Effects of thickness on fatigue crack initiation and growth in notched mild steel specimens

EFFECTS OF THICKNESS ON FATIGUE CRACK INITIATION GROWTH IN NOTCHED MILD STEEL SPECIMENS*

AND

A. R. JACK? and A. T. PRICES Fatigue tests have been carried out on edge notched mild steel specimens of various thicknesses. Results are presented showing the effect of thickness on crack initiation, crack growth and the geometry and fractography of the fracture surface. It was found that both crack initiation and crack growth were more rapid in the thinner specimens. The transition from a flat to a shear type of fracture was also dependent on thickness and the microscopic features of the fracture surfaces were different in the two modes. These effects are related to the state of stress at the crack tip and the conditions under which plane strain and plane stress obtain are determined. INFLUENCE FISSURES

DE

DE

L’EPAISSEUR

FATIGUE

DANS

SUR DES

L’INITIATION

ET

ECHANTILLONS

LA

CROISSANCE

ENTAILLES

DES

D’ACIER

DOUX

Des essais de fatigue ont Qte effectues sur des Bchantillons d’acier doux entail& et de differentes epaisseurs. Les resultats sont present&s et montrent I’influence de l’epaisseur sur l’initiation et la croissance des fissures, ainsi que sur la geometric et la fractographie de la surface de rupture. Les auteurs trouvent que l’initiation et la croissance des fissures sont toutes deux plus rapides dans les Qchantillons les mains , epais. La transition de la rupture plane L la rupture du type cisaillement depend Bgalement de l’epaisseur et les caracteristiques microscopiques des surfaces de rupture sont differentes dans les deux modes. Les auteurs ont relic ces effets a l’etat de la contrainte a la pointe de la fissure, et ont determine les conditions clans lesquelles on obtient une deformation plane et une contrainte plane. EINFLU5

DER

DICKE

AUF

DIE

ERMUDUNGSRISSEN

IN

BILDUNG

UND

GEKERBTEN

DAS

WACHSTUM

VON

FLUBSTAHLPROBEN

An gekerbten FluDstahlproben versohiedener Dicke wurden Ermiidungsversuche durchgefiihrt. ifber den Einflu5 der Dicke auf die Bildung und das Wachstum von Rissen und auf die Geometrie und Fraktographie der Bruohflache wird berichtet. In diinneren Proben erfolgte die Bildung der Risse schneller und die Wachstumsgeschwindigkeit war gro5er als in dicken Proben. Auch der U‘bergang von einem flachen Ri5 zu einem Scherri5 hiingt von der Probendicke ab und die mikroskopisohen Eigenschaften der Bruchfliichen waren in beiden Fallen verschieden. Diese Effekte werden mit dem Spannungszustand an der RiDspitze in Zusammenhang gebracht und es werden die Bedingungen bestimmt, unter denen ebene Dehnung und ebene Spannungen vorherrschen.

1. INTRODUCTION Studies specimens Generally

of fatigue have

crack growth

been

reported

mild in notched

by

many

sheet

authors.

it is found that cracks initiate at the notch

on a plane normal to both the applied stress and the

steel and an aluminium

and Johnston(2) growth In

after

contrast,

found

the

transition

Liu(l)

by Weibull(4)

case was the effect

with respect

studied specifically. In the present work, notched

plane has been associated

in fracture

with a change in the state

of stress ahead of the crack tip from plane strain to

of thickness

plane

tested

stress;(1*2)

this change

occurs

when

the size

number

of the crack tip plastic zone reaches a certain proportion of the specimen thickness. While the effect of specimen thickness has not been investigated specifically, it would

be expected

20, JULY

1972

rates

and Price,c5) but in neither

of thickness

in the range

to investigate of cycles

on crack initiation mild steel specimens

0.0550.90

the effect

in. have

of thickness

taken to initiate

been

on the

a crack and the

EXPERIMENTAL

Specimens of the type shown in Fig. 1 were machined from hot rolled mild steel strip with their long axes parallel to the rolling direction. was varied between 0.05 and were machined with root radii machining the specimens were for 1 hr at 88O”C, followed by

