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[Date RR # approved – ASTM to assign]
Committee E08 on Fatigue and Fracture
Subcommittee E08.06 on Crack Growth Behavior
Research Report [RR # – ASTM to assign]
Interlaboratory Study to Establish Precision Statements for ASTM E647, Standard Test Method for Measurement of Fatigue Crack Growth Rates
Prepared by: Peter C. McKeighan James H. Feiger Dustin H. McKnight
ASTM International 100 Barr Harbor Drive
West Conshohocken, PA 19428-2959
ROUND ROBIN TEST PROGRAM AND RESULTS FOR FATIGUE CRACK GROWTH MEASUREMENT
IN SUPPORT OF ASTM STANDARD E647
Prepared by
Peter C. McKeighan James H. Feiger
Dustin H. McKnight
Southwest Research Institute (SwRI®) San Antonio, Texas
Prepared for
ASTM International Committee E08 on Fatigue and Fracture
Subcommittee E08.06 on Crack Growth Behavior West Conshohocken, PA
February 2008
S O U T H W E S T R E S E A R C H I N S T I T U T E® SAN ANTONIO HOUSTON WASHINGTON, DC
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Acknowledgements
This effort would not have been possible without the input from all of the participants in
the round robin test program. The hard work provided gratis from each of the participants and
their labs is greatly appreciated. Furthermore, the United States Air Force is acknowledged for
graciously helping to provide the material for this program. MTS and Instron were kind enough
to supply most of the specimen machining with the remainder supplied by Southwest Research
Institute (SwRI). The Alcoa Technical Center provided machining of the notches in the
aluminum M(T) specimens. Finally, numerous ASTM Committee E08 individuals assisted in
this effort. Over the last decade, as this round robin evolved from idea to reality, excellent
support was consistently provided by John Ruschau (UDRI) and Steve Thompson (AFRL). Kind
acknowledgement is also extended to Ms. Loretta Mesa (SwRI) for preparing this manuscript
and the numerous ASTM members who reviewed this report prior to publication. Thanks to
everyone for making this collaboration a resounding success!
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TABLE OF CONTENTS Section Page Acknowledgements......................................................................................................................... ii Executive Summary ..................................................................................................................... viii 1.0 Introduction.............................................................................................................................1 2.0 Materials and Methods............................................................................................................3 2.1 Materials ........................................................................................................................3 2.2 Round Robin Participants ..............................................................................................4 2.3 Specimen Geometry.......................................................................................................5 2.4 Round Robin Rules ........................................................................................................5 3.0 Analysis Methodology..........................................................................................................13 3.1 Interpolating Crack Growth Rate Data ........................................................................13 3.2 Applying the Interpolation Approach ..........................................................................14 4.0 Results...................................................................................................................................27 4.1 Final Matrix of Testing and Conditions.......................................................................27 4.2 The Big Six ..................................................................................................................28 5.0 Discussion.............................................................................................................................43 5.1 Analysis Methodology.................................................................................................43 5.2 Interpolated Data for Each of the Six Conditions........................................................44 5.3 Interlaboratory Variability ...........................................................................................46 5.4 Intralaboratory Variability ...........................................................................................47 5.5 Variability Summary....................................................................................................47 5.6 Individual Laboratory Performance.............................................................................49 5.7 Statistical Anomalies?..................................................................................................50 5.8 Influence of Test Technique Variables ........................................................................51 6.0 Summarizing and Concluding Remarks ...............................................................................81 7.0 References.............................................................................................................................85 Appendix A – Supporting Guiding (Pretest) Documentation Appendix B – Individual Lab Data Plots
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LIST OF TABLES Table Page 2-1 Materials involved in the FCG round robin............................................................................8 2-2 Tensile properties of the materials involved in the FCG round robin ....................................8 2-3 Round robin participants.........................................................................................................9 2-4 Specimen IDs for different materials and specimen geometries ..........................................10 2-5 Generalized test conditions for the round robin testing including approximate lower
and upper bound envelope of crack growth rates and applied stress intensity factor ranges ....................................................................................................................................10
3-1 Tabulated values of average normalized growth rate (with standard deviation)
interpolated at various normalized ΔK levels .......................................................................16 4-1 Summary of round robin tests for each lab...........................................................................30 4-2 Specimen data summary for the 4130 steel material ............................................................31 4-3 Specimen data summary for the thinner 2024-T351 aluminum material .............................32 4-4 Specimen data summary for thicker 2024-T351 and 7075-T6 aluminum materials ............33 4-5 Primary test conditions for the different labs involved in the round robin...........................34 5-1 Processed statistics for the different labs testing condition STL-A and STL-B ...................53 5-2 Processed statistics for the different labs testing condition ALX-A and ALX-C.................54 5-3 Processed statistics for the different labs testing condition ALX-B and ALN-A.................55 5-4 Laboratory-by-laboratory breakout for testing conditions STL-A and STL-B ....................56 5-5 Laboratory-by-laboratory breakout for testing conditions ALX-A and ALX-C ..................57 5-6 Laboratory-by-laboratory breakout for testing conditions ALX-B and ALN-A ..................58 5-7 Influence of crack length measurement technique (DCPD and compliance) on
overall variability levels........................................................................................................59 5-8 Influence of loading method (constant amplitude versus K-control) on overall
variability levels....................................................................................................................60
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LIST OF FIGURES Figure Page 2-1 Notch requirements for the different specimens in E647-05 (scanned from
standard) ..............................................................................................................................11 2-2 Specimen geometries extracted from E647-05 illustrating specimen dimensions
for both C(T) and M(T) configurations (scanned from standard) .......................................12 3-1 Sample set of fatigue crack growth rate data ......................................................................17 3-2 Sample set of fatigue crack growth rate data with a subdivided ΔK in equal log
space increments (10 per decade)........................................................................................17 3-3 Interpolation strategy employed on either side of a ΔK increment .....................................18 3-4 Interpolation calculations for the data shown previously....................................................19 3-5 All of the data sets plotted on a common set of axes ..........................................................20 3-6 All data sets with the interpolated average da/dN rate at each normalized ΔK level..........21 3-7 All data sets with the interpolated average and ±2 SD’s on FCGR da/dN..........................22 3-8 Typical error bound of the crack growth rate data at a given normalized ΔK ....................23 3-9 Distribution of interpolated growth rates at a given normalized ΔK ..................................24 4-1 Typical data sets from two of the participating laboratories (all data is plotted in
Appendix B) ........................................................................................................................35 4-2 All fatigue crack growth associated with test condition STL-A .........................................36 4-3 All fatigue crack growth associated with test condition STL-B .........................................37 4-4 All fatigue crack growth associated with test condition ALX-A ........................................38 4-5 All fatigue crack growth associated with test condition ALX-C ........................................39 4-6 All fatigue crack growth associated with test condition ALX-B ........................................40 4-7 All fatigue crack growth associated with test condition ALN-A ........................................41
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LIST OF FIGURES (Cont’d) Figure Page 5-1 Schematic approach of how spreadsheet-based analysis is organized ................................61 5-2 Actual portion of the spreadsheet analysis for condition ALN-1........................................62 5-3 Comparing the interpolated data with the actual for condition STL-A in terms of
(a) growth rate and (b) variability .......................................................................................63 5-4 Comparing the interpolated data with the actual for condition STL-B in terms of
(a) growth rate and (b) variability .......................................................................................64 5-5 Comparing the interpolated data with the actual for condition ALX-A in terms of
(a) growth rate and (b) variability .......................................................................................65 5-6 Comparing the interpolated data with the actual for condition ALX-C in terms of
(a) growth rate and (b) variability .......................................................................................66 5-7 Comparing the interpolated data with the actual for condition ALX-B in terms of
(a) growth rate and (b) variability .......................................................................................67 5-8 Comparing the interpolated data with the actual for condition ALN-A in terms of
(a) growth rate and (b) variability .......................................................................................68 5-9 Average interlaboratory variability using (a) range extent ratio and (b) exponent .............69 5-10 Average intralaboratory variability using (a) range extent ratio and (b) exponent .............70 5-11 Relationship between inter- and intralaboratory variability using (a) range extent
ratio and (b) exponent..........................................................................................................71 5-12 Intralaboratory variability for conditions (a) STL-A and (b) STL-B..................................72 5-13 Intralaboratory variability for conditions (a) ALX-A and (b) ALX-C................................73 5-14 Intralaboratory variability for conditions (a) ALX-B and (b) ALN-A................................74 5-15 Laboratory performance for the different conditions (plot shows ranking method) ...........75 5-16 Comparing the interpolated data with the actual for Lab Q data in terms of (a)
growth rate and (b) variability.............................................................................................76
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LIST OF FIGURES (Cont’d) Figure Page 5-17 Anomalous Lab O data in terms of (a) growth rate (compared to interpolated) and
(b) variability .......................................................................................................................77 5-18 More typical Lab L data in terms of (a) growth rate (compared to interpolated) and
(b) variability .......................................................................................................................78 5-19 Effect of (a) crack length measurement method and (b) test control variability.................79
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EXECUTIVE SUMMARY About the same time the ASTM fatigue crack growth standard (E647) was drafted, a round
robin program was held to quantify the variability observed when measuring fatigue crack
growth rate. Over the ensuing 35 years, technology has evolved considerably which may have
an impact on crack growth rate variability. This report details the results from an extensive
round robin performed using three materials (a steel and two structural aluminum alloys) and
encompassing a variety of specimen geometries and load ratios. In total, 141 fatigue crack
growth rate tests were performed during this testing. A systematic method was developed that
allowed quantifying growth rate (and associated variability in growth rate) at specific ΔK levels
for each test. The steel material exhibited the lowest level of interlaboratory (between labs)
variability. In general for steel, the growth rate variability observed is 1.9x whereas for
aluminum it is 2.4x. For 2024 and 7075 (the aluminum alloys utilized during testing), the mean
growth rate variabilities are 2.3x and 2.6x, respectively. The intralaboratory (within a given lab)
variability for steel is 1.5x, whereas for aluminum it is 1.65x. For 2024 and 7075, the mean
growth rate variabiltities are 1.6x and 1.7x, respectively. The interlaboratory variability ranged
from a low of 1.2x to typically 2.5-3.0x for all of the materials considered. The variability data
suggests that there is little statistical difference between that measured today and that
documented 33 years ago in a previous round robin assessment. The data suggests a slight
decrease in intralaboratory variability over this time period. Some influence of specimen
geometry was noted with M(T) specimens exhibiting variability levels that are 30-40% less than
similar C(T) specimens. A comparison between tests performed using DCPD and compliance as
the continuous, non-visual crack length measurement suggests that variability levels are 20% less
for DCPD when compared to compliance. Conversely, no discernable difference in variability
level was noted between different load control methods (constant amplitude versus K-control).
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1.0 INTRODUCTION Thirty-six years ago, shortly after drafting the original version of the fatigue crack growth
(FCG) rate standard (ASTM E647 [1]), a round robin test program was performed to determine
the precision and bias of the test method. Since this time, gradual changes have occurred in the
body of the E647 test standard as a consequence of such things as servohydraulic control
capability improvements, test automation (few crack growth rate tests are performed manually
anymore), K-control test strategies and non-visual crack length technology.
The current ASTM E647-05 fatigue crack growth standard is a mature standard: the
version cited in Reference [1] totals 45 pages and cites 111 external references. However the
standard continues to evolve and embrace new approaches. For instance, a new method for
analyzing closure data (the ACR approach pioneered by Keith Donald at FTA) and a
compression load precracking methodology (spearheaded by Jim Newman at Mississippi State)
are both being drafted for likely inclusion in the standard.
This is not an easy test standard on which to perform round robin testing. Matters are
complicated by the flexibility that the current standard allows. For instance, a myriad of
different paths (i.e. specific test procedures) are allowed to generate FCG data for a given
material. Furthermore, a variety of nonvisual crack length measurement techniques are all
possible. Normally, in a round robin the test method is fixed and the single-valued output is then
assessed for variability. The absence of a single-valued result from FCG testing and the multiple
allowable paths seriously complicate a round robin test program for evaluating the E647
standard. Therefore, the intent of the round robin herein is to use whichever standard technique
desired to generate the FCG data for three materials (2024 aluminum, 7075 aluminum and 4130
steel). Different specimen geometries, specimen sizes and load ratios were perturbed during
testing. This report will describe the testing and the resulting data.
