Fatigue Crack-Growth and Crack Closure Behavior of

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Fatigue Crack-Growth and Crack Closure Behavior of Aluminum Fatigue Crack-Growth and Crack Closure Behavior of Aluminum

Alloy 7050 and 9310 Steel over a Wide Range in Load Ratios using Alloy 7050 and 9310 Steel over a Wide Range in Load Ratios using

Compression Pre-Cracking Test Methods Compression Pre-Cracking Test Methods

Talal Mehdi Senhaji

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Fatigue crack-growth and crack closure behavior of aluminum alloy 7050 and 9310 steel

over a wide range in load ratios using compression pre-cracking test methods

By

Talal Mehdi Senhaji

A Thesis Submitted to the Faculty of Mississippi State University

in Partial Fulfillment of the Requirements for the Degree of Master of Science

in Aerospace Engineering in the Department of Aerospace Engineering

Mississippi State, Mississippi

August 2016


Copyright 2016

By

Talal Mehdi Senhaji


____________________________________

____________________________________

____________________________________

____________________________________

____________________________________

Fatigue crack-growth and crack closure behavior of aluminum alloy 7050 and 9310 steel

over a wide range in load ratios using compression pre-cracking test methods

By

Talal Mehdi Senhaji

Approved:

James C. Newman, Jr (Major Professor)

Thomas E. Lacy (Committee Member)

Steven R. Daniewicz (Committee Member)

J. Mark Janus (Graduate Coordinator)

Jason M. Keith Dean

Bagley College of Engineering


Name: Talal Mehdi Senhaji

Date of Degree: August 12, 2016

Institution: Mississippi State University

Major Field: Aerospace Engineering

Major Professor: James C. Newman, Jr.

Title of Study: Fatigue crack-growth and crack closure behavior of aluminum alloy 7050 and 9310 steel over a wide range in load ratios using compression pre-cracking test methods

Pages in Study: 58

Candidate for Degree of Master of Science

Fatigue-crack-growth-rate tests were conducted on compact tension specimens

made of 7050-T7451 aluminum alloy and 9310 steel. Compact tension specimens were

tested over a wide range of load ratios (0.1 ≤ R ≤ 0.9) to generate crack-growth-rate data

from threshold to near fracture. Three methods were used to generate near threshold

data. A crack-closure analysis was performed on both materials using the FASTRAN

crack-closure model. The crack-growth-rate data for each material correlated very well

and each collapsed onto a nearly unique curve in the low- and mid-rate regimes using the

strip-yield model in the FASTRAN life-prediction code. For the 7050 alloy, a constraint

factor of α = 1.8 was required, while for the 9310 steel α = 2.5 worked very well in

correlating the test data over a very wide range in R values and rates from threshold to

near fracture.

DEDICATION

The author dedicates this thesis to his family for encouraging him to pursue a

college career in order to become an outstanding engineer abroad in the aerospace

industry.

ii

ACKNOWLEDGEMENTS

The author would like to express his gratitude towards everyone in the Aerospace

Engineering Department at Mississippi State University who helped to make this thesis

possible. Special thanks are given to Dr. James Newman, Jr. for all the assistance and

advice he provided during the course of this thesis. Also, special thanks is given to Dr.

Yoshiki Yamada for his previous research on the 7050 aluminum alloy; and to Dr. Brett

Zeigler for his previous research on the 9310 steel. Gratitude is expressed towards the

National Aeronautical and Space Administration, Langley Research Center, for providing

the 7050-T7451 aluminum alloy and 9310 steel compact specimens. The author would

like to further express his gratitude to his family: Jaouad Senhaji, Touria Razine,

Camélia-Sherry Senhaji for their support during his graduate career. Finally, special

thanks are given to the other members of the thesis committee, Dr. Thomas E. Lacy, Jr.,

and Dr. Steve Daniewicz for their extensive review of this thesis.

iii

TABLE OF CONTENTS

DEDICATION.................................................................................................................... ii

ACKNOWLEDGEMENTS............................................................................................... iii

LIST OF TABLES.............................................................................................................. v

LIST OF FIGURES ........................................................................................................... vi

NOMENCLATURE ........................................................................................................ viii

CHAPTER

I. INTRODUCTION ................................................................................................1

Aluminum Alloy 7050-T7451...............................................................................9 Steel 9310 ............................................................................................................10

II. TEST PROCEDURES........................................................................................11

III. MATERIAL TESTED AND ANALYZED........................................................14

Aluminum Alloy 7050-T7451.............................................................................14 Fatigue-crack-growth results .........................................................................14 Crack-closure measurements.........................................................................20 Crack-growth modeling.................................................................................25

Steel 9310 ............................................................................................................29 Fatigue-crack-growth results .........................................................................29 Crack-closure measurements.........................................................................38 Crack-growth modeling.................................................................................42

IV. DISCUSSION OF RESULTS ............................................................................47

Aluminum Alloy 7050-T7451.............................................................................47 Steel 9310 ............................................................................................................50

V. CONCLUDING REMARKS..............................................................................52

iv

LIST OF TABLES

1 Effective Stress-Intensity Factor Range against Rate Relation for 7050-T7451 Aluminum Alloy .............................................................27

2 Effective Stress-Intensity Factor Range against Rate Relation for 9310 steel. .....................................................................................................44

v

LIST OF FIGURES

1 Compact specimen with remote backface-strain (BFS) gage with and without beveled holes. ...........................................................................7

2 Load sequences for threshold and constant-amplitude testin ............................8

3 Fatigue-crack-growth-rate data for CPCA, CPLR, ASTM LR and CA tests at constant load ratios on 7075-T7451 aluminum alloy. .............16

4 Comparison of FCG data generated from CPCA, CPLR, ASTM LR and CA threshold testing on 7075-T7451 aluminum alloy at R = 0.1. ....................................................................................................18

5 Comparison of FCG data generated from CPCA, CPLR, ASTM LR and CA threshold testing on 7075-T7451 aluminum alloy at R = 0.7. ....................................................................................................19

6 Crack-opening load ratio as a function of crack length to width ratio generated from CPLR and ASTM LR for R = 0.1 tests on 7075-T7451 aluminum alloy................................................................22

7 Crack-opening load ratio as a function of crack length to width ratio generated from CPCA and CA for R = 0.1 tests on 7075-T7451 aluminum alloy. ...................................................................................23

8 Effective stress-intensity-factor ranges for R = 0.1 tests using measurements and K for R = 0.7 tests on 7075-T7451 aluminum alloy. ...................................................................................24

9 Effective stress-intensity-factor ranges against rate for all tests using FASTRAN model on 7075-T7451 aluminum alloy. ...........................28

10 Measured and calculated FCG behavior over wide range in load ratios from threshold to fracture on 7075-T7451 aluminum alloy. ...............29

11 Fatigue-crack-growth-rate data for CPCA, CPLR and CA tests at constant load ratios on 9310 steel. .......................................................31

12 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.1 on 9310 steel. ........................................34

vi




16 Remote reduced load-backface-strain records for various stress-intensity factor for R = 0.1 on 9310 steel.............................................40



19 Effective stress-intensity-factor ranges against rate for all tests using FASTRAN model on 9310 steel. .........................................................45

20 Measured and calculated FCG behavior over wide range in load ratios from threshold to fracture on 9310 steel. .............................................46

vii

c

NOMENCLATURE

Symbol Description

B Thickness, in.

Crack length, in.

dc/dN Crack growth rate, in./cycle

E Modulus of elasticity, ksi

Kcp Compressive stress-intensity factor during pre-cracking, ksi-in.1/2

KIe Maximum stress-intensity factor at failure, ksi-in.1/2

Kmax Maximum stress-intensity factor, ksi-in.1/2

Pmax Maximum applied load, kips

Pmin Minimum applied load, kips

Po Crack-opening load, kips

R Load (Pmin/Pmax) ratio

U Crack-opening function, (1 – Po/Pmax)/(1 – R)

W Specimen width, in.

h Height of the notch, in.

cn Notch length, in.

