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Environmental dependence of fatigue crack growth retardation following a single overload in 2024-Al alloy
Enpeering Fracrure Mechanics Vol. 26, No. 6, pp. 921-935, Printed m Great Britain.
1987
co13-7944/87 53.00 + 0.00 IQ 1987 Pergamon Journals Ltd.
ENVIRONMENTAL DEPENDENCE OF FATIGUE CRACK GROWTH RETARDATION FOLLOWING A SINGLE OVERLOAD IN 2024-AL ALLOY J. ZUIDEMAt,
P. J. M. MENSES and R. A. H. EDWARDS?
Abstract-Comparative tests in air and seawater were conducted to investigate the effect of environment on retardation by peak overloads in 2024-A] alloys. The seawater could either increase or decrease the amount of retardation, depending on the R-ratio used. This effect is ascribed to the competitive influence of straightforward environmental growth acceleration and retardation due to corrosion product wedging. Shear-lips give rise to asymmetrical plastic zones and deviation in the crack path. Cracks in single shear show more retardation than cracks in double shear.
INTRODUCTION controversy in the literature whether for aluminium alloys the environment affects the amount of fatigue crack closure. Such a dependence is reported in refs [14], but others have said it is negligible [S-8]. A problem is that the influence of the environment on the crack growth rate can be direct as well as via AK,@ Generally, a normal constant stress amplitude (constant AS) test or a constant stress intensity (constant AK) test fails to discriminate between these possibilities. The main aim of this work was to investigate this dichotomy in the literature. Since enhanced crack closure occurs after an overload it is pertinent to see whether the environment affects the amount of fatigue crack growth retardation which follows the application of an overload. For tests at constant AS Elber[9] proposed a correction factor U = AKJAK which accounted for the effect of crack closure on the AK experienced by the crack tip. He showed that U is a function of R = KmiJKm,, only. Later on Schijve[lO] produced a formula which was valid over a greater range of R-values. In a previous paper [ 1l] it was shown that Schijve’s formula was also satisfactory for a seawater environment, except for a small deviation at R = - 1, ascribed to corrosion product wedging. After an overload the compressive stresses in the overload plastic zone give rise to a lower effective R-value, and this is principally responsible for the retardation [12, 133. One might expect, therefore, that the effective R-value is brought into the domain where corrosion product wedging becomes important. However, most of the corrosion product wedging at R = - 1 was thought to occur several millimetres away from the crack tip [ 111, where there was a very much thicker layer of corrosion product. Since the effective R-value from the overload will only affect crack closure close to the tip, it is difficult to predict whether enhanced closure in seawater would show up in overload tests. The amount of crack growth retardation caused by an overload is usually characterized by the number of lost cycles, nd. To find this one starts with the measured number of cycles needed to grow through the overload-effect-zone and subtracts the number of cycles which would be needed if the overload were not applied. To get an accurate value we decided to grow the cracks at constant AK because then the crack growth rate in the absence of an overload is constant. Furthermore, it is possible to conduct more than one identical overload test on a single specimen, provided that they are separated far enough to avoid interactions. THERE IS
EXPERIMENTAL
PROCEDURE
Centre-cracked plate specimens, 100 mm wide and 6 mm thick, were cut from an aluminium 2024-T351 plate. The chemical composition and mechanical properties of the alloy are shown in the table. The other specimen dimensions are shown in Fig. 1. The plane of the crack is perpendicular to the rolling direction. The specimens were fatigued in either air or seawater (according to ASTM D1141-75) using a computer-controlled 350 kN servohydraulic MTS fatigue machine. Crack length was measured using a d.c. potential drop technique, converting the potential drops to crack lengths using the ‘r Delft University of Technology, Department
of Metallurgy, Rotterdamseweg $At present: Hoogovens Groep B.V., IJnuiden, The Netherlands. 927
137, 2628 AL Delft, The Netherlands.
