Meryl M. Hall, Jr.* Effect of cyclic frequency on fracture mode transitions during corrosion fatigue cracking of an Al-Zn-Mg-Cu alloy

Transcription

1 Corros Rev 2015; aop Original artile Meryl M Hall, Jr* Effet of yli frequeny on frature mode transitions during orrosion fatigue raking of an Al-Zn-Mg-Cu alloy DOI /orrrev Reeived Otober 7, 2014; aepted June 11, 2015 Abstrat: There are omplex issues remaining to be resolved before environment-assisted raking models an be inluded in strutural mehanis programs that are urrently used to analyze mehanial fatigue rak growth Considered here is the effet of yli frequeny on frature mode transitions that our during orrosion fatigue of high-strength Al-Zn-Mg-Cu alloys These alloys are used in ivilian and military airraft appliations where they are exposed to detrimental aqueous saline environments A previously developed ritial hydrogen at a ritial distane rak growth model is used to rationalize the observed transitions in rak-path fraturemodes, from intergranular (IG), to brittle transgranular (BTG), to dutile transgranular (DTG), as the alternating stress intensity fator and yli frequeny inrease beyond ritial values Corrosion fatigue rak growth rate data obtained on Al-Zn-Mg-Cu alloy 7017-T651 base metal and heat-affeted white zone metal tested in aqueous NaCl solutions over a frequeny range of Hz are analyzed For the white zone metal, dependene of the ritial rak veloity on the ritial frequeny, at whih the IG-BTG transition ours, undergoes an abrupt reversal as the ritial frequeny inreases above about 01 Hz Mehanisms potentially responsible for this hange in frequeny dependeny are disussed in the ontext of the ritial hydrogen model The transition from low to intermediate frequeny behavior is speulated to be due to a hange in the ritial distane from mirostrutural ontrol, for frequenies at or below 01 Hz, to ontrol by the ritial hydrogen riterion at higher frequenies The low frequeny behavior is disussed relative to the transition *Corresponding author: Meryl M Hall, Jr, MaRay Consulting, 1366 Hillsdale Dr, Monroeville, PA, USA, hallmm44@omastnet from stati load stress orrosion raking to low frequeny orrosion fatigue, whih ours as yli frequeny inreases above zero Keywords: aluminum alloy; orrosion fatigue; rak path; hydrogen embrittlement; modeling 1 Introdution 11 Available hydrogen embrittlement models Environmental effets on fatigue rak growth are urrently not inluded in ommerial frature mehanis based software suh as NASGRO (Southwest Researh Institute) and AFGROW (LexTeh, In), whih are used to analyze mehanial fatigue rak growth and frature of airraft omponents However, high-strength 7000-series aluminum alloys (Al-Zn-Mg-Cu) are used in ivilian and military airraft appliations, where they are subjet to aelerated fatigue raking when exposed to aqueous saline environments Inorporation of environmental effets requires that the rak advane mehanism be identified and that models be developed Gangloff (2003) summarized experimental data that support hydrogen embrittlement (HE)- indued raking of 7000 series aluminum alloys as the rak advane mehanism and hydrogen diffusion as the rate-liming proess for subritial rak growth A number of researhers (Gangloff, 2003; Gasem & Gangloff, 2000, 2001; Gingell & King, 1993, 1997; Green & Knott, 1989; Hall, 2014; Holroyd & Hardie, 1983; Kotsikos, Sutliff, & Holroyd, 2000; Mason & Gangloff, 1994) have explored HE models that assume rak advane is rate limited by the time for hydrogen to diffuse a ritial distane within the frature proess zone (FPZ), where the hydrogen reahes a ritial onentration

2 2 MM Hall, Jr: Effet of yli frequeny on frature mode transitions Gangloff (2003) summarized the funtional form of these ritial hydrogen models in a general expression for stati-load onstant-load stress orrosion raking (SCC) veloity given by da dt D C, D, E rit = ξ χ E rit χ C rit LS where ξ is a funtion of the variables, D E is the effetive hydrogen diffusivity, χ rit is the ritial hydrogen diffusion distane, C LS (H atoms/lattie volume) is the near-surfae diffusible (lattie) hydrogen onentration, and C rit is the ritial lattie hydrogen onentration at χ rit when rak advane ours Green and Knott (1989) developed a ritial hydrogen model to rationalize orrosion fatigue rak growth rate data They found that aluminium alloy 7475-T6 undergoes a transition in rak-path frature-mode from brittle transgranular (BTG) to dutile transgranular (DTG) at a ritial frequeny f rit Their model development assumes rate ontrol by hydrogen diffusion and predits that, as a onsequene, the ritial fatigue rak growth rate, at whih transition ours, is inversely proportional to f rit and is a funtion of the ratio C rit /C LS Their model equation is da d D C = E -1 rit 2 erf 1- N rit frit CLS In deriving their equation, Green and Knott followed the lead of Holroyd and Hardie (1983) by assuming that raks advane by an inremental distane Δa at eah load yle and that the ritial hydrogen diffusion distane is χ rit = (Δa/ΔN rit )N, where N = 1, and Δa/ΔN rit is the per yle rak advane inrement when the rak advanes Green and Knott ompare their data to their model and onlude that their model is onsistent with hydrogen diffusion as the rate ontrolling proess Aluminum alloy 7017-T651 base metal and heataffeted white zone metal also undergo transitions in frature modes, from intergranular (IG) to BTG then DTG (Holroyd & Hardie, 1983; Kotsikos et al, 2000) Corrosion fatigue data obtained on these alloy onditions are analyzed here using the ritial hydrogen model of rak advane developed below (1) (2) effets in software programs used to predit fatigue rak growth These issues inlude the following 121 Limitations of ontinuum models Bridging the gap between mehanisti understanding and engineering pratie requires that mehanisti understanding, formulated at the disloation, miro, and nano sales, ultimately must be expressible in the ontinuum variables and parameters that are aessible to the pratiing engineer The analyses performed here are based on priniples of ontinuum mehanis and therefore are not able to address details of the interations between rak tips and miron-sized mirostrutural features However, onsiderations of proesses that may our at the mirostrutural level may be used to rationalize data trends revealed by the ontinuum analyses An example of an effort underway to bridge the gap between mehanisti understanding and engineering pratie is the omputational modeling effort by Vashishta et al (2008) to model environmental raking (SCC) from moleular to