Keywords

1 Background and Introduction

High-cycle fatigue crack growth (HCFCG) behaviour may conveniently be considered in terms of three regimes, Fig. 1a. These are a low-ΔK regime close to the fatigue crack growth threshold Δ K th , a mid-K regime in which fatigue crack growth rates are represented by a power law [1], and a high-ΔK regime in which da/dN is high and K max approaches the critical stress intensity factor responsible for unstable fracture, K c [2]. The focus of the following paper is behaviour in the low-ΔK regime, in particular for high-R (K min/K max) load ratios at high temperatures .

Fig. 1
figure 1

a Schematic representation of high-cycle fatigue crack growth rate characteristics in low-, mid- and high-ΔK regimes; and b the influence of frequency, environment and R ratio on fatigue crack growth threshold values for 1CrMoV at 550 °C [2, 5]

Full size image

Conceptually, Δ K th is the maximum ΔK associated with no fatigue crack extension. Experimentally, it is assumed to be the ΔK consistent with da/dN 1 × 10−10 m/c [3] or da/dN 1 × 10−11 m/c [4]. At low temperatures, the ΔK th criteria difference may not be important, but this is not the case at high temperatures as will become apparent in the following paper.

In the low-ΔK regime, low da/dN and ΔK th are sensitive to load ratio (R = K min/K max), with the magnitude of ΔK th decreasing with increasing R (Fig. 1a). At ambient temperature (RT), higher Δ K th values at low-R are primarily the consequence of plasticity-induced crack closure, but may also be due to contributions from fracture surface roughness-induced closure and fretting oxide-induced closure.

At high temperatures , ΔK th(R) profiles become increasingly elevated with reducing frequency [2, 5], with the evidence for 1CrMoV steel at 550 °C (which also includes data collected at 0.01 Hz in vacuum), clearly indicating the enhancement of ΔK th to be mainly the consequence of oxide-induced crack closure , Fig. 1b, although plasticity-induced closure is influential at lower R due to lower R p0.2 at higher temperatures.

New high-temperature Δ K th results for three steels with different oxidation characteristics (respectively containing 1%Cr, 9%Cr and 17%Cr) have been assessed in terms of fracture surface oxide thickness measurements and a K(CTOD) analysis.

During the course of the study, it became apparent that creep cracking could occur at very low da/dN(ΔK) close to ΔK th under high-R conditions at high temperatures , even for high frequencies not normally expected to be affected by time-dependent cracking processes. A time-dependent failure assessment diagram (TDFAD) approach is adopted to predict the incidence of creep cracking at the tips of very slowly propagating high-R high-cycle fatigue cracks.

2 High-Temperature Fatigue Crack Growth Thresholds

High temperature Δ K th values were determined in accordance with [3] for three steels with different chromium levels, namely 1CrMoV, 9CrMoCo and 17Cr12Ni. As a generality, tests were conducted using compact tension (CT) specimens instrumented with electrical DCPD crack monitoring instrumentation at a frequency (f) of ~80 Hz. Typically, the tests were performed using proportional W(2B) CT specimens with thicknesses (B) of 12.5 or 25 mm. The results determined for a temperature of 550 °C are summarised as a function of R and K max in Fig. 2. The high-temperature values are compared with RT values when available and/or the lower bound RT Δ K th trend line defined in [6].

Fig. 2
figure 2

Variation of Δ K th with R and K max, respectively, at 550 °C for a, b 1CrMoV, c, d 9CrMoCo and e, f 17Cr12Ni (with filled data points representing those tests involving creep crack development when high-cycle fatigue cracking was almost stationary)

Full size image

As will be considered later, evidence of creep cracking in certain circumstances could be observed at high-R high-cycle fatigue Δ K th test crack tips (when K max and/or \(\sigma_{\text{ref}}^{ \hbox{max} }\) were high). The filled ΔK th data points in Fig. 2 acknowledge the incidence of creep cracking associated with these tests.

