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The effect of stress ratio on fatigue crack growth rates in steels
THE EFFECT OF STRESS RATIO ON FATIGUE CRACK GROWTH RATES IN STEELS 0. VOSIKOVSKY Departmentof Energy. Mines and Resources, Ottawa, Canada Ab&W-The effects of stress ratio on fatigue crack growth thresholdsand low and intermediatefatigue crack growth r8tes are ex8mined on steels with ferri+pearlii and tempered martensite micros~c~s, tested in air. The analysis of available experimentaldata shows that simple empiricalrelationshipscan be used to describe the stress ratio dependence of thresholds and fatigue crack growth rates. Results also indicatethat thresholdsdecrease linearlywith yield strength.
INTRODUCTION FATIGUEcrack growth (fcg) rates, do/dN, are generally presented in a log-log plot, against the stress intensity factor range, AK. The curves have tbe familiar sigmoidal shape, shown in Fig. 1. The middle, linear part of the curves, Region B, is described by the expression &
(1)
= AAhK”.
At low AK, Region A, the fcg rate decreases progressively faster until the threshold, AK,, for a non-propagating crack is reached. At high AK, Region C, the slope m of the curve increases as the maximum stress intensity approaches Kc The stress ratio, R = K&K-, as indicated in Fig. 1, strongly affects the fcg rate in the low and high growth rate Regions, A and C. In the intermediate Region B, relatively little effect is observed. In the present paper, the available experimental results on thresholds and fcg rates in low
REGION
THRESHOLD
LOG
E
/
AK
1. %bCm8tk ShapC Of fCg I&CCUWeS8t thret StreSS18tiOS.Region A-low kg rates 8pproaChiDg threshold, Region B-intermediite fcg rates with line8r log da/d?4- tog AR ~~a~nS~p, Region C-hi& fcg rates, Km, approachingthe critical stress intensity.
Fi.
t3kWVd.11.No.Z-H
595
0. VOSIKOVSKY
5%
and intermediate Regions A and B at positive stress ratios are compiled for steels tested in air[l-161. It appears that the threshold and fcg rate dependence on stress ratio can be expressed with useful accuracy by simple empirical relationships suggested in [16]. TEEESIIOLD DEPENDENCE ON SIRES RATIO To express the threshold-stress ratio relationship, eqn (2) originated by Klesnil and Lukas [2] has been most extensively used [6,8, 10,131. AK, = AK& -K)‘,
(2)
where AK, is a threshold at R = 0, and 7 is a material constant varying from 0.5 to 1 for different steels. A value of 7 close to 1, indicating a linear relationship and a constant K, equal to AK&, has been measured for several medium carbon steels [6,8]. For alloyed medium carbon martqnsitic steel[l3], 7 was close to 0.5, and for several low carbon structural steels, intermediate values of 7 were found[lO]. Recent measurements of thresholds on HY 130 steel [ 161fit a simple linear relationship AK,, = AK,,, - BR
(3)
Tsble 1.ThresholdSaadtbcird~p~ade~~~onst~~ssrstios forstds withfetitbpearlite&tsmpmdmartsasitc IlIiWOSWllCnrreS Refaranoe
Clark & Mager
erram an
[7] Reevera, Cooke, Knott and Ritchie 1975
[81 ya;;zave and
1975
CP carbon steel 917 0.5fC,2.23Mn P carbon steel 770 0.55C,O.66Mn Mp carbon steel1124 0.55C.2.23Mn 12-2 carbon steel 0.4CI0.7t4n 6-2 carbon steel o.rC, 0.7un 6-T carbon steel 0.4C,O.'lMn
399
8
12.60 12.30 0.989
* 434
5
8.59 7.24 0.985
753
5
11.55 10.94 0.998
493
4
6.31 5.82 0.999
477
5
11.10 11.50 0.999
477
3
12.60 13.25 0.999
592
The effect of stress ratio on fatigue crack growth rates in steels
Table l.(Contd) Reference [El
and 1975
OYS (UPa)
NO. of b=ot Data (MPa+%h)
B
E
I4amolmave
Bailon
%TS 04Pa)
Steel
gar;mo . ye&e1
532
*009~1;-1 carbon steel 0.8C,O.7Hn
5
11.04
10.20
4
10.01
9.73
191 Branco, Radon & Culver x) 1976
BSl5 mild steel 0.19c.0.59Mn
585
401
5
6.54
2.85
[lOI Sasaki, Ohta urd Koswe 1977
SMSOA structural
568
372
3
10.37
8.56
Quenched
111 FE=-&
steel
and tempered
steels
I
and
;o$
[lo] Suaki, Qhta 4 Kosuge 1977
o.14c,1.3Mnn.
