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Short fatigue crack growth behaviour in Al 5083 alloy
Int. J. Fatigue Vol. 19, No. 2, pp. 161-t68, 1907 (c~ 1997 Elsevier Science l,imited. All rights reserved Printed in Great Britain. 0102--I 1231971517.00+ 00
ELSEVIER
PII: S0142-1123(96)00047-3
Short fatigue crack growth behaviour in AI 5083 alloy J.D. Costa*, C.M. Brancot and J.C. Radon¢ *DEM, FCTUC, University of Coimbra, 3000 Coimbra, Portugal tCEMUL, Instituto Superior T6cnico, UTL, 1096 Lisboa Codex, Portugal tlmperial College, London SW7, UK (Received 26 February 1996; revised 20 May 1996; accepted 10 June 1996) This work presents the results of a study of fatigue crack growth in AI 5083 alloy starting from a micro comer notch of 40/xm depth in both directions. The fatigue tests were carried out with constant load amplitude in tension and in bending using three ratio values R = - I , 0.05 and 0.5. The crack aspect ratio a/c evolution as a function of the normalized crack depth, a/B, was influenced neither by the stress ratio nor by the type of loading for values of a/B 0.1. Threshold fatigue values obtained for short cracks were found to be lower than for long crack levels, obtained in previous work for R = 0.05 and 0.5. For R = - 1 the short fatigue crack threshold value was approximately the same as the long fatigue crack threshold obtained with compact tension (CT) specimens for R = 0.8. Crack opening values were obtained previously with CT specimens using an Elber type micro gauge and were used to calculate AKef,-values. When comparing the results obtained in this work for short fatigue cracks with the da/dN-AK~fr curves recorded for long cracks, it is concluded that in short cracks the crack opening values may be virtually nil in order to explain their higher crack growth rate. Copyright © 1997 Elsevier Science Ltd. All rights reserved (Keywords: AI 5083 a l u m i n i u m alloy; s h o r t fatigue cracks; crack closure)
INTRODUCTION
data were obtained for the three values of stress ratio. The crack closure parameter U, initially proposed by Elber, 7 was used to obtain AK,.r, the effective values of AK. The crack growth rate, da/dN, when plotted vs AKeff gave good correlation independent of stress ratio. A contribution to the fatigue strength characterization of the same material is presented in this work. The behaviour of short fatigue cracks initiated from a micro comer notch was assessed and the results were compared with long crack data. Short fatigue cracks analysed in this work were classified as mechanically short, i.e. typically 0.5-1 mm in length, but greater than about three times the grain size, d g = 20/xm. Also, the crack closure effect was analysed and considered to be one of the main causes of the different behaviour of short and long fatigue cracks. Three values of stress ratio were applied: R = - 1 , 0.05 and 0.5. Also, the loading mode (tension and bending) influence was assessed. The crack aspect ratio a/c development was compared with the theoretical predictions obtained with a computer program based on the linear elastic fracture mechanics concepts.
The object of considerable interest in fatigue research is the study of the initiation and propagation of short fatigue cracks. Subsequent to the studies by Pearson ~, great advances in knowledge of the behaviour of this tye of crack were acomplished. In general, short fatigue cracks have been found to grow at faster rates and to have lower thresholds than long fatigue cracks at the same stress intensity factory, AK2~. In Ritchie's work,-' comparison of results obtained in specimens with a micro comer crack against long crack data obtained in compact tension (CT) and centre cracked tension (CTT) specimens confirmed this trend. The possible absence of crack closure in short fatigue cracks discussed later seems to be the main explanation for the higher crack growth rates in very short cracks. One of the most important consequences of this behaviour is that the fatigue life prediction using the d a / d N - A K curves obtained at long cracks could lead to excessively optimistic estimates. Thus, the determination of the crack length above which its behaviour is similar to the long crack behaviour is very important. In previous work by the authors 5'6 fatigue strength and ductility parameters of the A1 5083 alloy and the long fatigue crack propagation values were obtained. The influence of the stress ratio (R = 0.05, 0.5 and 0.8) on the crack growth rate was analysed. Crack closure
M A T E R I A L AND E X P E R I M E N T A L DETAILS Chemical composition and the mechanical properties of the 5083 aluminium alloy are shown in Tables I and 2.
161
J.D. Costa et al.
162 Table 1 Mg
Chemical composition of 5083 AI alloy
Mn
Fe
Ni
4.5 0.55 0.37 <0.5
Table 2
Cr 0.12
Zn
Si
Sn
0.1 <0.1
Pb
Ti
AI
<0.05 <0.05 <0.05 Balance
Mechanical properties of 5083 A1 alloy
Ultimate strength, ouxs [MPa] Monotonic yield stress, ~rvs [MPa] Cyclic yield stress, OSvs [MPa] Elongation to rupture, Er [%]
321 180 310 18.2
Fatigue tests of the short cracks initiating from the root of a comer micro notch were conducted in tension and in bending loading modes. The specimens geometry is shown in Figure 1. The specimens were provided with a miro notch approx. 40/zm long in both directions (a and c). This micro notch was obtained by pressing a razor blade against the comer of one of the specimens with a controlled load of 2 N. The micro notch dimensions were checked in all the specimens before the fatigue tests. The specimen shape, with a progressive variation of shoulder width in the form of a circular arch, was adopted with the purpose of limiting the initiation of the crack to the micro notch. The stress concentration due to the width variation was calculated by the finite element method and the results obtained were integrated in the stress intensity factor formulation. The values obtained for Kt were 1.095 for bending and 1.089 for tension. From the results of the finite element method stress calculations, the variation of Kt with the distance c was derived and taken in account in the stress intensity factor calculation as a factor MK. The bending tests were performed in a fatigue testing rig specially built for that purpose. The tension tests were carried out in a load-controlled servohydraulic machine INSTRON model 1341, with 100kN of capacity. In both cases the load wave was of constant
a'l!
:7i
Esu
/
amplitude sinusoidal with a frequency of 25 Hz and temperature 25°C. The short crack measurements were made in a metallographic microscope with 1000× magnification. For that purpose the specimen was taken out from the machine at periodic intervals. With this technique it was possible to detect cracks 10/~m long measured from the notch root. The readings were made in both directions of the comer crack and a photographic record of the crack growth was obtained. One of the photographs obtained during the observations is shown in Figure 2 with a crack 20/xm long tested in bending. The specimens were previously polished by electrolytic process in the notch region to improve the observation. The electrolyte used was composed by 800 ml of ethanol (absolute), 140 ml of distilled water and 60 ml of perchloric acid (60%). The conditions of polishing were: a cell voltage of 60 V and a time of 20 s. The specimen contacted with the electrolyte through a small circular hole of 1 cm 2 existing at the top of the electrolytic cell. From the a and c crack lengths, the crack growth rates da/dN and dc/dN and the stress intensity factor ranges AKa and AK,., were calculated using a computer program developed for this prupose. The geometric factor Y used was obtained from the Pickard polynomial equations. 8 The secant method 9 was chosen to calculate the crack growth rate. Crack closure measurement (opening loads) were attempted using the Elber type micro gauge ~° placed near the crack tip with the measurement points above and below the crack surfaces. The distance between these points was 1.2 mm. For cracks < 1 mm of length it was impossible to detect the crack opening loads due to the insufficient sensitivity of the gauge. The change of compliance between the open and closed crack was too small to be detected by the gauge, as the distance of 1.24 mm between measuring points was too great when compared with the crack length. The crack closure loads were measured only for the stress ratio R = -1 because for the other stress ratios, R = 0.05 and 0.5, these measurements were obtained, previously 5"6 using CT specimens.
