Effect of cyclic frequency on fracture mode transitions during corrosion fatigue cracking of an Al-Zn-Mg-Cu alloy

1.1 Available hydrogen embrittlement models

Environmental effects on fatigue crack growth are currently not included in commercial fracture mechanics based software such as NASGRO (Southwest Research Institute) and AFGROW (LexTech, Inc.), which are used to analyze mechanical fatigue crack growth and fracture of aircraft components. However, high-strength 7000-series aluminum alloys (Al-Zn-Mg-Cu) are used in civilian and military aircraft applications, where they are subject to accelerated fatigue cracking when exposed to aqueous saline environments.

Incorporation of environmental effects requires that the crack advance mechanism be identified and that models be developed. Gangloff (2003) summarized experimental data that support hydrogen embrittlement (HE)-induced cracking of 7000 series aluminum alloys as the crack advance mechanism and hydrogen diffusion as the rate-liming process for subcritical crack growth. A number of researchers (Gangloff, 2003; Gasem & Gangloff, 2000, 2001; Gingell & King, 1993, 1997; Green & Knott, 1989; Hall, 2014; Holroyd & Hardie, 1983; Kotsikos, Sutcliff, & Holroyd, 2000; Mason & Gangloff, 1994) have explored HE models that assume crack advance is rate limited by the time for hydrogen to diffuse a critical distance within the fracture process zone (FPZ), where the hydrogen reaches a critical concentration.

Gangloff (2003) summarized the functional form of these “critical hydrogen” models in a general expression for static-load constant-load stress corrosion cracking (SCC) velocity given by

where ξ is a function of the variables, D_E is the effective hydrogen diffusivity, χ_crit is the critical hydrogen diffusion distance, C_LS (H atoms/lattice volume) is the near-surface diffusible (lattice) hydrogen concentration, and C_crit is the critical lattice hydrogen concentration at χ_crit when crack advance occurs.

Green and Knott (1989) developed a critical hydrogen model to rationalize corrosion fatigue crack growth rate data. They found that aluminium alloy 7475-T6 undergoes a transition in crack-path fracture-mode from brittle transgranular (BTG) to ductile transgranular (DTG) at a critical frequency f_crit. Their model development assumes rate control by hydrogen diffusion and predicts that, as a consequence, the critical fatigue crack growth rate, at which transition occurs, is inversely proportional to √f_crit and is a function of the ratio C_crit/C_LS. Their model equation is

In deriving their equation, Green and Knott followed the lead of Holroyd and Hardie (1983) by assuming that cracks advance by an incremental distance Δa at each load cycle and that the critical hydrogen diffusion distance is χ_crit=(Δa/ΔN_crit)N, where N=1, and Δa/ΔN_crit is the per cycle crack advance increment when the crack advances. Green and Knott compare their data to their model and conclude that their model is consistent with hydrogen diffusion as the rate controlling process.

Aluminum alloy 7017-T651 base metal and heat-affected “white zone” metal also undergo transitions in fracture modes, from intergranular (IG) to BTG then DTG (Holroyd & Hardie, 1983; Kotsikos et al., 2000). Corrosion fatigue data obtained on these alloy conditions are analyzed here using the critical hydrogen model of crack advance developed below.

1.2 Issues for the application of HE models

There are issues with the use of Eqs. (1) and (2) that must be resolved before HE models of this type can be used as a basis for data analyses and inclusion of environmental effects in software programs used to predict fatigue crack growth. These issues include the following.

2.1 Hydrogen embrittlement model

Hall (2011) developed a critical hydrogen SCC model based on the following assumptions:

1. Embrittlement occurs when hydrogen is diffusively segregated to and trapped at prospective fracture interfaces within the FPZ.

2. Cracks advance when hydrogen coverage of a fracture interface at a critical distance equals a critical value.

3. The critical hydrogen coverage is a decreasing function of increasing applied K.

4. Crack advance is rate limited by hydrogen diffusion.

5. Diffusible and trapped H are in thermodynamic equilibrium.

6. Cracks advance steadily and quasi-continuously.

In order to make model development tractable, macro-crack growth is treated as quasi-continuous for constant ΔK fatigue loading. This means that, although micro-crack growth may occur intermittently, individual transient corrosion events, which generate the rate-limiting hydrogen absorbed into the FPZ, may combine to establish steady values within the FPZ of a propagating macro-crack. Kolman and Scully (1999) showed experimentally that overlapping corrosion current transients due to sporadic intermittent events may sum to establish a condition of “quasi-continuous” activation of the crack tip, consistent with the steady-state, quasi-continuous crack propagation assumption.

The distribution of hydrogen within the FPZ can be predicted by adapting an expression derived by Atkinson (1971) for solute concentration ahead of a thin, plate-like precipitate growing by diffusion of solute atoms into the tip of the precipitate. Adapting Atkinson’s expression (Hall, 2014), the hydrogen concentration at a distance χ from the tip of a crack advancing steadily and quasi-continuously is given by

Where C_L is the diffusible hydrogen concentration (H atoms per lattice volume) at χ, C_LS is the diffusible hydrogen concentration near surface, a˙ is the crack velocity, D_E is the effective hydrogen diffusivity, and σ̅ is the hydrostatic stress within the FPZ. This equation was derived while assuming that the diffusion of H within the FPZ is driven by a concentration gradient, only, and that D_E is not a function of position within the FPZ and is not affected by the dynamic generation of hydrogen traps. The hydrostatic stress within the FPZ increases the solubility of hydrogen due to elastic expansion of the lattice (Wriedt & Oriani, 1970).

