NASA Technical Memorandum 4784

An Experimental Study of Fatigue Crack

Growth in Aluminum Sheet Subjected to

Combined Bending and Membrane Stresses

Edward P. Phillips

Langley Research Center • Hampton, Virginia

National Aeronautics and Space Administration

Langley Research Center • Hampton, Virginia 23681-2199

October 1997
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Abstract

An experimental study was conducted to determine the effects of combined bending and membrane cyclic stresses on the fatigue crack growth behavior of aluminum

sheet material. The materials used in the tests were O.040-in.-thick 2024-T3 alclad

and O.090-in.-thick 2024-T3 bare sheet. In the tests, the membrane stresses were

applied as a constant amplitude loading at a stress ratio (minimum to maximum

stress) of O.02, and the bending stresses were applied as a constant amplitude deflection in phase with the membrane stresses. Tests were conducted at ratios of bending

to membrane stresses (B/7t4) of O, 0.75, and 1.50. The general trends of the results

were for larger effects of bending for the higher B/M ratios, the lower membrane

stresses, and the thicker material. The addition of cyclic bending stresses to a test

with cyclic membrane stresses had only a small effect on the growth rates of throughthickness cracks in the thin material, but had a significant effect on the crack growth

rates of through-thickness cracks in the thick material. Adding bending stresses to a

test had the most effect on the initiation and early growth of cracks and had less effect

on the growth of long through-thickness cracks.

Introduction

Fatigue cracking in aircraft fuselage skin joints has

been a topic of considerable interest to airframe manufacturers, aircraft operators, and regulatory agencies in

recent years. The subject is of particular interest to those

responsible for assessing and ensuring the continued airworthiness of aircraft fleets that have been in service for

a long time. The research community has been challenged to provide the methodology necessary to predict

the fatigue crack growth behavior of the joints. To

develop the required methodology, potential shortcomings of current methodology must be explored to aid in

the development of improvements. One area requiring

investigation concerns the effect of local bending in the

joints on the crack growth behavior. Strain measurements made at a fuselage longitudinal skin joint during

fuselage pressurization have shown that significant bending occurs in the skin (refs. 1 and 2), but current crack

growth prediction models do not account for the bending

stresses. A survey of the literature did not reveal any pertinent experimental studies of the effect of combined

bending and membrane stresses on the crack growth

behavior of sheet material.

The objectives of the current study were (1) to determine the magnitude of the effect of bending stresses on

the crack growth behavior and (2) to provide data that

could be used to evaluate the capability of crack growth

models to account for the effects of bending stresses.

Because of the experimental difficulties involved in running tests in which both the membrane and bending

stresses are actively controlled, the tests were conducted

with constant-amplitude membrane loading and

constant-amplitude bending displacements. Tests were

conducted on two sheet thicknesses (0.040 and 0.090 in.)

and with ratios of bending to membrane stresses of 0,

0.75, and 1.50. The range of test conditions was selected

to span expected conditions in current fuselage

structures.

Tests

Materials and Specimens

Tests were conducted on center-cracked specimens

made of 0.040-in.-thick 2024-T3 alclad and 0.090-in.-

thick 2024-T3 bare aluminum alloy sheet. The long axis

of the specimen was perpendicular to the sheet rolling

direction. That is, crack growth was determined for the

T-L orientation. The specimen configuration is shown in

figure 1.

Test Apparatus

Tests were conducted in a conventional, singleactuator servohydraulic testing machine. The testing fixture is shown schematically in figure 2. The figure shows

an edge view of the specimen mounted in the fixture.

Loads were transmitted into the fixture through pinclevis connections at the top and bottom grips. The membrane stresses in the specimen were set by controlling the

axial load through the pins, and the bending stresses in

the specimen were set by varying the eccentricity

between the plane of the specimen and the loading line

through the pin. A plate (forcing plate) that connected to

the grip and extended almost to the test section was used

to force the highest bending stresses to occur in the sheet

at the test section. The surface of the forcing plate that

touched the specimen was coated with Teflon 1 and

lubricated with a light grease except in the gripping area.