12
fl 55
-
80
,
135
Thickness:
12 mm
l
I b) 3s
j
• '~
Figure 1
39
-
=
3o
t
50 faxn
x
~
135
Specimen geometries: (a) bending; (b) tension
Figure 2
Micro corner crack 20/zm long; AI 5083 alloy (200×)
Short fatigue crack growth behaviour in AI 5083 alloy
163
RESULTS AND DISCUSSION
Crack shape evolution Crack shape results are presented in Figure3. The curves refer to the plots of a/c against the normalized crack depth a/B, obtained for micro comer cracks in tension and bending. The short crack data are only for a/B < 0.1, that is, for the crack lengths a and c < 1 2 0 0 / x m . Some scatter may be noted in the a/c results of short cracks. This was due to the fact that crack initiation took place in some cases in only one direction (a or c), causing therefore a slight delay in the other direction. However, as the crack grew and a/B increased, crack propagation tended to equalize in both directions and the scatter was reduced close to a/c = 1 at higher values of a/B. In the range of values presented for a/B no influence of stress ratio and loading mode was noted. The influence of both loading mode and stress ratio can be seen in Figures 4 and 5 for tension and bending, respectively. These data present all the results obtained as plots of a/c against a/B values. In tension, Figure 4, the cracks were approximately of a semi-circular shape for a/B values >0.1. For a/B < 0.1 some scatter was recorded as mentioned earlier. Therefore, the crack growth rate in both directions was approximately the same. No influence was observed of the stress ratio on the crack shape in this loading mode. The crack aspect ratio in bending, was near to 1, for a/B < 0.1. However, for a/B > 0.1 the a/c decreased as a/B increased for all the three stress ratios analysed. Therefore in bending, the comer cracks have a greater growth rate in the c direction (parallel direction to the neutral bending axis) than in the a direction (perpendicular to the neutral axis). This behaviour shows, as expected, that in tension the cracks tend to stabilize in the quarter-circular shape while in bending, due the nonuniform stress through the thickness, the trend is towards the quarter-elliptical shape. Some influence of the stress ratio on the crack shape in bending (Figure 5) can also be observed: for the
•
.
•
-
•
0.75 "7"
0.50
Theoretical Predictions 0.25
,
0
-
l
,
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R=-I R=0.05
•
R=0.5 ,
l
(,.~
- "
l
,
0.3 ;fib (-)
I
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U.
Figure 4 ale vs alB: AI 5083 alloy, tension
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.
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Theoretical Predictions ~R=-I
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0 t~
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i
*
R=0.05
•
R=0.5
I
02
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I
0.3
Tensi°n { 3 R=0"05 R=0.5
,
l
0.02
,
l
0.04
i
{
,
0.06
{
a/c vs aIB for a l B < 0.1; AI 5083 alloy
*
05
Figure 5 a/c vs a/B; A1 5083 alloy, bending
i
0.08
0.10
a/B Figure 3
I
04
a/B
Bending [ : R=005 R=0.5
0,4
u
R = - 1 stress ratio, all the a/c values were lower than for the other stress ratios. Comparing the results obtained for the stress ratios R =0.05 and 0.5, we observe that each a/c range crosses the other. The a/c range for R = 0.5 is above the a/c range for R = 0.05
J.D. Costa et a l.
164
for lower values of a/B (i.e. a/B < 0.2), while for higher values of a/B, (i.e. a/B > 0.2), we observe the reverse. The crack closure phenomenon may probably provide the explanation for this behaviour. Both directions of propagation (a and c directions) are in the same stress condition, that is, in plane stress, and therefore the stress condition can not be the cause for the different values of crack closure. But, in bending the stress intensity factor ranges AK, and AK,. present different values, as shown in Figure 6. In this figure the values of AK,/AK,. are plotted against a/B for the two loading modes (tension and bending). The stress intensity factor AK,, is higher than the AK,, value. As the crack closure parameter U is a function of both AK and R, the corresponding values of the ratios AK,/AK,. and A g e f f , a / m g e f f , c will be different for different stress ratios and similarly the crack growth rates da/dN and dc/dN. This may be the main factor that explains the influence of the stress ratio on the crack aspect ratio a/c in bending. Similar results on the influence of the stress ratio on short crack shapes in steel BS360-50D were recently reported l~ and support the present conclusions. In tension a so clear influence of the stress ratio was not observed. This is in agreement with AK, and AK,. are similar and so are the stress conditions. Therefore, the crack closure parameter for the two directions, U, and U,., will be closely similar and so are the effective stress intensity factor ranges, AKefc, and AKeff.c, independently of stress ratio. Theoretical prediction of crack aspect evolution are also presented in Figures 4 and 5, using crack propagation data obtained with CT specimens. A computer program was used for these predictions assuming an equal material crack growth strength in both directions. Therefore, no crack closure model was used, that is Ag,. _ Ageff, c_
Comparison of short and long crack growth rates The short cracks are sometimes classified as microstructurally or mechanically short, depending on their size when compared with some relevant microstructural parameters. It was noted previously that this study deals only with microcracks emanated from a micro corner notch 40/xm deep. The minimal crack length detected was about l0/~m, and the grains are equiaxed with a size (determined by microstructural observation) of 20 p~m. The high accuracy in the manufacture of the notches obtained (see geometry in Figure 7) leads to a very small value of the notch plastic zone l, Indeed, applying the Smith and Miller 12 equation we obtain for 1, lo = 0.13 "~Doo= 0.13 ",/50-x-0.5 = 0.65 /xm
In tension the theoretical curve presents a constant value of the crack aspect ratio a/c = 1 independent of
1,4
,
,
,
D
,
U
01~0 0
u
1.0
(2)
where D is the notch depth and p is the notch tip radius. Alternatively, using the equation proposed by Dowling 13 and more appropriate for very severe notches:
D ,o=
40 _
1
_
l
o.
8
(l)
AK,, Ageff,a
:.
both crack size and stress ratio. This behaviour is in agreement with the experimental results obtained. In bending, the experimental results obtained for R=-I and R = 0 . 5 present the same trend as the theroetical predictions. For R = 0.05 such a good agreement was not observed. In both loading modes (tension and bending) the theoretical predictions of the crack aspect ratio a/c tend to the unity as the normalized crack length a/B tend to zero. This is in agreement with the experimental results observed in Figure3, despite the scatter previously explained.
(3) In this equation Y is the geometrical factor calculated using the Pickard 8 solution and Kt is the stress concen-
,
Uu
~ U
•
•
.,is== ~ •
p<0:5 Iztm dr.
0,8
/
io =o i
0,6
u
U
/
/
Bending
D=40 l.tm
0,4
.
