Short/small fatigue crack growth, thresholds and environmental effects: a tale of two engineering paradigms

2.1 Loads/stresses and critical components

For airframes the loads and static and cyclic stress analyses are the starting points. These analyses are conducted for the airframe as a whole, and also structural assemblies down to the component level. The analyses are supplemented and validated by Full Scale Fatigue Testing (FSFT) and component and specimen tests. For an overview see e.g. MIL-STD-1530D (2016).

For steam turbines the low pressure (LP) turbine blades are already known to be critical components. The steady and cyclic operational stresses are calculated using finite element (FE) analyses, including increases in cyclic stress owing to sustained operation at low power and/or high condenser back pressure (Salzman et al. 2013; Schönbauer et al. 2015a,b).

2.2 Fatigue analysis summaries

2.3 Scatter factors (SF) and safety margins (SM)

As shown in Table 1, the airframe DT and turbine blade SL design methodologies rely on scatter factors (SF) or safety margins (SM) and NDI to ensure safety. A common SF value for airframe NDI is 2, signifying that the time for FCG from an initial or subsequently detected discontinuity to the critical crack size is twice the required NDI interval. Other SF values are possible, depending on the criticality of detailed designs and components, the materials used, and the NDI capabilities.

The turbine blade methodology (Salzman et al. 2013) is less explicit. But one possibility for continued operation after a (planned) outage is that NDI-detected and documented corrosion pit widths are no more than half the calculated critical pit widths (Salzman et al. 2013). In other words, blades should be withdrawn from continued operation when any corrosion pits reach half the calculated critical pit widths with respect to fatigue failure at the same locations. N.B: The NDI will have a detection limit for very small fatigue cracks, if there are any, nucleating from the corrosion pits. A judicious safety margin should ensure that any such non-detectable cracks become non-propagating. This condition is not stated in the proposal for a safety margin derived from the measured pit widths, but may be regarded as implicit from the following: “Once the Kitagawa Diagram parameters were defined to be a function of R, these diagrams could then be applied to operating steam turbine blades to define a critical pit size (i.e. when the pit is at risk of forming a propagating fatigue crack)” (Salzman et al. 2013).

3.1 Airframe materials and structures

Since about 1990 it is known from QF of FCG in service failures and simulation tests that small fatigue cracks in airframe alloys can have FCG thresholds below those for long cracks (Barter et al. 1993; Blom 1990; Molent and Jones 2016; Tanaka et al. 1981; Wanhill 1991; Wanhill et al. 2019). An early test example for VA (flight simulation) loading is shown in Figure 2.

Figure 2:

Correlation of flight simulation small and long fatigue crack growth rates, da/dN, for AA2024-T3 sheet: data from Wanhill (1991). K_mf corresponds to the simulated mean stress in flight, S_mf.

More extensive FCG investigations, validated by QF data from service cracking, FSFTs and component and specimen tests, have shown that the small crack FCG thresholds under both CA and VA load histories must be much lower than the long crack thresholds, e.g. Jones et al. (2013), Jones (2014), Molent et al. (2011). An example of the use of this assumption for correlating small and long FCG under CA loading is given in Figure 3. The parameters A (the apparent fracture toughness under cyclic loading) and ΔK_thr (not the original ASTM Standard E647 parameter ΔK_th, see Jones et al. 2012) were chosen to collapse the small and long FCG data onto a single curve. To do this it was necessary to use a very low value of ΔK_thr for small cracks. N.B: A constant value of ΔK_thr = 0.1 MPa√m could be used, owing to the small dependency of small crack FCG rates on R: see Jones et al. (2013) and the current version of ASTM Standard E647.

Figure 3:

Correlation of constant amplitude small and long fatigue crack growth rates, da/dN, for AA7050-T7451 using a variant of the Hartman‒Schijve equation (Hartman and Schijve 1970) adapted by Jones et al. (2013): data provided by R. Jones.

3.2 Steam turbine LP blades

As mentioned in Section 2, K‒T diagrams are used in the LP turbine blade fatigue design methodology with the intention of defining safe and unsafe combinations of pit widths and mean + cyclic stresses with respect to nucleation of fatigue cracks from the pits. No fatigue crack nucleation and growth from corrosion pits is allowable.