I
I 666 I
5881
5
I 7.93
774
i2s
3
6.69
5.43 0.989
2
6.32
3.29
7.14 0.915
A553-A
[ll] Paria
1970
9310 0.1C,3NirlCr,
I121 Bucci, Cluk Paris 1972
i 0.961
1131 Cooke, Irving, Booth and Boevars 197: I141 Zf
[lS] Ritchie
1151 Mtchie
I
1970
1640
8
3.56
1.19
1070
2
6.44
5.42
993
3
5.74
2.97 0.999
1977
1977
1161 Vodkovmky
UOte8
D6 ac 0.48C,O.8Hn, 0.6Ni,l.lCr, lMo,O.lV
andx1 1976
1977
MY 130 O.O9C,SNi O.SCr,O.SMo
x) The grath xx) mrkrs
1034
rates were measured
indicate
xxx) The mlcrostructurc martensite
quenching
at constant
and tempering
will consist
-
mean stress
temperatures
of acicular
ferrite
rather
than
where B is a constant. On the assumption that eqn (3) might be valid for other steels, the relevant threshold measurements in air at positive stress ratios were compiled and least square lines fitted through the data. The resulting values of thresholds at zero stress ratio, A&, and constants B, are summarized in Table 1. The steels are divided into two groups. The first groi.~p includes steels with mixed ferrite-pear&e or fully pearlitic microstructure; the second, quenched and tempered steels with microstructures consisting predominantly of tempered martensite. An example of AK, vs R dependencies for two steels with each group on which the most extensive threshold measurements were made, is given in Fig. 2. As can be seen, the linear relationship (eqn 3) fits the measured data very well over the whole range of values. A similarly
0. VOSIKOVSKY 14r
h l
12
I
I
l-.-CP o-o-
1 (6)
En3A (4) I
ferrite-peorlite
1
T steels J
Fig. 2. The dependence of thresholds on stress ratio for four steels with the most extensive threshold measurements.
good fit, with one exception[9], was exhibited by other steels, as indicated by correspondingly high values of the correlation coefficients r, given in Table 1. The values of both AK,, and B, which can be considered as material characteristics, vary over a rather wide range, 3
(4)
The suggested values for pressure vessel steels were; AKo, = 7 MPadm and dimensionless constant b = B/AK,,, = 0.85. The data in Table 1 show that neither AK, nor b have constant values for various steels. The range for AK,, is indicated above and b varies from 1.05 to 0.31, decreasing with increasing yield strength similarly to B. FATIGUE CRACK GROWTH RATE DEPENDENCE ON STRESS RATIO The low and intermediate fcg rates for HY 130 steel[16] over a wide range of stress ratios were successfully normalized vs (AK + BR), where (-B) is the siope of the threshold dependence. This suggests a modilication of eqn (1) describing the linear intermediate fcg region to $
= A(AK + BR)“.
(5)
This in effect means that fcg rate curves are simply translated along the AK axis. It implies that at any growth rate within the A and B Regions AK should vary linearly with R with a constant slope (-B). To test this hypothesis, linear regression lines were fitted through AK vs R data at three growth rates, lo+, lo-’ and lO~mm/cycle for steels listed in Table 1, wherever the relevant measurements were available. The values of B for these regression lines, are plotted with respect to fcg rates in Figs. 3(a) and (b), for steels with ferrite-pearlite and tempered martensite microstructures respectively. The threshold values of growth rate are assumed to be lo-’ mm/cycle.
The effect of stress ratio on fatigue crack growth rates in steels
SM5CAI101
+-+ o-o
H
.---.
CP
m-s!
,FP
o---o
5MP
I
v-v
P
.-.
