- Email: [email protected]
Determination of the fatigue crack growth threshold in cold-worked Zr-2.5 wt% Nb in the acoustic frequency range
70
Journal of Nuclear Materials
132 (1985) 70-73 North-Holland. Amsterdam
LETTER
TO THE EDITORS
DETERMINATION Zr-2.5
OF THE
FATIGUE
wt% Nb IN THE ACOUSTIC
CRACK
FREQUENCY
Of the possible mechanisms for sub-critical crack growth in cold-worked Zr-2.5 wt% Nb pressure-tube material, delayed hydride cracking (DHC) has received by far the most attention [l]. Because of the generally lower growth rates, fatigue cracking is not considered to be a serious limitation on pressure-tube life. However, it is a viable mechanism for crack growth in this material, and if the conditions for DHC are not met [l], it becomes the most significant one. Data on fatigue crack growth rates in zirconium alloy pressure tubes are limited, especially data on threshold stress intensity factors. Pickles and Picker [2] reported fatigue crack growth thresholds for Zircaloy-2 in dry air at room temperature ranging from 3 MPa m’/2 at low R ratios to 1.6 MPa ml/’ for R = 0.92 (R = K,,,/K,,, where K,,, and K,,, are the minimum and maximum values of the stress intensity factor, respectively, during a fatigue cycle). Tests in water at 7 MPa and 260°C showed growth rates an order of magnitude higher than in air and a threshold near 1 MPa m’/2 Wilkins and Reich [3] measured growth rates in air at 20°C and 400°C in cold-worked Zr-2.5 wt% Nb. The growth rates at the higher temperature were only twice those at 20°C. A fatigue threshold was not clearly established, but at 20°C there was a suggestion one near 7 MPa m’12. Clearly, better information on crack growth thresholds is needed where fatigue is a consideration in design, or for fitness-for-purpose assessments of known flaws in a tube. The main difficulty in establishing fatigue threshold data for any material is the large number of cycles required to measure the small growth rates accurately. Conventional fatigue-testing equipment operates at maximum frequencies between 20 and 200 Hz. Recently, a number of papers have been published describing the use of ultrasonic frequencies (- 20 kHz) to measure low. fatigue-crack growth rates. Stickler and Weiss [4] have published a review of these methods. In this note, we report some preliminary results that illustrate the high potential of tests at acoustic frequen* Issued as AECL-8594. 0022-3115/85/$03.30
(North-Holland
0 Elsevier
Physics Publishing
Science
Publishers
Division)
GROWTH
THRESHOLD
IN COLD-WORKED
RANGE *
ties for establishing fatique thresholds in reasonable frames. We also confirm the existence of a fatigue threshold for Zr-2.5 wt% Nb. Several years ago, a program to measure DHC growth rates was initiated in which the change in resonant frequency of a single edge-notched beam subject to four-point bending was used to measure changes in crack length [5]. The beam was statically loaded and periodically vibrated in transverse flexure to look for changes in resonant frequency. It was observed that very rapid crack growth occurred at resonance, by a mechanism not related to DHC, but clearly fatigue related. Recently, a series of tests was carried out using the same apparatus, specifically to measure fatigue-crack growth rates at cyclic stress intensities near the threshold. Notched, four-point bend specimens, 9.5 cm long. were prepared from flattened, Zr-2.5 wt% Nb pressure-tube material, with the beam axis in the tube’s circumferential direction. A square cross-section of 0.35 cm x 0.35 cm was selected, with a 0.12-cm deep V-notch either in the tube radial (R) or axial (A) direction. A fatigue starter crack was induced at the notch tip by cycling under four-point bending in an Amsler Vibraphore. The specimen was then loaded (see fig. 1) with the loading points at the nodal positions of the second overtone of flexural vibration [4]. The analysis used to determine these positions is described by Rosinger et al. [6] and Ritchie [7]. The inner two loading points were, in fact, fine wires from which a bucket was suspended. The load was varied by adding (or removing) lead shot to (from) the bucket. The specimen was vibrated using a Magnatest Elastomat. Type FM500. with the circuitry shown in fig. 2. Vibrations were induced in a piezoelectric driver crystal and transmitted to the specimen by a fine wire. The frequency was adjusted either manually, using the oscillator and oscilloscope, or automatically, using the feedback from the displacement transducer and a phase adjuster [5-71. Six specimens were tested, two with cracks in the A orientation and four with cracks in the R orientation. An initial load was placed on the specimen to yield a static stress intensity factor K = 6 MPa m”‘. The specimen was then placed in resonance, which
B.V.