928
J. ZUIDEMA et al.
I i 8
0
J
0 66,
290
Fig. 1. Dimensions of the centre-cracked specimen (in mm).
theoretical formula and empirical corrections proposed in ref. [14]. Since the optically measured crack length could deviate from the theoretical one by up to 0.3 mm, a facility was built into the program to correct the crack length during the test. At the end of the tests an improved empirical correction formula was produced. Crack growth rate could in principle be measured to an accuracy of about 1O-6 mm/s (or 0.0001 w/cycle at 10 Hz). All tests were carried out at 10 Hz unless specified differently. The formula we used for K is:
where S = the nominal applied stress. Most of the experiments were done using constant AK and R. The accuracy desired gives limitations to the crack length range that can be used. Taking derivatives of eq. (1) we get: 2dK -=K
da a
If the inaccuracy in the crack length is equal to 0.3 mm we find from this equation a crack length dK region of 5 to 35 mm in which the relative accuracy K < 3%. All tests have been performed between these boundaries. For the experiments in seawater a Perspex cell was used which was supplied with aerated seawater by recirculating from an 80 litre tank, which was maintained at 21 f 0.5”C. Experiments in laboratory air were carried out at about 20°C. RESULTS AND DISCU~ION 1. Reference tests at constant AK Constant AK tests provide more accurate and reproducible crack growth rate data than constant amplitude tests. This is partly because the crack growth rate can be averaged over a longer crack length, and partly because the width of shear-lips for a given AK in a constant amplitude test depends on the R-ratio and other test conditions, as explained in ref. [12]. Figure 2 shows the crack growth rates measured at R = 0.1 and R = 0.4 for various AK in seawater and in air. The R-values lie in the range of validity of Elber’s equation for U(R) [9], and this was used to correlate all the points to a single da/dn vs A& relation for each environment. Table 1. Material used: 2024-T351 Alclad sheet (Alcoa) Chemical composition
cu Mg Mn Fe Si Zn Cr
4.40 wt% 1.36 0.67 0.26 0.08 0.01 0.01
Mechanical properties (Iongitudinal direction) oL = 395 MPa O;lr = 500 MPa 5UIl = 17 % E = 71.875 MPa
929
Environmental dependence of fatigue crack growth retardation
1.5-
-1 -
1.5-
-2-
SLl~~ I
1
I
I
I
I
L
.5
.6
.7
.6
.9
log A Keff.
-
Fig. 2. Log da/dn versus log AK,, in seawater and air, da/dn in m/cycle, AKeRin MPdm. from constant AK test, * point from slowly decreasing AK test.
0 point
The correlation was good for both environments, which is in agreement with previous amplitude work in this range of R-values [l 11. However, this does not necessarily prove is correct as previously pointed out [ 111. The correlation only proves that Elber’s equation predicts the change in A& with R. Figure 2 shows that seawater increases the crack growth rate by at least 25% at this and AK& range, and also substantially decreases the threshold A&s.
constantthat A& correctly frequency
2. Overload tests Figure 3 shows a typical result for the effect of an overload on the subsequent crack growth rate. If, as stated above, the retardation is principally a result of the compressive stresses in the overload plastic zone, one would expect that the affected crack length ad (see Fig. 3) would correlate with the plastic zone size of the overload cycle. The plastic zone has a complicated shape, but its size should be of the same order of magnitude and proportional to that calculated. For the extent of this zone we take the plane stress formula (using the Irwin approximation):
-------
G;n’
t I
I + I
ad
I -i I
Fig. 3. Qualitative figure of retardation after an overload.
930
J. ZUIDEMA et al.
Nd = 40125
cycles
/ Nd
= 78000
cycles
Ad=lZmm
-___seawater Nd = 55890 Ad=lbmm
cycles
seowoter
seawater-------I
Nd = 65810
Nd i 6375
cycles
/ Ad=?OSmm
cycles
Ad=O71mm
I
Fig. 4, Loading sequence of monotonic loads and overloads, effect on a, 2 m,nand Q. All results are i f1 the mean values of six identical overload tests.
For &zik = 22.2 MPaJm (Fig. 4) this formula gives 1.0 mm. This formula gives an upper bound for the extent of the plastic zone. The effect of the reversed plastic zone, which is given by: 3
P
g$.E2
=’ fr
i
2’Tys
1
is neglected because it has only a small effect on the extent of the peak load zone. It has of course an effect in reducing the compressive stresses and in reducing the number of lost cycles nd, but scarcely on the affected crack length a,+ Figure 4 shows the results of comparative measurements of retardation due to single peak overloads in air and in seawater. Two different KWakvalues are used, and two different R-values. The value for the number of lost cycles and the affected crack length are each the average for six overloads. The overloads were applied at crack lengths of 15 and 27 mm. The spread in the data of ad and nd was within 10% (except one measurement). Test C shows a smaller affected crack length although the size of the plastic zone from the overload is the same in each case. This is because the Km,, of test C is higher, which means that the active plastic zone is larger and reaches the end of the overload plastic zone some distance before the crack itself has grown beyond the overload zone. The fresh deformation removes any compressive stress left in the overload plastic zone. Comparing tests A and B we see that the value of Knin has very little influence on the affected crack length in air. One expects that a higher AK applied to a crack after an overload would reduce the number of lost cycles. This is indeed the case (compare A and B). Increasing the R-ratio at constant AK has a similar effect (compare A and C). Here the applied tensile component of the load tends to counteract the retarding effect of the compression in the plastic zone of the overload cycle. There are two effects we may expect from changing the environment from air to seawater. Firstly, seawater increases the crack growth rate for a given A&, and decreases the threshold AKcR,as shown by the reference tests. This leads to a reduction of the number of lost cycles after
Environmental
Fig. 5. Photograph
Fig. 6. Asymmetric
of reinitiation
plastic
dependence
of fatigue
crack
growth
931
retardation
of crack growth after a peak load (AK = 15 MPa,/m, overload ratio = 2).
