Factors influencing the analytical representation of creep crack development in Alloy 939

Abstract

Creep crack growth rates originally gathered for the 𝛾^′ strengthened cast nickel based superalloy Alloy-939 in terms of apparent stress intensity factor are re-evaluated as a function of the time dependent C* parameter, with crack propagation rates being insensitive to grain size at 750 and 850 °C. However, whereas ${\dot{a}}_{C}(K_{a})$ rates at 750 °C are significantly lower than those at 850 °C, equivalent ${\dot{a}}_{C}$ (C*) rates are relatively insensitive to temperature, comparing well with the plane strain ${\dot{a}}_{C}$ (C*) rates predicted using an approximate reference stress based C* model. While overall CT-specimen creep crack growth times for Alloy-939 can be predicted using uniaxial creep-rupture strength data when expressed in terms of reference stress at 850 °C, this appears not to be possible at 750 °C. The observation is explained with respect to evidence provided by a modified time dependent failure assessment diagram. The influence is examined of thermal transient durations at 850 °C (from 750 °C), or at 750 °C (from 850 °C) on ${\dot{a}}_{C}(K_{a})$ creep crack growth rates and t _R(𝜎_ref) overall lives.

Keywords

Alloy 939 creep crack incubation creep crack growth reference stress

Nomenclature

a, a _o

Crack length, Original crack length

Δa _C

Creep crack extension

ȧ _C

Creep crack growth rate (see da∕dt)

A _N

Constant in minimum (secondary) creep rate law (Norton law), Eq. (3)

Air cool

B, B _n

Specimen thickness, Net section thickness in side-grooved specimen

CCI, CCG

Creep crack incubation, Creep crack growth

COST

European Cooperation in Science and Technology

Compact tension (specimen)

CTOD

Crack tip opening displacement (see 𝛿)

C ^∗, C _o ^∗

Parameter characterising stress and strain rate fields at tip of crack in material deforming due to creep, Initial value of C* (in test)

da∕dt

Creep crack growth rate (see ȧ _C)

Constant in CCG law, Eq. (4)

DCPD

Direct current potential drop (electrical crack monitoring instrumentation)

K, ΔK

Stress intensity factor, Range of stress intensity factor

K _a

Apparent stress intensity factor

K _mat ^c

Critical stress intensity factor for unstable fracture

Stress exponent in minimum (secondary) creep rate law, Eq. (3)

Load

Prior exposed (in this study, for 10kh at 850 °C)

R′

Characteristic length (defined by Eq. (2))

R _p0.2, R _m

0.2% proof strength, Ultimate tensile strength

R _R

Uniaxial creep-rupture strength

t, t _R

Time, Time to creep-rupture

t _{i, x}

Time to onset of creep crack extension (incubation time)

Temperature

TDFAD

Time dependent failure assessment diagram

Specimen width

Crack initiation criterion, x =pre-specified value of Δa _C, e.g. 0.5mm (in this study)

𝜀, 𝜀_C

Strain, Creep strain

𝜀̇_{C, min}

Minimum (secondary) creep rate

𝜀_R, 𝜀_R ^∗

Uniaxial creep-rupture strain, Multiaxial creep-rupture strain

𝛿

Crack tip opening displacement (see CTOD)

𝛿_{I, x}

Critical crack tip opening displacement responsible for a creep crack extension of Δa _c = x

𝛾

C* exponent in CCG law (Eq. (4))

𝜎, 𝜎_app

Stress, Applied stress

𝜎_ref

Reference stress

1. Background and introduction

As gas turbine inlet temperatures progressively increased during the 1950s/60s, a new class of high strength cast nickel-base super-alloys was developed for first-stage rotating blade and vane applications. While Alloy-738LC was probably the best known of these, its development was closely followed by a similar more corrosion resistant variant referred to as Alloy-939 (also known as Nimocast-739), Table 1 [4]. The following paper is concerned with the creep crack development characteristics of the later alloy, their analytical representation, and a consideration of the effects of temperature, grain size, prior exposure and thermal transients. A nomenclature listing is given at the start of the paper.