0
i
0, I
*
i
0,2
,
¢
0,3
i
i
0,4
0,5
0,6
a/B
r
Figure 6 AK,,/AKc against a/B for corner cracks; tension and bending
1
a
Figure 7
Micro notch geometry
Short fatigue crack growth behaviour in AI 5083 alloy 10-4
tration factor and was calculated by the following equation K, = I + 2 4 D 0 = 1 + 2 ~ / ~
= 10
165
(4)
Equation (3) gives for the dimensions l0 a value that falls better within the range p/20 to p/4 quoted in the literature, ~' lot moderate and sharp notches respectively. Therefore, it can be suggested that the notch of depth D is a part of the total crack length, practically at the initiation. The first crack measurement presents values > 5 0 / x m , which is about 2.5x the grain size. Thus, the short cracks analysed here can be classified as mechanically short and must not be significantly affected by the microstructure. Indeed, the behaviour reported by some investigators, H- 16 in which the crack growth rate decreases significantly as the crack length approximates the grain size or other barriers, was not observed. The Figures 8 and 9 present the crack growth rate data da/dN and dc/dN as a function of a and c, for tension and bending. For micro cracks < 1 0 0 / x m the crack growth rate increases very quickly with the crack length. Between 100 and 300/xm crack growth rate increases more moderately than before. After 300/xm length the crack grows at a rate that increases linearly, but slowly, with the crack length. We will comment on this behaviour later. Figures lO and 11 show respectively the crack growth rate as a function of the stress intensity factor for both stress ratios R =0.05 and 0.5, for tension and bending loading modes. The da/dN-AK results obtained with long cracks (CT specimens) for three stress ratio values, R = 0 . 0 5 , 0.5 and 0.8, are also plotted for comparison. For corner micro cracks sizes < 3 0 0 / x m the crack growth rate is higher than for the long cracks (CT specimens). Also fatigue crack
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10-6
z
tl-
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z 10-7
,~ R=-I i
R=0.05
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0 Figure
9
,
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I
0.2
t
0.4
da/dN and dc/dN vs
ct
i
I
0.6 a,c (ram)
i
I
0.8
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and c, respectively; bending
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)
R=O
I0 a,c<300wn a.c>300 p.m
R=0.5 1 : a ' c < 3 0 0 I'tm a,c>300 gm
z
10-8
8
100
A
I
0.2
A
1
Figure 10 da/dN and dc/dN against AK. and AK,. respectively, ("I" curves; tension (R = 0.05 and 0.5)
R=0.5
•
Figure
,
AK, MPa'l--mm "~ R=-I * R=0.05
0
t lO
10-7
I0-8
a
,
I
0.4 0.6 a,e (ram)
,
I
0.8
da/dN and dc/dN vs a and c, respectively; tension
1.0
propagation still takes place at AK values below the threshold level AKth obtained for long cracks (e.g. long cracks have AK,h = 3.5 MPa m s for R = 0.05 and AK, h - 2.1 MPa m ~ for R = 0.5). For cracks :>300/xm
J.D. Costa
166
et
am.
1,2
16 2
],0q 16 3 Io m
0,8
%
•
16 4
#
R=0.5
_
R
R=0.05
different points for different specimens
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0,2
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,
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,
,
0,6
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c [mini •" CT specimens
•
Figure 12
U against a,c (R = 0.05); A1 5083 alloy
Micro comer cracks
I
o
R=0.05
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oo o o 16"
•
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,f
~O
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~
a,c<300 I.tm
.
a,¢~'~(YI~m
1,0 m'*~lj •
•
•
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100
m,',
0,8
Figure 11 da/dN and dc/dN against AK,, and AK,,, respectively. CT
curves; bending (R = 0.05 and 0.5)
there is a good agreement with the results in CT specimens. The long cracks curve for R = 0 . 8 , where crack closure is insignificant, 5'6 fits very well with the experimental data for short cracks, thus confirming the fact that crack closure is virtually absent in micro cracks significantly < 3 0 0 / z m . Note that as crack closure is increasing with crack length, the curves d a / d N - A K for long cracks join the micro comer crack data when the crack length is above 300 ~m. This behaviour was also noted but not clarified by other authors. ~6-]8 For example, James and Sharpe ]7 investigated steel A533B and suggested the same micro crack length (300/zm) as proposed in the present work for the transition crack length. Above this transition crack length they found that the crack closure level was constant and similar to the values typical for long cracks. It cannot be confirmed with certainty that in our A1 5083 alloy the observed behaviour was due to the same cause, because crack closure measurements were not obtained in the very short crack regime. However, the high values of crack closure level recorded for long cracks together with the fact that there are no conditions for a crack closure mechanism in microcracks, supports this hypothesis sufficiently. Our interpretation of the present results may therefore be applied in the study of mechanically short cracks in other materials. Figures 12 and 13 show that crack closure increases as the crack length increases. These plots were obtained assuming that crack closure is the only cause for the different behaviour of short and long cracks. In these figures U was calculated by the equation
•m~B
,,, • o
AK, MPa~/m
• •
R=0.5 different points for different specimens
0,6
0,4 0,0 Figure 13
U=
• • •
a
I
I
I
0,2
0,4
0,6
a
l
0,8 a, c lmm]
I
1 1,0
U against a,c (R = 0.5); AI 5083 alloy
AK ~ -
(5)
where AK ~ and A/~. 8 are the stress intensity factors for short and long cracks, respectively, for the same fatigue crack growth rate. A/~.8 is the value for R = 0.8, where crack closure is insignificant. Despite the considerable scatter of data, as a result of the d a / d N - A K data scatter for short cracks < 3 0 0 / z m , a clear decreasing trend of the U parameter with the increasing crack length can be observed until the crack length reaches approx. 300/zm. Afterwards U is independent of crack length. The results obtained for micro comer cracks at R = - 1 stress ratio are shown in Figures 14 and 15 as the variation of da/dN and dc/dN vs AK, and AK,, respectively. In these figures the long crack curves (solid lines) obtained for R = 0.05 and 0.8 are also presented to allow a comparison. The results in Figure 14 are for tension while Figure 15 shows the results in bending. AK for the stress ratio R = - 1 was calculated using Equation (6) recommended by ASTM E6479 for negative stress ratios, AK = Kmax
(6)
It will be seen that for this stress ratio (R = - 1 ) the crack growth rates for short comer cracks are faster than for long cracks obtained at the R = 0.05 stress
Short fatigue crack growth behaviour in AI 5083 alloy 10 -2
io-3
10-4'
glo-S
R=0.8
,-oS CT specimens
Micro comer craci~,
10-7
1: a,c<30o~ R=- |
lo-"E;,oo
a,c>300p.m
I
1
t
100
10 KmAx, MPa~m
167
ratio. Also, the experimental results for short cracks are very close to the curve obtained for the long cracks at R = 0.8. Another important aspect is that for R = - 1 the short and long cracks form on continuous band. This is contrary to what was found for R = 0.05 and 0.5. This behaviour can be explained, again using the crack closure phenomenon, and assuming that there is no perceptible change of closure level with crack length variation. As already explained in the experimental section above, crack closure was measured at this stress ratio only for crack lengths > 1 0 0 0 / z m . For cracks < 1 0 0 0 b t m long the available Elber gauge was not sensitive enough. Figure 16 shows the variation of crack closure parameter U against AK, for tension and bending. U was calculated using the definition for AK given by Equation (6). The value U ~ I for all AK values tested under both tension and bending loading modes. Therefore, for long cracks, Kop ~ 0 for R - - - 1 . Assuming now that for short cracks the same equation could be applied (i.e. Kop ~ 0), then the effective stress intensity factor AKcff is not influenced by the crack length. Consequently, there is no direct effect on the crack closure level. The agreement between the results obtained for short comer cracks at R = - 1 and the continuous line obtained for long cracks in CT specimens at R = 0.8 is thus explained because in both cases AK AKef f. The values of crack closure found fl)r R = - I (Figure 16) are lower than for R = 0.05 (cf. Figure •2). This is due to the effect of the low compressive stresses of the cycle, producing the flattening of fatigue crack surfaces. Similar conclusions were obtained elsewhere. ]9'2° In Ref. [20] an empirical equation was proposed [Equation (7)] for K,,p determination, appropriate for very low negative stress ratio cases. Although this equation has been established for the 2024-T3 aluminium alloy, the results obtained using the present material, agree very well with our experiments: =
Figure 14 da/dN, dc/dN against AK,, and AK., respectively; CT curves; tension (R =-1)
'0-31 // 162
ma.tE, +
O'max
O'ys /
1,25
\ O'ys /
]
,
,
v 16% 1,00
z
-5[
r-
./o'g/
•
•
OOOO
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• []
•
•
D
0 DD DD
0,75
[
~
CT specimens
:;.sion1
0,50
o
•
Bending]
0,25 lO-a~
o
=
110
,
100
0
10
20
Km,'f×, MPa~m Figure 15 a/dN, dc/dN against AK. and AK,,, respectively; C1" curves; bending (R =-1)
30 AK, MPax/m
Figure 16 U against AK; AI 5083 alloy: (R = - l )
J.D. Costa et a l.
