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A detailed study of the relationship between fatigue crack growth rate and striation spacing in a range of low alloy ferritic steels
Engineering Failure Analysis 17 (2010) 168–178
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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
A detailed study of the relationship between fatigue crack growth rate and striation spacing in a range of low alloy ferritic steels J.H. Bulloch *, A.G. Callagy Power Generation, ESB, Head Office, Dublin 2, Ireland
a r t i c l e
i n f o
Article history: Received 12 February 2009 Accepted 10 April 2009 Available online 13 May 2009 Keywords: Fatigue crack growth Fatigue striations Statistics Stress intensity range Probability
a b s t r a c t It was shown that the measured average fatigue striation spacings predicted the fatigue crack growth rates for low alloy ferritic steels to within a range of ±2% to 35% with an overall average error band value of ±10.1%. When we consider the fatigue stress range this average error was reduced to only some ±4%. This was good news to both failure analysts and other workers involved in the field of component remnant life and life extension since such predicted fatigue stress ranges use real fracture characteristics observed at some point on the actual component fracture surface. These findings were applied to a real cracking problem recently reported in a steam raising plant, viz., a cracked attemperator reducer weld. In this case an NDT assessment indicated that the maximum crack depth was 7 mm while the lower bound critical crack depth was estimated at 10 mm. As such, remnant life assessments can be estimated for a series of fatigue stress ranges through the use of a reported 450 °C fatigue crack growth law for C– Mn steels. Remnant life estimates of a 7 mm deep crack for a range of stress ranges varied from 3000 to 4000 starts where the chances of the real remnant life values being greater than the calculated values was only 1 in 2. However when a realistic failure probability which reflected the serious implications of a failure event of E4 was taken the remnant life values were reduced to around 100 starts or some 6 months of normal service. Ó 2009 Published by Elsevier Ltd.
1. Introduction Probably some of the initial mechanistic information regarding fatigue crack growth was recorded from fracture surface examinations. These found that many fracture surfaces formed under cyclic loading exhibited periodic markings on both a macroscopic and microscopic scale; the latter was known as fatigue striations which occurred during Stage 11 fatigue crack growth. During this particular fatigue stage a crack can often grow on multiple plateaus which are at different heights with respect to one another. Fatigue striations, which were first recognized by Zaffe and Worden [1] often bow out in the direction of crack growth and generally tend to align at right angles to the principal crack growth direction. There have been several models proposed to account for striation formation with Forsyth and Ryder [2] suggesting over six decades ago that fracture occurred ahead of the crack tip with the striation profile being formed by subsequent of the intermediate material. A more generalized approach was reported by Laird and Smith [3] where they described the growth process as one involving crack blunting on the tensile part of the cycle and re-sharpening during
* Corresponding author. E-mail address: [email protected] (J.H. Bulloch). 1350-6307/$ - see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.engfailanal.2009.04.028
169
FATIGUE CRACK GROWTH RATE (mm/c)
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0.01 CRACK GROWTH RATE
A533B STEEL PWR WATER HIGH TEMPERATURE; REF. 12
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
0.001
A533B STEEL AIR AMBIENT; REF. 8
0.0001 10
100
1000
DELTA K (MPa/m) Fig. 1. Fatigue crack growth data for A533B steel in high temperature PWR water and ambient air.
FATIGUE CRACK GROWTH RATE (mm/c)
0.01 DUCOL STEEL AIR AMBIENT REF. 15
A508 STEEL PWR WATER 290 DEGREES REF. 13
A533B STEEL AIR AMBIENT REF8
0.001 CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE
0.0001
STRIATION SPACING A533B STEEL PWR WATER 290 DEGREES REF 14
CRACK GROWTH RATE A508 STEEL PWR WATER AMBIENT
STRIATION SPACING
0.00001 10
100
1000
DELTA K (MPa/m) Fig. 2. Fatigue crack growth data for a series of low alloy ferritic pressure vessel steels.
Fig. 3. Ductile fatigue striations in a C–Mn steel component operating at high temperature. The average striation spacing at this point was assessed at 0.8 lm; after Ref. [24].
FATIGUE CRACK GROWTH RATE (mm/c)
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0.01 PWR HIGH TEMPERATURE WATER. REF. 18
AVERAGE ARGON STRIATION SPACING ARGON
Ni-Mo-V STEEL AMBIENT AIR REF. 8
AVERAGE PWR STRIATION SPACING PWR AVERAGE PWR STRIATION SPACING PWR
0.001
CRACK GROWTH RATE STRIATION SPACING
PWR AMBIENT WATER DATA REF 17
0.0001
ARGON DATA REF 17
0.00001 0
20
40
60
80
100
120
DELTA K (MPa/m) Fig. 4. Fatigue crack growth data for A508 steel in argon and PWR water environments and Ni–Mo–V steel in ambient air.
the compressive stroke. A third model, termed the crystallographic model, suggested that one or both sides of the striations are parallel to the slip systems, and in which the positions of the slip planes determine the local angle of the striations with respect to the general crack growth direction [4]. A similar, but more generalized approach is involved in the sliding-off or shear decohesion models in which separation occurs on alternating planes of maximum resolved shear stress [5]. The problem of establishing the actual, or real striation spacing, in a non-planar fracture surface has been examined in detail by Underwood and Starke [6] who showed that certain corrections for orientation and surface roughness effects were required to the striation spacing obtained in a scanning electron microscope, SEM, survey. However, when comparing striation spacing to fatigue crack growth rate no such corrections to the measured striation spacings are necessary since both are projected quantities. Nearly 50 years ago Forsyth and Ryder [7] reported some work on variable loading which showed that the striation spacings and numbers corresponded to that of the loading sequence thus establishing that striation spacings represented the growth distance per fatigue cycle. Almost a decade after this Bates and Clark [8] reported for a range three steels, two Al-alloys and a Ti-alloy that the striation spacing exhibited good agreement with measured fatigue crack growth data. Some 25 years ago Hertzberg and Euw [9] also reported a close correlation between crack growth rates and average striation spacing values in an Al-alloy. Around a decade later Au and Ke [10] reported the following conclusions for a high strength Ni–Cr–Mo martensitic steel; (a) good
0.01
FATIGUE CRACK GROWTH RATE (mm/c)
1/2 CTOD(max) LINE
0.001
CRACK GROWTH DATA
0.0001
SINGLE STRIATION SPACING COARSE STRIATION SPACING
0.00001 10
100
DELTA K (MPa/m) Fig. 5. Fatigue crack growth data for A C–Mn steel in argon at ambient temperature, Ref. [19].
