sensitive variationsin grain-to-grain closure, interaction with constituents, and grain-le-vel plasticity [7,41,50,52,71]. Marker-band progression never evi-denced crack arrest at grain boundaries, as reported in small crackstudies utilizing surface measurements [7,29,30,72]. This is reason-able as crack arrest at the surface need not correlate with the morerelevant arrest over a significant portion of the growing-crack front.Quantitatively comparable results were obtained by an independentmarker-band characterization on a separate two-holed specimensubjected to identical testing (Table 1) [2].

Analysis presented elsewhere shows that small-individual andmultiply-initiated coalesced cracks exhibit similar marker-bandmeasured growth rates when compared at the same crack depth,with da/dN for the smaller-size cracks being marginally faster[2]. Since small-individual cracks generally form later in life, highergrowth rates are attributed to increased driving force due to theproximity of large co-planar cracks [73–75]. The wide distributionof final crack sizes observed for a pristine specimen of 7075-T651is primarily governed by the order of magnitude variation in Ni (Ni

varied from <1000 cycles to 6000 cycles for the cracks representedin Figs. 3–5 and a single applied rmax) [55], with a secondary role ofmicrostructurally dependent growth rates.

1 For pristine and pitted specimens, reported crack lengths are referenced to thelocation on the micro-topographic feature perimeter from which the crack formedand grew [2,9,54].

3.3. Corroded specimen crack growth kinetics

The fatigue crack generally formed a continuous-regular frontacross multiple grains by about 20 lm crack depth ahead of thecorrosion pit surface. Fatigue cracking isolated within a single ora few grains was infrequent. On average there was only a singlecrack about the pit that did not coincide with the primary fractureplane; the effect of such cracks on driving force is assumed to benegligible. Crack front evolution from the corroded surface is illus-trated in Fig. 4c and d, where lines indicate marker band locations.

A comprehensive collection of small crack growth rate versuscrack length data is presented in Fig. 6 for all pre-corroded speci-mens (regular pit, baked-regular pit,2 short pit, long pit, and EXCO)and several applied-maximum stress levels at R = 0.5. The b values

2 To investigate the effect of H from pre-corrosion, a single fatigue experiment wascarried out on a controlled pit specimen baked at 110 �C for 72 h in a vacuum toremove locally absorbed hydrogen.

Fig. 4. Fractographs of the T–S surface of 7075-T651 tested in the moist environments showing formation sites (white outline) for: (a) pristine hole, illustrating crack frontgrowth (black lines) in several grains, (b) pristine hole illustrating crack growth across multiple grains. For corroded specimens, (c) and (d) illustrate a discontinuous andcontinuous crack front, respectively. The nominal crack growth direction is from bottom-to-top.

Fig. 5. Fatigue crack growth rate versus crack depth from the formation siteperimeter for a pristine two-hole specimen of 7075-T651 tested in laboratory air atrmax = 276 MPa and R = 0.5. Each symbol and line represents crack progressionalong a single vector. The data reflect both single grain and multiple grain growthrates, and are fit with a power-law trend line (exponent = 0.79). Also included areFASTRAN predictions using closure modified long crack growth data for humid airand an assumed-initiation flaw size of 3 � 9 lm [2]. (For interpretation to colors inthis figure, the reader is referred to the web version of this paper.)


for power-law trend lines for each symbol in Fig. 6 (Table 1) are sim-ilar (0.39–0.61) for all corroded data, but are less than the value forthe pristine specimen data in Fig. 5 (0.79). As with pristine data, thevariability within with each data set is significant; as examples,quantitative analyses of da/dN are performed for the 45–55 lmcrack depth range. For Regular-200 MPa the mean and SD of da/dNare 1.8 � 10�3 lm/cycle and 1.0 � 10�3 lm/cycle, respectively,whereas for Regular-100 MPa the mean is 1.5 � 10�4 lm/cycle andSD is 7.9 � 10�5 lm/cycle. Each case shows ±110% variations aboutthe mean; each data set in Fig. 6 exhibits similar variability. Mar-ker-bands highlighted with lines in Fig. 7 illustrate the highly irreg-ular crack front. The two vertical bars demonstrate the large

variation in marker-band spacing, for the same part of the load se-quence, which is at the root of da/dN variation. This variability ismitigated by fitting semi-ellipses (dotted-white lines) to representthe marker-bands; however, since this crack front irregularity repre-sents real microstructurally affected crack propagation, the associ-ated da/dN values are retained in Fig. 6 and ensuing plots.

Coupled marker-band small crack growth rate versus cracklength data are reported in Fig. 8 for pitted specimens tested at asingle stress range in the humid N2 environment. A set of mar-ker-bands along a single vector is represented by a line connectingthe da/dN data points. Initial data points, representing growthrates directly adjacent to the nucleation site, show high da/dN, fol-lowed by a drastic drop and subsequent steady increase. Theselarge undulations correspond to cracks nucleated in areas of mate-rial protruding into the corroded volume (jut-ins), as shown inFig. 4c. The same mechanism that localizes crack formation atjut-in tips (geometry enhanced high plastic strain plus potentialH embrittlement [54]) may degrade local material resistance andincrease the driving force for propagation, causing the observed in-crease in da/dN. Further growth beyond the corrosion feature elim-inates this effect, resulting in the decreased (but still significant)variability in crack growth rate. These topography-affected datado not represent intrinsic material behavior and are not reportedin Fig. 6. These examinations did not reveal that grain boundariesexclusively governs da/dN oscillation [22,24].

4. Discussion

Crack growth rate versus accurate crack tip driving force rela-tionships, validated by laboratory data, are necessary for modernprognosis modeling of component fatigue [76]. A substantial MSCgrowth rate database exists for precipitation hardened aluminumalloys. However, such data were invariably gathered using surfacemeasurement techniques that may not account for the 2-dimen-sional aspects of crack progression and shape which are criticalin understanding microstructure effects and computing crack tip

Fig. 6. Fatigue crack growth rate versus crack depth data from marker-band analysis of pre-corroded 7075-T651 specimens tested in room temperature water vaporsaturated N2. All tests were performed at R = 0.5 and f = 20 Hz. (For interpretation to colors in this figure, the reader is referred to the web version of this paper.)

Fig. 7. Scanning electron fractograph of the T–S fracture plane of a 7075-T651corroded specimen tested in water saturated N2. The blue lines highlight marker-bands illustrating the irregular crack front, red lines are the vectors along whichgrowth rates are measured, and white dashed lines are semi-elliptical fits to themarker-bands. (For interpretation to colors in this figure, the reader is referred tothe web version of this paper.)

Fig. 8. Fatigue crack growth rate versus crack depth data from marker-bandanalysis of 7075-T651 regular-controlled pit specimens tested in water saturatedN2 at rmax = 200 MPa and R = 0.5. Each line represents crack progression along asingle vector.


driving force parameters [7,30–32]. Interpretations of striationmeasurements are limited by continuous versus non-continuouscrack growth, with the latter dominant at lower stress intensitiestypical of the small crack regime [49,77]. Moreover, striationsmay not form, or be resolvable, for certain material-environmentdependent damage mechanisms [3,78]. The dependencies ofda/dN on applied stress, formation feature morphology and size,and microstructure remain unclear. The extensive data determinedfrom marker-band analyses of microstructure-scale crack growthin 7075-T651 contribute to correcting this deficiency and providean important resource to evaluate mechanical driving force corre-lations [79,80].