It is assumed that, due to creep relaxation of stress to a stress level equal to or perhaps greater than the nominal yield stress, there is no significant stress gradient within the FPZ. This assumption is considered to be acceptable for application to materials that undergo small-scale transient or steady-state creep confined to the FPZ. Polyanskii et al. (1990) obtained creep data for high-strength aluminum alloys tested in NaCl solutions. These data show that room temperature creep occurs at applied stresses greater than the yield stress, and that the yield strength increases with increasing creep 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 crack velocity (Hall, 2008a). Then, the assumption of a relaxed, low stress gradient within the FPZ may be appropriate for applications to steady-state crack growth.

By assuming that sustained steady crack growth requires that the hydrogen concentration within the FPZ reach a critical value C_crit at a critical diffusion distance χ_crit, Eq. (6) can be inverted to obtain an equation for the crack velocity

This equation is a specific expression of the more general Eq. (1).

Further assumptions are that embrittlement occurs when H is diffusively segregated to and trapped at prospective fracture interfaces within the FPZ, and that trapped and diffusible hydrogen are in thermodynamic equilibrium. With these assumptions, Hall and Symons (2001) and Hall (2011), showed that Eq. (7) can be rewritten as

Due to a misreading of Atkinson’s manuscript, previous versions of this equation mistakenly included a factor of 4D_E, Hall and Symons (2001) and Hall (2011, 2012).

This equation is adapted for modeling corrosion fatigue crack growth by noting that

In this equation, χ_crit is considered to be the per cycle hydrogen diffusion distance, which occurs in an elapsed time Δt=1/f. These equations are implicit functions of the applied K (SCC) or K_max (CF) through the dependence of θ_crit on these variables (Eq. 3). They predict a crack growth threshold, that is, a˙ and Δa/ΔN→0, as θ_crit→θ_TS or according to Eq. (3), K_max→K_H-crit. As θ_crit→0, that is, K_max→K_c, the equations predict that Δa/ΔN rapidly increases and becomes unbounded when K_max=K_c.

When χ_crit is a fixed dimension, independent of cyclic frequency, 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 function factor is independent of f. When χ_crit equals the per cycle increment in crack growth

When applied to critical conditions of Δa/ΔN and f for fracture mode transition, this equation is, within a factor of 2, equal to Green and Knott’s Eq. (2). Note that this equation predicts that the crack velocity Δa/Δtincreases in proportion to f provided that the inverse error function factor is independent of f.

An expression for the occupancy of near-surface hydrogen traps θ_TS can be obtained by rearranging Eq. (9) and substituting χ_crit for Δa/ΔN

Note that, when θ_crit is obtained using Eq. (3) and the experimentally determined values of K_max, K_H-crit, and K_c are used in the analysis, the only adjustable parameter in Eq. (11) is the effective hydrogen diffusion coefficient D_E.

Eqs. (9–11) are general and can be used to model corrosion fatigue crack growth assuming crack growth by a critical hydrogen mechanism. An unstated assumption is that these equations apply to crack growth at constant ΔK. As discussed below, additional considerations are required in order to apply these equations to an analysis of fracture mode transitions, for which ΔK_crit is not constant but decreases with increasing f_crit.

2.2 Active surface area fraction

The above discussion assumes metal dissolution and hydrogen production occurs at an electrochemically activated metal surface. Surface activation occurs due to dynamic straining at the crack tip, which exposes new reactive metallic surfaces by the rupture of protective oxides, when they are present, and by exposure of emerging dislocations and slip lines (Despic, Raicheff, & Bockris, 1968; Haruyama & Asawa, 1973; Hoar & West, 1962; Raicheff, Damjanovic, & Bockris, 1967), with or without the presence of a protective surface oxide.

To account for the simultaneous effects of crack tip strain rate and repassivation rate on crack tip corrosion activity, Hall (2009) introduced the concept of an equivalent active surface area fraction. The concept is based on an assumption that the anodic current density of a partially activated surface i_a can be expressed as a product of the current density of the fully activated surface ia∗ and the activated surface area fraction A^*. Operationally, the magnitude of A^* can be obtained from measurements on a straining electrode using A∗(t, ε˙)≡ia(t, ε˙)/ia∗, where ε˙ is the applied tensile strain rate. In principle, ia∗ is a material property that is dependent on material, temperature, and environment; is proportional to the exchange current density; and is a function of the usual electrochemical variables (see e.g. Anderko, 2010).