For each steel, there is indication of a ΔK th enhancement, which at high-R can almost exclusively be attributed to oxide-induced crack closure . The extent of high-R Δ K th enhancement (\({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\)) is not the same for each steel (Table 1) and appears to be related to the chromium content. This is examined further in the following section.

Table 1 Summary of oxide-induced crack closure data (550 °C)
Full size table

3 Oxide-Induced Crack Closure

The growth of oxide scales in air at elevated temperatures on the surfaces of many steels may be predicted with some certainty up to a thickness of ~100 μm by adopting parabolic growth kinetics, i.e.

$$x^{2} = \, k_{\text{p}} .t$$
(1)

where upper bound k p values for 1%Cr, 9%Cr and 17%Cr steels for a temperature of 550 °C are summarised in Table 1 [7]. For oxide thicknesses above ~100 μm, spallation becomes increasingly probable, and adoption of the listed \(k_{\text{p}}^{\text{UB}}\) values should be with caution. Typically, oxidation kinetics are relatively insensitive to chromium content up to ~10%, above which there is a significant increase in oxidation resistance to ~12%Cr, before a relative stabilization, Fig. 3. The variation in oxidation kinetics is accompanied by the changes in scale formation mechanism shown as insets in Fig. 3 which are likely to be influential in their contribution to \({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\).

Fig. 3
figure 3

Variation of oxide growth kinetics with chromium content in steels at 550 °C [8]

Full size image

Fracture surface oxide thickness measurements for the three steels were made immediately adjacent to the final crack tips established during Δ K th measurement campaigns conducted in accordance with [3]. With fracture surface oxide thicknesses being in the range 0.5–3.5 μm as a consequence of being exposed for ~24 h during the final very low da/dN(ΔK) phase of high-R Δ K th determination, an SEM-FIB drilling technique had to be adopted for maximum measurement accuracy. This involved FIB drilling a small trench, typically 1–2 mm deeper than the anticipated oxide scale thickness, with one vertical face and one stepped face. Prior to drilling, a platinum coating was locally sputter-deposited on the fracture surface to provide edge protection and a marker at the position of excavation. Following ‘rough’ drilling, the ion beam was used to polish the vertical surface of the trench. The sample could then be tilted for oxide thickness measurement directly in the SEM.

Observed FIB-determined oxide thickness measurements compare reasonably well with those calculated using the \(k_{\text{p}}^{\text{UB}}\) values established in [7], Table 1.

The apparent \({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\) enhancements experienced by the three steels at 550 °C (Fig. 2) are consistent with the oxide-induced crack closure Ks which may be predicted using the plane strain Rice relationship [9], i.e.

$${\text{CTOD}} = 0.225\left( {{K \mathord{\left/ {\vphantom {K {R_{{{\text{p0}} . 2}} }}} \right. \kern-0pt} {R_{{{\text{p0}} . 2}} }}} \right)^{2}$$
(2)

The degree of consistency is evident in Table 1 and Fig. 4. An alternative and widely adopted K(CTOD) formulation is that proposed by Stewart [10] (Eq. 3), although \({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\) predictions appear to be excessive using this relationship (Fig. 4).

Fig. 4
figure 4

Comparison of observed \({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\) for 1%Cr, 9%Cr and 17%Cr steels at 550 °C with predictions based on Rice and Stewart K(CTOD) formulations (respectively, Eqs. 2 and 3)

Full size image
$${\text{CTOD}} = \frac{{K^{2} \left( {1 - \upsilon^{2} } \right)}}{{2ER_{{{\text{p0}} . 2}} }}$$
(3)

4 Creep Cracking

An additional mechanism interaction which may be encountered in high-temperature high-R Δ K th tests is creep cracking (Fig. 5). Experience has shown that the incidence of creep cracking ahead of very slowly growing high-cycle fatigue cracks may go undetected by examination only of da/dN(ΔK) test records. Three additional examples are shown in Fig. 6. Perhaps surprisingly, in these circumstances, fracture surface post-test examination may be the only way to reveal the presence of creep cracking with certainty (e.g. Fig. 6c). However, it is shown that when fracture surface examination is not possible, a TDFAD approach may be adopted to predict the existence of creep cracking when K max approaches \(K_{\text{c}}^{\text{mat}}\) and/or σ ref approaches \(R_{ 0. 2}^{\text{C}}\).

