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8/20/2019 Fatigue Tanaka

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Enginmfng Fwctun Mechanics, 1974, Vol. 6, pp. 493-W.

Pergamon Press. Printed in Great Britain

FATIGUE CRACK PROPAGATION FROM A CRACK INCLINED

TO THE CYCLIC TENSILE AXIS

KEISUKE TANAKA

Department of Mechanical Engineering, Kyoto University, Kyoto, Japan

Ah&act-Cyclic stresses with stress ratio

R =

0.65 were applied to sheet specimens of ahuninium which

have an initial crack inclined to the tensile axis at angles of 30”, 45”, 72” or 90”. The threshold condition for the

non-propagation of the initial crack was found to be given by a quadratic form of the ranges of the stress

intensity factors of modes I and II. The direction of fatigue crack extension from the inclined crack was

roughly perpendicular to the tensile axis at stress ranges just above the threshold value for non-propagation.

On the other hand, at stress ranges 1.6 times higher than the threshold values the crack grew in the direction

of the initial crack. The rate of crack growth in the initial crack direction was found to be expressed by the

following function of stress intensity factor ranges of mode I, K,, and mode II,

K2:

dc/dN = C(K..)“, where

K,=

[K, + 8K,4]‘“. This law was derived on the basis of the fatigue crack propagation model proposed by

Weertman.

INTRODUCTION

FRACTUREechanics has been established as an important principle dealing with the

growth of fatigue cracks. Since Paris [ l] successfully correlated the rate with the stress

intensity factor, a number of investigators have reported the data on the relation

between the propagation rate and the stress intensity factor. The condition for the

non-propagation of fatigue cracks has also been expressed in terms of the threshold

value of the stress intensity factor[2,3]. Most of their experiments have been

concerned with crack growth under cyclic tensile loading of simple opening type,

mode I.

In practical situations, we sometimes meet the growth of fatigue cracks under

simultaneous application of cyclic loads of types of opening, mode I, in-plane sliding,

mode II, and anti-plane sliding, mode III. For example, a fatigue crack grows along slip

bands for a certain period after nucleation. The growth during this period is identified as

the growth under mode II or III cyclic stress, combined with mode I stress. The

combined mode growth is realized when a fatigue crack is nucleated along inclusions or

welded defects located making an angle with the axis of a tensile load. Fatigue crack

growth under applied multi-axial stress is, of course, of combined mode. In corrosion

fatigue, numerous cracks are usually formed throughout the specimen [3]. Each crack

grows under mutual interaction. The stress system at the crack tip become combined

mode in this situation.

The growth of fatigue cracks under combined mode of I and II was first studied by

Iida and Kobayashi[4]. They used a sheet of 7075T6 aluminium alloy with an initial

crack inclined to the axis of cyclic tensile loading. Their results showed that the initial

crack grew rapidly in the direction which caused the mode II component of the applied

load to go to zero. They also noticed that the presence of even a small cycling of mode

II stress increased the propagation rate significantly. Later, Roberts and Kilber[5] re-

ported the results of experiments on fatigue crack growth under in-plane, mode I,

extensional loads and transverse, mode II, bending loads. Their results indicated that in

certain cases the fatigue crack grew in a manner which did not reduce the mode II

493

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494 KEISUKE TANAKA

component of the load to zero and that the growth rate was accelerated by the mode II

component of stress applied simultaneously.

The original purpose of the present study was to establish the threshold condition of

fatigue crack growth under combined mode cycling of I and II. Like Iida and

Kobayashi, an initial crack was made in sheet material orientated at various angles to

the longitudinal direction of the plate. In the present experiments, it was found that in

certain situation the fatigue crack propagated in the direction of the initial crack. The

growth law of fatigue cracks under mode I and II stress cycling is discussed on the basis

of the theories of fatigue crack growth proposed by Weertman [6] and Lardner [7], and

a new propagation law under combined mode stressing is proposed. The threshold

condition for the non-propagation of fatigue cracks is discussed comparing the data

with the theories of maximum tangential stress criterion [8] and of strain energy density

criterion [9].

