residual stress at cold expanded holes

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2003 Lockheed Martin Corporation, All Rights Reserved.

Experimental and Analytical Studies of Residual Stress Field Evolution

and Fatigue Crack Growth at Cold Expanded Holes

Dale L. Ball

Mark T. Doerfler

Lockheed Martin Aeronautics Company1 Lockheed Blvd.

Fort Worth TX 76108

Ref: Ball, D.L. and Doerfler, M.T., Experimental and Analytical Studies of Residual Stress Field

Evolution and Fatigue Crack Growth at Cold Expanded Holes, 2003 USAF ASIP Conference, Savannah

GA, Dec. 2003.

Abstract

The process of cold expanding holes in metallic components in order to extend their

fatigue life is now widely used throughout the aircraft industry. Numerous experimentaland analytical programs over the past three decades have not only demonstrated how

effective the process can be at extending fatigue life, but have also shed considerablelight on the mechanics of both the cold expansion process and the growth of fatigue

cracks in the resulting residual stress fields. In spite of the progress that has been made,

however, there are a number of hole-cold-expansion related phenomena that have notbeen well characterized experimentally. In addition, the fatigue and fracture analysis

community has yet to adopt a standard, mechanics-based method for modeling the

growth of fatigue cracks at cold worked holes. This document describes recent

experimental work aimed at 1) evaluating two new residual stress measurementtechniques and 2) measuring the effects of compression loading on the effectivity of cold

work induced life extension. Mechanics-based models, both for the formation of residual

stress fields (due to the cold expansion process) and for the subsequent evolution of thesestress fields (due to service loading, particularly compression overloading) are discussed.

A method for incorporating the results from these models into a fatigue crack growth

analysis is described and then applied to the cold expanded hole problem. Finally, resultsfrom these models are compared with experimental data.

Background

The hole cold working process primarily involves the radial expansion of the hole by

drawing an oversized, tapered mandrel through it. In the split-sleeve process [1], a


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lubricated sleeve is placed on the mandrel prior to drawing the mandrel through the hole.

This is done both to protect the hole bore surface and to reduce the force required to pullthe mandrel. It has the added benefit of minimizing the out-of-plane deformation caused

by transverse motion of the mandrel. The process is designed such that the major

diameter of the mandrel plus the sleeve thickness is sufficiently larger than the initial

diameter of the hole so as to cause permanent plastic deformation around the hole whenthe mandrel is pulled through. At the completion of the expansion process (i.e., after the

mandrel and sleeve have been removed), the elastic material surrounding the hole and the

plastically deformed region attempts to return to its original shape. In so doing, itcompresses the annulus of plastically deformed material around the perimeter of the hole.

It is this force exerted on the plastic annulus that produces a compressive residual stress

field around the hole. It is very important to note that this is a self equilibrating stressfield the compressive residual stresses in the plastic annulus are balanced by tensile

residual stresses in the surrounding elastic body. It is also very important to note that if

there is no surrounding elastic material, then these residual stresses will not be produced.Or if there is insufficient surrounding elastic material, then their magnitude will be

reduced. The compressive residual stresses at the hole perimeter reduce the local stressesat this location when the component is subjected to remote tension. It is this reduction in

local stresses that can induce significant increases in fatigue crack growth life.

Over the past thirty years a variety of experimental programs have been conducted by

LM Aero which have either addressed hole cold working exclusively, or have at leastincluded the process as one of the structural aspects being studied. The majority of these

have been funded by specific aircraft programs and thus have tended to focus on

verification of life improvement ratios for the geometries, materials and loadings specificto each program [2-3] [4-12] [13-14]. In addition, a small number of research studies

have been conducted in an effort to address the mechanics of cold expansion and of crackgrowth in residual stress fields. These have been designed to be more generally

applicable and hence have been based on generic conditions [15-18]. More recently,

LM Aero has conducted programs aimed at the development of analytical tools capableof predicting fatigue life extension as a function of significant cold work process and

control point specific geometric, material and loading parameters [19-23].

In the current study, a series of experiments aimed at characterizing both the initial, cold-work-induced residual stress field and the subsequent, overload-modified stress fields

were conducted. Two emerging technologies which are able to detect cold expansion

effects and which may be able to characterize cold-work-induced residual stress or strainprofiles in aluminum were investigated. One was the photon induced positron

annihilation technique (PIPA); developed, patented and marketed by Positron Systems,

Inc., Boise ID (PSI) [24], and the other was the meandering winding magnetometer(MWM) method; developed, patented and marketed by JENTEK Sensors, Inc., Waltham

MA (JSI) [25]. All of the specimen preparation, hole cold expansion and fatigue testing

were performed by Fatigue Technology Inc., Seattle WA (FTI).

This study also addressed the further development of fatigue crack growth models that

have been under development at LM Aero for a number of years. These models use


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closed form calculated residual stress profiles as the initial condition from which a cyclic

elastic-plastic response analysis is conducted. In this way both cold work processinduced and service loading induced features of the response / residual stress profiles are

incorporated in the analysis. Stress intensity factors are calculated based on these cycle-

by-cycle results using new Greens functions which were developed during this program.

Once the cyclic SIF values are available, crack growth rates are found using standardda/dN vs. K relationships and crack growth life is found by repeating these calculationsand incrementing the crack size until failure occurs.

Experimental Program

The current experimental program was designed as an extension of an earlier LM Aero

program [17] [19]; the same material, hole geometry and expansion levels were used.The program consisted of two parts 1) evaluation of new non-destructive evaluation

(NDE) techniques for the detection of cold expansion effects and possibly the

characterization of residual stress or strain fields, and 2) generation of fatigue crack

growth data for cracks at cold worked holes.

Detection of Cold-Expansion Effect

Photon induced positron annihilation is an NDE technique that can be used to detect

relative changes in microstructure due to plastic deformation and/or fatigue [24]. The

technique uses a linear accelerator to inject high energy photons either directly into thematerial to be inspected, or into a positron source material (PSM). These photons have

sufficient energy to knock a neutron out of the nuclei of a small number of atoms in the

target. It is the decay of the resulting isotopes that produces the positrons. When the

target is the actual part to be inspected, positrons are produced in the bulk material. This

process is referred to as photon induced positron annihilation (PIPA). When the target isa PSM, the PSM is placed in contact with the part to be inspected and the positrons then

migrate from the PSM into the surface of the part. This process is referred to asdistributed source positron annihilation (DSPA). In both cases, the positrons, because of

their positive charge, migrate to vacancies / dislocations in the crystal lattice. Eventually,

they annihilate with low momentum electrons, and the gamma spectrometry response ofthe annihilation is measured. See Fig. 1. For the aluminum plates used in the current

program, the PIPA measured response was indicative of the bulk (through the thickness)

material state, while for DSPA, the response indicated surface condition only (to a depthof 1 to 2 mm).

Relative differences in dislocation density can be quantified because the energy of theannihilation gamma radiation is different in a damaged area than in a non-damaged area(511 keV versus all other energy levels see Fig. 2). The measured response is reported

in terms of an S (or shaping) parameter. In the current program, differences in

dislocation density (and therefore S parameter) were assumed to be the result ofdifferences in degree of plastic deformation alone. However, the measured response is

apparently affected by lattice dilatation as well. At present, it is not possible todistinguish what part of the signal is due to which effect.