Active surface area fraction is used to greatly simplify the complex coupling of surface reaction with near-surface lattice concentration θ_LS, which can be expressed as θLS=A∗θLS∗, where θLS∗ is the near-surface hydrogen coverage of normal interstitial lattice sites when the surface is fully activated. Hall (2009, 2014) showed that, for quasi-steady crack growth, A^* attains a steady value given by

where k is the time-based repassivation rate constant, and γ is the strain-based surface activation rate constant. This equation can be applied to cyclic loading assuming that the magnitude of ε˙ is constant during up- and down-load half-cycles and that the crack tip surface is activated during both half-cycles. For large strain rates such that γε˙/k≫1, the active surface area fraction approaches unity, that is, AS∗→1. When γε˙/k≪1,AS∗→γε˙/k, and approaches 0 when ε˙→0. Note that, for a propagating crack, there is a component of CTSR due to crack advance that is proportional to the crack velocity (Hall, 2008a,b), so that ε˙, and therefore AS∗, are not 0, even for a statically loaded propagating SCC crack. Note that derivation of this equation does not account for any effects CTSR may have on crack tip chemistry, which could affect the repassivation rate constant k.

2.3 Repassivation rate constants

An issue for this approach is how to establish the rate constants in Eq. (12). The strain-based activation rate constant has a value 0≤γ≤1. If it is assumed that all of the crack tip stretch goes to create additional active surface, γ=1. The time-based repassivation rate constant k is customarily obtained from transient current decay experiments in which bare metal is exposed suddenly to an environment thought to be representative of the crack tip chemistry (Al^-3, Cl^-, CrO₄^-2, pH) and electrochemistry (crack tip potential, which determines the hydrogen overpotential).

As discussed above, a preferred test method for obtaining the repassivation rate constant is to measure, as a function of constant applied strain rate, the transient and steady-state corrosion currents established on a straining electrode rather than the customary static electrode; see for example, Haruyama and Asawa (1973). Unfortunately, straining electrode 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 crack. There is a limited number of experiments in which crack tip chemistry and electrochemical potential have been determined. The experimental methods require specialized equipment and are costly in terms of time and resources to conduct. Moreover, application of experimental results has limitations as crack-tip chemistry may be dependent on crack tip opening, crack length, stress ratio, and cyclic frequency, greatly expanding the number of variables that can be characterized.

Turnbull (2001) has reviewed modelling of the chemistry and electrochemistry of crack tips and concludes that “crack chemistry modeling is at the stage where the primary uncertainty in prediction should be associated only with the paucity of data for the input parameters”. However, in their current state of development, these computational models are realistically useable only by specialists in electrochemistry having computational skills.

Having neither measurements nor calculations of crack tip chemistries for the HH and KSH alloys and environments, estimates for k must be obtained using the limited experimental measurements of crack tip chemistry, electrochemical potential, and repassivation rate data available on comparable 7000 series alloys. Cooper and Kelly (2007) experimentally characterized the Cl^- concentration, pH, and electrochemical potential within the crack enclave of a propagating SCC crack formed in aluminum alloy 7050 in an aqueous solution of 0.05 m NaCl+0.5 m Na₂CrO₄, pH 9.2, with an applied stress intensity factor of 14 MP√m. During an incubation period of slow crack growth (da/dt≈6×10^-10 m/s), they found the crack chemistry to be comparable to the bulk chemistry. However, after an incubation period of 4–50 h, the crack growth rate increased by a factor of 38 (da/dt≈2.3×10^-8 m/s). The crack chemistry was quite different from the bulk: chloride increased by a factor of 6–8 (0.3 m–0.4 m CI^-), pH decreased from 9.2 to 3, and the crack tip potential decreased to -0.85 V_sce while the applied (crack mouth) potential was -0.445 V_sce.

They found that microinjection at the crack tip of the bulk chemistry having the chromate inhibitor (0.5 m Na₂CrO₄, pH 9.2) decreased the crack velocity by 90%. However, injection of an aggressive low pH crack tip chemistry having an inhibitor (0.2 m AlCl₃+1 m Cr⁶⁺ as CrO₃+Na₂CrO₄, pH 3.1) prior to natural transition from slow to fast crack growth resulted in immediate (~10 min) rate increase, by a factor of 65, to the fast crack growth rate. These results show that chromates may not inhibit crack growth when a low-potential, acidic, crack tip chemistry is established. Gasem and Gangloff (2001) report that low concentrations of chromate inhibitor did not inhibit crack growth when the bulk NaCl solution was acidified. Gasem and Gangloff and Warner and Gangloff (2012) discuss the effect that cyclic frequency (CTSR) may have on destabilization of inhibiting films, noting that there are critical CTSRs above which inhibitors are ineffective.

The environment within a corrosion fatigue crack may not be as aggressive as that determined for an SCC crack. Combining modeling and experimental data, Cooper and Kelly (2001) conclude that crack potential distributions are strongly dependent on size of the crack tip opening and the thickness of resistive salt-films that are presumed to form at the crack tip. The IG SCC cracks in the 7000 series aluminum alloys are very sharp (CTOD ~0.2 μm at 1 μm behind the crack tip). However, blunter cracks having CTODs as large as predicted by continuum mechanics do not generate as large a potential drop, and therefore, as aggressive a crack tip chemistry. On the other hand, plastic straining of the crack tip is expected to disrupt crack tip films at a rate determined by ΔK and cyclic frequency, thereby increasing the electrochemical activity of the crack tip, tending to reestablish a crack tip environment having a lower potential, concentrated Al^-3 and Cl^- and lower pH. Therefore, measurements of repassivation rate constants on open surfaces of static electrodes can only provide an estimate of repassivation rates appropriate to propagating SCC and CF cracks.