* Received September 10, 1971; revised December 29, 1971. t CEGB North Eastern Region, Scientific Services Centre, Kirkstall Power Station, Leeds LS4 2HB, England. 2 Marchwood Engineering Laboratories, Marchwood, Southampton, England. VOL.

and Jack

2.

that it could be deduced

regarding the effect of this transition. Frost and Dugdalef3) found no effect on crack growth rates in

METALLURGICA,

alloys.

growth

crack growth rate.

from observations on the transition in the fracture plane. However, there is disagreement in the literature

ACTA

aluminium that

should be greater after the transition. Studies of fatigue crack initiation have been reported

increases the fracture plane rotates to a 45” orientation The change

while McEvily

of a lower rate of

in

concluded

plane of the sheet. In the early stages of growth the crack continues on this plane but as the crack length to the sheet.

alloy,

evidence

Specimen thickness 0.90 in.; all notches of ~0.010 in. After annealed in vacuum 6 hr at 600°C. This

treatment produced an average grain size of 0.02 mm, as measured by the linear intercept method, with a typical commercial mild steel structure. Composition 857

858

ACTA

METALLURGICA,

VOL.

20,

thickness. optically

1972

After testing, the specimens were examined and in the scanning electron microscope. 3. RESULTS

3.1 Crack initiation and growth in 0.2 in. thick specimens As reported previously, f5) the number of cycles taken to initiate a crack (NJ in notched specimens of annealed mild steel is independent of notch root radius, p, below a critical value of 0.010 in. sharp

notch

described

case where

by

the

AK, calculated sharp crack. are plotted

p < 0.010

range

of stress

in.,

For the

N,

can be

intensity

factor,

assuming that the notch behaves as a

Ni values for the 0.2 in. thick specimens against

AK

in Fig. 2 ; the relationship

derived from this plot is: FIG. 1. Form of test specimen.

and

some

mechanical

properties

Ni =

of

the

for Ni in cycles, AK in ksi l/in. Crack growth

of mild steel ( %)

crack

C

Si

S

P

MIl

Ni

Cu

Sn

0.23

0.15

0.03

0.018

0.45

0.07

0.07

0.011

Yield

point

U.T.S.

R. in A.

43%

59%

27.2 tsi

15.5 tsi

load

reversal

at preset

limits.

The

specimen

loading

arrangement

was such

All

that

of the ends of the specimen were restrained;

a compliance

calibration(s)

obtained

Gross et al .(‘) for the stress intensity

by

showed

that the formula

factor in a single edge notched tension specimen was valid for crack lengths up to half the width of the specimen. During the tests, crack length was monitored continuously by using the electrical potential drop technique developed by Gilbey and Pearson.@) Under the conditions used it was possible to measure crack length to within 0.005 in. and to detect changes in crack length of the order of 0.0005 in. The majority of the t(ests were carried out on 0.2 in. thick specimens with notches of various depths. These tests provided and growth; “base line” data on crack initiation a limited number of tests on specimens at thicknesses of0.05,0.08,0.40and0.90in.with0.1in.deepnotches then

served

to

illustrate

the

effects

of

by plotting

the

of cycles,

N,

A typical plot of

specimen

arithmetic

against

crack length

at two

The bars represent the extremes of up

to 9 determinations X lo6 psi

tests were carried out at 0.33 Hz under zero-tension conditions ; load control was within &2 per cent. rotations

is plotted

stress ranges. 29.9

the number

several tests are shown in Fig. 4 where the growth rate, da/dN,

using controlled lead screw movement testing machines allowed

rates were obtained

a against

a us N is shown in Fig. 3. Crack growth rates at the same stress range* and crack length obtained from

Fatigue tests were carried out at room temperature which

length,

and drawing tangents to the curve.

TABLE 2. Tensile properties of annealed material Elong. on 1 in.