ΔK Stress-intensity factor range, ksi-in.1/2

ΔKc Critical stress-intensity-factor range at failure, ksi-in.1/2

ΔKeff Effective stress-intensity-factor range, ksi-in.1/2

viii

L

ΔKi Initial stress-intensity-factor range before load reduction, ksi-in1/2

c Dugdale plastic-zone size under minimum compressive load, in.

o Flow stress (average of yield and ultimate tensile strength), ksi

ys Yield stress (0.2% offset), ksi

u Ultimate tensile strength, ksi

Acronyms:

BFS Backface strain gage

CMOD Crack-mouth-opening displacement

CPCA Compression pre-cracking and constant-amplitude test method

CPLR Compression pre-cracking and load-reduction test method

C(T) Compact specimen

ESE(T) Elongated single edge tension specimen

FCG Fatigue-crack growth

OPn Crack-opening load (Po/Pmax) ratio at n% compliance offset

PICC Plasticity-induced crack closure

DICC Debris-induced crack closure

RICC Roughness-induced crack closure

LaRC Langley Research Center

Direction of principal deformation (maximum grain flow)

NASA National Aeronautics and Space Administration

S Third orthogonal direction

T Direction of least deformation

ix

CHAPTER I

INTRODUCTION

Fatigue-crack growth (FCG) has been a major indicator in examining how

repeated or random load cycles can cause structural failure. Fatigue of structures is

mainly concerned with determining the damage and fatigue properties due to cyclic

loading in the crack growth threshold and near-threshold regions. Linear elastic fracture

mechanics (LEFM) developed by Irwin and Paris proved to be a powerful tool in the

understanding of fatigue-crack growth and in the quantification of cyclic stress-intensity

factor ΔK with respect to FCG rate, at a given load ratio (R = minimum to maximum load

ratio). The relation between ΔK and dc/dN was shown to be nearly linear on a log(ΔK)-

log(dc/dN) scale by Paris and Erdogan [1]. This relation between ΔK and dc/dN

becomes non-linear once cracked bodies are approaching fracture [2] or when the FCG

rate is very slow [3]. Therefore, fatigue-crack growth behavior of many materials can be

categorized into three regions: (1) threshold region (ΔK is too low to propagate a crack),

(2) mid-region (the rate of crack growth changes roughly linearly with a change in stress-

intensity fluctuation), and (3) fracture region (large increase in crack growth rate). Crack

closure was shown to be a major mechanism in explaining the effects of changing the R-

ratio, low ΔK crack growth (near-threshold), and retardation due to an overload, which

modify the stress-intensity factor range experienced by the crack tip and. Hence, the

crack growth rate, which resulted from contact of residual plastic deformation left in the

1

wake of the crack extension [4, 5], roughness of the crack surfaces [6], and debris created

along the crack surfaces [7]. Crack-growth data under constant-amplitude loading were

correlated using the crack-closure concept over a wide range in load levels, load ratios

and over a wide range in rates from threshold to fracture [8].

Standard mechanical measurements have been employed to measure bulk effects,

like crack-mouth-opening displacement (CMOD) gages or backface strain (BFS)

measurements. These remote methods give a measure of crack closure (or more correctly,

crack-opening load). Such techniques indicated that under high load ratio (R ≥ 0.7)

conditions produced no crack closure for a variety of materials. However Yamada and

Newman [9], using a local strain-gage method, showed that there is crack-closure

behavior attributed to residual plastic deformations, crack-surface roughness and/or

fretting-debris at least in the near-threshold and threshold regions. In the threshold and

near-threshold regions, debris-induced crack closure (DICC) [7, 10] and roughness-

induced crack closure (RICC) [6, 11] contributed to overall crack closure; plasticity-

induced crack closure (PICC) is still very relevant under all load-ratio conditions and

contributed strongly to crack-opening loads that were above the minimum load [8, 12].

PICC could not explain threshold and near threshold crack growth behavior as a function

of load ratio, but adding RICC and DICC contributions could correlate the data very well

[9].

ASTM E-647 defines load reduction to generate constant load-ratio data in the

threshold and near-threshold regions [13]. However, the ASTM load-reduction method

may produce higher thresholds and slower rates in the near-threshold regime than steady-

state constant amplitude data [14, 15]. The load reduction procedure also produced

2

fanning in the measured crack growth rates with load ratio in the threshold regime.

Fanning in the near-threshold regime gives more spread in the ΔK-rate data compared to

the mid-region. The load-reduction test method has been shown to induce high crack-

opening loads and remote crack-surface closure due to a load and/or environmental

history effect [12, 14, and 16]. Thus, a compression pre-cracking method had been

developed to generate constant-amplitude fatigue-crack-growth-rate data in the threshold

and near-threshold regimes with minimal or no load-history effects [17-19]. The

procedure involves cycling a notched specimen under a compression-compression

loading to initiate a crack at the crack-starter notch, and then testing the specimen under

constant-amplitude loading.

The starter crack is to be grown several compressive plastic zone sizes to

eliminate the effects of the tensile residual stresses, the crack-starter notch effect, and to

stabilize the crack-opening stress history [19, 20]. This procedure is called the

compression pre-cracking constant-amplitude (CPCA) loading test method. Another

procedure is compression pre-cracking load-reduction (CPLR) testing. The latter method

allows the crack to be grown at a much lower ΔK than needed or allowed in the ASTM

standard load-reduction test procedure, which requires tensile pre-cracking.

A test program was conducted to generate fatigue-crack-growth-rate data from

threshold to near fracture using several loading sequences: (1) compression pre-cracking

constant amplitude (CPCA), (2) compression pre-cracking load reduction (CPLR), (3)

ASTM load reduction (LR) and (4) constant-amplitude (CA) loading. Two materials

were tested. 7050-T7351 aluminum alloy and 9310 steel were each tested at load ratios of

0.1, 0.4, and 0.7. An R = 0.9 test was also conducted on a steel specimen. Results from

3

both materials were compared with previous literature test data generated by Newman et

al [21].

Results were compared with test data from the literature on the 7050 alloy that

was tested in a different material orientation and with existing test data on the 9310 steel

from the literature that was tested in a different thickness. In both the 7050 (SL-

orientation) and the 9310 material, very little difference was observed between the

ASTM load reduction (LR), CPLR and CPCA test methods, although compression pre-

cracking allowed much lower initial ∆K values than the ASTM standard. It had

previously been shown that the ASTM LR method induces a load-history effect which

may be caused by remote closure in the 7050 alloy that was tested in the LT-orientation.

The backface strain (BFS) gage method was used to monitor crack lengths and to

measure crack-opening loads from remote load-strain records during all tests as shown in

Figure 1(a). A crack-compliance method using BFS gages had previously been used to

determine that the crack-starter notch tensile residual-stress effects from compression

pre-cracking dissipated in about three compressive plastic-zone sizes; the crack-closure

behavior then stabilized to produce steady-state constant-amplitude data. In addition,

crack extension from the crack-starter notch beyond one notch height was shown to

eliminate the effects of the notch on the stress-intensity factor.

During all tests, the compliance off-set method was used to estimate the crack-

opening load as a function of stress ratio and crack length. A zero percent offset value

(OP0), similar to Elber’s crack-opening load, was extrapolated using the one-percent

(OP1) and two-percent (OP2) offset compliance values recorded from the BFS and crack-

monitoring software using Elber’s load-reduced-displacement approach.

4

For the 7050 alloy, a crack-closure analysis was performed to calculate the

effective stress-intensity factor (∆Keff) against rate using measured OP0 values for low R

(0.1) and these results were compared with the K-rate test data at high R. Past research

had shown that high R (≥ 0.7) test data is basically the ∆Keff-rate curve in the mid-crack-

growth-rate region. However, in the low-rate regime, previous testing had shown that

high-R closure develops due to the load-reduction method and/or faceted crack-growth

behavior causing roughness- or debris-induced crack closure, in addition to plasticity-

induced crack closure. For high R tests, plasticity is suspected to give a crack-opening

load at or near the minimum load, and, thus, roughness/fretting debris are assumed to

cause crack-opening loads above the minimum load. Unfortunately, the remote BFS

method was unreliable to measure OP0 values for higher stress ratios (R ≥ 0.7).

