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Influence of dwell time on fatigue crack growth in nickel-base superalloys
Materials Science and Engineering A336 (2002) 209– 214 www.elsevier.com/locate/msea
Influence of dwell time on fatigue crack growth in nickel-base superalloys Robert P. Wei *, Zhifan Huang Packard Laboratory, Department of Mechanical Engineering and Mechanics, Lehigh Uni6ersity, 19 Memorial Dri6e West, Bethlehem, PA 18015 -3085, USA Received 11 December 2000; received in revised form 26 November 2001
Abstract Engineered systems for high temperature service are often subjected to cyclic loads with dwell times at maximum load that can exacerbate fatigue damage evolution through creep and environment enhanced crack growth. Experiments are carried out to examine the influence of dwell time on fatigue crack growth in powder metallurgy (P/M) nickel-base superalloys in highpurity argon and oxygen at 873–973 K. This study complements a previous study on an ingot metallurgy (I/M) alloy. The data are analyzed using a general superposition model to capture the microstructural response to the conjoint actions of stress and environment. The model is validated through backward comparisons of the estimated time-dependent contributions with crack growth rate data from sustained-load tests. The mechanical and mechanistic implications of dwell time, the feasibility for inferring sustained-load crack growth rates from the dwell time tests, and the usefulness of the superposition model for life-cycle design and management of engineered structures are discussed. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Fatigue crack growth; Dwell time effect; Environmental effect; Temperature effect; Nickel-base superalloys
1. Introduction Engineering components and structures, designed for high-temperature service (such as those in chemical plants and stationary and aircraft turbine engines), are subjected to cyclic loads with dwell time, at maximum load, of different duration that can exacerbate the development of fatigue damage through creep and environment enhanced crack growth. An effective methodology to account for the influence of dwell time at load is needed, therefore, for use in the life-cycle design and management of such components and structures. The development of such a methodology requires mechanistic understanding of the processes of damage evolution and the interactions between loading and environmental variables. In this paper, the results from a study to examine the mechanical and mechanistic implications of dwell time, at maximum load, on fatigue crack growth in two powder metallurgy (P/M) nickel-base * Corresponding author. Tel.: +1-610-758-4100; fax: + 1-610-7586224 E-mail address: [email protected] (R.P. Wei).
superalloys are summarized. The base composition of the alloys is nearly that of IN100, except one of the alloys contained 5 wt.% of niobium. This study complements a previous study on an ingot metallurgy (I/M) Ni –18Cr –18Fe ternary alloy [1], and a companion study on oxygen enhanced, sustained-load crack growth in the P/M alloys [2,3]. The crack growth results are analyzed in terms of a general superposition model that had been proposed to account for the influence of dwell time on fatigue crack growth [1]. The model was derived from those developed for corrosion fatigue crack growth [4,5]. It incorporates the influence of environment on the cycle-dependent and time-dependent components of crack growth rate, and reflects the response of the alloy microstructure to the conjoint actions of stress and environment. Solomon and Coffin [6] developed the first derivative of the original superposition model by Wei and Landes [4] for use in high-temperature crack growth. To provide background for the experimental effort, the proposed general superposition model is first summarized.