An extensive round robin like the one described in this report takes an enormous amount of
time to plan and execute. The initial discussions raising the possibility of a fatigue crack growth
round robin were held in the mid-1990s at the biannual ASTM committee meetings. Several
informal meetings were held during this period with likely participants working through the
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details of how the program would be structured. The strong opinion of the group was that
variability should be measured without confining testing to a strict protocol. Rather, E647
should be used in all its perturbations during the testing so that the result was a true measure of
the variability that can occur with the entire standard.
The material for the program was originally purchased in December 1998. Finding funding
or donations for the machining of test specimens proved to be a challenge to produce the 185
specimens. Letters soliciting testing were sent in October 2003, with specimens finally
completed and distributed to interested parties a year later in October 2004. The data flowed in,
with the first data set received April 2005 and the last data set January 2008.
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2.0 MATERIALS AND METHODS The purpose of this section of the report is to discuss the materials utilized for testing, the
specimen designs selected, and the “rules” enforced during testing.
2.1 Materials
When this round robin was first conceived, the organizers felt that it was important to
utilize test materials that were structurally relevant. Since the vast majority of the fatigue crack
growth testing is performed for the aerospace community, aerospace materials were a natural
selection. The organizers did not want to limit the testing to a single type of material, for
instance aluminum. Therefore both aluminum and steel were tested during this program.
The thickness of the test material can have an impact on crack growth rate properties. In
order to achieve a range of behaviors, the following mix of materials was sought:
• Thin high-strength 7075 aluminum (theorized to be best behaved), • Well-behaved, high-strength steel in a medium thickness condition, and
• Thicker lower-strength 2024 aluminum (theorized to be less well behaved due
to the lower strength and expected high levels of crack closure).
The goal with these material-thickness selections was to have available a range of crack
propagation behavior during growth rate measurements for generating the round robin data.
The materials that were utilized were residual stock from past material characterization
programs. More specifically, the material utilized for round robin testing consisted of 4130 steel
bar and sheets of 2024 and 7075 aluminum. A further description of the materials is provided in
Table 2-1. The 4130 steel bar was normalized and heat treated to relatively high strength levels.
It should also be noted that the 36 feet of steel product length was cut into 23 pieces prior to heat
treating. Conversely, the aluminum sheets, each delivered in the temper of interest, consisted of
large, 4’ x 8’ sheets. The thin (1/8-inch thick) 7075-T6 was nominally a sheet product whereas
the thicker (3/8-inch thick) 2024-T351 was nominally classified as a plate product.
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All of the materials were supplied with property validation certificates in accordance with
usual practice when testing aerospace materials. Nevertheless, tensile testing was performed on
each of the materials in the longitudinal direction as shown in Table 2-2. Since the steel was
heat treated after cutting, ten of the bars were sampled for property variation. Little variation
was evident with an average ultimate strength of 175 ksi and a yield of 167 ksi. Little variation
was also apparent across the width of the bar as well (note that specimens STRR-1, -2 and -3 in
Table 2-2 were sampled across the width of the bar). Tensile properties for the two aluminum
products are also shown in Table 2-2 and compared with expected results from Reference [2].
Tensile properties were in accordance with expectation and no anomalies were noted during
testing.
2.2 Round Robin Participants
In October of 2003, a letter was mailed to 61 individuals all affiliated in some manner with
testing labs. This letter solicited support and resources for a fatigue crack growth round robin.
These 61 individuals, working for US and foreign entities, were identified from technical
contacts in the fatigue and fracture field. A number of the recipients had already expressed
interest in participating in the test program. The purpose of the letter was to outline the reason
for the round robin and provide a sense of the scope of testing required. One of the key reasons
for the letter was to understand how many specimens the different labs felt that they could test as
well as the relevant specimen geometry that their fixtures allowed.
In the end, 20 test labs volunteered to participate and data was received from the 18
described in Table 2-3. The two labs not able to participate had heavier-than-normal workloads
and could not prioritize jobs that were not revenue-generators. Of the 18 labs (described in
additional detail in Table 2-3) that participated, three were non-US labs (Australia, India and
Canada). The excellent return rate (18 of 20 labs or 90%) was due to the extended time period
given to generate the FCG data. As indicated in Table 2-3, the first lab returned data in April
2005 with the last data sets received at SwRI in January 2008.
In all subsequent tables and data descriptions, the laboratories participating in the round
robin will be identified by a random alphanumeric identifier.
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2.3 Specimen Geometry
The two most common fatigue crack growth rate specimen geometries, C(T) and M(T),
were utilized during testing. All specimens were oriented in the L-T direction (implying the
primary loading direction was L with the crack growing in the T direction). Schematics of the
notch and specimen geometries are provided in Figures 2-1 and 2-2 for background. The actual
specimen sizes utilized are indicated in Table 2-4. Considering the data in Table 2-4, two
different sized 4130 steel C(T) specimens were utilized with widths of 2 inch and 3 inch. These
51 specimens were all also notched and the specimen thickness was 0.25 inch.
Fifty-nine similar C(T) specimens were fabricated from the thicker 2024 material as
indicated in Table 2-4. Note that the specimen thickness was reduced to 0.25 inch from the
original product thickness of 0.375 inch. Each of the individual round robin test labs were also
responsible for notching these specimens.
Middle-cracked tension specimens were utilized from full-thickness 2024 and 7075
material as indicated in Table 2-4. Each of these specimens was 4-inch wide and 24-inch long.
The long specimen length was provided for gripping flexibility in the different labs. Given the
4” x 24” specimen, a 48” x 96” plate allowed removing 44 specimen: 11 from across the width
and 4 down the length.
2.4 Round Robin Rules
The rules of the round robin were explained in a document supplied to all labs when the
specimens were sent to the project participants. This document is the second document included
in Appendix A. The philosophy and rules for testing were described in detail. The intent of this
round robin was to evaluate the characteristics of the E647 test standard. As such, the
fundamental rules involved were few and simple:
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• Rule #1. Any method permitted by ASTM E647 to generate FCG data is
allowed (i.e. the organizers are not confining testing to one test methodology, for instance).
• Rule #2. The supplied specimens must be tested to the conditions indicated. • Rule #3. The testing must be performed to the ΔK regime indicated for the
materials (see Table 2-5). • Rule #4. Results and procedures must be fully documented so that the data
can be analyzed and the results understood (this point was really critical in view of the large amount of data involved in this testing).
The intention in this round robin was not to dictate the test conditions but rather to allow the user
to choose, within the overall context of E647, the method suitable for the laboratory
instrumentation. Summarized in Table 2-5 are the conditions that were to be evaluated during
the round robin. Note that the last column in Table 2-5 identifies the specific condition denoted
in each shipment to the testing labs.
When a round robin test program is performed, the participants are typically instructed in
detail specifically what needs to be done. The problem with this approach with the E647 test
standard is the complexity of the test and the inability of different labs to have duplicate
capabilities. For instance, one lab may be used to performing FCG tests under constant
amplitude loading. It would not be fair to ask them to perform a test using K-control methods.
Conversely, one lab may be making visual crack length measurements whereas another lab may
rely on compliance to yield continuous crack length measurements. Restricting testing to only
one method was not deemed valuable since testing labs are using different approaches in
practice. Using this approach then suggests that the variability measured would correspond to
the variability apparent with the complete test standard.
Not all testing labs would be evaluating the same test conditions. However, as a general
rule the low load ratio fatigue crack growth behavior was the primary focus of the vast majority
of the testing. The envelope of growth rates indicated in Table 2-5 are provided for guidance
only in terms of selecting the conditions for testing. Achieving the full range of growth rate data
indicated by the upper and lower bound values in Table 2-5 is unlikely given the specimen sizes
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involved in testing. Therefore, when test conditions were selected by a given laboratory, the
following were considered:
• For low load ratio testing (R = 0.1), the focus is on the growth rates starting at
ΔK = 10 ksi√in.
• For higher load ratio testing (R > 0.1), toughness limitations require generally starting lower, on the order of ΔK = 8 ksi√in. or so.
The participating laboratories were instructed to follow E647 whenever in doubt and attempting
to make decisions during testing.
With the relatively open philosophy (i.e. not confining testing to certain techniques and
methods) used during this testing, the burden when evaluating the results was to understand how
the testing was performed so as to potentially determine the roles of different variables. This
means that there is additional burden on the testing lab to provide sufficient, highly detailed
information to the round robin organizers concerning how testing was performed.
To assist in this process, Attachment A is provided at the end of the second document in
Appendix A to guide in the process of documenting the procedures followed. Items that are
included in this documentation include, for instance, complete detail regarding how the specimen
was precracked prior to starting the test. Once the test begins, details regarding how the
specimen was then loaded are also critically important. The analysis procedures used to create
the da/dN data are also important to document.
If non-visual crack length measurement was a part of a laboratory’s approach, it was
important to get a sense of the type of post-test correction strategy that was utilized to relate the
visual to the non-visual crack measurement data. Although a comparison between the visual
measurements and post-test corrected data would have been highly useful, none of the
participants utilizing this technique supplied this type of plot. Finally, it was important to ensure
that all of the elements that E647 requires in terms of reporting data were documented in the data
supplied to SwRI.
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Table 2-1. Materials involved in the FCG round robin.
Product Size Alloy or Material Temper or Condition Thick or Cross Section Other Dimensions
4130 Normalized and heat treated 4” x ¼” bar 36 ft (cut in 18” segments) 7075 -T6 0.125” sheet 4’ x 8’ sheet 2024 -T351 0.375” sheet 4’ x 8’ sheet
Table 2-2. Tensile properties of the materials involved in the FCG round robin.
Material Specimen ID YS, ksi UTS, ksi elong, % RA, % 4130 steel RRL1 162.5 171.2 18.0 62.5
RRL2 158.5 167.3 17.0 62.7 RRL3 155.7 164.0 17.0 64.3 RRH1 171.3 181.0 17.0 63.8 RRH2 168.1 178.0 16.0 63.8 RRH3 169.4 179.8 17.0 65.4 RRD1 167.2 176.0 17.0 65.6 RRD2 169.1 178.2 17.0 62.6 RRD3 166.3 169.6 17.0 64.3 STRR-1 169.9 178.7 17.0 59.0 STRR-2 171.9 181.1 16.0 56.7 STRR-3 170.7 180.1 16.0 57.4 average 166.7 175.4 16.8 62.3 std. dev. 5.2 5.9 0.6 3.0
7075-T6 7xRR-1 77.3 83.8 14.3 29.3 7xRR-2 76.6 83.2 13.6 30.5 7xRR-3 75.0 83.0 14.3 31.0 average 76.3 83.3 14.1 30.3 std. dev. 1.2 0.4 0.4 0.9 HNDBK 72 80 n/a n/a
2024-T351 2xRR-1 55.7 71.6 22.0 31.6 2xRR-2 55.4 70.4 18.0 34.4 2xRR-3 56.3 72.5 20.0 33.7 average 55.8 71.5 20.0 33.2 std. dev. 0.5 1.1 2.0 1.5 HNDBK 50 66 n/a n/a
HNDBK = MMPDS, Reference [2], B-basis
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Table 2-3. Round robin participants.