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FATIGUE CRACK GROWTH RATE (mm/c)
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0.01 R = -1 CRACK GROWTH RATE R = -1 STRIATION SPACING R = 0 CRACK GROWTH RATE R = 0 STRIATION SPACING
R-RATIO = ZERO AND 0.5 DATA
R = 0.5 CRACK GROWTH RATE R = 0.5 STRIATION SPACING
0.001
R-RATIO = -1 DATA
0.0001 100
10 DELTA K (MPa/m) Fig. 6. Fatigue crack growth data for a carbon, high Mn steel in ambient air, Ref. [20].
correlation was observed between the macroscopic crack growth rate and fatigue striation spacing for crack growth rates ranging from 103 to 104 mm/cycle and (b) this correlation was not affected by the R-ratio, frequency, environment and material strength. More recently, some 14 years ago Davidson and Lankford [11] published a detailed review on fatigue mechanisms and micromechanics in metals and alloys. Generally, they found in some cases that one striation may not necessarily correspond to one fatigue cycle; this was especially the case in the near threshold Stage 1 fatigue crack growth region. Indeed in this fatigue region fatigue striations can exceed measured crack growth rates by orders of magnitude. However the present paper deals only with stage 11 fatigue region correlations between striation spacings and crack growth rates and in this region the Davidson and Lankford data [11] exhibited good agreement in a range of materials. As such, it is clear that some reasonable correlation existed between crack growth and striation spacings and the aim of this paper is to try and quantify this correlation on a statistical basis for a range of commercial low alloy ferritic steels.
2. Fatigue crack growth–striation spacing data
FATIGUE CRACK GROWTH RATE (mm/c)
Perhaps the most significant amount of fatigue crack growth–striation spacing data has been reported by Bates and Clark [8] for a ferritic A533B pressure vessel steel in air at ambient temperatures, see Fig. 1 together with other results for a A508 pressure vessel steel in PWR water at elevated temperatures [12]. From this figure it was evident that the crack growth and striation spacing data exhibited reasonable agreement and contained over 50 data sets.
0.1 2900C Zero Hold
CRACK GROWTH RATE
2900C 30Sec Hold
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
0
290 C 1Min Hold
CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE
0.01
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
0.001 900C 1Min Hold
Sub-Zero A533B Steel Data Ref. 8
0.0001 10
100 DELTA K (MPa/m) Fig. 7. High temperature PWR data for A508 steel, Ref. [18] and sub-zero A533B steel air data, Ref. [8].
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FATIGUE CRACK GROWTH RATE (mm/c)
172
0.01
REF 21
0.001
0.0001 CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
REF 11
0.00001 10
100
DELTA K (MPa/m) Fig. 8. Fatigue crack growth data for a C–Mn steel in ambient air, Ref. [11] and A533B steel in high temperature PWR water, Ref. [21].
Ln CRACK GROWTH RATE / STRIATION SPACING (mm/c)
-5.00
-6.00
-7.00
-8.00
-9.00
-10.00 0
20
40
60
80
100
120
140
DELTA K (MPa/m)
Ln CRACK GROWTH RATE / STRIATION SPACING (mm/c)
Fig. 9. A statistical analysis of the bates and clark A533B ferritic A533B steel ambient air data, Ref. [8]. Growth rate striation spacing error ±6%.
-4.00
A508 STEEL PWR +/- 5%
CRACK GROWTH RATE
A533B STEEL PWR +/- 8%
DUCOL STEEL AIR +/- 4%
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE
-6.00
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
-8.00 A533B STEEL AIR AMBIENT +/- 6%
-10.00 A508 STEEL PWR AMBIENT +/- 6%
-12.00 0
20
40
60
80
100
120
140
DELTA K (MPa/m) Fig. 10. The statistical analysis of all the pressure vessel steel data; growth–striation spacing error was ±4% to 8%.
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Fig. 2 portrayed most of the reported data for ferritic pressure vessel steels [8,13–16] including, A533B, A508 and Ducol steels. Details of ductile striated fatigue crack growth found in a C–Mn steel attemperator reducer weld location at high temperature are shown in Fig. 3. In this particular instance the average striation spacing was assessed at 0.8 lm. Achilles and Bulloch [17] and Bamford [18] have also reported a series of data points, see Fig. 4, for A508 steel fatigue cycled in elevated temperature and ambient PWR waters and in an argon gas environment together with data for a Ni– Mo–V steel in ambient air [8]. Again good agreement between the three sets of data was observed. Details of ‘‘coarse” striations, within which ‘‘fine” single striations were observed were reported by McMinn [19] for a C–Mn steel fatigue cycled in an argon gas environment, see Fig. 5. From this figure it was evident that the coarse striation spacings resided about the half crack tip opening displacement, 1/2 CTOD, value while the fine striation spacings coincided with the fatigue crack growth rate. In this instance only the fine striations were considered in the statistical analysis. Other ambient air fatigue crack growth data and recorded striation spacing results have been reported for a high Mn carbon steel [20] for three separate mean stress or R-ratio values, see Fig. 6. In this case around thirty striation spacing were recorded which all resided about the fatigue crack growth results. A508 steel data at elevated temperatures in PWR waters [18] and for A533B steel in air at sub-zero temperatures [8] are illustrated in Fig. 7 Note that the elevated temperature data exhibited faster fatigue crack growth rates than the sub-zero temperature results. Finally, Fig. 8 shows the C–Mn steel data reported by Davidson and Lankford [11] and elevated temperature data for A533B steel in PWR waters [21]. In all, over some 160 fatigue striation spacing measurements for ferritic steels have been cited and will be statistically compared with the reported companion fatigue crack growth rates.
Ln CRACK GROWTH RATE / STRIATION SPACING (mm/c)
-6.00 -6.50
CRACK GROWTH RATE STRIATION SPACING
-7.00 -7.50 -8.00 -8.50 -9.00 0
10
20
30
40
50
60
70
80
90
100
DELTA K (MPa/m)
-5.00 STRIATION SPACING CRACK GROWTH RATE
-6.00
SPACING (mm/c)
Ln CRACK GROWTH RATE / STRIATION
Fig. 11. Statistical analysis of the bates and clark Ni–Mo–V low alloy ferritic steel data, Ref. [8]. Crack growth–striation spacing error ±5.5%.
-7.00 -8.00 -9.00 -10.00 -11.00 -12.00 0
10
20
30
40
50
60
70
80
90
DELTA K (MPa/m) Fig. 12. Statistical analysis of the C–Mn ferritic steel data, Ref. [19]. Crack growth–striation spacing error ±19%.