For the 9310 steel, the remote BFS method was unable to detect any OP1 and

OP2 compliance off-set values at any stress ratio, so a crack-closure analysis using OP0

values could not be performed. In the steel tests, the fatigue crack surfaces were very

flat, and roughness-induced crack closure was not expected. Debris-induced crack

closure may be caused by the environment (humidity levels). However, plasticity-

induced crack closure was expected to be the major crack-closure mechanism.

A crack-closure analysis was performed on both materials using the FASTRAN


and each collapsed onto a nearly unique curve in the low- and mid-rate regimes using the

strip-yield model in the FASTRAN life-prediction code. In the high rate regime, the

fracture toughness controlled the crack-growth-rate behavior. The Newman crack-

growth equation modeled the behavior in the threshold to fracture regimes fairly well.

5

For the 7050 alloy, a constraint factor of α = 1.8 was required, while for the 9310 steel α

= 2.5 worked very well in correlating the test data over a very wide range in R values and

rates from threshold to near fracture.

A test program was conducted to generate fatigue-crack-growth-rate data from

threshold to near fracture using several loading sequences: (1) compression pre-cracking

constant amplitude (CPCA), (2) compression pre-cracking load reduction (CPLR), (3)

ASTM load reduction (LR) and (4) constant-amplitude (CA) loading. Two materials

were tested. 7050-T7351 aluminum alloy and 9310 steel were each tested at load ratios of

0.1, 0.4, and 0.7. An R = 0.9 test was also conducted on a steel specimen. Results from

both materials were compared with previous literature test data generated by Newman et

al [21].

Remote BFS gages, as shown in Figure 1(a), were used to monitor crack growth

and to measure remote load-strain records. Based on these measurements, crack closure

(or crack-opening) loads and the effective stress-intensity-factor range against crack-

growth rate was calculated for the R = 0.1 tests conducted on the 7050 alloy. For the

higher R ratio (R ≥ 0.7) tests on the aluminum alloy and all tests on the 9310 steel, the

remote load-strain records did not produce any reliable indications of crack closure.

However, the FASTRAN crack-closure model was used to correlate the FCG rate data on

both materials over a wide range in stress ratios and rates using appropriate constraint

factors.

6

P

P

c

W

BFS

Beveled holes

hn cn

+ CLP

B

B/4r

1.1r

(a) Compact specimen (b) Beveled pin holes

(c) Effects of standard (straight) or beveled holes on crack-front straightness

Figure 1 Compact specimen with remote backface-strain (BFS) gage with and without beveled holes.

7

(a) Compression pre-cracking and constant-amplitude (CPCA) loading.

(b) Compression pre-cracking and load-reduction (CPLR) loading.

Figure 2 Load sequences for threshold and constant-amplitude testin

8

MATERIAL AND SPECIMEN CONFIGURATIONS

Two materials were used to generate FCG-rate data over a wide range in load

ratios (0.1 ≤ R ≤ 0.9) from threshold to near-fracture: 7050-T7451 aluminum alloy and

9310 steel. All of the compact specimens machined from these materials had an

electrical-discharge machined U-notch with a height of 0.02 inches and a notch-tip radius

of 0.01 inches. The notch length to width (cn/W) ratio was 0.2 for all specimens.

Aluminum Alloy 7050-T7451

Compact specimens made of aluminum alloy 7050-T7451 were obtained from the

NASA Langley Research Center that had been machined from a 6-inch thick forging

block. The forging block was in an over-aged T7451 heat-treat condition. Tensile tests

were conducted according to ASTM Standard E8 using 0.25-in. round-bar specimens.

The specimens were tested in the (L) longitudinal and (S) short transverse orientations at

room temperature. The yield stress, ultimate tensile strength, and modulus of elasticity

were calculated from tests for each orientation. For the L-orientation at room

temperature, the yield stress was 68 ksi, the ultimate tensile strength was 76 ksi, and the

modulus of elasticity was 11,000 ksi. The specimens had a width, W = 2 inches, and a

thickness, B = 0.25 inches. The edges of the pin holes in the 7050-T7451 alloy specimens

were beveled to avoid or minimize undesired out-of-plane bending influence on crack-

front shapes. The beveled pin holes, as shown in Figure 1(b), causes the pins to contact 9

near the mid-thickness of the specimen and produce a straight crack front, as shown in

Figure 1(c) by avoiding different stress-intensity factors at the crack tip on each side of

the specimen due to a slight misalignments in the compact clevis pin loading fixture.

Steel 9310

The C(T) specimens from a 9310 steel rod were in the longitudinal direction of

maximum grain flow (LR) orientation. These specimens were also obtained from the

NASA Langley Research Center. Tensile properties were not obtained on this particular

material. The stated yield stress and ultimate tensile strength were 155 and 174 ksi,

respectively. The tensile properties (yield stress and ultimate tensile strength) are

important in the fracture toughness assessment of the steel. Steel specimens also had a

width, W = 2 inches, and a thickness B = 0.4 inches. The edges of the pin holes in the

9310 specimens were not beveled because the material was too hard and the BFS gages

were already installed on the specimens.

10

TEST PROCEDURES

All fatigue crack growth tests were performed under laboratory air conditions at

room temperature in 5.6 kip (25 KN) servo-hydraulic test machines. Crack lengths were

monitored using compliance procedures from BFS gages. Acquisition and test control

data were provided by using the Fatigue Technology Associates (FTA) crack-monitoring

system developed by Donald [22]. The BFS and crack-monitoring software used crack-

compliance to measure and record the crack length, and to record load-strain records with

various compliance-offset values using Elber’s load reduced displacement approach [23].

Normally, ASTM E-647 standard recommends the 2% offset (OP2) value, but both OP1

and OP2 values were used instead to calculate the 0% offset (OP0), which is closer to

Elber’s crack-opening load.

A compression-compression pre-cracking method was used to eliminate or reduce

the history effect from load reduction in the fatigue-crack-growth-rate data in the

threshold and near-threshold regimes for different load ratios, R. The compact specimens

were compression loaded using the standard pins and they were compression pre-cracked

at |Kcp|/E = 0.001 in1/2 for about 50,000 cycles at 10 Hz, unless specified otherwise. For

the aluminum alloy, the maximum compressive load was -50 lbs and R = 13. For the

steel, the maximum compressive load was -50 lbs and R = 60 or 100. Using this

procedure, all specimens were fatigue pre-cracked under compression-compression

11

loading to initiate a crack at the electrical-discharge machined U-notch. The fatigue pre-

crack could not be seen by a low-power microscope, but the compliance from the FTA

system indicated that a very small crack was at the U-notch. The FTA system could not

record the crack length because the system would not allow compression-compression

loading. However, future modification would be very useful for compression pre-

cracking.

Transition effects generated from tensile residual stresses and compressive

loading were removed by extending the fatigue crack under a selected constant-amplitude

loading to Δc ≥ 3 (1-R) ρc, where ρc is the Dugdale compressive plastic-zone size

calculated from the plane-stress equation by ρc = (π/8)(|Kcp|/σo)2 [24, 25]. The crack

must also be grown to an adequate amount from the U-notch-tip by Δc ≥ h to minimize

the notch effect, where h is the height of the notch.

Data from threshold to near fracture were then obtained using either the CPCA or

CPLR loading, at constant R after a small amount of crack extension under constant-

amplitude loading to satisfy the crack-extension criteria for valid test data. The CPCA or

CPLR testing was performed at a nominal frequency of 18 Hz in the low-rate regime and

about 3 to 5 Hz in the high-rate regime. In the CPCA method, the constant-amplitude

loading was selected to be about 30% higher than the anticipated threshold stress-

intensity-factor range, and the loads were held constant until the crack grew to failure, as

shown in Figure 2(a).

