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Engineering applications of fracture analysis
Mode III fatigue crack propagation rates in 6061-T6 aluminium R. P. W r i g h t a n d R. A. Q u e e n e y Fatigue crack growth rates were studied in type 6061-T6 aluminium alloy. Unlike the preponderance of previous studies, the present observations were carried out on cracks driven by a Mode III, or antiplane shear, type of loading. The observed crack growth rates were precisely correlated with the Mode Ill stress intensity factor range, AKm. A simple power growth rate law, similar to that which predicts the growth rates of the more common Mode I driven crack, relates the incremental extension of the fatigue crack per cycle of loading to the stress intensity factor range. Fractographic examination of the fatigue crack surfaces indicated that the cracks propagated transgranularly, and did not seek out principal tensile stress planes, or Mode I growth habits. Key words: fatigue; crack propagation; Mode III; crack-growth rate; aluminium alloy; fractography Discussions of the growth of structural cracks under the influence of cyclic loading, or dynamic fatigue, are dominated by phenomena associated with the Mode I extension of the crack. The opening mode of crack propagation naturally preoccupies both the user of fracture mechanics and the design engineer since fatigue cracks most often seek out propagation planes that are normal to tensile principal stress states. The other modes/shear modes of crack propagation and fast fracture may well be introduced in structural members of particular loading and geometry including specially positioned precracks or crack initiators. A common structural example can be identified in shafting, carrying fluctuating twisting moments or torques, when the shaft is axially scored. Whether the scoring is accidently introduced or is an intentional axial slot such as a keyway, twisting the shaft will result in the establishment of an antiplane shear deformation of the crack faces. 1 Mode Ill fatigue crack propagation has been studied, moreover, in a superimposed Mode III, Mode I propagation of 'fingerlike' cracks in polymers. The present study was designed to initiate an examination of the behaviour of fatigue cracks being driven by wholly antiplane, or Mode III, displacements of the crack faces. The dependence of the incremental growth rate of the crack, per cycle of loading, on load parameters such as the stress intensity factor range AKIn, was examined for simple predictive equations such as exist for opening mode crack propagation. Appropriate fractographic observations were made to support hypotheses advanced to correlate crack propagation rates and stress intensity factors.
approximately 7 mm. Without this prior grooving, the beam-like nature of the three specimen arms gave rise to high bending stresses (beam length, a) and the Mode III cracks wandered towards the tensile stress planes, or normal to their intended growth plane. Finally, after all machining of the test specimens was complete, the specimens were solution treated, quenched, and aged to a standard-T6 temper.
Testing procedures All load cycling was carried out in air at room temperature at a frequency of 30 Hz. "Fne specimens were attached to the load train by sphericagy-seated screws, as depicted in Fig. 2, with the seats well-lubricated. "['he two outside specimen arms were joined to a yoke, from which the load was carried through a universal joint to the load ram. The middle arm of the specimen was attached to the load cell with an intervening universal joint. The above loading configuration was designed to impart vertical forces only to the specimen arms: spurious couples could not be generated with the universals and spherical-headed screws. All cycling was in tensile-tensile loading, with minimum loads of onetenth the maximum value. Maximum loads were of the order of 100 N. The flexure stresses induced in the middle beam
EXPERIMENTAL PROCEDURES Materials and test specimen A commercial grade of aluminium alloy 6061 was chosen for these studies. The plate specimens of Fig. I were cut from a 12.5 mm thick plate. Cracks (precracks, actually) greater than 50 mm deep were saw cut into the plates as indicated by the shaded interfaces in Fig. 1. These precracks were driven for another 1.0 mm or so with the appropriate test-level loading before actual growth studies were undertaken, to provide a more natural crack geometry. Grooves to guide the growth direction of the propagating cracks were cut into the plates as indicated (in an exaggerated fashion) in Fig. 1, leaving a ligament plate thickness of
~
J J ~ ' ~
~'~'-.~ ~
5 mm
i I
_..~J Fig. 1 Specimenand loading configuration for Mode III fatigue crack propagation studies
0142-1123/82/010027-04 $03.00 © 1982 Butterworth & Co (Publishers) Ltd
INT. J. FATIGUE January 1982
27
Fig. 1, with a reduced section of thickness, 'b' in the crack plane, caused by the crack guiding grooves. If the crosssections of the three 'beams' are alike, and a load P is applied to the center beam, the total strain energy of the three beams is: p2a 3
To Unlversc]l
u
- -
(5)
4EI where E is the elastic modulus and I the second area moment in each of the beams. I f the crack length a increases, the compliance of each beam is increased, and the elastic strain energy of the system is lowered. Of course, the reduction in stored strain energy is the driving force for crack extension. The reduction in strain energy, as the crack extends, is:
du
3p2a 2
.........