ontinuum sales Over a length sale that extends from a fration of a miron to tens of mirons, whih is the range of rak inrements per yle disussed here, metals display a strong size dependene when deformed non-uniformly into the plasti range (Huthinson, 2000) Plasti behavior at this sale annot be haraterized by onventional plastiity theories beause they inorporate no material length sale and predit no size effet However, ontinuum theories of strain gradient plastiity are being developed in the literature in order to inorporate size dependene (Huthinson, 2000) Continuum expressions for the mehanial rak driving fore are expressed in terms of the applied stress intensity fator K and Rie s J integral These are measures of the rate with whih elasti energy stored in the linear elasti and elasti-plasti strain fields that lie beyond the FPZ may be released during rak advane This ontinuum approah is valid, regardless of the proesses taking plae within the FPZ, so long as the zone of plastiity that surrounds the rak tip is small relative to the rak size and relevant speimen dimensions 12 Issues for the appliation of HE models There are issues with the use of Eqs (1) and (2) that must be resolved before HE models of this type an be used as a basis for data analyses and inlusion of environmental 122 Effetive diffusivity The effetive hydrogen diffusivity D E is not well known as it is diffiult to measure due to the low solubility of hydrogen in aluminum and the presene of a large density of

3 MM Hall, Jr: Effet of yli frequeny on frature mode transitions 3 hydrogen traps in 7000-series aluminium alloys (Sully, Young, & Smith, 2000) Test results are quite variable due in part to the formation of surfae oxides, whih are diffiult to avoid due to the high reativity of aluminium (Sully et al, 2000) Moreover, within the FPZ of a propagating rak, hydrogen diffusion may potentially be affeted by dynami generation of disloation and vaany traps Smith and Sully (2000) onduted thermal desorption tests to identify the fration of hydrogen oupying trap sites in hydrogen-harged AA 2090 (Al-215Li-256Cu- 012Zr) They found that dynami straining at room temperature while athodially harging under reduing onditions inreased the post-test hydrogen desorption rate assoiated with disloations by a fator of about 7 for the peak-aged alloy ondition with a modest effet ( < 2 ) for the under-aged alloy However, the total onentration of atomi hydrogen as a fration of the total number of trap sites available was found to be only atom fration for harging of a pre-strained speimen at an applied potential of -1 V se (hydrogen fugaity of atm) This is signifiantly less than the hydrogen onentrations measured by Young and Sully (2003), who used nulear reation analysis to measure hydrogen onentration profiles at rak flanks near the tips of SCC raks They found hydrogen onentrations of atomfration near the surfae, just below the surfae oxide, and as muh as 03 atom-fration and as far as 1 μm below the surfae This apparent hydrogen solubility is 11 orders of magnitude greater than what an be aounted for by saturation of interstitial and mirostrutural traps disussed by Smith and Sully Young and Sully speulate that the apparent hydrogen solubility of this magnitude may be due to the trapping of hydrogen by orrosioninjeted vaanies Birnbaum et al (1997) eletrohemially introdued very large onentrations of hydrogen in high purity aluminum and found that hydrogen was trapped at vaanies that entered with the hydrogen in a ratio of one hydrogen atom for eah injeted vaany They determined that the vaanies and hydrogen atoms formed Va-H omplexes having a binding energy of 461 kj/mol and that lusters of these omplexes formed platelets on the {111} slip planes, the presene of whih may assist transgranular raking by initiating miro-raks ahead of the maro-rak tip Lu et al, (2002) and Lu and Kaxiras (2005) onduted first-priniple alulations for aluminum base metal that demonstrate that Va-H lusters may form ontaining one or more H atoms (as many as 12), with a binding energy for the first H atom omparable to or greater than that of a disloation in aluminum (~35 kj/mol; Smith & Sully, 2000) Then, the ompetition between disloations and vaanies for hydrogen may favor vaanies due to their large number density and potential trapping apaity Kato, Iwakiri, and Morishita (2009) and Fukai (2003) onduted first-priniple alulations that show that vaany onentrations of atom-fration an be stabilized by hydrogen at 27 C (300 K) by forming Va-H lusters If this proess is ative for the introdution of hydrogen eletrolytially, this ould potentially aount for the apparent hydrogen solubility approahing 1 atom fration The relevane of this disussion to effetive diffusivity is that, aording to Lu and Kaxiras, the lattie mobility of H atoms in aluminum is not impeded by H trapping by mobile vaanies Hydrogen mobility may be enhaned when greater than one H atom is trapped by a vaany Moreover, given that H atoms and vaanies are ogenerated, trapping of H by vaanies may be immediate As the number of Va-H lusters may be signifiantly greater than the number density of disloation trapping sites, even under dynami straining, Va-H trapping is expeted to be ontrolling so that dynami generation of disloations at a propagating rak tip is not expeted to impede H mobility The formation of Va-H lusters provides a rationale for the very large rak tip hydrogen onentrations reported by Young and Sully and resolves the problem of how a suffiiently high H onentration an be attained in order to embrittle Al alloys, for whih the lattie hydrogen solubility is extremely low Hydrogen permeation measurements, suh as those of Huang, Nakajima, Nishikata, and Tsuru (2003), are needed on straining eletrodes in environments typial of propagating rak tips in order to evaluate these possibilities 123 Critial distane Independent knowledge of χ rit for SCC and CF rak advane in a hydrogen produing environment has long been an issue for understanding and development of HE models In modelling SCC using ritial hydrogen models, it is ustomary to assume that the ritial hydrogen onentration is attained at a fixed distane ahead of the propagating rak Moody, Stoltz, and Perra (1985) and Hall, Symons, and Kerns (1992) showed that this fixed distane is the grain diameter for IG raking of hydrogen pre-harged speimens of high-strength nikel base alloys However, Page and Gerberih (1982) showed that this distane may be muh smaller when hydrogen enters through the surfae of a sharp noth Based on an analysis of stati-load hydrogen-environment SCC data obtained