In the CPLR test method, the crack was grown under constant-amplitude loading

to again satisfy the plastic-zone and notch criteria, and then the standard ASTM LR

method was used to generate test data in the threshold regime, as depicted in Figure 2(b).

12

In the CPLR method, the initial K is much lower than would be obtained or be allowed

in the standard ASTM LR method using tensile pre-cracking. After reaching a threshold

stress-intensity factor range, Kth, it is customary to conduct a CA test to generate the

K-increasing data. To avoid history effects, the R value for the CA portion should be

higher than the R value used in the LR test. For example, if the LR test was at R = 0.1,

then the CA portion should be at R = 0.4; and if the LR test was at R = 0.4, then the CA

test should be at R = 0.7, as shown in Figure 2(b).

13

MATERIAL TESTED AND ANALYZED


Fatigue-crack-growth results

Fatigue crack growth properties from threshold to near fracture have been determined

for aluminum alloy 7050-T7451 on C(T) specimens to establish the ΔK-rate data for a

wide range in constant load-ratio values (R = 0.1, 0.4 , and 0.7). The fatigue-crack-

growth rate, log(dc/dN), is commonly plotted against log(ΔK). The fatigue-crack-growth

behavior may be categorized into three regions: threshold regime, mid-rate regime (Paris

region) and fracture regime. In the mid-rate regime, ΔK increases and unstable crack

growth is expected in the fracture region, as the crack grows under constant-amplitude

loading, But as ΔK decreases from the Paris region, the fatigue-crack-growth rate

drastically slows down in the threshold regime. The majority of fatigue life is spent

propagating a crack in the near-threshold region, whereas the Paris and fracture regions

consume smaller portions of the total fatigue life.

Multiple tests were conducted on C(T) specimens at different constant load ratios

R = 0.1, 0.4 and 0.7 and these results are shown in Figure 3. Four specimens were tested

using CPCA loading, CPLR loading, and both traditional ASTM LR and CA methods.

The solid symbols show the ASTM LR or CPLR test data, while the open symbols show

the CPCA or CA test results. For the three load ratios, the higher R data shows a faster

14

fatigue-crack-growth rate at the same ΔK, and the R = 0.7 test produced a lower threshold

than the R = 0.1 test. These results shows a slight fanning with the load ratio, where the

spread in data with ΔK in the mid- and higher-rate regions were smaller than in the low

rates region (greater spread in the threshold region). At higher rates, the critical stress-

intensity-factor at failure, ΔKc, is given by KIe (1 – R), where KIe is the elastic fracture

toughness or maximum stress-intensity factor at failure. Thus, tests at higher R failed at a

lower Kc than tests at lower R.

15

Figure 3 Fatigue-crack-growth-rate data for CPCA, CPLR, ASTM LR and CA tests at constant load ratios on 7075-T7451 aluminum alloy.

Figure 4 shows a comparison of test data generated at R = 0.1 loading using the

CPLR, CPCA and ASTM load-reduction (LR) test method from the literature and those

from the current study. The CPLR and CPCA tests were conducted by Newman et al.

[26], whereas the ASTM LR test was conducted by J.A. Newman et al. [27] at NASA

16

Langley Research Center on specimens machined from the same plate of material, but in

a different orientation (LT) than those used in the current study (SL).

These results show that the ASTM LR method for the SL-orientation gave nearly

the same results as CPLR. But the CPLR results were only slightly lower than the ASTM

LR method. However, the LT-orientation showed a much larger difference (from 2 to

2.8 ksi-in1/2) for the CPLR and ASTM LR methods, respectively. These results show that

the SL-orientation has a lower threshold (Kth at 4E-9 in/cycle) and faster rates than the

LT-orientation in the threshold and near-threshold regimes.

Figure 5 shows a comparison for tests conducted on the SL- and LT-orientations

at R = 0.7. Again, the SL-orientation produced a lower threshold (Kth at 4E-9 in/cycle)

and faster rates than the LT-orientation from threshold to fracture.

17

Figure 4 Comparison of FCG data generated from CPCA, CPLR, ASTM LR and CA threshold testing on 7075-T7451 aluminum alloy at R = 0.1.

18

Figure 5 Comparison of FCG data generated from CPCA, CPLR, ASTM LR and CA threshold testing on 7075-T7451 aluminum alloy at R = 0.7.

19

Crack-closure measurements

Crack-opening loads were measured during the fatigue-crack-growth tests using

compliance data from the remote BFS gage method. The FTA crack-monitoring system

recorded the crack-opening-load (Po/Pmax) ratios for 1% and 2% offset (OP1 and OP2,

respectively) compliance. In this paper, the zero-percent offset value, defined as OP0 = 2

OP1 – OP2, was used to approximate Elber’s definition of the crack-opening load. These

results will be used to help explain the load-ratio effects on FCG behavior. Based on the

ranges of crack-opening load determined for both 7050-T7451 aluminum alloy and 9310

steel, an effective stress-intensity factor range, ΔKeff, was calculated and compared with

the FASTRAN model that accounts for only plasticity-induced-crack-closure (PICC)

behavior.

Figure 6 shows the crack-opening-load ratio, as a function of crack length to width

ratio generated from CPLR, ASTM LR, CPCA and CA for R = 0.1 tests. (The Po/Pmax ratio

is the OP0 value.) The plot shows the crack starter notch and the two criteria [19, 28] (both

the plastic-zone criterion and the notch criterion gave the same value of crack extension) to

remove the effects of the tensile residual stresses caused by compressive loading and the

notch effect. In both the CPLR and ASTM LR methods, Figure 6(a), shows a rapid rise

in the crack-opening load ratio as the threshold stress-intensity factor is approached,

reaching a high value above c/W = 0.6. These results may be caused by a load-history

effect due to load shedding or the crack surfaces may become more faceted with an

increase in crack-surface roughness and RICC. During the CA and CPCA tests, as shown

in Figure 6(b), the Po/Pmax ratio started to about 0.45 and 0.6, respectively, and continued

to drop with further crack growth.

20

The solid horizontal line in Figure 6(a, b) represents the crack-opening-load ratio

calculated from the FASTRAN model for a constraint factor = 1.8. The PICC model

agreed well for 0.4 < c/W < 0.7 with a +/-10% allowance for scatter and variation. The

drop in the crack-opening-load ratio for c/W > 2/3 on C(T) (and ESE(T)) specimens has

been observed in the literature [29]. It is suspected that a deep crack in bending will

develop more plane-strain conditions and a high positive T-stress, which would cause

less crack closure.

Using the compliance offset at 0% (OP0), the ΔKeff values were determined in

Figure 7 for all of the R = 0.1 tests. The compliance offset measurements from the

remote BFS gage did not produce any (OP1 or OP2) values for the R = 0.4 and 0.7 tests.

However, the R = 0.7 data is shown as K (square symbols). The Keff results for the

R = 0.1 tests agreed very well with the R = 0.7 results in the mid-region, but fell well

below the R = 0.7 results in the threshold regime. In the mid-region, the R = 0.7 test is

expected to be closure free (K = Keff), while the R = 0.7 results in the near-threshold

region is expected to develop crack closure. Yamada and Newman [9, 21, 26] showed

that there is crack closure on the R = 0.7 tests, and tests at even higher R values, in the

threshold regime using local strain gages from the load-local-strain records.

21

Figure 6 Crack-opening load ratio as a function of crack length to width ratio generated from CPLR and ASTM LR for R = 0.1 tests on 7075-T7451 aluminum alloy.

22

Figure 7 Crack-opening load ratio as a function of crack length to width ratio generated from CPCA and CA for R = 0.1 tests on 7075-T7451 aluminum alloy.

23

Figure 8 Effective stress-intensity-factor ranges for R = 0.1 tests using measurements and K for R = 0.7 tests on 7075-T7451 aluminum alloy.