Table 1
Chemical composition of COST 50 Alloy-939 (TVV3464)

Ag Al B Bi C Co Cr Fe Mn N

ppm wt.% ppm ppm wt.% wt.% wt.% wt.% wt.% ppm

<0.1 1.89 80 <0.1 0.155 19.1 22.65 0.09 <0.01 <0.001

Nb Ni Pb S Si Ta Ti W Zr

wt.% wt.% ppm wt.% wt.% wt.% wt.% wt.% wt.%

0.98 Balance <0.1 0.005 <0.05 1.37 3.68 2.07 0.105

Ag	Al	B	Bi	C	Co	Cr	Fe	Mn	N
<0.1	1.89	80	<0.1	0.155	19.1	22.65	0.09	<0.01	<0.001
Nb	Ni	Pb	S	Si	Ta	Ti	W	Zr
wt.%	wt.%	ppm	wt.%	wt.%	wt.%	wt.%	wt.%	wt.%

0.98	Balance	<0.1	0.005	<0.05	1.37	3.68	2.07	0.105

Importantly, the paper also provides an example of how archive experimental data can be re-evaluated in the light of more recent analytical interpretations to enable further exploitation with respect to more modern applications.

In the early 1970s, creep crack growth rates were typically expressed as a function of apparent stress intensity factor, K _a [12], by means of a power law function, analogous to the way mid-ΔK fatigue crack growth rates were already expressed as a function of ΔK using the Paris law [11]. This being the case, most CCG tests were originally conducted using a fracture mechanics type specimen in load control, at the temperature of interest, with a focus on the continuous measurement of crack extension rather than crack opening displacement. Later in the 1970s, it was increasingly acknowledged that a time independent quantity such as K _a was unlikely to be an appropriate correlating parameter for creep crack growth rate, and an alternative time dependent C* parameter was proposed. However, initially, there was a reluctance to adopt C*, not least because of the lack of available analytical solutions for the parameter (relative to those for K), and the challenges associated with its determination for practical engineering situations. There was also a lack of evidence to demonstrate that ${\dot{a}}_{C}(C^{\ast })$ models determined using conventionally sized laboratory specimens could be reliably applied to relatively heavy section power plant components. Perhaps, more importantly, it was relatively easy to make apparently convincing justifications for the continued use of K _a for creep brittle situations, in particular those involving the use of nickel base superalloys, e.g. [5,6,9]. Since the mid-1980s, use of the C* parameter as a creep crack growth rate correlating parameter became more acceptable (e.g. [10,13]), not least with the availability of approximate methods of determination [13], i.e. $\begin{eqnarray}C^{\ast }={\sigma}_{\mathit{ref}}\cdot \dot{{\varepsilon}}_{C,\min }({\sigma}_{\mathit{ref}})\cdot R^{\prime }\end{eqnarray}$ (1) where $\begin{eqnarray}R^{\prime }=(K_{a}/{\sigma}_{\mathit{ref}})^{2}\end{eqnarray}$ (2) and $\begin{eqnarray}\dot{{\varepsilon}}_{C,\min }=A_{N}({\sigma}_{\mathit{ref}})^{n}.\end{eqnarray}$ (3)

Acknowledging their dependence on creep-rupture ductility, creep crack growth rates were then commonly expressed in terms of a power law [10], e.g. $\begin{eqnarray}{\dot{a}}_{c}=D({\varepsilon}_{R}^{\ast })\cdot [C^{\ast }]^{{\gamma}}\end{eqnarray}$ (4) which was shown to be effectively approximated by Eq. (5) in the absence of experimental data [13], $\begin{eqnarray}{\dot{a}}_{c}^{approx}=\frac{3}{{\varepsilon}_{R}^{\ast }}\cdot [C^{\ast }]^{0.85}\end{eqnarray}$ (5) where ${\dot{a}}_{C}$ and C* were respectively expressed in mm/h and MPa⋅m/h, and where ${\varepsilon}_{R}^{\ast }$ was multiaxial rupture strain, assumed to be 𝜀_R/30 for plane strain deformation.