4 4 MM Hall, Jr: Effet of yli frequeny on frature mode transitions on a broad seletion of high-strength alloys having hydrogen diffusivities over six orders of magnitude, Gangloff (2008) onluded that χ rit is < 1 μm when hydrogen enters through the rak tip In modelling orrosion fatigue rak growth in the Paris regime, it is ustomary to assume per yle rak advane and equate χ rit to the per yle inrement in rak length Δa/ΔN Early modelling and data analyses (Holroyd and Hardie, Green and Knott, Gingell and King) assumed that χ rit is the hydrogen diffusion distane over whih the rak tip onentration C exeeds a ritial value C rit suffiient to sustain rak advane by a given frature mode Transitions in frature mode our when the hydrogen onentration at a distane Δa/ΔN rit no longer exeeds the C rit neessary to sustain rak growth by that frature mode This assumption is adopted here with an additional ondition that C rit is a funtion of the applied stress intensity fator K max It has been proposed [Gasem and Gangloff, Kotsikos, Sutliffe and Holroyd (KSH)] that χ rit is equal to the distane to the loation of maximum tensile and hydrostati stresses ahead of the rak tip, whih is at a distane of approximately 2 rak tip opening displaement (CTOD) However, Gasem and Gangloff pointed out that this assumption does not aount for omparisons among the data obtained on alloys having different yield strengths Gingell and King (1997) onjeture that hydrogen will be driven to regions of high hydrostati stress ahead of the rak tip when disussing the effet of stress on diffusion; however, this plays no part in their model development and data analysis In an earlier paper (Gingell & King, 1993), they ompare measured ritial values of Δa/ΔN to alulated CTODs and onlude that the ritial ondition for transition of rak path from IG to BTG is dependent on the per yle hydrogen diffusion distane, not on the position of maximum stress KSH (2000) equated the hydrogen diffusion distane 4 D / f to 2 CTOD and onluded E 2 that K ~1/ f, whih they onsider is supported by rit rit analysis of their data However, similar omparisons of the Holroyd and Hardie (HH) and KSH data, whih are provided here in Setion 30 below, supports the Gingell and King onlusion that the maximum stress assumption is not supported by the data Another possibility is that χ rit may be a fixed distane established by mirostrutural features, suh as the size of a grain (faet, subgrain) in the ase of IG raking, and the size and spaing of preipitates and disloation band spaing in the ase of TG raking Davidson and Lankford (1985) onluded that the relevant mirostrutural features influening transgranular fatigue rak propagation in AA 7075-T651 are the intermetalli (IM) partiles, whih provide obstales to disloation movement and thereby limit slip distanes Lankford and Davidson (1983) performed detailed fratographi analyses of AA 7075-T651 to haraterize striations found on fatigue surfaes formed in moist air and for ΔK below the Paris regime They onluded that under these onditions, 1) fatigue rak growth is intermittent (not yle-by-yle), 2) rak growth is a two-step proess of rak tip blunting followed by an inrement of brittle rak advane, and 3) striation spaing orresponds to an inrement in rak advane The effet of the moist air environment is to redue the level of rak blunting required to advane the rak Davidson and Lankford s results provide guidane for interpreting trends in the HH and KSH data 124 Near-surfae and ritial hydrogen onentrations There has been a lak of independent knowledge of the ratio C rit /C LS as both C rit and C LS are relatively inaessible When seeking to validate Eqs (1) and (2) in the past, the ratio C rit /C LS has been treated as an adjustable parameter Then, using arbitrarily hosen values of C rit /C LS and equations of the Eq (1) type, measured values of SCC rak veloity da/dt an be used to obtain the ratio D E /χ rit The results are then used either to obtain estimates of χ rit using the best available estimate of D E (Gangloff, 2003) or to obtain estimates of D E using assumptions regarding the magnitude of χ rit (Holroyd & Hardie, 1983) These approahes to validation are, of ourse, dependent upon assumptions for whih there is muh unertainty More reently, Hall and Symons (2001) and Hall (2011, 2014) developed an expression that relates C rit /C LS to θ rit /θ TS, where θ rit is the ritial hydrogen oupany of trap sites lying along a prospetive frature interfae, and θ TS is the hydrogen oupany of near-surfae hydrogen trap sites In this expression, θ TS ats as a proxy for the near-surfae diffusible hydrogen θ LS, whih establishes the hydrogen gradient that drives diffusion within the FPZ Hall and Symons (2001) developed a phenomenologial interpolation expression for θ rit based on an analysis of HE data obtained by Symons (1999) on a hydrogen-harged high-strength Ni alloy that undergoes IG frature θ rit KK - = K -K H-rit 1-, H-rit Where K is the applied stress intensity fator, K is the inert environment frature toughness, and K H-rit is the lower-bound hydrogen-affeted frature toughness K H 2 (3)

5 MM Hall, Jr: Effet of yli frequeny on frature mode transitions 5 This equation says that the ritial interfaial hydrogen overage dereases as the applied stress intensity fator inreases, from a maximum of θ rit = 1 when K = K H-rit, to a minimum of θ rit = 0 when K = K Assuming that during load yling rak advane ours at the maximum applied stress intensity fator, appliation of this equation to fatigue rak growth is aomplished by inserting K = K max Appliation of this equation to high-strength aluminum alloy frature data has not been investigated and would be diffiult to do so given the low solubility of matrix hydrogen and the overwhelming density of moderate to strong hydrogen traps However, Hall (2012) showed that a similar interpolation equation an be developed based on the energetis of hydrogen-affeted interfae deohesion Although Dadfarnia et al (2008) s development provides an interpolation expression for θ rit having a more fundamental basis, Eq (3) is used here as the two equations are similar, having the same limiting values, but Eq (3) better fits the data that were used to develop the equation With this independent knowledge of θ rit, equations of types (1) and (2) an now be evaluated as funtions of K (SCC) and K max (CF) one a value for θ TS is established 125 Oupany of near-surfae trap sites as a proxy for oupany of near-surfae normal interstitial lattie sites Hydrogen oupany of