The spring-loaded roller clamp shown near the test

1Trademark of E. I. duPont deNemours Company.
sectionalsoservedtolocalizethebendingatthetestsection.Thesprings(restrainingsprings)shownattachedto

theforcingplateandanexternalsupportwereusedto

ensurethat the outer fiber strains in the specimen would

vary monotonically with load (discussed further in the

following section). Sliding supports at the top and bottom grips prevented side loads from being applied to the

load cell or testing machine actuator.

desired alignment and ratio of bending to membrane

strains were being attained. Initial setup to achieve a particular strain ratio was based on a calibration curve made

with the unnotched specimen. Even so, some adjustments

to the test fixture spacers were required in some cases to

achieve desired results. Care was taken to ensure that

maximum outer fiber strains experienced in test setup did

not exceed the test strains.

Test Procedures

All fatigue crack growth tests were constant-load

amplitude tests that had an applied load ratio (minimum/

maximum) of 0.02. Therefore, the membrane stress ratio

was also controlled to remain at 0.02 throughout the test.

Because the bending was induced by the applied load,

the bending and membrane stresses were always in phase

(minima and maxima occurring at the same time), but the

bending stresses could not be actively controlled during

the test. Instead, the test was set up so that the bending

displacements remained constant during the test. Measurements confirmed that the bending displacement was

not a function of the specimen bending stiffness and that

the bending displacement remained constant as the crack

grew during the tests.

Before any crack growth tests were run, an

unnotched specimen with five pairs (gages on front and

back surfaces at same width location) of strain gages

spaced across the width at the test section was mounted

and loaded to typical test levels. Measured strains confirmed that the strain distribution across the width was

uniform and that the membrane strains were consistent

with the material modulus and loading level. Checks also

were made to confirm that there were no significant

dynamic effects on the strains at the test cycling frequency of 2 Hz.

Each test was set up with a pair of front and back

strain gages located at each edge of the specimen at the

test section. The gages were used to confirm proper

alignment and to determine the ratio of bending to membrane strains. The procedure for each test was as follows:

1. The specimen assembly (specimen and grips) was

installed in the machine, and the specimen was held in an

unstressed, vertical position by an additional fixture until

the restraining springs were attached to the forcing

plates. The restraining springs resisted any movement of

the forcing plates.

2. With the springs in place, the additional fixture

was removed and the test minimum load was applied to

keep the loading pins in contact with the clevises. The

strain gages were zeroed at this condition.

3. Load was applied in increments, and the strains

were measured at each step to determine whether the

The variation of strain with load at the outer fibers

was not linear, but it was monotonic. A typical example

is shown in figure 3 for a test with a ratio of bending to

membrane strain of 1.50. Because the bending strain did

not vary linearly with load, the ratio of bending to membrane strains also varied during the loading cycle. The

tests were set up so that the desired ratio was achieved at

the maximum load in the cycle, and because the strain

gages were zeroed at the minimum load in the cycle, the

ratio of the range in bending strain to the range in membrane strain was the same as the instantaneous value at

maximum load.

During the crack growth tests, crack length measurements were made optically with micrometer slides and

60X microscopes. Crack lengths (four locations) and

cycles were recorded at approximately every 0.020 in. of

growth at each crack tip.

Tests were conducted at several maximum load levels in order to cover a reasonably large range in crack

growth rates for each strain ratio and material thickness.

Test parameters for each test are listed in table 1.

Results and Discussion

Results for 0.040-In.-Thick 2024-T3 Alclad Sheet

Tests were conducted with B/M of 0, 0.75, and 1.50.