100
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3. Statistical analysis
Ln FATIGUE CRACK GROWTH RATE / STRIATION SPACING (mm/c)
For convenience sake the fatigue crack growth data were plotted as the natural logarithm while the DK, or stress intensity range, was portrayed on a linear scale. The ambient air pressure vessel steel A533B fatigue crack growth data are illustrated in Fig. 9, where it was evident that the fatigue striation spacing results were contained within a ±6% error band in fatigue crack growth. The vast majority of the low alloy ferritic pressure vessel steel data are shown in Fig. 10. From this figure it was clear that the various fatigue striation spacing results were contained within error bands of between ±4% and 8%. The results of a statistical analysis involving A Ni–Mo–V steel data, see Fig. 11, indicated that the striation spacing values were contained within an error band of ±5.5%. In the case of the C–Mn steel data reported by McMinn [19] the calculated error band was ±19%, see Fig. 12. Finally, the results of a statistical analysis involving the C–Mn steel data reported by Davidson and Lankford [11] are portrayed in Fig. 13 where it was evident that the striation spacing results were contained within an error band of ±9%. When all the over 160 striation spacing results were statistically tested it was found that the average error band between fatigue crack growth and striation spacing in commercial low alloy ferritic steels was some ±10.1%. The standard deviation for this data was calculated as ±6.1%.
-5 -6 -7 -8 -9 -10 -11 0
10
20
30
40
50
60
70
80
90
100
DELTA K (MPa/m) Fig. 13. Davidson and Lankford C–Mn steel data, Ref. [11]. Crack growth–striation spacing error ±9%.
80 70
AIR; Average error 9.6%; St Deviation 4.3% WATER ENVIROMENTS; Average Error 10.3%; St Deviation 8.1%
% FREQUENCY
60 50 40 30 20 10 0 0 to 5
6 to 10
11 to 15
16 to 20
21 to 25
% ERROR RANGE
26 to 30
31 to 35
36 to 40
40 to 45
Fig. 14. A comparison of the frequency distribution of the % error between crack growth and striation spacing in air and water environments for ferritic low alloy steels.
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When this data was considered in terms of environmental conditions, viz., air and aqueous, see Fig. 14, the average errors were 9.6% and 10.3%, respectively while the standard deviations were 4.3% and 8.1%. The fatigue crack growth rate, da/dt, in the Stage 11 fatigue region is linearly related to the stress intensity range, DK, as follows:
da=dtðmm=cÞ ¼ CðDKÞm
ð1Þ
where C and m are scaling constants. This expression is known as the Paris–Erdogan Law [22] and describes fatigue crack growth in the intermediate or Stage II region. The stress intensity range can be given in the following expression:
DKðMPa=mÞ ¼ Y Dr
pffiffiffiffi
pa
ð2Þ
FATIGUE CRACK GROWTH RATE (mm/c)
where a is the crack depth, Dr is the fatigue stress range and Y is a crack geometry correction factor. In order to calculate the error band in the fatigue stress range from that of overall average ±10.1 error in fatigue crack growth for ferritic steels, using Eq. (1), the fatigue crack growth data reported by Lindley and Richards [23] for ferritic steels was adopted and the results are shown in Fig. 15. In this case it was assumed that an average striation spacing of 0.1 lm was
0.00015 For a 10mm Deep Crack with a Local Striation Spacing of 0.1µm; Delta K = 26.2 MPa/m and an Observed +/-10.1% Error Band for Ferritic Steels
2.84
da/dn(mm/c) = 9.4E-9(Delta K)
0.0001
+/- 3.8% in Delta K or Stress Range
0.00005 24
25
26
27
28
DELTA K (MPa/m) Fig. 15. Schematic of the calculated error in stress range of ±3.8% for a measured crack growth–striation spacing error of ±10.1% for ferritic steels. Low alloy steel fatigue data, Ref. [22].
FATIGUE CRACK GROWTH RATE (mm/c)
0.0008
For a 6mm Deep Crack in a C-Mn Steel Pipe Attemperator Reducer weld with a Local Striation Spacing of 0.5 µm; Delta K = 12.7 MPa/m and an Observed +/-10.3% Error Band for Ferritic Steels
24mm Thick
320mm
0.0006
0.0004 2
+/- 5.3% in Delta K or Stress Range
da/dn(mm/c) = 3.08E-6(Delta K)
4500C C-Mn Steel Fatigue Law REF. 25
0.0002 11
12
13
14
15
DELTA K (MPa/m) Fig. 16. Schematic of the calculated error in stress range of ±5.3% for a measured crack growth–striation spacing error of ±10.3% for ferritic steels. C–Mn steel attemperator reducer weld.
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found at a crack depth of 10 mm in an important engineering component. From Fig. 15 it was evident that the calculated error band for the fatigue stress range was only around ±4%
4. Discussion and final remarks
CALCULATED FATIGUE STRESS RANGE (MPa)
It has been demonstrated that measured average fatigue striation spacings predicted the fatigue crack growth rates for low alloy ferritic steels to within a range of ±2% to 35% with an overall average error band value of ±10.1%. The standard deviation was assessed at ±6.1%. When the data was considered in terms of environment, viz. air and aqueous, the average errors were 9.6% and 10.3%, respectively while the standard deviation for the aqueous environments was almost double that for air being 8.1% and 4.3%, respectively. These correlations should prove more than useful to workers in the field of component failure analysis where fatigue striations are found at some point on the component fracture surface. Also fatigue striations reflect the real conditions which were prevalent at some point in the defect extension process. Furthermore, when the specific location of the striation formations are known, such as the crack depth, the stress levels involved in driving the fatigue crack growth process can be easily calculated. Obviously some knowledge of the fatigue stress level which was actually acting during the component crack growth period represents a powerful piece of information especially when component remnant life considerations are required. Such a small error Indeed from the details shown in Fig. 15 it was clear that when fatigue stress values were evaluated the average overall error band was reduced from ±10.1% to only some ±4%. band value in the real predicted fatigue stress values that are involved in commercial component cracks or failures is certainly very encouraging to both failure analysts and other workers in the field of component remnant life and life extension. Remember that these fatigue stress value predictions are soundly based upon quantifiable real fracture characteristics observed at some point on the actual component failure surface. Furthermore, through the use of observed standard deviation data added confidence in the calculated fatigue stress values can be achieved by combining standard deviation values with the overall average ±10.1% error in fatigue crack growth predictions. Basically when the average ferritic steel value of ±10.1% is used to calculate the fatigue stress range value there is a 1 in 2 chance that the real fatigue stress range value could be larger than the calculated value. However when two or three standard deviations are added the chances of the real fatigue stress range being greater than the calculated value are reduced to a 1 in 44 chance and a 1 in 714 chance, respectively. The effect of adding standard deviations to the average error band value of ±10.1% on the value of the fatigue stress range are illustrated in Fig. 15 where it was clear that the stress range increased from 136 MPa to 142 MPa when three standard deviations were considered. Thus when a ±10% error band was superimposed on the original ±9% error the stress range value only increased by some ±4%. Perhaps the most cogent way of examining the above facts is to apply them to a real cracking problem which was identified in a electricity producing steam-raising plant. A few years ago Bulloch and Bernard [24] reported a detailed study on cracks in a C–Mn steel attemperator reducer weld operating at 450 °C which had a minimum wall thickness of 24 mm and an OD of 320 mm. At a 6 mm deep wall crack location an average striation spacing of 0.5 lm was recorded microscopically and using a 450 °C fatigue crack growth law for ferritic steels [25] and the statistical figures for a water environment the error in
105
100 Stress Range 99MPa
95 Stress Range 95MPa
90 Stress Range 87MPa
85 Only Average Striation Spacing Considered; Stress Range 83MPa
80 -1
0
1
2
3
4
5
NUMBER OF STANDARD DEVIATIONS Fig. 17. The effect of adding standard deviations to the average error band for ferritic steels on the calculated fatigue stress range value for a 6 mm deep cracked attemperator reducer weld striation spacing 0f 0.0005 mm.