Raetzer-Scheibe and Tuck (1994) obtained repassivation rate data on open surfaces of aluminum AA7010-T651 in chemistries and applied potentials comparable to that of the Cooper and Kelly crack tip measurements. Using a microtome to remove metal chips in situ, they measured transient current-time data on bared metal surfaces in an aqueous solution having 0.34 m NaCI adjusted with HCl to pH=3 and with an applied potential of -0.762 V_sce to -0.842 V_sce, for which the repassivation rate constant can be determined to be 2.5 s^-1≤k≤6.0 s^-1. Based on the discussion above, these repassivation rate data, obtained without chromate inhibitor, are considered most applicable to the occluded crack tip chemistry of a fast propagating SCC crack. Having no information to the contrary, these data also are applied to the HH-KSH experimental results.

2.4 Crack tip strain rate

According to Eq. (12), crack tip strain rate (CTSR) plays an important role in activating a crack tip so that hydrogen may be evolved and absorbed into the FPZ. Treating the instantaneous crack tip opening displacement (CTOD) δ as a gage section, crack tip strain can be defined in terms of the stretch ratio λ=δ/δ_i, where δ_i is the initial CTOD. The Cauchy engineering extensional strain or “nominal” strain e can be expressed as the change in CTOD Δδ divided by the initial CTOD as

The Hencky logarithmic strain or “true” strain ε is given by

These equations, respectively, represent the average nominal and true strains over the strain path. In order to take into account the influence of a non-linear strain path, the incremental form of Eq. (14) dε=dδ/δ can be integrated to obtain a correct measure of the final strain.

An average cyclic crack tip strain rate (C-CTSR) can be defined in terms of both the nominal and true strains, Eqs. (13) and (14), respectively. Only the nominal strain is considered here as the nominal strain, defined in terms of the stretch ratio λ, is considered to be more consistent with an assumption that all of the crack tip stretch goes to create additional active surface. Note that this approach will overpredict the true C-CTSR. Lidbury (1983) provides a more extensive discussion of similar strain derivations by a number of researchers.

Considering the up-load half-cycle having a rise time t_r=Δt/2, where Δt=1/f is the cyclic period, the average nominal C-CTSR can be expressed as

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 complex functions of f and ΔK when all components for a propagating crack are considered. This equation is used here to evaluate Eq. (12) for A^* and to evaluate the C-CTSR corresponding to fracture mode transitions.

2.5 Adaption of the RDS equations for cyclic loading

Rice and Sorensen (1978) and Rice, Drugan, and Sham (1980) developed continuum mechanics-based CODR and COD equations for a crack propagating in an elastic-ideally plastic (non-hardening) material. These equations are considered to be applicable to high-strength, low-strain hardening aluminum alloys (cyclic strain hardening ≈0.06; Benson and Hancock, 1974).

The Rice, Drugan, and Sham (RDS) equations, which are applicable to monotonically increasing load, can be expressed as

and

where J=K²/E′ for small-scale plasticity, a is the crack size, da/dt is the crack velocity, σ_o is the yield stress, χ is the distance behind the crack tip, and E′ is the generalized elastic modulus. The notation ϕ for COD is introduced in order to distinguish ϕ in the RDS equations for a propagating crack from the more commonly discussed stationary crack CTOD, δ. These equations were derived for χ→0 and are valid only for distances less than an undefined fraction of the plastic zone size χ/R_P«1, where RP=λE′J/σo2. Based on finite element analyses of an elastic-plastic crack propagating under small-scale plasticity conditions, RDS determined that α=0.65, β=5.46, and λ=0.235.

RDS also proposed a COD criterion for sustained crack growth, which is that a steadily propagating crack must maintain a geometrically similar profile. This means that the crack must maintain a constant COD ϕ_c at a distance behind the crack χ_c that is equal to the size to the FPZ. This criterion is equivalent to an assumption that steady-state crack propagation occurs at a fixed CTSR with a constant crack opening angle given by ϕ_c/χ_c.

The first term on the RHS of Eq. (16) represents the CODR due to monotonically increasing the applied J at a rate dJ/dt. The second term represents the CODR due to steady-state propagation of cracks, with velocity da/dt, into the logarithmic strain field ahead of the advancing crack. The applied “tearing modulus” introduced by Paris et al., (1979) is proportional to the factor dJ/da in the first term on the RHS of Eq. (17), that is, T_app=(E/σ_o)(dJ/da). During monotonic up-loading, T_app will attain a steady value equal to the materials resistance to tearing T_mat (see Rice et al., 1980). When exposed to an environment that reduces the magnitude of T_mat, the crack COD will be reduced. In an aggressive crack tip environment, the material resistance may be reduced to T_mat=0 such that dJ/da=0. In this limiting case, the COD is due solely to the second term on the RHS of Eq.(17), and the CODR is due solely to the second term on the RHS of Eq. (16). As discussed in Section 3.3 below, these limiting cases have implications for transitions from static load SCC to low and intermediate cyclic frequency corrosion fatigue.