near-surfae trap sites θ TS was hosen as a proxy for the oupany of normal interstitial sites θ LS due to the diffiulty in measuring interstitial hydrogen in aluminum and its alloys However, measurement of the total (lattie plus trapped) hydrogen at a rak tip allows estimates of θ LS by assuming the equilibrium trapping theory of Oriani (1970), whih an be expressed as θ θ T L = K, T (4) θ θ T L 1-1- Where K T = exp(δh B /RT), and ΔH B (a negative quantity) is the trap binding energy Rearranging Oriani s equation, θ LS an be expressed as θ LS θ / K TS T = 1- θ + θ / K TS TS T This equation shows that θ LS 1 as θ TS 1, whih, aording the disussion above, appears to be a possibility if Va-H lusters are formed at a surfae where orrosion-injeted vaanies and eletrolyti hydrogen are being absorbed simultaneously (5) 2 Model development 21 Hydrogen embrittlement model Hall (2011) developed a ritial hydrogen SCC model based on the following assumptions: 1 Embrittlement ours when hydrogen is diffusively segregated to and trapped at prospetive frature interfaes within the FPZ 2 Craks advane when hydrogen overage of a frature interfae at a ritial distane equals a ritial value 3 The ritial hydrogen overage is a dereasing funtion of inreasing applied K 4 Crak advane is rate limited by hydrogen diffusion 5 Diffusible and trapped H are in thermodynami equilibrium 6 Craks advane steadily and quasi-ontinuously In order to make model development tratable, marorak growth is treated as quasi-ontinuous for onstant ΔK fatigue loading This means that, although mirorak growth may our intermittently, individual transient orrosion events, whih generate the rate-limiting hydrogen absorbed into the FPZ, may ombine to establish steady values within the FPZ of a propagating marorak Kolman and Sully (1999) showed experimentally that overlapping orrosion urrent transients due to sporadi intermittent events may sum to establish a ondition of quasi-ontinuous ativation of the rak tip, onsistent with the steady-state, quasi-ontinuous rak propagation assumption The distribution of hydrogen within the FPZ an be predited by adapting an expression derived by Atkinson (1971) for solute onentration ahead of a thin, plate-like preipitate growing by diffusion of solute atoms into the tip of the preipitate Adapting Atkinson s expression (Hall, 2014), the hydrogen onentration at a distane χ from the tip of a rak advaning steadily and quasiontinuously is given by ( ) C ( σ, χ, a ) = C ( σ)erf χa /D (6) L LS E Where C L is the diffusible hydrogen onentration (H atoms per lattie volume) at χ, C LS is the diffusible hydrogen onentration near surfae, ȧ is the rak veloity, D E is the effetive hydrogen diffusivity, and σ is the hydrostati stress within the FPZ This equation was derived while assuming that the diffusion of H within the FPZ is driven by a onentration gradient, only, and that D E is not a funtion of position within the FPZ and is not affeted by the dynami generation of hydrogen traps The hydrostati stress within

6 6 MM Hall, Jr: Effet of yli frequeny on frature mode transitions the FPZ inreases the solubility of hydrogen due to elasti expansion of the lattie (Wriedt & Oriani, 1970) It is assumed that, due to reep relaxation of stress to a stress level equal to or perhaps greater than the nominal yield stress, there is no signifiant stress gradient within the FPZ This assumption is onsidered to be aeptable for appliation to materials that undergo small-sale transient or steady-state reep onfined to the FPZ Polyanskii et al (1990) obtained reep data for high-strength aluminum alloys tested in NaCl solutions These data show that room temperature reep ours at applied stresses greater than the yield stress, and that the yield strength inreases with inreasing reep strain This means that the stresses within the FPZ will undergo transient relaxation to a stress at or above the original yield stress and may be weakly dependent on the rak veloity (Hall, 2008a) Then, the assumption of a relaxed, low stress gradient within the FPZ may be appropriate for appliations to steady-state rak growth By assuming that sustained steady rak growth requires that the hydrogen onentration within the FPZ reah a ritial value C rit at a ritial diffusion distane χ rit, Eq (6) an be inverted to obtain an equation for the rak veloity 2 D E -1 C erf 1- rit a = χ C (7) rit LS This equation is a speifi expression of the more general Eq (1) Further assumptions are that embrittlement ours when H is diffusively segregated to and trapped at prospetive frature interfaes within the FPZ, and that trapped and diffusible hydrogen are in thermodynami equilibrium With these assumptions, Hall and Symons (2001) and Hall (2011), showed that Eq (7) an be rewritten as D 2 E θ / θ erf rit TS χ 1-θ rit rit a = (8) Due to a misreading of Atkinson s manusript, previous versions of this equation mistakenly inluded a fator of 4D E, Hall and Symons (2001) and Hall (2011, 2012) This equation is adapted for modeling orrosion fatigue rak growth by noting that a 1 a D 1- θ / θ N f t f χ 1-θ rit rit E -1 rit TS = = erf 2 In this equation, χ rit is onsidered to be the per yle hydrogen diffusion distane, whih ours in an elapsed (9) time Δt = 1/f These equations are impliit funtions of the applied K (SCC) or K max (CF) through the dependene of θ rit on these variables (Eq 3) They predit a rak growth threshold, that is, ȧ and Δa/ΔN 0, as θ rit θ TS or aording to Eq (3), K max K H-rit As θ rit 0, that is, K max K, the equations predit that Δa/ΔN rapidly inreases and beomes unbounded when K max = K When χ rit is a fixed dimension, independent of yli frequeny, Δa/ΔN is inversely proportional to f, and Δa/Δt = f Δa/ΔN may be independent of f (Eq 9), provided that the inverse error funtion fator is independent of f When χ rit equals the per yle inrement in rak growth a 1- θ / θ = N D E erf -1 rit TS f 1-θrit (10) When applied to ritial onditions of Δa/ΔN and f for frature mode transition, this equation is, within a fator of 2, equal to Green and Knott s Eq (2) Note that this equation predits that the rak veloity Δa/Δt inreases in proportion to f provided that the inverse error funtion fator is independent of f An expression for the oupany of near-surfae hydrogen traps θ TS an be obtained by rearranging Eq (9) and substituting χ rit for Δa/ΔN θ TS θrit = 1-(1- θ )erf χ rit rit f DE (11) Note that, when θ rit is obtained using Eq (3) and the experimentally determined values of K max, K H-rit, and K are used in the analysis, the only adjustable parameter in Eq (11) is the effetive hydrogen diffusion oeffiient D E Eqs (9 11) are general and an be used to model orrosion fatigue rak growth assuming rak growth by a ritial hydrogen mehanism An unstated assumption is that these equations apply to rak growth at onstant ΔK As disussed below, additional onsiderations are required in order to apply these equations to an analysis of frature mode transitions, for whih ΔK rit is not onstant but dereases with inreasing f rit 22 Ative surfae area fration The above disussion assumes metal dissolution and hydrogen prodution ours at an eletrohemially ativated metal surfae Surfae ativation ours due to dynami straining at the rak tip, whih exposes new reative metalli surfaes by the rupture of protetive