4.1. Small crack growth rate theories

Small crack data analysis requires a distinction between thecontinuum and microstructurally-small crack (MSC) regimes. Con-tinuum elastic and elastic–plastic analyses assume that the crackfront encounters sufficient grains to justify a driving force not

affected by deformation and crack path differences between indi-vidual grains. Cappelli determined the transition from MSC to con-tinuum behavior occurred at approximately 350 lm for 7075-typealloys of grain size and shape similar to the current alloy [81]. Gi-ven similar grain sizes, the 350 lm boundary is a reasonable crite-rion [72]. The majority of data in Figs. 6 and 8 were obtained forcrack sizes below 350 lm and the observed growth rate variabilitysuggests a microstructure dependence. However, this boundary isapproximate. As such, da/dN data are analyzed by prominent con-tinuum methods based on elastic stress intensity factor (K, as DKand Kmax) and elastic–plastic crack tip opening displacement (/,as cyclic range, /c and maximum monotonic, /m).

4.1.1. Stress intensity factorDespite well-known concerns regarding plastic zone to crack

size similarity and grain-scale plasticity, successes have beenachieved using several stress intensity-based approaches to corre-late laboratory MSC growth rate data for use in component progno-sis [7,9,10,31,71].

4.1.1.1. Stress intensity factor calculation. A K-solution is not avail-able for a crack which forms at varying points along the perimeterof an ellipsoidal 3-D pit, progresses as a bump, and transitions to a

Fig. 10. Calculated stress intensity range versus crack depth (marker-bandlocation) from the formation site perimeter for pits in 7075-T651 specimens testedin water vapor saturated N2 at rmax = 200 MPa and R = 0.5. Various elastic stressintensity estimation methods are compared. (For interpretation to colors in thisfigure, the reader is referred to the web version of this paper.)


full-pit periphery crack, Fig. 2. For this geometry, K is estimatedusing an approach termed ‘‘Modified Bump’’. The Newman/Raju(NR) semi-elliptical surface crack solution [82,83] is employedwith crack depth referenced from the pit perimeter, crack depthto half-surface length (a/c) equaling one (consistent with experi-mental observations), and K computed at the deepest depth point(a) along the crack perimeter. While recent analysis suggests thatthe NR solution may underestimate K [82], this error is likely lessthan 10% for tensile loading and the depth point of interest.

The pit concentrates the remote stress field contained in the NRsolution for the surface-bump crack, with the level depending on3-D pit size and shape. Stress gradients for the mean short, regularand elongated pits are calculated via an elastic FEA model describedin Ref. [54]. Since the stress gradient depends on latitudinal positionabout the pit surface, several gradients are calculated and assignedbased on crack formation location within the pit. The stress gradientis generally independent of longitudinal position, but is adjusted sothat the maximum concentrated stress correctly represents that atthe crack formation site. The concentrated stress field increasesthe tensile stress (rtension) and introduces a bending component(rbend) in the NR solution. The rtension and rbend are calculated usingr1 and r2 shown in Fig. 9, where the fatigue crack plane is normal tothe L-direction. At any crack length (x = a) the area bounded by thevertical axis and concentrated stress function (rt(x)) is approxi-mated using rectangular and triangular components. r2 equals theconcentrated stress function evaluated at the measured crack length(rt(x = a)). The r1 is estimated by equating the integral ofrt(x) (eval-uated from 0 to a) to the total area of the rectangle and triangle; r1 isthus calculated at each crack length (x = a) [55]. Calculated rtension

and rbend exceed the yield strength of the material for appliedrmax = 300 MPa, but local yielding is rare for lower rmax.

Values of DK calculated from the Modified Bump method for allregular pit 200 MPa data (4) are plotted in Fig. 10 where mean pitdimensions were used to determine the elastic kt�e at the forma-tion location (Ref. [54]; Fig. 6). The three different trends for (N) re-flect the latitude-dependent stress gradients discussed above, thusbounding DK. Also included are three alternate estimates of DK,which each use the NR surface crack solution [83]. The PeripheryCrack estimates use applied stress, and surface crack dimensionsobtained by adding measured crack depth (Fig. 6) to the pit depth

Fig. 9. A schematic illustrating the concentrated macro-elastic stress distribution atthe 90� location of a controlled pit, normal to the T–S fatigue crack plane. Thisdistribution is approximated using geometric assumptions, and the tensile andbending stresses calculated as shown in the inset. (For interpretation to colors inthis figure, the reader is referred to the web version of this paper.)

and assuming this Da extends about the entire-pit periphery. Forsmall crack sizes, the a/c is roughly that of the pit (�0.7) and in-creases towards unity as crack size increases. In Periphery Crack cal-culations, the variability in DK reflects measured differences in thepit dimensions. Engineering analyses of crack growth from corrosioncommonly use this method [9,10,12,71,84,85], which provides areasonable upper bound stress intensity and converges with the lo-cal-gradient methods as crack size becomes large relative to the pitsize. Experimental observations show that cracks approach aperiphery crack after �200 lm (Fig. 2), which aligns well with theModified Bump convergence. Consistent with Modified Bump, theVanStone/Yau and AFGROW Gradient methods in Fig. 10 set crackdepth equal to the measured crack length referenced from the pitperimeter (Fig. 6) and a/c = 1. The gradient used in each is essentiallythe same as the gradient at the center-middle region of the pit, usedto calculate the highest Modified Bump trend [55]. VanStone/Yauincorporates the notch stress gradient in a weight function calcula-tion of K and is the likely gold standard solution [86,87], whereas theAFGROW Gradient approach uses a point load solution [21]. Reason-able comparison of the techniques can be made since: (1) the samemacro-pit dimensions are considered and (2) nearly exact stress gra-dients are used if the highest Modified Bump K trend is considered.The maximum variation in the DK estimates for the three gradientmethods is 20%. This difference is of secondary importance because:(1) a 20% error in DK equates to less than a factor of 2 uncertainty inda/dN, which is small compared to the intrinsic da/dN variabilityshown in Fig. 6 and (2) each analysis ignores plasticity introducedby the microfeatures at the formation site [54]. The Modified Bumpcalculations of K are used to correlate MSC da/dN data owing to sim-plicity of the analysis.

While specific pit depth and surface length are observed forcracking from an EXCO corroded surface, the axial dimension (pitheight) and latitudinal formation position are not known [10].Accordingly, DK is computed assuming pit height (LP) equals surfacewidth (SP) and crack formation from the pit center using the Modi-fied Bump technique. Cracks in pristine two-holed specimens formabout a constituent particle cluster and progress as bumps, then(at �15–75 lm) transition to perimeter cracks. An elastic–plasticFEA model of the two-hole specimen shows that there is minimalinteraction of the stress fields between the holes over the region ofinterest (0–500 lm); as such the driving force is estimated using aK-solution for a single offset hole in a finite body with a semi-ellip-tical surface crack emanating from the hole [88,89]. The input cracksize is cluster depth and width with the measured crack size added

Fig. 11. Fatigue crack growth rate from marker-band measurements versus DK from Modified Bump analysis of all 7075-T651 controlled pit (regular, short, long) specimenstested at rmax = 100, 200, or 300 MPa and R = 0.5 in water vapor saturated N2. Also included are high constant Kmax-decreasing DK relationships for long cracks from: two CTtests, one SEN test, and estimation from CT results at various constant R-ratios [2]. Light-blue dashed lines represent the mean trend and three extrapolations of these SEN andCT trend lines to the low DK regime. (For interpretation to colors in this figure, the reader is referred to the web version of this paper.)


to both; the high-initial a/c ratios tend to 1.0 with increasing cracksize. The stress input is the applied stress (kt�e = 1.0), since the stressgradient of the hole is included in the K-solution. Consistent withcontrolled pit results, pristine solutions are likely accurate aftercrack extension of approximately half the constituent size, or forcracks larger than about 10 lm, and over-predict K for cracksizes <10 lm.