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Two 2124-T851 plate specimens, each with nine holes, were manufactured and processedby FTI. The holes were cold worked to expansion levels of 0% (no cold work), 2.1%,

3.1%, 3.8%, 4.2%, and 5.2% per the standard split-sleeve process [26] [27]. Each hole

was reamed after cold expansion. Note that three holes in each plate were cold worked to

the same level.

Figure 1. Photon induced positron annihilation process,

Positron Systems, Inc. developed and patented technology [24].

Figure 2. S parameter analysis,

Positron Systems, Inc. developed and patented technology [24].


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S parameter measurements were taken at each of the holes in both plates using the PIPA

process. As shown in Fig. 3, the data indicate that there is a well defined relationshipbetween the expansion level and PIPA measured S parameter. As the expansion level

increases, the amount of plastic deformation increases and the measured S parameter

increases.

PIPA (bulk) S-Parameter

vs. Cold Expansion Level in

2124-T851 Aluminum Plate

0.546

0.548

0.550

0.552

0.554

0 1 2 3 4 5 6

Applied expansion (%)

PIPAS-parameter

Figure 3. PIPA S-parameter results

volumetric measurements across full range of cold expansion.

Similar measurements were taken using the DSPA process. See Fig. 4. It was suggested

that the high S parameter result at 3.14% expansion was due to PSM positioning, and thatprocess improvements should minimize such variation. The majority of the surface

measurements were taken inside the hole, but some measurements were taken on the

surface of the plate. The larger range in S parameter values for the latter measurementsindicate the potential for greater sensitivity when measuring on the surface than when

measuring inside the hole.

The second NDE technology investigated during this study was the scanning meandering

winding magnetometer array (MWM-Array) eddy current sensor with a GridStation

system [25]. This technology is also capable of measuring plastic deformation. JENTEKused high-resolution imaging MWM-Arrays (see Fig. 5) to scan both sides of the plate

specimens. The MWM-Arrays provide directional measurements of electricalconductivity and as shown in separate tests, are sensitive to changes caused by cold work.

Scans were performed both parallel to the rolling direction (i.e. longitudinal graindirection) and perpendicular to the rolling direction. Initial measurements were taken at

multiple frequencies while subsequent measurements utilized only two frequencies inorder to obtain results more quickly.


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DSPA (surface) S-Parameter

vs. Cold Expansion Level in


0.540

0.542

0.544

0.546

0.548

0.550

0 1 2 3 4 5 6

Applied expansion (%)

DSPAS-Parame

ter DSPA base metal

DSPA inside hole

DSPA adjacent to hole

Figure 4. DSPA S-parameter results

near-surface measurements across full range of cold expansion.

Figure 5. Photograph and schematic of thirty-seven element FA28 MWM-Array sensor,

JENTEK Sensors, Inc. developed and patented technology [25].


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Results of the MWM-Array scanning of the plate specimens are presented in Fig. 6. The

MWM Feature is a computed parameter that was calculated at JENTEK by averagingthe signatures of three holes cold worked to the same expansion level. The two parallel

scans indicate that the technique has the ability to distinguish between different levels of

cold expansion. It was not clear why the perpendicular scan did not indicate a similar

trend; no difference would be expected between parallel and perpendicular scans for anisotropic material with no significant residual stresses prior to cold work and uniform

plastic deformation. It is likely that the actual material had some degree of anisotropy

caused by prior processing, e.g., rolling, and may have had significantly varying residualstresses prior to cold work. Further investigation will be required to understand whether

these differences could have produced variations in plastic deformation around a hole that

would explain the observed trends.

MWM Feature vs

Cold Expansion Level in


0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 1 2 3 4 5 6

Applied Expansion (%)

MWMFea

ture

scan parallel to grain, 1

scan parallel to grain, 2

scan perpendicular to grain

Figure 6. MWM-Array scanning results cold worked holes.

Measurement of Initial, Cold-Work-induced Residual Strain Profiles

In previous studies [17] [18], direct measurement of cold-work-induced residual stress

profiles in 2000 series aluminums proved to be problematic. Historically, the method of

choice for such measurements has been X-ray diffraction, but for the aluminum alloys of

interest for the F-16, the scatter introduced by grain size and texturing effects has made it

impossible to obtain precise, quantitative information. The PIPA and DSPA technologieswere evaluated during this test program to determine if better results could be obtained.

The test coupons required for this portion of test program were manufactured by FTI;

these specimens were also used during the fatigue crack growth portion of the program.

The specimen consisted of a dog bone design with a single 5/16 diameter hole in thecenter, see Fig. 7. The hole in each specimen was cold worked to a nominal 4.0%

applied expansion level. Table 1 lists test specimen information.


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As listed in Table 1, eight specimens were subjected to PIPA and DSPA measurementsafter being cold worked. The hole in every specimen was subjected to the same level of

expansion (4% nominal). DSPA measurements were performed inside the hole and at

various distances from the hole on the surface of the specimen. A reference S parameter

measurement was taken on undeformed material away from the hole; the measuredreference value (average of two readings) was 0.5473. For each of the DSPA readings

either in or in the vicinity of the hole, the difference between the measured S-parameter

and the reference S-parameter was normalized with respect to the reference S-parameter

CL (sym)

CL (sym)

CL (sym)

CL (sym)

0.125 (T/2)0.125 (T/2)

0.250

11.0

5.5003.0 3.00

1.500

(W/2)

1.500(W/2)

1.750

3.500

Grain Direction

1.0

Ref

R = 4.06(4 plc)

(no mismatch in runout typ.)

R = 2.125 (4 plc.)

(no mismatch in runout typ.)

0.500

Sleeve Gap

Figure 7. Test specimen for modified residual stress distribution testsand cyclic fatigue tests.

Table 1. Modified residual stress distribution test matrix.

SpecimenID

Coldworked?

(Cx)

PIPA/DSPA

measurement

afterCx?

Compressive

loadapplied?

PIPA/DSPA

measurement

afterload?

2A no no yes no

2B no no yes no

3A yes yes no no

3B yes yes no no4A yes yes yes yes

4B yes yes yes yes

5A yes yes yes yes

5B yes yes yes yes

7A yes yes no no

7B yes yes no no


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ref,p

ref,pp*

S

SSS

= (1)

The results of these measurements are shown in Fig 8. The readings taken on the surfaceof the plate are shown with a horizontal bar to indicate that the spatial resolution of the

reading is limited by the physical size of the PSM and by the fact that the detected

annihilations are from positrons that have diffused away from the point of introductioninto the plate. These aspects of the process place rather significant limitations on the

utility of DSPA for the quantification of strain or damageprofilesat geometric details.

Normalized DSPA S-Parameter Change

for 4% Cold Expanded Hole in

2124-T851 Al. Plate, ref Sp=0.5473

-0.010

-0.005

0.000

0.005

0.010

0 0.5 1 1.5 2 2.5 3x/R

normalizedS

-para

meter

3A

3B

4A

4B

5A

5B

7A

7B

edge of hole

surface readings, spatial resolution

approx. 0.10 in.

in-hole

readings

Figure 8. Normalized DSPA S-parameter results near-surface measurements at 4 locations in and near cold worked holes.