The tests without bending (B/M = 0) showed symmetrical crack growth about the specimen longitudinal centerline and the specimen midthickness. In tests with

bending, the cracks were symmetrical about the specimen longitudinal centerline, but the cracks did not grow

symmetrically about the specimen midthickness. The differences in crack half-length at the two surfaces (normalized by the specimen thickness) are shown in figure 4

plotted against the crack half-length on the high-strain

surface. The results for B/M = 0.75 and for B/M = 1.50

are shown in figures 4(a) and 4(b), respectively. The

plotted crack half-lengths are the averages of the two

lengths measured from the specimen longitudinal centerline on each surface. The cracks started growing on the

high-strain surface first and grew for a time as partthrough cracks, such that the largest differences in length
Table 1. Fatigue Crack Growth Tests and Test Parameters

[Membrane stress ratio = 0.02; cyclic frequency = 2 Hz; and air at room temperature]

Bending to Test maximum Test maximum

membrane strain load, membrane stress, Number of

ratio Ib ksi tests

0.040-in.-thick 2024-T3 alclad sheet

0

0

0

0

0

0.75

0.75

1.50

1.50

700

800

1000

1200

1600

800

1200

800

1200

5.8

6.7

8.3

10.0

13.3

6.7

10.0

6.7

10.0

0.090-in.-thick 2024-T3 bare sheet

0

0

0

0.75

0.75

0.75

1.50

1.50

1.50

1.50

18_

24_

31_

18_

24_

31_

1450

18_

31_

6.7

8.9

11.5

6.7

8.9

11.5

5.4

6.7

8.9

11.5

occurred at the start of the tests. After the cracks started

growing at the low-strain surface, the cracks at that surface tended to grow faster than those at the high-strain

surface, and the length difference between the surfaces

gradually decreased (but not to zero) as the cracks grew

longer. The tests at B/M = 1.50 always showed greater

length differences at a given crack length and test membrane stress than did the tests at B/M = 0.75.

The crack growth rate results for B/M = 0.75 and

B/M = 1.50 are shown in figures 5 and 6, respectively.

The results for B/M = 0 are also plotted in each figure for

comparison. The results are shown as plots of crack

growth rate against stress intensity factor range (AK),

where (1) results are shown only for through cracks,

(2) the crack half-length used in computing rates and

stress intensity factors was the average of crack lengths

measured on both surfaces at both crack fronts (four halflength measurements), (3) rates were calculated with the

secant method of ASTM Standard E647 (ref. 3), (4) only

the membrane stresses were used to calculate AK, and

(5) AK was calculated with the following expression

given in ASTM E647:

AK = AP/B_(r_o_/2W) sec(_ot/2) (1)

where t_ = 2a/W, a is the crack half-length, W is the specimen width, AP is the cyclic load range, and B is the

specimen thickness.

The intent of plotting the results in this manner was

to illustrate the increase in average crack growth rates

that could be caused by the addition of cyclic bending

stresses to a cyclic membrane stress test.

The results for B/M = 0.75 in figure 5 show that the

addition of bending stresses caused some increase in rate

at the lower AK levels, but not at higher AK values.

There was very little effect at values of AK greater than

10 ksi-in 1/2. The results for B/M = 1.5 in figure 6 show

the same trends as results for B/M = 0.75, but the

increase in rate caused by bending was somewhat larger

at the low AK values and persisted to a higher AK value

(about 13 ksi-inl/2).

Although the addition of bending did not cause large

differences in crack growth rate, the bending did cause

shorter overall test lives. This result is shown in figure 7,

where the life ratios (life with bending/life without bending) are plotted. Two life ratios are plotted for each test

based on (1) cycles to start and grow a crack from the

notch to a half-length of 0.7 in. and (2) cycles to grow a

through crack from 0.5 to 0.7 in. in half-length. All of the

ratios are less than one, indicating an effect of the bending, but only the test at B/M = 1.50 at the low membrane

stress showed a substantial reduction in life. In that test,

life (initiation and growth to half-length of 0.7 in.) with

bending was about one-half that for the test without

bending. Comparison of the two life ratios plotted for

that test indicates that the bending had the most effect on

initiation and early growth of the cracks and had less

effect on the growth of the long through-thickness

cracks.