0921-5093/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 9 5 7 - 8
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
210
Following the early work of Wei and Landes [4], Wei and Gao [5] and Solomon and Coffin [6], the following general superposition model was proposed for use as a working hypothesis for the interpretation of environmentally enhanced fatigue crack growth rates in fatigue at elevated temperatures [1]. The model is based on the premise that the cycle-dependent (fatigue) and time-dependent (sustained-load) components of crack growth rates may be treated as contributions from two ‘independent’ sequential processes, with the overall fatigue crack growth rate given by:
da dN
da = dN e
da + dN cycle
(1)
da dN
=
cycle
da da (1− c) + c dN r dN c
& n & n ~
=
0
time
da dt ~
+
(2)
0
dt (1 − EAC)
creep
da dt
e
da da (1−c)+ dN r dN c c ~
+
0
~
+
0
da dt
da dN
dt (1−EAC)
creep
dt EAC
(4)
EAC
For trapezoidal loading, the load is constant during the dwell time and, therefore, K and the corresponding da/dt may be taken to be constant. Then, Eq. (4) may be simplified, in terms of the dwell time (~) at load, to:
da dN
=
e
da da (1−c)+ c dN r dN c
+
da dt
creep
(1−EAC)+
da dt
dt EAC
n
EAC ×~
EAC
(5)
In Eq. (2), (da/dN)r is the pure-mechanical fatigue crack growth rate; (da/dN)c is the pure-corrosion fatigue crack growth rate; and c, is the areal fraction of pure-corrosion fatigue. Similarly, the time-dependent crack growth rate is the weighted average of the pure-mechanical (or creep) and pure-environmental contributions integrated over one loading cycle, and is expressed by: da dN
=
time
In Eq. (1), (da/dN)cycle and (da/dN)time are the cycle-dependent and time-dependent rates, respectively. Within each of these processes, the mechanical (deformation) and environmental contributions are treated as being from independent parallel processes [5]; namely, a pure-mechanical and a pure-environmental contribution to the crack growth rate. The cycle-dependent crack growth rate is the weighted average of the pure-mechanical fatigue and pure-corrosion fatigue components, and is expressed by [5]:
& n & n da dN
2. General superposition model
(3)
EAC
In Eq. (3), (da/dt)creep and (da/dt)EAC are the K-dependent pure-mechanical and pure-environmentally assisted crack growth rates, respectively; and EAC is the areal fraction of the environmentally affected component of crack growth. The integration is taken over one fatigue cycle (or period ~) and reflects the changes in the steady-state, sustained-load crack growth rate with K during that cycle. By combining Eqs. (2) and (3), the overall fatigue crack growth rate is then given by:
The individual rates in Eq. (5) may be determined from fatigue and sustained-load tests in inert and ‘fully deleterious’ environments, respectively. Formulation of the model reflects the fact that the alloy microstructure responds differently to the conjoint actions of mechanical loading and the environment, which is reflected in the micromechanisms for crack growth. For example, for the niobium-free alloy, sustained-load cracking in an inert environment (high-purity argon), was by a microvoid coalescence mechanism. Whereas, cracking was predominately along the interfaces between the g matrix and the gamma-prime (g%) precipitates and grain boundaries to reflect the impact of oxidation (see Fig. 1) [2,3]. Typical changes in cracking mechanisms (or, crack paths) with dwell time are illustrated in Fig. 2 for the niobium-containing P/M alloy, showing the transition to predominant intergranular (IG) mode of fracture with increased dwell time from a mixture of IG and transgranular (TG) modes. 3. Material and experimental procedures The high-purity, P/M alloys were prepared by Homogeneous Metals, Inc.1 The niobium content in the alloys was chosen to be 0 and 5 wt.%. Their Co, Cr, Al and Ti concentrations were chosen so that the alloys would contain approximately the same amount of g% precipitates (about 53 vol.%). The niobium-free alloy is designated as alloy 1, and the niobium-containing alloy as alloy 3 [3]. Their chemical compositions are given in Table 1. Extruded bars of the P/M alloys (63.5 mm diameter by 165 mm long) were isothermally (pancake) forged into 6.35 mm thick plates at Pratt and Whitney, West Palm Beach, FL. They were heat treated as follows: solution treated in air at 1440 K for 1 h, air cooled to 1
Homogenous Metals, Inc., Clayville, NY 13322.
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
211
room temperature; carbide dispersion treated at 1145 K for 1 h, air cooled followed by 1255 K for 1 h, air cooled; and then aged at 1035 K for 4 h, air cooled to room temperature. The hardness is about Rockwell C 45 and 47, and the average grain size is 10 and 45 mm for alloys 1 and 3, respectively. The average size of the g% precipitates within the Ni-based g matrix for both alloys is approximately 150 nm, except for the presence of about 5 vol.% of micrometer sized coarse g% precipitates in alloy 1.
Fig. 2. S.E.M. microfractographs showing the difference in the micromechanisms for crack growth in alloy 3 in high-purity oxygen with changes in dwell time from 0 to 10 s.