Test Laboratory Contact Person Country Data Complete
AFRL – Wright Labs Steve Thompson USA 1 / 06
Alcoa Rich Brazill USA 10 / 06
CNRCC Peter Au Canada 2 / 06
DSTO Kevin Walker Australia 9 / 07
Fatigue Technology Incorporated (FTI)
Joy Ransom USA 1 / 08
Fracture Technology Associates (FTA)
Keith Donald USA 11 / 07
Honeywell Jim Hartman USA 4 / 07
Martest Robert Diamond USA 5 / 07
Metcut Research Phil Bretz USA 4 / 05
NAL C. Manunatha India 8 / 05
NASA − Houston Royce Forman USA 8 / 06
NASA − Langley Scott Forth USA 9 / 05
NAVAIR – Pax River Mike Leap USA 3 / 06
Siemens Westinghouse Joe Anello USA 4 / 05
Southwest Research Institute (SwRI)
Jim Feiger USA 1 / 06
US Air Force Academy Scott Fawaz USA 11 / 06
US Naval Academy Rick Link USA 3 / 06
Westmoreland Jim Rossi USA 2 / 06
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Table 2-4. Specimen IDs for different materials and specimen geometries.
Material Thickness
B, in. SpecimenGeometry Notched?
WidthW, in.
No. ofSpec.
Specimen Identification Nos.
4130 steel ∼0.25 C(T) yes 2.0 24 2xy where x = A-K, y = 1-4
C(T) yes 3.0 27 3xy where x = A-K, y = 1-4
2024-T351 ∼0.25 C(T) no 2.0 30 W2-2-x where x = 1-30
C(T) no 3.0 29 W3-2-x where x = 1-30
∼0.375 M(T) no 4.0 32 AL-2- x where x = 1-32
7075-T6 ∼0.125 M(T) no 4.0 44 AL-7- x where x = 1-44
Table 2-5. Generalized test conditions for the round robin testing including approximate lower
and upper bound envelope of crack growth rates and applied stress intensity factor ranges.
Lower Bound Upper Bound
Material Thickness
B, in. Load Ratio
ΔK, ksi√in.
da/dN, in./cyc
ΔK, ksi√in.
da/dN, in./cyc
Round-RobinCondition ID
4130 steel ∼0.25 0.1 8 1 (10-7) 30 6 (10-6) STL-A
0.8 8 3 (10-7) 30 1 (10-5) STL-B
2024-T351 ∼0.25 0.1 5 2 (10-7) 40 1 (10-3) ALX-A
0.5 5 1 (10-6) 20 1 (10-4) ALX-C
∼0.375 0.1 5 2 (10-7) 40 1 (10-3) ALX-B
7075-T6 ∼0.125 0.1 5 3 (10-7) 40 1 (10-3) ALN-A
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Figure 2-1. Notch requirements for the different specimens in E647-05 [1]
(scanned from standard).
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Figure 2-2. Specimen geometries extracted from E647-05 [1] illustrating specimen dimensions for both C(T) and M(T) configurations (scanned from standard).
c:\data\pcm\rr\fr-round robin.doc 13
3.0 ANALYSIS METHODOLOGY The primary result from a fatigue crack growth rate test is the crack growth rate (da/dN) as
a function of applied stress intensity factor range (ΔK). Comparing results from two crack
growth rate tests is complicated by not having similar ΔK levels to make a growth rate
comparison. To overcome this issue and compare on an equal ΔK basis, an analysis
methodology was developed as will be described in this section of the report. This approach is
extracted from work originally performed in support of ASTM activities [3].
3.1 Interpolating Crack Growth Rate Data
The absence of similar ΔK levels for comparative assessment can be overcome by applying
an interpolation scheme to a given data set. This approach will be further described with a
typical crack growth rate data set shown in Figure 3-1. Although this is a single data set, if we
were to repeat this test and plot the data, the basic problem is that none of the applied ΔK levels
would agree with each other. Consequently, the data set shown in Figure 3-1 needs to be re-
characterized in a standard manner to allow comparison to other data sets.
The basic approach consists of first dividing up each ΔK decade into ten equal increments
in log space. These increments are shown schematically with the data in Figure 3-2 (only the
increments relevant to the range of the data are shown). The approach now will be to interpolate
the data to determine the effective da/dN for the different increments. The interpolation scheme
is further described in Figure 3-3 focusing on the 100.7 (which equals 5.012) interval.
The points that are interpolated are the two points bridging the incremental ΔK level.
These adjacent points are connected by the straight line in Figure 3-3. In order to interpolate, the
functional relationship between the fatigue crack growth rate points must be known. The Paris
relationship, namely da/dN = C ΔKm, is used herein to provide this link. On a log-log plot such
as Figure 3-3, this relationship is linear with a slope of m and a da/dN intercept of magnitude
logC. The functional form is approximate; however, the closer the ΔK data is spaced, the less
difference functional form matters.
c:\data\pcm\rr\fr-round robin.doc 14
The actual interpolation for the data shown in Figure 3-3 is further described by the
calculations in Figure 3-4. The actual steps to calculate the interpolated da/dN point in
Figure 3-3 are in Figure 3-4. This algorithm was implemented in a generalized FORTRAN
program to perform this interpolation on a given set of da/dN versus ΔK data. This method was
used to characterize each set of da/dN data generated during the round robin test program.
3.2 Applying the Interpolation Approach
Prior to applying this automated approach to the round robin data, it was first applied to
data that came from ASTM committee work. Eric Tuegel leads a Structural Applications
(E08.04) Task Group E08.04.04 entitled, “Variability, Statistics and Probabilistic Modeling”.
This group was provided 74 sets of Alcoa lot release data from fatigue crack growth rate testing.
This data was supplied by Markus Heinimann and Rich Brazill (both from Alcoa) with ΔK
normalized by some toughness level to guard the proprietary nature of the data (it is unknown to
us what aluminum alloy is considered). For reference, the data are reproduced in Figure 3-5.
To provide context for the statistical analysis, the focus of this effort is to assess the
variability in the context of what E647 suggests. For reference, the portion of E647 [1] related to
precision and bias is reproduced below:
“…variability in da/dN versus ΔK is available from results of an interlaboratory test program in which 14 laboratories participated. These data, obtained on a highly homogeneous 10 Ni steel, showed the reproducibility in da/dN within a laboratory to average ±27% and range from ±13 to ±50%, depending on laboratory; the repeatability between laboratories was ±32%. Values cited are standard errors based on ±2 residual standard deviations about the mean response determined from regression analysis. In computing these statistics, abnormal results from two laboratories were not considered due to improper precracking and suspected errors in force calibration…..”
The original round robin study for E647 referenced in the preceding paragraph can be found
documented in Reference [4]. It should be kept in mind that ±32% difference implies an
absolute range of approximately 2x on FCG rate (±32% = 1.32/0.67 ∼ 2). Similarly, a difference
of ±50% would imply a factor of 3x and ±27%, a factor of 1.75x.
c:\data\pcm\rr\fr-round robin.doc 15
The data set interpolation was carried out with a simple FORTRAN program that parsed
the input data. Once interpolated, the individual da/dN’s at a given ΔK level were statistically
processed to determine averages and standard deviations. Note that averages and standard
deviations (see Table 3-1) are in log(da/dN) space. For reference, Figure 3-6 provides the
average da/dN values at nine levels (see Table 3-1 for the raw data). Note that the ninth level, at
ΔK normalized to 1, included only five data points (interpolated results from only 5 of the 74)
and hence was not statistically processed any further since it was of limited value.
For reference, error bars are shown on top of the averages in Figure 3-7. These error bars
provide a range of ±2 standard deviations on the mean FCG rate responses. The associated
variability range of these standard deviations numbers, computed in the last column of Table 3-1,
are shown in Figure 3-8 for the Alcoa74 data. In this plot, the variability is noted as a FCGR
ratio (as described earlier). Note that the average variability was 2.008 which is extremely
similar to the quoted ASTM level. However, the Alcoa74 data was supplied from one lab but it
represented seventy-four different lots of material, so any further comment relative to what is
stated in E647 is not possible. Moreover, for further reference, the distributions of the da/dN
data (interpolated, of course) are shown for each ΔK level in Figure 3-9. The distributions
appear fairly log-normal or normal in type.
Although the data included in this section of the report was ΔK normalized and the
pedigree of the material is not supplied, the data nevertheless presented a unique opportunity to
develop and apply the statistical analysis approach intended for the round robin data with the
large number of da/dN values available for data processing.
c:\data\pcm\rr\fr-round robin.doc 16
Table 3-1. Tabulated values of average normalized growth rate (with standard deviation)
interpolated at various normalized ΔK levels.
Interpolated log(da/dN in in./cycle) value Interpolated
log(ΔK norm) No. of Pts. Average, A Std. dev., b da/dN variability range 10(A+2b)/10(A-2b) or 104b
-0.1 74 -3.8144 0.0791 2.072
-0.2 74 -4.2557 0.0871 2.230
-0.3 74 -4.4565 0.0716 1.933
-0.4 74 -4.6209 0.0631 1.789
-0.5 74 -4.8344 0.0475 1.549
-0.6 74 -5.1179 0.0582 1.709
-0.7 74 -5.5266 0.0834 2.157
-0.8 73 -6.1444 0.1278 3.244
Note: Number of points is the same as number of interpolated data sets.
c:\data\pcm\rr\fr-round robin.doc 17
ΔK, ksi√in1 10
da/d
N,
inch
/cyc
le
10-8
10-7
10-6
Figure 3-1. Sample set of fatigue crack growth rate data.
ΔK, ksi√in1 10
da/d
N,
inch
/cyc
le
10-8
10-7
10-6100.5 100.7 100.9 101.1 101.3
Figure 3-2. Sample set of fatigue crack growth rate
data with a subdivided ΔK in equal log space increments (10 per decade).
c:\data\pcm\rr\fr-round robin.doc
18 ΔK, ksi√in1 10
da/d
N,
inch
/cyc
le
10-8
10-7
10-610
0.510
0.9 101.3
ΔK, ksi√in
4 5 6 7
da/d
N,
inch
/cyc
le
2x10-8
3x10-8
4x10-8
5x10-8
6x10-8
100.7 100.8
(4.81, 3.31e-8)
(5.33, 4.26e-8)
Interpolated(100.7 or 5.012, 3.66e-8)
Figure 3-3. Interpolation strategy employed on either side of a ΔK increment.
c:\data\pcm\rr\fr-round robin.doc 19
Figure 3-4. Interpolation calculations for the data shown previously.
c:\data\pcm\rr\fr-round robin.doc 20
Alcoa Supplied Lot Release FCGR Test Data
Normalized K0.1 1
Fatig
ue C
rack
Gro
wth
Rat
e, i
nch/
cycl
e
10-7
10-6
10-5
10-4
10-3
10-2
datasets 1 - 20datasets 21 - 40datasets 41 - 60datasets 61 - 74
Figure 3-5. All of the data sets plotted on a common set of axes.
c:\data\pcm\rr\fr-round robin.doc 21
Alcoa Supplied Lot Release FCGR Test Data
Normalized K0.1 1
Fatig
ue C
rack
Gro
wth
Rat
e, i
nch/
cycl
e
10-7
10-6
10-5
10-4
10-3
10-2
datasets 1 - 20datasets 21 - 40datasets 41 - 60datasets 61 - 74average (interpolated)
Figure 3-6. All data sets with the interpolated average da/dN rate at each normalized ΔK level.
c:\data\pcm\rr\fr-round robin.doc 22
Alcoa Supplied Lot Release FCGR Test Data
Normalized K0.1 1
Fatig
ue C
rack
Gro
wth
Rat
e, i
nch/
cycl
e
10-7
10-6
10-5
10-4
10-3
10-2
datasets 1 - 20datasets 21 - 40datasets 41 - 60datasets 61 - 74average (interpolated)±2 standard deviations
Figure 3-7. All data sets with the interpolated average and ±2 SD’s on FCGR da/dN.
c:\data\pcm\rr\fr-round robin.doc 23
Alcoa Supplied Lot Release FCGR Test Data
Normalized K0.1 1
FCG
R R
atio
, da
/dN
+2st
ddev
/ da
/dN
-2st
ddev
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Figure 3-8. Typical error bound of the crack growth rate data at a given normalized ΔK. Dashed lines indicate average with ±2 standard deviations of the mean.