Fig. 11 plots da/dN from marker-band analysis of controlled pitspecimens (Fig. 6) versus DK calculated with the Modified Bumpmethod. Neither initial-local topography-affected data points (ini-tial crack growth interval of �10 lm, Fig. 8), nor results for crackslonger than 500 lm, are plotted due to K-solution inaccuracy fromnot accounting for local plasticity and long crack interaction,respectively. Fig. 11 establishes that DK collapses marker-bandcrack growth rate data for various pit shapes and stress levels(see Fig. 6) into a single distribution, albeit with considerable var-iability. The 100 MPa growth rates are systematically lower. Thisshift does not appear to be based on compromised stress intensityas the level of local plasticity is lowest for the 100 MPa stress caseand absolute crack sizes are similar in the low-DK regime. Achange in crack tip slip mode/morphology is possible, but fracturesurface analysis did not reveal a morphology variation betweenstress levels. An environmental explanation is therefore reason-able. Speculatively, decreased crack mouth opening, proportionalto the product of low stress and small-crack size, could retardmolecular flow of water vapor to the crack tip [5,90,91] and thusreduce H uptake for slower da/dN but similar crack surface appear-ance. The few low growth rate outliers at higher DK are also trou-blesome; crack tip retardation from non-coplanar cracks [73,74] orlocally resistant microstructure features may cause this behavior.

4.1.1.2. Comparison with long crack da/dN versus DK trends. Fig. 11provides a large database that, only in part, supports the literatureproposal that MSC growth rates are upper-bounded by long crackda/dN values measured under decreasing DK at high-constant Kmax

to minimize the role of crack closure [30]. The MSC data in Fig. 11 arecompared with long crack trend lines determined for high-constantKmax (16–17 MPa

pm) loading of single-edge notch (SEN), and com-

pact tension (CT) specimens. These specimens were machined fromthe current lot of 7075-T651 plate at the same thickness as the pittedfatigue specimens, and tested in the same water saturated N2 envi-

ronment. The Newman trend estimates the high-constant Kmax rela-tionship using data reported for several constant-R experiments [2].The large-dashed lines qualitatively estimate the mean of these longcrack data sets. Overall, the long crack trends are consistent with theMSC data, but do not provide an upper bound for the important-lowDK regime below about 3 MPa

pm. Previous comparisons which

support the constant-Kmax approach focused on higher DK levels[30]. Long crack near-threshold behavior is argued to be an artifactof the bending-type specimens and K-shedding protocol [92–94].The present results in Fig. 11 support this concern; MSC growth ratestypical of the pitted specimens are substantially higher than theda/dN trends for the SEN and CT specimens at DK below about1.3 MPa

pm and at very high R (>0.8). The constant Kmax approach

better bounds the MSC behavior at DK levels below 1 MPap

m ifthe plateau regime growth rates, just above threshold, are extrapo-lated, as provided by the dashed line (labeled 1 with m = 1.3 for da/dN � DKm) in Fig. 11. This plateau was not apparent in the constantDK-constant Kmax CT data; as such, extrapolations of the 2–3 MPa

pm regime (2, m = 3.3) or the 1.7–2 MPa

pm regime

(3, m = 5.7) are also shown in Fig. 11. The exact form of the high Kmax

extrapolation is critical to capturing the proper growth rates for MSCin this very low stress intensity regime. The range of possible longcrack extrapolations (1–3) shown in Fig. 11 demonstrates that thisapproach can induce large errors and must be used with caution.

4.1.1.3. Effect of crack formation source. The comprehensive smallcrack data set in Fig. 12 establishes the first-extensive combinationof MSC growth rates from different specimen morphologies, testconfigurations, stress levels, concentrated stress fields, and crackformation features. The complete controlled pit data set (Fig. 11)is combined in Fig. 12 with marker-band results for the pitted-baked, EXCO corroded, and pristine two-holed cases. The corre-spondence between these varied sets of data demonstrates thatelastic DK reasonably correlates MSC growth rates, independentof crack formation feature. Despite the exclusion of marker-bandresults within 10 lm of the formation feature; cracks within thefirst 30 lm (circled in Fig. 12) may be influenced by local plasticstrain from initiation feature geometry [54]. This would increasethe local driving force to explain these marginally higher growthrates. On the whole, DK acceptably correlates microstructure-scalecrack growth rates.

Fig. 12. Water vapor saturated N2 fatigue crack growth rate versus DK and continuum elastic–plastic /c (Eq. (2)) from marker-band analysis of 7075-T651. Included are alldata for controlled pit, EXCO, and baked-specimens, each stressed at constant R of 0.5, as well as data from a pristine two-hole specimen tested in ambient air atrmax = 276 MPa and R = 0.5. A single trend line (yellow) and four separate trend-line segments (pink) are qualitatively fit to these MSC data, with the slope regions labeled 1–4. The black-dashed line represents da=dN � /1

c � DK2 and data points that are likely affected by local plasticity are circled. (For interpretation to colors in this figure, thereader is referred to the web version of this paper.)


Fatigue crack growth in aluminum alloys exhibits a complexda/dN versusDK relationship that is mechanistically explained basedon either microstructure interaction with the process zone [95,96], ormoist environment production of adsorbed H2O and atomic hydro-gen production [4,97,98]. The MSC growth rate results support com-plex multiple power law da/dN versus DK behavior; however,microstructure induced variability hinders quantitative analysis.Qualitatively, the dashed long-crack trend lines in Fig. 11 reflect mul-tiple power-law regimes. For the larger set of marker-band data inFig. 12, a qualitative analysis is presented. Region 4 suggests a transi-tion to m� 7 above 3.5 MPa

pm, consistent with CT/SEN results in

Fig. 11. The MSC data below 3.5 MPap

m are described by multiple(solid) power-law segments with m� 3.7, 0.7, and 2.9 for Regions1, 2, 3, respectively. For engineering purposes, the single power lawtrend (dashed with m = 2.5) may be adequate. Regardless of the formof the trend for DK below 3.5 MPa

pm, the MSC and long crack data

affirm that: (1) long crack and marker-band growth rates agree inthe higher DK regime (1.8–4 MPa

pm) regime, (2) the lowerDK small

crack da/dN is not bounded by extrapolation of the mean Paris regimegrowth rates (Fig. 11, extrapolation 2), (3) da/dN variability increasesfor DK levels below 1 MPa

pm and (4) environmental fatigue is not

comprehensively described by a single power law relationship.Continuum DK correlation of MSC da/dN is affirmed by the com-

parison in Fig. 13. Here, MSC growth rates are reported for 2024-T351 stressed in moist air and based on surface-optical measure-ments of cracking from a 250 lm deep laser-machined surface notchto a total depth of up to 1.3 mm [49]. The 4-stage trend line for 7075-T651 (solid line from Fig. 12) demonstrates that the present MSCda/dN results were obtained for a substantially lower DK regime,owing to smaller crack sizes and lower-applied stresses. The slopeof the dashed-average trend line, m = 2.5 from Fig. 12, agrees withthe value reported for the 2024-T351 data where m = 2.2 at R = 0.5[49]. Moreover, it is well known that long crack da/dN values forpeak aged 7075 are several times faster than those for naturally-under aged 2024. For example, the ratio of long crack da/dN for7075-T651 at DK of 4 MPa

pm and Kmax of 16.5 MPa

pm in Fig. 11

is 4.2 times faster than the da/dN for 2024-T351 measured for theidentical stress intensity conditions [99]. The dotted trend line

shown in Fig. 13 is the dashed trend for 7075-T651, with da/dNreduced by a factor of 4.2. This adjusted trend extrapolates throughthe midst of the MSC rates reported for 2024-T351; confirming theengineering relevance of an elastic stress intensity correlation.