(1)

(AK)4

annealed

material are given in Tables 1 and 2. TABLE 1. Composition

2.63 x lo*

means

of da/dN, while the points are the The scatter in values.

of these

crack growth rates at the same crack length and stress range was up to a factor

of 3.

The scatter was not

evident in the number of cycles spent in propagating the crack to failure, N,, in duplicate

specimens

tested

at the same stress range, for which the scatter typically value.

of the order of *15

was

per cent of the mean

The mean values of crack growth rates from Fig. 4, together with the mean data obtained stress ranges have been plotted except

at two further

in Fig. 5.

All data,

for those results at O-15 ksi where AK > 65

ksi l/in. fell within a scatterband which covered a factor of 3 on da/dN. The mean line had a slope of 3 indicating

a relationship -$

: oc (AK)3

The results at O-15 ksi in Fig. 5 which were below the scatter band were obtained at crack lengths greater than 0.5 W, where W is the width of the specimen, and it is therefore probable that the Gross, Srawley and Brown”) expression used to calculate AK was not valid for these points. * Note that in all cases the stress referred to is the applied load divided by the gross cross sectional area.

JACK

AND

PRICE:

FATIGUE

CRACK

INITIATION

859

20 ksi

AK,

/In.

IO

IO-

IO-

FIG. 2. The influence

NL,

IO5

IO

cycles

of the range of stress intensity factor (AK) on the number of cycles to initiate a crack (iVi) from sharp notches in 1.0 in. wide x 0.2 in. thick specimens.

0.4 CRACK LENGTH, I”.

O-3

0.2

01

1

0

IO

I

I

I

I

I

I

I

20

30

40

50

60

70

80

90

N, k cycles

FIG. 3. Crack length vs. number of cycles (N) for a 1.0 in. wide

x 0.2 in. thick specimen containing a 0.1 in. deep sharp notch tested at O-20 ksi.

3.2 The effect

of specimen

thickness

at the higher stress levels.

The results of tests on 0.05, 0.08, 0.40 and 0.90 in. thick specimens

containing

given in Table 3, together

0.1 in. deep notches with the scatter

from 0.2 in. t’hick specimens.

are

in data

The results of some of

these tests are plotted in Fig. 6 where Ni and N, are plotted against thickness as a function of alternating stress. The data indicate that Ni was independent of thickness above 0.2 in. at all stresses although the result of the test at O-17.5 ksi on a 0.4 in. thick specimen was a little below the 0.2 in. thick scatter band. Below 0.2 in. there was a reduction in Ni, particularly

ent reduction thick specimen

in N,

There was a stress depend-

below 0.2 in. but for the 0.9 in.

there was an increase in N, compared

with the 0.2 in. thick data. The results from the 0.4 in. thick specimens fell within the scatter of data for 0.2 in. thick specimens. Crack growth rates in the 0.05 and 0.08 in. thick specimens fell at the top or above the scatter of data from 0.2 in. thick specimens shown in Fig. 5 while the results for the tests on 0.4 in. thick specimens were within the scatter band; these results are shown in Fig. 7. No crack growth

data

are

available

for

the

0.9

in.

thick

ACTA

860 I

I

1

1

METALLURGICA, I

I

VOL.

20,

1972

stress and the plane

1

of the specimen.

This region

had small shear lips at the edges ; these were often 300

s 0 - 30ksi

200

1

da,

dN

inlcyc Ie I IO6

T

T

I

h

15ksl

0.6

07

0-

OoO Crack

Iength,a,

specimens

because

2. A

particularly

transition

at low stresses.

region

in which

surface.

Usually,

plane at 45’ stresses,

the

particularly

shear

lips

at the high

developed

int,o a double

plane stress region, in which the crack propagated

(da/dN) as a 0.2 in. thick

loads

used

in the

o =O-15 ksi A =0-20 ksc =0-25 ksl v-O-30 ksi

q

Each point represents me mean of up to 9 results

I

20

I

1

30 40

I

60

AK,ksi

referred to as the tensile

or plane strain region, which was normal to the applied

FIG. 5.