It was soon appreciated that (unlike fatigue crack propagation) the development of creep cracks from pre-existing defects could first involve an incubation period [7]. Creep crack extension could occur during service from pre-existing flaws or from defects generated as a consequence of the high temperature operating regime, and it was important to differentiate between these two situations. The onset of creep crack growth from a pre-existing defect was generally preceded by an incubation period during which time sufficient creep damage was generated at the crack tip for initiation to occur (Fig. 1). In the case of creep ductile materials, in particular, the incubation period could occupy a significant proportion of overall life, and its consideration was a necessary part of defect assessment to avoid excessively conservative life predictions. Incubation period durations were directly related to material creep ductility, and reduced in magnitude with decreasing ${\varepsilon}_{R}^{\ast }$ . In the assessment of creep crack growth from defects generated during high temperature service, it may not be appropriate to include the consideration of an incubation period since the necessary creep damage may have already been established as part of the mechanism of formation of such cracking (Fig. 1).

Fig. 1.

Schematic representation of the development of a crack subjected to constant applied stress at elevated temperature.

Conceptually, following the logic outlined in Fig. 1, creep crack extension only proceeded on attainment of a critical value of crack tip opening displacement, 𝛿_{i, x} (related to the creep ductility of the material). The terminology adopted for incubation time purposely qualified the parameter in terms of crack initiation criterion (x). This was because the time to generate a 50 μm deep crack ahead of a pre-existing defect was significantly lower than the time for 0.5 mm crack extension, in particular in creep ductile materials [7]. In the present study, x = Δa _C was taken to be 0.5 mm (after [7]). Creep crack incubation periods were initially predicted as a function of critical crack tip displacement, i.e. $\begin{eqnarray}t_{i,x}=\left\{\frac{1}{\dot{{\varepsilon}}_{C,\min }({\sigma}_{\mathit{ref}})}\cdot \left(\frac{\dot{{\varepsilon}}_{C,\min }({\sigma}_{\mathit{ref}})\cdot {\delta}_{i,x}}{C_{o}^{\ast }}\right)^{n/n+1}\right\}\end{eqnarray}$ (6) with an approximate solution provided by Eq. (7) [13] $\begin{eqnarray}t_{i,x}^{approx}=\frac{{\rm\Delta}a_{C}\cdot {\varepsilon}_{R}^{\ast }}{3\cdot [C_{o}^{\ast }]^{0.85}}.\end{eqnarray}$ (7)

Individual constant-load CCG tests represented in the form of ${\dot{a}}_{C}(K_{a})$ (and also ${\dot{a}}_{C}(C^{\ast })$ ) exhibited an apparent threshold regime (more commonly referred to as a ‘tail’), a mid-K _a (or mid-C*) regime, which was relatively insensitive to load, and ultimately an unstable regime associated with final creep rupture (Fig. 2). Importantly, unlike the situation for fatigue crack growth, the apparent threshold regimes were not unique to material and temperature, but were load dependent and, in fact, reflected the generation of creep damage ahead of the crack tip prior to the attainment of a critical CTOD responsible for creep crack extension (Figs 1, 2).

Fig. 2.

Schematic representations of a series of constant-load creep crack growth tests, showing (a) original a (t) observations, and (b) processed ${\dot{a}}_{C}(K_{a})$ results.

Overall rupture times for creep crack growth tests involving a fracture mechanics specimen could then be regarded as being the sum of creep crack incubation and creep crack growth times, i.e. $\begin{eqnarray}t_{R}=t_{\text{CCI}}+t_{\text{CCG}}=t_{i,x}+t_{\text{CCG}}.\end{eqnarray}$ (8) Importantly, there were circumstances when the overall lives of creep resistant steel structures could be predicted with a knowledge of the reference stress at the critical feature, and uniaxial creep-rupture strength data. It will be seen that while this observation also applied to Alloy-939 at 850 °C, it was not necessarily the case at 750 °C.