3
Results for 0.090-1n.-Thick 2024-T3 Bare Sheet

Tests were conducted with B/M ratios of 0, 0.75, and

1.50. For tests with bending, the differences in crack

length on the two surfaces were recorded and analyzed in

the same manner as was done for the 0.040-in.-thick

material. The results for B/M = 0.75 and for B/M = 1.50

are shown in figures 8(a) and 8(b), respectively. The

trends in the results for the 0.090-in.-thick material were

similar to those observed for the 0.040-in.-thick material,

but the normalized length differences observed for the

thicker material were always greater at a given crack

length and membrane stress than was observed in the

thinner material. For example, tests with B/M = 1.50 on

the thin material showed a maximum length difference of

about 1.5 sheet thicknesses early in the test, whereas the

thicker material showed a difference of about 3.0 thicknesses. Also, in the thicker material, there was a more

distinct trend for the length differences during early

growth to be a function of test maximum membrane

stress. Tests with a lower membrane stress sustained

longer part-through cracks before crack growth started

on the low-strain surface. The dependence of the crack

length differences on membrane stress and the magnitude

of the crack length differences decreased as the cracks

grew longer. The difference in crack length at the end of

a B/M -- 1.50 test was typically about 1.0 thickness.

The crack growth rate results for B/M = 0.75 and

B/M = 1.5 are shown in figures 9 and 10, respectively.

The procedures for analyzing and plotting the data are

the same as those described above for the 0.040-in.-thick

material. The results for B/M = 0.75 in figure 9 show the

same trends that were observed for the thinner material

for both B/M ratios. That is, the addition of the bending

stresses caused somewhat higher rates at the lower AK

values, but at higher AK values, the rates became the

same as for the no-bending case. For the thicker material,

the increase in rates was greater and the difference

between the bending and no-bending cases persisted to a

higher AK than was observed for the thinner material.

The results for B/M = 1.50 in figure 10 show a different behavior than that observed in the other tests.

Early in the tests, when there was a large difference in

crack length at the two surfaces, the tests with bending

showed a much larger growth rate than did the tests without bending. This difference was largely caused by the

very rapid growth on the low-strain surface just after the

crack had started growing on that surface. However, even

at long crack lengths after the length difference between

the surfaces had stopped changing rapidly, the growth

rates of the tests with bending were about twice the rates

of the no-bending tests. The difference in growth rates

persisted over the entire AK range of the data.

As would be expected from the crack growth rate

data, the reduction in test lives that resulted from the

addition of bending was greater in the 0.090-in. material

than in the 0.040-in. material. The life ratios for the tests

on the 0.090-in. material are shown in figure 11 in the

same way they were shown for the 0.040-in. material in

figure 7. As for the thin material, the greatest reduction in

life occurred in the test with B/M = 1.5 and the lowest

membrane stress level. For this test, the life (initiation

and growth to half-length of 0.7 in.) with bending was

only about one-third that of the test without bending. The

results in figure I 1 also show that the bending had more

effect on the initiation and initial growth than it did on

the growth of long cracks. For the B/M = 1.5 tests, even

the growth lives of long through-cracks were reduced

significantly by the bending. The other trend evident in

figure 11 is that the bending effects were more pronounced in the tests with lower membrane stresses.

Conclusions

An experimental study was conducted to determine

the effects of combined bending and membrane cyclic

stresses on the fatigue crack growth behavior of

aluminum sheet material. The materials used in the tests

were 0.040-in.-thick 2024-T3 alclad and 0.090-in.-thick

2024-T3 bare sheet. In the tests, the membrane stresses

were applied as a constant amplitude loading at a stress

ratio of 0.02, and the bending stresses were applied as a

constant amplitude deflection in phase with the membrane stresses. Tests were conducted at ratios of bending

to membrane stresses (B/M) of 0, 0.75, and 1.50. The following conclusions were drawn from the results of the

tests:

1. The general trends of the results were for larger

effects of bending for the higher B/M, the lower membrane stresses, and the thicker material.

2. The effect of adding cyclic bending stresses to a

test with cyclic membrane stresses was always to reduce

test lives. For the most extreme case, the life of the test

with bending was only one-third that of the test without

bending. The bending had the most effect on the initiation and early growth of cracks and had less effect on the

growth of long through-thickness cracks.