I

I

80 100

vs. AK as a function of stress range for 1.0 in. wide x 0.2 in. thick specimens. containing

0.1 in.

Scatter band from 0.2 in. thick specimens Specimen thickness (in.)

Stress range (ksi)

0.05

o-20 o-25 O-30 O-20 O-25 O-30 o-17.5 o-25 O-30 o-22.22 O-27.78

0.90

Ni (k cycles) 7 i.25 z.5 0.5 11 2.7 1 4-8 2.5

I 200

fi

da/dN

TABLE 3. The effect of specimen thickness on Nj and N, in 1 in. wide specimens deep sharp notches

0.40

on

x

in Fig. 8.

0.08

8(a)];

those tested at higher

45” shear [Fig. S(b)]. 3. An inclined region, usually termed the shear or

from the testing machine

usually

such

a single

to the plane of the sheet [Fig.

of specimens

1. A flat region,

lips

the shear lips were inclined

on some specimens,

On the basis of macroscopic appearance the fracture surfaces could be divided into four parts, as shown schematically

shear

that at the end of this region they formed

resulted in poor test records. 3.3 Examination

the

increased in size until they covered the entire fracture

in

FIQ. 4. The rate of crack propagation function of crack length for 1.0 in. wide specimens.

tests electrical interference

insignificant,

N, (k cycles) 62 21 6 29 8 123 35 15.5 71-75 30

Ni

N,

7.5-13 2.2-4.8 0.8-2.1 7-13 2.2-4.8 0.8-2.1 14-24 2.2-4.8 0.8-2.1 4.1-8.2 1.3-3.0

54-8 1 21-32 13-18.5 54-81 21-32 13-18.5 110-160 21-32 13-18.5 34-52 15-22

JACK

IO5

FATIGUE

CRACK

AK vs.

i ---I--

I

I

PRICE:

AND

B

861

INITIATION

on a log-log

scale in Fig. 10.

Some of the fracture surfaces were examined scanning electron microscope.

0-2Oksi

from a 1 in. wide x 0.4 in. thick specimen a 0.1 in. deep notch, Figs.

11-13.

were typical

The

in the

A series of fractographs containing

tested at O-30 ksi is shown in fractographic

of all the specimens

features

observed

examined.

In the

early stages of crack growth the fracture surface was made up entirely of fatigue striations or ripples, but

IO4

__-----

-

-

-

as crack length increased a mixed ripple/dimple surface was observed. In the latter stage of fracture

-0-25ksi

the surface was almost entirely composed

b d

lI

N.

d

and

cycles

0

r IO’

-

fracture. --

-

-

marked

o o

N,

/

-Open

Points.

Dashed

- Solid

Pants

Unbroken

NP

/ /

o -

The mixed

O-20

ksi

p -

ksl

O-30

ripple/dimple

at about

I

I

0080

0200 Tbicknoss,

fracture

tensile surface

the crack length which region,

but within

between the flat region in the centre and the shear lips, both of which contained only ripples. While no

Lines. Lines

IO-

I

4_

I l

0-3Oksi

li

O-25

ksi

-I

0 400

I.0

I”

daIO”5_

FIG. 6. The effect

of thickness on Ni and N, in 1.0 in. containing 0.1 in. deep edge notches at three stress ranges.

wide specimens

of dimples final

region there was no marked difference

IO’

1

the

ksi

b -0-25

I.050

from

the end of the transition

the transition

/ d

indistinguishable

was first observed

-0-30ksi

/m /

was

dn’ in!cycla

the single 45” plane or the double 45” planes formed in the second region. 4. A final fracture region.

lo-’

Qualitatively,

lengths

specimen greater

at higher

thickness, specimen

stress

levels

and at longer

thickness

crack

In thin (0.05 and 0.08 in.) specimens stress

levels

virtually

the

flat

regions

between

regions

3 and 4 were poorly

lengths

3

at

region

10-4 -

was

of the fracture

da 5’ in/cycle

fully.