7 MM Hall, Jr: Effet of yli frequeny on frature mode transitions 7 oxides, when they are present, and by exposure of emerging disloations and slip lines (Despi, Raiheff, & Bokris, 1968; Haruyama & Asawa, 1973; Hoar & West, 1962; Raiheff, Damjanovi, & Bokris, 1967), with or without the presene of a protetive surfae oxide To aount for the simultaneous effets of rak tip strain rate and repassivation rate on rak tip orrosion ativity, Hall (2009) introdued the onept of an equivalent ative surfae area fration The onept is based on an assumption that the anodi urrent density of a partially ativated surfae i a an be expressed as a produt of the urrent density of the fully ativated surfae i a and the ativated surfae area fration A * Operationally, the magnitude of A * an be obtained from measurements on a straining eletrode using A ( t, ε ) i ( t, ε )/ i, where ε a a is the applied tensile strain rate In priniple, i is a material property that is dependent on material, temperature, a and environment; is proportional to the exhange urrent density; and is a funtion of the usual eletrohemial variables (see eg Anderko, 2010) Ative surfae area fration is used to greatly simplify the omplex oupling of surfae reation with near-surfae lattie onentration θ LS, whih an be expressed as θ = A θ, where θ is the near-surfae hydrogen overage of normal interstitial lattie sites when the surfae is LS LS LS fully ativated Hall (2009, 2014) showed that, for quasisteady rak growth, A * attains a steady value given by γε/k A = S 1 + γε /k (12) where k is the time-based repassivation rate onstant, and γ is the strain-based surfae ativation rate onstant This equation an be applied to yli loading assuming that the magnitude of ε is onstant during up- and down-load halfyles and that the rak tip surfae is ativated during both half-yles For large strain rates suh that γε /k 1, the ative surfae area fration approahes unity, that is, A 1 S When γε /k 1, A γε /k, and approahes 0 when ε 0 S Note that, for a propagating rak, there is a omponent of CTSR due to rak advane that is proportional to the rak veloity (Hall, 2008a,b), so that ε, and therefore A, are not S 0, even for a statially loaded propagating SCC rak Note that derivation of this equation does not aount for any effets CTSR may have on rak tip hemistry, whih ould affet the repassivation rate onstant k 23 Repassivation rate onstants An issue for this approah is how to establish the rate onstants in Eq (12) The strain-based ativation rate onstant has a value 0 γ 1 If it is assumed that all of the rak tip streth goes to reate additional ative surfae, γ = 1 The time-based repassivation rate onstant k is ustomarily obtained from transient urrent deay experiments in whih bare metal is exposed suddenly to an environment thought to be representative of the rak tip hemistry (Al -3, Cl -, CrO 4-2, ph) and eletrohemistry (rak tip potential, whih determines the hydrogen overpotential) As disussed above, a preferred test method for obtaining the repassivation rate onstant is to measure, as a funtion of onstant applied strain rate, the transient and steady-state orrosion urrents established on a straining eletrode rather than the ustomary stati eletrode; see for example, Haruyama and Asawa (1973) Unfortunately, straining eletrode tests of this kind have not been performed on 7000 series aluminum alloys, and there is limited knowledge regarding the environment at the tip of a propagating fatigue rak There is a limited number of experiments in whih rak tip hemistry and eletrohemial potential have been determined The experimental methods require speialized equipment and are ostly in terms of time and resoures to ondut Moreover, appliation of experimental results has limitations as rak-tip hemistry may be dependent on rak tip opening, rak length, stress ratio, and yli frequeny, greatly expanding the number of variables that an be haraterized Turnbull (2001) has reviewed modelling of the hemistry and eletrohemistry of rak tips and onludes that rak hemistry modeling is at the stage where the primary unertainty in predition should be assoiated only with the pauity of data for the input parameters However, in their urrent state of development, these omputational models are realistially useable only by speialists in eletrohemistry having omputational skills Having neither measurements nor alulations of rak tip hemistries for the HH and KSH alloys and environments, estimates for k must be obtained using the limited experimental measurements of rak tip hemistry, eletrohemial potential, and repassivation rate data available on omparable 7000 series alloys Cooper and Kelly (2007) experimentally haraterized the Cl - onentration, ph, and eletrohemial potential within the rak enlave of a propagating SCC rak formed in aluminum alloy 7050 in an aqueous solution of 005 m NaCl+05 m Na 2 CrO 4, ph 92, with an applied stress intensity fator of 14 MP m During an inubation period of slow rak growth (da/dt m/s), they found the rak hemistry to be omparable to the bulk hemistry However, after an inubation period of 4 50 h, the rak growth rate inreased by a fator of 38 (da/dt m/s) The rak hemistry