24

Crack-growth modeling

FASTRAN is a life-prediction code based on the plasticity-induced crack-closure

concept [4, 5] and the modified Dugdale [30] or strip-yield model. The code is used to

predict crack length against cycles from a specified initial crack size to failure for many

common crack configurations found in structural components. In general, for any crack

configuration, the effective stress-intensity factor is given by

ΔKeff = U ΔK = [(1 – Po/Pmax)/(1 – R)] ΔK (1)

The crack-growth relation used in FASTRAN [33, 34] is

dc/dN = C1i(ΔKeff)C2i [1 – (ΔKo/ΔKeff)p]/[1 – (Kmax/C5)q] (2)

where C1i and C2i are the coefficient and power for each linear segment, ΔKeff is the

effective stress-intensity factor range, ΔKo is the effective stress-intensity factor range at

threshold, Kmax is the maximum stress-intensity factor, C5 is the cyclic elastic fracture

toughness (usually C5 is set equal to KIe, which is generally a function of crack length,

specimen width, and specimen type), p and q are constants selected to fit test data in

either the threshold or fracture regimes. Whenever the applied Kmax value reaches or

exceeds C5 (or KIe), then the specimen or component would fail and the crack-growth rate

goes to infinity. Currently, the effective threshold stress-intensity-factor range, ΔKo, is

expressed as a function of load ratio. For positive load ratios (R ≥ 0),

ΔKo = C3 (1 + C4 R) for negative C4 (3)

or

ΔKo = C3 (1 – R) C4 for positive C4 (4)

C3 and C4 are determined from experimental test data in the threshold regime.

25

The sharp changes in the crack-growth-rate curves at unique values of rates have

been associated with monotonic and cyclic plastic-zone sizes, grain sizes, and

environments [31, 32].

The crack-closure model FASTRAN [33, 34] was used to correlate the ΔK-rate

data into a tight band on the ΔKeff plot using a constraint factor of α = 1.8, as shown in

Figure 8. The test data correlated very well and even collapsed onto a unique curve from

threshold to near fracture. In the upper rate regime, the Keff at fracture is a function of

R. High R tests will have a lower critical Keff value than low R. The curve with open

circular symbols is the Keff baseline curve selected to fit these data.

The data shown in Figure 8 were very different from the measured ΔKeff values,

as shown in Figure 7. This discrepancy was mainly due to the fact that the FASTRAN

model is based on PICC, while in the threshold regime all the three shielding mechanisms

PICC, RICC and DICC have an impact to the ΔK-rate data.

Life prediction can be accurately obtained using a combination of plasticity,

roughness and debris [35-37] crack-closure modeling for large cracks. However, these

three crack-growth mechanisms (PICC, RICC and DICC) have not been incorporated into

any of the major life-prediction codes, like FASTRAN [34], NASGRO [38] and

AFGROW [39].

But as shown in Figure 8, the FASTRAN PICC model was able to correlate the

K-rate data for all tests onto a nearly unique Keff-rate curve. Thus, from a Fracture

Mechanics similitude perspective, the PICC model can be used to predict crack growth

under CA loading very well. However, caution must be exercised when trying to predict

crack growth under spectrum loading because RICC and DICC mechanisms are not

26

modeled. Further research is needed to model crack growth under spectrum loading that

includes the three major crack-shielding mechanisms.

The solid curve with open symbols in Figure 8 shows the ΔKeff-rate baseline

curve (see Table 1) for the aluminum alloy. Figure 9 shows that the FASTRAN model

with a constraint factor of α = 1.8 modeled the fatigue-crack-growth test (K-rate) data at

R = 0.1, 0.4 and 0.7 fairly well. The coefficients in the threshold and fracture terms of

Equation (2) were evaluated from the test data presented in Figure 3. The ΔKo value was

zero because the Keff-rate data in the threshold regime didn’t vary with load ratio R.

Several C(T) specimens were cycled to failure at both low and high R. The cyclic

fracture toughness, C5 = 23.33 ksi-in1/2, was used to fit the FCG data as the specimens

failed. However, it is suspected that KIe values are not constant, but vary with crack

length and specimen width. The exponent, q = 6, was selected to best match the shape of

the ΔK-rate curve from the CA test. Insufficient test data was available to conduct a

Two-Parameter Fracture Criterion (TPFC) analysis [40].

Table 1 Effective Stress-Intensity Factor Range against Rate Relation for 7050-T7451 Aluminum Alloy

ΔKeff, ksi-in1/2 dc/dN, in/cycle 0.94 4.0e-9 1.00 1.7e-8 1.20 5.2e-8 1.80 1.6e-7 3.15 5.5e-7 4.70 1.9e-6 7.50 1.5e-5 10.0 5.2e-5 13.0 5.8e-4

= 1.8 All rates C3 = 0 ksi-in1/2 C4 = 0

C5 = 23.33 ksi-in1/2 q = 6 27

Figure 9 Effective stress-intensity-factor ranges against rate for all tests using FASTRAN model on 7075-T7451 aluminum alloy.

28

Figure 10 Measured and calculated FCG behavior over wide range in load ratios from threshold to fracture on 7075-T7451 aluminum alloy.

Steel 9310

Fatigue-crack-growth results

Fatigue crack growth properties from threshold to near fracture have been

determined for 9310 steel on C(T) specimens to establish the ΔK-rate data for a wide

29

range in constant load-ratio values (R = 0.1, 0.4 , 0.7 and 0.9). The fatigue-crack-growth

rate log(dc/dN) is commonly plotted against log(ΔK). The fatigue-crack-growth behavior

can be categorized into three regions: threshold regime, mid-rate regime (Paris region)

and fracture regime. In the mid-rate regime, ΔK increases and unstable crack growth is

expected in the fracture region, as the crack grows under constant-amplitude loading.

But as ΔK decreases from the Paris region, the fatigue crack growth rate drastically slows

down in the threshold regime. The majority of fatigue life is spent propagating a crack in

the near-threshold region, whereas the Paris and fracture regions consume smaller

portions of the total fatigue life.

Testing on 9310 steel was made on five C(T) specimens to generate fatigue-crack-

growth-rate data. Tests were conducted using CPCA, CPLR and CA test methods.

These tests have been performed at a constant load ratio values (R = 0.1, 0.4, 0.7 and

0.9). After compression pre-cracking, all tests were subjected to CA loading to grow the

crack to satisfy the crack-growth criteria, and then either CA was continued (CPCA test)

or a LR test was conducted (CPLR). Figure 10 shows the measured test data, which

generally ranged from threshold to near fracture. The solid symbols show the CPLR test

results, while the open symbols show the CPCA and CA test results. The two tests

conducted at R = 0.1 under CPCA loading with a time delay or no time delay after CP

loading will be discussed later. Only once specimen was delayed two months after CP

loading and all the rest of the specimens were tested immediately.

30

Figure 11 Fatigue-crack-growth-rate data for CPCA, CPLR and CA tests at constant load ratios on 9310 steel.

31

In the near-threshold regime, the R = 0.9 rates were slightly higher than the rates

for R = 0.7 at the same ΔK value. The test results for low R (0.1) in the mid- and upper-

rate regimes show the usually parallel shift along ΔK axis with load ratio. For the four

load ratios, the higher R shows faster fatigue crack growth rate at the same ΔK, and the R

= 0.9 test produced a lower threshold than the R = 0.7 test. In the threshold regime, there

is a slight spread between 0.7 and 0.9 rates, which may indicate that the R = 0.7 test had

some crack-closure behavior during the load-reduction procedure, as observed by

Yamada and Newman [28, 41].

There is a large spread in the test data in the threshold and mid-rate regions for

one of the R = 0.1 CPCA tests due to pre-cracking the specimen two months before

conducting the CA portion of the test. This specimen was the only one to be delayed and

was compression pre-cracked at |Kcp|/E = 0.0008 in1/2. These results showed a very

strange behavior in the early stage of crack growth and showed very low crack-growth

rates. It was suspected that the tensile residual stresses due to compression pre-cracking

relaxed at the crack tip during the long hold time. A second specimen was compression

pre-cracked (|Kcp|/E = 0.0016 in1/2), but tested immediately under CPCA loading. These

results did not show the very low crack-growth rates, as were observed in the earlier test.