Fig. 12 illustrates that the growth rate data for as-pitted andbaked specimens are equivalent for the range of DK levels examined.This behavior may be attributed to two factors. First, H can bestrongly trapped to vacancies, dislocations, precipitates, and constit-uent particles proximate to the pit perimeter [100]. It is possible thatthese binding energies were not exceeded by baking; however, suchH could be attracted to the crack tip hydrostatic stress field duringloading allowing for embrittlement with or without baking[54,101–104]. The more plausible explanation is that H, producedby crack surface Al reaction with water vapor during loading, dom-inates fatigue crack growth for the high humidity level examined.Both H-precharging and residual chloride deliquescence wouldcause pit-originated crack growth rates to be higher than da/dNfor pristine specimens at a given DK, which was not observed(Fig. 12). These results suggest that internal hydrogen embrittle-ment and trace chloride from corrosion [55], are not important fac-tors for the corrosion to fatigue transition in moist air or nitrogen at23 �C. The contributions of precharged and environmental H to MSCbehavior may be particularly sensitive to stressing temperature, asdetailed in companion work [55].

4.1.1.4. Two-parameter stress intensity approach. Differences in MSCand long crack kinetics have been attributed to the interaction ofcrack length (wake) and stress dependent crack closure, suggestingthat da/dN is a unique function of a closure-minimized DKeff [7,29–31,33]. Newman performed a FASTRAN analysis on the pristinetwo-hole specimens of SIPS 7075-T651 assuming [2]: (a) an initialbore surface crack size of a = 3 lm, c = 9 lm, (b) constant aspect ra-tio (a/c) with crack extension, and (c) closure corrected long crackda/dN versus DKeff behavior from compact tension (CT) measure-ments at multiple R-values (Fig. 11) [6,7]. Consistent with resultsfor a separate heat of 7075-T6 [7,31], for crack lengths greater than5 lm Fig. 5 shows good agreement between the predicted depen-dence of da/dN on crack length and pristine experimental data

Fig. 13. Comparison of the 4-stage (solid) and single-stage averaged (dashed) trend lines from Fig. 12 for 7075-T651 with MSC growth rates from surface measurements ofcracking from a laser-machined surface notch in 2024-T351 (symbols) [48,49]. The averaged dashed trend line for 7075-T651 is reduced by a factor of 4.2-times (dotted)based on long crack data obtained for 2024-T351 [99]. All specimens were tested in moist air at a frequency of 10 Hz (2024) compared to 5 Hz or 30 Hz for 7075.


from the present marker-band experiments on the same lot of al-loy. This comparison validates the engineering relevance of thestress intensity approach, here augmented with a strip-yield modelof plasticity induced crack closure and DKeff. However, this ap-proach has fundamental shortcomings. Microstructure inducedda/dN variability about the deterministic-single growth law isnot captured. Moreover, the slope change at �5 lm is not consis-tent with experimental MSC data and reflects the use of an inaccu-rate near-threshold growth law. Finally, the model aligns well withthe a0.79–1.1 growth rate dependence for pristine specimens, but notwith the a0.39–0.61 relationships for the small cracks associated withpits (Table 1). A multiple-slope growth law input is necessary tocapture the small crack and moist environment behavior summa-rized in Fig. 12.

An alternate continuum two-parameter stress intensity ap-proach, which reduces to the Frost–Dugdale model, correlatedMSC rate data [32,34]. By hypothesizing that da/dN depends on atwo parameter stress intensity model and crack size, the modelavoids explicitly accounting for crack closure [35,36]. The follow-ing relationship was proposed:

dadN¼ C� DKpðKmaxÞð1�pÞ a

2�c2c

h icð1Þ

where DK and Kmax are the Modified-Bump stress intensities calcu-lated at each crack depth (Fig. 10), a is crack depth (Fig. 6), and theremaining terms are material-dependent constants determinedfrom literature-based long-crack growth rate data for 7075-T6, spe-cifically: C⁄ = 1.8 � 10�11, p = 0.75 and c = 3 with da/dN in mm/cycleand stress intensity as MPa

pmm (the units for this correlation are

assumed but not explicitly presented) [32]. Using these parameters,predicted da/dN values were plotted versus DK and compared toexperimental MSC da/dN versus DK data for all stress levels andpit morphologies (this plot is presented elsewhere [55]). Eq. (1),using these literature experimental constants, over-predictedgrowth rates by an order of magnitude; however, the power-lawtrend was effectively captured with this literature value of c, anddecreasing C⁄ to 2.5 � 10�12 reasonably aligned model predictionswith mean experimental MSC behavior. The variability in Eq. (1)predictions, due to the different-pit stress gradients used to calcu-late DK for a given crack size, is much less than the variability inmeasured MSC rates attributed to microstructure sensitivity. Thismechanics-based driving force does not capture microstructuresensitivity or the multiple growth regimes characteristic of environ-mentally enhanced fatigue.

4.1.2. Crack tip opening displacementFatigue crack growth kinetics are often hypothesized to depend

on a function of cyclic crack tip opening displacement (/c, equivalentto actual D/ = /max � /min) for Mode I cracks or cyclic crack tip dis-placement range for mixed mode [6,38,42,80,105,106]. This is rea-sonable since /c directly governs crack tip plastic strain range,which plays an important role in process zone damage. The powerof this approach for MSC behavior is that /c can be determined bycontinuum or microstructure-based mechanics depending on cracksize relative to microstructure. In order to theoretically predict amechanism-informed microstructure-level da/dN versus /c model,two elements must be realized [6]. First, crystal plasticity must becoupled with a dislocation-based model, finite element analysis, ordata-based reasoning to capture the dependence of /c on remoteload and crack size/geometry; with cyclic loading, grain orientation,2nd phase, and grain boundary effects included [38,39,47]. Second, afundamental crack tip damage model must be formulated to includelocal stress and strain accumulation, thus to explicitly relate MSC da/dN to the /-based driving force. This damage model must includethe effect of moist environment, and not a priori assume occurrenceof slip plane decohesion, or otherwise the MSC predictions are per-tinent only to inert environments such as high vacuum. In spite ofsubstantial research on each issue, models are limited by unsubstan-tiated assumptions, computational complexity, and a lack of exper-imental validation [6,37–39,42–46]. As such, models resort toempirical da/dN versus crack size data input for a given materialand environment, [40,107] or to ad hoc assumptions to formulateDa and DN that yield da/dN [48,49].

4.1.2.1. Fracture mechanics estimate of /c. A first step to evaluatecrack tip opening displacement correlation of MSC da/dN is basedon continuum transformation of elastic DK and Kmax to elastic–plastic /c and /m. For long cracks intersecting many grains, contin-uum fracture mechanics relates /c to crack size, geometry, andloading following the plastic zone superposition concept by Rice[19,108,109].

/c ¼dn DK2

E02rfð2Þ

where rf is flow strength (the mean of rys and rUTS, 553 MPa for7075-T651), E0 is generalized modulus (80,460 MPa for planestrain), and dn is a dimensionless constant dependent on workhardening (0.6 for 7075-T651 under plane strain and based on


J-integral analysis) [108,110]. The /c calculated using this relation-ship is plotted on the top axis of Fig. 12. The MSC da/dN data corre-late with this continuum /c and exhibit the same environmentinduced multiple cracking regimes as discussed for DK. Consistentwith Section 4.1.1.2 and Eq. (2), the /c exponents for correlationwith da/dN are 1.85, 0.35, 1.45, and 3.5 for Regimes, 1, 2, 3, and 4(solid-pink lines), respectively, and 1.25 for the single power law(dashed) trend. Hypothesized crack advance per cycle and by thestriation mechanism is interpreted as da/dN directly proportionalto /c [19,108], somewhat consistent with the correlation inFig. 12. However, this simplistic concept is complicated by non-con-tinuous crack growth in the low-driving-force regime that is typicalof small cracks, as well as environmental and microstructure effectswhich promote the multi-power law behavior evident in Fig. 12[4,95–98]. Additionally, there is substantial uncertainty in extrapo-lating continuum long crack /c trends to the small crack regime.