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REMNANT LIFE (STARTS)
6000 Remnant Life 4300 Starts from Recorded Average Striation Spacing 0.5µm
5000 Remnant Life 2940 Starts when 3 Standard Deviations Added to +/- 10.1% Error Band
4000
3000 Remnant Life 3900 Starts when +/- 10.3% Error Band Considered for Ferritic Steels
2000 70
75
80
85
90
95
100
105
110
115
UPPER STRESS RANGE (MPa) Fig. 18. Remnant life of a 7 mm deep crack in a C–Mn steel attemperator reducer weld for a failure probability of 0.5. Effect of stress range obtained from fatigue crack growth–striation spacing error band considerations in low alloy ferritic steels.
REMNANT LIFE (STARTS)
120 Remnant Life 86 Starts from Recorded Average Striation Spacing 0.5µm
100 Remnant Life 60 Starts when 3 Standard Deviations Added to +/- 10.3% Error Band
80
60 Remnant Life 77 Starts when +/- 10.3% Error Band Considered for Ferritic Steels
40 70
80
90
100
110
UPPER BOUND FATIGUE STRESS RANGE (MPa) Fig. 19. Remnant life of a 7 mm deep crack in a C–Mn steel attemperator reducer weld for a failure probability of 104. Effect of stress range obtained from fatigue crack growth–striation spacing error band considerations in low alloy ferritic steels.
the stress range value was estimated from Fig. 16. From this figure it was evident that the calculated error in fatigue stress range was only just over 5%. The effect of adding standard deviations, which was mentioned earlier, to this average error of 5.3% on the upper bound fatigue stress range value is illustrated in Fig. 17. From this figure the calculated stress range was 83 MPa based on average striation spacing results while a value of 87 MPa was estimated from the average error of 10.3% for ferritic steels in water environments. When one and three standard deviations were built into the calculations the stress range values increased to 91 and 99 MPa, respectively. Failure probability, Pf, values can be assigned to these calculated values such that for the average% error value of 87 MPa the chances that the real stress range value was greater than this calculated value was only 1 in 2. For additions of one and three standard deviations the chances are reduced to 1 in 4 and 1 in over 700, respectively. In the case of this particular cracked attemperator reducer weld problem an NDT assessment suggested that the maximum crack depth was 7 mm while the lower bound critical crack depth was estimated at 10 mm. As such, remnant life assessments can be estimated for a series of fatigue stress ranges through the use of a reported 450 °C fatigue crack growth law for C–Mn steels [25] which can be expressed as
da=dnðmm=cÞ ¼ 3:08E 6ðDKÞ2
ð3Þ
where DK was the stress intensity range. Remnant life estimates for a range of stress ranges are shown in Fig. 18 where the chances of the real remnant life values being greater than the calculated values was only 1 in 2. Note that when three standard deviations are considered the rem-
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nant life was reduced by over some 30%. Fig. 19 shows the remnant life values for a failure probability of E4 where it was evident that they were somewhat less than 100 starts. As such, these represented a working life for a 7 mm deep defect of only 6 months. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
Zaffe CA, Worden CO. Trans ASM 1951;43:958–63. Forsyth PJE, Ryder DA. Metallurgica 1961;63:117–28. Laird C, Smith GC. Philos Mag 1962;7:47–858. McMillan JC, Pelloux RMN. Fatigue crack propagation. ASTM, STP 415. p. 505–21. McLintock JA, Pelloux RMN. Boeing Science Research Labs. Document 01-82-0708; 1968. Underwood EE, Starke EA. Fatigue mechanisms ASTM STP 675, ASTM; 1979. p. 633–82. Forsyth PJE, Ryder DA. Aircraft Eng 1960;32:96–103. Bates RC, Clark WG. Trans ASM 1969;62:380–9. Hertzberg RW, Euw J. Metall Trans 1973;4:887–9. Au JJ, Ke JS. Fractography and material science. ASTM, STP 733, ASTM; 1981. p. 202–21. Davidson DL, Lankford J. Inter Mater Rev 1992;37:45–75. Rinaldi C, Gabetta G. CISE Topical Report No. SMS-RT-85-001. CISE, Milan, Italy; October 1985. A508 DATA fractography. Bulloch, Buchanan. Corr Sci 1984;24:661–74. Bulloch JH, Buchanan LW. Res Mech 1986;19:227–46. Achilles RD, Bulloch JH. Int J Pres Ves Pip 1987;30:375–89. Achilles RD, Bulloch JH. In: Transactions of the ninth international conference on structural mechanics in reactor technology. Lausanne, Switz, vol. F. August; 1987. p. 143–8. Bamford WH. Oak Ridge National Laboratory Report No. NUREG/CR-5020 ORNL/Sub/82-21598/1; April, 1988. McMinn A. Ukaea, Northern Division Report No. ND-R-435(S); June 1981. Murakami Y, Furukawa K. Procs Case Histories on Integrity and Failures in Industry, Milan; June 2001. p. 321–30. Torronen K, Kemppainen M, Hanninen H. EPRI Report No. EPRI NP-3483 Project 1325–7; May 1984. Paris PC, Erdogan F. J Basic Engng 1963;85:528–37. Lindley TC, Richards CE. Mater Sci Engng 1974;14:281–93. Bulloch JH, Bernard P. Engng Failure Anal 2001;8:529–40. Bulloch JH. Int J Pres Ves Pip 1998;75:805–18.