Thus, all other specimens were compression pre-cracked at the higher |Kcp|/E ratio, just

before testing. These results show no fanning in the threshold region due to the parallel

shift of data with the load ratio. At higher rates, the critical stress-intensity-factor range

at failure, ΔKc, is given by KIe (1 – R), where KIe is the elastic fracture toughness or

32

maximum stress-intensity factor at failure, then a crack in this regime will grow to failure

at lower ΔKc values for higher R.

Figures 11 through 14 show comparisons of test data from the literature and the

current study for R = 0.1, 0.4, 0.7, and 0.9, respectfully. There was excellent agreement

between the current tests and the literature results for a wide range of load ratios.

33

Figure 12 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.1 on 9310 steel.

34


35


36


37

Crack-closure measurements

For the 9310 steel, the remote load-strain method using the FTA crack monitoring

system produced no information on OP1 and OP2 for all tests. However, using the

ASTM E-647 procedure [13], crack-opening loads may be determined by a deviation

point from the loading curve on the load against reduced strain records. If there is no

crack-surface contact, the load reduced strain record would show only linearity. Elber’s

crack-opening load was defined at the first indication where the loading slope equals the

unloading slope [23]. For constant amplitude loadings, the compliance is constant at high

loads (open crack) which appear as a linear section. During unloading, a large portion of

the crack surface closes; this compliance change is very dramatic (change in slope).

During loading, as the crack surfaces open the compliance changes until the crack is fully

open and then when the opening compliance is equal to the unloading compliance,

Elber’s crack opening load is defined. This difficulty arises when determining the correct

crack-opening load from the load-reduced-strain record with electronic and mechanical

noise in the record. Some typical load-reduced-strain records were measured from the

BFS gage at various stress-intensity factor ranges for a cracked specimen at different load

ratios (R = 0.1, 0.4 and 0.7). For R = 0.1 and 0.4, the remote gage showed some

indication of crack closure at different stress-intensity factor ranges, but the record was

not clear enough to deduce accurate crack-opening values, as shown in Figure 15(a) and

15(b). The ASTM E-647 method of calculating the crack-opening load was inconclusive

for low R (< 0.4) due to the fact that the remote gage lacked the required fidelity to

determine crack-opening loads in the threshold and near-threshold regimes. But for the R

= 0.7 test, Figure 15(c), the results from the BFS showed a tail-swing associated with the

38

crack closure in the threshold region. The curvature between Po/Pmax of 0.785 and 0.925

showed a noticeable difference at ΔK = 2.82 ksi-in1/2. Whereas, at ΔK = 13.93 ksi-in1/2,

the remote load-reduced-strain record was very linear and didn’t show any crack closure

(K = Keff). The ΔKeff values couldn’t be determined from load-strain or reduced-strain

records due to the poor sensitivity to crack-tip events [35]. The remote BFS gages are

not sufficient to determine crack-opening loads from remote measurements. Changes in

compliance are sensitive to crack closure. To better determine the crack-opening loads

and to improve sensitivity, load-strain records should be measured using near crack tip

local gages, as shown by Yamada and Newman [28].

39

Figure 16 Remote reduced load-backface-strain records for various stress-intensity factor for R = 0.1 on 9310 steel.

40


41


Crack-growth modeling

The crack-closure model FASTRAN [33, 34] was again used to correlate the ΔK-

rate data into a tight band on the ΔKeff plot using a constraint factor of α = 2.5, as shown

in Figure 16. The value of constraint was selected to collapse the K-rate data in the

42

near-threshold regime. The data correlated very well and even collapsed into a unique

curve from threshold to near the fracture regime. The R = 0.9 constant-amplitude test

deviated at the high rates because the specimen was going to fracture. The 9310 steel

produced a very flat crack surface which would greatly reduce the effects of roughness

and debris, thus plasticity was the dominant shielding mechanism for crack closure. The

plasticity-induced crack-closure model was able to collapse the K-rate data into a tight

band over a wide range in R and rates. The solid curve with open symbols show the

ΔKeff-rate baseline curve (see Table 2).

Figure 17 shows that the crack-growth equation (Eqn. 2) with a constraint factor

of α = 2.5 matched the K-rate data very well at R = 0.1, 0.4, 0.7 and 0.9. The

coefficients in the threshold and fracture terms of Equation (2) were evaluated from test

data presented in Figure 16. The ΔKo value was again selected as zero because the K-

rate data in the threshold regime didn’t vary with load ratio R. Several C(T) specimens

were cycled to failure at both low and high R. The cyclic fracture toughness,

C5 = 150 ksi-in1/2, to fit the FCG data as cracks grew to failure. The power term, q = 6,

was selected to best match the shape of the ΔK-rate curve from the CA test. Again,

insufficient test data was available to conduct a Two-Parameter Fracture Criterion

(TPFC) analysis [40].

43

Table 2 Effective Stress-Intensity Factor Range against Rate Relation for 9310 steel.

ΔKeff, ksi-in1/2 dc/dN, in/cycle 2.62 3.0e-9 2.86 1.7e-8 3.50 5.2e-8 5.00 1.3e-7 10.00 6.5e-7 15.00 2.4e-6 23.00 6.8e-6 40.00 2.2e-5 66.00 1.0e-4 77.00 2.0e-4 = 2.5 All rates

C3 = 0 ksi-in1/2 C4 = 0 C5 = 150 ksi-in1/2 q = 6

44

Figure 19 Effective stress-intensity-factor ranges against rate for all tests using FASTRAN model on 9310 steel.

45

Figure 20 Measured and calculated FCG behavior over wide range in load ratios from threshold to fracture on 9310 steel.

46

DISCUSSION OF RESULTS


Testing on 7050-T7451 aluminum alloy in the SL-orientation has shown that the

FCG rates were faster over the complete range in K, the thresholds are lower, and has

lower fracture toughness than the LT-orientation. Thus, cracks will grow faster and

critical crack lengths will be smaller in the SL-orientation than in the LT-orientation.

A rapid rise in the crack-opening-load ratio was shown for both the CPLR and

ASTM LR tests, reaching a value greater than c/W = 0.6. During the CPCA and CA

tests, the crack-opening-load ratio was about 0.5 and leveled off to roughly 0.4 with crack

extension, but dropped as the cracks became larger (c/W > 0.6). Thus, the load-reduction

test causes a quite different crack-opening-load history than the constant-amplitude tests.

These results may be caused by a load-history effect due to load shedding and/or the

crack surfaces may become more faceted with an increase in crack-surface roughness as

the stress-intensity factor level was reduced.

In the literature, plasticity effects have been dismissed because the plasticity-zone

sizes are very small near threshold conditions, but crack-surface displacements are also

very small. PICC is due to the interference between the residual plastic deformations and

crack-surface displacements. Thus in the threshold regime, PICC is still a very dominant

shielding mechanism at any R-value. The FASTRAN PICC model predicts that above

47

R ≥ 0.7, the cracks should be fully open under plane-stress or plane-strain conditions, so

PICC is not the complete reason for high R closure. But under high R conditions, the

crack-opening load is at the minimum load and, thus, a small influence of roughness

and/or debris will cause the crack-opening load to be higher than the minimum load. It

was suspected that the threshold tests at R = 0.7 would develop high-R closure. Thus,

Figure 18 shows the comparison of the Keff results on the R = 0.1 tests and estimated

Keff results that would match the R = 0.1 results. In the mid-rate regime, Keff = K (U

= 1). But at the threshold rate (4E-09 in./cycle), the U value was estimated at 0.55

(Keff = U, K = 0.55 K), which gives Po/Pmax = 0.835. Thus, PICC would give 70%

contribution (crack-opening load equal to minimum load) and RICC/DICC would

contribute the remainder of 0.135. While roughness/debris contributions are important,

plasticity effects are still dominant. If it had not been for the residual plastic

deformations from plasticity and cyclic crack growth at R = 0.7 loading, then the

RICC/DICC contribution would have been insignificant. Further study is needed on

measuring crack-opening loads using “local” methods, like Elber’s original work.