While it does appear that the PIPA or DSPA S-parameter may be used directly as a bulk

damage index, for cold worked hole applications it would be beneficial if a relationship

between the S-parameter and some calculable mechanical response could be found. To

this end, a 3-D (solid) FEM of the test specimen was developed and used to calculate theelastic-plastic stress-strain response at a cold worked hole. (This model will be discussed

in more detail below.) The cold expansion process was modeled by subjecting the hole

perimeter to a radial (in-plane) expansion and then release. The hole post-ream processwas then simulated by removing the appropriate thickness of material from the hole

perimeter. The calculated stresses and strains along a radial line on the plate surface,

extending from the hole center to the edge of the specimen were used to calculate thevarious plastic strain increments. Since the S-parameter is assumed to be a measure of

dislocation density and since it is not directionally dependent, it was postulated that the

equivalent plastic strain, which is a scalar quantity, could be correlated with it. Theequivalent plastic strain was calculated as


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( ) ( ) ( ) ++

2py

px

2py

px

2py

px

pe dddddd

3

2d (2)

( ) ( ) ( ) 21

2pxy

2pxy

2pxy ddd6

+++

As shown in Fig. 9, by considering only the DSPA measurements taken on the plate

surface and by plotting the results at the approximate mid-point of the measurementposition a rough correlation was found. Note that this a very preliminary finding and that

it does not account for any contribution that lattice dilatation (residual stress) may make

to the S-parameter. This could explain why the origins on the equivalent strain and S-parameter scales are offset.

4% Cw and Post Reamed Hole

2124-T851 Al. Plate

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4x/R

equ

iva

len

tp

las

tics

tra

in

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

norma

lize

dS

-parame

ter

equiv plastic strain inc

DSPA S parameter

Figure 9. Comparison between normalized DSPA S-parameter

And FE calculated equivalent plastic strain at the surface of a 4% cold worked hole.

Measurement of Overload Modified Residual Stress

The benefit of cold expansion to fatigue life is caused by the region of compressive

residual stress near the hole. This residual stress field can be altered, however, by

subsequent tensile or compressive overloads. A tensile overload can reinforce thecompressive residual, while a compressive overload can reduce or even eliminate the

residual stress. As shown in Table 1, four test specimens were subjected to acompressive overload after cold working. The -25 ksi gross stress applied to each

specimen was sufficient to cause additional yielding around the hole, and therefore the

initial residual stress distribution resulting from cold working was modified. Anti-

buckling supports were utilized during load application to ensure that buckling did not


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occur. Additional PIPA and DSPA measurements were then taken to determine if

changes in the residual stress and/or strain fields could be detected.

As shown in Fig. 10, there was a marked difference between the DSPA S-parameter

readings taken before the compression overload and those taken after. Three of the four

data sets seem to indicate an increase in S-parameter in the region between 0.5 and 1.0radii away from the hole. At present, it is not clear how these changes relate to changes

in the residual stress or strain fields; further study (more data) will be required. (Similar

results were found for bulk (PIPA) measurements at the hole.)

Normalized DSPA S-Parameter


2124-T851 Al. Plate, ref Sp=0.5473

-0.010

-0.005

0.000

0.005

0.010

0 0.5 1 1.5 2 2.5 3

x(mid)/R

norm

alizedS

-parameter

before 25 ksi compression

after 25 ksi compression

edge of hole

spatial resolution:

approx. 0.10 in.

specimen 4A



2124-T851 Al. Plate, ref Sp=0.5473

-0.010

-0.005

0.000

0.005

0.010

0 0.5 1 1.5 2 2.5 3

x(mid)/R

normalizedS

-parameter



edge of hole

spatial resolution:

approx. 0.10 in.

specimen 4B



2124-T851 Al. Plate, ref Sp=0.5473

-0.010

-0.005

0.000

0.005

0.010

0 0.5 1 1.5 2 2.5 3

x(mid)/R

normalizedS

-parameter



edge of hole

spatial resolution:

approx. 0.10 in.

specimen 5A



2124-T851 Al. Plate, ref Sp=0.5473

-0.010

-0.005

0.000

0.005

0.010

0 0.5 1 1.5 2 2.5 3

x(mid)/R

normalizedS

-parameter



edge of hole

spatial resolution:

approx. 0.10 in.

specimen 5B

Figure 10. DSPA Normalized S-parameter results

Before and after application of one 25 ksi compression stress cycle.

Constant Amplitude Fatigue Crack Growth

A series of constant amplitude fatigue crack growth tests were conducted in which the

effects of a single compression overload and of fully reversed loading on cold work life

improvement were investigated. Twelve tests were performed using specimens machinedfrom 1.75 inch thick 2124-T851 aluminum plate stock. The specimen design was the

same as that used for the modified residual stress measurement portion of this task (Fig.

7). As shown in Table 2, tests were performed with and without cold working and withand without the compression overload, allowing a number of comparisons to be made.

Half of the specimens were cold worked to a 4% nominal applied expansion per the


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standard split-sleeve process. Prior to fatigue cycling, a 0.01 inch through-thickness

EDM notch was installed in one side of each hole. All of the tests were performed byFTI and were run to failure (defined as separation into two pieces). In all tests, crack

length was measured optically at regular intervals.

Table 2. Constant amplitude fatigue crack growth test matrix,Smax=25 ksi in all cases.

SpecimenID

Coldworked?

Compressive

loadapplied?

Stressratio

1A no no 0.1

1B no no 0.1

2A no yes 0.1

2B no yes 0.1

3A yes no 0.1

3B yes no 0.1

4A yes yes 0.14B yes yes 0.1

6A no no -1.0

6B no no -1.0

7A yes no -1.0

7B yes no -1.0

Figure 11 presents a comparison of three tests performed at a stress ratio of R=0.1 (no

compression) and a maximum stress of 25 ksi. Two of the specimens were cold workedto a 4% level of applied expansion while the other one was not. The fatigue lives of the

two cold worked specimens were 5 to 7 times as long as the life of the non-cold worked

specimen.

In assessing the impact of a compressive overload, the objective of this study included

not only the attempt to characterize changes in the residual stress and strain fields at thehole, but also the evaluation of the effect on fatigue crack growth. Four of the constant

amplitude, R=0.1 test specimens were subjected to a single compressive stress cycle (-25

ksi), two cold worked and two non-cold worked. (The EDM notches described abovewere installed after application of the single compressive load).

As shown in Fig. 12, for the non-cold worked condition, application of the compressive

overload caused a slight acceleration in crack growth rate and, therefore, a slightreduction in crack growth life. However, for the specimens with cold worked holes, the

compression overload had a significant impact on fatigue life see Fig. 13. The two tests

that included the 25 ksi compressive stress (specimens 4A and 4B) had about half of thelife of the two tests that did not (3A and 3B). Test 1B is presented for comparison, and

from that result it can be seen that while the compressive load applied to specimens 4A

and 4B significantly reduced the advantage of cold expansion, it did not completelyeliminate it. The life improvement ratios dropped from 5 to 7 down to about 2.5.