da
(4)
4EI
As the crack extends by da, four additional increments of crack surface area are created, each b • da. The Mode [II strain energy release rate, GIII, is defined by:
1
du
To yoke, Un~vers(]l
GIII .. Fig. 2 Mode I I I fatigue specimen loading details
4bda
5p2a 2
of the specimen, due to this 100 N maximum load, are about 40% of the yield strength of 6061-T6 alloy. No discernible plastic deformation of the specimen was noted during any test. A total of four specimens were tested and the growth rates of both cracks in each specimen were measured with an optical comparator.
(5 )
16bEI Following the analysis of Tada, 3 the strain energy release rate GIII is related to the Mode III stress intensity factor Kin by: GIII = KIII2(1 + v)/2E
(6)
where v = Poisson's ratio. For the present case,
EXPERIMENTAL RESUL TS
3Pa
Data obtained, in the form of crack length a versus the number of load cycles N to obtain a given crack length, are shown in Fig. 3. The data for all four specimens tested, with two cracks monitored per specimen, is combined to determine the single composite response indicated in Fig. 3. To avoid interjecting the inaccuracies encountered in the graphical manipulation of Fig. 5 to obtain crack growth rates da/dN, the data were numerically fitted to a general polynomial'in N, using a least squares technique to minimize the deviations between actual data points and data points predicted by the polynomial. Computations indicated that, at least in the present case, a second order polynomial of the form a = C 1 + C2N+ CsN2
/
/
55"
/
/
!
/ /
(I)
possessed sufficient accuracy. The crack growth rate da/dN can then be calculated from:
da/dN = C 2 + 2CsN
(2)
Computations gave C2 = - 4 . 2 5 × l 0 -8 meters per cycle, and CS= 5.86 x 10- 1S m/(cycle).2
/
A N A L YSIS OF RESUL TS Tada 3 has calculated a Mode I I I stress intensity factor, KIII, for a plate w i t h a single slit, or crack, loaded in a fashion similar to the specimen in Fig. I. His analysis is based on the strain energy of the beam-like arms being lowered as the crack length, or beam length, increases. A similar analysis was carried out on the double-shtted specimen of
28
INT. J. F A T I G U E January 1982
N (cycles x 104) Fig. 3 Crack length a vs cycles N of applied load in mode I I I fatigue crack propagation in 6061 -T6 a l u m i n i u m alloy
approximately 7 mm. Without this prior grooving, the beam-like nature of the three specimen arms gave rise to high bending stresses (beam length, a) and the Mode III cracks wandered towards the tensile stress planes, or normal to their intended growth plane. Finally, after all machining of the test specimens was complete, the specimens were solution treated, quenched, and aged to a standard-T6 temper.
