The mechanism of fatigue crack propagation in pure aluminum single crystals

Scripta METALLURGICA

Vol. 20, pp. 977-982, 1986 Printed in the U.S.A.

Pergamon Journals Ltd. All rights reserved

THE MECHANISM OF FATIGUE CRACK PROPAGATION IN PURE ALUMINUM SINGLE CRYSTALS Zhao-xiong Tong, Shi Lin and Chi-mei Hsiao (Beijing University of Iron and Steel Technology, Beijing, PRC) (Received December 30, 1985) (Revised May I, 1986) Introductio~ Our previous reports about the kinetic and mophological studies of fatigue crack propagation in pure aluminum single crystals indicate that: (I) the shear stress is the primary factor controlling the process of fatigue crack propagation, and the tensile stress can accelerate the rate of this process (I); (2) the deformation during fatigue in front of the crack tip strongly affect the morphology of fatigue crack propagation. Whether the ~rack propagates steadily or with branching, the damage accumulation mechanism (2,3) rather than the alternate slip mechanism (4-6) appears to be more suitable in expl&ining the observed phenomena (7). As a part of our investigation, this paper will quantitatively treat the dependence of da/dN on the shear stress ( T ) and the normal stress ( ~ ) , and will confirm the applicability of the damage accumulation mechanism by means of specially designed experiments. Experimental An ingot of high purity (99.999%) aluminum was forged and then machined into rods of 50 mm in diameter. Very large grains (greater than 50 mm in diameter) were obtained by deformation-recrystallization of these rods. After the crystallographic orientation of the grains had been determined by x-ray diffraction, the notched plate specimens were prepared. The geometry and the coordinate system are shown in Figure I. The crystallographic directions of the coordinate axes of Mode II specimens are listed in Table I. This selection of the orientations was based on the consideration that slip should be confined to one slip system. The results of the calculation indicate that in the case of Mode II specimens, the greatest shear stress exists on the x-z plane and along the x-axis. Therefore if a 11111 plane coincides with the x-z plane and a (110 ~direction coincides with the x-axis, as in specimen A1 (or B2), the slip ahead of the crack tip will tend to be confined to this system. In order to investigate the influence of the orientation on fatigue crack propagation, the specimens were prepared by one of the following procedures. (i) the {iii} plane was keptparallel to the xz plane, and the direction was rotated from the x-axis to the z-axis;(2)the(110~direction was kept parallel to the x-axis, and the [111) plane the was rotated around the x-axis. Thus, two roups of orientations were obtained: AI to A4 specimens and BI to B5 specimens AI is the same as B2).

~

The orientations

of all Mode I-II specimens

are the same:

977 0036-9748/86 $3.00 + .00 Copyright (c) 1986 Pergamon Journals

Ltd.

978

MECHANISM OF FATIGUE CRACKING

Vol.

20, No. 7

x //[112], y//[111], z// [110] but the tensile axes are different from each other. The inclination angles of the cracks ~ (Figure Ib) are 23 ° , 37 ° and 52 ° respectively. The push-pull fatigue tests with R=Pmin/Pmax=-1 in dry air (RH • 209,4) at room temperature (18 o ~ 2 5 o C ) were performed with an AMSLER fatigue test machine. the frequency of tests was 55 to 77 Hz. In order to investigate the applicability of the damage accumulation mechanism,aKII was designed to change as follows. At first, the fatigue crack began to grow under a large load (point A in Figure 2a), then the load was decreased gradually until da/dN was less than 10-7 mm/c~cle (point B in Figure 2a). After maintaining this low load for about 2-3xI0~ cycles, the load was increased gradually (curve BC in Figure 2a). The change of the load, AP, was about 10 to 25% for each step during the decreasing load portion (curve AB in Figure 2a), and 5 to 10% for each step during the increasing load portion (curve BC in Figure 2a). The increment of crack length, aa, between two consecutive changes was ~ess than 0.5 mm. Therefore the difference in A KII between two consecutive loadings was small. For Mode II loading, Kii was calculated with: KII : 1 . 1 2 1 5 ~ - ~ . T and for Mode I-II loading, K I and KII were calculated by: KI = YI~