The original K‒T approach (Kitagawa and Takahashi 1976) envisaged that approximate regions of safe and unsafe combinations on K‒T diagrams are given by boundaries representing the HCF smooth specimen endurance limit, ΔS₀, and a slant line representing fatigue failure stress ranges, ΔS, calculated from combinations of the long crack FCG threshold, ΔK_th, and characteristic crack sizes. However, to capture small crack growth behavior below ΔK_th (already observed by Kitagawa and Takahashi), El Haddad et al. (1979) proposed an empirical expression for ΔS, whereby an ‘effective crack size’ is added to the actual crack size. This empirical expression has been modified for corrosion pitting in 12% Cr steam turbine blades as follows:

and

where c is the half-width of a corrosion pit; Y is a geometry factor (assumed to be 0.65); and (c + c₀) is the effective half-width of the corrosion pit (Schönbauer et al. 2012). This modified approach means that corrosion pits are treated as if they are small cracks with approximate semi-elliptical shapes. This assumption is based on the fractography of corrosion pitting, e.g. Chen et al. (1996), Schönbauer et al. (2015), Stanzl-Tschegg (2019). Another significant point is that ΔS₀ is the fatigue limit at 10⁹ cycles (not the more common value of 10⁷ cycles), owing to the VHCF nature of fatigue in steam turbine blades.

Figure 4 gives examples of K‒T diagrams using this modified approach, with ΔS₀ from smooth specimen tests and (failure/no failure) ΔS values from pre-pitted specimen tests. The tests were done with an ultrasonic resonance fatigue machine and hourglass-shaped specimens under strain control (Stanzl 1981). The specimen stresses were calculated assuming fully elastic behaviour. The advantage of this type of testing at ultrasonic frequencies is the ability to achieve very long fatigue lives (>10⁹ cycles) within reasonable testing times.

Figure 4:

Kitagawa‒Takahashi (K–T) diagrams for pre-pitted 12% Cr martensitic steel specimens tested in (A) air and (B) a dilute aqueous NaCl solution at 90 °C (Schönbauer et al. 2012): data provided by B. Schönbauer.

The diagrams in Figure 4 include (i) the effects of R on ΔS₀, ΔK_th and the El Haddad et al. empirical expression, (ii) the effects of test environments (air and a dilute aqueous NaCl solution), and (iii) ranges of corrosion pit sizes for the pre-pitted specimens. The ΔK_th values were those for the test environments (Schönbauer et al. 2012). These diagrams show that the modified approach, represented by the El Haddad et al. dotted curves, provides reasonable (but not precise) lower bounds for the failure/no failure data. In other words, use of equations (1) and (2) provides reasonable first estimates of the maximum allowable ΔS values for a range of pit sizes and R values. N.B: Some follow-up research has shown that choosing Y = 0.42 for the pit depth and consequent changes in equation (1) (c and c₀ replaced by a and a_0, the actual and effective pit depths) gives equally good results (Schönbauer et al. 2015a).

In view of the foregoing results, the El Haddad et al. estimates of the maximum allowable ΔS values appear suitable for use with a judicious safety margin (SM), see Section 2, as aids to assessing whether individual corrosion-pitted blades can continue in service until the next outage. However, it is advisable also to consider environmental effects on the long crack ΔK_th values used for the K‒T diagrams: see subsection 4.2.

4.1 Aircraft fatigue: role of the service environment

Corrosion in aircraft is a very important problem, e.g. Wanhill and Koolloos (2001), Shoales et al. (2009). These examples, investigating long-service aircraft, show that widespread corrosion can lead to numerous fatigue cracks late in the service life, whereby the cracks are usually of secondary consideration compared to the damage caused directly by corrosion.

In contrast, corrosion pitting may occur relatively early in the service life and in some cases provide primary fatigue nucleation sites (Barter and Molent 2013; Campbell and Lahey 1984; Molent 2014, 2015; Wanhill 2007; Wanhill et al. 1974). A survey by Campbell and Lacey (1984) covers 574 cases in both fixed wing and rotary wing aircraft, of which 62 (10.8%) were attributed to corrosion. The main causes of airframe fatigue are stress concentrations and high local stresses (Campbell and Lahey 1984; Wanhill et al. 2019). More specifically, there are many types of pre-existing discontinuities that provide potential (and actual) fatigue nucleation sites immediately, or very soon after, an aircraft enters service (Barter et al. 2012).