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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
A detailed study of the relationship between fatigue crack growth rate and striation spacing in a range of low alloy ferritic steels J.H. Bulloch *, A.G. Callagy Power Generation, ESB, Head Office, Dublin 2, Ireland
a r t i c l e
i n f o
Article history: Received 12 February 2009 Accepted 10 April 2009 Available online 13 May 2009 Keywords: Fatigue crack growth Fatigue striations Statistics Stress intensity range Probability
a b s t r a c t It was shown that the measured average fatigue striation spacings predicted the fatigue crack growth rates for low alloy ferritic steels to within a range of ±2% to 35% with an overall average error band value of ±10.1%. When we consider the fatigue stress range this average error was reduced to only some ±4%. This was good news to both failure analysts and other workers involved in the field of component remnant life and life extension since such predicted fatigue stress ranges use real fracture characteristics observed at some point on the actual component fracture surface. These findings were applied to a real cracking problem recently reported in a steam raising plant, viz., a cracked attemperator reducer weld. In this case an NDT assessment indicated that the maximum crack depth was 7 mm while the lower bound critical crack depth was estimated at 10 mm. As such, remnant life assessments can be estimated for a series of fatigue stress ranges through the use of a reported 450 °C fatigue crack growth law for C– Mn steels. Remnant life estimates of a 7 mm deep crack for a range of stress ranges varied from 3000 to 4000 starts where the chances of the real remnant life values being greater than the calculated values was only 1 in 2. However when a realistic failure probability which reflected the serious implications of a failure event of E4 was taken the remnant life values were reduced to around 100 starts or some 6 months of normal service. Ó 2009 Published by Elsevier Ltd.
1. Introduction Probably some of the initial mechanistic information regarding fatigue crack growth was recorded from fracture surface examinations. These found that many fracture surfaces formed under cyclic loading exhibited periodic markings on both a macroscopic and microscopic scale; the latter was known as fatigue striations which occurred during Stage 11 fatigue crack growth. During this particular fatigue stage a crack can often grow on multiple plateaus which are at different heights with respect to one another. Fatigue striations, which were first recognized by Zaffe and Worden [1] often bow out in the direction of crack growth and generally tend to align at right angles to the principal crack growth direction. There have been several models proposed to account for striation formation with Forsyth and Ryder [2] suggesting over six decades ago that fracture occurred ahead of the crack tip with the striation profile being formed by subsequent of the intermediate material. A more generalized approach was reported by Laird and Smith [3] where they described the growth process as one involving crack blunting on the tensile part of the cycle and re-sharpening during
* Corresponding author. E-mail address: [email protected] (J.H. Bulloch). 1350-6307/$ - see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.engfailanal.2009.04.028
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FATIGUE CRACK GROWTH RATE (mm/c)
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0.01 CRACK GROWTH RATE
A533B STEEL PWR WATER HIGH TEMPERATURE; REF. 12
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
0.001
A533B STEEL AIR AMBIENT; REF. 8
0.0001 10
100
1000
DELTA K (MPa/m) Fig. 1. Fatigue crack growth data for A533B steel in high temperature PWR water and ambient air.
FATIGUE CRACK GROWTH RATE (mm/c)
0.01 DUCOL STEEL AIR AMBIENT REF. 15
A508 STEEL PWR WATER 290 DEGREES REF. 13
A533B STEEL AIR AMBIENT REF8
0.001 CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE
0.0001
STRIATION SPACING A533B STEEL PWR WATER 290 DEGREES REF 14
CRACK GROWTH RATE A508 STEEL PWR WATER AMBIENT
STRIATION SPACING
0.00001 10
100
1000
DELTA K (MPa/m) Fig. 2. Fatigue crack growth data for a series of low alloy ferritic pressure vessel steels.
Fig. 3. Ductile fatigue striations in a C–Mn steel component operating at high temperature. The average striation spacing at this point was assessed at 0.8 lm; after Ref. [24].
FATIGUE CRACK GROWTH RATE (mm/c)
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0.01 PWR HIGH TEMPERATURE WATER. REF. 18
AVERAGE ARGON STRIATION SPACING ARGON
Ni-Mo-V STEEL AMBIENT AIR REF. 8
AVERAGE PWR STRIATION SPACING PWR AVERAGE PWR STRIATION SPACING PWR
0.001
CRACK GROWTH RATE STRIATION SPACING
PWR AMBIENT WATER DATA REF 17
0.0001
ARGON DATA REF 17
0.00001 0
20
40
60
80
100
120
DELTA K (MPa/m) Fig. 4. Fatigue crack growth data for A508 steel in argon and PWR water environments and Ni–Mo–V steel in ambient air.
the compressive stroke. A third model, termed the crystallographic model, suggested that one or both sides of the striations are parallel to the slip systems, and in which the positions of the slip planes determine the local angle of the striations with respect to the general crack growth direction [4]. A similar, but more generalized approach is involved in the sliding-off or shear decohesion models in which separation occurs on alternating planes of maximum resolved shear stress [5]. The problem of establishing the actual, or real striation spacing, in a non-planar fracture surface has been examined in detail by Underwood and Starke [6] who showed that certain corrections for orientation and surface roughness effects were required to the striation spacing obtained in a scanning electron microscope, SEM, survey. However, when comparing striation spacing to fatigue crack growth rate no such corrections to the measured striation spacings are necessary since both are projected quantities. Nearly 50 years ago Forsyth and Ryder [7] reported some work on variable loading which showed that the striation spacings and numbers corresponded to that of the loading sequence thus establishing that striation spacings represented the growth distance per fatigue cycle. Almost a decade after this Bates and Clark [8] reported for a range three steels, two Al-alloys and a Ti-alloy that the striation spacing exhibited good agreement with measured fatigue crack growth data. Some 25 years ago Hertzberg and Euw [9] also reported a close correlation between crack growth rates and average striation spacing values in an Al-alloy. Around a decade later Au and Ke [10] reported the following conclusions for a high strength Ni–Cr–Mo martensitic steel; (a) good
0.01
FATIGUE CRACK GROWTH RATE (mm/c)
1/2 CTOD(max) LINE
0.001
CRACK GROWTH DATA
0.0001
SINGLE STRIATION SPACING COARSE STRIATION SPACING
0.00001 10
100
DELTA K (MPa/m) Fig. 5. Fatigue crack growth data for A C–Mn steel in argon at ambient temperature, Ref. [19].