168
= - 0 . 5 (1-0.75) ~/2 [1-(-1)e(0.75)2] 2 = 0.05
(7) 6
and then U-- 0.95.
7
CONCLUSIONS 1. For micro corner cracks < 1 2 0 0 / x m and at a/B < 0.1, the crack aspect ratio a/c is of a quartercircular shape independently of both stress ratio and loading mode. However, for a/B < 0.02 a considerable scatter was observed due to the fact that crack initiation took place in most cases in one direction only (a or c) therefore causing delay in the other direction. However, as the crack grows and a/B increases, crack propagation tends to equalize in both directions and the scatter is reduced close to a/c= 1. Some influence of loading mode on the crack aspect ratio was observed for a/B > 0.1. In tension the cracks tend to stabilize in the quartercircular shape while in bending the trend is towards the quarter-elliptical shape. 2. Good correlation was obtained in both tension and bending between the experimental results of crack aspect ratio a/c vs a/B and the theoretical predictions. 3. For micro cracks with size < 3 0 0 txm, and for the stress ratio values of R = 0.05 and 0.5, fatigue crack propagation is faster than for long cracks when correlated with the nominal stress intensity factor range AK. Also fatigue crack propagation occurs for AK values below the threshold AK~h for long cracks. For R = 0 . 8 fatigue crack rate for short cracks and long cracks is not significantly different and this suggests that the crack closure is virtually absent in short cracks. 4. For the stress ratio value of R = - I crack closure parameter value is U -~ I and this explains the good agreement obtained between the fatigue crack growth rate of short cracks tested at this stress ratio (R = - 1 ) and the results obtained with CT specimens tested with R = 0 . 8 stress ratio. The low value of crack closure level found for R = - I can be explained by the effect of the compressive part of the cycle producing the flattening of the fatigue crack surfaces.
8
9
10 II 12 13 14 15 16 17 18
19
20
strength AI-Mg 5083', Advances in Fracture Research (ICF7). V4 Poc. ConJi, Houston, TX, USA, 1990, pp. 2467-2475 Costa, J.D., Branco, C.M. and Radon, J.C. 'Fatigue Analysis ol a Medium Strength AI-Mg Alloy 5083', (Ed. D. Firrao) ECF8 EMAS, Torino, 1990 pp. 1342-1348 Elber, W. 'Damage tolerance in aircraft structures" ASTM S~I'P 486, American Society for Testing and Materials, Philadelphia, PA, 1971 p. 230 Pickard, A.C. 'Stress intensity factors with circular and ellipuc cracks fronts, determined by 3D finite element methods' Proc. 3rd Int. Cor(j~ Numerical Methods in Fracture Mechanics, Pineridge Press, Swansea, 1984, p. 599 American Society for Testing of Materials. "Standard Test Method for Measurement of Fatigue Crack Growth Rates', Annual Book of ASTM Standards, Vol 03.01, E 647-93, American Society [or Testing of Materials, Philadelphia, PA, 1993 Elber, W. Engng Fract. Mech. 1970, 2, 37-45 Radon, J.C. hit. J. Pres. Ves. Pip. 1993, 275-285 Smith, R.A. and Miller, K.J. hu. J. Mech. Sei. 1977, 19, 11-12 Dowling, N.E. Fatigue Fraet. Engng Mat. Struct. 2, 129-138 Lanklk~rd, J. Fatigue Fract. Engng Mat. Struct. 1982, g, 233-248 Lankford, J. Fatigue Fract. Engng Mat. Struct. 1983, 6, 15-31 Journet. B.G., LeFrancois, A. and Pineau, A. Fatigue Fra~t. Engng Mat. Struct. 1989, 12, 237-246 James, M.N. and Sharpe, W.N. Jr. Fatigue Fract. Engng Mat. Struct. 1989, 12, 347-361 Tokaji, K., Ogawa, T, Osako, S. and Harada~ Y. 'The growth behaviour of small fatigue cracks: the effect of microstructure and crack closure, Proc. Int. Conf. Fatigue 87 3 Int. Conl~ Fatigue Fatigue Thresholds' Charlottesville, VA, (Eds R.O. Ritchie and E.A. Starke), EMAS, Walley, 1987, pp. 313 322 Kemper, H., Weiss, B. and R. Stickler "Effect of compressive portion of loading cycles on the near threshold fatigue closure behaviour', Proc. Int. Conf Fatigue 87 3rd hu. Con[2 Fatigue Fatigue Thresholds, CharlottesvilLe, VA (Eds R.O. Ritchie and E.A. Starke), EMAS, Walley, 1987 Ibrahim, F.K Fatigue Fract. Engng Mat. Struct. 1989. 12, I 8
NOMENCLATURE B dg C
D da/dN dc/dN Y K Kmax
AK
AK. AK, AYe. AK~...
ACKNOWLEDGEMENTS This work was financed by the Structures and Materials Panel of AGARD/NATO under the program Additional Support to Portugal (Project P 6 4 ~ S h o r t crack studies in high strength aluminium alloys).