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0.00

0.25

0.50

0.75

1.00

1.25

0 20,000 40,000 60,000 80,000

N (cycles)

cracklength(inch

)

1B: not coldworked

3A: coldworked

3B: coldworked

Figure 11. Constant amplitude fatigue crack growth results

effect of cold working (R=0.1).

0.00

0.25

0.50

0.75

1.00

1.25

0 2,000 4,000 6,000 8,000 10,000 12,000 14,000

N (cycles)

cracklength

(inch)

1B: no compressive load

2A: compressive load

2B: compressive load


effect of one compressive cycle on non-cold worked holes (R=0.1).

The results of the four fully-reversed (R=-1.0) fatigue tests are presented in Fig. 14.Since these tests had the same maximum stress as the R=0.1 tests but a much lower R, the

resulting fatigue lives were much shorter. The existence of the compression loading


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reduced the benefit of cold expansion. The fatigue lives of the cold worked specimens

were approximately 2 times as long as the lives of the non-cold worked specimens.

0.00

0.25

0.50

0.75

1.00

1.25

0 20,000 40,000 60,000 80,000

N (cycles)

cracklength(inch)

3A: no compressive load

3B: no compressive load4A: compressive load4B: compressive load(1B: not coldworked)


effect of one compressive cycle on cold worked holes (R=0.1).

0.00

0.25

0.50

0.75

1.00

1.25

0 2,000 4,000 6,000 8,000 10,000N (cycles)

cracklength(inch)

6A: not coldworked6B: not coldworked7A: coldworked

7B: coldworked


effect of cold working (R= -1).


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Variable Amplitude Fatigue Crack Growth

The effects of compression were also studied for variable amplitude spectrum loading.

Eight specimens were machined from 1.75 inch thick 2124-T851 aluminum plate stock

(with the same configuration as the constant amplitude tests, Fig. 7) and subjected to

either a tension only spectrum or a combined tension / compression spectrum. Half of thespecimens were cold worked to a 4% nominal applied expansion per the standard split-

sleeve process [26] [27]. Prior to fatigue cycling, a 0.01 inch EDM notch was installed in

one side of each hole. Table 3 presents the test matrix for the variable amplitude tests.

Table 3. Variable amplitude fatigue crack growth test matrix.

SpecimenID

Coldworked?

Spectrum

8A no 1

8B no 1

9A no 2

9B no 2

10A yes 1

10B yes 1

11A yes 2

11B yes 2

Spectrum 1: tensile stresses only (clipped at 0.0 ksi)Spectrum 2: tensile and compressive stresses (not clipped)

Spectrum information is presented in Fig. 15 and Table 4. The stress histories were

based on wing root bending moment for a fighter aircraft [28] modifications were madein order to include a larger number of compressive cycles. Both spectra were shifted by -

4 ksi and edit truncated at 15% of maximum spectrum stress (MSS). Spectrum 1 stressesbelow 0 ksi were then clipped. All tests were continued to failure (defined as separation

into two pieces). In all tests, crack length was measured optically at regular intervals.

The variable amplitude loading tests were initially run with MSS=30 ksi. Results from

these tests are presented in Fig. 16 where two different effects can be seen. First, cold

working (at 4% applied expansion) clearly extended the fatigue lives of the specimens the two non-cold worked specimens failed at 6,600 and 13,000 flight hours, while the

cold worked tests still contained small cracks after 20,000 flight hours. A second effect

evident from Fig. 16 is that of clipping on the fatigue lives. Two of the tests (specimens8A and 10A) were loaded with spectrum #1 that only included tensile loads (i.e., allcompressive loads had been clipped). The effect upon the cold worked specimens cannot

be clearly seen because the tests ran out, but the expected effect on the clipped tests is

clear.


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Spectrum 2 (tension and compression)

-20

-10

0

10

20

30

40

1 18 35 52 69 86 103 120 137 154 171 188 205 222 239 256 273 290 307 324 341 358 375 392

Flight

Smin&

Smax

(ksi)

Spectrum 1 (tension only)

-20

-10

0

10

20

30

40

1 18 35 52 69 86 103 120 137 154 171 188 205 222 239 256 273 290 307 324 341 358 375 392

Flight

Smin&

Smax(ksi)

Figure 15. Spectrum information variable amplitude tests (for MSS=30 ksi).

Table 4. Spectrum information (normalized) variable amplitude tests.

Spectrum 1

(tension only)

Spectrum 2

(tension and

compression)

Flights 406 Flights 406

Cycles 20,308 Cycles 22,545

Hours 500 Hours 500

SMAX 1.000 SMAX 1.000

SMIN 0.0 SMIN -0.568

SMEAN 0.117 SMEAN 0.028

SRMS 0.200 SRMS 0.225

Std. dev. 0.163 Std. dev. 0.223

Because the lives of the cold worked specimens were so long, the maximum spectrum

stress was increased to 40 ksi for the next set of tests. Fig. 17 presents results from thesetests. Results were similar to the tests with the less severe loading, although the effect of

clipping on the cold worked specimens is more clearly seen. The existence of

compressive stresses in the load history significantly reduced fatigue lives during testing.This was a result of larger stress amplitudes, and it was also likely due to modification of


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the beneficial residual stress field as fatigue cycling progressed. For both the clipped and

unclipped spectra, cold working was seen to extend fatigue lives.

0.00

0.25

0.50

0.75

1.00

0 2,500 5,000 7,500 10,000 12,500 15,000 17,500 20,000

N (flight hours)

cracklength(inch)

8A: no c/w, clipped

9A: no c/w, not clipped

10A: c/w, clipped11A: c/w, not clipped

Figure 16. Variable amplitude fatigue crack growth results

effect of cold working (MSS=30 ksi).

0.00

0.25

0.50

0.75

1.00

0 5,000 10,000 15,000 20,000 25,000

N (flight hours)

crac

kleng

th(inc

h)

8B: no c/w, clipped

9B: no c/w, not clipped

10B: c/w, clipped

11B: c/w, not clipped

Figure 17. Variable amplitude fatigue crack growth results

effect of cold working (MSS=40 ksi).


18/40

18

Model Development

One of the primary objectives of this study was to further develop selected mechanics-

based models for the growth of fatigue cracks in cold work induced residual stress fields.

The models utilize previously developed, closed form solutions for both the formation of

residual stress fields (due to the cold expansion process) and the subsequent evolution ofthese stress fields (due to service loading, particularly compression overloading). During

this study, methods for the calculation of stress intensity factors based on these stressfields using Greens functions were further developed. Finally, both the stress and SIF

models were incorporated into a fatigue crack growth analysis algorithm which was then

applied to the cold expanded hole problem.

Estimation of residual and response stress distributions

Since it is the residual strain and stress fields introduced by the cold expansion processwhich so dramatically influence crack growth life, the first step in the model development

process must be a formal treatment of these fields.

The most rigorous characterization of cold work induced residual strain and stress

distributions requires fully three-dimensional, non-linear finite element analysis (FEA).