zone at the tip of a crack in shear length = 18.5 mm, magnification 24 x
mode.
Load
R = 0.1 and
= 85 kN.
crack
932
J. ZUIDEMA et al.
Fig. 7. Symmetric plastic zone at the tip of a crack in tensile mode. Load = 85 kN, crack length = 18.5mm, magnification 24 x
c
*
Fig. 9. Photograph of a direction change of a crack in shear mode.
Environmental
dependence
of fatigue
crack
growth
933
retardation
an overload. Secondly, the thicker oxide layer leads to corrosion product wedging and this tends to increase the number of lost cycles. The results show that seawater can either increase or reduce the number of lost cycles. Therefore, the two effects are of similar magnitude. When tests are conducted at low R-values (test A) there is a larger effect of crack closure, and the corrosion product wedging effect dominates, leading to an increase in the number of lost cycles. Where the R-ratio is greater (B) and/or where the overload ratio (Kpeak/Kmax) is lower (C), there is less crack closure and here the first effect of the seawater dominates, so that the crack grows faster through the overload region because of the straightforward
increase of 2
caused by the environment.
If
we look at test B we see that the number of lost cycles to failure is reduced by about 18%. According to the reference graph, the seawater increases the crack growth rate for a given A&s by at least 25% (and much more at lower AKes values). This shows that seawater must reduce the AKerrin the overload region, compared to air, even though few cycles are actually lost. The interaction of these two effects explains why, in some overload tests, no environmental effect is seen. Near the crack tip there was little visible corrosion product. However, Auger depth profile measurements showed that the thickness of the oxide layer was on average 15 times thicker in seawater than in air. The oxide has more time to thicken when the crack is retarded by the overload. This could explain why corrosion product wedging has a greater effect on the crack growth rate after an overload than was found even for R = - 1 in constant amplitude tests [ 111. The fact that there is a noticeable increase in the size of the crack closure wedge is shown by the increase in the affected crack length for test A in seawater. This increase in affected length cannot be seen in the other two tests because the R-value is too high to give crack closure at any distance from the crack tip. 3. TROUBLE
WITH SHEAR-LIPS
Tests were also carried out using a higher AK, 15 MPaJm, R = 0.1, and the same overload ratio, Kpeak.Kmax= 2. In this case there was more variation in the number of lost cycles, with the result that one of the cracks in the centre-cracked specimen almost always emerged from the overload zone before the other. The asymmetrical growth interfered with the crack length measurement and invalidated the constant AK control. This problem was especially acute when one crack happened to be in single shear and the opposite one in double shear. The crack which emerged first from the overload region was always the one in double shear.
Fig. 8. Sketch
of asymmetric
plastic
zone in single shear and double
shear.
934
J. ZUIDEMA et al.
Fig. 10. A possible explanation of the changes in direction of crack growth by growing asymmetry in the plastic zones.