1 and 2, and between defined

40

stress level.

and the shear region never developed

The divisions

20 AK.ksifi.

tested at high

strain)

the majority

IO

40

constant

absent while in the 0.90 in. thick specimens

the flat region covered surface

(plane

AK, ksifi

at shorter at

at constant

20

the transi-

tion from one region to the next occurred crack

6_

10-S -

and the crack

lengths at which they occurred could not be measured. The divisions between regions 2 and 3 were usually more definite and the crack length (al) which marked the end of the transition region was measured in those specimens where it could be determined. The results are listed alternating factor 2

in Table 4 and are plotted as a, vs. stress range in Fig. 9. The stress intensity

at a, is also given

in Table 4 and plotted

as

20 A K , ksi fi

FIG. 7. The effect of specimen thickness on crack growth r&es in 1.0 in. wide specimens. (a) 0.40 in. thick; (b) 0.08 in. thick; (c) 0.05 in. thick. The scatter band from Fig. 5 is shown for comparison.

-

ACTA

METAT,LUHGICA,

VOL.

20,

19i2

It must be concluded that, at t.hese low crack growth rates the ripple spacing does not correspond to the actual crack growth rate and it is clear that further work is needed. 4. DISCUSSION

4.1 Crack initiation The effect of specimen thickness on crack initiation appears to be related t.o the state of stress at the notch tip. At a particular range of stress intensity (a) 20(

-1

I

I

.

7

.

. .

FIG. R. Schrxx~t.ic

wpln.~entation surfaccts.

of

typical

frnctuw

comprehensive examination was made of the rclationxhip between ripple spacing and crack growth rates deduced from a vs. N curves, it is significant that ripples were observed immediately adjacent to the notch even when the crack gr0wt.h rate was less than the resolution of the scanning electron microscope.

. . AK.

ksl

/iii

-s .. .

08 IL

07

. al

n

04OlN

THICK

SPECIMELI!

0

0 20 IN THICK

SFEClMEh’

Al

0

0 08lN

THICK

SPEC.ME?,!

o

0 OSIN

THICK

SPECIUEN:

06 0

OS

0

0.20

08 8,

05

FIG. 10. The range of strorss intensity factor vs. spocimcn t.hickness (B).

at.

in

0.40

In

(AK) at a,

04

03

0

0.2

P

0

01

15

FIG. 9. The crack length (ar) at the start of the shear region of the fracture surface vs. applied stress range for 1.0 in. wide specimens.

factor the number of cycles to initiate a crack was independent of specimen thickness above a critical raluc, which it is presumed represents the plane strain Below this value Ni represents a gradual condition. change from plane strain to plane stress and it is expected that a lower limiting value would be found under conditions of complete plane stress. The maximum degree of plane stress in the prewnt tests occurred in a 0.05 in. thick specimen tested at O-30 ksi and Ni was reduced by a factor of about 4 compared with the plane strain value.

JACK

AND

PRICE:

FATIGUE

CRACK

INITIATION

863

then since rP CC K2(lo) conditions

of complet,e

plane

strain will exist when

This implies

(4)*

2.65 x 103B

K2 <

that at stress ranges of O-25 ksi

O-16.6 ksi 2/G.)

(K =

and O-20 ksi (K = O-13.3 ksi l/G.)

Ni should be independent

of thickness

and 0.067 in., respectively,

down to 0.104

which is not inconsistent

with the data in Fig. 6. 4.2 Crack growth The effect of specimen rates was complicated

thickness

on crack growth

by the change in the condition

of stress at the crack tip as growth occurred. crack growth

was usually

Initial

in a tensile? plane strain

FIQ. 11. Fracture surfaces of 0.4 in. thick specimen tested at O--30 ksi. Crack length = 0.105 in. (X 1.96K).