The original ${\dot{a}}(K_{a})$ and t _R(𝜎_ref) data for Alloy-939 were determined as part of the COST 50 initiative in the early 1980s [5,6], but have been re-visited here and re-assessed in the light of the subsequent developments introduced in the preceding text.

2. Experimental details

The CCG tests considered in the following paper were conducted using fatigue pre-cracked 25 mm thick side-grooved compact tension testpieces at temperatures of 750 and 850 °C (Fig. 3).

Fig. 3.

CT CCG specimen with loading pin hole ceramic inserts to provide DCPD electrical insulation.

The specimens were extracted from two series of cast blocks, prepared using the same melt (Table 1); the first (Series-1) being poured from 1380 °C to give a grain size of ∼2–3 mm, and the second (Series-2) being poured from 1500 °C to give a larger grain size of ∼6–8 mm. The Series-1 grain size was regarded as being characteristic of the 32 mm ruling section of the cast blocks from which the CT-specimens were machined. The larger grain size (exhibited by Series 2 specimens) was more typical of that existing in heavier section land based gas turbine hot gas path parts. The following 4-stage heat treatment was then applied to all cast blocks: $\begin{eqnarray}4∼\text{h}∼1150∼^{\circ }\text{C},\text{AC}+6∼\text{h}∼1000∼^{\circ }\text{C},\text{AC}+24∼\text{h}∼900∼^{\circ }\text{C},\text{AC}+16∼\text{h}∼700∼^{\circ }\text{C},\text{AC}\end{eqnarray}$

Complementary tensile and creep properties for the 4-stage heat treated COST 50 Alloy-939 TVV3464 melt originated from [1,2,3,4], e.g. Table 2. Mean uniaxial creep-rupture strength properties were determined in terms of a minimum-commitment model based on experimental observations from the source references.

Table 2

Summary of tensile and creep properties of COST 50 Alloy-939 (TVV3464)

	750 °C	850 °C
R _p0.2, MPa	647	409
R _m, MPa	834	635
$K_{mat}^{c}$ , MPa $\surd$ m	63	69
$\dot{{\varepsilon}}_{C,\min }$ , -/h	1.30 × 10⁻³⁰	2.30 × 10⁻²⁰
n	9.5	6.2
${\varepsilon}_{R,\min }^{\ast }$ , -	0.0011	0.0015

Series-1 material was also tested following a 10,000 h at 850 °C ageing treatment.

Crack growth was continuously monitored by means of DC potential drop measurements. For this reason, the CT specimen loading pin holes had been modified with ceramic inserts to ensure electrical isolation from the test machine (Fig. 3).

In addition to the conventional isothermal creep crack growth tests, a number of thermal transient tests were conducted. These involved: (a) constant-load tests conducted at 750 °C, but with thermal transients to 850 °C for 24 h or 168 h, every 168 h, and (b) constant-load tests conducted at 850 °C, with thermal transients to 750 °C for 24 h or 168 h, every 168 h.

3. Creep crack development

3.1. Crack growth

Creep crack growth rates for Alloy-939 in this study were originally determined in terms of K _a, i.e. as ${\dot{a}}_{c}(K_{a})$ diagrams (Fig. 4) [5]. The ${\dot{a}}_{C}(K_{a})$ data plots for 750 and 850 °C (complete with ‘tails’) appeared to be realistically related as a function of temperature. Creep crack growth rates expressed as a function of K _a appeared to be independent of grain size and prior exposure.

Fig. 4.

Influence of temperature on creep crack growth rates for Alloy-939 expressed as a function of K _a.

In hindsight, with knowledge from later developments, it has been possible to convert K _a to equivalent C* values by substituting the appropriate levels of 𝜎_ref and $\dot{{\varepsilon}}_{C,\min }({\sigma}_{ref})$ in Eqs (1) and (2) (Table 2). This enabled the creep crack growth rates determined for Alloy-939 at 750 and 850 °C to be expressed as a function of C* (Fig. 5). Notably, with the time dependent parameter, ${\dot{a}}_{C}(C^{\ast })$ data were relatively independent of temperature, although the model represented by Eq. (5) predicted marginally faster propagation rates at 750 °C as a consequence of the lower minimum creep-rupture ductility exhibited by Alloy-939 at the lower temperature (Table 2). Converted ${\dot{a}}_{C}(C^{\ast })$ results for the Series 1 PE tests are not given in Fig. 5 because there were no $\dot{{\varepsilon}}_{C,\min }$ data available for the prior exposed Series 1 material.