4.1.2.2. Plastic zone correlation. Important early approaches relatedMSC da/dN to a fraction of the measured-monotonic [111] or calcu-lated-cyclic [107] plastic zone sizes. For example, Shiozawa et al. fitthe following equation to measurements of MSC growth rate: [40]

d ð2cÞdN

inm

cycle¼ 3:1� 10�4 ra

rUTS

� �4:8

2c1:0 in mm ð3Þ

for two cast aluminum alloys (rUTS = 300–330 MPa) based on replicameasurements of surface crack length (2c) over the range from 50 lmto 1000 lm. Testing was accomplished in moist air with R = �1 andstress amplitude (ra = Dr/2 = rmax) varied from 0.4 to 0.7 of rUTS.Similar experiments with low-carbon steel produced identical expo-nents for stress (4.8) and crack length (1.0) [2]. Detailed analysis ofthe current MSC da/dN data, plotted versus ((ra/rUTS)4.8 a) indicatedthat Eq. (3) collapses the data from both the corrosion pit and constit-uent cluster crack formation sites into a single functional relationshipwith the expected microstructure-sensitive variability in da/dN typ-ified in Figs. 11 and 12 [55]. However, regression analysis establisheda power-law trend-line exponent of 0.6 instead of 1.0 suggested byEq. (3), as well as poor agreement with the surface-measured da/dN data for the two cast Al–Li alloys reported by Shiozawa et al.[40]. Varying the stress exponent from 1 to 12 did not align the da/dN data as proportional to crack size, as suggested by Eq. (3), nordid it reduce data-scatter [55].

This result is important because models that similarly assumeda/dN proportional to crack size are the basis for /c-based progno-sis modeling [2,42,76]. As justified in the discussion that ensues,additional research is required for this approach to better modelMSC growth rates beyond continuum DK-based correlations ofthe sort illustrated in Figs. 12 and 13.

4.1.2.3. Dislocation elastic–plastic /c. Bilby, Cottrell and Swindon(BCS) modeled localized crack-tip yielding by a continuously dis-tributed dislocation density field collinear within a one-dimen-sional plastic zone ahead of a through-crack in an infinitely largeplate under plane strain [47,112–114]. Integrating this functionfor an assumed edge dislocation distribution, over the plastic zoneyielded an expression for opening displacement. This analysis wasfollowed by Burdekin and Stone with a continuum strip-yieldWestergaard-type stress analysis for a through crack in an infiniteplate [47,108,113,115]. These models result in the well-knownrelationship for monotonic crack tip opening displacement:

/m ¼8rysð1� m2Þa

pEln Sec

prmax

2rys

� �� ð4Þ

where m is Poisson’s ratio and other terms have been defined. Eq. (5)follows from Eq. (4) based on Rice’s assumption of supposition ofcrack tip plastic zone unloading from tensile yield [109].

/c ¼16rysð1� m2Þa

pEln Sec

prmaxð1� RÞ4rys

� �� ð5Þ

Consistent with others [38,39,105,116], McDowell assumed aproportionality between da/dN and /c based on shear strain local-ization and geometric crack advance by tip blunting [6,42].Specifically,

dadN¼ Cð/c � /c-THÞ

n ð6Þ

where /c-TH is the threshold per-cycle crack tip displacement range(assumed to be negligible for current modeling), and C and n areconstants with n often set at 1.0. From Table 1, current MSC datashow that, on average, da/dN � a0.53. Considering Eqs. (5) and (6),this comparison implies that n �½, at odds with the assumedn = 1. Amplifying this comparison, current marker-band da/dN val-ues are plotted in Fig. 14 versus a2/c where /c is given by Eq. (5)and a is the ratio of DK calculated using current methods (Figs. 10and 12) to that for a through crack in an infinite plate(DK = Dr

p(pa)) pertinent to Eq. (5). The rmax term is considered

the maximum applied stress in the fatigue experiment. The a ac-counts for the effects of applied stress gradient (from the pristinehole or pre-corroded pit) and crack shape not captured in Eq. (5);and is squared based on the relationship between /c and DK (Eq.(2)). This model reasonably collapses the experimental da/dN datafrom the various crack formation and MSC growth morphologiesinto a single distribution. Regression analysis of the entire da/dNpopulation produces an exponential dependence of n = 0.77 (solid-black line, Fig. 14), which reasonably aligns with the hypothesizedda=dN � /1

c (Eq. (6)). Essentially identical to the DK results inFig. 12, variability (2 � SD/mean) is ±120% for a2/c of 4 � 10�2 lm.At lower driving forces, variability increases to a maximumof ±240%. The 100 MPa growth rates are somewhat lower than thehigh stress trend leading to the increased variability; this is attrib-uted to retardation of the H embrittlement process, as discussed inthe DK analysis (Section 4.1.1.1). While this is an elastic–plasticrelationship, the formation site-concentrated stress gradient andcrack geometry effects are accounted for using a determined fromelastic stress intensity analyses that include the gradient inducedpseudo-stresses. The next level of complexity would decouple thea-term such that a crack shape correction factor would operate oncrack size and the stress correction would operate on rmax in Eq. (6).

Shyam et al. proposed a crack opening displacement-basedmodel accompanied by extensive experimental MSC da/dN datafor Ti, Ni and Al-based alloys: [47–49]

dadN¼ lð/m /c rysÞm ð7Þ

where m = 1 and l is an empirically (or theoretically) determinedconstant in idealized form [48]. This function captures the hypoth-esis that a cyclic driving force, /c from the BCS Eq. (5), governs cyc-lic-plastic strain accumulation, while tensile stress (or equivalently,strain energy release rate) in the plastic zone controls crack tip dec-ohesion. This idea is analogous to two-parameter DK � Kmax controlof da/dN [35,36], and can be justified physically based on plasticity-environment interaction [78,117]. Since /m in Eq. (4) is infinite forrmax above rys, this model does not describe large-scale yieldingassociated with pit or hole stress concentration, unless a flowstrength is used. The Shyam MSC da/dN data were obtained usingsurface optical measurements of a fatigue crack progressing froma 250 to 300 lm deep laser-machined surface notch in two castAl alloys, wrought 2024-T351, Rene 88, and Ti-6246 stressed inmoist air at �1.0 < R < 0.5. The best fit power law exponent (m inEq. (7)) for each of 22 individual data sets ranged from 0.3 to 1.1with an average of 0.7 [48,49]. Assuming that m = 1, l = 10�5 m2/Jproduced the best fit for the entire population [47,49]. The model

Fig. 14. Fatigue crack growth rate versus cyclic crack tip opening displacement and a K-based correction factor, a. Growth rates are from marker-band analysis of 7075-T651pit specimens tested at rmax = 100, 200, and 300 MPa (R = 0.5) at room temperature in water vapor saturated N2, and from pristine two-holed specimens (rmax = 276 MPa,R = 0.5) in room temperature ambient air. The exponents from regression analysis (solid) of the marker-band data is 0.77 for da/dN � (a2 /c)n. The green lines marked 1 and 2are replotted from the corresponding DK-based long crack trends in Fig. 11 using Eq. (2). (For interpretation to colors in this figure, the reader is referred to the web version ofthis paper.)