3. The addition of cyclic bending had very little

effect on the growth rates of through-thickness cracks in

the thin material over most of the growth rate range

investigated. Some increase in rates was evident at the

lower end of the growth rate range.

4. The bending significantly increased the growth

rates of through-thickness cracks in tests of the thick
material at B/M = 1.5. The growth rates were increased

by about a factor of two at long crack lengths.

5. The thick material sustained long part-through

cracks early in the tests. For the most extreme case, the

crack was about 0.3 in. long on one surface before

growth started on the other surface.

NASA Langley Research Center

Hampton, VA 23681-2199

June 12, 1997

References

1. Phillips, Edward P.; and Britt, Vicki O.: Measurements of

Fuselage Skin Strains and Displacements Near a Longitudinal

Lap Joint in a Pressurized Aircraft. NASA TM-104163, 1991.

2. Jeong, David Y.; Roach, Dennis P.; Canha, Joseph V.; Brewer,

John C.; and Flournoy, Thomas H.: Strain Fields in Boeing

737 Fuselage Lap Splices Field and Laboratory Measurements With Analytical Correlations. DOT-VNTSCFAA-95-10, U. S. Dept. Transp., June 1995.

3. Metals Test Methods and Analytical Standards. Volume 03.01

of the 1995 Annual Book of ASTM Standards, ASTM, 1995,

pp. 578-614.
11.00

It

Sheet rolling

direction

Gripped

al'efl

z- -x

/ \

\ /

Gripped

area

3.000

Notch detail

(notch centered

on centerlines)

;¢ k_O0_Ora_ius--_

at ends of slot 0.020

3.00

2.50

Figure 1. Specimen configuration; dimensions are in inches.
Pin

Grip

P Specimen centerline

__.._..-.

f Grip bolt

_-- Lubricated Teflon surface

/ V (to bottom edge of grip)

_S Forcing plate

_- Restraining spring

Spring-loaded roller clamp

------- Test section

.loaded roller clamp

Restraining spring

I

P

Figure 2. Schematic of testing fixture used to apply combined bending and membrane stresses (edge view).

7
1400

.=.

o

,b

0"2

1200

1000

800

60O

4O0

200

0

-200

-4OO

0

Low-strain surface

- _ 0 0 0

i I i I i I L I

400 800 1200 1600

Load, lb

Figure 3. Variation of strain with load in a test with a ratio of bending to membrane strain of 1.50.

8
4

h5

_9

N

O

Z

2

1-

4 m

Test maximum

stress, ksi

O 6.7

A 10.0

.2 .4 .6

Crack length on high-strain surface, in.

(a) B/M = 0.75.

I i I

.8 1.0

_9 3

2

O

Z i

Test maximum

stress, ksi

O 6.7

A 10.0

i I

0 1.0

t I i I i i t I

.2 .4 .6 .8

Crack length on high-strain surface, in.

(b) B/M = 1.50.

Figure 4. Differences in crack length on two surfaces of 0.040-in.-thick specimens. Differences normalized by specimen

thickness.
10-4 _

_ x 0

_ o 0.75

/x 0.75

¢d

10 .5

_ 10--6

10-7 L

100

B/M No. of tests

6

1

1

0 x

xx

t I I I I I tl i J I I _ I i iI

102 1o2

Membrane ilK, ksi-in 1/2

Figure 5. Fatigue crack growth rate data from tests of 0.040-in.-thick specimens with bending to membrane stress ratios

of 0 and 0.75.

10-5

_10 _

20-4 -

B/M No. of tests

× 0 6

o !.50 1

zx i.50 1

[] 1.50 1

x

O

?

x'x

x _

10-7 I t J I t t I II t i _ t I I I tl

10 0 101 102

Membrane AK, ksi-in 1/2

Figure 6. Fatigue crack growth rate data from tests of 0.040-in.-thick specimens with bending to membrane stress ratios

of 0 and 1.50.

10
._=

t-,

O

_3

,...,

6

,.d

1,0 I

0

6

[]

........ ZZZ_ _

B/M Growth interval

O 0.75 0.5 to 0.7 in.

• 0.75 0.15 to 0.7 in.