c:\data\pcm\rr\fr-round robin.doc 24
Raw Data
-6.6 -6.5 -6.4 -6.3 -6.2 -6.1 -6.0 -5.9 -5.8
Cou
nt
0
2
4
6
8
10
12
14
16
Raw Data
-5.9 -5.8 -5.7 -5.6 -5.5 -5.4 -5.3
Cou
nt
0
2
4
6
8
10
12
14
16
18
Raw Data
-5.5 -5.4 -5.3 -5.2 -5.1 -5.0 -4.9
Cou
nt
0
5
10
15
20
25
30
35
Raw Data
-5.00 -4.95 -4.90 -4.85 -4.80 -4.75 -4.70 -4.65
Cou
nt
0
2
4
6
8
10
12
14
16
Raw Data
-4.80 -4.75 -4.70 -4.65 -4.60 -4.55 -4.50 -4.45
Cou
nt
0
2
4
6
8
10
12
Raw Data
-4.7 -4.6 -4.5 -4.4 -4.3 -4.2
Cou
nt
0
5
10
15
20
25
30
ΔΚnorm=10^(-0.8) ΔΚnorm=10^(-0.7)
ΔΚnorm=10^(-0.6) ΔΚnorm=10^(-0.5)
ΔΚnorm=10^(-0.4) ΔΚnorm=10^(-0.3)
Figure 3-9. Distribution of interpolated growth rates at a given normalized ΔK.
c:\data\pcm\rr\fr-round robin.doc 25
Raw Data
-4.6 -4.5 -4.4 -4.3 -4.2 -4.1 -4.0
Cou
nt
0
2
4
6
8
10
12
14
16
18
20
Raw Data
-4.1 -4.0 -3.9 -3.8 -3.7 -3.6 -3.5
Cou
nt
0
5
10
15
20
25
ΔΚnorm=10^(-0.2) ΔΚnorm=10^(-0.1)
Figure 3-9. continued
c:\data\pcm\rr\fr-round robin.doc 26
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c:\data\pcm\rr\fr-round robin.doc 27
4.0 RESULTS The purpose of this section of the report is to describe the data sets generated during the
round robin testing on a lab-per-lab basis. The fatigue crack growth results will also be
presented and summarized for each material and condition.
4.1 Final Matrix of Testing and Conditions
The testing performed for the six different FCG test conditions is summarized in Table 4-1.
In each of the boxes in Table 4-1, the number of tests/specimens that each lab performed for each
different test condition is described. Five of the 18 labs performed all of the crack growth test
conditions. The condition evaluated by the greatest number of labs was the low load ratio, C(T)
specimens fabricated from 2024 (ALX-A). The least common test condition, with eight labs,
was the high load ratio steel (STL-B). In total, 141 tests were performed during the round robin
testing. All but 37 of these (104 total), or 74%, were under low load ratio conditions. Most (2/3)
of the test specimens were compact tension specimens with the remainder being of the M(T)
geometry.
A comprehensive listing of the specimen ID Nos. tested in each lab is further shown in
Tables 4-2, 4-3 and 4-4. Each individual table treats two distinct material/test conditions.
However note that only the prefix of the specimen ID is included in this tabulated summary.
Any anomalies or unusual circumstances noted during testing are also indicated in the farthest
right column of the tabular summaries.
A summary is further provided in Table 4-5 that assesses some of the variables specifically
involved in the test procedures. Although most users supplied more detail, this particular
summary highlights some of the key variables including software utilized, crack length
measuring method and test mode (for instance, K-control or constant amplitude).
c:\data\pcm\rr\fr-round robin.doc 28
4.2 The Big Six
Plots of the fatigue crack growth rate curves for each of the six material/test conditions
comprise what is termed the “big six” plots in the context of this report. First, considering the
individual labs only, plots of all of the raw fatigue crack growth rate data are contained in
Appendix B. For each lab, the relevant plots of the six test conditions are presented in the
appendix, illustrating data from each of the individual tests. For reference, data from two labs
are shown in Figure 4-1 for the low R, M(T) specimen testing in condition ALX-B. In one case
(the plot inset on the left of Figure 4-1), three replicate data sets are included. This is contrasted
with the four data sets from the two specimens tested to similar conditions in Lab I in the plot
inset to the right in Figure 4-1. Note that both K-decreasing and K-increasing data are shown in
this plot as well as others in Appendix B.
Where possible, the data has been examined for E647 “validity”. It was not uncommon
that only da/dN-ΔK data was available, in which case the data was accepted as valid.
Occasionally, a spurious data point that was clearly an artifact was digitally eliminated (however
this was quite rare). When possible, the plasticity assessments in E647 were calculated and
compared to the test data to ensure that ligament yield conditions were not exceeded.
The big six plots are shown in Figures 4-2 through 4-7. In each of these plots, for a given
material/test condition, all of the data from each of the individual labs that tested this condition
are plotted coincidently on the same graph. For instance, Figure 4-2 depicts low R behavior of
4130 steel. Some fanning of the data is evident at lower ΔK as the crack growth response was
initiated.
The overall shape of the crack growth curves for the steel test conditions (Figures 4-2 and
4-3) appear fairly linear. Higher levels of curvature are clearly evident throughout the crack
growth rate curves for the 2024 and 7075 data shown in Figures 4-4, 4-5, 4-6 and 4-7. Low
apparent variability was evident for the low load ratio, 2024 condition tested with an M(T)
specimen (condition ALX-B shown in Figure 4-6). This condition is nearly identical to the C(T)
specimen (condition ALX-A shown in Figure 4-4) except the C(T) specimen was only 0.25-inch
thick as opposed to the 0.375-inch thick M(T). In and of itself, this thickness difference is not an
c:\data\pcm\rr\fr-round robin.doc 29
issue that we would expect to make a significant difference in fatigue crack growth rate behavior.
Either 0.25- or 0.375-inch would nominally be considered fairly thick-ish in section.
c:\data\pcm\rr\fr-round robin.doc 30
Table 4-1. Summary of round robin tests for each lab.
Number of Specimens for Each Test Condition ID Lab
ID No. STL-A STL-B ALX-A ALX-C ALX-B ALN-A
A 1 3 3
B 2 2 2 2 2 2
C 2 2 2
D 3 3
E 2 2 2 2
F 4 2 2 2 2 2
G 3 2 3 2 1 2
H 2 2 2
I 2 2 2 2 2 2
J 2 2 3
K 2 2 2
L 2 2 3 3
M 3 3
N 2 2
O 2 2 2
P 2 2 2 2 2 2
Q 2
R 1 3
Sum 28 17 29 20 23 24
c:\data\pcm\rr\fr-round robin.doc 31
Table 4-2. Specimen data summary for the 4130 steel material.
Specimen ID Nos.
Material B,
inch Load Ratio
ConditionID No.
Lab ID No. #1 #2 #3 #4
Miscellaneous Comments
4130 0.25 0.1 STL-A A 2F3 B 3C4 3E1 Missing 3E2, 3E3 data C 2K1 2K2 D no testing E 3L1 3L2 F 2A1 2B1 3A1 3A2 G 3B3 3B4 3C1 H 2J1 2J2 I 2G1 2G2 J 2I1 2I2 K 3F2 3G1 L no testing M no testing N 3K1 3K2 O 2J4 2J3 P 2C1 2E1 Q no testing R
4130 0.25 0.8 STL-B A 2F4 3B1 3B2 2F4, tested at wrong R B 3E4 3F1 C no testing D no testing E no testing F 3A3 3A4 G 3C2 3C3 H no testing I 2G3 2G4 J 2I3 2I4 K no testing L no testing M no testing N 3I1 3I2 O no testing P 2F1 2F2 Q no testing R
c:\data\pcm\rr\fr-round robin.doc 32
Table 4-3. Specimen data summary for the thinner 2024-T351 aluminum material.
Specimen ID Nos.
Material B,
inch Load Ratio
ConditionID No.
Lab ID No. prefix #1 #2 #3
Miscellaneous Comments
2024 0.25 0.1 ALX-A A W2-2 -5 -6 -7 B W3-2 -10 -11 missing -12, -13 data C W2-2 -23 -24 D no testing E W2-2 -29 -30 F W3-2 -1 -2 G W3-2 -5 -6 -7 H W2-2 -15 -16 I W2-2 -8 -9 J W2-2 -12 -13 -14 K W3-2 -16B -28B L W3-2 -18 -19 M no testing N no testing O W2-2 -19 -20 P W2-2 -1 -2 Q no testing R
2024 0.25 0.5 ALX-C A no testing B W3-2 -14 -15 C W3-2 -22 -23 D no testing E no testing F W3-2 -3 -4 G W3-2 -8 -9 H W2-2 -17 -18 I W2-2 -10 -11 J no testing K W3-2 -17B -29B tested at R = 0.7 L W3-2 -20 -21 M no testing N no testing O W2-2 -21 -22 P W2-2 -3 -4 Q no testing R
c:\data\pcm\rr\fr-round robin.doc 33
Table 4-4. Specimen data summary for thicker 2024-T351 and 7075-T6 aluminum materials.
Specimen ID Nos.
Material B,
inch Load Ratio
ConditionID No.
Lab ID No. prefix #1 #2 #3
Miscellaneous Comments
2024 0.375 0.1 ALX-B A no testing B AL-2 -10 -11 C no testing D AL-2 -26 -27 -28 E AL-2 -20 -21 F AL-2 -1 -2 G AL-2 -7 -8 -9 -7/-8 invalid data, side-
to-side crk. len. diffs. H no testing I AL-2 -5 -6 Side-to-Side
diff > 0.025W J no testing K no testing L AL-2 -12 -13 -14 M AL-2 -29 -30 -33 -28 dup (-33) N no testing O no testing P AL-2 -3 -4 Q none 001 301 Re-machined C(T)’s R AL-2 25
7075 0.125 0.1 ALN-A A no testing B AL-7 -9 -10 C no testing D AL-7 -21 -22 -23 E AL-7 -30 -31 F AL-7 -1 -2 G AL-7 -7 -8 H no testing I AL-7 -5 -6 -5 overloaded
(censored) J no testing K no testing L AL-7 -11 -12 -13 M AL-7 -32 -33 -34 N no testing O no testing P AL-7 -3 -4 Q no testing R AL-7 -18 -19 -20
c:\data\pcm\rr\fr-round robin.doc
34
Table 4-5. Primary test conditions for the different labs involved in the round robin. Lab ID Control Software
Crack Length Measurement Humidity
Test Mode
Freq, Hz
da/dN calculation
A Digital FTA DCPD 45 K-inc. +3 20-30 secant B Analog FTA DCPD 20-30 CA: STL, ALX-C
K-inc.: ALX-A, ALX-B, ALN-A
10 secant
C Digital Instron compliance n/r K-dec. -2, CA 15 7 pt. poly D Digital in-house visual 40 CA 5-10 7 pt. poly E Analog FTA C(T): compliance
M(T): DCPD 40 CA: STL, ALX-B, ALN-A
K-inc. +2: ALX-A 20 mod. secant
F Analog in-house compliance 35-55 CA 20-30 mod. secant G Digital in-house DCPD 35-50 CA 10 secant, mod., 7 pt H Digital FTA DCPD 3-21 K-dec. -2, CA 20 mod. secant I Analog FTA C(T): compliance
M(T): DCPD 21-57 K-dec. -2, K-inc. +2 10 7 pt. poly
J Analog in-house compliance n/r K-inc. +2, +2.5 25-35 secant K Digital FTA KRAK-gage 40 K-inc. +1.7, +2.25, +3 50 mod. secant L Digital FTA compliance 30-50 K-inc. +1.8, +2.25 25 7 pt. poly M Digital in-house/MTS visual: ALX-B
compliance: ALN-A 15-25 CA: ALX-B
K-inc. +2.5: ALN-A 15 secant
N Digital FTA DCPD 15-30 K-dec. -2, K-inc +5 1-5 7 pt. poly, mod. sec. O n/r n/r DCPD 45 K-inc. +1.6 20 7 pt. poly P Digital MTS compliance 25-60 CA 10 secant Q Analog FTA compliance 40 K-dec. -5, K-inc. +2.5, +5 5-16 7 pt. poly R Digital MTS KRAK-gage 40 CA 10 secant
c:\data\pcm\rr\fr-round robin.doc
35
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
ΔK, MPa√m10 100
da/d
N, m
/cyc
le
10-9
10-8
10-7
10-6
10-5
10-4
Lab D (AL-2-27)Lab D (AL-2-28)Lab D (AL-2-26)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
ΔK, MPa√m10 100
da/d
N, m
/cyc
le
10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab I (AL-2-5 K-increase)Lab I (AL-2-6 K-increase)Lab I (AL-2-5 K-decrease)Lab I (AL-2-6 K-decrease)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
Figure 4-1. Typical data sets from two of the participating laboratories (all data is plotted in Appendix B).