In the current study, a 3-D solid finite element model of the open hole coupon (Fig. 18)was built. An analysis of the cold expansion process was performed (using ABAQUS

[29]) by subjecting the perimeter of the hole to a uniform, radial expansion. Note that

while the plate model was three-dimensional, the loading was two-dimensional; neitherthe mandrel nor the transverse motion of the mandrel were modeled). The plate material

was taken to be 2124-T851 aluminum with modulus of 10400 ksi, Poissons ratio of 0.33,

yield strength of 57 ksi and strain hardening exponent of 4.59. The analysis assumed

kinematic hardening with a bi-linear stress-strain curve. The calculated residual stressesalong a line from the hole to the edge of the plate, at both the plate surface and the mid-

plane, are shown in Fig. 19.

Since it is not practical to develop a detailed finite element model every time a cold

worked hole is to be analyzed, it is desirable to have a reasonably accurate and compact

closed form solution. In virtually all closed form treatments of interference fit and / orcold work, the process is treated as the two dimensional radial expansion of an

axisymmetric, thick walled cylinder. In this study, the plane stress solution of Wanlin

[30] and the plane strain solution of Wang [31], along with adaptations to account forelastic behavior of the insert (mandrel or bushing), were utilized. For the typical problem

of a hole near the edge of a plate, the geometry is taken to be that of an annulus withinner radius, ra, equal to the radius of the hole and outer radius, rb, equal to the edge

distance, thus axisymmetry may be assumed. See Fig. 20. A plane polar coordinatesystem is fixed at the center of the hole with the z-axis along the axis of the hole (i.e. in

the plate thickness direction). In both cases, only the radial displacement caused by theinsertion of an oversized elastic mandrel or bushing is considered.


19/40

19

Figure 18. ABAQUS V6.3-2 3D FEA model of dogbone specimen(xy, xz, & yz symmetry).

Residual Tangential Stress at 4% Cw Hole

3D Elastic-Plastic ABAQUS FEA

-80

-60

-40

-20

0

20

40

0 1 2 3 4 5x/R

Stres

s(ksi)

mid-plane

surface

Steel Insert

E=30000 ksi

=0.33

y =200 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y =57 ksi

n=4.59

Figure 19. Residual Tangential Stress Profiles for Open Hole

Test Coupon, Calculated Using 3D FEA.


20/40

20

rb

ra

rd

rcReverse

yield

boundary

Elastic

plastic

boundary

Figure 20. Region Around Hole at Edge of PlateModeled As Thick Walled Cylinder.

Analytically, the cold working procedure is treated as a two step process. The first step

(loading) is the radial expansion corresponding to the insertion of the mandrel. As the

displacement at the mandrel/plate interface (ua) increases, an annulus of plasticallydeformed material develops around the perimeter of the hole. The outer radius of this

annulus (the elastic-plastic boundary), rc, continues to increase as ua is increased. The

second step (unloading) is the radial contraction corresponding to the removal of themandrel. For both the plane stress and plane strain solutions, a kinematic hardening rule

is assumed. (The stress at which plastic flow begins in compression is dependent on the

prior tension flow stress, i.e. the Bauschinger effect [32].) During unloading, a second

annulus will form around the hole in which the plate material experiences reversedyielding; that is yielding in compression. The radial distance to this second elastic-plastic

boundary is rd. The plane stress solution provides a better representation of the state ofaffairs at the surface than the plane strain solution does, particularly in so far as

calculated strains are concerned. This is of vital importance since for most experimental

techniques it is surface strain that is the measured quantity; residual stresses are theninferred. However, in the interior of the plate, plane strain conditions may develop,

particularly for thick plates. A detailed presentation of these solutions, along with a

discussion of their implementation in software is given in [21].

In reference [21], the closed form solutions were evaluated by comparing calculated

residual stress profiles with experimental and finite element results. As indicated earlier,because of grain size and texturing effects, only qualitative agreement was achieved

between the various models and the XRD data. In the current study, the closed form

results were again compared with finite element data. As shown in Fig. 21, the closed

form results for the open hole test coupon compare very well with the average of thesurface and mid-plane results from the 3D FEA.


21/40

21

Now, if the fatigue loading on a component with a cold worked hole is sufficiently

benign, then the cyclic response will be predominantly elastic. Under these conditions,the total response may be found simply by superimposing the residual stress distribution

with the applied (cyclic) stress distributions. In an elastic analysis, it is assumed that the

cold work induced residual stress profile is not altered by subsequent loading. However,

for nominal or severe loading, it is often the case that service loads will cause repeatedplastic deformation, which in turn will significantly alter the residual stresses. Under

these conditions, some form of cyclic plasticity analysis is required in which the initial

residual stress and strain profiles define the initial condition from which the cyclic,elastic-plastic response calculations are made.

Residual Tangentia l Stress at 4% Cw Hole

-80

-60

-40

-20

0

20

40

0 1 2 3 4 5x/R

Stress(ksi)

2D EP closed form soln.

3D EP FEA, avg of surface and mid-plane results

Steel Insert

E=30000 ksi

=0.33

y =200 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y =57 ksi

n=4.59

Figure 21. Comparison of Closed Form vs. Finite Element CalculatedTangential Residual Stress Fields due to the 4% Cold Expansion of a

0.284 inch Hole in a 3.0 inch Wide 2124-T851 Aluminum Plate.

In the current study, the approximate elastic-plastic response algorithm developed in [33]

was utilized. In this approach, the response stress and strain distributions are calculatedat each load point using generalized forms of either Neubers rule [34] or Glinkas

equivalent strain energy density method [35] [36] to estimate the response stresses and

strains. The analysis is based on the equivalent stress, which is written in terms of thethree components of the principal stress and back stress. With this formulation, both

kinematic hardening and the so called memory effect are captured in the analysis. The

elastic-plastic response algorithm utilizes the material cyclic stress-strain curve [37] [38].For the material studied in this program, 2124-T851 aluminum plate, the cyclic stress-


22/40

22

strain data and corresponding Ramberg-Osgood equation were given in [39]. These data

are shown in Fig. 22.

The importance of the inclusion of non-linear response was demonstrated by analyzing

the test coupons that were subjected to a 25 ksi compression overload after cold working.

As shown in Fig. 23, an elastic analysis of the response (i.e. superposition of residual andapplied stress distributions), clearly does not produce realistic results, where as the

approximate elastic-plastic analysis does. As shown in Fig. 23a, when the -25 ksi load is

applied, significant reverse yielding occurs at the side of the hole. This is evidenced bythe fact the magnitude of the elastic-plastic response is so much lower than that of the

elastic response in the vicinity of the hole. When the specimen is unloaded, we find that

the reverse yielding has removed much of the beneficial, compressive residual stress.See Fig. 23b. And when subsequent tension loading is applied, the response distribution

is clearly different than it would have been had the compression overload not been

applied, Fig. 23c. When the material response is non-linear, the stress distribution at eachload point is dependent on the prior load history.


Longitudinal, Lab Air

0

20

40

60

80

0 0.005 0.01 0.015 0.02 0.025

true strain

trues

tress

(ksi)

data

equation

Ramberg-Osgood Equation:

modulus: E=10400 ksiflow stress: o=45 ksi

coefficient: =5.277e-4

exponent: n=11.358

Figure 22. Cyclic Stress-Strain Data and Corresponding Ramberg-Osgood

Equation for 2124-T851 Aluminum Plate.