MP
(71
15)
IO-’
~-m/c dN
THRESHOLD
(a)
201
A-A
A553A
o-o
kne-
.---. A-AA
300 H - (I51
)
,,;J “O’ WF
v----o
9310
ill1
HY I30
(161
15En24
87001100
o---m
670/300
-m
670/470
A-
670/650
o---o
12001300
l ---•
670&M
(121
+-+ x---x
o-0
II31 STEP COOLED
Fig. 3. The variation of B from AK vs K regression lines with fcg rate: (a) steels with ferrite-pearlite microstructures; fb) steels with tempered martensitic microstructures.
599
0.VOSIKOVSKY
600
As the fcg rate curves for various values of R in Region B lie quite close together (see Fig. I), the natural scatter inherent in growth rate measurements caused quite a wide variation in B, particularly at higher growth fates. For about half of the steels in the group with ferrite-pearlite microstructure, Fig. 3(a),the constant E decreases with increasing growth rate, for one quarter it decreases, and for the remaining quarter it stays constant. For steels in the group with martens& micros~c~re, Fii. 3(b), B tends to increase with increasing growth rates, particularly at growth rates above lo-‘mm/cycle. This probably caused by the fact that at high stress ratios, as K- approaches the critical stress intensity the fcg rates reach Region C and the resulting static modes of fracture[7, i3,15] accelerate the crack growth. Although the evidence in Figs. 3(a) and (b) does not demonstrate that fcg rate curves at different stress ratios are exactly parallel, eqn (5) reduces the data into a relatively narrow scatter band[lti] and appears to be useful for some predictive purposes. THRESHOLDD~~D~CE ON STRENGTH Examination of threshold data in Table 1 indicates that both A&, and B decrease with increasing strength. The degree of correlation is shown in Figs. 4 and 5 where zero stress ratio thresholds A& are piotted vs ultimate tensile strength and yield strength respectively. For steels where either cys or uW were not given, estimates were used. The thresholds, despite considerablescatter, particularlyfor steels with ferrite-pear&e microstructures, seem to decrease linearly with both yield and ultimate tensile strengths. Least square regression lines are given by eqns (6). A&, = Il. 17- O.O032u,, (6) AKot= 11.40- O.OO&r~~* Thresholds correlate better with uys than with PUTSas is evident from comparison of Figs. 4 and 5. The correiation coefficient for yield strength is 0.678 compared to 0.513 for UTS. The parallel straight-line 95% confidence interval[l7], calculated within the range 300< UYS< 1800MPa is kO.94MPa; this interval is indicated in Fig. 5. The conelation of B withyield strength, shown in Fig. 6, shows somewhat more dispersion than A&,,, for both ferrite-pearlite and martensitic steels. Again, it can be approximated by a linear dependence with regression line B = 10.39- O.O052rys,
(7)
with a 95% confidence interval of 2 1.19MPavm.
t4
1
o- ferrtte-pearhte *a
12t 1 E
0
steels steels
i
0 00
4
000
_~
0 ;:
0
IO
D
*
8‘ $8 z
0
O. 0
0 0
X Q
martensitic
lo
l
6t
l
*
.
.
0
4 .
.
. 41
I--,
I
500
I
1500
lo00 UTS-
Fig. 4. The variation of A&,,
z
.
1
I
2000
MPa
the threshold at R = 0, with ultimate tensile strength for steels listed in Table I. The solid lint is the least square regression line.
The effect of stress ratio on fatigue crack growth rates in steels
I
I
16
I
o-ferrite-peorlite
14-
+martensltic 00
601
steels steels
0
12-
2-
0
I 500
1 . 1000 Um-hlPO
1 1500
2000
Fig. 5. The variation of AKo, with ykld strength for steels listed in Tabk 1. The solid line is the least squares regression line; dashed lines delineate the 95% confidence interval.
I
I
I6
o-ferrite-pearlite
I4 -
l-mortenaitic
0
0
500 or,-
1000 M Pa
1 steels steek
1500
2000
Fig. 6. The variation of B with yield strengthfor steels listed in Table 1. The solid line is the kast squares regression line: dashed lines delineate the 95% confidence interval.
.