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0.01 R = -1 CRACK GROWTH RATE R = -1 STRIATION SPACING R = 0 CRACK GROWTH RATE R = 0 STRIATION SPACING
R-RATIO = ZERO AND 0.5 DATA
R = 0.5 CRACK GROWTH RATE R = 0.5 STRIATION SPACING
0.001
R-RATIO = -1 DATA
0.0001 100
10 DELTA K (MPa/m) Fig. 6. Fatigue crack growth data for a carbon, high Mn steel in ambient air, Ref. [20].
correlation was observed between the macroscopic crack growth rate and fatigue striation spacing for crack growth rates ranging from 103 to 104 mm/cycle and (b) this correlation was not affected by the R-ratio, frequency, environment and material strength. More recently, some 14 years ago Davidson and Lankford [11] published a detailed review on fatigue mechanisms and micromechanics in metals and alloys. Generally, they found in some cases that one striation may not necessarily correspond to one fatigue cycle; this was especially the case in the near threshold Stage 1 fatigue crack growth region. Indeed in this fatigue region fatigue striations can exceed measured crack growth rates by orders of magnitude. However the present paper deals only with stage 11 fatigue region correlations between striation spacings and crack growth rates and in this region the Davidson and Lankford data [11] exhibited good agreement in a range of materials. As such, it is clear that some reasonable correlation existed between crack growth and striation spacings and the aim of this paper is to try and quantify this correlation on a statistical basis for a range of commercial low alloy ferritic steels.
2. Fatigue crack growth–striation spacing data
FATIGUE CRACK GROWTH RATE (mm/c)
Perhaps the most significant amount of fatigue crack growth–striation spacing data has been reported by Bates and Clark [8] for a ferritic A533B pressure vessel steel in air at ambient temperatures, see Fig. 1 together with other results for a A508 pressure vessel steel in PWR water at elevated temperatures [12]. From this figure it was evident that the crack growth and striation spacing data exhibited reasonable agreement and contained over 50 data sets.
0.1 2900C Zero Hold
CRACK GROWTH RATE
2900C 30Sec Hold
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
0
290 C 1Min Hold
CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE
0.01
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
0.001 900C 1Min Hold
Sub-Zero A533B Steel Data Ref. 8
0.0001 10
100 DELTA K (MPa/m) Fig. 7. High temperature PWR data for A508 steel, Ref. [18] and sub-zero A533B steel air data, Ref. [8].
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0.01
REF 21
0.001
0.0001 CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
REF 11
0.00001 10
100
DELTA K (MPa/m) Fig. 8. Fatigue crack growth data for a C–Mn steel in ambient air, Ref. [11] and A533B steel in high temperature PWR water, Ref. [21].
Ln CRACK GROWTH RATE / STRIATION SPACING (mm/c)
-5.00
-6.00
-7.00
-8.00
-9.00
-10.00 0
20
40
60
80
100
120
140
DELTA K (MPa/m)
Ln CRACK GROWTH RATE / STRIATION SPACING (mm/c)
Fig. 9. A statistical analysis of the bates and clark A533B ferritic A533B steel ambient air data, Ref. [8]. Growth rate striation spacing error ±6%.
-4.00
A508 STEEL PWR +/- 5%
CRACK GROWTH RATE
A533B STEEL PWR +/- 8%
DUCOL STEEL AIR +/- 4%
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE
-6.00
STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING CRACK GROWTH RATE STRIATION SPACING
-8.00 A533B STEEL AIR AMBIENT +/- 6%
-10.00 A508 STEEL PWR AMBIENT +/- 6%
-12.00 0
20
40
60
80
100
120
140
DELTA K (MPa/m) Fig. 10. The statistical analysis of all the pressure vessel steel data; growth–striation spacing error was ±4% to 8%.
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Fig. 2 portrayed most of the reported data for ferritic pressure vessel steels [8,13–16] including, A533B, A508 and Ducol steels. Details of ductile striated fatigue crack growth found in a C–Mn steel attemperator reducer weld location at high temperature are shown in Fig. 3. In this particular instance the average striation spacing was assessed at 0.8 lm. Achilles and Bulloch [17] and Bamford [18] have also reported a series of data points, see Fig. 4, for A508 steel fatigue cycled in elevated temperature and ambient PWR waters and in an argon gas environment together with data for a Ni– Mo–V steel in ambient air [8]. Again good agreement between the three sets of data was observed. Details of ‘‘coarse” striations, within which ‘‘fine” single striations were observed were reported by McMinn [19] for a C–Mn steel fatigue cycled in an argon gas environment, see Fig. 5. From this figure it was evident that the coarse striation spacings resided about the half crack tip opening displacement, 1/2 CTOD, value while the fine striation spacings coincided with the fatigue crack growth rate. In this instance only the fine striations were considered in the statistical analysis. Other ambient air fatigue crack growth data and recorded striation spacing results have been reported for a high Mn carbon steel [20] for three separate mean stress or R-ratio values, see Fig. 6. In this case around thirty striation spacing were recorded which all resided about the fatigue crack growth results. A508 steel data at elevated temperatures in PWR waters [18] and for A533B steel in air at sub-zero temperatures [8] are illustrated in Fig. 7 Note that the elevated temperature data exhibited faster fatigue crack growth rates than the sub-zero temperature results. Finally, Fig. 8 shows the C–Mn steel data reported by Davidson and Lankford [11] and elevated temperature data for A533B steel in PWR waters [21]. In all, over some 160 fatigue striation spacing measurements for ferritic steels have been cited and will be statistically compared with the reported companion fatigue crack growth rates.
Ln CRACK GROWTH RATE / STRIATION SPACING (mm/c)
-6.00 -6.50
CRACK GROWTH RATE STRIATION SPACING
-7.00 -7.50 -8.00 -8.50 -9.00 0
10
20
30
40
50
60
70
80
90
100
DELTA K (MPa/m)
-5.00 STRIATION SPACING CRACK GROWTH RATE
-6.00
SPACING (mm/c)
Ln CRACK GROWTH RATE / STRIATION
Fig. 11. Statistical analysis of the bates and clark Ni–Mo–V low alloy ferritic steel data, Ref. [8]. Crack growth–striation spacing error ±5.5%.
-7.00 -8.00 -9.00 -10.00 -11.00 -12.00 0
10
20
30
40
50
60
70
80
90
DELTA K (MPa/m) Fig. 12. Statistical analysis of the C–Mn ferritic steel data, Ref. [19]. Crack growth–striation spacing error ±19%.