Fig. 5
figure 5

Evidence of creep cracking (dark bands) at the ends of three high-R Δ K th fatigue cracking campaigns in a W(2B)12.5 CT specimen (with inset showing W(2B)12.5 CT specimen with DCPD instrumentation attached)

Full size image
Fig. 6
figure 6

Examples of high-R high-cycle da/dN(ΔK) records (with accompanying post-test fracture surfaces) for Δ K th tests during which creep cracking has occurred with; a expected da/dN(ΔK) response, b a discernible but unexpected da/dN(ΔK) response and c a hardly discernible da/dN(ΔK) response (W(2B)12.5 CT specimens are 12.5 mm thick)

Full size image

While there are two types of high-temperature failure assessment diagram [11], the one favoured for this application is the R5 TDFAD construction [12]. The failure envelope for this diagram is defined by:

$$K_{\text{r}} = \left[ {\frac{{E\varepsilon_{\text{ref}} }}{{L_{\text{r}} R_{ 0. 2}^{\text{C}} }} + \frac{{\left( {L_{\text{r}} } \right){}^{3}R_{0.2}^{\text{C}} }}{{2E\varepsilon_{\text{ref}} }}} \right]\quad {\text{for}}\;L_{\text{r}} \le L_{\text{r}}^{ \hbox{max} }$$
(4)
$$K_{\text{r}} = 0\quad {\text{for}}\;\;L_{\text{r}} > L_{\text{r}}^{ \hbox{max} }$$

where \(K_{\text{r}} = {K \mathord{\left/ {\vphantom {K {K_{\text{mat}}^{\text{C}} }}} \right. \kern-0pt} {K_{\text{mat}}^{\text{C}} }}\), \(L_{\text{r}} = {{\sigma_{\text{ref}} } \mathord{\left/ {\vphantom {{\sigma_{\text{ref}} } {R_{ 0. 2}^{\text{C}} }}} \right. \kern-0pt} {R_{ 0. 2}^{\text{C}} }}\) and \(L_{\text{r}}^{ \hbox{max} } = {{R_{\text{R}} } \mathord{\left/ {\vphantom {{R_{\text{R}} } {R_{ 0. 2}^{\text{C}} }}} \right. \kern-0pt} {R_{ 0. 2}^{\text{C}} }}\). The parameters used for TDFAD construction for the three steels considered in this study at 550 °C are summarised in Table 2.

Table 2 Summary of TDFAD material parameter data (550 °C)
Full size table

Important information for construction of the TDFAD envelope (Eq. 4) is isochronous ε(σ, t) data for the time period of interest. Typically, for Δ K th tests involving an ASTM da/dN(ΔK) criteria [3], high-cycle fatigue cracks can be almost stationary for ~24 h, and ε(σ) for this period are modelled from data from various sources (e.g. [11, 13]), Table 2, using:

$$\varepsilon = \frac{\sigma }{E} + \left( {\frac{\sigma }{{k^{\prime } }}} \right)^{\beta }$$
(5)

TDFADs for the three steels at 550 °C are given in Fig. 7. As in Fig. 2, filled co-ordinates are used to represent those high-R Δ K th tests involving creep crack development when high-cycle fatigue cracking is almost stationary. The TDFAD envelope acceptably predicts creep crack development in high-R ΔK th tests for the 1CrMoV and 9CrMoCo steels at 550 °C. There is not yet the same evidence for 17Cr12Ni in Fig. 7, primarily because 550 °C is low in the creep range for this steel.