The data presented show that both thresholds and their stress ratio dependence decrease, probably linearly, with increasing yield strength. This dependence has been demonstrated most clearly for steels with tempered martensite microstructures. With ferrite-pearlite steels the data are more scattered and cover a relatively narrow range of strengths: thus the strength dependence of thresholds is not so evident. The two main sources of scatter are experimental procedures used to determine the thresholds and microstructural effects. The thresholds are usually quoted as AK values corresponding to growth rates in the range 10-‘-104 mm/cycle. As fcg rates depend on stress history, the load-reducing procedures used in the.determination of thresholds can strongly affect the resulting values. The influence of microstructure is very complex, and is apparently related to environmental effects, such as hydrogen embrittlement
602
0. VOSIKOVSKY
frommoist air. A detailed discussion of the dependence of thresholds on microstructure and environment is given by Ritchie[ 151. CONCLUSIONS Based on an examination of published experimental data on fatigue crack growth thresholds, fatigue crack growth rates, and their dependence on stress ratio for 33 steels tested in air, the following conclusions can be made. Thresholds decrease linearly with increasing stress ratio, AK, = A& - BR. The values of A& and B can be considered as material constants. Low and intermediate fatigue crack growth rates at different stress ratios can be reduced to a relatively narrow scatterband vs (AK + BR). Both A&, and B decrease with increasing yield strength. The data are widely dispersed but suggest that the relationships are likely linear. The scatter probably results from microstructural effects and variations in experimental procedures used to determine thresholds. Acknowlcdgrmmt--The
author wishes to acknowledge
L. P. Trudeau for helpful comments.
REFERENCES
III N. E. Frost.L. D.
Pook and K. Denton, A fracture mechanics analysis of fatigue crack growth data for various materials. Engng Fracture Mech. 3, lO!M26 (1971). (21 Ffitesnil and P. L&as. Effect of stress cycle assymetry on fatigue crack growth. Mater. Sci Engng 9, 231-239 131 P. C. &is. R. J. Bucci, E. T. Wessel, W. G. Clark and T. R Mager, An extensive study on low fatigue crack growth rates in A533 and A508 steels. ASTM STP 513, 141-176 (1972). 141 K. Jerram and E. K. Priddle, System for determining the critical range of stress-intensity factor necessary for fatigue crack propagation. 1. Mech. Engng Sci. 15(4), 271-273 (1973). IS] R. J. Cooke and C. 1. Becvers, The effect of load ratio on the stresses for fatigue crack growth in medium carbon steels. Engng Fracture hfech. 5. 1061-1071 (1973). [6] R. J. Cooke and C. J. Beevers, Slow fatigue crack propagation in pearlitic steels. Mol. Sci. Engng 13, 201-210 (1974). 171 C. J. Beevers. R. J. Cooke, J. F. Knott and R. 0. Ritchie, Some considerations of the influence of sub-critical cleavage growth during fatigue crack propagation in steels. Metal Sci. 9, II%128 (1975). 181 J. Masounave and J. P. Bailon, The dependence of the threshold stress intensity factor on the cyclic stress ratio in fatigue of ferritic-pearlitic steels. Scripta Metallurgica 9, 72>730 (1975). [9] C. M. Branco, J. C. Radon and L. E. Culver, Growth of fatigue cracks in steels. Metal Sci. 10, 14%155 (1976). [IO] E. Sasaki. A. Ohta and hi. Kosuge. Fatigue crack propagation rate and stress intensity threshold level of several structural materials at varying stress ratios. Trans. Nat. Res. Inst. for Metals 19(4), 183-199 (1977). [I I] P. C. Paris. Testing for very slow growth of fatigue cracks. Closed Loop 2(5). 11-14 (1970). [ 121 R. J. Bucci. W. G. Clark and P. C. Paris, Fatigue crack propagation growth rates under a wide variation of AK for an ASTM A517 Gr. F (T-l) steel. ASTM STP 513, 177-195 (1972). [I4 R. J. Cooke. P. E. Irving, G. S. Booth and C. J. Beevers. The slow fatigue crack growth and threshold behaviour of a medium carbon alloy steel in air and vacuum. Engng Fracture Mech. 7.69-77 (1975). [I41 1. Mautz and V. Weiss. Mean stress and environmental effects on near threshold fatigue crack growth. ASTM STP 6.1, 154-168 (1976). [IS] R. 0. Ritchie. Influence of microstructure on near-threshold fatigue-crack propagation in ultra-high strength steel. Metal Sci. ll(8.9). 368-381 (1977). [16] 0. Vosikovsky. Frequency, stress ratio and potential effects on fatigue crack growth of HY 130 steel in salt water. I. Testing and Eualuotion 6, 175-182 (1977). [ 17]R. E. Little and E. H. Jebc, Statistical &sign of Fatigue Experiments. Applied Science (1975). [I81 I. M. Barsom, Fatigue behavior of pressure vessel steels. WRC Bulletin 194 (May 1974). (Rereiced
IO May 1978: received for publicorion 7 lul.v 1978)
INTRODUCTION FATIGUEcrack growth (fcg) rates, do/dN, are generally presented in a log-log plot, against the stress intensity factor range, AK. The curves have tbe familiar sigmoidal shape, shown in Fig. 1. The middle, linear part of the curves, Region B, is described by the expression &
(1)
= AAhK”.