Fig. 1. S.E.M. microfractographs showing the difference in the micromechanisms for sustained-load crack growth in alloy 1 in high-purity argon and oxygen (arrows indicate some of the coarse g% precipitates) [3].
Compact-tension (CT) specimens (width: 50.8 mm, thickness: 3.2 mm) were cut from the forged pancake (away from the central region) such that specimens were equidistant from the center of the forging and the direction of crack growth was radial. In other words, the specimens were in the CR (circumferential-radial) orientation, with the crack plane perpendicular to the circumferential direction and crack growth in the radial direction. Crack growth experiments were conducted, under constant DK (stress intensity factor range) con-
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
212
Table 1 Compositions of the P/M alloys (wt.%) Alloy
Ni
Cr
Co
Ti
Al
Mo
Nb
C
B
Zr
Alloy 1 Alloy 3
56.28 54.5
12.7 12.3
18.9 18.2
3.9 3.0
4.8 3.7
3.3 3.3
B0.01 4.9
0.032 0.029
0.034 0.031
0.05 0.038
trol, at DK =27 MPa m1/2 with a load ratio R =0.1, in high-purity argon and oxygen at 873, 923 and 973 K. Due to the very slow rates of crack growth in argon and the limited number of specimens, a trapezoidal waveform was used, with 0.05 s up and down ramps and dwell times of 0, 3, 10 and 30 s. The 0 s dwell time corresponded to a cyclic load frequency of 10 Hz. More detailed information on the test procedures may be found in [1]. The crack growth responses are analyzed in terms of the general superposition model that considers the cycle- and time-dependent contributions, as well as mechanical and environmental contributions, and in terms of the microstructural variables.
involved extrapolations from K= 30 to about 60 MPa m1/2. These findings provide further support for the superposition model and the previous finding on the I/M Ni –18Cr–18Fe alloy [1]. The comparisons suggest that dwell time response can be directly estimated from the fatigue (cycle-dependent) and sustained-load crack growth data using the proposed superposition model. Conversely, dwell time experiments can be used to estimate sustained-load crack growth response as a means of reducing test time. From a lifecycle design and management perspective, the general superposition model can serve as a basis for structural performance and reliability analyses to examine conditions that extend beyond the range of the supporting data.
4. Results and discussion 5. Summary Typical crack growth data obtained from the DK controlled tests are shown in Fig. 3. The growth rates, (da/dN)dwell =(da/dN)e (see Eq. (5)), are determined from least squares linear regression fit to the crack length versus number of elapsed cycle data in Fig. 3, and are shown in Fig. 4. By identifying the first two terms on the right-hand side of Eq. (5) with the cycledependent fatigue crack growth rate (i.e. 0 s dwell time), the time-dependent contribution may be obtained; that is from Eq. (6).
da dN
=
time
=
da dN
da dt
−
dwell
da dN
cycle
(1 − EAC) +
creep
da dt
n
EAC × ~
EAC
Experiments were conducted on P/M nickel-base superalloys, in high-purity argon and oxygen at 873–973 K, to examine the mechanical and mechanistic aspects of dwell time, at maximum load, on fatigue crack growth. Analyses and interpretation of the results were made using a general superposition model for fatigue crack growth. The results showed that the crack growth rates increased linearly with increasing dwell time. The increase reflected the contribution by creep crack growth in argon, and by environmentally enhanced crack growth in oxygen. It is directly correlated with the relevant sustained-load crack growth rates, and is associated with changes in the micromechanisms for crack growth. The superposition model was validated
(6) These contributions are shown as a function of dwell time in Fig. 5 for alloy 1, and in Figs. 6 and 7 for alloy 3. The linear dependence attests to the efficacy of the proposed superposition model. By least squares linear regression fit to the data in Figs. 5– 7, sustained-load crack growth rates in highpurity argon and oxygen were estimated. Since the rates in argon are orders of magnitude slower than that in oxygen, their impact on the latter rates was neglected. The estimated rates (converted to K = 30 MPa m1/2 from DK =27 MPa m1/2) are shown in Figs. 8 and 9 in comparison with those determined from sustained-load tests. The estimated results are seen to be in good agreement; albeit the comparisons for the data in argon
Fig. 3. Typical crack growth data obtained from a constant DK test of alloy 1 as a function of dwell time.