Fig. 5.

Influence of temperature on creep crack growth rates for Alloy-939 expressed as a function of C*.

Fig. 6.

Comparison of t _R(𝜎_ref) values for Alloy-939 CCG tests at 700 and 850 °C compared with mean creep-rupture strength lines for the cast alloy at these two temperatures.

3.2. CT-specimen overall rupture times

In common with prior experience with creep resistant steels (e.g. [8]), the overall rupture times for Alloy-939 CT-specimens could be reasonably predicted by using reference stress and uniaxial creep-rupture strength data at 850 °C (Fig. 6). In contrast, t _R(𝜎_ref) values for CT-specimens at 750 °C were significantly over-predicted using uniaxial creep-rupture strength data. The inability to predict CT-specimen overall rupture times in terms of reference stress and uniaxial rupture time data at 750 °C was judged to be a consequence of the lower $K_{mat}^{c}$ and creep-rupture ductility values for the alloy at the lower temperature (Table 2). This aspect is considered further with reference to a time dependent failure assessment diagram (TDFAD) construction in Section 3.3.

Overall CT-specimen creep-rupture times may also be plotted as functions of initial K _a values and initial C* values. In terms of initial K _a, t _R(K _{a, o}) values at 850 °C are shorter than those at 750 °C, apart from at very short times when the lower $K_{mat}^{c}$ at 750 °C determines fracture behaviour (Fig. 7). This trend was in contrast to that exhibited by the data expressed in terms of initial C*, Fig. 8, which indicated that t _R( $C_{o}^{\ast }$ ) for 750 °C are shorter than those for t _R( $C_{o}^{\ast }$ ) for 850 °C (consistent with the approximate t _{i, x}( $C_{o}^{\ast }$ ) values predicted using Eq. (6)). Converted t _R( $C_{o}^{\ast }$ ) results for the Series 1 PE tests are not given in Fig. 8 because there were no $\dot{{\varepsilon}}_{C,\min }$ data available for the prior exposed Series 1 material.

Fig. 7.

Influence of temperature on t _R(K _{a, o}).

Fig. 8.

Comparison of t _R( $C_{o}^{\ast }$ ) with $t_{i,0.5}^{approx}(C_{o}^{\ast })$ for Alloy-939 at 750 and 850 °C.

3.3. TDFAD

The prediction of overall rupture times for Alloy-939 at 750 °C, in terms of reference stress and with respect to t _R(R _R), in particular for relatively short durations, appeared to be compromised by the lower $K_{mat}^{c}$ (at short times) and the lower ${\varepsilon}_{R,\min }^{\ast }$ values at 750 °C relative to those at 850 °C (Fig. 6). It was possible to illustrate the influence of $K_{mat}^{c}$ with reference to a modified version of the TDFAD, as shown in Fig. 9. While K _a(𝜎_ref) co-ordinates for 850 °C CT-specimen tests cross the appropriate rupture boundaries in the stress-controlled creep-rupture/collapse regime (Fig. 9b), those for 750 °C CT-specimen tests do so in the K-controlled fracture regime (Fig. 9a).

Fig. 9.

Modified TDFAD constructions comparing K _{a, o}(𝜎_ref) co-ordinates representing Alloy-939 CT-specimen tests with K _a(𝜎_ref) TDFAD envelopes for times of 0 h, 100 h and 1 kh, for (a) 750 °C and (b) 850 °C.The arrow in Fig. 9b represents theK _a(𝜎_ref) locus, for increasing creep crack size, for a single test.