At low AK, Region A, the fcg rate decreases progressively faster until the threshold, AK,, for a non-propagating crack is reached. At high AK, Region C, the slope m of the curve increases as the maximum stress intensity approaches Kc The stress ratio, R = K&K-, as indicated in Fig. 1, strongly affects the fcg rate in the low and high growth rate Regions, A and C. In the intermediate Region B, relatively little effect is observed. In the present paper, the available experimental results on thresholds and fcg rates in low
REGION
THRESHOLD
LOG
E
/
AK
1. %bCm8tk ShapC Of fCg I&CCUWeS8t thret StreSS18tiOS.Region A-low kg rates 8pproaChiDg threshold, Region B-intermediite fcg rates with line8r log da/d?4- tog AR ~~a~nS~p, Region C-hi& fcg rates, Km, approachingthe critical stress intensity.
Fi.
t3kWVd.11.No.Z-H
595
0. VOSIKOVSKY
5%
and intermediate Regions A and B at positive stress ratios are compiled for steels tested in air[l-161. It appears that the threshold and fcg rate dependence on stress ratio can be expressed with useful accuracy by simple empirical relationships suggested in [16]. TEEESIIOLD DEPENDENCE ON SIRES RATIO To express the threshold-stress ratio relationship, eqn (2) originated by Klesnil and Lukas [2] has been most extensively used [6,8, 10,131. AK, = AK& -K)‘,
(2)
where AK, is a threshold at R = 0, and 7 is a material constant varying from 0.5 to 1 for different steels. A value of 7 close to 1, indicating a linear relationship and a constant K, equal to AK&, has been measured for several medium carbon steels [6,8]. For alloyed medium carbon martqnsitic steel[l3], 7 was close to 0.5, and for several low carbon structural steels, intermediate values of 7 were found[lO]. Recent measurements of thresholds on HY 130 steel [ 161fit a simple linear relationship AK,, = AK,,, - BR
(3)
Tsble 1.ThresholdSaadtbcird~p~ade~~~onst~~ssrstios forstds withfetitbpearlite&tsmpmdmartsasitc IlIiWOSWllCnrreS Refaranoe
Clark & Mager
erram an
[7] Reevera, Cooke, Knott and Ritchie 1975
[81 ya;;zave and
1975
CP carbon steel 917 0.5fC,2.23Mn P carbon steel 770 0.55C,O.66Mn Mp carbon steel1124 0.55C.2.23Mn 12-2 carbon steel 0.4CI0.7t4n 6-2 carbon steel o.rC, 0.7un 6-T carbon steel 0.4C,O.'lMn
399
8
12.60 12.30 0.989
* 434
5
8.59 7.24 0.985
753
5
11.55 10.94 0.998
493
4
6.31 5.82 0.999
477
5
11.10 11.50 0.999
477
3
12.60 13.25 0.999
592
The effect of stress ratio on fatigue crack growth rates in steels
Table l.(Contd) Reference [El
and 1975
OYS (UPa)
NO. of b=ot Data (MPa+%h)
B
E
I4amolmave
Bailon
%TS 04Pa)
Steel
gar;mo . ye&e1
532
*009~1;-1 carbon steel 0.8C,O.7Hn
5
11.04
10.20
4
10.01
9.73
191 Branco, Radon & Culver x) 1976
BSl5 mild steel 0.19c.0.59Mn
585
401
5
6.54
2.85
[lOI Sasaki, Ohta urd Koswe 1977
SMSOA structural
568
372
3
10.37
8.56
Quenched
111 FE=-&
steel
and tempered
steels
I
and
;o$
[lo] Suaki, Qhta 4 Kosuge 1977
o.14c,1.3Mnn.