From O-30

ksi

Fig. 6, crack initiation

(K =

O-19

ksi l/E.)

at a stress range of was independent

thickness above 0.150 in. Assuming represent the limiting conditions following

Liu,‘l)

that

under

for plane strain and, these

plastic zone size (TV) is proportional of the specimen

thickness,

of

t,hat these values conditions

the

to some fraction

i.e.

rD oc

B

(3)

Pm.

13. Fracture surface of 0.4 in. thick specimen tested at O-30 ksi. Crack length = 0.475 in. (X 1.92K).

mode which shear, plane

underwent a gradual transition to a stress, mode. The conditions under

which deviation from complete plane strain occurs have been calculated from the results on crack initiation,

but cannot

growth data. ditions

easily be checked

However,

using the crack

Fig. 10 summarises

for the end of the transition.

the con-

If it is again

assumed(l) that this occurs at a constant stress intensity factor for a particular specimen thickness, an estimate of the condition for complete plane stress can be made from equation (3) and the data in. thick specimens given in Table 4.

for

0.2

FIG. 12. Fracture surface of 0.4 in. thick specimen tested at O-30 ksi. Crack length = 0.250 in. ( x 1.95K).

* Since the tests have been carried out at O--maximum stress conditions, the range of stress intensity factor, AK, is equal to the maximum stress intensity factor.

ACTA

864

METALLURGICA,

Stress range (ksi)

at (in.)

25

0.138 0.197 0.197 0.550 0.691 0.611 0.433 0.500 0.400 0.355 0.235 0.355 0.355 0.355 0.315 0.711 0.750 0.472

0.05 0.08

f: 15 18 18 20 20 22.5 22.5 25

0.20

ii 27 30 ii.5 17.5 30

0.4

These data show that complete at a mean stress intensity giving a relationship

at

factor

of 2 less than the observed

about

150 ksi z/G.

In obtaining

stress

of the stress intensity

factor

accurate

since

did not

the

0.25W

so that,

calibration,

compliance

extend

the stress intensity

beyond

factor

even

small

a of

at crack lengths of 0.61 and 0.69 because the calculated

with

cannot

values

be considered

calibration 0.5W.

occurred

of

The greatest

at the higher stress levels,

lower

stresses,

there

strain region

in thin

was less variation

(see Fig.

3) where

plane

at all thicknesses.

stress range N,

in N,

strain

conditions

From Table 3 the data extrapolate

was 6 x lo3 cycles

at 0.90 in. thick

to N,

about 4.3. Liuo) and McClintock(g)

(5) the

in. have been excluded

there was no plane

on 0.90 in. thick specimens

figure

equation

in N,

at which

with speci-

proportion

to a value of

N, at a stress range of O-30 ksi of about 26 x 103 cycles, while N, for a 0.05 in. thick specimen at this

is about

mean

variation

prevailed

data in Fig. 10 for 0.05 and 0.08 in. thick specimens but the figure for the 0.40 in. specimens

due to the increasing

lengths

(5)

complete

stress range, N, increased

men thickness

since the major part of N, was spent at small crack

intensity factors of 26,33 and 75 ksi din., respectively. These values are in reasonable agreement with the

out@)

corre-

approaching

At a particular

At

of 0.05, 0.08 and 0.40 in. this implies

two points obtained

thickness

closely

specimens and no plane stress region in thick specimens.

plane stress occurs

be

more

life spent in the plane strain region.

factor of about 53 ksi d/in.,

should

specimen

conditions

The influence of stress state on crack growth rates can best be inferred from values of N, given in Table 3.

20.7 26.6 32.0 66.2 155.7 103.1 54.2 70.9 53.1 44.7 31.4 49.7 53.6 53.6 51.3 159.3 197.1 93.8

:

transition

to

plane stress. (ksi$K.)

K2 > 1.4 x 104B At thicknesses

1972

with decreasing

sponding

Specimen thickness (in.)

the

20,

increases

TABLE 4

that

VOL.

effects derived

in relation

expressions

growth rate is expressed zone size.

the

have discussed

to fatigue

theoretical

and

ratio

at 0.05 in. thick

crack

as a function

The size of the plastic

plasticity

growth.

in which

of was

They

the crack

of the plastic

zone is greater in

plane stress than in plane strain due to reduced constraint and Liuo) has shown that, in plane stress, the plastic plane growth

zone is about

strain.