Fig. 7
figure 7

TDFAD constructions for 1CrMoV, 9CrMoC and 17Cr12Ni steels at 550 °C (with filled data points representing those tests involving creep crack development when high-cycle fatigue cracking was almost stationary)

Full size image

5 Practical Implications

5.1 da/dN(Δ K th ) Criterion Sensitivity: Oxidation

It has already been acknowledged that there are two international standards covering the determination of ΔK th with very different da/dN criteria defining fatigue crack growth threshold stress intensity factor. The Δ K th da/dN criterion in the ASTM standard is 1 × 10−10 m/c [3], whereas that in the ISO standard is 1 × 10−11 m/c [4].

While this anomaly is unlikely to have a big influence at low temperatures for materials tested in what for them are relatively inert conditions, the evidence indicates that the situation is very different at high temperatures .

Depending on the oxidation resistance of a material at a given temperature, ΔK th can be significantly enhanced as a consequence of oxide-induced crack closure . For example, for a Δ K th da/dN criterion of 1 × 10−10 m/c, high-cycle fatigue cracking can be close to stationary for ~24 h, and \({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\) is ~2.7 MPa√m for 1CrMoV at 550 °C (Table 1). For a ΔK th da/dN criterion of 1 × 10−11 m/c, high-cycle fatigue cracking may be close to stationary for >100 h, and, in these circumstances, \({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\) could be >4 MPa√m for 1CrMoV at 550 °C (i.e. with ΔK th > 6 MPa√m for R = 0.9).

The situation is illustrated in Fig. 8. This shows a relatively material independent reducing high-R da/dN(ΔK) record representative of time insensitive conditions (connected black crosses). It also shows three diagonal iso-da/f da/dN(\({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\)) lines (one for each of the Cr steels) representing crack size resolution (~0.25 mm [3]) and minimum test times (with the iso-da/f da/dN(\({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\)) reference lines being determined by substituting dt = da(dN/da)/f into Eq. 2).

Fig. 8
figure 8

Influence of time (oxidation) on da/dN(\({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\)) (diagonal broken lines for three steels) and ultimately on material independent high-R da/dN(ΔK) (connected black crosses), and the consequence of different Δ K th da/dN criteria [3, 4] (for crack size resolution of 0.25 mm [3])

Full size image

With longer test times at temperature, the diagonal da/dN(\({\text{d}}\Delta K_{\text{th}}^{\text{ox}}\)) lines move towards the right (Fig. 8). The consequence of this is enhanced Δ K th values. Importantly, if the adopted ΔK th test ΔK reduction rates are slower than the oxidation rates, da/dN(ΔK) can be prevented from reducing to the standard defined Δ K th da/dN criteria.

5.2 da/dN(Δ K th ) Criterion Sensitivity: Creep Cracking

The evidence in Fig. 7 indicates that, while it could have been possible to predict the incidence of creep cracking during high-R Δ K th determinations for the 1CrMoV steel with only a knowledge of \(K_{\text{mat}}^{\text{C}}\), it would not for the 9%Cr and in 17%Cr steels, for which a TDFAD analysis is required.

6 Concluding Remarks

High-R high-cycle fatigue crack growth thresholds for power plant steels are enhanced at high temperatures due to oxide-induced crack closure .

The extent of any enhancement of Δ K th due to oxide-induced crack closure depends on time at low da/dN, temperature and material/oxidation mechanism. Consequently, the adopted standard defined da/dN(ΔK th) criterion becomes increasingly important with increasing temperature.

High-R Δ K th values are increasingly influenced by the development of creep cracking at very low da/dN with increasing temperature. While this may only be possible to detect with certainty by fracture surface examination, evidence is presented to show that creep cracking in these circumstances may be predicted using a TDFAD analysis.