100
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3. Statistical analysis
Ln FATIGUE CRACK GROWTH RATE / STRIATION SPACING (mm/c)
For convenience sake the fatigue crack growth data were plotted as the natural logarithm while the DK, or stress intensity range, was portrayed on a linear scale. The ambient air pressure vessel steel A533B fatigue crack growth data are illustrated in Fig. 9, where it was evident that the fatigue striation spacing results were contained within a ±6% error band in fatigue crack growth. The vast majority of the low alloy ferritic pressure vessel steel data are shown in Fig. 10. From this figure it was clear that the various fatigue striation spacing results were contained within error bands of between ±4% and 8%. The results of a statistical analysis involving A Ni–Mo–V steel data, see Fig. 11, indicated that the striation spacing values were contained within an error band of ±5.5%. In the case of the C–Mn steel data reported by McMinn [19] the calculated error band was ±19%, see Fig. 12. Finally, the results of a statistical analysis involving the C–Mn steel data reported by Davidson and Lankford [11] are portrayed in Fig. 13 where it was evident that the striation spacing results were contained within an error band of ±9%. When all the over 160 striation spacing results were statistically tested it was found that the average error band between fatigue crack growth and striation spacing in commercial low alloy ferritic steels was some ±10.1%. The standard deviation for this data was calculated as ±6.1%.
-5 -6 -7 -8 -9 -10 -11 0
10
20
30
40
50
60
70
80
90
100
DELTA K (MPa/m) Fig. 13. Davidson and Lankford C–Mn steel data, Ref. [11]. Crack growth–striation spacing error ±9%.
80 70
AIR; Average error 9.6%; St Deviation 4.3% WATER ENVIROMENTS; Average Error 10.3%; St Deviation 8.1%
% FREQUENCY
60 50 40 30 20 10 0 0 to 5
6 to 10
11 to 15
16 to 20
21 to 25
% ERROR RANGE
26 to 30
31 to 35
36 to 40
40 to 45
Fig. 14. A comparison of the frequency distribution of the % error between crack growth and striation spacing in air and water environments for ferritic low alloy steels.
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When this data was considered in terms of environmental conditions, viz., air and aqueous, see Fig. 14, the average errors were 9.6% and 10.3%, respectively while the standard deviations were 4.3% and 8.1%. The fatigue crack growth rate, da/dt, in the Stage 11 fatigue region is linearly related to the stress intensity range, DK, as follows:
da=dtðmm=cÞ ¼ CðDKÞm
ð1Þ
where C and m are scaling constants. This expression is known as the Paris–Erdogan Law [22] and describes fatigue crack growth in the intermediate or Stage II region. The stress intensity range can be given in the following expression:
DKðMPa=mÞ ¼ Y Dr
pffiffiffiffi
pa
ð2Þ
FATIGUE CRACK GROWTH RATE (mm/c)
where a is the crack depth, Dr is the fatigue stress range and Y is a crack geometry correction factor. In order to calculate the error band in the fatigue stress range from that of overall average ±10.1 error in fatigue crack growth for ferritic steels, using Eq. (1), the fatigue crack growth data reported by Lindley and Richards [23] for ferritic steels was adopted and the results are shown in Fig. 15. In this case it was assumed that an average striation spacing of 0.1 lm was
0.00015 For a 10mm Deep Crack with a Local Striation Spacing of 0.1µm; Delta K = 26.2 MPa/m and an Observed +/-10.1% Error Band for Ferritic Steels
2.84
da/dn(mm/c) = 9.4E-9(Delta K)
0.0001
+/- 3.8% in Delta K or Stress Range
0.00005 24
25
26
27
28
DELTA K (MPa/m) Fig. 15. Schematic of the calculated error in stress range of ±3.8% for a measured crack growth–striation spacing error of ±10.1% for ferritic steels. Low alloy steel fatigue data, Ref. [22].
FATIGUE CRACK GROWTH RATE (mm/c)
0.0008
For a 6mm Deep Crack in a C-Mn Steel Pipe Attemperator Reducer weld with a Local Striation Spacing of 0.5 µm; Delta K = 12.7 MPa/m and an Observed +/-10.3% Error Band for Ferritic Steels
24mm Thick
320mm
0.0006
0.0004 2
+/- 5.3% in Delta K or Stress Range
da/dn(mm/c) = 3.08E-6(Delta K)
4500C C-Mn Steel Fatigue Law REF. 25
0.0002 11
12
13
14
15
DELTA K (MPa/m) Fig. 16. Schematic of the calculated error in stress range of ±5.3% for a measured crack growth–striation spacing error of ±10.3% for ferritic steels. C–Mn steel attemperator reducer weld.
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found at a crack depth of 10 mm in an important engineering component. From Fig. 15 it was evident that the calculated error band for the fatigue stress range was only around ±4%
4. Discussion and final remarks
CALCULATED FATIGUE STRESS RANGE (MPa)
It has been demonstrated that measured average fatigue striation spacings predicted the fatigue crack growth rates for low alloy ferritic steels to within a range of ±2% to 35% with an overall average error band value of ±10.1%. The standard deviation was assessed at ±6.1%. When the data was considered in terms of environment, viz. air and aqueous, the average errors were 9.6% and 10.3%, respectively while the standard deviation for the aqueous environments was almost double that for air being 8.1% and 4.3%, respectively. These correlations should prove more than useful to workers in the field of component failure analysis where fatigue striations are found at some point on the component fracture surface. Also fatigue striations reflect the real conditions which were prevalent at some point in the defect extension process. Furthermore, when the specific location of the striation formations are known, such as the crack depth, the stress levels involved in driving the fatigue crack growth process can be easily calculated. Obviously some knowledge of the fatigue stress level which was actually acting during the component crack growth period represents a powerful piece of information especially when component remnant life considerations are required. Such a small error Indeed from the details shown in Fig. 15 it was clear that when fatigue stress values were evaluated the average overall error band was reduced from ±10.1% to only some ±4%. band value in the real predicted fatigue stress values that are involved in commercial component cracks or failures is certainly very encouraging to both failure analysts and other workers in the field of component remnant life and life extension. Remember that these fatigue stress value predictions are soundly based upon quantifiable real fracture characteristics observed at some point on the actual component failure surface. Furthermore, through the use of observed standard deviation data added confidence in the calculated fatigue stress values can be achieved by combining standard deviation values with the overall average ±10.1% error in fatigue crack growth predictions. Basically when the average ferritic steel value of ±10.1% is used to calculate the fatigue stress range value there is a 1 in 2 chance that the real fatigue stress range value could be larger than the calculated value. However when two or three standard deviations are added the chances of the real fatigue stress range being greater than the calculated value are reduced to a 1 in 44 chance and a 1 in 714 chance, respectively. The effect of adding standard deviations to the average error band value of ±10.1% on the value of the fatigue stress range are illustrated in Fig. 15 where it was clear that the stress range increased from 136 MPa to 142 MPa when three standard deviations were considered. Thus when a ±10% error band was superimposed on the original ±9% error the stress range value only increased by some ±4%. Perhaps the most cogent way of examining the above facts is to apply them to a real cracking problem which was identified in a electricity producing steam-raising plant. A few years ago Bulloch and Bernard [24] reported a detailed study on cracks in a C–Mn steel attemperator reducer weld operating at 450 °C which had a minimum wall thickness of 24 mm and an OD of 320 mm. At a 6 mm deep wall crack location an average striation spacing of 0.5 lm was recorded microscopically and using a 450 °C fatigue crack growth law for ferritic steels [25] and the statistical figures for a water environment the error in
105
100 Stress Range 99MPa
95 Stress Range 95MPa
90 Stress Range 87MPa
85 Only Average Striation Spacing Considered; Stress Range 83MPa
80 -1
0
1
2
3
4
5
NUMBER OF STANDARD DEVIATIONS Fig. 17. The effect of adding standard deviations to the average error band for ferritic steels on the calculated fatigue stress range value for a 6 mm deep cracked attemperator reducer weld striation spacing 0f 0.0005 mm.