[] 1.50 0.5 to0.7 in.

• 1.50 0.15 to 0.7 in.

I I I I

7 8 9 10

Test maximum membrane stress, ksi

Figure 7. Effect of bending on lives of 0.040-in.-thick specimens.

I

11

11
4 -

8

N

O

Z

4 m

Test maximum

stress, ksi

O 6.7

[] 8.9

zx 11.5

I i I J I I I

.2 .4 .6 .8

Crack length on high-strain surface, in.

(a) B/M = 0.75.

I

1.0

3

2

O

Z 1

j i I

0 1.0

Test maximum

stress, ksi

0 5.4

O 6.7

[] 8.9

A

I i t I I I 1

.2 .4 .6 .8

Crack length on high-strain surface, in.

(b) B/M = 1.50.

Figure 8. Differences in crack length on two surfaces of 0.090-in.-thick specimens. Differences normalized by specimen

thickness.

12
g

e_

o

L_

10-4 _

10-5

10-6

B/M No. of tests

× 0 3

o 0.75 1

z_ 0.75 1

n 0.75 1

¢r 0.75 1

/1 x

O

/x x

x

x

10-7 J L I I J I I il t I I i I i i _1

100 101 102

Membrane &K, ksi-in 1/2

Figure 9. Fatigue crack growth rate data from tests of 0.090-in.-thick specimens with bending to membrane stress ratios

of 0 and 0.75.

"_ 10-5

-6

10-4 -

B/M No. of tests

× 0 3

o 1.50 1

1.50 1

[] ! .50 1

_r 1.50 1

jS

¢

x

x

x X

10-7 I t I I I I I II L I I I i i i Jl

100 101 102

Membrane z_tK, ksi-in !/2

Figure 10. Fatigue crack growth rate data from tests of 0.090-in.-thick specimens with bending to membrane stress

ratios of 0 and 1.50.

13
¢.

.,=

_5

1.0 --

.8

.6

.4

.2

06

G ................. --(3,---

0- -D

[] ---El .....

J

m

B/M

O 0.75

• 0.75

[] 1.50

• 1.50

I I I

7 8 9

Growth interval

0.5 to 0.7 in.

0.15 to 0.7 in.

0.5 to 0.7 in.

0.15 to 0.7 in.

I I

10 11

Test maximum membrane stress, ksi

Figure 11. Effect of bending on lives of 0.090-in.-thick specimens.

I

12

14

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

October 1997 Technical Memorandum

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

An Experimental Study of Fatigue Crack Growth in Aluminum Sheet

Subjected to Combined Bending and Membrane Stresses WU 538-02-10-01

5. AUTHOR(S)

Edward P. Phillips

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

8. PERFORMING ORGANIZATION

REPORT NUMBER

L-17617

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4784

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13. ABSTRACT (Maximum 200 words)

An experimental study was conducted to determine the effects of combined bending and membrane cyclic stresses

on the fatigue crack growth behavior of aluminum sheet material. The materials used in the tests were 0.040-in.-

thick 2024-T3 alclad and 0.090-in.-thick 2024-T3 bare sheet. In the tests, the membrane stresses were applied as a

constant amplitude loading at a stress ratio (minimum to maximum stress) of 0.02, and the bending stresses were

applied as a constant amplitude deflection in phase with the membrane stresses. Tests were conducted at ratios of

bending to membrane stresses (B/M) of 0, 0.75, and 1.50. The general trends of the results were for larger effects of

bending for the higher B/M ratios, the lower membrane stresses, and the thicker material. The addition of cyclic

bending stresses to a test with cyclic membrane stresses had only a small effect on the growth rates of throughthickness cracks in the thin material, but had a significant effect on the crack growth rates of through-thickness

cracks in the thick material. Adding bending stresses to a test had the most effect on the initiation and early growth

of cracks and had less effect on the growth of long through-thickness cracks.

14. SUBJECT TERMS

Material fatigue; Metal fatigue; Crack propagation; Fatigue tests; Combined stress;

Bending; Axial stress; Aluminum alloys

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