c:\data\pcm\rr\fr-round robin.doc 36
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab A (1 Set)Lab B (2 Sets)Lab C (2 Sets)Lab E (2 Sets)Lab F (4 Sets)Lab G (3 Sets)Lab H (2 Sets)Lab I (2 Sets)Lab J (2 Sets)Lab K (2 Sets)Lab N (2 Sets)Lab O (2 Sets)Lab P (2 Sets)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
Figure 4-2. All fatigue crack growth associated with test condition STL-A.
c:\data\pcm\rr\fr-round robin.doc 37
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
Lab A (3 Sets)Lab B (2 Sets)Lab F (2 Sets)Lab G (2 Sets)Lab I (2 Sets)Lab J (2 Sets)Lab N (2 Sets)Lab P (2 sets)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
Figure 4-3. All fatigue crack growth associated with test condition STL-B.
c:\data\pcm\rr\fr-round robin.doc 38
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab A (3 Sets)Lab B (2 Sets)Lab C (2 Sets)Lab E (2 Sets)Lab F (2 Sets)Lab G (3 Sets)Lab H (2 Sets)Lab I (2 Sets)Lab J (3 Sets)Lab K (1 Set)Lab L (2 Sets)Lab O (2 Sets)Lab P (2 Sets)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
Figure 4-4. All fatigue crack growth associated with test condition ALX-A.
c:\data\pcm\rr\fr-round robin.doc 39
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (2 Sets)Lab C (2 Sets)Lab F (2 Sets)Lab G (2 Sets)Lab H (2 Sets)Lab I (2 Sets)Lab L (2 Sets)Lab O (2 Sets)Lab P (2 Sets)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
Figure 4-5. All fatigue crack growth associated with test condition ALX-C. Note that the unusual features of the lab 0 data will be discussed elsewhere in this report.
c:\data\pcm\rr\fr-round robin.doc 40
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (2 Sets)Lab D (3 Sets)Lab E (2 Sets)Lab F (2 Sets)Lab G (1 Set)Lab I (2 Sets)Lab L (3 Sets)Lab M (3 Sets)Lab P (2 Sets)Lab Q (2 Sets)Lab R (1 Set)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
Figure 4-6. All fatigue crack growth associated with test condition ALX-B.
c:\data\pcm\rr\fr-round robin.doc 41
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (2 Sets)Lab D (3 Sets)Lab E (2 Sets)Lab F (2 Sets)Lab G (2 Sets)Lab I (2 Sets)Lab L (3 Sets)Lab M (3 Sets)Lab P (2 Sets)Lab R (3 Sets)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
Figure 4-7. All fatigue crack growth associated with test condition ALN-A.
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5.0 DISCUSSION Whereas the previous section of the report presented the basic results, these results are
further examined in this section, and the statistics associated with variability are calculated and
described. The intent of this discussion is a thorough, though not exhaustive, analysis of the
round robin results; this analysis provides a framework that others can work with in the future to
determine the full implications of these results.
The key quantity from all of the statistical analysis is a measure of data variability.
Essentially variability is represented as the range of da/dN growth rate at a given ΔK level. It
can be calculated from the standard deviation (b) of the average log(da/dN) data. In terms of a
factor on growth rate, variability can be quantified by the ratio 10(a+2b)/10(a-2b) which can be
algebraically shown to be 104b (recall that the average log(da/dN) is the quantity “a” and the
standard deviation is “b”). Two variability measures are possible: one representing variability
across all of the labs (interlaboratory variability) or one representing variability within a lab
(intralaboratory variability). In this section of the report, both of these variability measures will
be quantified and further examined.
5.1 Analysis Methodology
The basic tool utilized in analyzing these results was described in Chapter 3 of this report.
A FORTRAN program was utilized to provide interpolated fatigue crack growth rate data
specific ΔK levels. Each decade of ΔK was divided up into ten equal log(ΔK) intervals and each
of these levels was used to calculate an interpolated da/dN growth rate. This method was applied
to each individual crack growth data set to yield an array of different growth rate points
(essentially key da/dN at fixed ΔK points). These data were then processed as indicated in
Figure 5-1 importing the interpolated data into a spreadsheet for further statistical analysis.
The analysis method is schematically shown in Figure 5-1. At the heart of the approach is
the interpolated da/dN data at different vertical lines of the lab data, with each different column
representing sequential ΔK magnitudes. Averages and standard deviations summed down each
column represent interlaboratory analysis. This is contrasted to the summation for each lab to
c:\data\pcm\rr\fr-round robin.doc 44
the right side of the basic data. Whereas Figure 5-1 illustrates the approach with a schematic,
Figure 5-2 provides an actual portion of the spreadsheet with the three analysis zones clearly
evident for one of the six material test conditions (ALN-1 which is thin 7075 material tested at a
low R-ratio condition using M(T) specimens).
5.2 Interpolated Data for Each of the Six Conditions
The interpolated results for each of the six round robin test conditions are shown in
Tables 5-1 through 5-3 and in Figures 5-3 through 5-8. In each of these figures, two plots are
shown: an FCG rate plot (left side) and a variability plot (right side). The FCG rate plot on the
left side in Figure 5-3 illustrates all of the round robin experimental data (the gray data points)
with the distinct interpolated data overlaid with the average (open data point) bounded by error
bars that represent a ±2 standard deviations growth rate range. The growth rate variability range,
expressed as a ratio, is depicted in the plot shown on the right side of Figure 5-3. This plot
indicates how variability changes with applied ΔK level.
A close examination of the six plots in Figures 5-3 through 5-8 shows that in general the
range represented by ±2 standard deviations on the average growth rate provides an excellent
description of the observed range of the growth rate data. There are clear instances where data is
beyond this range, but in the vast majority the range does an excellent job capturing the extent of
the data. There is no clear trend of variability with applied ΔK level (the plots on the right-hand
side of Figures 5-3 to 5-8). In some cases, for instance STL-A in Figure 5-3, the variability is
constant with a jump at the highest ΔK as the data fans out in the Stage III regime. This is
contrasted to STL-B in Figure 5-4 where the highest variability is observed at the start due to
fanning at the lowest ΔK level.
Some variability differences are apparent in what one would nominally consider to be
similar test conditions. For instance, if the 2024,low R, C(T) data (Figure 5-5) is compared with
that from the M(T) specimens (identical test conditions) in Figure 5-7, the overall level of scatter
is much greater for the C(T) when contrasted to the M(T) specimen. Is this effect real or simply
a consequence one condition including more data than the other (i.e. comparing results from few
data to results from many data and seeing more effect from the tail of the growth rate
c:\data\pcm\rr\fr-round robin.doc 45
distributions)? To answer this question, the number of tests involved in each condition is
described in Table 4-1. An examination of the data suggests:
• condition ALX-A – 29 data sets from 13 labs (Figure 5-5, C(T) specimen
geometry), and • condition ALX-B – 23 data sets from 11 labs (Figure 5-7, M(T) specimen
geometry).
Hence the more scattered data in Figure 5-5 is from 25% more labs than the less scattered data in
Figure 5-7. However, with both populations totaling over 20 data sets, it is unlikely that the
difference is due to sampling effects since each includes a high number of tests.
Variability can also be a function of the “shape” of the fatigue crack growth rate curve. In
the case of the two steel material test conditions (Figures 5-3 and 5-4), the growth rate curve is
fairly linear and the observed variability is for the most part constant as a function of ΔK. This is
contrasted to varying levels of variability for 2024 that is partially due to the shape of the growth
rate curve. This is most clearly understood by examining the data in Figure 5-7. As the lowest
ΔK level, the near vertical growth rate curve and fanning of the data causes a higher level of
variability. At the fourth interpolated data point (ΔK about 6 ksi√in), the variability also
increases as a consequence of the knee in the da/dN-ΔK data. As the growth rate data becomes
more vertical, the associated level of scatter will increase. Finally, as the Stage III regime is
approached, an increase in variability is apparent at the third to last interpolated point (the
decrease in variability at the higher ΔK points is simply due to fewer data sets, see detail in
Table 5-3).
The influence of number of data sets is probably most striking in Figure 5-8 where the
7075 was fatigue tested. For the first two and last two interpolated points, where variability
levels are quite low, there were less than 10 data sets (on average) included in the calculation.
This is contrasted to the middle region of the growth rate data where greater than 20 data sets
were involved.
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5.3 Interlaboratory Variability
There are numerous ways to calculate overall variability levels. In Figures 5-3 to 5-8, the
da/dN variability ratio is plotted for each interpolation point. However one usually isn’t
interested in variability as a function of ΔK; rather, an overall variability that applies to a given
material test condition would likely be desired. One way to quantify the overall variability for a
given material condition is to simply average the da/dN variability ratios (resulting in the average
da/dN variability ratio). Hence, the ratio is averaged and in effect the averaging occurs “outside”
of the log space. This is contrasted to the idea of averaging the standard deviations “b” for each
ΔK level, resulting in an average b level and simply calculating 104b where bavg is used for the
calculation. In a sense, this averaging is occurring “inside” of the log space. In theory, both of
these parameters should be the same as long as both are normal distributions.
Both of these approaches for determining an overall variability level are used in Figure 5-9
for the six material test conditions. The plot shown in Figure 5-9(a) averages the variability ratio
whereas in Figure 5-9(b) the average b is calculated and then used in 104b to calculate an average
variability. A close examination of Figure 5-9 shows that little difference is apparent between
the two calculation methods. Averaging the ratio yields slightly higher average variability
levels. The difference ranges from 3% higher for the steel to 12% higher for the 2024 C(T)
specimens. On average the average of the variability ratio is 7% higher than the variability
derived from an average b.
It is interesting to compare the different conditions in Figure 5-9(b) to examine the possible
impact on variability. First, with regard to the 4130 steel data, the observed variability is the
lowest for this material considering both high and low load ratio (approximately a factor of 1.9x
on FCG rate on average). However for the 2024 aluminum, compact tension specimens yielded
a variability of approximately 2.5x compared to 1.8x for the M(T) specimens. Note that these
specimens were fabricated from the same material but the M(T) specimens retained full
thickness (0.375-inch) and the C(T) was machined thinner (0.25 inch). It is unlikely that much
of the variability difference was due to the slight thickness difference although the thicker M(T)
specimens would retain surface microstructure that could differ from processing. Ignoring
microstructural differences (if they exist), the foregoing conclusion is that specimen geometry
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influences variability, with M(T) specimens exhibiting 30-40% less variability when compared
to C(T) specimens. If this difference is true, it suggests that 7075 material variability is greater
than 2024 since the variability for ALN-A (2.56) with the M(T) geometry is on par with the C(T)
2024 variability (2.63).
5.4 Intralaboratory Variability
The same two measures are used in Figure 5-10 to compare intralaboratory variability.
Note that the basic data for these plots is included in Tables 5-4 to 5-6. Several observations are
notable. First, the difference between the two methods of quantifying variability is similar to
that observed previously. The variability level when b is averaged (as opposed to averaging the
variability ratio) is slightly less with the minor variability difference caused from analysis
methodology. The observed intralaboratory variability level is less than the interlaboratory
variability magnitude. Furthermore, less difference is noted between conditions when
intralaboratory variability is used as the measure. In other words, regardless of material,
specimen geometry or load ratio, da/dN error is typically on the order of 1.50-1.75x.