Corrosion-enhanced FCG (corrosion fatigue) has been observed in some military aircraft components (Barter et al. 1994; Byrnes et al. 2014), but this is unusual and not to be generally expected (Barter and Molent 2013; Lang et al. 2001; Molent 2015; Molent et al. 2015; Trathan 2011). Also, there was some evidence of corrosion fatigue in extensively corroded pressure cabin lap joints in ageing civil transport aircraft (Wanhill and Koolloos 2001). However, QF of lap joints from the most famous (or infamous) ageing aircraft accident, the Aloha Airlines Boeing 737 pressure cabin failure in 1988, found fatigue striation spacings down to less than 0.1 µm (Aircraft Accident Report, Aloha Airlines, Flight 243, 1989, Boeing 737-200, N73711, Near Maui, Hawaii, April 28, 1988). This would not have been possible if corrosion had played a significant role during the FCG process. N.B: A recent summary of more information on the accident-causing factors— which did include corrosion, but not of the lap joints—is given by Wanhill et al. (2016).

All the foregoing observations lead to the conclusion that, in general, the influences of corrosion and fatigue on aircraft service lives can be decoupled (Lang et al. 2001; Molent et al. 2015). In other words, although corrosion is a very important problem for airframe structures, it can—and should—be treated separately from fatigue design methodologies, and included only in later maintenance analyses; these may require revised estimates of FCG lives for corrosion-susceptible locations (Molent 2014; Molent et al. 2015).

4.2 Steam turbine LP blades

For steam turbine 12% Cr steel LP blades corrosion pitting and pit growth occur mainly during off-load conditions, when oxygen is present with chloride contaminants. During operation the condensate is oxygen-free and pitting is arrested. This means that the corrosion fatigue process is predominantly corrosion followed by high-frequency fatigue, rather than simultaneous corrosion + fatigue. It follows that corrosion-enhanced FCG should not be a design issue. On the other hand, the question arises whether the totality of the steam turbine internal environment could promote FCG from corrosion pits by lowering the long crack ΔK_th values used for K‒T diagrams like those in Figure 4.

4.3 Environmental effects on the long crack ΔK_th values

FCG tests on 12% Cr martensitic steels at 90 °C and over a wide range of R (−1 to 0.9) have shown that the long crack ΔK_th values tend to be slightly higher in dilute aqueous NaCl solutions than in air (Schönbauer et al. 2012). This was an unexpected result, and fractographic examination suggested that the reason is a combination of enhanced crack closure owing to increased fracture surface roughness and corrosion product (oxides) build-up on the fracture surfaces, for example Figure 5. There was also some evidence of intergranular fracture, circled in Figure 5B, which would also have increased the fracture surface roughness (Suresh and Ritchie 1984).

Figure 5:

SEM secondary electron (SE) near-ΔK_th fractographs of 12% Cr martensitic steel specimens tested at 90 °C in (A) air and (B) a dilute aqueous NaCl solution (Schönbauer et al. 2012). The fracture surface produced during fatigue crack growth in the aqueous NaCl solution is rougher and shows evidence of corrosion product (oxides) accumulated on the fracture surface, and also intergranular fracture (circled in Figure 5B): original fractographs provided by B. Schönbauer.

For 12% Cr martensitic steels the result of slightly higher long crack ΔK_th values in dilute aqueous solutions signifies that tests in air at 90 °C are sufficiently conservative for K‒T design diagrams. This can greatly facilitate testing, as may be inferred from Schönbauer et al. (2012). However, this fortuitous result does not necessarily apply to other turbine blade materials. An important example is 17-4PH martensitic stainless steel, for which the long crack ΔK_th values are significantly decreased by corrosive environments (Schönbauer et al. 2015b).

5.1 Loads, stresses, critical components and materials (alloys)

PMI: The design loads and stresses have to be determined for the complete aircraft before selecting the fatigue-critical components for further analysis. The service loads are usually VA-HCF, although pressure cabins, for example, experience predominantly CA low-cycle fatigue (LCF) pressurisation cycles with superpositions of fuselage bending loads. The main classes of alloys are aluminium, titanium and high-strength steels.

PMII: In this context the critical components are stainless steel LP steam turbine blades. The service cyclic loads and stresses are assumed to be basically CA-VHCF, but with a wide range of R in both the spanwise and chordwise directions. Both the static and cyclic stress distributions require detailed FE analyses.

For these topics there is hardly any commonality between the two paradigms. We note that stainless steels are used in aircraft, but mainly for fuel lines and hydraulic tubing, which are not considered fatigue-critical items. In fact, their main potential (and actual) problem is stress corrosion cracking (Wanhill and Byrnes 2017).