Figure 5 shows a photomicrograph (magnification 25 x) of the side of the polished specimen under these loading conditions showing how the crack grows out of the overload region. Crack growth is from right to left. It is evident that the crack does not grow on from the point where it stopped, but appears to reinitiate along another path. Since the cracks are not continuous with each other, it is obvious that the crack has emerged to the surface after having started growing deeper in the specimen. It is also clear in Fig. 5 that the plastic zone of the overload is not symmetrical. We suspected that this asymmetry might be due to the presence of shear-lips. To investigate this we did two tests. In the first specimen we made by spark erosion two 18.5 mm long notches. Next a small fatigue crack was grown with a low amplitude. The crack now was in the tensile mode, i.e. the plane of the crack was normal to the plate surface. In the second specimen we made notches at 45” with the surface. The fatigue crack was grown here with higher loads so that the crack remained slant. After polishing the specimens were treated with a photographic lacquer. Both specimens were loaded to 85 kN. After loading they have been immersed in warm water (70°C) for about 2.5 minutes. This procedure causes small cracks in the lacquer on places where the material has been strongly plastically deformed. With a microscope (magnification 30 x ) we made the photographs shown as Figs 6 and 7. Figure 8 shows a schematic diagram of the pattern of the plastic zones in the specimen for single and double shear. It is known that aggressive environments suppress shear-lip formation. This should be taken into account when investigating whether environment affects plastic zone size. When the crack was growing on double shear, the crack tended to deviate from the centre line of the specimen. When the deviation reached a certain angle, though, the crack suddenly changed direction and started curving in the opposite direction. Such a change of direction is photographed in Fig. 9. In double shear the crack grows along a curved path such that the centre of the crack (which passes through tensile mode) grows faster than the sides. This is consistent with the observation that cracks grow faster in tensile mode than shear mode for the same AK [12]. When the deviation reaches so far that the crack is trying to grow into its own plastic zone, at the surface, the crack is forced to change direction (Fig. 10). We observed also periodic variations in crack growth rate, although a constant AK,, was applied. The minima in crack growth rate appeared to coincide with the sudden changes in direction (although it is difficult to be sure using the potential drop method for crack length measurement, because the up-and-down cycles were rarely in phase on both sides of the specimen). We attempted to change to CT-type specimens, to avoid problems associated with asymmetrical crack growth. However, the effects of the curved crack path in double shear were disastrous: the crack did not cease to deviate from the mid-plane of the specimen, but continued growing in a perfect arc, aiming at one side of the specimen. CONCLUSIONS
(1) Seawater increases the crack growth rate of 2024-Al alloy at 10 Hz by a factor of at least 25% for a given A&s compared with air.
(2) This is the cause of one effect of seawater crack growth retardation
after a single peak overload. This mechanism dominates at high R-ratios and reduces the number of lost cycles. (3) At low R-ratios the corrosion product wedging effect dominates; the number of lost cycles following a single peak overload is increased because of the extra crack closure. (4) Reports that environment does not affect retardation after overloads are the result of these two effects cancelling out under certain conditions. (5) The suppression of shear-lip formation by aggressive environments can lead to erroneous plastic zone size measurements, since shear-lips give rise to asymmetrical plastic zones.
Environmental
dependence
of fatigue
crack
growth
retardation
935
(6) Cracks growing in double shear zig-zag either side of the mid-plane of the specimen. This probably results in variations in crack growth rates even in constant AK tests. (7) Cracks in double shear show less retardation after an overload than cracks in single shear. Acknowledgement-The
authors
are grateful
to Mrs Anneke
van Veen for her help in preparing
the manuscript.
REFERENCES [l] [2] [3] [4] [S] [6] [7] [8] [9] [lo] [I l]
[I23 [I31 [14]
N. Ranganathan, J. Petit and B. Bouchet, Engng Fracture Mech. 11, 7755789 (1979). M. C. Lafarie-Frenot, J. Petit and C. Gasc, Farigue ofEngng Mater. Structures 1, 431438 (1979). 0. Buck, J. D. Frandsen and H. L. Marcus, Engng Fracrure Mech. 7, 1677171 (1975). A. Clerivet and C. Bathias, Engng Fracture Mech. 12, 559961 I (1979). H. L. Ewalds, Engng Fructure Mech. 13, 100~1007 (1980). J. Schijve and W. J. Arkema. Report VTH-217, Department of Aerospace Engineering, T. H. Delft (April 1976). H. L. Ewalds, F. C. van Doorn and W. G. Sloof. ASTM STP 801, 115-134 (1983). R. P. Wei, N. R. Fenelli, K. D. Unangst and T. T. Shih. J. Engng Marer. Technol. 102, 28C292 (1980). W. Elber, ASTM STP 486, 23&242 (1971). J. Schijve, Memorandum M-336, Department of Aerospace Engineering, T. H. Delft (August 1979). H. L. Ewarlds and R. A. H. Edwards, Effect of crack surface corrosion layers on fatigue crack growth, Paper presented at EFC-meeting on Low frequency cyclic loading effects in environment sensitive fracture, Milan, Italy (March 911, 1982). R. A. H. Edwards, E. M. De Jong and J. Zuidema, Proc. Fatigue ‘84 (Edited by C. J. Beevers), p. 463, University of Birmingham (Sept. 1984). C. Robin, M. Louah and G. Pluvinage, Fatigue of Engng Ma/er. Srrucrure 6, 1 13 (1983). H. H. Johnson, Muter. Res. Smds, pp. 442445 (Sept. 1965). (Received
22 August
1986)
1987
co13-7944/87 53.00 + 0.00 IQ 1987 Pergamon Journals Ltd.