Although Eq. (16) has no provision for rate-dependent deformation or creep, it may be acceptable for application to materials that undergo small-scale creep confined to the near-tip plastic zone. In this case, CODR due to small-scale creep is expected to be much less than that described in Eq. (16).

Modifications are necessary in order to apply Eqs. (16) and (17) to cyclic load. Using a superposition argument, Rice (1967) determined, for a stationary crack, the relationships between monotonic and cyclic versions of the plastic zone size (PZS), CTOD, and strain variation ahead of a crack tip embedded in a cyclic plastic zone. Rice showed that the needed modifications can be accomplished by substituting ΔK for K and 2σ′o for σ_o, where σ′o is the cyclic yield stress.

For cyclic loading, the RDS crack similarity criterion for steady crack growth is adopted by requiring that the C-COD range Δϕ_c=ϕ_max-ϕ_min must remain constant when evaluated at a distance χ_c behind the propagating crack, where χ_c is set equal to the FPZ size. As discussed above, this may be either a fixed distance characteristic of the material or a variable distance equal to the per cycle increment in physical crack size Δa. Note that the subscript “c” refers to the RDS similarity criterion and should not be confused with the subscript “crit”, which refers to critical conditions associated with fracture mode transitions.

Adopting the above assumptions and using ΔJ=ΔK²/E′ (Anderson, 2005), Eq. (16) becomes

and assuming per cycle crack growth, Eq. (17) becomes

Eq. (18) shows that C-CODR is proportional to the cyclic frequency f, χ_c, and a function of ΔK². The first term on the right hand side of Eq.(19) is one-half of the stationary crack CTOD, which is consistent with Rice’s superposition model, and the second term is the crack opening due to crack advance by the distance χ_c. Application of Rice’s superposition methodology for extending Eqs. (16) and (17) to propagating fatigue cracks was introduced by Hall (2014) and, to the author’s knowledge, has not been considered elswhere.

The validity of these equations rests with the justifications given by Rice for his superposition arguments. Rice and Sorensen (1978) provide a detailed discussion of the equation development and applicability of the crack similarity criterion for steady crack growth. Although the derivation of their equations does not consider the strain distribution ahead of a cyclically loaded propagating crack, the analysis for a growing crack may be considered applicable when unloading strains are negligible.

Experimental support for the use of Eqs. (18) and (19) is provided by comparisons, shown in Figure 1, of measured and predicted COD profiles of propagating fatigue cracks. The measured fatigue crack profiles were obtained by Cooper (2001) on AA 7050-T651 fatigue cracks grown at 10 Hz, R=0.3, in air (ΔK=13.3 MPa√m) and in 0.05 m NaCl+0.5 m Na₂CrO₄, pH 9.2 at E_app=-0.445 V_sce (ΔK=12.3 MPa√m). Shown for comparison to the CF crack profile is the predicted C-COD obtained using Eq.(19) and ΔK=12.3 MPa√m. This figure shows that the predicted C-COD profile (solid curve) is comparable to the measured fatigue crack profile data trend (dashed curve).

Figure 1:

Measured and predicted cyclic crack opening displacement (C-COD) profiles of propagating fatigue and IGSCC cracks obtained by Cooper (2001) on AA 7050-T651. The predicted fatigue crack profile, obtained using Eq. (19), is comparable to the measured fatigue crack profile data trend (dashed line). The closed symbol is the C-COD predicted using only the second term of Eq. (19).

Also shown is the measured COD profile of an IGSCC crack (K=12.9 MPa√m) grown by Cooper in the above environment. The IGSCC crack profile is sharper, by more than an order of magnitude, than the measured and predicted air and CF crack profiles. Shown for comparison is the C-COD predicted using only the second term on the RHS of Eq. (19) and using ΔK_crit=12.9 MPa√m and plotted at χ_crit=2.4 μm (choice of this distance is discussed below). As discussed above, use of only the term due to crack advance is appropriate for the limiting case where the material resistance to tearing under rising load conditions T_mat approaches zero due to exposure to an environment that sufficiently embrittles the FPZ. This comparison suggests that corrosion fatigue cracks may have similar profiles to static load SCC cracks for low cyclic frequencies, where CF and IGSCC crack velocities are comparable.

Consideration of the separate effects that load variation and crack advance may have on CODR, COD and enviroment-assisted crack growth rate can be found only in a limited number of studies. Somerday, Young, and Gangloff (2000) used Eq. (16) to rationalize the separate effects of dK/dt and da/dt on environment-assisted cracking of beta-titanium alloys during up- and down-load testing in aqueous NaCl. Hall (2014) used C-CODR, Eq. (18), to analyze the HH corrosion fatigue data.

3.1 The HH and KSH data sets

Detailed discussions of the CF experiments carried out by Holroyd and Hardie (1983) and Kotsikos et al. (2000) can be found in the references. Briefly, base and recrystallized heat-affected “white zone” metals of aluminum alloy 7017 were tested at room temperature in pH 8.2 natural sea water and dry air (base metal) and in 2.5% NaCl+0.5% Na₂CrO₄ solution acidified to pH 3 with HCl and laboratory air (white zone). Tests were conducted using a triangular wave form, R=0.1, and frequencies from 0.1 to 70 Hz (base metal) and using a sinusoidal wave form, R=0.1, and frequencies from 0.01 Hz to 10 Hz (white metal). Tests were conducted under load control so that ΔK increased during crack growth (base metal) and ΔK held constant (white zone).