Similar trends in variability are observed when either the inter- and intralaboratory
measures are compared. Given this, the key question then is whether there is a functional
relationship between the two. To understand this, the two measures are plotted against each
other for both the average da/dN variability ratio and the average variability in Figure 5-11. This
plot suggests that there appears to be a linear link between the two, with the intralaboratory
variability trending toward 30-40% of the interlaboratory variability. However the observation
of nonzero intralaboratory variability when interlaboratory variability is zero makes little
physical sense. Although the correlation coefficient is high, its value and the observation of a
nonzero intercept suggests that the link between inter- and intralaboratory variability is weak at
best.
5.5 Variability Summary
For the purposes of this summary, the da/dN variability measure quoted is the average
da/dN variability determined from 104b where b is the calculated average value. Based on
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Figures 5-9 and 5-10 and the data tabulated in Tables 5-1 to 5-6, the following observations can
be made:
• The variability in crack growth rate measurement observed with steel is slightly less than with aluminum. Considering like specimen geometries, thicker 2024 appears to have less variability than thin 7075. The M(T) specimen geometry exhibits 30-40% less variability when compared to the C(T) specimen geometry.
• The interlaboratory variability for steel is approximately 1.9x whereas for
aluminum it is 2.4x. For 2024 and 7075 the mean growth rate variabilities are 2.3x and 2.6x, respectively.
• The intralaboratory variability for steel is approximately 1.5x whereas for
aluminum it is 1.65x. For 2024 and 7075 the mean growth rate variabilities are 1.6x and 1.7x, respectively.
• The intralaboratory variability observed basically ranged from a low of 1.2x to
typically 2.5-3.0x for all of the materials combined. The two steel conditions had intralaboratory variability levels that ranged from 1.2x to 2.4x.
Given these observations, the natural question is: How do they compare to the earlier
round robin assessment of E647 performed 33 years ago [4]? The paragraph from E647 in
Section 3.2 of this report suggests that the previous interlaboratory variability was quantified as
1.94x (1.32/0.68). This is contrasted to previous intralaboratory variability that was on average
1.74x (1.27/0.73) with a range of 1.3x (1.13/0.87) to 3.0x (1.5/0.5). The previous round robin
examined only one material, a highly homogeneous rotor steel.
In the strictest sense, only the steel results can be compared to the previous round robin
study results. With:
• overall interlaboratory variability of 1.9x (now) versus 1.94x (then), and
• overall intralaboratory variability of 1.5x (now) versus 1.74x (then) with a range for steel of 1.2x to 2.4x (now) versus 1.3x to 3.0x (then),
it can be concluded that there is little statistical difference between variability levels today versus
33 years ago. These data suggest that it can be argued that the intralaboratory variability has
likely decreased some. However, on balance when everything is averaged between labs, crack
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growth rate measurement variability is approximately the same between labs as it was 33 years
ago. Although these results are somewhat disappointing, they likely suggest that the process
simply has an inherent variability level that improvements in technology can not overcome.
Finally, it should also be pointed out that previous to the testing in this round robin, no replicate
data existed regarding variability for aluminum material. 5.6 Individual Laboratory Performance The intralaboratory variabilities presented in Tables 5-3 to 5-6 are replotted in Figures 5-12
to 5-14 illustrating individual lab performance. In these bar charts, the blue bars are for labs that
exhibited better than average variability whereas the yellow bars are for labs that exceeded the
average variability level. It is interesting to note that the statistics tend to be dominated by the
occasional lab that had high variability. This is reflected in the fewer number of yellow bars
when compared to the blue bars in Figures 5-12 to 5-14.
It should be noted that in generating these statistics, no attempt has been made to censor the
data, with one notable exception. One lab, Lab O, generated data for condition ALX-C
(Figure 5-13(b)) where the variability was 14.6x. This level is clearly way out of bounds with
the other data and was censored in any data processing examining overall variability. This issue
will be explored in additional detail in a subsequent section of this report.
Individual lab performance is further assessed by examining how an individual lab’s
variability compared to the mean level in Figure 5-15. For each of the six material conditions,
the position relative to the mean level was ranked as shown in the balloons in the schematic at
the top of Figure 5-15. Each variability level position was then recorded and if it happened to be
in the top 3 or top 2 lowest variabilities (depending on number of labs), this was also noted. The
matrix of positions is shown in the matrix in the lower part of Figure 5-15. The matrix in
Figure 5-15 provides individual labs with a generic, qualitative metric that they can use to assess
performance. The laboratories with minimum variability in Figure 5-15 appear to be Lab E (all
four conditions in lowest variability quartile), Lab B (half in lowest quartile, remainder better
than average), Lab G (half in lowest quartile, remaining half better than average) and Lab P
(40% in lowest quartile, remaining portion better than average).
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5.7 Statistical Anomalies?
There is danger when averaging is used to represent overall behavior. As an example of
this, examine the performance of Lab Q for condition ALX-B in Figure 5-14(a). The average
da/dN variability ratio is 1.44x when all the data is included. However, a close examination of
the data for Lab Q, shown in Figure 5-16, indicates that the average value is skewed by two
outlier variability levels in the near threshold (the initial, lowest ΔK interpolation point) and the
knee in the data (the fourth lowest ΔK interpolation point). If these points are omitted from the
averaging, as they should be since they simply represent erroneous values due to the shape of the
growth rate curve, the average variability drops from 1.44x to 1.15x. A close examination of
Figure 5-14(a) shows that 1.15x would be the lowest value observed of all the laboratories. So,
the implication is that if all the data is treated as a whole, results can be skewed by features that
do not necessarily reflect the nature of the growth rate data measured.
The opposite is true for the condition that exhibited the highest variability in the whole
round robin. Recall that Lab O exhibited a variability of 14.6x as observed in Figure 5-13(b) for
the high load ratio, 2024 test condition. The two data sets that this variability was derived from
are shown in Figure 5-17(a). Clearly, the data sets are disparate and inconsistent, as sometimes
occurs in practice. A close examination of the data suggests that there is no apparent reason for
the difference and there does not appear to be anything in the processed data that would suggest
why a large difference would be manifested. Therefore, in this case the observed variability does
represent reality.
The two foregoing examples do not represent the typical data observed for most of the
laboratories. A more typical result that represents the majority of observed behavior is shown in
Figure 5-18 where the resulting statistics make sense relative to the overall data. A close
examination between the data and the interpolation points clearly illustrates that the error bar
range encompasses the experimental data. Therefore the average da/dN variability ratio, in this
case 1.47x, is consistent with the variability apparent in the actual crack growth rate data.
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5.8 Influence of Test Technique Variables
The purpose of constructing Table 4-5 was to determine the range of test techniques
utilized by the different laboratories. Although in some cases it was difficult to extract the
information from the documentation supplied by each lab to construct Table 4-5, it is believed
that the data shown captures the major experimental differences between the approaches used in
the different laboratories. The obvious question is whether different methods result in different
levels of variability. Although this question can likely be answered rigorously using an
advanced statistical assessment, an engineering approach is presented herein to isolate a couple
of the key variables and assess whether there are clear differences in crack growth variability.
Two characteristics of test technique will be examined. First, the method used for crack length
measurement will be examined followed by the load control mode used during the test.
Four methods were used for crack length measurement at all of the laboratories: DCPD,
compliance, KRAK gages (indirect DCPD) and near-continuous visual measurements. The only
methods that had sufficient numbers of labs (3 or greater) to examine possible differences were
DCPD and compliance. The average “b” parameter (standard deviation on crack growth rate) is
indicated in Table 5-7 as a function of material condition, laboratory and crack length
measurement method. As can be observed, the number of laboratories involved is likely
sufficient to produce statistically meaningful data.
The overall difference in variability is summarized in Figure 5-19(a). It is interesting to
note that for the three material conditions examined, there is a systematic difference in behavior
with variability levels less for DCPD when compared to compliance. However, in a strict
numerical sense the statistician would argue that the standard deviations captured in Table 5-7
are too high to come to a strict statistical conclusion. Nevertheless, from an engineering
viewpoint there does appear to be some difference due to the two measurement techniques.
Keep in mind that other variables were perturbed in this cross section: most notably material
(steel and aluminum) and specimen geometry (all C(T) except for ALN-A which is an M(T)
specimen geometry). It is surprising that the least difference is noted for condition ALN-A
where DCPD is easiest and compliance is most difficult (due to insensitivity related to little
stiffness change).
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It is tempting to suggest that DCPD yields less variability than compliance. However,
Lab E had lower variability using compliance for two of three cases compared to all DCPD
participants. Hence, it is not easy to decouple overall trends. Finally, whereas DCPD may on
average yield lower variability, is it actually easier or harder to do well?
A similar comparison is provided for constant amplitude loaded conditions versus K-
control methods in Table 5-8 and Figure 5-19(b). Whereas some difference was apparent for
crack length measurement method, there does not appear to be any real difference between test
load control method. All of these techniques appear to yield approximately the same variability
level.
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Table 5-1. Processed statistics for the different labs testing condition STL-A and STL-B.
Material Condition
log(ΔK) magnitude
Average Parameter, A
Std. Dev. Parameter, b
Number of Points
Variability104b
STL-A 0.7 -7.385 n/a 1 n/a 0.8 -7.081 0.0583 3 1.710 0.9 -6.761 0.0549 13 1.659 1 -6.448 0.0796 23 2.082 1.1 -6.165 0.0842 26 2.172 1.2 -5.894 0.0931 29 2.358 1.3 -5.647 0.0766 30 2.024 1.4 -5.387 0.0641 28 1.805 1.5 -5.136 0.0423 25 1.476 1.6 -4.935 0.0440 18 1.499 1.7 -4.696 0.0587 14 1.717 1.8 -4.411 0.0758 11 2.011 1.9 -4.078 0.0661 7 1.839 2 -3.745 0.1349 3 3.465 2.1 -3.203 n/a 1 n/a
STL-B 0.6 -7.182 0.1197 6 3.012 0.7 -6.950 0.0464 6 1.534 0.8 -6.721 0.0925 9 2.343 0.9 -6.553 0.0884 11 2.257 1 -6.310 0.0765 14 2.023 1.1 -6.054 0.0662 14 1.840 1.2 -5.791 0.0494 14 1.577 1.3 -5.510 0.0441 12 1.501 1.4 -5.218 0.0549 9 1.657 1.5 -4.902 0.0594 7 1.728
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Table 5-2. Processed statistics for the different labs testing condition ALX-A and ALX-C.
Material Condition
log(ΔK) magnitude
Average Parameter, A
Std. Dev. Parameter, b
Number of Points
Variability104b
ALX-A 0.5 -7.213 0.0399 2 1.444 0.6 -6.941 0.0336 4 1.363 0.7 -6.776 0.0682 15 1.874 0.8 -6.543 0.1260 20 3.192 0.9 -5.681 0.1603 28 4.378 1 -5.234 0.0935 28 2.365 1.1 -4.935 0.0527 26 1.624 1.2 -4.660 0.0952 25 2.404 1.3 -4.387 0.1170 26 2.936 1.4 -3.973 0.1600 22 4.363 1.5 -3.475 0.1080 13 2.705 1.6 -2.841 0.2057 4 6.649 1.7 -2.131 n/a 1 n/a
ALX-C 0.3 -8.190 0.0719 2 1.938 0.4 -7.074 0.0224 2 1.230 0.5 -6.911 0.0093 2 1.090 0.6 -6.650 0.0895 8 2.280 0.7 -6.215 0.2000 14 6.311 0.8 -5.695 0.0896 22 2.282 0.9 -5.321 0.0933 24 2.362 1 -5.009 0.1169 20 2.935 1.1 -4.712 0.1154 17 2.894 1.2 -4.398 0.1202 11 3.026 1.3 -3.904 0.1341 9 3.440
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Table 5-3. Processed statistics for the different labs testing condition ALX-B and ALN-A.