8 8 MM Hall, Jr: Effet of yli frequeny on frature mode transitions was quite different from the bulk: hloride inreased by a fator of 6 8 (03 m 04 m CI - ), ph dereased from 92 to 3, and the rak tip potential dereased to -085 V se while the applied (rak mouth) potential was V se They found that miroinjetion at the rak tip of the bulk hemistry having the hromate inhibitor (05 m Na 2 CrO 4, ph 92) dereased the rak veloity by 90% However, injetion of an aggressive low ph rak tip hemistry having an inhibitor (02 m AlCl 3 +1 m Cr 6+ as CrO 3 +Na 2 CrO 4, ph 31) prior to natural transition from slow to fast rak growth resulted in immediate (~10 min) rate inrease, by a fator of 65, to the fast rak growth rate These results show that hromates may not inhibit rak growth when a low-potential, aidi, rak tip hemistry is established Gasem and Gangloff (2001) report that low onentrations of hromate inhibitor did not inhibit rak growth when the bulk NaCl solution was aidified Gasem and Gangloff and Warner and Gangloff (2012) disuss the effet that yli frequeny (CTSR) may have on destabilization of inhibiting films, noting that there are ritial CTSRs above whih inhibitors are ineffetive The environment within a orrosion fatigue rak may not be as aggressive as that determined for an SCC rak Combining modeling and experimental data, Cooper and Kelly (2001) onlude that rak potential distributions are strongly dependent on size of the rak tip opening and the thikness of resistive salt-films that are presumed to form at the rak tip The IG SCC raks in the 7000 series aluminum alloys are very sharp (CTOD ~02 μm at 1 μm behind the rak tip) However, blunter raks having CTODs as large as predited by ontinuum mehanis do not generate as large a potential drop, and therefore, as aggressive a rak tip hemistry On the other hand, plasti straining of the rak tip is expeted to disrupt rak tip films at a rate determined by ΔK and yli frequeny, thereby inreasing the eletrohemial ativity of the rak tip, tending to reestablish a rak tip environment having a lower potential, onentrated Al -3 and Cl - and lower ph Therefore, measurements of repassivation rate onstants on open surfaes of stati eletrodes an only provide an estimate of repassivation rates appropriate to propagating SCC and CF raks Raetzer-Sheibe and Tuk (1994) obtained repassivation rate data on open surfaes of aluminum AA7010-T651 in hemistries and applied potentials omparable to that of the Cooper and Kelly rak tip measurements Using a mirotome to remove metal hips in situ, they measured transient urrent-time data on bared metal surfaes in an aqueous solution having 034 m NaCI adjusted with HCl to ph = 3 and with an applied potential of V se to V se, for whih the repassivation rate onstant an be determined to be 25 s -1 k 60 s -1 Based on the disussion above, these repassivation rate data, obtained without hromate inhibitor, are onsidered most appliable to the oluded rak tip hemistry of a fast propagating SCC rak Having no information to the ontrary, these data also are applied to the HH-KSH experimental results 24 Crak tip strain rate Aording to Eq (12), rak tip strain rate (CTSR) plays an important role in ativating a rak tip so that hydrogen may be evolved and absorbed into the FPZ Treating the instantaneous rak tip opening displaement (CTOD) δ as a gage setion, rak tip strain an be defined in terms of the streth ratio λ = δ/δ i, where δ i is the initial CTOD The Cauhy engineering extensional strain or nominal strain e an be expressed as the hange in CTOD Δδ divided by the initial CTOD as e δ δ = i = λ-1 (13) i δδ - δ i The Henky logarithmi strain or true strain ε is given by δ ε= ln = λ = + δ ln( ) ln(1 e ) (14) i These equations, respetively, represent the average nominal and true strains over the strain path In order to take into aount the influene of a non-linear strain path, the inremental form of Eq (14) dε = dδ/δ an be integrated to obtain a orret measure of the final strain An average yli rak tip strain rate (C-CTSR) an be defined in terms of both the nominal and true strains, Eqs (13) and (14), respetively Only the nominal strain is onsidered here as the nominal strain, defined in terms of the streth ratio λ, is onsidered to be more onsistent with an assumption that all of the rak tip streth goes to reate additional ative surfae Note that this approah will overpredit the true C-CTSR Lidbury (1983) provides a more extensive disussion of similar strain derivations by a number of researhers Considering the up-load half-yle having a rise time t r = Δt/2, where Δt = 1/f is the yli period, the average nominal C-CTSR an be expressed as e ( δ - δ )/ t δ/ t 2 δ/ (1- R ) 2 max min r r t = = 2 (15) δ δ δ min min 2-(1- R)

9 MM Hall, Jr: Effet of yli frequeny on frature mode transitions 9 where δ min = δ max [1-(1-R) 2 /2], and δ max = 2Δδ/(1-R) 2 Note that Δδ/Δt and Δδ are separately omplex funtions of f and ΔK when all omponents for a propagating rak are onsidered This equation is used here to evaluate Eq (12) for A * and to evaluate the C-CTSR orresponding to frature mode transitions 25 Adaption of the RDS equations for yli loading Rie and Sorensen (1978) and Rie, Drugan, and Sham (1980) developed ontinuum mehanis-based CODR and COD equations for a rak propagating in an elasti-ideally plasti (non-hardening) material These equations are onsidered to be appliable to high-strength, low-strain hardening aluminum alloys (yli strain hardening 006; Benson and Hanok, 1974) The Rie, Drugan, and Sham (RDS) equations, whih are appliable to monotonially inreasing load, an be expressed as and dφ α d J βσ o da λ EJ = + ln 2 dt σ dt E dt χ o σ o αχ d J βσ χ λ E J o φ= + 1+ ln σ 2 da E o χ σ o (16) (17) where J = K 2 /E for small-sale plastiity, a is the rak size, da/dt is the rak veloity, σ o is the yield stress, χ is the distane behind the rak tip, and E is the generalized elasti modulus The notation φ for COD is introdued in order to distinguish φ in the RDS equations for a propagating rak from the more ommonly disussed stationary rak CTOD, δ These equations were derived for χ 0 and are valid only for distanes less than an undefined fration of the plasti zone size χ/r P 1, where 2 R = λe J / σ Based on finite element analyses of an elasti-plasti rak propagating under small-sale plastiity P o onditions, RDS determined that α = 065, β = 546, and λ = 0235 RDS also proposed a COD riterion for sustained rak growth, whih is that a steadily propagating rak must maintain a geometrially similar profile This means that the rak must maintain a onstant COD φ at a distane behind the rak χ that is equal to the size to the FPZ This riterion is equivalent to an assumption that steady-state rak propagation ours at a fixed CTSR with a onstant rak opening angle given by φ /χ The first term on the RHS of Eq (16) represents the CODR due to monotonially inreasing the applied J at a rate dj/dt The seond term represents the CODR due to steady-state propagation of raks, with veloity da/dt, into the logarithmi strain field ahead of the advaning rak The applied tearing modulus introdued by Paris et al, (1979) is proportional to the fator dj/da in the first term on the RHS of Eq (17), that is, T app = (E/σ o )(dj/da) During monotoni up-loading, T app will attain