The rolled plate base metal (T651) has an unrecrystallized pancake structure elongated in the rolling direction. Grain size information was not provided; however, a 7000 series alloy given a similar mechanical-thermal treatment has grain dimensions of 130, 60, and 18 μm in the L, T, and S directions, respectively. Cracks were oriented so as to propagate in the rolling plane. The fracture surfaces denoted as “IG” showed equiaxed features measuring about 15±3 μm, which suggests that the IG crack growth is along subgrain boundaries. The heat-affected white zone metal has an equiaxed recrystallized structure with a grain diameter of 10.5±3 μm. Cracks were oriented so as to propagate within the thin heat-affected white zone metal separating the base and weld metal. The fracture 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 includes the KSH data and is focused on additional aspects of the observed fracture mode transitions.

3.2 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 elastic modulus E′=E/(1-ν²)=72.3 GPa was determined using the tensile modulus E=65.8 GPa reported for 7017-T651 by Ruiz and Elices (1997) and assuming that ν=0.3. The cyclic yield stress was assumed to be equal to the monotonic yield stress based on the finding by Benson and Hancock (1974) that two aluminum alloys 7075-T6 and 6061-T651 showed stable cyclic 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 0.5 mm. However, Bloem, Salvador, Amigó, and Vergara (2011) report micro-hardness of about 140–145 VH for the volume of metal (WZ) that lies within 0.5 mm of the weld fusion line of an aluminum alloy 7020 weld, which is approximately equivalent to a yield stress of 407–428 MPa.

HH report an average value for K_c of 31.5 MPa√m for the base metal data. Holroyd (private communication) confirmed that K_c of 25.0 MPa√m is representative of the WZ metal. As there are no data available for K_H-crit and having no better alternative, the apparent threshold values for K_max of about 8.8 MPa√m for the base metal and 11.1 MPa√m for the WZ were used as default values. The value for k of 2.5 s^-1 from the Raetzer-Scheibe and Tuck data corresponding to a potential of -0.762 V_sce was chosen as it conservatively represents the crack tip potential measured by Cooper and Kelly within 1 mm of the crack tip, where the crack tip chemistry is concentrated.

A value for the effective hydrogen diffusivity was obtained from a critical review by Young and Scully (2003) of the available diffusivity data. They conclude that the value of 3.37×10^-12 m²/s obtained from their isothermal desorption measurements is most representative of peak aged alloy 7050-T6 condition. Use of this value in the data analyses below is based on an assumption that dynamic straining within the FPZ does not alter the hydrogen diffusivity, which, as discussed above, is conjectured to be the case when trapping by corrosion-injected vacancies is dominant.

3.3 Critical conditions for fracture mode transitions

Time-domain plots of the HH and KSH crack velocity data Δa/Δt obtained on base and heat-affected white zone metals, respectively, can be found in their publications. Also found in the HH publication 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 microstructures are quite different, cyclic wave forms are different, and the base metal test environment had no inhibitor, while the white zone environment included chromate inhibitor. The data show that CF crack velocities are comparable and increase with increasing cyclic frequency at similar rates at all values of ΔK. For the lowest frequencies and K_max values, the white zone CF crack velocities are comparable to the base metal SCC crack velocities. Moreover, KSH note that at frequencies below 0.1 Hz, there are striations on IG-CF fracture surfaces, similar to the ones observed by Scamans (1980) on IGSCC fracture surfaces of AA 7018. Based on high-resolution fractographic studies, Scamans concludes that these are crack arrest markings rather than fatigue striations. KSH speculate that, given the similarities in crack velocity and fracture surface striations and that these markings are not related to load cycling, corrosion fatigue cracks advance by an IGSCC mechanism for frequencies below 0.1 Hz.

Figure 2 is a fracture mode diagram showing the critical values of applied f and ΔK, for the HH and KSH data, corresponding to transitions in fracture modes, from IG to BTG and then to DTG in the case of the HH data. Figure 2 shows that as the cyclic frequency increases (cycle time decreases), decreasing the mechanical driving force ΔK is required to sustain cracking along the more brittle IG and BTG fracture paths. Above a frequency of about 4 Hz, ΔK_crit becomes less dependent on frequency for the IG fracture mode and approaches a value just above the ΔK used to fatigue pre-crack specimens (ΔK=8.5 MPa√m).

Figure 2:

Crack-path fracture mode diagram showing critical values of f and ΔK associated with fracture mode transitions for AA 7017-T651 base metal and heat effected “white zone” metal tested in aqueous chloride solutions. Transitions in fracture modes, from brittle to more ductile, occur as frequency and ΔK are increased above critical values.