EXPERIMENTAL PROCEDURE

Specimens were cut out from a commercially pure aluminium plates of 3*2mm

(l/8 in.) thickness. The preliminary specimens of a wide plate was fatigued after getting

a mechanical slit with band saw and razer blade perpendicular to the tensile axis. A

fatigue crack was grown to a length of about l-5 mm from each end of the mechanical

slit. Then fatigue specimens of final shapes were cut out from cracked preliminary

specimens in the manner that the initial slit and crack were orientated at angles of 30”,

45”, 72” and 90” with respect to the longitudinal direction of the final specimen. The final

dimensions of the fatigue specimen is shown in Fig. 1, where the rolling direction of the

sheet is the direction of the initial slit and crack. For each inclined angle, (Y, he initial

slit-crack lengths adopted are

CYdeg) = 90,72,45,30

2c(mm) = 21 and 10 11,15,21.

All the specimens were annealed at 270°C for 2 hr before subjecting them to fatigue

testing. Table 1 gives the mechanical properties of a strip which was prepared following

the same heat treatment as in the case of fatigue specimen preparation. As can be seen

in the table, the mechanical properties of the material is almost isotropic.

The fatigue tests were conducted in Losenhausenwerk operated at a rate of

.5

saw-cut

Fatigue

-- -_

c crock

3-T

-Ql

y- 1.5

Thickness f =32

Fig. 1.Shapes and dimensions of fatigue specimen (dimension mm).

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Fatigue crack propagation

495

Table 1. Mechanical properties of aluminium sheet.

Rolling direction

Yield stress

Tensile True

Reduction

vs

(0.2% off-set) strength strength of area

stress axis

(kg/mm’)

(kg/mm2) hdmm2)

(%I

Parallel 10.0

10.5 27 77

45” 9.6

9.7 25 78

Perpendicular 10.2

10.4 24 72

1000 cpm. The ratio R of the minimum stress omin o the maximum stress a,, was kept

at a constant value of 0.65 for all fatigue tests. The growth of fatigue cracks was

monitored with a travelling microscope attached to the fatigue testing machine.

NON-PROPAGATION CONDITION AND CRACK GROWTH DIRECTION

Several specimens were fatigued under stress ranges near the situation of the

non-propagation of an initial crack which was estimated from the data of preparatory

experiments. The results are summarized in Table 2. In some experiments, the stress

range was raised step-wise when the initial crack was detected not to grow with a

microscope after applying 3

x

lo5 stress cycles. Since the limit of detection of crack

growth length is about 0.05 mm, a growth rate higher than l-7 x lo-‘mm/cycle can be

detected by this method.

The elastic stress near the tip of a crack which is inclined to the tensile axis is

characterized as mixed mode of opening, mode I, and in-plane sliding, mode II. The

stress intensity factors k, and

kz

of modes I and II due to a tensile stress u are given by

k, =

k

sin’cu (la)

k = kA sina COW

(lb)

with

where c is the half crack length and (Y is the angle between the crack and the axis of

Table 2. Experimental results for determining the threshold condition of fatigue crack

propagation.

Initial

Crack

crack Stress intensity factor

Crack growth growth

Specimen

angle

KI

K,

rate, dcldN angle

No.

(deg)

(kg/z”“) (“)

(“)

(mm/cycle)

Udeg)

4

90

5 90

7

90

7

90

10 72

10 72

13 45

13 45

17 30

17 30

17 30

19 30

19 30

6.52

5.54

6.00

6.38

5.93

6.29

7.24

764

9.49

997

10.9

9.55

10.0

6.52 0

5.8 x lo-’

5.54 0 Nogrowth

6.00 0

Nogrowth

6.38 0

7.9 x lo-’

5.35

1.74 Nogrowth

5.67

1.85 7.4 x lo-’

3.62

3.62 Nogrowth

3.82

3.82

7.2 x lo-’

2.37

4.11

Nogrowth

2.49

4.32 No growth

2,74

4.74

1.4 x lo+

2.39

4.14 Nogrowth

2.50

4.33 2-