a steady value equal to the materials resistane to tearing T mat (see Rie et al, 1980) When exposed to an environment that redues the magnitude of T mat, the rak COD will be redued In an aggressive rak tip environment, the material resistane may be redued to T mat = 0 suh that dj/da = 0 In this limiting ase, the COD is due solely to the seond term on the RHS of Eq(17), and the CODR is due solely to the seond term on the RHS of Eq (16) As disussed in Setion 33 below, these limiting ases have impliations for transitions from stati load SCC to low and intermediate yli frequeny orrosion fatigue Although Eq (16) has no provision for rate-dependent deformation or reep, it may be aeptable for appliation to materials that undergo small-sale reep onfined to the near-tip plasti zone In this ase, CODR due to smallsale reep is expeted to be muh less than that desribed in Eq (16) Modifiations are neessary in order to apply Eqs (16) and (17) to yli load Using a superposition argument, Rie (1967) determined, for a stationary rak, the relationships between monotoni and yli versions of the plasti zone size (PZS), CTOD, and strain variation ahead of a rak tip embedded in a yli plasti zone Rie showed that the needed modifiations an be aomplished by substituting ΔK for K and 2σ o for σ o, where σ o is the yli yield stress For yli loading, the RDS rak similarity riterion for steady rak growth is adopted by requiring that the C-COD range Δφ = φ max -φ min must remain onstant when evaluated at a distane χ behind the propagating rak, where χ is set equal to the FPZ size As disussed above, this may be either a fixed distane harateristi of the material or a variable distane equal to the per yle inrement in physial rak size Δa Note that the subsript refers to the RDS similarity riterion and should not be onfused with the subsript rit, whih refers to ritial onditions assoiated with frature mode transitions Adopting the above assumptions and using ΔJ = ΔK 2 /E (Anderson, 2005), Eq (16) beomes 2 2 φ ( χ ) α f K 2 βσ f χ o λ ln K = + 2 t 2E σ E 4χ o σ o (18)

10 10 MM Hall, Jr: Effet of yli frequeny on frature mode transitions and assuming per yle rak growth, Eq (17) beomes 2 2 α K 2βσ χ o λ K φ ( χ ) = + 1+ ln 2 2E σ E 4χ o σ o (19) Eq (18) shows that C-CODR is proportional to the yli frequeny f, χ, and a funtion of ΔK 2 The first term on the right hand side of Eq(19) is one-half of the stationary rak CTOD, whih is onsistent with Rie s superposition model, and the seond term is the rak opening due to rak advane by the distane χ Appliation of Rie s superposition methodology for extending Eqs (16) and (17) to propagating fatigue raks was introdued by Hall (2014) and, to the author s knowledge, has not been onsidered elswhere The validity of these equations rests with the justifiations given by Rie for his superposition arguments Rie and Sorensen (1978) provide a detailed disussion of the equation development and appliability of the rak similarity riterion for steady rak growth Although the derivation of their equations does not onsider the strain distribution ahead of a ylially loaded propagating rak, the analysis for a growing rak may be onsidered appliable when unloading strains are negligible Experimental support for the use of Eqs (18) and (19) is provided by omparisons, shown in Figure 1, of measured and predited COD profiles of propagating fatigue raks The measured fatigue rak profiles were obtained by Cooper (2001) on AA 7050-T651 fatigue raks grown at 10 Hz, R = 03, in air (ΔK = 133 MPa m) and in 005 m NaCl+05 m Na 2 CrO 4, ph 92 at E app = V se (ΔK = 123 MPa m) Shown for omparison to the CF rak profile is the predited C-COD obtained using Eq(19) and ΔK = 123 MPa m This figure shows that the predited C-COD profile (solid urve) is omparable to the measured fatigue rak profile data trend (dashed urve) Also shown is the measured COD profile of an IGSCC rak (K = 129 MPa m) grown by Cooper in the above environment The IGSCC rak profile is sharper, by more than an order of magnitude, than the measured and predited air and CF rak profiles Shown for omparison is the C-COD predited using only the seond term on the RHS of Eq (19) and using ΔK rit = 129 MPa m and plotted at χ rit = 24 μm (hoie of this distane is disussed below) As disussed above, use of only the term due to rak advane is appropriate for the limiting ase where the material resistane to tearing under rising load onditions T mat approahes zero due to exposure to an environment that suffiiently embrittles the FPZ This omparison suggests that orrosion fatigue raks may have similar profiles to stati load SCC raks for low yli frequenies, where CF and IGSCC rak veloities are omparable C-COD (fat) or COD (IGSCC) (µm) Air fat Corr fat IGSCC Eq (19) 2nd term Eq (19) Distane from rak tip (µm) Figure 1: Measured and predited yli rak opening displaement (C-COD) profiles of propagating fatigue and IGSCC raks obtained by Cooper (2001) on AA 7050-T651 The predited fatigue rak profile, obtained using Eq (19), is omparable to the measured fatigue rak profile data trend (dashed line) The losed symbol is the C-COD predited using only the seond term of Eq (19) Consideration of the separate effets that load variation and rak advane may have on CODR, COD and enviroment-assisted rak growth rate an be found only in a limited number of studies Somerday, Young, and Gangloff (2000) used Eq (16) to rationalize the separate effets of dk/dt and da/dt on environment-assisted raking of beta-titanium alloys during up- and down-load testing in aqueous NaCl Hall (2014) used C-CODR, Eq (18), to analyze the HH orrosion fatigue data 3 Data analysis and disussion 31 The HH and KSH data sets Detailed disussions of the CF experiments arried out by Holroyd and Hardie (1983) and Kotsikos et al (2000) an be found in the referenes Briefly, base and rerystallized heat-affeted white zone metals of aluminum alloy 7017 were tested at room temperature in ph 82 natural sea water and dry air (base metal) and in 25% NaCl+05% Na 2 CrO 4 solution aidified to ph 3 with HCl and laboratory air (white zone) Tests were onduted using a triangular wave form, R = 01, and frequenies from 01 to 70 Hz (base metal) and using a sinusoidal wave form, R = 01, and