Fig. 15. Fatigue crack growth rate versus the product of yield strength and cyclic and monotonic crack tip opening displacements. Growth rates are from marker-bandanalysis of 7075-T651 pit specimens tested at rmax = 100, 200, and 300 MPa (R = 0.5) at room temperature in water vapor saturated N2, and from pristine two-holedspecimens (rmax = 276 MPa, R = 0.5) in room temperature ambient air. Also included is the range of growth rate data for 2024-T351 (red box and Fig. 13) [49]. Exponents fromregression analysis of the marker-band data (m = 0.36, solid) are listed for da/dN = l (rys /m /c)m, as well as the mean trend line for the entire Shyam dataset (m = 1.0, bluedashed) and 2024-T351 (m = 0.48, red dashed) [48,49]. The thin-solid line (red) represents a 4.2-times reduction in da/dN for 7075-T651 to project the behavior of 2024-T351based on current marker band results. (For interpretation to colors in this figure, the reader is referred to the web version of this paper.)


represented in Eq. (7) generally correlated this extensive MSC data;comparison with current da/dN results provides additional insights.

The model represented by Eq. (7) reasonably collapses the cur-rent experimental da/dN data from the various crack formation sitesinto a single distribution. Fig. 15 plots these marker-band growthrates versus this /-based two parameter model for the simplethrough crack geometry (Eq. (5)) without using the a approach tocapture crack shape and stress gradient effects. The variability inda/dN shown in Fig. 15 is identical to that discussed for the contin-uum DK and dislocation-based single parameter (/c) correlations;at a /c /m rys of 2 � 10�5 m2Pa, 2 � SD/mean is ±120%. Regressionanalysis of the entire da/dN population produces a power law expo-nent (m) equal to 0.36, with an intercept of l = 1.8 � 10�7 m2/J (so-lid-black line, Fig. 15). Also included in Fig. 15 are the 2024-T351data range (red box with average m = 0.48 and consistent value of

l = 1 � 10�7 m2/J), and power law trend for the entire data set withm forced to be 1.0 and best fit l = 1 � 10�5 m2/J [49]. The slope fromregression analysis of the Shyam-correlated 7075-T651 marker-band data (m = 0.36, Fig. 15) is consistent with these literature re-sults for wrought 2024-T351 (m = 0.48), but is not consistent withthe theoretical prediction (m = 1) [49]. Stated alternately, the mea-sured b values (Table 1) in the proportionality relationship forMSC da/dN � ab vary from 0.39 to 0.79, with an average of b = 0.53for the current data. Eqs. (4), (5), and (7) predict that MSC da/dN � a2m, suggesting da/dN � a2 for m = 1 (Shyam) which is not ob-served experimentally. This discrepancy was reported for all alloysstudied by Shyam [48,49].

It is important to understand the cause of the MSC growth ratedifference between peak aged 7075 and naturally aged 2024,Fig. 15. Recall that Fig. 13 shows that the elastic DK analysis

Table 2Statistical parameters for crack growth rate data in Fig. 12 for 7075-T651 pristine andcorroded specimens fatigued at various stress levels in moist air or N2.

Interval of DK over which data are collected (MPap

m)

0.70–0.80 0.95–1.05 1.95–2.05 2.95–3.05

Specimen type da/dNrmax (MPa) Sample size

Mean (lm/cycle)Standard deviation (lm/cycle)±% Variation (2 SD/Mean)K–S normality test result

Regular200

16 26 40 101.0 � 10�3 1.2 � 10�3 2.8 � 10�3 1.1 � 10�2

3.5 � 10�4 7.3 � 10�4 1.6 � 10�3 4.8 � 10�3

70 126 116 86Pass Fail Fail Pass

EXCO200

3 6 6–a 1.8 � 10�3 3.4 � 10�3 6.6 � 10�3

3.1 � 10�4 1.1 � 10�3 1.9 � 10�3

34 68 58Pass Pass Pass

Pristine276

5 7 5–a 1.4 � 10�3 3.4 � 10�3 8.8 � 10�3

8.8 � 10�4 1.5 � 10�3 1.5 � 10�3

124 86 34Pass Pass Pass

All 61 61 64 457.4 � 10�4 1.2 � 10�3 3.2 � 10�3 7.8 � 10�3

6.6 � 10�4 8.6 � 10�4 2.4 � 10�3 3.5 � 10�3

180 144 148 92Fail Pass Fail Fail

a Insufficient data.


successfully correlated average but distinct rates of MSC growthfor these two alloys, based on a 4.2-times reduction of da/dN for7075-T651 justified by long crack data. This same growth ratereduction is represented by the shifted-solid line in Fig. 15 and re-sults in good agreement with the Shyam et al. results for 2024-T351. This comparison affirms the basic form of the crack tip open-ing displacement model represented by Eqs. (4), (5), and (7). This isan important result because the current da/dN measurements arebased on marker-bands that depict the behavior of the completecrack perimeter (Fig. 7) compared to surface-optical measure-ments which are limited. This agreement suggests that: (a) the er-ror introduced by reliance on surface measurements is not ofprimary importance, at least for precipitation hardened aluminumalloys stressed in moist air and (b) ignoring the laser notch stressconcentration effect on / [47–49] is of secondary importance forthe associated crack sizes measured by Shyam et al. and the com-pressed scale of /m /c rys in Fig. 15. The comparison in Fig. 13 sug-gests that DK (and Kmax) effectively describes MSC rates for verysmall crack sizes associated with several initiation site morpholo-gies. The comparison in Fig. 15 suggests that crack tip opening dis-placement provides an alternate-similar capability, and criticallyprovides a method to incorporate microstructure-scale quantita-tive crystal plasticity estimates of /c and /m in place of the contin-uum-dislocation estimates provided by Eqs. (4) and (5) [6].

The values of l and m in the Shyam MSC model are not simple-universal constants. First, the comparison presented in Fig. 15clearly demonstrates that l values are alloy-environment specific,in contrast to the similar results for Ni, Ti and Al alloys [48,49]. Sec-ond, the collective results in Fig. 15 and elsewhere [49] establish thatda/dN is not directly proportional to cyclic crack tip opening dis-placement (or to crack length, Table 1), as originally suggested withm = 1 in Eq. (7) [48]. Third, neither the Shyam nor the McDowell cyc-lic crack tip opening displacement model captures multiple powerlaw behavior that is unique to the strong role of environment in fa-tigue damage as discussed previously. Essentially, m and l must bepredicted through a damage mechanism-informed model that cou-ples plastic strain accumulation due to cyclic deformation, stressdevelopment due to local hardening/softening, and environmentalinteraction which is likely hydrogen-based for the conditions repre-sented in Fig. 15. This problem was recognized by Shyam et al. [48]who proposed that da/dN is given by the ratio of Da to DN for discon-tinuous crack advance; Da equals (a /m rys) and DN equals /cr/(f /c)where f is a slip irreversibility parameter (0 is full reversibility and 1is full irreversibility), /cr is the accrued-critical amount of cycliccrack opening required for crack advance over Da, and a is a geomet-ric scaling factor that can be determined from striation measure-ments if such features occur and are resolvable [48,49]. From thismodel, l = (f a)//cr which introduces material-environment sensi-tive behavior to the da/dN relationship. For example, as comparedto 2024-T351, for 7075-T651 the f should be larger and speculatively/cr should be less owing to higher crack tip stresses and/or increasedH-embrittlement. Consistent with the trend in Fig. 15, these contri-butions to l suggest faster da/dN for 7075 at a given driving force;the above variations in f and /cr (thus l) would therefore result inimproved correspondence between 2024 and 7075 data. Consider-ing the power law slope, striation spacing measurements lead tothe result that /cr � ah, justified based on crack wake plasticity ortip blunting, and thus da/dN � a2�h [49]. For 2024-T351 and R of0.5, h was reported to equal 0.65; thus, da/dN � a1.35 which is incon-sistent with the measured results for 7075-T651 in Table 1. Whilethese factors may be determinable experimentally; the interpreta-tions are speculative, sometimes at odds with experimental results,and introduce adjustable parameters.

