Mississippi State University Mississippi State University
Scholars Junction Scholars Junction
Theses and Dissertations Theses and Dissertations
1-1-2016
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
Follow this and additional works at: https://scholarsjunction.msstate.edu/td
Recommended Citation Recommended Citation Senhaji, Talal Mehdi, "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" (2016). Theses and Dissertations. 2252. https://scholarsjunction.msstate.edu/td/2252
This Graduate Thesis - Open Access is brought to you for free and open access by the Theses and Dissertations at Scholars Junction. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of Scholars Junction. For more information, please contact [email protected].
Template Created By: James Nail 2010
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
Template Created By: James Nail 2010
Copyright 2016
By
Talal Mehdi Senhaji
Template Created By: James Nail 2010
____________________________________
____________________________________
____________________________________
____________________________________
____________________________________
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
Template Created By: James Nail 2010
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
13 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.4 on 9310 steel. ........................................35
14 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.7 on 9310 steel. ........................................36
15 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.9 on 9310 steel. ........................................37
16 Remote reduced load-backface-strain records for various stress-intensity factor for R = 0.1 on 9310 steel.............................................40
17 Remote reduced load-backface-strain records for various stress-intensity factor for R = 0.4 on 9310 steel.............................................41
18 Remote reduced load-backface-strain records for various stress-intensity factor for R = 0.7 on 9310 steel.............................................42
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
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. 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
Aluminum Alloy 7050-T7451
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
Figure 13 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.4 on 9310 steel.
35
Figure 14 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.7 on 9310 steel.
36
Figure 15 Comparison of FCG data generated from CPCA, CPLR and CA tests at constant load ratio R = 0.9 on 9310 steel.
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
Figure 17 Remote reduced load-backface-strain records for various stress-intensity factor for R = 0.4 on 9310 steel.
41
Figure 18 Remote reduced load-backface-strain records for various stress-intensity factor for R = 0.7 on 9310 steel.
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
Aluminum Alloy 7050-T7451
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
crack-closure model. The crack-growth-rate data for each material correlated very well
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.
55
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.
56
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.
57
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.
58