ENVIRONMENTAL DEPENDENCE OF FATIGUE CRACK GROWTH RETARDATION FOLLOWING A SINGLE OVERLOAD IN 2024-AL ALLOY J. ZUIDEMAt,
P. J. M. MENSES and R. A. H. EDWARDS?
Abstract-Comparative tests in air and seawater were conducted to investigate the effect of environment on retardation by peak overloads in 2024-A] alloys. The seawater could either increase or decrease the amount of retardation, depending on the R-ratio used. This effect is ascribed to the competitive influence of straightforward environmental growth acceleration and retardation due to corrosion product wedging. Shear-lips give rise to asymmetrical plastic zones and deviation in the crack path. Cracks in single shear show more retardation than cracks in double shear.
INTRODUCTION controversy in the literature whether for aluminium alloys the environment affects the amount of fatigue crack closure. Such a dependence is reported in refs [14], but others have said it is negligible [S-8]. A problem is that the influence of the environment on the crack growth rate can be direct as well as via AK,@ Generally, a normal constant stress amplitude (constant AS) test or a constant stress intensity (constant AK) test fails to discriminate between these possibilities. The main aim of this work was to investigate this dichotomy in the literature. Since enhanced crack closure occurs after an overload it is pertinent to see whether the environment affects the amount of fatigue crack growth retardation which follows the application of an overload. For tests at constant AS Elber[9] proposed a correction factor U = AKJAK which accounted for the effect of crack closure on the AK experienced by the crack tip. He showed that U is a function of R = KmiJKm,, only. Later on Schijve[lO] produced a formula which was valid over a greater range of R-values. In a previous paper [ 1l] it was shown that Schijve’s formula was also satisfactory for a seawater environment, except for a small deviation at R = - 1, ascribed to corrosion product wedging. After an overload the compressive stresses in the overload plastic zone give rise to a lower effective R-value, and this is principally responsible for the retardation [12, 133. One might expect, therefore, that the effective R-value is brought into the domain where corrosion product wedging becomes important. However, most of the corrosion product wedging at R = - 1 was thought to occur several millimetres away from the crack tip [ 111, where there was a very much thicker layer of corrosion product. Since the effective R-value from the overload will only affect crack closure close to the tip, it is difficult to predict whether enhanced closure in seawater would show up in overload tests. The amount of crack growth retardation caused by an overload is usually characterized by the number of lost cycles, nd. To find this one starts with the measured number of cycles needed to grow through the overload-effect-zone and subtracts the number of cycles which would be needed if the overload were not applied. To get an accurate value we decided to grow the cracks at constant AK because then the crack growth rate in the absence of an overload is constant. Furthermore, it is possible to conduct more than one identical overload test on a single specimen, provided that they are separated far enough to avoid interactions. THERE IS
EXPERIMENTAL
PROCEDURE
Centre-cracked plate specimens, 100 mm wide and 6 mm thick, were cut from an aluminium 2024-T351 plate. The chemical composition and mechanical properties of the alloy are shown in the table. The other specimen dimensions are shown in Fig. 1. The plane of the crack is perpendicular to the rolling direction. The specimens were fatigued in either air or seawater (according to ASTM D1141-75) using a computer-controlled 350 kN servohydraulic MTS fatigue machine. Crack length was measured using a d.c. potential drop technique, converting the potential drops to crack lengths using the ‘r Delft University of Technology, Department
of Metallurgy, Rotterdamseweg $At present: Hoogovens Groep B.V., IJnuiden, The Netherlands. 927
137, 2628 AL Delft, The Netherlands.
928
J. ZUIDEMA et al.
I i 8
0
J
0 66,
290
Fig. 1. Dimensions of the centre-cracked specimen (in mm).