An important conclusion that can be drawn from the data in Figure 2 and Eq. (3) for θ_crit is that as f_crit increases (and ΔK_crit decreases) the hydrogen coverage of grain boundaries θ_int must increase in order to satisfy the critical hydrogen criterion θ_int=θ_crit. Figure 3 shows that, for fracture mode transitions from IG to BTG for both base and WZ metal, θ_crit increases from a value as low as 0.002 atom fraction, where ΔK_crit has a maximum value of 22 MPa√m, to a high value of 1.0 atom fraction, where ΔK_crit has a minimum value of 8.8 MPa√m, as the cyclic frequency increases from 0.01 to 70 Hz. This means that the critical distance at which θ_crit is attained must decrease as the cyclic frequency increases, as the hydrogen diffusion time per cycle decreases as the frequency increases.

Figure 3:

Critical values of the hydrogen coverage Eq. (3) of IG and TG fracture interfaces at transition in fracture modes plotted versus critical frequency. An assumption of the critical hydrogen model is that a crack advances when hydrogen occupancy of the crack path interface, θ_int, attains the critical occupancy, θ_crit. Critical occupancy increases as frequency increases due the fact that the critical ΔK necessary to avoid fracture mode transitions decreases with increasing frequency.

These results are consistent with the results of Holroyd and Hardie (1981), who concluded, based on fractographic examinations of using slow strain rate tests of high-strength aluminum alloy 7049-T651 in saltwater, that the transition from IG fracture to BTG fracture occurs at higher local hydrogen concentrations as the strain-rate is increased. Fracture mode transition from BTG to DTG (base metal) occurs for significantly lower critical values of θ_int=θ_crit at all frequencies.

Establishing separate dependencies of critical crack velocity Δa/Δt_crit on ΔK_crit and f_crit is not possible due to the fact that these are inseparable co-variables. However, Eqs. (18), (19), and (15) show that C-CTSR is a function of both of these variables and therefore provides a measure of their concomitant effects on the crack driving force at fracture mode transition. Using the full HH dataset, Hall (2014) showed more generally that there is a correlation between Stage II crack velocity and C-CODR, the latter evaluated at a distance behind the propagating crack equal to the hydrogen diffusion distance per cycle. This correlation holds for all cyclic frequency -ΔK data combinations and fracture modes, which suggests that C-CODR, or equivalently C-CTSR, is the more fundamental crack driving force variable.

Figure 4 shows the critical C-CTSR e˙crit (Eq. 15) plotted as a function of f_crit. Per cycle crack growth was assumed for f_crit≥0.1 Hz. This figure shows that for frequencies greater than 0.1 Hz, e˙crit is simply proportional to f_crit, where the proportionality factors are 1.31 (WZ IG-BTG), 1.52 (base metal BTG-DTG), and 1.66 (base metal IG-BTG). This shows the dominance of the first terms on the right hand side of Eqs. (18) and (19) for f_crit≥0.1 Hz. This result provides justification for previous interpretations of Δa/ΔN_crit versus f_crit plots as showing frequency effects even though in these plots ΔK_crit varies with frequency; see for example, Holroyd and Hardie (1983), Green and Knott (1989), and Kotsikos et al. (2000).

Figure 4:

Critical cyclic crack tip strain rate (C-CTSR) versus critical cyclic frequency. C-CTSR is proportional to critical frequency for frequencies greater than 0.1 Hz but decreases more slowly for frequencies lower than 0.1 Hz due to the increasing contribution to CTSR by the velocity-dependent term of Eq. (16).

As discussed above, Scamans (1980) concluded that the striation markings observed on static load IGSCC fracture surfaces of aluminum alloy 7017 are crack arrest markings. Given the similarities between these features and those observed by KSH on IGCF fracture surfaces, for critical frequencies <0.1 Hz, it is assumed here that, in this low-frequency regime, striation markings are crack arrest markings, independent of frequency. Consistent with these assumptions, it is assumed that the critical hydrogen criterion is met at a fixed distance ahead of the propagating crack, independent of frequency. This distance was taken to be 2.4 μm, which is the per cycle value of Δa/ΔN_crit for the WZ metal at f_crit=0.1 Hz (see Table 1). This distance is comparable to the striation spacings observed by Scamans and KSH. With this assumption, the predicted C-CTSR is increasingly larger than that predicted based on the per cycle assumption (dashed curve) as f_crit decreases below 0.1 Hz. This is due to the fact that the COD at a fixed distance behind the crack increases as f_crit decreases (ΔK_crit increases). The fixed distance assumption means that, as the crack advance per cycle increases with decreasing f_crit, this distance is traversed as many as 22 times per load cycle at 0.01 Hz (Δa=52 μm).

The proposal that χ_crit is determined by the location of maximum tensile and hydrostatic stress (~2 CTOD from crack tip) can be evaluated simply by comparing entries in Table 1, which provides the calculated C-COD values and the corresponding Δa/ΔN_crit. The comparison shows that Δa/ΔN_crit, as a fraction of 2 C-COD, for the IG-BTG transition (WZ), ranges from 0.08 for the highest frequency data to 0.3 for the lowest frequency data, with similar trends for the base metal transitions. One must conclude, as did Gingell and King (1993), that the transitions in crack path are not dependent on the location of the maximum stress located at a distance of 2 CTOD ahead of the crack tip.