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
213
Fig. 6. Effect of dwell time on the time-dependent component of fatigue crack growth rate for alloy 3 in argon at DK=27 MPa m1/2 (using normalized least squares linear regression fitting).
Fig. 4. Effect of dwell time on fatigue crack growth rate for alloy 1 in argon (top) and oxygen (bottom) at DK= 27 MPa m1/2.
Fig. 7. Effect of dwell time on the time-dependent component of fatigue crack growth rate for alloy 3 in oxygen at DK= 27 MPa m1/2.
Fig. 5. Effect of dwell time on the time-dependent component of fatigue crack growth rate for alloy 1 in argon and oxygen at DK=27 MPa m1/2.
through ex post facto comparisons of the estimated time-dependent contributions with independently obtained crack growth rate data from sustained-load tests.
Fig. 8. Comparisons between sustained-load crack growth rates inferred from the dwell time fatigue tests and those from direct measurements for alloy 1.
214
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
ologies for life-cycle design and management of engineered systems is recommended.
Acknowledgements This research is supported by the Division of Materials Research, National Science Foundation, under Grant No. DMR-9632994.
References
Fig. 9. Comparisons between sustained-load crack growth rates inferred from the dwell time fatigue tests and those from direct measurements for alloy 3.
The model facilitates estimation of service performance and offers a simplified procedure for estimating sustained-load crack growth data from dwell time tests. Its development and incorporation into suitable method-
[1] Chen Shyuan-Fang, R.P. Wei, Mat. Sci. Eng. A256 (1998) 197 –207. [2] Robert P. Wei, Oxygen enhanced crack growth in nickel-based P/M superalloys, in: K.-M. Chang, S.K. Srivastava, D.U. Furrer, K.R. Bain (Eds.), Advanced Technologies for Superalloy Affordability, The Minerals, Metals Materials Society, Warrendale, PA, 2000, pp. 103 – 112. [3] Z. Huang, et al., Metall. Mater. Trans. A (2002) in press. [4] R.P. Wei, J.D. Landes, Materials Research & Standards 9 (7) (1969) 25 – 46. [5] R.P. Wei, Ming Gao, Scr. Met. 17 (1983) 959 – 962. [6] H.D. Solomon, L.F. Coffin Jr, Effects of frequency and environment on fatigue crack growth in A286 at 1100 F, in: A.E. Carden, A.J. McEvily, C.H. Wells (Eds.), Fatigue at Elevated Temperatures, ASTM STP 520, American Society for Testing and Materials, Philadelphia, PA, 1973, pp. 112 – 124.
Influence of dwell time on fatigue crack growth in nickel-base superalloys Robert P. Wei *, Zhifan Huang Packard Laboratory, Department of Mechanical Engineering and Mechanics, Lehigh Uni6ersity, 19 Memorial Dri6e West, Bethlehem, PA 18015 -3085, USA Received 11 December 2000; received in revised form 26 November 2001
Abstract Engineered systems for high temperature service are often subjected to cyclic loads with dwell times at maximum load that can exacerbate fatigue damage evolution through creep and environment enhanced crack growth. Experiments are carried out to examine the influence of dwell time on fatigue crack growth in powder metallurgy (P/M) nickel-base superalloys in highpurity argon and oxygen at 873–973 K. This study complements a previous study on an ingot metallurgy (I/M) alloy. The data are analyzed using a general superposition model to capture the microstructural response to the conjoint actions of stress and environment. The model is validated through backward comparisons of the estimated time-dependent contributions with crack growth rate data from sustained-load tests. The mechanical and mechanistic implications of dwell time, the feasibility for inferring sustained-load crack growth rates from the dwell time tests, and the usefulness of the superposition model for life-cycle design and management of engineered structures are discussed. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Fatigue crack growth; Dwell time effect; Environmental effect; Temperature effect; Nickel-base superalloys
1. Introduction Engineering components and structures, designed for high-temperature service (such as those in chemical plants and stationary and aircraft turbine engines), are subjected to cyclic loads with dwell time, at maximum load, of different duration that can exacerbate the development of fatigue damage through creep and environment enhanced crack growth. An effective methodology to account for the influence of dwell time at load is needed, therefore, for use in the life-cycle design and management of such components and structures. The development of such a methodology requires mechanistic understanding of the processes of damage evolution and the interactions between loading and environmental variables. In this paper, the results from a study to examine the mechanical and mechanistic implications of dwell time, at maximum load, on fatigue crack growth in two powder metallurgy (P/M) nickel-base * Corresponding author. Tel.: +1-610-758-4100; fax: + 1-610-7586224 E-mail address: [email protected] (R.P. Wei).