theoretical formula and empirical corrections proposed in ref. [14]. Since the optically measured crack length could deviate from the theoretical one by up to 0.3 mm, a facility was built into the program to correct the crack length during the test. At the end of the tests an improved empirical correction formula was produced. Crack growth rate could in principle be measured to an accuracy of about 1O-6 mm/s (or 0.0001 w/cycle at 10 Hz). All tests were carried out at 10 Hz unless specified differently. The formula we used for K is:
where S = the nominal applied stress. Most of the experiments were done using constant AK and R. The accuracy desired gives limitations to the crack length range that can be used. Taking derivatives of eq. (1) we get: 2dK -=K
da a
If the inaccuracy in the crack length is equal to 0.3 mm we find from this equation a crack length dK region of 5 to 35 mm in which the relative accuracy K < 3%. All tests have been performed between these boundaries. For the experiments in seawater a Perspex cell was used which was supplied with aerated seawater by recirculating from an 80 litre tank, which was maintained at 21 f 0.5”C. Experiments in laboratory air were carried out at about 20°C. RESULTS AND DISCU~ION 1. Reference tests at constant AK Constant AK tests provide more accurate and reproducible crack growth rate data than constant amplitude tests. This is partly because the crack growth rate can be averaged over a longer crack length, and partly because the width of shear-lips for a given AK in a constant amplitude test depends on the R-ratio and other test conditions, as explained in ref. [12]. Figure 2 shows the crack growth rates measured at R = 0.1 and R = 0.4 for various AK in seawater and in air. The R-values lie in the range of validity of Elber’s equation for U(R) [9], and this was used to correlate all the points to a single da/dn vs A& relation for each environment. Table 1. Material used: 2024-T351 Alclad sheet (Alcoa) Chemical composition
cu Mg Mn Fe Si Zn Cr
4.40 wt% 1.36 0.67 0.26 0.08 0.01 0.01
Mechanical properties (Iongitudinal direction) oL = 395 MPa O;lr = 500 MPa 5UIl = 17 % E = 71.875 MPa
929
Environmental dependence of fatigue crack growth retardation
1.5-
-1 -
1.5-
-2-
SLl~~ I
1
I
I
I
I
L
.5
.6
.7
.6
.9
log A Keff.
-
Fig. 2. Log da/dn versus log AK,, in seawater and air, da/dn in m/cycle, AKeRin MPdm. from constant AK test, * point from slowly decreasing AK test.
0 point
The correlation was good for both environments, which is in agreement with previous amplitude work in this range of R-values [l 11. However, this does not necessarily prove is correct as previously pointed out [ 111. The correlation only proves that Elber’s equation predicts the change in A& with R. Figure 2 shows that seawater increases the crack growth rate by at least 25% at this and AK& range, and also substantially decreases the threshold A&s.
constantthat A& correctly frequency
2. Overload tests Figure 3 shows a typical result for the effect of an overload on the subsequent crack growth rate. If, as stated above, the retardation is principally a result of the compressive stresses in the overload plastic zone, one would expect that the affected crack length ad (see Fig. 3) would correlate with the plastic zone size of the overload cycle. The plastic zone has a complicated shape, but its size should be of the same order of magnitude and proportional to that calculated. For the extent of this zone we take the plane stress formula (using the Irwin approximation):
-------
G;n’
t I
I + I
ad
I -i I
Fig. 3. Qualitative figure of retardation after an overload.
930
J. ZUIDEMA et al.
Nd = 40125
cycles
/ Nd
= 78000
cycles
Ad=lZmm
-___seawater Nd = 55890 Ad=lbmm
cycles
seowoter
seawater-------I
Nd = 65810
Nd i 6375
cycles
/ Ad=?OSmm
cycles
Ad=O71mm
I
Fig. 4, Loading sequence of monotonic loads and overloads, effect on a, 2 m,nand Q. All results are i f1 the mean values of six identical overload tests.
For &zik = 22.2 MPaJm (Fig. 4) this formula gives 1.0 mm. This formula gives an upper bound for the extent of the plastic zone. The effect of the reversed plastic zone, which is given by: 3
P
g$.E2
=’ fr
i
2’Tys
1
is neglected because it has only a small effect on the extent of the peak load zone. It has of course an effect in reducing the compressive stresses and in reducing the number of lost cycles nd, but scarcely on the affected crack length a,+ Figure 4 shows the results of comparative measurements of retardation due to single peak overloads in air and in seawater. Two different KWakvalues are used, and two different R-values. The value for the number of lost cycles and the affected crack length are each the average for six overloads. The overloads were applied at crack lengths of 15 and 27 mm. The spread in the data of ad and nd was within 10% (except one measurement). Test C shows a smaller affected crack length although the size of the plastic zone from the overload is the same in each case. This is because the Km,, of test C is higher, which means that the active plastic zone is larger and reaches the end of the overload plastic zone some distance before the crack itself has grown beyond the overload zone. The fresh deformation removes any compressive stress left in the overload plastic zone. Comparing tests A and B we see that the value of Knin has very little influence on the affected crack length in air. One expects that a higher AK applied to a crack after an overload would reduce the number of lost cycles. This is indeed the case (compare A and B). Increasing the R-ratio at constant AK has a similar effect (compare A and C). Here the applied tensile component of the load tends to counteract the retarding effect of the compression in the plastic zone of the overload cycle. There are two effects we may expect from changing the environment from air to seawater. Firstly, seawater increases the crack growth rate for a given A&, and decreases the threshold AKcR,as shown by the reference tests. This leads to a reduction of the number of lost cycles after
Environmental
Fig. 5. Photograph
Fig. 6. Asymmetric
of reinitiation
plastic
dependence
of fatigue
crack
growth
931
retardation
of crack growth after a peak load (AK = 15 MPa,/m, overload ratio = 2).