Testing procedures All load cycling was carried out in air at room temperature at a frequency of 30 Hz. "Fne specimens were attached to the load train by sphericagy-seated screws, as depicted in Fig. 2, with the seats well-lubricated. "['he two outside specimen arms were joined to a yoke, from which the load was carried through a universal joint to the load ram. The middle arm of the specimen was attached to the load cell with an intervening universal joint. The above loading configuration was designed to impart vertical forces only to the specimen arms: spurious couples could not be generated with the universals and spherical-headed screws. All cycling was in tensile-tensile loading, with minimum loads of onetenth the maximum value. Maximum loads were of the order of 100 N. The flexure stresses induced in the middle beam
EXPERIMENTAL PROCEDURES Materials and test specimen A commercial grade of aluminium alloy 6061 was chosen for these studies. The plate specimens of Fig. I were cut from a 12.5 mm thick plate. Cracks (precracks, actually) greater than 50 mm deep were saw cut into the plates as indicated by the shaded interfaces in Fig. 1. These precracks were driven for another 1.0 mm or so with the appropriate test-level loading before actual growth studies were undertaken, to provide a more natural crack geometry. Grooves to guide the growth direction of the propagating cracks were cut into the plates as indicated (in an exaggerated fashion) in Fig. 1, leaving a ligament plate thickness of
~
J J ~ ' ~
~'~'-.~ ~
5 mm
i I
_..~J Fig. 1 Specimenand loading configuration for Mode III fatigue crack propagation studies
0142-1123/82/010027-04 $03.00 © 1982 Butterworth & Co (Publishers) Ltd
INT. J. FATIGUE January 1982
27
Fig. 1, with a reduced section of thickness, 'b' in the crack plane, caused by the crack guiding grooves. If the crosssections of the three 'beams' are alike, and a load P is applied to the center beam, the total strain energy of the three beams is: p2a 3
To Unlversc]l
u
- -
(5)
4EI where E is the elastic modulus and I the second area moment in each of the beams. I f the crack length a increases, the compliance of each beam is increased, and the elastic strain energy of the system is lowered. Of course, the reduction in stored strain energy is the driving force for crack extension. The reduction in strain energy, as the crack extends, is:
du
3p2a 2
.........
da
(4)
4EI
As the crack extends by da, four additional increments of crack surface area are created, each b • da. The Mode [II strain energy release rate, GIII, is defined by:
1
du
To yoke, Un~vers(]l
GIII .. Fig. 2 Mode I I I fatigue specimen loading details
4bda
5p2a 2
of the specimen, due to this 100 N maximum load, are about 40% of the yield strength of 6061-T6 alloy. No discernible plastic deformation of the specimen was noted during any test. A total of four specimens were tested and the growth rates of both cracks in each specimen were measured with an optical comparator.
(5 )
16bEI Following the analysis of Tada, 3 the strain energy release rate GIII is related to the Mode III stress intensity factor Kin by: GIII = KIII2(1 + v)/2E
(6)
where v = Poisson's ratio. For the present case,
EXPERIMENTAL RESUL TS
3Pa
Data obtained, in the form of crack length a versus the number of load cycles N to obtain a given crack length, are shown in Fig. 3. The data for all four specimens tested, with two cracks monitored per specimen, is combined to determine the single composite response indicated in Fig. 3. To avoid interjecting the inaccuracies encountered in the graphical manipulation of Fig. 5 to obtain crack growth rates da/dN, the data were numerically fitted to a general polynomial'in N, using a least squares technique to minimize the deviations between actual data points and data points predicted by the polynomial. Computations indicated that, at least in the present case, a second order polynomial of the form a = C 1 + C2N+ CsN2
/
/
55"
/
/
!
/ /
(I)
possessed sufficient accuracy. The crack growth rate da/dN can then be calculated from:
da/dN = C 2 + 2CsN
(2)
Computations gave C2 = - 4 . 2 5 × l 0 -8 meters per cycle, and CS= 5.86 x 10- 1S m/(cycle).2
/
A N A L YSIS OF RESUL TS Tada 3 has calculated a Mode I I I stress intensity factor, KIII, for a plate w i t h a single slit, or crack, loaded in a fashion similar to the specimen in Fig. I. His analysis is based on the strain energy of the beam-like arms being lowered as the crack length, or beam length, increases. A similar analysis was carried out on the double-shtted specimen of
28
INT. J. F A T I G U E January 1982
N (cycles x 104) Fig. 3 Crack length a vs cycles N of applied load in mode I I I fatigue crack propagation in 6061 -T6 a l u m i n i u m alloy