superalloys are summarized. The base composition of the alloys is nearly that of IN100, except one of the alloys contained 5 wt.% of niobium. This study complements a previous study on an ingot metallurgy (I/M) Ni –18Cr –18Fe ternary alloy [1], and a companion study on oxygen enhanced, sustained-load crack growth in the P/M alloys [2,3]. The crack growth results are analyzed in terms of a general superposition model that had been proposed to account for the influence of dwell time on fatigue crack growth [1]. The model was derived from those developed for corrosion fatigue crack growth [4,5]. It incorporates the influence of environment on the cycle-dependent and time-dependent components of crack growth rate, and reflects the response of the alloy microstructure to the conjoint actions of stress and environment. Solomon and Coffin [6] developed the first derivative of the original superposition model by Wei and Landes [4] for use in high-temperature crack growth. To provide background for the experimental effort, the proposed general superposition model is first summarized.
0921-5093/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 1 ) 0 1 9 5 7 - 8
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
210
Following the early work of Wei and Landes [4], Wei and Gao [5] and Solomon and Coffin [6], the following general superposition model was proposed for use as a working hypothesis for the interpretation of environmentally enhanced fatigue crack growth rates in fatigue at elevated temperatures [1]. The model is based on the premise that the cycle-dependent (fatigue) and time-dependent (sustained-load) components of crack growth rates may be treated as contributions from two ‘independent’ sequential processes, with the overall fatigue crack growth rate given by:
da dN
da = dN e
da + dN cycle
(1)
da dN
=
cycle
da da (1− c) + c dN r dN c
& n & n ~
=
0
time
da dt ~
+
(2)
0
dt (1 − EAC)
creep
da dt
e
da da (1−c)+ dN r dN c c ~
+
0
~
+
0
da dt
da dN
dt (1−EAC)
creep
dt EAC
(4)
EAC
For trapezoidal loading, the load is constant during the dwell time and, therefore, K and the corresponding da/dt may be taken to be constant. Then, Eq. (4) may be simplified, in terms of the dwell time (~) at load, to:
da dN
=
e
da da (1−c)+ c dN r dN c
+
da dt
creep
(1−EAC)+
da dt
dt EAC
n
EAC ×~
EAC
(5)
In Eq. (2), (da/dN)r is the pure-mechanical fatigue crack growth rate; (da/dN)c is the pure-corrosion fatigue crack growth rate; and c, is the areal fraction of pure-corrosion fatigue. Similarly, the time-dependent crack growth rate is the weighted average of the pure-mechanical (or creep) and pure-environmental contributions integrated over one loading cycle, and is expressed by: da dN
=
time
In Eq. (1), (da/dN)cycle and (da/dN)time are the cycle-dependent and time-dependent rates, respectively. Within each of these processes, the mechanical (deformation) and environmental contributions are treated as being from independent parallel processes [5]; namely, a pure-mechanical and a pure-environmental contribution to the crack growth rate. The cycle-dependent crack growth rate is the weighted average of the pure-mechanical fatigue and pure-corrosion fatigue components, and is expressed by [5]:
& n & n da dN
2. General superposition model
(3)
EAC
In Eq. (3), (da/dt)creep and (da/dt)EAC are the K-dependent pure-mechanical and pure-environmentally assisted crack growth rates, respectively; and EAC is the areal fraction of the environmentally affected component of crack growth. The integration is taken over one fatigue cycle (or period ~) and reflects the changes in the steady-state, sustained-load crack growth rate with K during that cycle. By combining Eqs. (2) and (3), the overall fatigue crack growth rate is then given by:
The individual rates in Eq. (5) may be determined from fatigue and sustained-load tests in inert and ‘fully deleterious’ environments, respectively. Formulation of the model reflects the fact that the alloy microstructure responds differently to the conjoint actions of mechanical loading and the environment, which is reflected in the micromechanisms for crack growth. For example, for the niobium-free alloy, sustained-load cracking in an inert environment (high-purity argon), was by a microvoid coalescence mechanism. Whereas, cracking was predominately along the interfaces between the g matrix and the gamma-prime (g%) precipitates and grain boundaries to reflect the impact of oxidation (see Fig. 1) [2,3]. Typical changes in cracking mechanisms (or, crack paths) with dwell time are illustrated in Fig. 2 for the niobium-containing P/M alloy, showing the transition to predominant intergranular (IG) mode of fracture with increased dwell time from a mixture of IG and transgranular (TG) modes. 3. Material and experimental procedures The high-purity, P/M alloys were prepared by Homogeneous Metals, Inc.1 The niobium content in the alloys was chosen to be 0 and 5 wt.%. Their Co, Cr, Al and Ti concentrations were chosen so that the alloys would contain approximately the same amount of g% precipitates (about 53 vol.%). The niobium-free alloy is designated as alloy 1, and the niobium-containing alloy as alloy 3 [3]. Their chemical compositions are given in Table 1. Extruded bars of the P/M alloys (63.5 mm diameter by 165 mm long) were isothermally (pancake) forged into 6.35 mm thick plates at Pratt and Whitney, West Palm Beach, FL. They were heat treated as follows: solution treated in air at 1440 K for 1 h, air cooled to 1
Homogenous Metals, Inc., Clayville, NY 13322.
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
211
room temperature; carbide dispersion treated at 1145 K for 1 h, air cooled followed by 1255 K for 1 h, air cooled; and then aged at 1035 K for 4 h, air cooled to room temperature. The hardness is about Rockwell C 45 and 47, and the average grain size is 10 and 45 mm for alloys 1 and 3, respectively. The average size of the g% precipitates within the Ni-based g matrix for both alloys is approximately 150 nm, except for the presence of about 5 vol.% of micrometer sized coarse g% precipitates in alloy 1.
Fig. 2. S.E.M. microfractographs showing the difference in the micromechanisms for crack growth in alloy 3 in high-purity oxygen with changes in dwell time from 0 to 10 s.
Fig. 1. S.E.M. microfractographs showing the difference in the micromechanisms for sustained-load crack growth in alloy 1 in high-purity argon and oxygen (arrows indicate some of the coarse g% precipitates) [3].
Compact-tension (CT) specimens (width: 50.8 mm, thickness: 3.2 mm) were cut from the forged pancake (away from the central region) such that specimens were equidistant from the center of the forging and the direction of crack growth was radial. In other words, the specimens were in the CR (circumferential-radial) orientation, with the crack plane perpendicular to the circumferential direction and crack growth in the radial direction. Crack growth experiments were conducted, under constant DK (stress intensity factor range) con-
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
212
Table 1 Compositions of the P/M alloys (wt.%) Alloy
Ni
Cr
Co
Ti
Al
Mo
Nb
C
B
Zr
Alloy 1 Alloy 3
56.28 54.5
12.7 12.3
18.9 18.2
3.9 3.0
4.8 3.7
3.3 3.3
B0.01 4.9
0.032 0.029
0.034 0.031
0.05 0.038
trol, at DK =27 MPa m1/2 with a load ratio R =0.1, in high-purity argon and oxygen at 873, 923 and 973 K. Due to the very slow rates of crack growth in argon and the limited number of specimens, a trapezoidal waveform was used, with 0.05 s up and down ramps and dwell times of 0, 3, 10 and 30 s. The 0 s dwell time corresponded to a cyclic load frequency of 10 Hz. More detailed information on the test procedures may be found in [1]. The crack growth responses are analyzed in terms of the general superposition model that considers the cycle- and time-dependent contributions, as well as mechanical and environmental contributions, and in terms of the microstructural variables.
involved extrapolations from K= 30 to about 60 MPa m1/2. These findings provide further support for the superposition model and the previous finding on the I/M Ni –18Cr–18Fe alloy [1]. The comparisons suggest that dwell time response can be directly estimated from the fatigue (cycle-dependent) and sustained-load crack growth data using the proposed superposition model. Conversely, dwell time experiments can be used to estimate sustained-load crack growth response as a means of reducing test time. From a lifecycle design and management perspective, the general superposition model can serve as a basis for structural performance and reliability analyses to examine conditions that extend beyond the range of the supporting data.