AK~,r,, Kop
AK,h AKIth
REFERENCES 1 2
3 4
5
Pearson, S. Engng Fract. Mech. 1975, 7, 235-247 Ritchie, R.O. and Yu, W. 'Short crack effects in fatigue, a consequence of crack tip shielding'. 'Small Fatigue Cracks' (eds R.O. Ritchie and J. Lankford), The Metallurgical Society, Warrandale, PA, pp. 167-189 Miller, K.J. Fatigue Fract. Engng Mat. Struct. 1987, 10, 75 113 Miller, K.J. and Yates, J.R. 'Non propagating fatigue cracks: the true fatigue limit', Proc. NATO ASI Advances Fatigue Sei. Techn. (Eds C.M. Branco and L.G. Rosa), Kluwer Academic, Portugal, 1989, pp. 253-265 Costa, J.D. and Branco, C.M. "Fatigue behaviour of medium
K, MK R U F OUTS O-ys O'tys Er
O'nlax
Crack depth Thickness Grain size Crack length in surface direction Notch size (depth) Fatigue crack growth rate at a Fatigue crack growth rate at c Geometry factor Stress intensity factor Maximum stress intensity factor Stress intensity factor range Stress intensity factor range for a Stress intensity factor range for c Effective stress intensity factor range Effective stress intensity factor range for a Effective stress intensity factor range for c Crack opening level effective stress intensity factor range Threshold stress intensity level Threshold stress intensity level for long cracks Stress concentration factor Magnification factor Stress ratio Ratio of AKerr to AK Notch tip radius Ultimate strength Monotonic yield stress Cyclic yield stress Elongation to rupture Maximum stress
ELSEVIER
PII: S0142-1123(96)00047-3
Short fatigue crack growth behaviour in AI 5083 alloy J.D. Costa*, C.M. Brancot and J.C. Radon¢ *DEM, FCTUC, University of Coimbra, 3000 Coimbra, Portugal tCEMUL, Instituto Superior T6cnico, UTL, 1096 Lisboa Codex, Portugal tlmperial College, London SW7, UK (Received 26 February 1996; revised 20 May 1996; accepted 10 June 1996) This work presents the results of a study of fatigue crack growth in AI 5083 alloy starting from a micro comer notch of 40/xm depth in both directions. The fatigue tests were carried out with constant load amplitude in tension and in bending using three ratio values R = - I , 0.05 and 0.5. The crack aspect ratio a/c evolution as a function of the normalized crack depth, a/B, was influenced neither by the stress ratio nor by the type of loading for values of a/B 0.1. Threshold fatigue values obtained for short cracks were found to be lower than for long crack levels, obtained in previous work for R = 0.05 and 0.5. For R = - 1 the short fatigue crack threshold value was approximately the same as the long fatigue crack threshold obtained with compact tension (CT) specimens for R = 0.8. Crack opening values were obtained previously with CT specimens using an Elber type micro gauge and were used to calculate AKef,-values. When comparing the results obtained in this work for short fatigue cracks with the da/dN-AK~fr curves recorded for long cracks, it is concluded that in short cracks the crack opening values may be virtually nil in order to explain their higher crack growth rate. Copyright © 1997 Elsevier Science Ltd. All rights reserved (Keywords: AI 5083 a l u m i n i u m alloy; s h o r t fatigue cracks; crack closure)
INTRODUCTION
data were obtained for the three values of stress ratio. The crack closure parameter U, initially proposed by Elber, 7 was used to obtain AK,.r, the effective values of AK. The crack growth rate, da/dN, when plotted vs AKeff gave good correlation independent of stress ratio. A contribution to the fatigue strength characterization of the same material is presented in this work. The behaviour of short fatigue cracks initiated from a micro comer notch was assessed and the results were compared with long crack data. Short fatigue cracks analysed in this work were classified as mechanically short, i.e. typically 0.5-1 mm in length, but greater than about three times the grain size, d g = 20/xm. Also, the crack closure effect was analysed and considered to be one of the main causes of the different behaviour of short and long fatigue cracks. Three values of stress ratio were applied: R = - 1 , 0.05 and 0.5. Also, the loading mode (tension and bending) influence was assessed. The crack aspect ratio a/c development was compared with the theoretical predictions obtained with a computer program based on the linear elastic fracture mechanics concepts.
The object of considerable interest in fatigue research is the study of the initiation and propagation of short fatigue cracks. Subsequent to the studies by Pearson ~, great advances in knowledge of the behaviour of this tye of crack were acomplished. In general, short fatigue cracks have been found to grow at faster rates and to have lower thresholds than long fatigue cracks at the same stress intensity factory, AK2~. In Ritchie's work,-' comparison of results obtained in specimens with a micro comer crack against long crack data obtained in compact tension (CT) and centre cracked tension (CTT) specimens confirmed this trend. The possible absence of crack closure in short fatigue cracks discussed later seems to be the main explanation for the higher crack growth rates in very short cracks. One of the most important consequences of this behaviour is that the fatigue life prediction using the d a / d N - A K curves obtained at long cracks could lead to excessively optimistic estimates. Thus, the determination of the crack length above which its behaviour is similar to the long crack behaviour is very important. In previous work by the authors 5'6 fatigue strength and ductility parameters of the A1 5083 alloy and the long fatigue crack propagation values were obtained. The influence of the stress ratio (R = 0.05, 0.5 and 0.8) on the crack growth rate was analysed. Crack closure
M A T E R I A L AND E X P E R I M E N T A L DETAILS Chemical composition and the mechanical properties of the 5083 aluminium alloy are shown in Tables I and 2.
161
J.D. Costa et al.
162 Table 1 Mg
Chemical composition of 5083 AI alloy
Mn
Fe
Ni
4.5 0.55 0.37 <0.5
Table 2
Cr 0.12
Zn
Si
Sn
0.1 <0.1
Pb
Ti
AI
<0.05 <0.05 <0.05 Balance
Mechanical properties of 5083 A1 alloy
Ultimate strength, ouxs [MPa] Monotonic yield stress, ~rvs [MPa] Cyclic yield stress, OSvs [MPa] Elongation to rupture, Er [%]
321 180 310 18.2
Fatigue tests of the short cracks initiating from the root of a comer micro notch were conducted in tension and in bending loading modes. The specimens geometry is shown in Figure 1. The specimens were provided with a miro notch approx. 40/zm long in both directions (a and c). This micro notch was obtained by pressing a razor blade against the comer of one of the specimens with a controlled load of 2 N. The micro notch dimensions were checked in all the specimens before the fatigue tests. The specimen shape, with a progressive variation of shoulder width in the form of a circular arch, was adopted with the purpose of limiting the initiation of the crack to the micro notch. The stress concentration due to the width variation was calculated by the finite element method and the results obtained were integrated in the stress intensity factor formulation. The values obtained for Kt were 1.095 for bending and 1.089 for tension. From the results of the finite element method stress calculations, the variation of Kt with the distance c was derived and taken in account in the stress intensity factor calculation as a factor MK. The bending tests were performed in a fatigue testing rig specially built for that purpose. The tension tests were carried out in a load-controlled servohydraulic machine INSTRON model 1341, with 100kN of capacity. In both cases the load wave was of constant
a'l!
:7i
Esu
/
amplitude sinusoidal with a frequency of 25 Hz and temperature 25°C. The short crack measurements were made in a metallographic microscope with 1000× magnification. For that purpose the specimen was taken out from the machine at periodic intervals. With this technique it was possible to detect cracks 10/~m long measured from the notch root. The readings were made in both directions of the comer crack and a photographic record of the crack growth was obtained. One of the photographs obtained during the observations is shown in Figure 2 with a crack 20/xm long tested in bending. The specimens were previously polished by electrolytic process in the notch region to improve the observation. The electrolyte used was composed by 800 ml of ethanol (absolute), 140 ml of distilled water and 60 ml of perchloric acid (60%). The conditions of polishing were: a cell voltage of 60 V and a time of 20 s. The specimen contacted with the electrolyte through a small circular hole of 1 cm 2 existing at the top of the electrolytic cell. From the a and c crack lengths, the crack growth rates da/dN and dc/dN and the stress intensity factor ranges AKa and AK,., were calculated using a computer program developed for this prupose. The geometric factor Y used was obtained from the Pickard polynomial equations. 8 The secant method 9 was chosen to calculate the crack growth rate. Crack closure measurement (opening loads) were attempted using the Elber type micro gauge ~° placed near the crack tip with the measurement points above and below the crack surfaces. The distance between these points was 1.2 mm. For cracks < 1 mm of length it was impossible to detect the crack opening loads due to the insufficient sensitivity of the gauge. The change of compliance between the open and closed crack was too small to be detected by the gauge, as the distance of 1.24 mm between measuring points was too great when compared with the crack length. The crack closure loads were measured only for the stress ratio R = -1 because for the other stress ratios, R = 0.05 and 0.5, these measurements were obtained, previously 5"6 using CT specimens.