L.A. Simpson / Determination of the faiigue crack growth threshold LOAD I
Y
t
Ix
Fig. 1. Specimen loading arrangement overtone. transverse flexural mode.
for vibration
in first
occurred between 7 and 8 kHz. Resonance in the second flexural overtone was confirmed by traversing the length of the specimen with an optical transducer [5] to map the shape of the vibrating specimen. The transducer was then placed opposite the crack (fig. 2) to measure the vibration amplitude at that point.
I
L
3d SELECTOR
CONTROLLED AMPLIFIER
I--
A decrease in resonant frequency indicated crack propagation. If the resonance frequency did not change after a reasonable period of time (10 to 20 min), the applied stress intensity factor was increased by 1 to 2 MPa m’/‘. When crack propagation started, the system was allowed to run for a short period, usually between 30 s and 15 min depending on the growth rate, to yield an increment of crack growth of several tenths of a millimetre. The specimen was then heat tinted and broken open to measure the crack growth accurately. The results of the tests are summarized in table 1. Usually, a minimum applied stress intensity factor (mean load) was necessary before crack propagation occurred, but the magnitude of this was highly variable from test to test, and did not appear to be related to the crack growth rates. The applied stress intensity factor was calculated using the moment for four-point loading and the standard ASTM equations. The alternating stress intensity factor was calculated from the additional bending moment induced by the vibration. The vibration shape is virtually sinusoidal [6,8] between the inner loading points and is given by (see fig. 1)
(1)
y = 6 sin(mx/s), where s = the nodal length.
spacing = 0.288 f., and L = beam
FEEDBACK
,
NON-CONTACTING
SWITCH
OPTICAL
TRANSDUCER’
77 DRIVER
VARIABLE OSCILLATOR
1
1
COUPLING WIRE
\~/qiiiKF
AND POWER AMPL;FIER
]
OSCILLOSCOPE (L ISSAJOU FIG)
Fig. 2. Basic electronic
instrumentation
incorporating
the non-contacting
71
optical
sensor as pick-up
transducer.
L.A. Smpson / Determinatron of the fatigue crack growth threshold
12 Table 1 Fatigue test results Specimen number
2(R) 4W) ’ 4(R) a 5(R) 6(R) l(A) 2(A)
Final crack length
K
Vibration amplitude
a1 (mm)
a2
(MPa ml/*)
AQm)
1.63 1.53 1.67 1.42 1.37 1.37 1.43
1.90 1.67 1.99 1.96 1.62 2.51 2.09
a Two consecutive
The bending is given by d2y __= 2 dx
R
Initial crack length
_- M EI
Mean
EI$AS,
(MPa m”*)
runs carried
moment,
34.0 19.7 20.0 16.3 18.7 11.7 12.2
0.87 0.88 0.75 0.65 0.78 0.72 0.84
2.35 1.30 2.83 3.85 2.02 2.23 1.17
4.83 2.51 5.69 7.00 3.50 3.88 2.12
Test duration
(Hz)
(s)
7528 1564 1356 1675 7718 7246 7612
563 172 30 31 830 161 180
-da dN
63.1 108.0 1450.0 2270.0 39.0 974.0 482.0
out on this specimen
M, induced
by this vibration
d
(2)
T
. ” . . P
lO-6
I
.