An assessment of the quality of the elastic-plastic response approximation was made bycomparing the estimated response stress profiles with those found by 3D, elastic-plasticFEA (ABAQUS). As shown in Fig. 24, the approximate solution tends to over-predict

the extent to which the cold work induced residual stresses are removed. While it is clear

that the approximate solution needs refinement, it should be noted that some of thedifferences between the results are due to differences between material constitutive

relations (bi-linear vs. power law hardening) and modeling technique (load redistribution

vs. no load redistribution).


23/40

23

-140

-120

-100

-80

-60

-40

-20

0

0 1 2 3 4 5x/R

stress(ksi)

elastic-plastic analysis

elastic analysis

Steel Insert

E=30000 ksi

=0.33

y=200 ksi

significant reverse yielding

occurs at egde of hole

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksi

n=4.59

a) Plate Subjected to -25 ksi Remote Compression

-60

-40

-20

0

20

40

60

0 1 2 3 4 5

x/R

stress

(ksi)

residual stress after -25 ksi overload

initial, Cw induced residual stress

Steel Insert

E=30000 ksi=0.33

y=200 ksi

reverse yielding removes

much of Cw induced

residual stress distribution

2124-T851 Al Plate

E=10400 ksi=0.33

y=57 ksi

n=4.59

b) Plate with Compression Load Removed

-60

-40

-20

0

20

40

60

0 1 2 3 4 5x/R

stress(ksi)

elastic-plastic analysis

elastic analysis

Steel Insert

E=30000 ksi

=0.33

y=200 ksi

benefit due to Cw on

subsequent tension loading

is reduced

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksi

n=4.59

c) Plate Subjected to 25 ksi Remote Tension

Figure 23. Comparison Between Elastic and Elastic-Plastic Calculated

Tangential Stress Distributions at Open, 4% Cold Worked Holein a Plate Subjected to 25 ksi Remote Tension


24/40

24

-100

-80

-60

-40

-20

0

20

0 1 2 3 4 5x/R

stress

(ksi)

2D EP closed form

3D EP FE A, avg of mid-plane & surface results

Steel Insert

E=30000 ksi

=0.33

y =200 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksi

n=4.59

a) Plate Subjected to -25 ksi Remote Compression

-60

-40

-20

0

20

40

60

0 1 2 3 4 5

x/R

stress

(ksi)

2D EP closed form

3D EP FEA, avg of surface & mid-plane results

Steel Insert

E=30000 ksi

=0.33

y=200 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksi

n=4.59

b) Plate with Compression Load Removed

-40

-20

0

20

40

60

80

0 1 2 3 4 5

x/R

stress(ksi)

2D EP closed form

3D EP FEA, avg. of surface & mid-plane results

Steel Insert

E=30000 ksi

=0.33

y=200 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksi

n=4.59

c) Plate Subjected to 25 ksi Remote Tension

Figure 24. Comparison Between 2D Closed Form and 3D FEA (ABAQUS)

Calculated Tangential Stress Distributions at Open, 4% Cold Worked Holein a Plate Subjected to 25 ksi Remote Tension


25/40

25

Similar results on the effect of compression overloads were reported by Armen, Levy and

Eidinoff [40].

Stress intensity factor solution development

With the residual strain and stress fields defined, a damage or fracture parameter that isdependent on those fields must be calculated. The stress intensity factor (SIF) is by far

the most commonly used parameter. For a crack growing either completely or partially

within a residual stress field the SIF is generally calculated using either the weightfunction [41] [42] or Green's function [43] technique (both of which rely on the principle

of superposition). While the two methods are closely related, from an application point

of view, they are distinct. The weight function method, as defined by Beukner and Rice,requires knowledge of the crack opening displacement profile for some reference loading

condition. The Greens function method, on the other hand, is based on the bodys

response to a unit point load (hence the term Greens function). In general, given anarbitrary stress distribution and the Greens function for the crack / geometry being

analyzed, the corresponding SIF is found by integrating the product of the normalizedstress distribution and the Greens function over the crack area.

KI yGdAA= (3)

where y is the component of stress producing mode I crack face displacement. TheGreens function approach was utilized in this study.

The two crack configurations considered in this study were a through thickness crack and

a quarter-elliptical corner crack at a hole in a finite with and thickness plate. SIFsolutions for these cases were initially developed in an earlier study [21] [22] and

modified during the current program. For a single through thickness crack, the SIF is

written as

1FWGFTI cSK = (4)

where the expressions for GFT is based on the Greens function given by Shivakumarand Forman [44] and FW1 is a finite width correction. For a quarter-elliptical cornercrack it is

1FW32TGFCIcSK = (5)

In this case, the expression for GFCwas developed based on 3-D FEA as described in

[21] and [22]. T, 2, 3are boundary correction factors for a corner crack at a hole in aplate and were given by Newman and Raju [45] and, again, FW1 is a finite widthcorrection.


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26

Fatigue crack growth analysis

Finally, in order to permit the calculation of fatigue crack growth life at cold worked

holes, the hole expansion and response stress distribution calculation algorithms and the

SIF calculation algorithms discussed above were utilized in a detailed, cycle-by-cycle

crack growth model [46]. In this model, the initial residual stress and strain profiles(such as those induced by cold work) were used to define the initial condition from which

the cyclic, elastic-plastic response calculations are made. The calculated SIFs were either

used directly to calculate crack growth increments, or they were used in a preliminarycrack closure model to determine effective SIFs, which were then used to calculate

growth increments. In either case, the growth increment was found using the Forman

crack growth rate equation. The overall analysis is carried out on a cycle-by-cycle basisand consists of the following primary steps:

1) calculate response stress (elastic-plastic),2) calculate response SIFs (both the x- and z- directions),

3) calculate effective SIFs,4) calculate the crack growth rates and crack growth increments in each direction,5) increment the crack size6) repeat process (steps 1 thru 5) until failure, i.e. until crack size or SIF reaches

critical value.

When plastic deformation (notch plasticity) occurs, the elastic-plastic response stress

distribution will not be the same as the elastic distribution. Likewise, SIFs calculated

based on the elastic-plastic response will not be same as those based on the elastic

response. For cycle-by-cycle fatigue analysis, the process of calculating the responsestress distribution and then the response SIF is repeated from turning point to turning

point. As a result, the response distribution at each point includes the effect of priorplastic deformation. This would include, of course, the plastic deformation caused bycold expansion.

It is important to note that since the response stress distributions are estimated for anuncracked cross-section, they do not reflect the influence of the crack. This obviously

places a restriction on the range of crack sizes for which the over-all crack growth model

can be used: the quality of the approximation decreases with increasing crack size. Thisalso means that the estimated response distributions contain no information about crack

closure. As a result, the minimum response SIF is not corrected for closure; it is based

strictly on the response stress distribution at the cycle minimum.