zone at the tip of a crack in shear length = 18.5 mm, magnification 24 x
mode.
Load
R = 0.1 and
= 85 kN.
crack
932
J. ZUIDEMA et al.
Fig. 7. Symmetric plastic zone at the tip of a crack in tensile mode. Load = 85 kN, crack length = 18.5mm, magnification 24 x
c
*
Fig. 9. Photograph of a direction change of a crack in shear mode.
Environmental
dependence
of fatigue
crack
growth
933
retardation
an overload. Secondly, the thicker oxide layer leads to corrosion product wedging and this tends to increase the number of lost cycles. The results show that seawater can either increase or reduce the number of lost cycles. Therefore, the two effects are of similar magnitude. When tests are conducted at low R-values (test A) there is a larger effect of crack closure, and the corrosion product wedging effect dominates, leading to an increase in the number of lost cycles. Where the R-ratio is greater (B) and/or where the overload ratio (Kpeak/Kmax) is lower (C), there is less crack closure and here the first effect of the seawater dominates, so that the crack grows faster through the overload region because of the straightforward
increase of 2
caused by the environment.
If
we look at test B we see that the number of lost cycles to failure is reduced by about 18%. According to the reference graph, the seawater increases the crack growth rate for a given A&s by at least 25% (and much more at lower AKes values). This shows that seawater must reduce the AKerrin the overload region, compared to air, even though few cycles are actually lost. The interaction of these two effects explains why, in some overload tests, no environmental effect is seen. Near the crack tip there was little visible corrosion product. However, Auger depth profile measurements showed that the thickness of the oxide layer was on average 15 times thicker in seawater than in air. The oxide has more time to thicken when the crack is retarded by the overload. This could explain why corrosion product wedging has a greater effect on the crack growth rate after an overload than was found even for R = - 1 in constant amplitude tests [ 111. The fact that there is a noticeable increase in the size of the crack closure wedge is shown by the increase in the affected crack length for test A in seawater. This increase in affected length cannot be seen in the other two tests because the R-value is too high to give crack closure at any distance from the crack tip. 3. TROUBLE
WITH SHEAR-LIPS
Tests were also carried out using a higher AK, 15 MPaJm, R = 0.1, and the same overload ratio, Kpeak.Kmax= 2. In this case there was more variation in the number of lost cycles, with the result that one of the cracks in the centre-cracked specimen almost always emerged from the overload zone before the other. The asymmetrical growth interfered with the crack length measurement and invalidated the constant AK control. This problem was especially acute when one crack happened to be in single shear and the opposite one in double shear. The crack which emerged first from the overload region was always the one in double shear.
Fig. 8. Sketch
of asymmetric
plastic
zone in single shear and double
shear.
934
J. ZUIDEMA et al.
Fig. 10. A possible explanation of the changes in direction of crack growth by growing asymmetry in the plastic zones.