12
fl 55
-
80
,
135
Thickness:
12 mm
l
I b) 3s
j
• '~
Figure 1
39
-
=
3o
t
50 faxn
x
~
135
Specimen geometries: (a) bending; (b) tension
Figure 2
Micro corner crack 20/zm long; AI 5083 alloy (200×)
Short fatigue crack growth behaviour in AI 5083 alloy
163
RESULTS AND DISCUSSION
Crack shape evolution Crack shape results are presented in Figure3. The curves refer to the plots of a/c against the normalized crack depth a/B, obtained for micro comer cracks in tension and bending. The short crack data are only for a/B < 0.1, that is, for the crack lengths a and c < 1 2 0 0 / x m . Some scatter may be noted in the a/c results of short cracks. This was due to the fact that crack initiation took place in some cases in only one direction (a or c), causing therefore a slight delay in the other direction. However, as the crack grew and a/B increased, crack propagation tended to equalize in both directions and the scatter was reduced close to a/c = 1 at higher values of a/B. In the range of values presented for a/B no influence of stress ratio and loading mode was noted. The influence of both loading mode and stress ratio can be seen in Figures 4 and 5 for tension and bending, respectively. These data present all the results obtained as plots of a/c against a/B values. In tension, Figure 4, the cracks were approximately of a semi-circular shape for a/B values >0.1. For a/B < 0.1 some scatter was recorded as mentioned earlier. Therefore, the crack growth rate in both directions was approximately the same. No influence was observed of the stress ratio on the crack shape in this loading mode. The crack aspect ratio in bending, was near to 1, for a/B < 0.1. However, for a/B > 0.1 the a/c decreased as a/B increased for all the three stress ratios analysed. Therefore in bending, the comer cracks have a greater growth rate in the c direction (parallel direction to the neutral bending axis) than in the a direction (perpendicular to the neutral axis). This behaviour shows, as expected, that in tension the cracks tend to stabilize in the quarter-circular shape while in bending, due the nonuniform stress through the thickness, the trend is towards the quarter-elliptical shape. Some influence of the stress ratio on the crack shape in bending (Figure 5) can also be observed: for the
•
.
•
-
•
0.75 "7"
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Theoretical Predictions 0.25
,
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-
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,
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,
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Figure 4 ale vs alB: AI 5083 alloy, tension
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i
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I
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,
l
0.02
,
l
0.04
i
{
,
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a/c vs aIB for a l B < 0.1; AI 5083 alloy
*
05
Figure 5 a/c vs a/B; A1 5083 alloy, bending
i
0.08
0.10
a/B Figure 3
I
04
a/B
Bending [ : R=005 R=0.5
0,4
u
R = - 1 stress ratio, all the a/c values were lower than for the other stress ratios. Comparing the results obtained for the stress ratios R =0.05 and 0.5, we observe that each a/c range crosses the other. The a/c range for R = 0.5 is above the a/c range for R = 0.05
J.D. Costa et a l.
164
for lower values of a/B (i.e. a/B < 0.2), while for higher values of a/B, (i.e. a/B > 0.2), we observe the reverse. The crack closure phenomenon may probably provide the explanation for this behaviour. Both directions of propagation (a and c directions) are in the same stress condition, that is, in plane stress, and therefore the stress condition can not be the cause for the different values of crack closure. But, in bending the stress intensity factor ranges AK, and AK,. present different values, as shown in Figure 6. In this figure the values of AK,/AK,. are plotted against a/B for the two loading modes (tension and bending). The stress intensity factor AK,, is higher than the AK,, value. As the crack closure parameter U is a function of both AK and R, the corresponding values of the ratios AK,/AK,. and A g e f f , a / m g e f f , c will be different for different stress ratios and similarly the crack growth rates da/dN and dc/dN. This may be the main factor that explains the influence of the stress ratio on the crack aspect ratio a/c in bending. Similar results on the influence of the stress ratio on short crack shapes in steel BS360-50D were recently reported l~ and support the present conclusions. In tension a so clear influence of the stress ratio was not observed. This is in agreement with AK, and AK,. are similar and so are the stress conditions. Therefore, the crack closure parameter for the two directions, U, and U,., will be closely similar and so are the effective stress intensity factor ranges, AKefc, and AKeff.c, independently of stress ratio. Theoretical prediction of crack aspect evolution are also presented in Figures 4 and 5, using crack propagation data obtained with CT specimens. A computer program was used for these predictions assuming an equal material crack growth strength in both directions. Therefore, no crack closure model was used, that is Ag,. _ Ageff, c_
Comparison of short and long crack growth rates The short cracks are sometimes classified as microstructurally or mechanically short, depending on their size when compared with some relevant microstructural parameters. It was noted previously that this study deals only with microcracks emanated from a micro corner notch 40/xm deep. The minimal crack length detected was about l0/~m, and the grains are equiaxed with a size (determined by microstructural observation) of 20 p~m. The high accuracy in the manufacture of the notches obtained (see geometry in Figure 7) leads to a very small value of the notch plastic zone l, Indeed, applying the Smith and Miller 12 equation we obtain for 1, lo = 0.13 "~Doo= 0.13 ",/50-x-0.5 = 0.65 /xm
In tension the theoretical curve presents a constant value of the crack aspect ratio a/c = 1 independent of
1,4
,
,
,
D
,
U
01~0 0
u
1.0
(2)
where D is the notch depth and p is the notch tip radius. Alternatively, using the equation proposed by Dowling 13 and more appropriate for very severe notches:
D ,o=
40 _
1
_
l
o.
8
(l)
AK,, Ageff,a
:.
both crack size and stress ratio. This behaviour is in agreement with the experimental results obtained. In bending, the experimental results obtained for R=-I and R = 0 . 5 present the same trend as the theroetical predictions. For R = 0.05 such a good agreement was not observed. In both loading modes (tension and bending) the theoretical predictions of the crack aspect ratio a/c tend to the unity as the normalized crack length a/B tend to zero. This is in agreement with the experimental results observed in Figure3, despite the scatter previously explained.
(3) In this equation Y is the geometrical factor calculated using the Pickard 8 solution and Kt is the stress concen-
,
Uu
~ U
•
•
.,is== ~ •
p<0:5 Iztm dr.
0,8
/
io =o i
0,6
u
U
/
/
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D=40 l.tm
0,4
.