In an effort to overcome this second limitation, the preliminary crack closure model given

in [47] was used in the current study. This model is based on the simple stress ratiodependent closure model developed by Newman [48]. The closure factor is given as

( )

+

+++==

RAA

RARARAA,Rmax

K

KC

10

33

2210

max

openf

0R2

0R


27/40

27

where

( ) ( )1C2

1

refc

2ecec0

ec

plc

SF

2cosC2.0C48.0535.0A

+

+= for Sref/plc1 (8)

( )plc

SFC142.0344.0A refcec1 = (9)

3102 AAA1A = (10)

1AA2A 103 += (11)

Cec is the constraint index defined such that Cec=0 indicates plane stress while Cec=1

indicates plane strain. Sref is the effective reference stress from the SIF calculation. It is

found as

iG

maxref

FFc

KS

= (12)

Finally, plc is the cyclic proportional limit and Fc is a fitting parameter that essentially

scales the ref-to-plc ratio and allows the overall crack growth analysis model to betuned when correlating to test data.

Example calculations showing the dependence of the closure factor on stress ratio, R, atvarious ref-to-plc ratios are shown in Fig 25(a) and 25(b) for plane stress and plane strain

conditions respectively.

As indicated above, the fatigue crack growth life algorithm operates on a cycle-by-cycle

basis with the response SIFs for a given cycle being determined based on the response

stress distributions. Effective SIFs are then found using the modified closure model,

specifically:

resmaxfopeneffmin

KCKK

== (13)

resmaxeffmax KK = (14)

As in standard, LEFM-based fatigue crack growth analysis, in the current analysis,

fatigue crack growth rate is based on SIF range and SIF ratio. These values are found

simply as


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28

effmineffmaxeff KKK = (15)

effmaxeffmineff K/KR = (16)

-1.0

-0.5

0.0

0.5

1.0

-2 -1 0 1stress ratio, R

closurefactor,Cf Sref/plc=0.2

0.4

0.6

0.8

1.0

Modified Newman Closure Model

Cec=0 (plane stress)

1.2

(a) plane stress

-1.0

-0.5

0.0

0.5

1.0

-2 -1 0 1stress ratio, R

closurefactor,Cf

Sref/plc=0.2

0.40.6

0.8

1.0

Modified Newman Closure Model

Cec=1 (plane strain)

(b) plane strain

Figure 25. Ratio of Crack Opening Stress to Cycle Maximum Stress

as a function of Cycle Stress Ratio.


29/40

29

For each load cycle, the crack growth rate, da/dN, is found using the Forman equation

[49].

( )

( ) effFeff

FeffF

KKR1

nKC

dN

da

= (17)

Note that stress ratio dependence is incorporated via the (1-Reff) term in the denominator

and that the growth rate acceleration due to incipient failure (region 3) is predicted when

Keff approaches (1-Reff)KF. A typical set of da/dN data along with the corresponding

Forman equations is shown in Fig 26. Separate equations are defined two K segmentsand constants CF, nFand KFare defined for each segment.

2124-T851 Al. Plate, L-T

Sump Tank Water1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1 10 100

K (ksi*(in)^1/2)

da/dN(in/cycle)

R=0.1

R=0.3

R=0.5

Forman Eqn., R=0.1

Forman Eqn., R=0.3

Forman Eqn., R=0.5

Figure 26. Example Fatigue Crack Growth Rate Dataset and

Corresponding Two Segment Forman Equation

One very significant difference between the current elastic-plastic fatigue crack growth

analysis method and traditional, LEFM-based methods, is the fact that Kmin-eff can be

negative. It is thus necessary to treat R effects when calculating crack growth rate. In

[50] Chang proposed an adaptation of the Walker fatigue crack growth rate equation [51]to account for R induced crack growth rate acceleration. His model was based on the

proposition that the growth rate at a negative stress ratio is equal to some constant times

the growth rate at a stress ratio of zero (for the same Keff).

0R0R dN

daA

dN

da

=1). Note that =1 doesnot indicate the absence of acceleration, it indicates the acceleration provided by theForman equation alone.

Once a crack growth rate is determined, the corresponding crack growth increments areknown (since N=1 for a cycle-by-cycle analysis). Starting from the prescribed initial

size, the crack size is increased by the calculated crack length / depth increment at eachcycle. This calculation is repeated until one of several events occurs. If the calculatedSIF exceeds the fracture toughness of the material, then failure is indicated. At this point,

the accumulated number of cycles represents the predicted crack growth life. Prior to

actual failure, the crack may transition from one configuration to another. The transitionevents considered in the current program include:


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31

Semi-elliptical transitions to quarter-elliptical (one tip reaches a surface before theother)

Semi-elliptical transitions to through-thickness (both tips reach the surfaces at thesame time)

A quarter-elliptical transitions into a through thickness crack

Note that the transition of a semi-elliptical into a quarter-elliptical is possible because the

SIF formulation permits the crack to be eccentrically located with respect to the platesurfaces.

Model demonstration and evaluation

The overall fatigue crack growth model was evaluated by conducting a series of analysesand comparing the results with experimental data. The geometric and material

parameters used for the analyses are summarized in Table 5. It should be pointed out that

the only data required for this model that is over and above that normally required for atraditional fatigue crack growth analysis is the cyclic stress-strain curve for the materialbeing analyzed.

Table 5. Open Hole Test Coupon Analysis Parameters.MODEL

geometry code HA (open hole in a plate)

Width 3.0

hole radius 0.156

edge distance 1.5 (centered hole)

Thickness 0.25

MATERIAL

Title 2124-T851 Aluminum Plate, L-TEnvironment HHA

E 10400 ksi

0.33Fty 57.0 ksi

Cyclic proportional limit 36.0 ksi

Ramberg-Osgood eqn.flow stress, 45.0 ksiCoefficient, 5.277E-04exponent, n 11.358

K-thresh @ R=0 1.5Gamma 0.

Forman eqn, 0


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32

Stress Intensity Factor Analysis

When the residual SIF for a through thickness crack due to 4% cold work is

superimposed with the SIF due to the applied (bypass) stress, the result is as shown in

Fig. 27. The beneficial impact of the compressive residual stress distribution in the

vicinity of the hole is evident. Note, however, that as the crack becomes longer, it willmove into the influence of the equilibrating tensile residual stress field. Similar

calculations were made using the new corner crack Greens function model. Again, it isclear that as long as the crack is within the residual compressive well, the effective SIF is

significantly reduced. See Fig. 28.

-20

0

20

40

60

0 0.2 0.4 0.6 0.8 1

c/(b-R)

SIF(ksi*SQRT(in)

SIF due to applied stress alone

Total SIF with 4% Cold Expansion

Steel Insert

E=30000 ksi

=0.33

y=200 ksi

SA=25 ksi

SA=2.5 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksi

n=4.59

Figure 27. SIF for a Through Thickness Crack at Hole in a Plate

Subjected to Remote Tension With And Without 4% Cold Expansion.

Fatigue crack growth analysis

Some of the phenomena observed in the Phase 1 tests of the current program were a

direct result of the occurrence of notch plasticity at the hole. A series of FCG analyseswere attempted in order to further evaluate the overall model. In the first problem set, the

results of the CA-1 tests were contrasted with those of the CA-2 tests. Recall that the

CA-1 specimens were subjected to R=0.1 constant amplitude loading only, while the CA-2 specimens were subjected to an initial, -25 ksi compression overload. One would

expect that the application of the compression overload would cause the formation of a

slight tensile residual at the side of the open hole (cause an increase the local meanstress). This in turn would lead to an acceleration of crack growth rate. As shown in Fig.