4. Thermal transients

4.1. Crack growth

In addition to the isothermal creep crack growth tests reported in [5], the influence of thermal transients on propagation rates and overall CT-specimen rupture lives was later investigated in a number of constant-load tests [6]. The crack propagation results of these tests are summarised in Fig. 10. As mentioned previously, these involved: (a) constant-load tests conducted at a datum temperature of 750 °C, but with thermal transients to 850 °C for 24 h or 168 h, every 168 h, and (b) constant-load CCG tests at a datum temperature of 850 °C, with thermal transients to 750 °C for 24 h or 168 h, every 168 h.

Fig. 10.

Influence of magnitude and duration of thermal transient on CT-specimen constant-load creep crack growth rates for Alloy 939 expressed as a function of K _a.

Fig. 11.

Influence of magnitude and duration of thermal transient on CT-specimen t _R(𝜎_ref) for Alloy-939.

When the duration of the thermal transient matched that of the datum temperature condition (168 h), the intermediate ${\dot{a}}_{C}(K_{a})$ rates observed in the anisothermal tests were similar (Fig. 10). Comparable intermediate ${\dot{a}}_{C}(K_{a})$ rates were exhibited in the 168 h/850 °C + 24 h/750 °C test, but not in the 168 h/750 °C + 24 h/850 °C test. The shorter-duration transient from the lower datum temperature had only a marginal effect on ${\dot{a}}_{C}(K_{a})$ rates at 750 °C.

In hindsight, evidence concerning the influence of recovery during these transients would have been more revealing, had crack propagation data been accompanied by load point displacement observations. This was a recommended action for the future.

4.2. CT-specimen overall rupture times

The influence of the applied thermal transients on CT-specimen overall rupture times was explored with respect to t _R(𝜎_ref), Fig. 11, and t _R(K _{a, o}), Fig. 12. In terms of both parameters, transients from 750 °C to 850 °C increasingly reduced overall rupture times, with increasing transient duration, such that t _R(𝜎_ref) and t _R(K _{a, o}) for 168 h/750 °C + 168 h/850 °C transients were essentially identical to those for isothermal 850 °C conditions. Temperature reductions from 850 °C to 750 °C appeared not to be responsible for a significant increase in overall rupture times from those for a temperature of 850 °C.

Fig. 12.

Influence of magnitude and duration of thermal transient on CT-specimen t _R(K _a) for Alloy-939.

5. Conclusion

Historic creep crack growth results for the 𝛾′ strengthened cast nickel based superalloy Alloy-939 at temperatures of 750 and 850 °C have been re-assessed as a consequence of knowledge relating to more recent developments, with the following observations:

Creep crack growth rates originally gathered in terms of apparent stress intensity factor, and re-evaluated as a function of a time dependent C* parameter both exhibit insensitivity to grain size. However, whereas ${\dot{a}}_{C}(K_{a})$ rates at 750 °C are significantly lower than those at 850 °C, equivalent ${\dot{a}}_{C}(C^{\ast })$ rates are relatively insensitive to temperature, comparing well with the plane strain ${\dot{a}}_{C}(C^{\ast })$ rates predicted using an approximate reference stress based C*.

While overall CT-specimen creep crack growth times for Alloy-939 can be predicted using uniaxial creep-rupture strength data when expressed in terms of reference stress at 850 °C, this appears not to be possible at 750 °C. The observation is explained with respect to evidence provided by a modified time dependent failure assessment diagram.

As the duration of thermal transients to 850 °C and 750 °C increase in magnitude to be the same as those of the respective datum conditions at 750^° and 850 °C, ${\dot{a}}_{C}(K_{a})$ creep crack growth rates attain a common level, intermediate to those for the two investigated bounding temperatures. Shorter duration transients from 750 °C to 850 °C appear not to significantly increase ${\dot{a}}_{C}(K_{a})$ above creep crack growth rates for 750 °C.

As thermal transient durations at 850 °C (from 750 °C) or at 750 °C (from 850 °C) exceed 24 h, t _R(𝜎_ref) overall lives may be predicted using mean 850 °C uniaxial creep rupture strength data for Alloy-939.

Footnotes

Conflict of interest

None to report.

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