0
i
0, I
*
i
0,2
,
¢
0,3
i
i
0,4
0,5
0,6
a/B
r
Figure 6 AK,,/AKc against a/B for corner cracks; tension and bending
1
a
Figure 7
Micro notch geometry
Short fatigue crack growth behaviour in AI 5083 alloy 10-4
tration factor and was calculated by the following equation K, = I + 2 4 D 0 = 1 + 2 ~ / ~
= 10
165
(4)
Equation (3) gives for the dimensions l0 a value that falls better within the range p/20 to p/4 quoted in the literature, ~' lot moderate and sharp notches respectively. Therefore, it can be suggested that the notch of depth D is a part of the total crack length, practically at the initiation. The first crack measurement presents values > 5 0 / x m , which is about 2.5x the grain size. Thus, the short cracks analysed here can be classified as mechanically short and must not be significantly affected by the microstructure. Indeed, the behaviour reported by some investigators, H- 16 in which the crack growth rate decreases significantly as the crack length approximates the grain size or other barriers, was not observed. The Figures 8 and 9 present the crack growth rate data da/dN and dc/dN as a function of a and c, for tension and bending. For micro cracks < 1 0 0 / x m the crack growth rate increases very quickly with the crack length. Between 100 and 300/xm crack growth rate increases more moderately than before. After 300/xm length the crack grows at a rate that increases linearly, but slowly, with the crack length. We will comment on this behaviour later. Figures lO and 11 show respectively the crack growth rate as a function of the stress intensity factor for both stress ratios R =0.05 and 0.5, for tension and bending loading modes. The da/dN-AK results obtained with long cracks (CT specimens) for three stress ratio values, R = 0 . 0 5 , 0.5 and 0.8, are also plotted for comparison. For corner micro cracks sizes < 3 0 0 / x m the crack growth rate is higher than for the long cracks (CT specimens). Also fatigue crack
.-¢
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9
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i
I
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i
I
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and c, respectively; bending
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)
R=O
I0 a,c<300wn a.c>300 p.m
R=0.5 1 : a ' c < 3 0 0 I'tm a,c>300 gm
z
10-8
8
100
A
I
0.2
A
1
Figure 10 da/dN and dc/dN against AK. and AK,. respectively, ("I" curves; tension (R = 0.05 and 0.5)
R=0.5
•
Figure
,
AK, MPa'l--mm "~ R=-I * R=0.05
0
t lO
10-7
I0-8
a
,
I
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,
I
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da/dN and dc/dN vs a and c, respectively; tension
1.0
propagation still takes place at AK values below the threshold level AKth obtained for long cracks (e.g. long cracks have AK,h = 3.5 MPa m s for R = 0.05 and AK, h - 2.1 MPa m ~ for R = 0.5). For cracks :>300/xm
J.D. Costa
166
et
am.
1,2
16 2
],0q 16 3 Io m
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%
•
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_
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,
m
,
,
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•
Figure 12
U against a,c (R = 0.05); A1 5083 alloy
Micro comer cracks
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o
R=0.05
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.
a,¢~'~(YI~m
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Figure 11 da/dN and dc/dN against AK,, and AK,,, respectively. CT
curves; bending (R = 0.05 and 0.5)
there is a good agreement with the results in CT specimens. The long cracks curve for R = 0 . 8 , where crack closure is insignificant, 5'6 fits very well with the experimental data for short cracks, thus confirming the fact that crack closure is virtually absent in micro cracks significantly < 3 0 0 / z m . Note that as crack closure is increasing with crack length, the curves d a / d N - A K for long cracks join the micro comer crack data when the crack length is above 300 ~m. This behaviour was also noted but not clarified by other authors. ~6-]8 For example, James and Sharpe ]7 investigated steel A533B and suggested the same micro crack length (300/zm) as proposed in the present work for the transition crack length. Above this transition crack length they found that the crack closure level was constant and similar to the values typical for long cracks. It cannot be confirmed with certainty that in our A1 5083 alloy the observed behaviour was due to the same cause, because crack closure measurements were not obtained in the very short crack regime. However, the high values of crack closure level recorded for long cracks together with the fact that there are no conditions for a crack closure mechanism in microcracks, supports this hypothesis sufficiently. Our interpretation of the present results may therefore be applied in the study of mechanically short cracks in other materials. Figures 12 and 13 show that crack closure increases as the crack length increases. These plots were obtained assuming that crack closure is the only cause for the different behaviour of short and long cracks. In these figures U was calculated by the equation
•m~B
,,, • o
AK, MPa~/m
• •
R=0.5 different points for different specimens
0,6
0,4 0,0 Figure 13
U=
• • •
a
I
I
I
0,2
0,4
0,6
a
l
0,8 a, c lmm]
I
1 1,0
U against a,c (R = 0.5); AI 5083 alloy
AK ~ -
(5)
where AK ~ and A/~. 8 are the stress intensity factors for short and long cracks, respectively, for the same fatigue crack growth rate. A/~.8 is the value for R = 0.8, where crack closure is insignificant. Despite the considerable scatter of data, as a result of the d a / d N - A K data scatter for short cracks < 3 0 0 / z m , a clear decreasing trend of the U parameter with the increasing crack length can be observed until the crack length reaches approx. 300/zm. Afterwards U is independent of crack length. The results obtained for micro comer cracks at R = - 1 stress ratio are shown in Figures 14 and 15 as the variation of da/dN and dc/dN vs AK, and AK,, respectively. In these figures the long crack curves (solid lines) obtained for R = 0.05 and 0.8 are also presented to allow a comparison. The results in Figure 14 are for tension while Figure 15 shows the results in bending. AK for the stress ratio R = - 1 was calculated using Equation (6) recommended by ASTM E6479 for negative stress ratios, AK = Kmax
(6)
It will be seen that for this stress ratio (R = - 1 ) the crack growth rates for short comer cracks are faster than for long cracks obtained at the R = 0.05 stress
Short fatigue crack growth behaviour in AI 5083 alloy 10 -2
io-3
10-4'
glo-S
R=0.8
,-oS CT specimens
Micro comer craci~,
10-7
1: a,c<30o~ R=- |
lo-"E;,oo
a,c>300p.m
I
1
t
100
10 KmAx, MPa~m
167
ratio. Also, the experimental results for short cracks are very close to the curve obtained for the long cracks at R = 0.8. Another important aspect is that for R = - 1 the short and long cracks form on continuous band. This is contrary to what was found for R = 0.05 and 0.5. This behaviour can be explained, again using the crack closure phenomenon, and assuming that there is no perceptible change of closure level with crack length variation. As already explained in the experimental section above, crack closure was measured at this stress ratio only for crack lengths > 1 0 0 0 / z m . For cracks < 1 0 0 0 b t m long the available Elber gauge was not sensitive enough. Figure 16 shows the variation of crack closure parameter U against AK, for tension and bending. U was calculated using the definition for AK given by Equation (6). The value U ~ I for all AK values tested under both tension and bending loading modes. Therefore, for long cracks, Kop ~ 0 for R - - - 1 . Assuming now that for short cracks the same equation could be applied (i.e. Kop ~ 0), then the effective stress intensity factor AKcff is not influenced by the crack length. Consequently, there is no direct effect on the crack closure level. The agreement between the results obtained for short comer cracks at R = - 1 and the continuous line obtained for long cracks in CT specimens at R = 0.8 is thus explained because in both cases AK AKef f. The values of crack closure found fl)r R = - I (Figure 16) are lower than for R = 0.05 (cf. Figure •2). This is due to the effect of the low compressive stresses of the cycle, producing the flattening of fatigue crack surfaces. Similar conclusions were obtained elsewhere. ]9'2° In Ref. [20] an empirical equation was proposed [Equation (7)] for K,,p determination, appropriate for very low negative stress ratio cases. Although this equation has been established for the 2024-T3 aluminium alloy, the results obtained using the present material, agree very well with our experiments: =
Figure 14 da/dN, dc/dN against AK,, and AK., respectively; CT curves; tension (R =-1)
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./o'g/
•
•
OOOO
o/"7 o~
• []
•
•
D
0 DD DD
0,75
[
~
CT specimens
:;.sion1
0,50
o
•
Bending]
0,25 lO-a~
o
=
110
,
100
0
10
20
Km,'f×, MPa~m Figure 15 a/dN, dc/dN against AK. and AK,,, respectively; C1" curves; bending (R =-1)
30 AK, MPax/m
Figure 16 U against AK; AI 5083 alloy: (R = - l )
J.D. Costa et a l.