(3)
16'
where AS = 28. The alternating stress intensity factor, AK, being linear in the bending moment, can be calculated from AK=$!K,
Average frequency
(mm)
where E = Young’s modulus, and I = moment of inertia. At the position of the crack (x = s/2), where the displacement is a maximum (*S), the cyclic bending moment is (from eqs. (1) and (2)) AM=
AK
(4)
where M and K are the applied bending moment and stress intensity factor, respectively. The results of the tests are plotted in fig. 3 along with the results of Wilkins and Reich [3] for 20°C. While the scatter for a given AK is high, the results suggest a very steep dependence on that factor, consistent with the implied threshold of Wilkins and Reich’s data at AK = 7 MPa m”‘. It is arguable whether this represents a threshold effect or a change in the crack growth mechanism, but the steep slope of our data indicates that the effect is essentially that of a threshold. A change in mechanism is not unexpected, as the data in fig. 3 include growth rates less than one atomic spacing per cycle. Thus, the conventional fatigue mechanisms involving alternating slip lose their physical significance.
( I I
2 10-e 2
I
2
;o”
02 DO ?
iO-g
“I I
A
. Ref 3 o Radial A Axial
i
d
“I
p” 16"
I
1.0
I
100
IO
AK (MPa
rnh)
Fig. 3. Fatigue crack growth rate vs. cyclic factor for Zr-2.5 wt% Nb at 2O’C.
stress
intensity
L.A. Simpson
/ Determination
Much of the scatter in the data may be a result of using equipment and a test procedure that were not specifically designed for fatigue studies. However, these results demonstrate that testing at acoustic frequencies facilitates the measurement of crack growth rates three orders of magnitude less than by using conventional methods. The method described here has certain advantages over other ultrasonic methods currently in use. Many of the latter use longitudinal vibrations in a tensile specimen to drive the crack, and such methods are often restricted to a tensile/compression mode (R < 0). In our method, any mean load can be applied and R values approaching unity are possible. This is important since our results suggest a minimum mean load requirement may exist. Secondly, by placing the loading points at the nodal positions and using a non-contacting displacement transducer, there is no interference with the specimen vibration from external sources. Because this method is amenable to operation in an environmental chamber, it shows good potential as a method for fully characterizing the near-threshold fatique behaviour of Zr-2.5 wt% Nb.
Received
15 December
1984; accepted
25 January
1985
of the fatigue crack growth threshold
73
Acknowledgements The author is grateful to A.J. Shillinglaw for modifying the equipment and carrying out the fatigue experiments.
References [l] L.A. Simpson and M.P. Puls, Met. Trans. 10A (1979) 1093. [2] B.W. Pickles and C. Picker, in: Proc. 6th Intern. Conf. on Structural Mechanics in Reactor Technology, 1981, Paris (North Holland, Amsterdam, 1981) Vol. F, Paper No. 6/4. [3] B.J.S. Wilkins and A.R. Reich, Probabilistic aspects of fatigue crack propagation data for zirconium-2.58 niobium, Atomic Energy of Canada Limited Report, AECL-5529 (November 1976). [4] R. Stickler and B. Weiss, in: Ultrasonic Fatigue, Eds. J.M. Wells. 0. Buck, L.D. Roth and J.K. Tien, (Met. Sot. AIME, Warrendale, PA, 1982) p. 135. [5] I.G. Ritchie, H.E. Rosinger and A.J. Shillinglaw, J. American Ceram. Sot. 57 (1974) 453. [6] H.E. Rosinger, LG. Ritchie and A.J. Shillinglaw, Improved measurements of elastic properties at acoustic resonant frequencies, Atomic Energy of Canada Limited Report, AECL-5114 (January 1976). [7] I.G. Ritchie, J. Sound Vib. 31 (1973) 453. [8] I.G. Ritchie. unpublished results.