The crack tip opening displacement basis for modeling MSCda/dN is reasonable, but not sufficiently grounded in an explicitmechanism of crack tip damage traced to plasticity-environment

(H)-microstructure interaction. The following consideration shouldguide future research. /-based models are often viewed from theperspective of a slip plane-based cracking (SBC) mechanism[6,36,38,44,118] which does not appear to occur as broadly asprojected in high-strength aluminum alloys stressed in moistenvironments. Quantitative EBSD and stereo-imaging of Al–Cu–Mg, Al–Cu–Li and Al–Zn–Mg–Cu alloys demonstrated broadoccurrence of SBC, particularly for planar slip alloys stressed at lowerDK levels [3,4,78,119]. However, such SBC was only observed forfatigue in ultra-high vacuum and never for crack growth in a moistenvironment, including either long cracks [3,78,119,120] or micro-structure-scale cracks adjacent to constituent particle nucleationsites [68]. While this does not prove that SBC never occurs for singlegrain (Stage I) cracks in Al alloys, away from local stress concentra-tion and in moist environments, the burden of such proof falls tothose using an MSC model based on SBC controlled by /. To date,claims of SBC have been based on qualitative appearance, which isonly sometimes convincing [118]. The lack of SBC is reasonablegiven: (a) the high crack tip strain gradient which could promote acomplex slip structure, (b) evolution of planar slip bands duringdiscontinuous cracking into a dynamically recovered dislocation cellstructure, as reported for fatigue in several Al alloys [117,121–123],and the likely impact of atomic hydrogen trapped at such cellboundaries [114].

4.1.3. MSC growth rate variability4.1.3.1. Experimental variability. Statistical analysis of the da/dNversus DK data in Figs. 11 and 12 affirms the similitude betweenMSC data sets. Values of mean and SD for three of the eight setsof da/dN measurements (Regular-200 MPa, EXCO-200 MPa, andPristine-276 MPa) are presented in Table 2 for specified DKintervals. Also included is the number of data points used in thecalculations and ±percent variation about the mean (2SD/mean).

Fig. 16. Fatigue crack growth rate versus DK from marker-band analysis of a 7075-T651 regular pit specimen tested at rmax = 200 MPa and R = 0.5 in water vaporsaturated N2. Data are gathered along the different vectors shown in Fig. 7 at theintersection of either the actual marker-band or an elliptical fit.


Based on the Kolmogorov–Smirnov (K–S) test (where statisticalsignificance, p = 0.05), all but two individual da/dN sets (the Regu-lar-200 MPa at 1 and 2 MPa) are well described by a normal distri-bution, as such the use of mean and standard deviation analysis isjustified [124]. Additionally, mean and SD are presented (Table 2)for a collective data set of da/dN measurements from all eight testconditions (Fig. 12). These mean values are similar to those of theindividual datasets and the variability is not increased. At ap = 0.05, two-sample t-tests (or Mann–Whitney Rank Sum testsfor non-normal distributions) demonstrate no significant differ-ences in the mean (or median) values between the individual setsand the collective set at each DK. From these statistical compari-sons, it is concluded that stress intensity range provides an effec-tive similitude description of MSC da/dN for these three differentcrack formation sites. These substantial distributions of crackgrowth rate in each collective bin of near-constant DK representedin Table 2 provide a basis for an empirical-statistical simulation ofgrowing MSC front shape through the peak aged 7075 microstruc-ture, perhaps using Monte-Carlo selection. Note that three of thecollective distributions failed the K–S normality test; as such amore rigorous statistical representation is necessary.

The growth rate variability reported in Table 2 and Fig. 8 is dueto crack-to-crack differences in growth rate plus microstructure in-duced variation along a single crack perimeter-path. The origin ofthe latter is illustrated in Fig. 7 where the bars highlight crack frontundulations attributed to the crack interaction with microstructurefeatures that increase (or decrease) the local damage resistanceand/or driving force. Marker-band growth rate data for a singleRegular-200 MPa crack path measured along vector 1 (Fig. 7), arereported in Fig. 16. Crack front irregularity is eliminated by quali-tatively fitting ellipses to the marker-bands (white-dashed lines inFig. 7) and gathering growth rates at the intersection of the ellipsesand vector 1. These ellipse data in Fig. 16 show limited variationalong a single crack path. While this smoothing technique reducesvariability, it does not represent true MSC growth. To quantify thevariation associated with the yellow bars in Fig. 7 and determinethe influence of vector selection on mean behavior, da/dN is gath-ered along two additional vectors (2–3, dashed; Fig. 7). Growthrate data from vectors 2–3 illustrate substantial point to point var-iation (�100%), similar to the maximum variations reported in Ta-ble 2 and Fig. 6. The source of the additional �50% variation in thecombined data sets can be attributed to more severe undulationsthan reported in Fig. 7 or increased variability inherent in forminga single dataset from multiple crack paths. The results presented in

Table 2, and Figs. 11, 12, 15 and 16 can be compared to microstruc-ture-scale models of fatigue damage to provide insight regardingthe impact of grain-scale and 2nd phase effects on the localda/dN variation.

4.1.3.2. Stress intensity factor approach. Johnston and coworkersproposed that variability in MSC da/dN is due to the effect of grainorientation on local plasticity and shielding by crack-wake closure[41]. A three-dimensional finite element analysis including grainorientation dependent slip modeled elastic–plastic crack tip open-ing, equivalent plastic strain, and opening stress for separate grainsin 7075-T651 [41]. Opening stresses were coupled with standardDKeff calculations, which established local da/dN from closure-free(R P 0.5) long crack data [41,50]. Grain orientation dependent de-gree of closure produced only ±30% variation in da/dN at R = 0.05(Fig. 9 of Ref. [41]). Wang et al. performed a two-level factorial de-sign-of-experiments analysis of the effects of microstructure-scaleparameters on local da/dN using a similar FEA-based model ofcrystal plasticity-sensitive crack opening stress during cyclic load-ing [125]. Results suggest that constituent particle size and modu-lus, grain boundary mis-orientation angle, and number of activeslip systems cause a � 15% variation in local da/dN (Table 3, Ref.[125]). Each input was generally extreme to elicit discernabletrends and as such, the �15% variation likely represents an upperlimit [125]. In contrast to these closure-based models of micro-structure-scale variability, the variation in marker-band MSCda/dN for a given DK is ±150% (Table 2, Figs. 12 and 16), suggestingthat this closure model does not capture the dominant microstruc-ture effect on MSC rates for the present study. Moreover, the cur-rent experiments were performed at R = 0.5 where plasticityinduced crack closure is likely a less significant factor.

Johnston et al. reported a ± 80% variation about the mean peakequivalent plastic strain (ep�max) accumulated in five separate sin-gle grain orientations by load cycling [41]. Cyclic plastic strainrange (Dep) likely controls process zone damage and thus da/dN;however the functional dependence of da/dN on either Dep orep�max is unknown. If da/dN change scales with ep�max, then thepredicted variation in MSC rate (±80%) is consistent with a portionof the experimental variability quantified in Table 2. The remainingdifference between the FEA-crystal plasticity models and observedvariability may be due to factors such as roughness-based closure,crack deflection, and strain range concentration due to near-grainboundary deformation, constituent particle clusters and surround-ing hard or soft grains [72,81,125,126].