The 7050-T7451 alloy creates a very rough and tortuous fatigue crack-surface

compared to 2024-T3 or 7075-T6. Thus, for high-R conditions, RICC is suspected to be

a major contributor to the rise in the crack-opening-ratio level as the threshold is

approached. Very rough crack surfaces with asperities may also create debris along the

crack surfaces, so DICC is also suspected to be a major contributor to the rise in the

crack-opening-ratio levels in the threshold regime for high R [28, 41]. However, the

FASTRAN model correlated the data fairly well using a constraint factor (α = 1.8), but

48

the true Keff-rate curve in the threshold regime is suspected to be much lower, as shown

in Figure 7 and 18, due to RICC and DICC mechanisms.

Figure 18. Effective stress-intensity-factor ranges for R = 0.1 tests using measurements and estimates for R = 0.7 tests on 7075-T7451 aluminum alloy.

49

Steel 9310

Testing on 9310 steel has shown that compression pre-cracking the specimens

two months before testing under constant-amplitude loading resulted in greatly reduced

tensile residual stresses at the crack-starter notch tip. A specimen was re-tested under a

larger compression pre-cracking load and immediately tested under constant-amplitude

loading (CPCA test); and the results were as expected based on previous test data on

9310 steel [9] and did not show the unusual behavior that was observed in the first test.

The remote load-strain method using the FTA crack monitoring system did not

detect any local crack closure (1 or 2% offset compliance values). Thus, the ASTM

method (load-reduced-strain records measured from the BFS gage) was used to extract

Elber’s crack-opening load, but unfortunately these results were inconclusive due to the

fact that remote gage lacked the required fidelity to determine local crack-closure

behavior. For R = 0.7 loading, the existence of crack closure was shown in Figure 15(c)

where the tail-swing (non linear load-strain records) associated with the crack closure in

the threshold region was observed. However, the remote gages are still inadequate to

determine crack-opening loads from remote measurements. For better understanding and

determination of crack-opening loads and even improvement in sensitivity, local gages

near the anticipated crack path should be used to record load-strain records as the crack

approaches these gages in order to depict in a very precise and accurate manner the

crack-closure behavior [9].

The 9310 steel creates a very smooth and flat fatigue-crack surface, but the

fracture surface showed nearly double shear fracture (V-shear). RICC and DICC are

suspected to be a minor contribution to the crack-growth rates except the one specimen

50

that was delayed in testing for two months after compression pre-cracking. This

specimen showed a dark appearance compared to all others specimens, which indicated a

build-up in debris. Again, the FASTRAN model correlated the test data very well using

high constraint factor (α = 2.5) indicating that PICC was a dominant mechanism.

51

CONCLUDING REMARKS

Fatigue-crack-growth-rate tests were conducted on compact, C(T), specimens

made of 7050-T7451 aluminum alloy and 9310 steel. Compact tension specimens were

tested over a wide range of load ratios (0.1 ≤ R ≤ 0.9) to generate crack-growth-rate data

from threshold to near fracture. Three methods were used to generate near threshold

data: (1) ASTM Standard E647 load reduction (LR), (2) compression pre-cracking

constant-amplitude (CPCA), and (3) compression pre-cracking load reduction (CPLR).

Results were compared with existing test data on the 9310 steel from the literature that

was tested in a different thickness, and with test data from the literature on the 7050 alloy

that was tested in a different material orientation. In both the 7050 (SL-orientation) and

the 9310 material, very little difference was observed between the ASTM load reduction

(LR), CPLR and CPCA test methods, although compression pre-cracking allowed much

lower initial ∆K values than the ASTM standard. It had previously been shown that the

ASTM LR method induces a load-history effect which may be caused by remote closure

in the 7050 alloy that was tested in the LT-orientation.

The backface strain (BFS) gage method was used to monitor crack lengths and to

measure crack-opening loads from remote load-strain records during all tests. A crack-

compliance method using BFS gages had previously been used to determine that the

crack-starter notch tensile residual-stress effects from compression pre-cracking

52

dissipated in about three compressive plastic-zone sizes and the crack-closure behavior

stabilized to produce steady-state constant-amplitude data. In addition, crack extension

from the crack-starter notch beyond one notch height was shown herein to eliminate the

effects of the notch on the stress-intensity factor.

During all tests, the compliance off-set method was used to estimate the crack-

opening load as a function of stress ratio and crack length. A zero percent offset value

(OP0), similar to Elber’s crack-opening load, was extrapolated using the one-percent

(OP1) and two-percent (OP2) offset compliance values recorded from the BFS and crack-

monitoring software using Elber’s load-reduced-displacement approach.

For the 7050 alloy, a crack-closure analysis was performed to calculate the

effective stress-intensity factor (∆Keff) against rate using measured (OP0) values for low

R (0.1) and these results were compared with the K-rate test data at high R. Past

research had shown that high R (≥ 0.7) test data is basically the ∆Keff-rate curve in the

mid-rate region. However, in the low-rate regime, previous testing had shown that high-

R closure develops due to the load-reduction method and/or faceted crack-growth

behavior causing roughness- or debris-induced crack closure, in addition to plasticity-

induced crack closure. For high R, plasticity is suspected to give a crack-opening load at

or near the minimum load, and, thus, roughness/fretting debris are suspected to cause

crack-opening loads above the minimum load. Unfortunately, the remote BFS method

was unreliable to measure OP0 values for high stress ratios (R ≥ 0.4). In order to get

more reliable crack opening values, local gages should be used.

For the 9310 steel, the remote BFS method was unable to detect any OP1 and

OP2 compliance off-set values at any stress ratio, so a crack-closure analysis using OP0

53

values could not be preformed. In the steel tests, the fatigue crack surfaces were very

flat, and roughness-induced crack closure was not expected. Debris-induced crack

closure may be caused by the environment (humidity levels). However, plasticity-

induced crack closure was expected to be the major crack-closure mechanism.

A crack-closure analysis was performed on both materials using the FASTRAN


and collapsed onto a nearly unique curve in the low- and mid-rate regimes using the strip-

yield model in the FASTRAN life-prediction code. In the high rate regime, the fracture

toughness controlled the crack-growth-rate behavior. The Newman crack-growth

equation modeled the behavior in the threshold to fracture regimes fairly well. For the

7050 alloy, a constraint factor of α = 1.8 was required, while for the 9310 steel α = 2.5

worked very well in correlating the test data over a very wide range in R values and rates

from threshold to near fracture.

The major contribution of this work was to generate the K-rate data to help

industries conduct damage tolerance analyses. In addition, crack-growth-rate data needs

to be generated using local-strain gages for their sensitivity to determine local crack

opening behavior. Further studies are required to understand the impact of a time delay,

after compression pre-cracking, on the constant amplitude results.

54

REFERENCES

1. Paris, P. C. and Erdogan, F., “A critical analysis of crack propagation laws,” Journal of Basic Engineering, Vol. 85, No. 3, 1963, pp. 528-534.

2. Barsom, J. M., “Fatigue-crack propagation in steels of various yield strengths,” Journal of Engineering for Industry, Vol. 93, No. 4, 1971, pp. 1190-1196.

3. McEvily, A. J., Jr. and Illg, W. “The rate of fatigue-crack propagation in two aluminum alloys,” NACA TN 4394, 1958.

4. Elber, W., “Fatigue crack closure under cyclic tension,” Engineering Fracture Mechanics, Vol. 2, No. 1, 1970, pp. 37-45.

5. Elber, W., “The significance of fatigue crack closure,” ASTM STP 486, American Society for Testing and Materials, 1971, pp. 230-242.

6. Walker, N. and Beevers, C. J., “A fatigue crack closure mechanism in titanium,” Fatigue of Engineering Materials and Structures, Vol. 1, No. 1, 1979, pp. 135-148.