,

KII=YII~

where YI and YII are shape factors which can be found from handbooks (8). Results and Discussions (I) The da/dN "loop" corrgspondin~ to v a r 2 i n g A E T ~

process

The da/dN v e r s u s A K i i curve of Mode II specimens in all orientations, as well as Mode I-II specimens with various inclinations of the cracks, manifested themselves as a "loop" as shown schematically in Figure 2a. The experimental data for four duplicate B3 specimens are shown in Figure 2b. The "loop" consists of two branches: the left one AB corresponds to t h e ~ K i i - d e c r e a s i n g process, which is described as the AKli-decreasing branch, while the right one BC corresponds to t h e A K i i - i n c r e a s i n g process, which is described as the AKii-increasing branch. The da/dN "loop" indicates the "history effect" of A K I 1 on the fatigue crack propagation rate. For the same value of AKII , da/d~ measured in the ~ K I i decreasing process is always greater than that measured in t h e A K i i - i n c r e a s i n g process by about one order in magnitude (Figure 2b). This history effect could not be explained by the alternate slip mechnism (4-6), but could be explained satisfactorily by the damage accumulation mechanism (2,3). For the same i n s t a n t a n e o u s ~ K i I in Figure 2b if E >N', then EII(~) < KII (E') in t h e ~ K i i - d e c r e a s i n g process, while KII(~I > KII(N') in the4 KII-increasing process. When the crack tip corresponds to cycle N, the matrix at this point will have undergone more deformation in t h e A K I i - d e c r e a s i n g process than that in t h e ~ K I ] - i n c r e a s i n g process, if the idea thaZ the greater t h e ~ K I i is, the more strongly the deformation occurs is accepted. Therefore, in t h e A K i i - d e c r e a s i n g process, there would be more damage accumulated during fatigue, and thereby a greater da/dN would be expected. (2) The influence of shear s~ress component along slid direction on da/dR From fracture mechanics,

the stress components can be calculated with:

Vol. 20, Ne. 7

MECHANISM OF FATIGUE CRACKING

(Yx (r's)

KII 2 r

(yy(r,e)= KII 2 r

@

8

3e

sin~(2+cos~cos 2

e

979

)

e

sln~c°s~c°s2

"~xy (r'0)= KII2r cos~(1-sin~sin23~) For the ease of calculations, point (I/2~,8) is selected for the calculation of these 3 stress components. Through transformation of axes, the normal stress and shear stress components of ~x,~v,~xy. On four I111~ planes can be calculated. The shear stress components on the ~111~ planes and along the three posible slip directions were further calculated. The results of these calculations are listed in Table 2, where the shear stress component on 11111 planes along the slip directions is denoted as • . As the change of load in the A Kii-increasing branch (BC in Figure 2a) is small, so that its history effect is small, it is reasonable to compare da/dE vs a ~ in this branch (Figure 3) for various orientation in order to study the influence of the shear stress component on the slip plane along the slip direction. As shown in Figure 3, the experimental data for specimens AI(B2), A2, B3 and B5 are all located within a narrow band, but those for specimens BI, A3, A4 and B4 deviate from this band. Some reasons for retarding or accelerating the propagation rate have to be found to explain these mentioned deviations. If the idea that all of the slip processes could contribute to the total damage accumulsted according to the relative shear stress component along the slip direction, then the slower.da/dN would be expected for specimen B4, since the operation of only slip system (111)[110] (Table 2) is favored. This deduction is confirmed by the observations of the PSB on the surface of specimen B4. In this case, only primary PSB can be observed and the crack propagates along these primary PSB (Figure 4). On thD same reasoning, the faster da~dN would be expected forospecimens BI and A3. For specimen BI, slip systems (111)[110], (111)[110], (111) [110land (111)[110] (Table 2) should be equally active, and all of these would contribute to the damage accumulated and thus increas9 da/dN. Similarly for specimen A3, the three slip systems, (111)[110], (111) 1110] and (111)[110] should be operative, and this postulate is supported by the surface observation of PSB on specimen A3. As shown in Figure 5, there are three groups of PSB near the crack tip of specimen A3. Although the shear stress distributions for A3 and AI at 8=0 are similar as shown in Table 2, the results of detailed calculation for other values of 8 indicate that T values are higher for A3 than those for AI, which may be used to explain the difference between A3 and AI. Also the dislocation interactions likely to be dominant have very different end products (10). The much stronger hardening effect for new glissile co-planar dislocations in [122] cystals has recently been found by Jin and Winter (9), and this effect may be used to explain the slower da/dN for A4 and B4, as shown in Table 2, this dislocation interaction is possible for A4 on (111) and (111) planes, and for B4 on (111) and (111) planes. (3) The influence of the normal stress on the fatigue crack propagation As in the case of Mode II specimens, the da/dN vs A K I I curves for the Mode I+II specimens also appear like a "loop" (Figure 2a). Since all of the Mode I+II specimens with different inclination angles ~ were oriented in the same direction, corresponding to specimen A4, these A KTi-increasing branches of da/dN-~KIi can be compared directly as shown in Figure ~. It can be seen from Figure 6 that the curves move to the left when the inclination angle ~ is increased. T h i s result indicates that the normal stress can accelerate the da/dN, although it does not affect the slip along the primary slip plane, as has been reported in reference (I). However, in this investigation,

980

MECHANISM OF FATIGUE CRACKING

Vol, 20, No. 7

all specimens had the same orientation for the Mode II component, so that the effect of the different secondary slip systems can be eliminated. Conclusions (I) The fatigue crack propagation rate is influence by the loading history of AKII. Its value measured in the a~II-decreasing process is always greater than that in the aKii-increasing process. (2) The shear stress component along the slip direction on the primary slip plane is the basic factor controlling the fatigue crack propagation rate. (3) The normal stress acting on the primary slip plane can accelerate the fatigue crack propagation rate. The greater ~ / T is, the more is the acceleration. (4) The above phenomena can be explained satisfactorily by a damage accumulation mechanism.