I
I 666 I
5881
5
I 7.93
774
i2s
3
6.69
5.43 0.989
2
6.32
3.29
7.14 0.915
A553-A
[ll] Paria
1970
9310 0.1C,3NirlCr,
I121 Bucci, Cluk Paris 1972
i 0.961
1131 Cooke, Irving, Booth and Boevars 197: I141 Zf
[lS] Ritchie
1151 Mtchie
I
1970
1640
8
3.56
1.19
1070
2
6.44
5.42
993
3
5.74
2.97 0.999
1977
1977
1161 Vodkovmky
UOte8
D6 ac 0.48C,O.8Hn, 0.6Ni,l.lCr, lMo,O.lV
andx1 1976
1977
MY 130 O.O9C,SNi O.SCr,O.SMo
x) The grath xx) mrkrs
1034
rates were measured
indicate
xxx) The mlcrostructurc martensite
quenching
at constant
and tempering
will consist
-
mean stress
temperatures
of acicular
ferrite
rather
than
where B is a constant. On the assumption that eqn (3) might be valid for other steels, the relevant threshold measurements in air at positive stress ratios were compiled and least square lines fitted through the data. The resulting values of thresholds at zero stress ratio, A&, and constants B, are summarized in Table 1. The steels are divided into two groups. The first groi.~p includes steels with mixed ferrite-pear&e or fully pearlitic microstructure; the second, quenched and tempered steels with microstructures consisting predominantly of tempered martensite. An example of AK, vs R dependencies for two steels with each group on which the most extensive threshold measurements were made, is given in Fig. 2. As can be seen, the linear relationship (eqn 3) fits the measured data very well over the whole range of values. A similarly
0. VOSIKOVSKY 14r
h l
12
I
I
l-.-CP o-o-
1 (6)
En3A (4) I
ferrite-peorlite
1
T steels J
Fig. 2. The dependence of thresholds on stress ratio for four steels with the most extensive threshold measurements.
good fit, with one exception[9], was exhibited by other steels, as indicated by correspondingly high values of the correlation coefficients r, given in Table 1. The values of both AK,, and B, which can be considered as material characteristics, vary over a rather wide range, 3
(4)
The suggested values for pressure vessel steels were; AKo, = 7 MPadm and dimensionless constant b = B/AK,,, = 0.85. The data in Table 1 show that neither AK, nor b have constant values for various steels. The range for AK,, is indicated above and b varies from 1.05 to 0.31, decreasing with increasing yield strength similarly to B. FATIGUE CRACK GROWTH RATE DEPENDENCE ON STRESS RATIO The low and intermediate fcg rates for HY 130 steel[16] over a wide range of stress ratios were successfully normalized vs (AK + BR), where (-B) is the siope of the threshold dependence. This suggests a modilication of eqn (1) describing the linear intermediate fcg region to $
= A(AK + BR)“.
(5)
This in effect means that fcg rate curves are simply translated along the AK axis. It implies that at any growth rate within the A and B Regions AK should vary linearly with R with a constant slope (-B). To test this hypothesis, linear regression lines were fitted through AK vs R data at three growth rates, lo+, lo-’ and lO~mm/cycle for steels listed in Table 1, wherever the relevant measurements were available. The values of B for these regression lines, are plotted with respect to fcg rates in Figs. 3(a) and (b), for steels with ferrite-pearlite and tempered martensite microstructures respectively. The threshold values of growth rate are assumed to be lo-’ mm/cycle.
The effect of stress ratio on fatigue crack growth rates in steels
SM5CAI101
+-+ o-o
H
.---.
CP
m-s!
,FP
o---o
5MP
I
v-v
P
.-.
MP
(71
15)
IO-’
~-m/c dN
THRESHOLD
(a)
201
A-A
A553A
o-o
kne-
.---. A-AA
300 H - (I51
)
,,;J “O’ WF
v----o
9310
ill1
HY I30
(161
15En24
87001100
o---m
670/300
-m
670/470
A-
670/650
o---o
12001300
l ---•
670&M
(121
+-+ x---x
o-0
II31 STEP COOLED
Fig. 3. The variation of B from AK vs K regression lines with fcg rate: (a) steels with ferrite-pearlite microstructures; fb) steels with tempered martensitic microstructures.