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REMNANT LIFE (STARTS)
6000 Remnant Life 4300 Starts from Recorded Average Striation Spacing 0.5µm
5000 Remnant Life 2940 Starts when 3 Standard Deviations Added to +/- 10.1% Error Band
4000
3000 Remnant Life 3900 Starts when +/- 10.3% Error Band Considered for Ferritic Steels
2000 70
75
80
85
90
95
100
105
110
115
UPPER STRESS RANGE (MPa) Fig. 18. Remnant life of a 7 mm deep crack in a C–Mn steel attemperator reducer weld for a failure probability of 0.5. Effect of stress range obtained from fatigue crack growth–striation spacing error band considerations in low alloy ferritic steels.
REMNANT LIFE (STARTS)
120 Remnant Life 86 Starts from Recorded Average Striation Spacing 0.5µm
100 Remnant Life 60 Starts when 3 Standard Deviations Added to +/- 10.3% Error Band
80
60 Remnant Life 77 Starts when +/- 10.3% Error Band Considered for Ferritic Steels
40 70
80
90
100
110
UPPER BOUND FATIGUE STRESS RANGE (MPa) Fig. 19. Remnant life of a 7 mm deep crack in a C–Mn steel attemperator reducer weld for a failure probability of 104. Effect of stress range obtained from fatigue crack growth–striation spacing error band considerations in low alloy ferritic steels.
the stress range value was estimated from Fig. 16. From this figure it was evident that the calculated error in fatigue stress range was only just over 5%. The effect of adding standard deviations, which was mentioned earlier, to this average error of 5.3% on the upper bound fatigue stress range value is illustrated in Fig. 17. From this figure the calculated stress range was 83 MPa based on average striation spacing results while a value of 87 MPa was estimated from the average error of 10.3% for ferritic steels in water environments. When one and three standard deviations were built into the calculations the stress range values increased to 91 and 99 MPa, respectively. Failure probability, Pf, values can be assigned to these calculated values such that for the average% error value of 87 MPa the chances that the real stress range value was greater than this calculated value was only 1 in 2. For additions of one and three standard deviations the chances are reduced to 1 in 4 and 1 in over 700, respectively. In the case of this particular cracked attemperator reducer weld problem an NDT assessment suggested that the maximum crack depth was 7 mm while the lower bound critical crack depth was estimated at 10 mm. As such, remnant life assessments can be estimated for a series of fatigue stress ranges through the use of a reported 450 °C fatigue crack growth law for C–Mn steels [25] which can be expressed as
da=dnðmm=cÞ ¼ 3:08E 6ðDKÞ2
ð3Þ
where DK was the stress intensity range. Remnant life estimates for a range of stress ranges are shown in Fig. 18 where the chances of the real remnant life values being greater than the calculated values was only 1 in 2. Note that when three standard deviations are considered the rem-
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nant life was reduced by over some 30%. Fig. 19 shows the remnant life values for a failure probability of E4 where it was evident that they were somewhat less than 100 starts. As such, these represented a working life for a 7 mm deep defect of only 6 months. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
Zaffe CA, Worden CO. Trans ASM 1951;43:958–63. Forsyth PJE, Ryder DA. Metallurgica 1961;63:117–28. Laird C, Smith GC. Philos Mag 1962;7:47–858. McMillan JC, Pelloux RMN. Fatigue crack propagation. ASTM, STP 415. p. 505–21. McLintock JA, Pelloux RMN. Boeing Science Research Labs. Document 01-82-0708; 1968. Underwood EE, Starke EA. Fatigue mechanisms ASTM STP 675, ASTM; 1979. p. 633–82. Forsyth PJE, Ryder DA. Aircraft Eng 1960;32:96–103. Bates RC, Clark WG. Trans ASM 1969;62:380–9. Hertzberg RW, Euw J. Metall Trans 1973;4:887–9. Au JJ, Ke JS. Fractography and material science. ASTM, STP 733, ASTM; 1981. p. 202–21. Davidson DL, Lankford J. Inter Mater Rev 1992;37:45–75. Rinaldi C, Gabetta G. CISE Topical Report No. SMS-RT-85-001. CISE, Milan, Italy; October 1985. A508 DATA fractography. Bulloch, Buchanan. Corr Sci 1984;24:661–74. Bulloch JH, Buchanan LW. Res Mech 1986;19:227–46. Achilles RD, Bulloch JH. Int J Pres Ves Pip 1987;30:375–89. Achilles RD, Bulloch JH. In: Transactions of the ninth international conference on structural mechanics in reactor technology. Lausanne, Switz, vol. F. August; 1987. p. 143–8. Bamford WH. Oak Ridge National Laboratory Report No. NUREG/CR-5020 ORNL/Sub/82-21598/1; April, 1988. McMinn A. Ukaea, Northern Division Report No. ND-R-435(S); June 1981. Murakami Y, Furukawa K. Procs Case Histories on Integrity and Failures in Industry, Milan; June 2001. p. 321–30. Torronen K, Kemppainen M, Hanninen H. EPRI Report No. EPRI NP-3483 Project 1325–7; May 1984. Paris PC, Erdogan F. J Basic Engng 1963;85:528–37. Lindley TC, Richards CE. Mater Sci Engng 1974;14:281–93. Bulloch JH, Bernard P. Engng Failure Anal 2001;8:529–40. Bulloch JH. Int J Pres Ves Pip 1998;75:805–18.