11 MM Hall, Jr: Effet of yli frequeny on frature mode transitions 11 frequenies from 001 Hz to 10 Hz (white metal) Tests were onduted under load ontrol so that ΔK inreased during rak growth (base metal) and ΔK held onstant (white zone) The rolled plate base metal (T651) has an unrerystallized panake struture elongated in the rolling diretion Grain size information was not provided; however, a 7000 series alloy given a similar mehanial-thermal treatment has grain dimensions of 130, 60, and 18 μm in the L, T, and S diretions, respetively Craks were oriented so as to propagate in the rolling plane The frature surfaes denoted as IG showed equiaxed features measuring about 15±3 μm, whih suggests that the IG rak growth is along subgrain boundaries The heataffeted white zone metal has an equiaxed rerystallized struture with a grain diameter of 105±3 μm Craks were oriented so as to propagate within the thin heataffeted white zone metal separating the base and weld metal The frature mode transition data for both base and WZ metal are found in Table 1 Hall (2014) previously performed a detailed analysis of the HH base metal data The present analysis inludes the KSH data and is foused on additional aspets of the observed frature mode transitions 32 Values of material parameters used in data analysis Values of the parameters used in the data analyses are provided in Table 2 These values represent best estimates based on very limited independently determined information The plane strain elasti modulus E = E/(1-ν 2 ) = 723 GPa was determined using the tensile modulus E = 658 GPa reported for 7017-T651 by Ruiz and Elies (1997) and assuming that ν = 03 The yli yield stress was assumed to be equal to the monotoni yield stress based on the finding by Benson and Hanok (1974) that two aluminum alloys 7075-T6 and 6061-T651 showed stable yli behavior A yield stress of 435 MPa was reported by HH for the base metal The yield stress of the WZ metal is unknown and would be hard to measure due to its width of only 05 mm However, Bloem, Salvador, Amigó, and Vergara (2011) report miro-hardness of about VH for the volume of metal (WZ) that lies within 05 mm of the weld fusion line of an aluminum alloy 7020 weld, whih is approximately equivalent to a yield stress of MPa HH report an average value for K of 315 MPa m for the base metal data Holroyd (private ommuniation) onfirmed that K of 250 MPa m is representative of the WZ metal As there are no data available for K H-rit and having no better alternative, the apparent threshold values for K max of about 88 MPa m for the base metal and 111 MPa m for the WZ were used as default values The value for k of 25 s -1 from the Raetzer-Sheibe and Tuk data orresponding to a potential of V se was hosen as it onservatively represents the rak tip potential measured by Cooper and Kelly within 1 mm of the rak tip, where the rak tip hemistry is onentrated A value for the effetive hydrogen diffusivity was obtained from a ritial review by Young and Sully (2003) of the available diffusivity data They onlude that the Table 1: Critial onditions assoiated with transitions in rak-path frature-mode Base metal IG to BTG Base metal BTG to DTG WZ IG to BTG f rit 1/s ΔK rit MPa m Δa/ΔN rit μm/yle C-COD μm ΔK rit MPa m Δa/ΔN rit μm/yle C-COD μm ΔK rit MPa m Δa/ΔN rit μm/yle C-COD μm

12 12 MM Hall, Jr: Effet of yli frequeny on frature mode transitions Table 2: Values of parameters used in data analyses Base metal WZ E GPa k 1/s D E m 2 /s K MPa m K H-rit MPa m σ o MPa K MPa m K H-rit MPa m σ o MPa value of m 2 /s obtained from their isothermal desorption measurements is most representative of peak aged alloy 7050-T6 ondition Use of this value in the data analyses below is based on an assumption that dynami straining within the FPZ does not alter the hydrogen diffusivity, whih, as disussed above, is onjetured to be the ase when trapping by orrosion-injeted vaanies is dominant 33 Critial onditions for frature mode transitions Time-domain plots of the HH and KSH rak veloity data Δa/Δt obtained on base and heat-affeted white zone metals, respetively, an be found in their publiations Also found in the HH publiation are the IGSCC data obtained on the base metal The HH and KSH data are quite similar even though the base and white zone metal mirostrutures are quite different, yli wave forms are different, and the base metal test environment had no inhibitor, while the white zone environment inluded hromate inhibitor The data show that CF rak veloities are omparable and inrease with inreasing yli frequeny at similar rates at all values of ΔK For the lowest frequenies and K max values, the white zone CF rak veloities are omparable to the base metal SCC rak veloities Moreover, KSH note that at frequenies below 01 Hz, there are striations on IG-CF frature surfaes, similar to the ones observed by Samans (1980) on IGSCC frature surfaes of AA 7018 Based on high-resolution fratographi studies, Samans onludes that these are rak arrest markings rather than fatigue striations KSH speulate that, given the similarities in rak veloity and frature surfae striations and that these markings are not related to load yling, orrosion fatigue raks advane by an IGSCC mehanism for frequenies below 01 Hz Figure 2 is a frature mode diagram showing the ritial values of applied f and ΔK, for the HH and KSH data, orresponding to transitions in frature modes, from IG to BTG and then to DTG in the ase of the HH data Figure 2 shows that as the yli frequeny inreases (yle time dereases), dereasing the mehanial driving fore ΔK is required to sustain raking along the more brittle IG and BTG frature paths Above a frequeny of about 4 Hz, ΔK rit beomes less dependent on frequeny for the IG frature mode and approahes a value just above the ΔK used to fatigue pre-rak speimens (ΔK = 85 MPa m) An important onlusion that an be drawn from the data in Figure 2 and Eq (3) for θ rit is that as f rit inreases (and ΔK rit dereases) the hydrogen overage of grain boundaries θ int must inrease in order to satisfy the ritial hydrogen riterion θ int = θ rit Figure 3 shows that, for frature mode transitions from IG to BTG for both base and WZ metal, θ rit inreases from a value as low as 0002 atom fration, where ΔK rit has a maximum value of 22 MPa m, to a high value of 10 atom fration, where ΔK rit has a minimum value of 88 MPa m, as the yli frequeny inreases from 001 to 70 Hz This means that the ritial distane at whih θ rit is attained must derease as the K rit (MPaSrtm) IG Closed=base metal Open=white zone TGbrittle faets TG-dutile striations f rit (Hz) Figure 2: Crak-path frature mode diagram showing ritial values of f and ΔK assoiated with frature mode transitions for AA 7017-T651 base metal and heat effeted white zone metal tested in aqueous hloride solutions Transitions in frature modes, from brittle to more dutile, our as frequeny and ΔK are inreased above ritial values