Thus

rate would

be greater

present results indicate proportional

three times as large as in

it is expected

that

the

crack

in plane stress.

The

that the crack growth rate is

to (AK)3, and since the plastic zone size

is proportional

to (AK)2, it would be expected

that :

carried

In addition,

rises rapidly

above

an accurate

about

compliance

errors in the measurement

of a,

Thus the ratio of crack growth and plane strain would in good agreement

rates in plane stress

be expected

to be about

5,

with this work.

can lead to large errors in the calculated value of K. This explanation could also account for the disFor crepancy found for the 0.4 in. specimens.

tion from plane strain to plane stress involved either no change in crack growth ratet3) or a reduction in

comparison,

growth ratef2) for which the fact that the crack front

equation

(4)

indicates

that

complete

plane strain is obtained at thicknesses of 0.05, 0.08, 0.20 and 0.40 in., only when the stress intensity factors are less than 11.5, 14.5, 23 and 32.5 ksi 2/G., respectively. It is therefore apparent that in the majority of tests, the crack growth rates were determined under mixed plane strain/plane stress conditions and do not indicate directly the effect of stress state. Nevertheless, it is clear from Fig. 7 that for a given range of stress intensity factor the crack growth rate

Previous

investigators

have found that the transi-

was bowed with the centre (plane strain) leading the edges Liuu) strain bursts

(plane stress) was quoted as supporting evidence. considered that a higher growth rate in plane could be caused in high strength materials by of cleavage crack growth in the centre of the

specimen where the stress intensity could approach the plane strain fracture toughness of the material; in this case the crack front would be bowed with the centre leading the edges. In the case of the lower

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strength materials Liu concluded that this mechanism did not operate and the crack front should be bowed in the opposite sense. The present results, which showed that cracks grew faster in plane stress with the centre leading the edges, conflict with these observations and conclusions. That some other investigators did not observe a change in crack growth rate is possibly due to the fact that the transition from plane strain to plane stress is gradual rather than instantaneous. The observed shape of the crack front is apparently in conflict with a higher growth rate in plane stress. However, Richaids has suggested that if fatigue crack growth is regarded as a consequence of plastic deformation in a direction normal to the fracture surface at the crack tip this anomaly is resolved since, whatever the average state of stress along the major part of the crack front, lateral contractions at the surface will reduce the crack opening displacements there which will, in turn, reduce the crack growth rate at the surface. Finally, equation(5) can be used to indicate the value of yield stress t,o be used in estimating the plastic zone size when materials are tested in fatigue. The plastic zone size in plane stress is given by Irwin :(11) I

m-t2

where a,, is the yield stress of the material. Using the suggestion(i) that plane stress is obtained when rD is equal to B/2, equations (5) and (7) give a value of eYa of 31.4 tsi, which is twice the value obtained in a conventional tensile test as given in Table 1. Ric#*) considers that under fatigue loading conditions the appropriate value of 6, in equation (7) is twice the monotonic value to take account of the reversed stressing. The estimate for G,, obtained here suggests that this approach is realistic, although the almost exact agreement must be fortuitous since no account has been taken of work hardening. 4.3 E”ractographic features The microscopic features of the fracture surfaces showed a transition from fatigue ripples in the flat region to ductile dimples in the shear region. It is significant that in the area defined as the transition region there was no difference between the fracture surfaee in the centre of the specimen and on the shear lips at the edges, suggesting that the appearance of the fracture surface represents the average state of stress along the crack front. The relationship between fractographic features and the state of stress at the crack tip has been