LA. Simpson Atomrc Energy of Canada Limited Whiteshell Nuclear Research Establishment Pmawa, Manrtoba ROE IL0 Canada
Journal of Nuclear Materials
132 (1985) 70-73 North-Holland. Amsterdam
LETTER
TO THE EDITORS
DETERMINATION Zr-2.5
OF THE
FATIGUE
wt% Nb IN THE ACOUSTIC
CRACK
FREQUENCY
Of the possible mechanisms for sub-critical crack growth in cold-worked Zr-2.5 wt% Nb pressure-tube material, delayed hydride cracking (DHC) has received by far the most attention [l]. Because of the generally lower growth rates, fatigue cracking is not considered to be a serious limitation on pressure-tube life. However, it is a viable mechanism for crack growth in this material, and if the conditions for DHC are not met [l], it becomes the most significant one. Data on fatigue crack growth rates in zirconium alloy pressure tubes are limited, especially data on threshold stress intensity factors. Pickles and Picker [2] reported fatigue crack growth thresholds for Zircaloy-2 in dry air at room temperature ranging from 3 MPa m’/2 at low R ratios to 1.6 MPa ml/’ for R = 0.92 (R = K,,,/K,,, where K,,, and K,,, are the minimum and maximum values of the stress intensity factor, respectively, during a fatigue cycle). Tests in water at 7 MPa and 260°C showed growth rates an order of magnitude higher than in air and a threshold near 1 MPa m’/2 Wilkins and Reich [3] measured growth rates in air at 20°C and 400°C in cold-worked Zr-2.5 wt% Nb. The growth rates at the higher temperature were only twice those at 20°C. A fatigue threshold was not clearly established, but at 20°C there was a suggestion one near 7 MPa m’12. Clearly, better information on crack growth thresholds is needed where fatigue is a consideration in design, or for fitness-for-purpose assessments of known flaws in a tube. The main difficulty in establishing fatigue threshold data for any material is the large number of cycles required to measure the small growth rates accurately. Conventional fatigue-testing equipment operates at maximum frequencies between 20 and 200 Hz. Recently, a number of papers have been published describing the use of ultrasonic frequencies (- 20 kHz) to measure low. fatigue-crack growth rates. Stickler and Weiss [4] have published a review of these methods. In this note, we report some preliminary results that illustrate the high potential of tests at acoustic frequen* Issued as AECL-8594. 0022-3115/85/$03.30
(North-Holland
0 Elsevier
Physics Publishing
Science
Publishers
Division)
GROWTH
THRESHOLD
IN COLD-WORKED
RANGE *
ties for establishing fatique thresholds in reasonable frames. We also confirm the existence of a fatigue threshold for Zr-2.5 wt% Nb. Several years ago, a program to measure DHC growth rates was initiated in which the change in resonant frequency of a single edge-notched beam subject to four-point bending was used to measure changes in crack length [5]. The beam was statically loaded and periodically vibrated in transverse flexure to look for changes in resonant frequency. It was observed that very rapid crack growth occurred at resonance, by a mechanism not related to DHC, but clearly fatigue related. Recently, a series of tests was carried out using the same apparatus, specifically to measure fatigue-crack growth rates at cyclic stress intensities near the threshold. Notched, four-point bend specimens, 9.5 cm long. were prepared from flattened, Zr-2.5 wt% Nb pressure-tube material, with the beam axis in the tube’s circumferential direction. A square cross-section of 0.35 cm x 0.35 cm was selected, with a 0.12-cm deep V-notch either in the tube radial (R) or axial (A) direction. A fatigue starter crack was induced at the notch tip by cycling under four-point bending in an Amsler Vibraphore. The specimen was then loaded (see fig. 1) with the loading points at the nodal positions of the second overtone of flexural vibration [4]. The analysis used to determine these positions is described by Rosinger et al. [6] and Ritchie [7]. The inner two loading points were, in fact, fine wires from which a bucket was suspended. The load was varied by adding (or removing) lead shot to (from) the bucket. The specimen was vibrated using a Magnatest Elastomat. Type FM500. with the circuitry shown in fig. 2. Vibrations were induced in a piezoelectric driver crystal and transmitted to the specimen by a fine wire. The frequency was adjusted either manually, using the oscillator and oscilloscope, or automatically, using the feedback from the displacement transducer and a phase adjuster [5-71. Six specimens were tested, two with cracks in the A orientation and four with cracks in the R orientation. An initial load was placed on the specimen to yield a static stress intensity factor K = 6 MPa m”‘. The specimen was then placed in resonance, which
B.V.