29, this phenomenon did occur in the tests and it is also captured in the EPFCG model.


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33

-20

0

20

40

0 0.2 0.4 0.6 0.8 1

a/t

SIF(ksi*SQRT(in)



Steel Insert

E=30000 ksi

=0.33

y=200 ksi SA=25 ksi

SA=2.5 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksin=4.59

SIF at c (phi=5)

a) length direction

-20

0

20

40

0 0.2 0.4 0.6 0.8 1

a/t

SIF(ksi*SQRT(in))



Steel Insert

E=30000 ksi

=0.33

y=200 ksi

SA=25 ksi

SA=2.5 ksi

2124-T851 Al Plate

E=10400 ksi

=0.33

y=57 ksi

n=4.59

SIF at a (phi=80)

b) depth direction

Figure 28. SIF for a Corner Crack at Hole in a Plate Subjectedto Remote Tension With And Without 4% Cold Expansion.


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34

In the next problem set, the fatigue crack growth behavior at a cold worked hole is

contrasted with that at a non-cold-worked hole. In this case the CA-1 test, and thecorresponding analysis, are compared with the CA-3 results. The hole in the CA-3

specimens was subjected to a 4% cold expansion. As shown in Fig. 30, this resulted in

about a 5 to 7 fold increase in life. (The life of specimen CA-3B was shorter than that of

CA-3A apparently because of significant cracking at the opposite side of the hole.) Theanalytical results shown are not strictly consistent with those shown in Fig. 29. It was

necessary to increase the closure fitting parameter, Fc, to achieve the life prediction forthe cold worked hole. At this point, the closure behavior of cracks growing from cold

worked holes has not been studied, and it is not at all clear whether simple closure

models can be applied in these circumstances.

Finally, the effect of a 25 ksi compression overload, applied after hole cold working, was

studied in with the CA-4 specimens. As shown in Fig. 31, the application of this load

clearly reduces the effectiveness (in terms of life extension) of the cold-work inducedresidual stress field. The stress analysis results presented above clearly indicated that the

application of a compression overload to a specimen with an open hole, can removemuch of the cold work induced residual. Since the crack growth model accounted for thischange in the local stress distribution, the calculated crack growth life was reduced

significantly. (It was again necessary to tune the Fc parameter to achieve this result.)

0

0.2

0.4

0.6

0.8

1

1.2

0 5000 10000 15000cycles

cracklength,c

test, CA-1Banalysis CA-1test, CA-2Atest, CA-2Banalysis CA-2

Through Crack at

Open Hole (HA1)

W=3.0

R=0.156

b=1.5

t=0.252124-T851 Al. P lt.

Constant Amplitude Loading,

Smax=25 ksi, R=0.1

Figure 29. Comparison of Predicted vs. Measured Crack Growth for

Specimens Tested with 25 ksi Constant Amplitude Spectrum.


35/40

35

0

0.2

0.4

0.6

0.8

1

1.2

0 20000 40000 60000 80000

cycles

cracklength,c

test, CA-1Banalysis, CA-1test, CA-3Atest, CA-3B

analysis, CA-3

Through Crack at

Open Hole (HA1)

W=3.0

R=0.156

b=1.5

t=0.25

2124-T851 Al. Plt.

Constant Amplitude Loading,

Smax=25, R=0.1


Cold Worked and Non-Cold-Worked Specimens Subjected to

Constant Amplitude, Smax=25 ksi, R=0.1 Loading.

0

0.2

0.4

0.6

0.8

1

1.2

0 20000 40000 60000 80000

cycles

crack

length,c

test, CA-1Banalysis, CA-1test, CA-4Atest, CA-4Banalysis, CA-4test, CA-3Atest, CA-3Banalysis, CA-3

Through Crack at

Open Hole (HA1)

W=3.0

R=0.156

b=1.5

t=0.25

2124-T851 Al. Plt.

Constant Amplitude Loading

Smax=25, R=0.1


Cold Worked and Non-Cold-Worked Specimens Subjected to Constant

Amplitude Loading With and Without Compression Overload.


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Conclusions

The viabilities of two emerging NDE technologies for the assessment of cold expansion

were evaluated. Both photon induced positron annihilation and meandering windingmagnetometer arrays were clearly and reliably able to detect the presence and degree of

cold expansion.

Photon induced positron annihilation was evaluated for its ability to quantify residualstress and/or strain profiles in the vicinity of a cold worked hole. It was shown that the

DSPA S-parameter exhibited some position-dependent variability in the region of the

hole; however, it was not clear how that data could be related to stress or strain profiles.It seems likely that further development of this technology will be required before such

quantification will be possible. The primary reasons for this are limitations on spatial

resolution of S-parameter measurements and the inability to discriminate lattice damagefrom lattice dilatation effects.

The effects of compression loading on cold work effectivity were characterized usingconstant amplitude tests. Constant amplitude tests with tension-only loading indicated acold work life improvement ratio of about 5 to 7. When a compression overload was

applied once at the beginning of the test, the life improvement ratio dropped to about 2,

clearly indicating that compression overloads can cause reverse yielding, which in turncan reduce or even eliminate the cold work benefit. Similarly, life improvement ratios

for fully reversed (R=-1) constant amplitude loading were not as high as those for R=0.1

loading.

A preliminary model for the growth of fatigue cracks at cold expanded holes has been

developed. This model includes the ability to calculate cold work induced residual strain

and stress fields in closed form. It can then use those fields as the initial state from whicheither elastic or elastic-plastic, cyclic response calculations are made. The response stress

distribution for each cycle is used to calculate a response stress intensity factor, using the

Greens function approach. Greens function models for both a through thickness crackand a corner crack at the hole were obtained. The model was used with limited success to

simulate some of the cracking behavior observed in the constant amplitude tests. The

will require further development, however, before it can be reliably used for productionanalyses. Specifically, the role of crack closure during growth from cold worked holes

must be examined in detail (experimentally) and either existing closure models must be

modified or new ones must be developed in order accommodate the highly compressivelocal environment.

Acknowledgements

The technical activity reported herein was performed under Delivery Order 0003 ofUSAF contract F42620-01-D-0058 - F-16 Aircraft Structural Integrity Program (ASIP) -

Common Tasks - SOW Paragraph 3.1.4.6. The technical monitor for the contracting

agency, the Ogden Air Logistics Center (OO-ALC/YPVS) was Mr. Robert McCowin,


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whose support for this activity is gratefully acknowledged. In addition, the authors

would like to thank the following individuals for their contribution to this effort: Ms JoyRansom of Fatigue Technology Inc., for the preparation of the test specimens and the

performance of the fatigue tests; Mr. Scott Ritchie and Dr. Doug Akers of Positron

Systems, Inc. for the PIPA and DSPA NDE of the specimens; and Dr. Neil Goldfine and

Dr. Vladimir Zilberstein of JENTEK Sensors, Inc. for the MWM-Array NDE of thespecimens.

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