599
0.VOSIKOVSKY
600
As the fcg rate curves for various values of R in Region B lie quite close together (see Fig. I), the natural scatter inherent in growth rate measurements caused quite a wide variation in B, particularly at higher growth fates. For about half of the steels in the group with ferrite-pearlite microstructure, Fig. 3(a),the constant E decreases with increasing growth rate, for one quarter it decreases, and for the remaining quarter it stays constant. For steels in the group with martens& micros~c~re, Fii. 3(b), B tends to increase with increasing growth rates, particularly at growth rates above lo-‘mm/cycle. This probably caused by the fact that at high stress ratios, as K- approaches the critical stress intensity the fcg rates reach Region C and the resulting static modes of fracture[7, i3,15] accelerate the crack growth. Although the evidence in Figs. 3(a) and (b) does not demonstrate that fcg rate curves at different stress ratios are exactly parallel, eqn (5) reduces the data into a relatively narrow scatter band[lti] and appears to be useful for some predictive purposes. THRESHOLDD~~D~CE ON STRENGTH Examination of threshold data in Table 1 indicates that both A&, and B decrease with increasing strength. The degree of correlation is shown in Figs. 4 and 5 where zero stress ratio thresholds A& are piotted vs ultimate tensile strength and yield strength respectively. For steels where either cys or uW were not given, estimates were used. The thresholds, despite considerablescatter, particularlyfor steels with ferrite-pear&e microstructures, seem to decrease linearly with both yield and ultimate tensile strengths. Least square regression lines are given by eqns (6). A&, = Il. 17- O.O032u,, (6) AKot= 11.40- O.OO&r~~* Thresholds correlate better with uys than with PUTSas is evident from comparison of Figs. 4 and 5. The correiation coefficient for yield strength is 0.678 compared to 0.513 for UTS. The parallel straight-line 95% confidence interval[l7], calculated within the range 300< UYS< 1800MPa is kO.94MPa; this interval is indicated in Fig. 5. The conelation of B withyield strength, shown in Fig. 6, shows somewhat more dispersion than A&,,, for both ferrite-pearlite and martensitic steels. Again, it can be approximated by a linear dependence with regression line B = 10.39- O.O052rys,
(7)
with a 95% confidence interval of 2 1.19MPavm.
t4
1
o- ferrtte-pearhte *a
12t 1 E
0
steels steels
i
0 00
4
000
_~
0 ;:
0
IO
D
*
8‘ $8 z
0
O. 0
0 0
X Q
martensitic
lo
l
6t
l
*
.
.
0
4 .
.
. 41
I--,
I
500
I
1500
lo00 UTS-
Fig. 4. The variation of A&,,
z
.
1
I
2000
MPa
the threshold at R = 0, with ultimate tensile strength for steels listed in Table I. The solid lint is the least square regression line.
The effect of stress ratio on fatigue crack growth rates in steels
I
I
16
I
o-ferrite-peorlite
14-
+martensltic 00
601
steels steels
0
12-
2-
0
I 500
1 . 1000 Um-hlPO
1 1500
2000
Fig. 5. The variation of AKo, with ykld strength for steels listed in Tabk 1. The solid line is the least squares regression line; dashed lines delineate the 95% confidence interval.
I
I
I6
o-ferrite-pearlite
I4 -
l-mortenaitic
0
0
500 or,-
1000 M Pa
1 steels steek
1500
2000
Fig. 6. The variation of B with yield strengthfor steels listed in Table 1. The solid line is the kast squares regression line: dashed lines delineate the 95% confidence interval.
.