L.A. Simpson / Determination of the faiigue crack growth threshold LOAD I
Y
t
Ix
Fig. 1. Specimen loading arrangement overtone. transverse flexural mode.
for vibration
in first
occurred between 7 and 8 kHz. Resonance in the second flexural overtone was confirmed by traversing the length of the specimen with an optical transducer [5] to map the shape of the vibrating specimen. The transducer was then placed opposite the crack (fig. 2) to measure the vibration amplitude at that point.
I
L
3d SELECTOR
CONTROLLED AMPLIFIER
I--
A decrease in resonant frequency indicated crack propagation. If the resonance frequency did not change after a reasonable period of time (10 to 20 min), the applied stress intensity factor was increased by 1 to 2 MPa m’/‘. When crack propagation started, the system was allowed to run for a short period, usually between 30 s and 15 min depending on the growth rate, to yield an increment of crack growth of several tenths of a millimetre. The specimen was then heat tinted and broken open to measure the crack growth accurately. The results of the tests are summarized in table 1. Usually, a minimum applied stress intensity factor (mean load) was necessary before crack propagation occurred, but the magnitude of this was highly variable from test to test, and did not appear to be related to the crack growth rates. The applied stress intensity factor was calculated using the moment for four-point loading and the standard ASTM equations. The alternating stress intensity factor was calculated from the additional bending moment induced by the vibration. The vibration shape is virtually sinusoidal [6,8] between the inner loading points and is given by (see fig. 1)
(1)
y = 6 sin(mx/s), where s = the nodal length.
spacing = 0.288 f., and L = beam
FEEDBACK
,
NON-CONTACTING
SWITCH
OPTICAL
TRANSDUCER’
77 DRIVER
VARIABLE OSCILLATOR
1
1
COUPLING WIRE
\~/qiiiKF
AND POWER AMPL;FIER
]
OSCILLOSCOPE (L ISSAJOU FIG)
Fig. 2. Basic electronic
instrumentation
incorporating
the non-contacting
71
optical
sensor as pick-up
transducer.
L.A. Smpson / Determinatron of the fatigue crack growth threshold
12 Table 1 Fatigue test results Specimen number
2(R) 4W) ’ 4(R) a 5(R) 6(R) l(A) 2(A)
Final crack length
K
Vibration amplitude
a1 (mm)
a2
(MPa ml/*)
AQm)
1.63 1.53 1.67 1.42 1.37 1.37 1.43
1.90 1.67 1.99 1.96 1.62 2.51 2.09
a Two consecutive
The bending is given by d2y __= 2 dx
R
Initial crack length
_- M EI
Mean
EI$AS,
(MPa m”*)
runs carried
moment,
34.0 19.7 20.0 16.3 18.7 11.7 12.2
0.87 0.88 0.75 0.65 0.78 0.72 0.84
2.35 1.30 2.83 3.85 2.02 2.23 1.17
4.83 2.51 5.69 7.00 3.50 3.88 2.12
Test duration
(Hz)
(s)
7528 1564 1356 1675 7718 7246 7612
563 172 30 31 830 161 180
-da dN
63.1 108.0 1450.0 2270.0 39.0 974.0 482.0
out on this specimen
M, induced
by this vibration
d
(2)
T
. ” . . P
lO-6
I
.