7. Paris, P. C., Bucci, R. J., Wessel, E. T., Clark, W. G., and Mager, T. R., “Extensive study of low fatigue crack growth rates in A533 and A508 steels,” ASTM STP-513, 1972, pp. 141-176.

8. Newman, J. C., Jr., “Effects of constraint on crack growth under aircraft spectrum loading,” Fatigue of Aircraft Materials, Delft University Press, The Netherlands, 1992, pp. 83-109.

9. Yamada, Y. and Newman, J. C., Jr., Crack closure under high load ratio and Kmax test conditions, Fatigue 2010, Procedia Engineering, Vol. 2, Issue 1, 2010, pp. 71–82.

10. Suresh, S., Zaminski, G. F. and Ritchie, R. O., “Oxide induced crack closure: an explanation for near-threshold corrosion fatigue crack growth behavior,” Metallurgical Transactions, Vol. A12A, 1981, pp. 1435-1443.

11. Kirby, B. R. and Beevers, C. J., “Slow fatigue crack growth and threshold behaviour in air and vacuum of commercial aluminium alloys,” Fatigue and Fracture of Engineering Materials and Structures, Vol. 1, 1979, pp. 203-216.

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12. Newman, J. C., Jr., “Analysis of fatigue crack growth and closure near threshold conditions,” ASTM STP-1372, American Society for Testing Materials, 2000, pp. 227-251.

13. ASTM Standard E-647-08, “Standard Test Method for Measurement of Fatigue Crack Growth Rates,” ASTM International, West Conshohocken, Pennsylvania, 2009.

14. Newman, J. C., Jr., “A nonlinear fracture mechanics approach to the growth of small cracks. In: Behavior of short cracks in airframe components,” AGARD CP-328, 1983, pp. 6.1-6.27.

15. Ruschau, J. and Newman, J. C., Jr., " Improved test methods for very low fatigue-crack-growth-rate data," American Helicopter Society International 64th Annual Forum & Technology Display, Montréal, Canada, 2008.

16. McClung, R. C., “Analysis of fatigue crack closure during simulated threshold testing,” ASTM STP-1372, American Society for Testing Materials, 2000, pp. 209-226.

17. Pippan, R., “The growth of short cracks under cyclic compression,” Fatigue and Fracture of Engineering Materials and Structures Journal, Vol. 9, 1987, pp. 319-328.

18. Topper, T. H. and Au, P., “Fatigue test methodology,” AGARD Lecture Series 118, The Technical University of Denmark, Denmark, 1981.

19. Newman, J. C., Jr., Schneider, J., Daniel, A. and McKnight, D., “Compression pre-cracking to generate near threshold fatigue-crack-growth rates in two aluminum alloys,” International Journal of Fatigue, Vol. 27, 2005, pp. 1432-1440.

20. Yamada, Y., Newman, J. C., III and Newman, J. C., Jr., “Elastic-plastic finite-element analyses of compression pre-cracking and its influence on subsequent fatigue-crack growth,” Journal of ASTM International, Vol. 5, No. 8, 2008.

21. Newman, J. C., Jr., Yamada, Y., Ziegler, B.M., Shaw, J.W., ”Small and Large Crack Damage Tolerance Databases for Rotorcraft Materials,” DOT/FAA/TC-13/29, June 2014.

22. Donald, J. K., “A procedure for standardizing crack closure levels,” Mechanics of Fatigue Crack Closure, ASTM STP 982, American Society for Testing and Materials, 1988, pp. 222-229.

23. Elber, W., “Crack-closure and crack-growth measurements in surface-flawed titanium alloy Ti-6Al-4V,” NASA TN D-8010, September 1975.

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24. Forth, S. C., Newman, J. C., Jr. and Forman, R. G. “On generating fatigue crack growth thresholds,”. International Journal of Fatigue 2003; 25:9-15.

25. Ruschau, J. R. and Newman, J. C., Jr. “Compression pre-cracking to generate near threshold fatigue-crack growth rates in an aluminum and titanium alloy,” Journal of ASTM International, Vol. 5, No. 7, 2008.

26. Newman, J. C., Jr., Yamada, Y. and Newman, J. A., “Crack closure behavior of 7050 aluminum alloy near threshold conditions for a wide range in load ratios and constant Kmax cests,” Journal of ASTM International, Vol.7, No. 4, 2010.

27. Newman, J. A., James, M.A., Johnston, W. M. and Le, D. D., “Fatigue crack growth threshold testing of metallic rotorcraft materials,” NASA/TM-2008-215331, ARL-TR-4472, July 2008.

28. Yamada, Y. and Newman, J. C., Jr., “Crack closure under high load-ratio conditions for Inconel-718 near threshold conditions,” Engineering Fracture Mechanics, Vol. 76, pp. 209-220, 2008.

29. Newman, J. C., Jr., Ziegler, B. M., Shaw, J. W., Cordes, T. S. and Lingenfelser, D. J. “Fatigue crack growth rate behavior of A36 steel using ASTM load-reduction and compression pre-cracking test methods,” Journal of ASTM International, Vol. 9, pp. 1-9, 2012.

30. Dugdale, D. S., "Yielding of steel sheets containing slits, Journal of Mechanics and Physics of Solids," Vol. 8, No.2, 1960, pp. 100-104.

31. Yoder, G. R., Cooley, L. and Crooker, T. W., “On microstructural control on near-threshold fatigue crack growth in 7000-series aluminum alloys,” Scripta Metallurgica, Vol. 16, pp. 1021-1025, 1982.

32. Piascik, R. S. and Gangloff, R. P., “Environmental fatigue of an Al-Li-Cu alloy: Part II. Microscopic hydrogen cracking process,” Metallurgical Transactions, Vol. 24A, pp. 2751-2762, 1993.

33. Newman, J. C., Jr., “A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading,” ASTM STP 748, American Society for Testing and Materials, Philadelphia, PA., 1981, pp. 53-84.

34. Newman, J. C., Jr., “FASTRAN II- A fatigue crack growth structural analysis program,” NASA TM 104159, 1992.

35. Newman, J. A., “The effects of load ratio on threshold fatigue crack growth of aluminum alloys,” Ph.D. Thesis, Virginia Polytechnic Institute and State University, October 2000.

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36. Newman, J. A., Riddell, W. T. and Piascik, R. S., “A threshold fatigue crack closure model: Part I- model development,” Fatigue and Fracture Engineering Materials and Structures, Vol. 26, pp.603-614, 2003.

37. Kim, J. H. and Lee, S. B., “Behavior of plasticity-induced crack closure and roughness-induced crack closure in aluminum alloy,” International Journal of Fatigue, Vol. 23, pp. S247-S251, 2001.

38. NASGRO Reference Manual, Version 5.2, Southwest Research Institute and NASA Johnson Space Center, 2008.

39. Harter, J. A., “AFGROW Users Guide and Technical Manual,” AFRL-VA-WP-TR-2002, Version 4.0005.12.10, Air Force Research Laboratory, Wright Patterson Air Force Base, Ohio, July 2002.

40. Newman. J. C., Jr., “Fracture analysis of various cracked configurations in sheet and plate materials,” ASTM STP 605, American Society for Testing and Materials, Philadelphia, PA, pp. 104-123, 1976.

41. Yamada, Y. and Newman, J. C., Jr., "Crack-closure behavior of 2324-T39 aluminum alloy near threshold conditions for high load ratio and constant Kmax tests," International Journal of Fatigue, doi:10.1016/j.ijfatigue.2008.11.010.

42. Phillips, E. P., “Results of the second round robin on opening-load measurements conducted by ASTM Task Group E24.04.04 on crack closure measurements and analysis,” NASA Technical Memorandum 109032, November 1993.

43. Newman, J. C., Jr., “Analysis of fatigue crack growth and closure near threshold conditions”, ASTM STP-1372, American Society for Testing and Materials, West Conshohocken, PA, pp. 227-251, 2000.

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