Figure 5 shows the critical crack velocity Δa/Δt_crit plotted versus the critical value of C-CTSR e˙c calculated using Eqs. (15), (16), and (19) and the values found in Table 1. Also shown on a second horizontal axis are values of f_crit corresponding to e˙c. This figure is plotted versus e˙c instead of f_crit in order to capture a more physically correct representation for frequencies <0.1 Hz. Figure 5 shows that Δa/Δt_crit first decreases and then increases at e˙c=0.13 s-1 (f_crit=0.1 Hz), raising questions as to why this occurs and why it occurs at 0.1 Hz and a crack advance increment of 2.4 μm.

Figure 5:

Critical cycle-domain crack growth rates (m/s) associated with fracture mode transitions versus critical C-CTSR. Different C-CTSR (frequency) dependencies are observed in low, intermediate and high frequency regimes. A change in slope indicates transition in the rate limiting step.

A slope of about ~0.5, for the base metal BTG to DTG transition and the IG to BTG transition for the base and white zone metals in the intermediate frequency regime, is consistent with hydrogen diffusion as the rate-limiting crack growth process. A slope of about ~1 for the IG to BTG transition in the high frequency regime is consistent with frequency independent per cycle crack growth, which indicates a change in rate limiting step at a frequency of about 10 Hz, from time-cycle-dependent to cycle-dependent crack growth. The negative slope for frequencies below 0.1 Hz indicates that slow – large amplitude load cycles retard crack growth while time dependent – cycle independent crack growth might otherwise be expected (see e.g. Anderson, 2005).

Increasing crack velocity with increasing e˙c is expected as the active surface area, as shown in Figure 6, is expected to increase with increasing CTSR (Eq. 12), thereby increasing the subsurface hydrogen activity. The trends in Δa/Δt_crit and θ_TS below 0.1 Hz are surprising as Eq. (12) for the active surface area fraction predicts As∗ increases monotonically from a low value of 0.02 at the lowest to 0.979 at the highest e˙c, as shown in Figure 6.

Figure 6:

Hydrogen occupancy of near-surface hydrogen traps, active surface area fraction and fraction of the crack tip strain due to crack advance versus the critical C-CTSR necessary to sustain IG crack growth. The data trends can be rationalized based on considerations of the effect of load cycling on crack opening and the effect that this may have on crack tip chemistry, effect of the dominant crack tip strain rate components and strain-induced activation of the crack tip.

The trend in Δa/Δt_crit at or below a frequency of 0.1 Hz then suggests that the electrochemical reactivity at a crack tip first decreases and then increases with increasing frequency. This is consistent with the predictions of Eq. (11) for the hydrogen occupancy of near-surface traps, which, as shown in Figure 6, θ_TS=0.962 for e˙c=0.06 s-1 (0.01 Hz), decreases to θ_TS=0.21 at e˙c=0.13 s-1 (0.1 Hz), and then increases with increasing e˙c to a value of θ_TS=1.0 at e˙c=144 s-1 (70 Hz). Recall that Young and Scully (2003) found hydrogen concentrations of 0.6–0.8 atom-fraction near the surface of an IGSCC crack.

This suggests that narrow IGSCC cracks may develop a more aggressive crack tip chemistry than a more open low-frequency IGCF crack. Kelher and Scully (2008) argue that tight cracks can develop a low potential, low pH, and concentrated chloride crack tip chemistry that inhibits the formation of protective surface films. They argue that the ability to develop this environment decreases as the crack opening increases relative to the crack length. Development of an aggressive crack tip environment, supporting increased electrochemical activity, independent of load cycling, is not anticipated in the derivation of Eq. (12).

The possibility of near saturation of near-surface traps during IGSCC crack advance is supported by the crack tip conditions observed by Cooper and Kelly (2007), pH 3 and 0.3 m–0.4 m Cl^-, which may destabilize otherwise protective oxide films. The crack tip surface may be expected to be electrochemically reactive under these conditions. When hydrogen entry is unimpeded by protective surface films, the measured crack tip potential of -0.88 V_sce results in a very large hydrogen fugacity that can easily saturate near-surface strong traps such as corrosion-generated Vac-H clusters.

Figure 6 shows that the fraction of e˙c due to crack advance e˙adv/e˙total increases by 4-fold and is the dominant CTSR term as f_crit decreases from 0.1 to 0.01 Hz. In the low-frequency limit approaching static load, this CTSR component and any creep component, when present, can promote self-sustaining crack growth whenever the crack tip chemistry prevents repassivation. Figure 6 illustrates the increasing importance of the CTSR component due to crack advance as the frequency decreases, conceivably becoming the only contribution to CTSR, in the absence of a creep contribution, as the cyclic frequency approaches zero, the static-load SCC limit.

Above 0.1 Hz, the CTSR component due to the applied cyclic load is the dominant term, and e˙c≈αf, where 1.3≤α≤1.7, depending on materials and fracture mode transition. Then, the slope of the Δa/Δt_crit curves for e˙c≥0.13 s-1 (0.1 Hz), which is about 0.45–0.5, is consistent with Eq. (10), the development of which assumes that hydrogen diffusion is rate limiting and that cracks advance at each load cycle. The slope for e˙c≥16.7 s-1 (10 Hz), which is ~1.0, implies that Δa/ΔN_crit=Δa/Δt_crit/f is independent of frequency, which is a characteristic of “true” corrosion fatigue.