Figure 5 shows a photomicrograph (magnification 25 x) of the side of the polished specimen under these loading conditions showing how the crack grows out of the overload region. Crack growth is from right to left. It is evident that the crack does not grow on from the point where it stopped, but appears to reinitiate along another path. Since the cracks are not continuous with each other, it is obvious that the crack has emerged to the surface after having started growing deeper in the specimen. It is also clear in Fig. 5 that the plastic zone of the overload is not symmetrical. We suspected that this asymmetry might be due to the presence of shear-lips. To investigate this we did two tests. In the first specimen we made by spark erosion two 18.5 mm long notches. Next a small fatigue crack was grown with a low amplitude. The crack now was in the tensile mode, i.e. the plane of the crack was normal to the plate surface. In the second specimen we made notches at 45” with the surface. The fatigue crack was grown here with higher loads so that the crack remained slant. After polishing the specimens were treated with a photographic lacquer. Both specimens were loaded to 85 kN. After loading they have been immersed in warm water (70°C) for about 2.5 minutes. This procedure causes small cracks in the lacquer on places where the material has been strongly plastically deformed. With a microscope (magnification 30 x ) we made the photographs shown as Figs 6 and 7. Figure 8 shows a schematic diagram of the pattern of the plastic zones in the specimen for single and double shear. It is known that aggressive environments suppress shear-lip formation. This should be taken into account when investigating whether environment affects plastic zone size. When the crack was growing on double shear, the crack tended to deviate from the centre line of the specimen. When the deviation reached a certain angle, though, the crack suddenly changed direction and started curving in the opposite direction. Such a change of direction is photographed in Fig. 9. In double shear the crack grows along a curved path such that the centre of the crack (which passes through tensile mode) grows faster than the sides. This is consistent with the observation that cracks grow faster in tensile mode than shear mode for the same AK [12]. When the deviation reaches so far that the crack is trying to grow into its own plastic zone, at the surface, the crack is forced to change direction (Fig. 10). We observed also periodic variations in crack growth rate, although a constant AK,, was applied. The minima in crack growth rate appeared to coincide with the sudden changes in direction (although it is difficult to be sure using the potential drop method for crack length measurement, because the up-and-down cycles were rarely in phase on both sides of the specimen). We attempted to change to CT-type specimens, to avoid problems associated with asymmetrical crack growth. However, the effects of the curved crack path in double shear were disastrous: the crack did not cease to deviate from the mid-plane of the specimen, but continued growing in a perfect arc, aiming at one side of the specimen. CONCLUSIONS
(1) Seawater increases the crack growth rate of 2024-Al alloy at 10 Hz by a factor of at least 25% for a given A&s compared with air.
(2) This is the cause of one effect of seawater crack growth retardation
after a single peak overload. This mechanism dominates at high R-ratios and reduces the number of lost cycles. (3) At low R-ratios the corrosion product wedging effect dominates; the number of lost cycles following a single peak overload is increased because of the extra crack closure. (4) Reports that environment does not affect retardation after overloads are the result of these two effects cancelling out under certain conditions. (5) The suppression of shear-lip formation by aggressive environments can lead to erroneous plastic zone size measurements, since shear-lips give rise to asymmetrical plastic zones.
Environmental
dependence
of fatigue
crack
growth
retardation
935
(6) Cracks growing in double shear zig-zag either side of the mid-plane of the specimen. This probably results in variations in crack growth rates even in constant AK tests. (7) Cracks in double shear show less retardation after an overload than cracks in single shear. Acknowledgement-The
authors
are grateful
to Mrs Anneke
van Veen for her help in preparing
the manuscript.
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[I23 [I31 [14]
N. Ranganathan, J. Petit and B. Bouchet, Engng Fracture Mech. 11, 7755789 (1979). M. C. Lafarie-Frenot, J. Petit and C. Gasc, Farigue ofEngng Mater. Structures 1, 431438 (1979). 0. Buck, J. D. Frandsen and H. L. Marcus, Engng Fracrure Mech. 7, 1677171 (1975). A. Clerivet and C. Bathias, Engng Fracture Mech. 12, 559961 I (1979). H. L. Ewalds, Engng Fructure Mech. 13, 100~1007 (1980). J. Schijve and W. J. Arkema. Report VTH-217, Department of Aerospace Engineering, T. H. Delft (April 1976). H. L. Ewalds, F. C. van Doorn and W. G. Sloof. ASTM STP 801, 115-134 (1983). R. P. Wei, N. R. Fenelli, K. D. Unangst and T. T. Shih. J. Engng Marer. Technol. 102, 28C292 (1980). W. Elber, ASTM STP 486, 23&242 (1971). J. Schijve, Memorandum M-336, Department of Aerospace Engineering, T. H. Delft (August 1979). H. L. Ewarlds and R. A. H. Edwards, Effect of crack surface corrosion layers on fatigue crack growth, Paper presented at EFC-meeting on Low frequency cyclic loading effects in environment sensitive fracture, Milan, Italy (March 911, 1982). R. A. H. Edwards, E. M. De Jong and J. Zuidema, Proc. Fatigue ‘84 (Edited by C. J. Beevers), p. 463, University of Birmingham (Sept. 1984). C. Robin, M. Louah and G. Pluvinage, Fatigue of Engng Ma/er. Srrucrure 6, 1 13 (1983). H. H. Johnson, Muter. Res. Smds, pp. 442445 (Sept. 1965). (Received
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