Material Condition
log(ΔK) magnitude
Average Parameter, A
Std. Dev. Parameter, b
Number of Points
Variability 104b
ALX-B 0.5 -7.403 0.1528 2 4.087 0.6 -6.862 0.0758 7 2.009 0.7 -6.684 0.0389 9 1.431 0.8 -6.343 0.1103 17 2.761 0.9 -5.488 0.0531 18 1.631 1 -5.129 0.0281 21 1.295 1.1 -4.833 0.0373 21 1.410 1.2 -4.547 0.0814 18 2.117 1.3 -4.239 0.0598 15 1.734 1.4 -3.834 0.1016 12 2.550 1.5 -3.294 0.0455 8 1.520 1.6 -2.739 0.0101 2 1.098
ALN-A 0.6 -6.534 0.0278 5 1.292 0.7 -6.034 0.0833 8 2.154 0.8 -5.408 0.1306 16 3.330 0.9 -5.083 0.1179 20 2.962 1 -4.820 0.1626 21 4.471 1.1 -4.572 0.1289 22 3.279 1.2 -4.388 0.1411 18 3.667 1.3 -4.084 0.0971 16 2.445 1.4 -3.678 0.0552 10 1.663 1.5 -3.112 0.0756 7 2.006
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Table 5-4. Laboratory-by-laboratory breakout for testing conditions STL-A and STL-B.
Statistics for b parameter Material
Condition Lab ID average 2 std. dev. min max
Variability104b
STL-A Lab I 0.0164 0.0164 0.0045 0.0257 1.163
Lab E 0.0235 0.0417 0.0012 0.0655 1.242
Lab G 0.0238 0.0299 0.0103 0.0558 1.245
Lab H 0.0280 0.0333 0.0085 0.0575 1.294
Lab O 0.0293 0.0439 0.0031 0.0652 1.310
Lab P 0.0332 0.0679 0.0024 0.0774 1.357
Lab B 0.0335 0.1063 0.0066 0.1533 1.362
Lab N 0.0353 0.0155 0.0246 0.0431 1.385
Lab J 0.0551 0.1030 0.0195 0.1142 1.661
Lab F 0.0636 0.0506 0.0134 0.0899 1.796
Lab K 0.0926 0.1180 0.0257 0.1802 2.347
Lab C 0.0956 0.0716 0.0190 0.1373 2.411
STL-B Lab I 0.0215 0.0118 0.0128 0.0262 1.219
Lab B 0.0289 0.0331 0.0034 0.0538 1.306
Lab P 0.0349 0.0186 0.0242 0.0458 1.379
Lab G 0.0369 0.0432 0.0099 0.0665 1.405
Lab N 0.0458 0.0717 0.0034 0.0910 1.524
Lab A 0.0547 0.0601 0.0276 0.1143 1.655
Lab F 0.0694 0.0814 0.0395 0.1399 1.896
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Table 5-5. Laboratory-by-laboratory breakout for testing conditions ALX-A and ALX-C.
Statistics for b parameter Material
Condition Lab ID average 2 std. dev. min max
Variability104b
ALX-A Lab E 0.0182 0.0343 0.0018 0.0566 1.182
Lab B 0.0215 0.0276 0.0018 0.0447 1.219
Lab G 0.0308 0.0303 0.0113 0.0506 1.328
Lab F 0.0563 0.1680 0.0070 0.2057 1.680
Lab H 0.0584 0.0739 0.0227 0.1212 1.712
Lab L 0.0689 0.1373 0.0048 0.1933 1.887
Lab A 0.0749 0.0480 0.0472 0.1180 1.994
Lab C 0.0796 0.1581 0.0153 0.2180 2.081
Lab J 0.0876 0.1346 0.0307 0.2285 2.240
Lab I 0.0989 0.0776 0.0618 0.1719 2.486
ALX-C Lab B 0.0157 0.0238 0.0009 0.0323 1.155
Lab G 0.0218 0.0517 0.0002 0.0699 1.223
Lab P 0.0301 0.0309 0.0192 0.0410 1.320
Lab L 0.0301 0.0347 0.0078 0.0537 1.320
Lab H 0.0425 0.0536 0.0013 0.0760 1.479
Lab I 0.0455 0.0422 0.0247 0.0733 1.521
Lab K 0.0476 0.0682 0.0085 0.0921 1.551
Lab F 0.0842 0.2380 0.0210 0.2626 2.171
Lab C 0.1094 0.1294 0.0320 0.2066 2.740
Lab O 0.2909 0.0391 0.2672 0.3070 14.577
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Table 5-6. Laboratory-by-laboratory breakout for testing conditions ALX-B and ALN-A.
Statistics for b parameter Material
Condition Lab ID average 2 std. dev. min max
Variability104b
ALX-B Lab M 0.0118 0.0174 0.0009 0.0247 1.115
Lab D 0.0272 0.0405 0.0106 0.0562 1.285
Lab E 0.0316 0.0875 0.0012 0.1180 1.337
Lab B 0.0316 0.0689 0.0011 0.0987 1.337
Lab Q 0.0398 0.0905 0.0030 0.1528 1.443
Lab P 0.0402 0.0138 0.0316 0.0479 1.448
Lab F 0.0720 0.0601 0.0380 0.0950 1.941
Lab I 0.0839 0.1823 0.0317 0.2204 2.165
ALN-A Lab I 0.0106 0.0175 0.0042 0.0206 1.102
Lab E 0.0159 0.0195 0.0031 0.0264 1.158
Lab P 0.0409 0.0875 0.0080 0.1284 1.458
Lab L 0.0420 0.0504 0.0054 0.0814 1.472
Lab B 0.0497 0.0612 0.0049 0.0938 1.580
Lab D 0.0504 0.0551 0.0217 0.0766 1.591
Lab G 0.0583 0.0824 0.0070 0.1008 1.711
Lab M 0.0708 0.0714 0.0301 0.1167 1.919
Lab R 0.1291 0.1594 0.0694 0.2421 3.284
c:\data\pcm\rr\fr-round robin.doc 59
Table 5-7. Influence of crack length measurement technique (DCPD
and compliance) on overall variability levels.
Average b parameter Measurement Method
Lab ID STL-A ALX-A ALN-A
DCPD A 0.074911
B 0.033516 0.021489 0.049695
E 0.015925
G 0.023788 0.03081 0.058282
H 0.027970 0.058393
I 0.010553
N 0.035349
O 0.029323
Avg. = 0.029989 0.046401 0.033614
2σ = 0.009173 0.049265 0.047775
COMPL. C 0.095567 0.079563
E 0.023517 0.018186 0.015925
F 0.063594 0.056311
I 0.016431 0.098868 0.010553
J 0.055101 0.087573
L 0.068938 0.042007
M 0.070785
P 0.033172 0.040904
Avg. = 0.047897 0.068240 0.036035
2σ = 0.059141 0.057189 0.048173
c:\data\pcm\rr\fr-round robin.doc 60
Table 5-8. Influence of loading method (constant amplitude versus
K-control) on overall variability levels.
Average b parameter Load Type
Lab ID STL-A ALX-A ALN-A
CA B 0.033516 C 0.095567 0.079563 D 0.050442 E 0.023517 0.015925 F 0.063594 0.056311 G 0.023788 0.030810 0.058282 H 0.027970 0.058393 P 0.033172 0.040904 R 0.129085 Avg. = 0.043018 0.056269 0.058928 2σ = 0.053843 0.039921 0.084667
K-control A 0.074911 B 0.021489 0.049695 E 0.018186 I 0.016431 0.098868 0.010553 J 0.055101 0.087573 K 0.092626 L 0.068938 0.042007 M 0.070785 N 0.035349 O 0.029323 Avg. = 0.045766 0.052388 0.052010 2σ = 0.059350 0.065110 0.063242
c:\data\pcm\rr\fr-round robin.doc
61
FCG Round Robin Data Analysis Approach
ALN-AB(AL-7-9)4.525094 5.25398E-074.563668 5.57183E-074.616022 6.02534E-074.656641 5.94642E-074.71172 6.76569E-074.75313 7.77531E-074.806246 7.76214E-07etc etc etc.....
ΔK and da/dNraw data
FORTRANprogram
ProjectID=ALN-A FileID=B(AL-7-9) 0.70 -6.015229 0.80 -5.399114 0.90 -5.1489631.00 -4.933981 1.10 -4.763005 1.20 -4.512465 1.30 -4.166721 1.40 -3.692932 1.50 -3.164770 FileID=B(AL-7-10)0.70 -6.087634 0.80 -5.524089 etc....etc....etc....
log(ΔK) intervals and interpolated da/dN (each file)
labs
log(ΔK)
data fromFORTRANprogram
InterlaboratoryStatistics
labs
log(ΔK)
IntralaboratoryStatistics
spreadsheet
Figure 5-1. Schematic approach of how spreadsheet-based analysis is organized.