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considered by many investigators. For example, booths et aZ.(l") carried out tests at constant stress intensity factor range on a ferritic weld metal and observed ripples in plane strain when the fracture surface was normal to the plane of the sheet and “tensile” dimples in plane stress when the fracture surface was at 45O to the plane of the sheet. Hertzberg(l*) reported similar features in an Al-Cu-Mg alloy. However, Griffiths et aZ.(13) also observed ripples at low crack growth rates on a 4V (plane stress) fracture surface in mild steel, and McEvily (see Ref. 14) found ripples on plane stress fracture surfaces in copper. On the other hand, Croaker et c&(15)have shown that at high growth rates dimples can be formed under plane strain conditions in a 9 Ni4Co-0.025 C steel. and Also, Plumbridge Ryder(l@ reported a study of crack growth in aluminium alloys in which dimples were observed in the flat fracture region. These authors considered that their specimens were in plane stress because the specimen thicknesses were less than 2.5 (~~~~~~~ which is the ASTM criterion for fracture toughness testing. Since Rice(12) has shown that the appropriate value of o,, to use in a fatigue situation is twice the tensile yield stress it is likely that the specimens tested by Plumbridge and Ryder were in plane strain during the “‘flat” stage of crack growth where dimples were observed. In the present work, the transition from ripples to dimples occurred over a wide range of crack growth rates due to the large variation in specimen thickness. It is clear that there was no direct relationship between crack growth rate at the transition and the dimple size, which is characteristic of the material. From the work reviewed above, it appears that in the general ease the microscopic features of the fracture surfaces are controlled by the state of stress ahead of the crack tip, ripples being produced in plane strain and dimples in plane stress. However, where the crack growth rate is small compared with the dimple size it is reasonable to suggest that crack growth will be accompanied by the formation of ripples in both plane stress and plane strain. Conversely where the crack growth rate is large compared with the dimple size both states of stress will produce dimpled fracture surfaces. 5. CONCLUSIONS 1. The number of cycles taken to initiate a crack (NJ and the crack growth rate (da/dN) are influenced by the state of stress at the crack tip. N, is reduced and ~/dN increased by the transition from plane strain to plane stress. The change in crack growth rate can be related to the change in plastic zone size.

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2. The rotation of the fracture plane during crack growth is accompanied by a change in the microscopic features of fracture from ripples to dimples and is associated with the transition from plane strain to plane stress. ACKNOWLEDGEMENT

This paper is published by permission of the Director General, Central Electricity Generating Board, Midlands Region. REFERENCES 1. H. W. LIU, Applied Materials Research, p. 229 (1964). 2. A. J. MCEVILY and T. L. JOHNSTON, Int. J. Fracture Mech. 3. 45 (1967). 3. N. E. FROSTYand’D. S. DUGDALE, J. Mech. Phys. Solids 6, 92 (1958).

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WEIBULL, Proceedings of the Crack Propagation 4. W. Symposium, p. 271. Cranfield (1961). 5. A. R. JACK and A. T. PRICE. Int. J. Fracture Me&. 6. 401 (1967). 6. A. R. JACK, Engng Fmctwe Me&. 3, 349 (1971). 7. B. GROSS, J. E. SRAWLEY and W. F. BROU’N, NASA Technical Note TN D-2395 (1964). Royal Aircraft Estab8. D. M. GILBEY and S. PEA&ON; lishment Technical Report 66402 (1966). of Solids. Interscience 9. F. A. MCCL~NTOCK, Fmcture (1963). 10. C. E. RICHARDS, privat,e communication. 11. G. R. IRwIN, Engng Fracture Mech. 1,241 (1968). 12. J. R. RICE. ASTM Soecial Technical Publication STP 415, p. 247 i1967). I 13. J. R. GRIFFITHS, I. L. MOG~ORD and C. E. RICHARDS, Metal Sci. J. 5, 150 (1971). 14. R. W. HERTZBERG, ASTM Special Technical Publication STP 415, p. 205 (1967). 15. T. W. CROOKER, L. A. COOLEY, E. A. LANGE and C. N. FREED, Trans. Am. Sot. Metals 61,568 (196s). 16. W. J. PLUMBRIDGE and D. A. RYDER, Acta Met. 17,144s (1969).