4.1.3.3. / Approach. Grain level variations in flow stress could affectda/dN through crack tip opening displacement, Eqs. (4)–(7). Anupper bound Taylor factor analysis for an fcc crystal suggests thatgrain-to-grain variation in flow strength is ±20% for uniaxial load-ing [127]. This difference results in +70% higher and �20% lowerlevels of the Shyam parameter (/c /m rys) for a ‘‘Regular Pit’’stressed at rmax = 200 MPa, as well as +25% and �20% forrmax = 100 MPa. The MSC growth rate results in Fig. 15 show thatthese variations in driving force do not result in changes in da/dN which are significant compared to the measured variability.While not predicted by a continuum Taylor factor model, a ±50%variation in rys results in +180% higher and �50% lower levels ofthe /c /m rys for a ‘‘Regular Pit’’ stressed at rmax = 200 MPa, as wellas +110% and �50% for rmax = 100 MPa. A plus/minus factor of twovariation in /c /m rys only explains about one-third of the da/dNvariability illustrated in Fig. 15.

Grain level three-dimensional crystal plasticity FEA models ofmicrostructure-based variation in /c provide results which can becompared to the current experimental data [6,37–39,43,44]. John-ston found a 30% grain-to-grain variation in /c. If da=dN � /0:77

c

Fig. 17. Measured MSC growth rates correlated with the driving force parameter of /c /m rys proposed by Shyam et al. [48,49], and compared to the long crack trend lines(dashed) marked 1 and 2 which are replotted from the corresponding DK-based trends in Fig. 11 using Eq. (2). (For interpretation to colors in this figure, the reader is referredto the web version of this paper.)


(Fig. 14), then this difference leads to ±25% predicted variation inda/dN. Simonovski reported up to a 4-fold difference in /m between‘‘soft’’ grain clusters proximate to the crack tip producing high strainlocalization (high /m) and ‘‘soft’’ grains away from the crack. This 4-fold difference results in 3–4-fold differences in da/dN, which alignwith the large variation in experimental MSC da/dN seen in Fig. 14.However, this model was developed for monotonic loading, and thelocal texture and work hardening responses of 7075-T651 and 316Lsteel may yield different /c variation. The effect of such heteroge-neous-local microstructure on /c and /m must be established andrelated to da/dN by a damage-mechanism informed version of therelationship in Eq. (7).

4.2. Prognosis significance

Aircraft teardowns [128,129] and failure analyses [17] establishthe relevance of corrosion-formed fatigue for airframe prognosis.Four aspects need to be addressed before prognosis of corrodedcomponents replaces the current remove-when-detected approach[130,131]: (1) a corrosion topographic metric, (b) high resolutionnon-destructive inspection (NDI) techniques to characterize thiscorrosion metric, (c) a fatigue crack formation model, and (d) a sci-entifically validated MSC propagation rate model. In lieu of sophis-ticated NDI characterization, a two-dimensional corrosionmodified-equivalent initial flaw size (CM-EIFS), obtained via lim-ited testing of laboratory or service exposed fatigue specimens[9,10,84], can quantify the corrosion damage state. Recent workdemonstrated that a low cycle fatigue model quantifies crack for-mation about the perimeter of localized corrosion [54]. The presentstudy provides important data and insights regarding the form ofthe MSC propagation model.

The results of this study justify consideration of the followingapproach to determining an appropriate crack growth rate rela-tionship for MSC. As a first step, the long crack constant Kmax-decreasing DK method (or multiple sets of constant R-decreasingDK data) describes long crack growth rate behavior for a given al-loy-environment system, as shown by the trend lines and extrapo-lations 1–3 in Fig. 11 for 7075-T651. These data are transformed toan elastic–plastic /c basis using a continuum J-integral analysispertinent to a long crack (Eq. (2)); the resulting long crack trendis shown by the two solid-trend lines (1) and (2) in Fig. 14. Theselong crack da/dN are proportional to multiple power law-/c seg-ments which are in excellent agreement with the mean of theextensive MSC measurements plotted against the BCS dislocation

formulation of cyclic crack tip opening. This agreement in Fig. 14validates the hypothesis that the long crack trend is directlydescriptive of mean da/dN for an MSC, provided that /c is properlycomputed for the small crack using either BCS-type dislocationplasticity (Eq. (5)) or finite element crystal plasticity. The substan-tial amount of MSC da/dN data shown in Figs. 11 and 12, character-ized statistically in Table 2, provides the input distribution todescribe the variation in MSC da/dN for a given driving force, per-haps selected using Monte-Carlo selection. In this approach, the ef-fect of Kmax must also be considered [34–36], Fig. 17 shows that thetwo parameter /c /m rys driving force model does not provide thesame level of agreement between the continuum elastic–plastictransformation of long crack da/dN � DK data using Eq. (2) com-pared to measured MSC growth rates. While the uncertain extrap-olation of long crack da/dN obscures this comparison, themultiplicative effect of the cyclic and monotonic opening displace-ments which each depend on DK2 results in a sharp divergence inthe power law slopes of the long crack based growth trends.Additional research is required to establish the implicationsof this comparison to determination of the basic dependence ofda/dN on cyclic and maximum-monotonic crack tip openingdisplacement.

5. Conclusions

Extensive microstructure-scale fatigue crack (MSC) growth ratedata are reported for 7075-T651 stressed in moist air at 23 �C; fo-cused on cracks sized from 1 to 1000 lm, at several stress levels,for different corrosion morphologies, and for a pristine two-holedspecimen. These data allow for evaluation of various stress inten-sity (K) and crack tip opening displacement (/)-based driving forcemodels necessary for next generation prognosis of fatigue life. Thefollowing conclusions are established:

– A controlled fatigue loading sequence that systematically marksthe fracture surface, coupled with fracture surface microscopy,effectively quantifies the microstructure sensitive size and localshape of MSC progression from constituent particle and corro-sion pit sites in 7075-T651.

– Extensive MSC growth rate data for pristine and corroded spec-imens are successfully correlated in a single distribution usingcontinuum K-solution and dislocation-based / estimates; onlythe former accounts for crack geometry and stress concentra-tion gradient due to the 3-dimensional initiating feature.


– Mean rates of MSC growth are reasonably described by extrap-olations of high-constant Kmax long crack da/dN data, usingeither DK or DK � Kmax formulations.

– Mean rates of MSC growth are reasonably described by a dislo-cation-based / model that includes both cyclic and monotonicterms; this approach provides a promising framework to incor-porate local slip structure evolution and environmental degra-dation in a more fundamental damage mechanism-basedsmall crack growth theory.

– Fatigue crack growth rates vary by up to an order of magnitudeat fixed DK or cyclic-/, predominantly due to microstructuralinfluences that result in a locally irregular crack front.

– Literature models of grain-to-grain variability in da/dN basedon crack closure or slip-based crystal plasticity do not captureexperimental variability in crack growth rate.

– An elastic DK-based description of long crack da/dN data for agiven alloy-environment can be transformed to a continuumelastic–plastic /c basis to provide a mean crack growth ratedescription. Coupling mean rates with a statistical descriptionof microstructure sensitive variability, and dislocation or crystalplasticity-finite element modeling of component /c for non-continuum cracking, will enhance prognosis in the MSC regime.

Acknowledgements

This research was sponsored by the United States Air Force Re-search Laboratory (AFRL), Materials and Manufacturing Director-ate, and the University Corrosion Collaboration managed by theDoD Office of Corrosion Policy and Oversight through a fundingagreement administered by Valdez International Corporation.Drs. John Papazian and Elias Anagnostou of Northrop GrummanCorporation provided 7075-T651, as well as Northrop GrummanIndustry Liaison funding. Professors R.G. Kelly and J.R. Scully inthe Center for Electrochemical Science and Engineering at the Uni-versity of Virginia guided the controlled pit experiments and Dr.Scott Fawaz provided important insights on solid mechanics anal-yses. Mr. Phil Blosser and Mark Ruddell assisted with fatigueexperiments at AFRL.

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Effect of initiation feature on microstructure-scale fatigue crack propagation in Al–Zn–Mg–Cu