4. Results and discussion 5. Summary Typical crack growth data obtained from the DK controlled tests are shown in Fig. 3. The growth rates, (da/dN)dwell =(da/dN)e (see Eq. (5)), are determined from least squares linear regression fit to the crack length versus number of elapsed cycle data in Fig. 3, and are shown in Fig. 4. By identifying the first two terms on the right-hand side of Eq. (5) with the cycledependent fatigue crack growth rate (i.e. 0 s dwell time), the time-dependent contribution may be obtained; that is from Eq. (6).
da dN
=
time
=
da dN
da dt
−
dwell
da dN
cycle
(1 − EAC) +
creep
da dt
n
EAC × ~
EAC
Experiments were conducted on P/M nickel-base superalloys, in high-purity argon and oxygen at 873–973 K, to examine the mechanical and mechanistic aspects of dwell time, at maximum load, on fatigue crack growth. Analyses and interpretation of the results were made using a general superposition model for fatigue crack growth. The results showed that the crack growth rates increased linearly with increasing dwell time. The increase reflected the contribution by creep crack growth in argon, and by environmentally enhanced crack growth in oxygen. It is directly correlated with the relevant sustained-load crack growth rates, and is associated with changes in the micromechanisms for crack growth. The superposition model was validated
(6) These contributions are shown as a function of dwell time in Fig. 5 for alloy 1, and in Figs. 6 and 7 for alloy 3. The linear dependence attests to the efficacy of the proposed superposition model. By least squares linear regression fit to the data in Figs. 5– 7, sustained-load crack growth rates in highpurity argon and oxygen were estimated. Since the rates in argon are orders of magnitude slower than that in oxygen, their impact on the latter rates was neglected. The estimated rates (converted to K = 30 MPa m1/2 from DK =27 MPa m1/2) are shown in Figs. 8 and 9 in comparison with those determined from sustained-load tests. The estimated results are seen to be in good agreement; albeit the comparisons for the data in argon
Fig. 3. Typical crack growth data obtained from a constant DK test of alloy 1 as a function of dwell time.
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
213
Fig. 6. Effect of dwell time on the time-dependent component of fatigue crack growth rate for alloy 3 in argon at DK=27 MPa m1/2 (using normalized least squares linear regression fitting).
Fig. 4. Effect of dwell time on fatigue crack growth rate for alloy 1 in argon (top) and oxygen (bottom) at DK= 27 MPa m1/2.
Fig. 7. Effect of dwell time on the time-dependent component of fatigue crack growth rate for alloy 3 in oxygen at DK= 27 MPa m1/2.
Fig. 5. Effect of dwell time on the time-dependent component of fatigue crack growth rate for alloy 1 in argon and oxygen at DK=27 MPa m1/2.
through ex post facto comparisons of the estimated time-dependent contributions with independently obtained crack growth rate data from sustained-load tests.
Fig. 8. Comparisons between sustained-load crack growth rates inferred from the dwell time fatigue tests and those from direct measurements for alloy 1.
214
R.P. Wei, Z. Huang / Materials Science and Engineering A336 (2002) 209–214
ologies for life-cycle design and management of engineered systems is recommended.
Acknowledgements This research is supported by the Division of Materials Research, National Science Foundation, under Grant No. DMR-9632994.
References
Fig. 9. Comparisons between sustained-load crack growth rates inferred from the dwell time fatigue tests and those from direct measurements for alloy 3.
The model facilitates estimation of service performance and offers a simplified procedure for estimating sustained-load crack growth data from dwell time tests. Its development and incorporation into suitable method-
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