The data presented show that both thresholds and their stress ratio dependence decrease, probably linearly, with increasing yield strength. This dependence has been demonstrated most clearly for steels with tempered martensite microstructures. With ferrite-pearlite steels the data are more scattered and cover a relatively narrow range of strengths: thus the strength dependence of thresholds is not so evident. The two main sources of scatter are experimental procedures used to determine the thresholds and microstructural effects. The thresholds are usually quoted as AK values corresponding to growth rates in the range 10-‘-104 mm/cycle. As fcg rates depend on stress history, the load-reducing procedures used in the.determination of thresholds can strongly affect the resulting values. The influence of microstructure is very complex, and is apparently related to environmental effects, such as hydrogen embrittlement
602
0. VOSIKOVSKY
frommoist air. A detailed discussion of the dependence of thresholds on microstructure and environment is given by Ritchie[ 151. CONCLUSIONS Based on an examination of published experimental data on fatigue crack growth thresholds, fatigue crack growth rates, and their dependence on stress ratio for 33 steels tested in air, the following conclusions can be made. Thresholds decrease linearly with increasing stress ratio, AK, = A& - BR. The values of A& and B can be considered as material constants. Low and intermediate fatigue crack growth rates at different stress ratios can be reduced to a relatively narrow scatterband vs (AK + BR). Both A&, and B decrease with increasing yield strength. The data are widely dispersed but suggest that the relationships are likely linear. The scatter probably results from microstructural effects and variations in experimental procedures used to determine thresholds. Acknowlcdgrmmt--The
author wishes to acknowledge
L. P. Trudeau for helpful comments.
REFERENCES
III N. E. Frost.L. D.
Pook and K. Denton, A fracture mechanics analysis of fatigue crack growth data for various materials. Engng Fracture Mech. 3, lO!M26 (1971). (21 Ffitesnil and P. L&as. Effect of stress cycle assymetry on fatigue crack growth. Mater. Sci Engng 9, 231-239 131 P. C. &is. R. J. Bucci, E. T. Wessel, W. G. Clark and T. R Mager, An extensive study on low fatigue crack growth rates in A533 and A508 steels. ASTM STP 513, 141-176 (1972). 141 K. Jerram and E. K. Priddle, System for determining the critical range of stress-intensity factor necessary for fatigue crack propagation. 1. Mech. Engng Sci. 15(4), 271-273 (1973). IS] R. J. Cooke and C. 1. Becvers, The effect of load ratio on the stresses for fatigue crack growth in medium carbon steels. Engng Fracture hfech. 5. 1061-1071 (1973). [6] R. J. Cooke and C. J. Beevers, Slow fatigue crack propagation in pearlitic steels. Mol. Sci. Engng 13, 201-210 (1974). 171 C. J. Beevers. R. J. Cooke, J. F. Knott and R. 0. Ritchie, Some considerations of the influence of sub-critical cleavage growth during fatigue crack propagation in steels. Metal Sci. 9, II%128 (1975). 181 J. Masounave and J. P. Bailon, The dependence of the threshold stress intensity factor on the cyclic stress ratio in fatigue of ferritic-pearlitic steels. Scripta Metallurgica 9, 72>730 (1975). [9] C. M. Branco, J. C. Radon and L. E. Culver, Growth of fatigue cracks in steels. Metal Sci. 10, 14%155 (1976). [IO] E. Sasaki. A. Ohta and hi. Kosuge. Fatigue crack propagation rate and stress intensity threshold level of several structural materials at varying stress ratios. Trans. Nat. Res. Inst. for Metals 19(4), 183-199 (1977). [I I] P. C. Paris. Testing for very slow growth of fatigue cracks. Closed Loop 2(5). 11-14 (1970). [ 121 R. J. Bucci. W. G. Clark and P. C. Paris, Fatigue crack propagation growth rates under a wide variation of AK for an ASTM A517 Gr. F (T-l) steel. ASTM STP 513, 177-195 (1972). [I4 R. J. Cooke. P. E. Irving, G. S. Booth and C. J. Beevers. The slow fatigue crack growth and threshold behaviour of a medium carbon alloy steel in air and vacuum. Engng Fracture Mech. 7.69-77 (1975). [I41 1. Mautz and V. Weiss. Mean stress and environmental effects on near threshold fatigue crack growth. ASTM STP 6.1, 154-168 (1976). [IS] R. 0. Ritchie. Influence of microstructure on near-threshold fatigue-crack propagation in ultra-high strength steel. Metal Sci. ll(8.9). 368-381 (1977). [16] 0. Vosikovsky. Frequency, stress ratio and potential effects on fatigue crack growth of HY 130 steel in salt water. I. Testing and Eualuotion 6, 175-182 (1977). [ 17]R. E. Little and E. H. Jebc, Statistical &sign of Fatigue Experiments. Applied Science (1975). [I81 I. M. Barsom, Fatigue behavior of pressure vessel steels. WRC Bulletin 194 (May 1974). (Rereiced
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