168
= - 0 . 5 (1-0.75) ~/2 [1-(-1)e(0.75)2] 2 = 0.05
(7) 6
and then U-- 0.95.
7
CONCLUSIONS 1. For micro corner cracks < 1 2 0 0 / x m and at a/B < 0.1, the crack aspect ratio a/c is of a quartercircular shape independently of both stress ratio and loading mode. However, for a/B < 0.02 a considerable scatter was observed due to the fact that crack initiation took place in most cases in one direction only (a or c) therefore causing delay in the other direction. However, as the crack grows and a/B increases, crack propagation tends to equalize in both directions and the scatter is reduced close to a/c= 1. Some influence of loading mode on the crack aspect ratio was observed for a/B > 0.1. In tension the cracks tend to stabilize in the quartercircular shape while in bending the trend is towards the quarter-elliptical shape. 2. Good correlation was obtained in both tension and bending between the experimental results of crack aspect ratio a/c vs a/B and the theoretical predictions. 3. For micro cracks with size < 3 0 0 txm, and for the stress ratio values of R = 0.05 and 0.5, fatigue crack propagation is faster than for long cracks when correlated with the nominal stress intensity factor range AK. Also fatigue crack propagation occurs for AK values below the threshold AK~h for long cracks. For R = 0 . 8 fatigue crack rate for short cracks and long cracks is not significantly different and this suggests that the crack closure is virtually absent in short cracks. 4. For the stress ratio value of R = - I crack closure parameter value is U -~ I and this explains the good agreement obtained between the fatigue crack growth rate of short cracks tested at this stress ratio (R = - 1 ) and the results obtained with CT specimens tested with R = 0 . 8 stress ratio. The low value of crack closure level found for R = - I can be explained by the effect of the compressive part of the cycle producing the flattening of the fatigue crack surfaces.
8
9
10 II 12 13 14 15 16 17 18
19
20
strength AI-Mg 5083', Advances in Fracture Research (ICF7). V4 Poc. ConJi, Houston, TX, USA, 1990, pp. 2467-2475 Costa, J.D., Branco, C.M. and Radon, J.C. 'Fatigue Analysis ol a Medium Strength AI-Mg Alloy 5083', (Ed. D. Firrao) ECF8 EMAS, Torino, 1990 pp. 1342-1348 Elber, W. 'Damage tolerance in aircraft structures" ASTM S~I'P 486, American Society for Testing and Materials, Philadelphia, PA, 1971 p. 230 Pickard, A.C. 'Stress intensity factors with circular and ellipuc cracks fronts, determined by 3D finite element methods' Proc. 3rd Int. Cor(j~ Numerical Methods in Fracture Mechanics, Pineridge Press, Swansea, 1984, p. 599 American Society for Testing of Materials. "Standard Test Method for Measurement of Fatigue Crack Growth Rates', Annual Book of ASTM Standards, Vol 03.01, E 647-93, American Society [or Testing of Materials, Philadelphia, PA, 1993 Elber, W. Engng Fract. Mech. 1970, 2, 37-45 Radon, J.C. hit. J. Pres. Ves. Pip. 1993, 275-285 Smith, R.A. and Miller, K.J. hu. J. Mech. Sei. 1977, 19, 11-12 Dowling, N.E. Fatigue Fraet. Engng Mat. Struct. 2, 129-138 Lanklk~rd, J. Fatigue Fract. Engng Mat. Struct. 1982, g, 233-248 Lankford, J. Fatigue Fract. Engng Mat. Struct. 1983, 6, 15-31 Journet. B.G., LeFrancois, A. and Pineau, A. Fatigue Fra~t. Engng Mat. Struct. 1989, 12, 237-246 James, M.N. and Sharpe, W.N. Jr. Fatigue Fract. Engng Mat. Struct. 1989, 12, 347-361 Tokaji, K., Ogawa, T, Osako, S. and Harada~ Y. 'The growth behaviour of small fatigue cracks: the effect of microstructure and crack closure, Proc. Int. Conf. Fatigue 87 3 Int. Conl~ Fatigue Fatigue Thresholds' Charlottesville, VA, (Eds R.O. Ritchie and E.A. Starke), EMAS, Walley, 1987, pp. 313 322 Kemper, H., Weiss, B. and R. Stickler "Effect of compressive portion of loading cycles on the near threshold fatigue closure behaviour', Proc. Int. Conf Fatigue 87 3rd hu. Con[2 Fatigue Fatigue Thresholds, CharlottesvilLe, VA (Eds R.O. Ritchie and E.A. Starke), EMAS, Walley, 1987 Ibrahim, F.K Fatigue Fract. Engng Mat. Struct. 1989. 12, I 8
NOMENCLATURE B dg C
D da/dN dc/dN Y K Kmax
AK
AK. AK, AYe. AK~...
ACKNOWLEDGEMENTS This work was financed by the Structures and Materials Panel of AGARD/NATO under the program Additional Support to Portugal (Project P 6 4 ~ S h o r t crack studies in high strength aluminium alloys).
AK~,r,, Kop
AK,h AKIth
REFERENCES 1 2
3 4
5
Pearson, S. Engng Fract. Mech. 1975, 7, 235-247 Ritchie, R.O. and Yu, W. 'Short crack effects in fatigue, a consequence of crack tip shielding'. 'Small Fatigue Cracks' (eds R.O. Ritchie and J. Lankford), The Metallurgical Society, Warrandale, PA, pp. 167-189 Miller, K.J. Fatigue Fract. Engng Mat. Struct. 1987, 10, 75 113 Miller, K.J. and Yates, J.R. 'Non propagating fatigue cracks: the true fatigue limit', Proc. NATO ASI Advances Fatigue Sei. Techn. (Eds C.M. Branco and L.G. Rosa), Kluwer Academic, Portugal, 1989, pp. 253-265 Costa, J.D. and Branco, C.M. "Fatigue behaviour of medium
K, MK R U F OUTS O-ys O'tys Er
O'nlax
Crack depth Thickness Grain size Crack length in surface direction Notch size (depth) Fatigue crack growth rate at a Fatigue crack growth rate at c Geometry factor Stress intensity factor Maximum stress intensity factor Stress intensity factor range Stress intensity factor range for a Stress intensity factor range for c Effective stress intensity factor range Effective stress intensity factor range for a Effective stress intensity factor range for c Crack opening level effective stress intensity factor range Threshold stress intensity level Threshold stress intensity level for long cracks Stress concentration factor Magnification factor Stress ratio Ratio of AKerr to AK Notch tip radius Ultimate strength Monotonic yield stress Cyclic yield stress Elongation to rupture Maximum stress