(3)
16'
where AS = 28. The alternating stress intensity factor, AK, being linear in the bending moment, can be calculated from AK=$!K,
Average frequency
(mm)
where E = Young’s modulus, and I = moment of inertia. At the position of the crack (x = s/2), where the displacement is a maximum (*S), the cyclic bending moment is (from eqs. (1) and (2)) AM=
AK
(4)
where M and K are the applied bending moment and stress intensity factor, respectively. The results of the tests are plotted in fig. 3 along with the results of Wilkins and Reich [3] for 20°C. While the scatter for a given AK is high, the results suggest a very steep dependence on that factor, consistent with the implied threshold of Wilkins and Reich’s data at AK = 7 MPa m”‘. It is arguable whether this represents a threshold effect or a change in the crack growth mechanism, but the steep slope of our data indicates that the effect is essentially that of a threshold. A change in mechanism is not unexpected, as the data in fig. 3 include growth rates less than one atomic spacing per cycle. Thus, the conventional fatigue mechanisms involving alternating slip lose their physical significance.
( I I
2 10-e 2
I
2
;o”
02 DO ?
iO-g
“I I
A
. Ref 3 o Radial A Axial
i
d
“I
p” 16"
I
1.0
I
100
IO
AK (MPa
rnh)
Fig. 3. Fatigue crack growth rate vs. cyclic factor for Zr-2.5 wt% Nb at 2O’C.
stress
intensity
L.A. Simpson
/ Determination
Much of the scatter in the data may be a result of using equipment and a test procedure that were not specifically designed for fatigue studies. However, these results demonstrate that testing at acoustic frequencies facilitates the measurement of crack growth rates three orders of magnitude less than by using conventional methods. The method described here has certain advantages over other ultrasonic methods currently in use. Many of the latter use longitudinal vibrations in a tensile specimen to drive the crack, and such methods are often restricted to a tensile/compression mode (R < 0). In our method, any mean load can be applied and R values approaching unity are possible. This is important since our results suggest a minimum mean load requirement may exist. Secondly, by placing the loading points at the nodal positions and using a non-contacting displacement transducer, there is no interference with the specimen vibration from external sources. Because this method is amenable to operation in an environmental chamber, it shows good potential as a method for fully characterizing the near-threshold fatique behaviour of Zr-2.5 wt% Nb.
Received
15 December
1984; accepted
25 January
1985
of the fatigue crack growth threshold
73
Acknowledgements The author is grateful to A.J. Shillinglaw for modifying the equipment and carrying out the fatigue experiments.
References [l] L.A. Simpson and M.P. Puls, Met. Trans. 10A (1979) 1093. [2] B.W. Pickles and C. Picker, in: Proc. 6th Intern. Conf. on Structural Mechanics in Reactor Technology, 1981, Paris (North Holland, Amsterdam, 1981) Vol. F, Paper No. 6/4. [3] B.J.S. Wilkins and A.R. Reich, Probabilistic aspects of fatigue crack propagation data for zirconium-2.58 niobium, Atomic Energy of Canada Limited Report, AECL-5529 (November 1976). [4] R. Stickler and B. Weiss, in: Ultrasonic Fatigue, Eds. J.M. Wells. 0. Buck, L.D. Roth and J.K. Tien, (Met. Sot. AIME, Warrendale, PA, 1982) p. 135. [5] I.G. Ritchie, H.E. Rosinger and A.J. Shillinglaw, J. American Ceram. Sot. 57 (1974) 453. [6] H.E. Rosinger, LG. Ritchie and A.J. Shillinglaw, Improved measurements of elastic properties at acoustic resonant frequencies, Atomic Energy of Canada Limited Report, AECL-5114 (January 1976). [7] I.G. Ritchie, J. Sound Vib. 31 (1973) 453. [8] I.G. Ritchie. unpublished results.
LA. Simpson Atomrc Energy of Canada Limited Whiteshell Nuclear Research Establishment Pmawa, Manrtoba ROE IL0 Canada