5.2 Fatigue design approaches: initial and time-dependent discontinuities

PMI: Aircraft fatigue design has seen a steady evolution from Safe-Life (defect-free) to DT since the mid-1950s. A broad-based consensus has recently been reached on the specification of effective pre-crack sizes (EPS) for initial discontinuities (Gallagher and Molent 2015). The EPS values, derived from QF of discontinuity depths, are much smaller than the 1.27 mm equivalent initial flaw size (EIFS) proposed by the United States Air Force in MIL-A-83444 (1974). Typical EPS values are below 0.1 mm, which is a convenient starting point for FCG safety and sustainability analyses and, as must be noted, well within the short/small crack regime.

Time-dependent discontinuities include corrosion pitting and fretting damage. These are NDI-detected, along with any associated fatigue cracking, during periodic maintenance that includes any refurbishments, repairs or replacements. A survey of managing corrosion and any associated fatigue cracking, including the estimation of EPS values when only corrosion is detected, is given by Molent (2014, 2015).

PMII: The steam turbine LP blade design approach considers corrosion pitting discontinuities that occur during service. As mentioned in subsection 2.2, the current proposed methodology begins with outage-coordinated NDI inspections of the LP turbine blade and root surfaces, and documenting the sizes and locations of corrosion pits (Salzman et al. 2013). The need to examine the blade roots means removing the blades for NDI, which gives easier access and is consequently beneficial to the NDI.

Detailed light microscopy and fractography have shown that for 12% Cr martensitic stainless steels the pits have semi-elliptical shapes with depth-to-width ratios a/2c ≈ 0.95; and also that fatigue cracks nucleate at the surface corners of the pits (Schönbauer et al. 2015a). Thus the preferred pit metrics are their widths normal to the principal steady stress, and not the pit depths— which are anyway not easily measurable by NDI. N.B: There is no need to convert pit widths to effective crack sizes, since progressive FCG is not allowed, and the pits behave in an analogous way to small cracks in K‒T diagrams, e.g. Figure 4. Also, the NDI will have a detection limit for very small fatigue cracks nucleating from the corrosion pits. This can be accounted for by imposing a judicious safety margin, as is implicit in the proposed fatigue design methodology by Salzman et al. (2013).

Two further points should be noted:

1. The depth-to-width ratios of corrosion pits in 12% Cr martensitic steels do not necessarily apply to other materials. For 17-4PH martensitic steel the average value was found to be a/2c ≈ 0.61 for pit sizes below 0.2 mm (Schönbauer et al. 2015b). This means that the pit shapes for 17-4PH steels were significantly shallower than those for 12%Cr steels.

2. The sizes of representative corrosion pits for both types of steels are less than 0.2 mm (see Figure 4 also). Hence, although they are not fatigue cracks, these pit sizes, like airframe EPS values, are well within the short/small crack regime.

5.3 Short/small fatigue cracks and FCG thresholds

Both PMI and PMII recognize that (i) the behavior of short/small fatigue cracks is related to FCG thresholds; (ii) the sizes of important design and in-service discontinuities, represented by airframe EPS values and steam turbine blade corrosion pits, are within the short/small crack regime; and (iii) long crack ΔK_th values do not directly apply with respect to preventing fatigue cracking from these discontinuities. But there the similarities end, since the fatigue analysis methods are very different. Most of the PMI FCG analyses are not based on approaches using long crack ΔK_th values (Wanhill et al. 2019). The PMII analyses use long crack ΔK_th values, since these are inherent to the K‒T approach (Kitagawa and Takahashi 1976), but the limitations of this approach are explicitly demonstrated by small crack FCG data like those in Figure 4. However, this diagram also shows that the El Haddad et al. (1979) empirical estimates of the maximum allowable ΔS values capture most of the short (small) crack data. Thus these empirical estimates appear suitable for use, albeit with a judicious safety margin (SM), as discussed in section 2.3.

5.4 Environmental effects

For both PMI and PMII the available evidence concerning service environments is that corrosion and fatigue can generally be decoupled, even though corrosion is an important problem for (ageing) aircraft and steam turbine martensitic steel LP blades, see section 4. In other words, corrosion-enhanced FCG need not be a design consideration.

However, environmental effects on the long crack ΔK_th values can be design considerations; see the discussion in subsection 4.2. It must be noted that although the long crack ΔK_th values do not necessarily represent short/small crack FCG thresholds, they are used together with the El Haddad et al. curves to help define the boundaries between safe and unsafe regions on the K‒T diagrams. This demonstrates the usefulness of PMII-type testing in evaluating environmental effects relevant to the service operation of steam turbine LP blades.