References. i. 2. 3. 4. 5. 6. 7. 8. 9. i0.

Zhao-xiong, Lun Liu, Shi Lin and Chi-mei Hsiao, "Kinetic Study on the Propagation of Fatigue Crack in Pure Aluminum Single Crystals under Different Modes of Loading," to be published. P.J.E. Forshth, Proc. Roy. Soc., A242, 198, (1957). M. Wilhehn, M. Nageswararao and R. Meyer, "Fatigue Mechanisms", 21, (1979). P. Neumann, Acta Met., 22, i155, (1974). P. Neumann, H. Vehoff and H. Fuhlrott, Fracture, ICF 2, 1513, (1977). C. Laird and G.C. Smigh, Phil. Mag.+ 7, 847, (1962). Zhao-xiong Tong, Shi Lin and Chi-mei Hsiao, "The ~rystallographic Characteristics of Fatigue Crack Propagation in PureAluminum Single Crystals", to be published. G.C. Sih, Mechanics of Fracture, Vol. I, 51, (1973). N.Y. Jin and A.T. Winter, Acta. Met., 52, 989, (1984). J.P. Hirth and J. Lothe, Theory of Dislocations, 2nd ed., Wiley, (1982). Table I

Specimens AI A2 A3 A4

x ~I0 ~51 ~31 121

The Crystallographic Direction of Coordinate Axes of Mode II Specimen~ 2 z Specimens x y 111 112 BI 1i0 110 111 213 B2 110 111 111 415 B3 110 ~3 ~11 101 B4 110 !12 B5 110 3310

z 001 112 334 111 553

Vol. 20, No. 7

Table 2

MECHANISM OF FATIGUE CRACKING

The Relative Shear Stress Components on Slip Planes Along Slip Directions while 0toO

(111)

Specimen

lOl

BI A3 Al(B2)

981

(111)

Ol]

11o 1.oo

0.50 0.20 O. 50

(111),

(11])

11o I.OO

o11 0.50

1oi 0.50

1.00 I.O0

0.50 0.80 O. 50

0.60 0.67

0.27 0.50

0.33 0.17

B3

o. 50

I.oo

o. 50

o.57

0.07

o.5o

B5 A2 A4 B4

O. 50 0.33 0.00 0.50

I.O0 I .00 1.00 1.00

O. 50 0.67 I .00 0.50

0.38 0.63 0.55

0.12 0.22 0.33

0.50 0.41 0.22

0.50

o.oo

0.50

11o

o11

Ioi

1.0o 0.73 0.67 0.57 0.38 0.70 0.78

0.50 0.67 0.50 0.50 0.50 0.59 0.78

0.50 0.06 0.17 0.07 0.12 0.11 0.00

011 0.50 0.40 0.17 0.07 0.13 0.33 0.55 0.50 0.50 o.oo 0.00

I01 0.50 O.O7 0.17

O.O7 0.13 0.03 0.22 0.00

P

0.13

!

i

.-".-~

110 1.00 0.33 0.34 0.14 0.26 0.3_0 0.33. 0.00

o

g.4.5

o

kO

2O

4a

Ip

(a) Mode II Specimen

(b) Mode I-II Specimen

FIG. I The Geometry and the Coordinate System of the Specimens (The z-axis is perpendicular . to the Paper)

I

-

A

10 -5

10 -5 _

i

1

|

i

,

2AKII3 4 5 Mp~

i

0.5

1

I

,I

(b)

2~KII3 4 5 Mpad

FIG. 2 Variation of da/dN withAEii (a) The General Form corresponding to AKII-decreasing Process (AB) and aEii-increasing Process (BC); (b) The Typical Experimental Curve for Mode II Specimen B3

982

MECHANISM OF FATIGUE CRACKING

/

I

iI

J

lo";

Vol. 20, No. 7

'

I I I

,o~ ,

t

I

!

B1 ~ _ ,

A3

~4 _A2. ]33

1

1.5

2

3

4Mp ~

I II

1°-71/,L,,,,,,,, 0.5

I

1.5 2

3

I

AT

FIG.3 The da/dN Curves for Various Orientations

FIG.4 Photomicrograph of the Surface of Specimen B4 (Only one set of PSB can be seen)

FIG.6 The Influence of Inclination Angle on da/dN vs n K I I Curve (The Curve for @ =0 was obtained from the Mode II Specimen A4

FIG.5 Photomicrograph of the Surface of Specimen A4 (Three sets of PSB can be seen)