c:\data\pcm\rr\fr-round robin.doc
62
Log DK levels across the top, log dadN down below Log DK levels across the top, log dadN down below
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
FileID=B(AL-7-9) -6.01523 -5.39911 -5.14896 -4.93398 -4.76301 -4.51247 -4.16672 -3.69293 -3.16477 Lab B AVG A = -6.05143 -5.4616 -5.21528 -4.9805 -4.76646 -4.52906 -4.14592 -3.67364 -3.12019FileID=B(AL-7-10) -6.08763 -5.52409 -5.2816 -5.02703 -4.76992 -4.54566 -4.12513 -3.65434 -3.07561 STD b = 0.051198 0.088371 0.093791 0.065794 0.004888 0.023474 0.029411 0.027287 0.063046
numpts = 2 2 2 2 2 2 2 2 2N ratio = 1.602479 2.256746 2.372262 1.83306 1.046044 1.241353 1.31113 1.285719 1.787239
FileID=D(AL-7-21) -4.60048 -4.45104 -4.12819 Lab D AVG A = -4.92411 -4.65466 -4.46418 -4.16571 -3.73534 -3.18314FileID=D(AL-7-22) -4.48918 -4.20322 -3.73534 -3.18314 STD b = 0.076619 0.021657 0.05305FileID=D(AL-7-23) -4.92411 -4.70884 -4.45233 numpts = 1 2 3 2 1 1
N ratio = 2.025243 1.220753 1.630046
FileID=E(AL-7-30) -4.70712 -4.4424 -4.17169 -3.95959 -3.66526 Lab E AVG A = -4.99548 -4.7 -4.44456 -4.18889 -3.94096 -3.65408 -3.18637FileID=E(AL-7-31) -4.99548 -4.69288 -4.44672 -4.20609 -3.92233 -3.64289 -3.18637 STD b = 0.010066 0.003061 0.024327 0.026352 0.015822
numpts = 1 2 2 2 2 2 1N ratio = 1.097149 1.028595 1.251141 1.274697 1.156874
FileID=F(AL-7-1-d) -6.48492 AVG A = -6.52587 -6.14871 -5.57208 -5.33189 -5.23854FileID=F(AL-7-2-d) -6.54697 Lab F STD b = 0.035468FileID=F(AL-7-2-i) -6.54571 -6.14871 -5.57208 -5.33189 -5.23854 numpts = 3 1 1 1 1
N ratio = 1.386346
FileID=G(AL-7-7) -5.36404 -5.02297 -4.69407 -4.41496 -4.18393 -4.02133 -3.67627 Lab G AVG A = -5.35912 -5.0392 -4.74533 -4.4862 -4.24634 -4.02133 -3.67627FileID=G(AL-7-8) -5.35421 -5.05542 -4.79659 -4.55744 -4.30875 STD b = 0.006954 0.022948 0.072493 0.100754 0.088262
numpts = 2 2 2 2 2 1 1N ratio = 1.066148 1.235361 1.949724 2.52938 2.254484
FileID=I(AL-7-5-d) -4.46997 Lab I AVG A = -5.00365 -4.71423 -4.44625 -4.17498 -3.91265FileID=I(AL-7-5-i) -5.00422 STD b = 0.006867 0.004226 0.020567FileID=I(AL-7-6-d) -5.01022 -4.71125 -4.43341 numpts = 3 2 3 1 1FileID=I(AL-7-6-i) -4.99652 -4.71722 -4.43536 -4.17498 -3.91265 N ratio = 1.065294 1.039687 1.208559
FileID=L(AL-7-11) -5.38723 -5.09382 -4.90746 -4.70721 -4.53997 -4.16159 -3.63263 -3.12193 Lab L AVG A = -6.54731 -5.92178 -5.32875 -5.03278 -4.81911 -4.63557 -4.5125 -4.1693 -3.63514 -3.09885FileID=L(AL-7-12) -6.54348 -5.88441 -5.27192 -4.99885 -4.80263 -4.63548 -4.52022 -4.18597 -3.65534 -3.07576 STD b = 0.005406 0.052849 0.057674 0.05297 0.081373 0.071595 0.032037 0.014454 0.019067 0.03265FileID=L(AL-7-13) -6.55113 -5.95915 -5.32709 -5.00567 -4.74723 -4.56402 -4.47731 -4.16033 -3.61746 numpts = 2 2 3 3 3 3 3 3 3 2
N ratio = 1.05105 1.627034 1.700973 1.628843 2.115877 1.93366 1.343218 1.142395 1.191981 1.350827
FileID=M(AL-7-32) -6.04438 -5.65117 -5.21247 -4.95271 -4.76611 -4.47631 -4.07779 Lab M AVG A = -6.05858 -5.58987 -5.16693 -4.88885 -4.6895 -4.4747 -4.08351 -3.80344 -2.97732FileID=M(AL-7-33) -6.03313 -5.66314 -5.23659 -4.9248 -4.70983 -4.50396 -4.04937 -3.80344 -2.97732 STD b = 0.034808 0.116698 0.100488 0.087546 0.088541 0.030093 0.037323FileID=M(AL-7-34) -6.09825 -5.4553 -5.05174 -4.78906 -4.59257 -4.44384 -4.12336 numpts = 3 3 3 3 3 3 3 1 1
N ratio = 1.377946 2.929498 2.523195 2.239677 2.260285 1.319383 1.410233
FileID=P(AL-7-3) -5.29421 -4.9312 -4.63559 -4.38192 -4.27767 -3.98255 Lab P AVG A = -5.28855 -4.94589 -4.65613 -4.40586 -4.25975 -4.07336FileID=P(AL-7-4) -5.2829 -4.96058 -4.67667 -4.4298 -4.24184 -4.16417 STD b = 0.007995 0.020775 0.029044 0.033854 0.025332 0.128424
numpts = 2 2 2 2 2 2N ratio = 1.076411 1.210875 1.306705 1.365893 1.262782 3.263594
FileID=R(AL-7-18) -5.30165 -5.19893 -4.56292 -4.50621 Lab R AVG A = -5.32555 -5.11 -4.78076 -4.58645FileID=R(AL-7-19) -5.27126 -4.96361 -4.73791 -4.65989 STD b = 0.069399 0.127749 0.242128 0.077062FileID=R(AL-7-20) -5.40374 -5.16747 -5.04145 -4.59326 numpts = 3 3 3 3
N ratio = 1.894943 3.243367 9.300629 2.033519
AVG A = -6.53444 -6.03386 -5.4077 -5.08341 -4.82006 -4.57222 -4.38762 -4.08402 -3.67759 -3.11213STD b = 0.027824 0.083324 0.130612 0.117901 0.162601 0.128946 0.141074 0.097075 0.055215 0.075556
numpts = 5 8 16 20 21 22 18 16 10 7N ratio = 1.292104 2.154249 3.330032 2.962127 4.471011 3.279334 3.666868 2.445129 1.662871 2.005508
DK = 3.981072 5.011872 6.309573 7.943282 10 12.58925 15.84893 19.95262 25.11886 31.62278dadN = 2.92E-07 9.25E-07 3.91E-06 8.25E-06 1.51E-05 2.68E-05 4.1E-05 8.24E-05 0.00021 0.000772
10^(A+2b) = 3.32E-07 1.36E-06 7.14E-06 1.42E-05 3.2E-05 4.85E-05 7.84E-05 0.000129 0.000271 0.00109410^(A-2b) = 2.57E-07 6.3E-07 2.14E-06 4.79E-06 7.16E-06 1.48E-05 2.14E-05 5.27E-05 0.000163 0.000545
Interlaboratory Variability
Avg N 2stdev N min max2.726923 1.974085 1.292104 4.471011
Avg b 2stdev b min max 10^4b0.102013 0.083693 0.027824 0.162601 2.55889
Figure 5-2. Actual portion of the spreadsheet analysis for condition ALN-1.
c:\data\pcm\rr\fr-round robin.doc
63
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
Material:B:
Geometry:R:
4130 steel0.25-inchC(T)0.1
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6Material:
B:Geometry:
R:
4130 steel0.25-inchC(T)0.1
(a) (b)
Figure 5-3. Comparing the interpolated data with the actual for condition STL-A in terms of (a) growth rate and (b) variability.
c:\data\pcm\rr\fr-round robin.doc
64
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
Material:B:
Geometry:R:
4130 steel0.25-inchC(T)0.5
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6Material:
B:Geometry:
R:
4130 steel0.25-inchC(T)0.5
(a) (b)
Figure 5-4. Comparing the interpolated data with the actual for condition STL-B in terms of (a) growth rate and (b) variability.
c:\data\pcm\rr\fr-round robin.doc
65
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Material:B:
Geometry:R:
2024 aluminum0.25-inchC(T)0.1
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6Material:
B:Geometry:
R:
2024 aluminum0.25-inchC(T)0.1
(a) (b)
Figure 5-5. Comparing the interpolated data with the actual for condition ALX-A in terms of (a) growth rate and (b) variability.
c:\data\pcm\rr\fr-round robin.doc
66
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Material:B:
Geometry:R:
2024 aluminum0.25-inchC(T)0.5
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6Material:
B:Geometry:
R:
2024 aluminum0.25-inchC(T)0.5
(a) (b)
Figure 5-6. Comparing the interpolated data with the actual for condition ALX-C in terms of (a) growth rate and (b) variability.
c:\data\pcm\rr\fr-round robin.doc
67
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Material:B:
Geometry:R:
2024 aluminum0.375-inchM(T)0.1
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6Material:
B:Geometry:
R:
2024 aluminum0.375-inchM(T)0.1
(a) (b)
Figure 5-7. Comparing the interpolated data with the actual for condition ALX-B in terms of (a) growth rate and (b) variability.
c:\data\pcm\rr\fr-round robin.doc
68
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Material:B:
Geometry:R:
7075 aluminum0.125-inchM(T)0.1
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6Material:
B:Geometry:
R:
7075 aluminum0.125-inchM(T)0.1
(a) (b)
Figure 5-8. Comparing the interpolated data with the actual for condition ALN-A in terms of (a) growth rate and (b) variability.
c:\data\pcm\rr\fr-round robin.doc 69
STL-A STL-B ALX-A ALX-C ALX-B ALN-A
aver
age
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4130 steel2024 aluminum7075 aluminum
Low R, C(T)
High R, C(T)
Low R, C(T)
High R, C(T)
Low R, M(T)
Low R, M(T)
1.99 1.95
2.94
2.71
1.97
2.73
Interlaboratory
(a)
STL-A STL-B ALX-A ALX-C ALX-B ALN-A
aver
age
da/d
N v
aria
bilit
y, 1
04b
0
1
2
3
4130 steel2024 aluminum7075 aluminum
Low R, C(T)
High R, C(T)
Low R, C(T)
High R, C(T)
Low R, M(T)
Low R, M(T)
1.94 1.90
2.632.43
1.84
2.56
Interlaboratory
(b)
Figure 5-9. Average interlaboratory variability using (a) range extent ratio and (b) exponent.
c:\data\pcm\rr\fr-round robin.doc 70
STL-A STL-B ALX-A ALX-C ALX-B ALN-A
aver
age
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4130 steel2024 aluminum7075 aluminum
Low R, C(T)
High R, C(T)
Low R, C(T)
High R, C(T)
Low R, M(T)
Low R, M(T)
1.621.52
2.031.85
1.61
1.83
Intralaboratory
(a)
STL-A STL-B ALX-A ALX-C ALX-B ALN-A0
1
2
3
4130 steel2024 aluminum7075 aluminum
Low R, C(T)
High R, C(T)
Low R, C(T)
High R, C(T)
Low R, M(T)
Low R, M(T)
1.55 1.48
1.781.61
1.511.70
Intralaboratory
aver
age
da/d
N v
aria
bilit
y, 1
04b
(b)
Figure 5-10. Average intralaboratory variability using (a) range extent ratio and (b) exponent.
c:\data\pcm\rr\fr-round robin.doc 71
Interlaboratory variability ratio1.75 2.00 2.25 2.50 2.75 3.00
Intr
alab
orat
ory
varia
bilit
y ra
tio
1.50
1.75
2.00
4130 steel2024 aluminum7075 aluminum
Vintra = 0.781 + 0.404 Vinter
r2 = 0.94
(a)
Interlaboratory variability1.75 2.00 2.25 2.50 2.75
Intr
alab
orat
ory
varia
bilit
y
1.4
1.5
1.6
1.7
1.84130 steel2024 aluminum7075 aluminum
Vintra = 0.942 + 0.299 Vinter
r2 = 0.88
(b)
Figure 5-11. Relationship between inter- and intralaboratory variability using
(a) range extent ratio and (b) exponent.
c:\data\pcm\rr\fr-round robin.doc 72
Lab
I
Lab
E
Lab
G
Lab
H
Lab
O
Lab
P
Lab
B
Lab
N
Lab
J
Lab
F
Lab
K
Lab
C
aver
age
da/d
N v
aria
bilit
y, 1
04b
0.0
0.5
1.0
1.5
2.0
2.5
3.0
average = 1.55
Material:B:
Geom:R:
4130 steel0.250-inchC(T)0.1
(a)
Lab
I
Lab
B
Lab
P
Lab
G
Lab
N
Lab
A
Lab
F
aver
age
da/d
N v
aria
bilit
y, 1
04b
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
average = 1.48
Material:B:
Geom:R:
4130 steel0.375-inchC(T)0.8
(b)
Figure 5-12. Intralaboratory variability for conditions (a) STL-A and (b) STL-B.
c:\data\pcm\rr\fr-round robin.doc 73
Lab
E
Lab
B
Lab
G
Lab
F
Lab
H
Lab
L
Lab
A
Lab
C
Lab
J
Lab
I
aver
age
da/d
N v
aria
bilit
y, 1
04b
0
1
2
3
average = 1.78
Material:B:
Geom:R:
2024 aluminum0.25-inchC(T)0.1
(a)
Lab
B
Lab
G
Lab
P
Lab
L
Lab
H
Lab
I
Lab
K
Lab
F
Lab
C
Lab
O
aver
age
da/d
N v
aria
bilit
y, 1
04b
0.0
0.5
1.0
1.5
2.0
2.5
3.0
14.015.0
average = 1.61
Material:B:
Geom:R:
2024 aluminum0.25-inchC(T)0.5
(b)
Figure 5-13. Intralaboratory variability for conditions (a) ALX-A and (b) ALX-C.
c:\data\pcm\rr\fr-round robin.doc 74
Lab
M
Lab
D
Lab
E
Lab
B
Lab
Q
Lab
P
Lab
F
Lab
I
aver
age
da/d
N v
aria
bilit
y, 1
04b
0
1
2
3
average = 1.51
Material:B:
Geom:R:
2024 aluminum0.375-inchM(T)0.1
(a)
Lab
I
Lab
E
Lab
P
Lab
L
Lab
B
Lab
D
Lab
G
Lab
M
Lab
R
aver
age
da/d
N v
aria
bilit
y, 1
04b
0
1
2
3
average = 1.70
Material:B:
Geom:R:
7075 aluminum0.125-inchM(T)0.1
(b)
Figure 5-14. Intralaboratory variability for conditions (a) ALX-B and (b) ALN-A.
c:\data\pcm\rr\fr-round robin.doc 75
Lab
M
Lab
D
Lab
E
Lab
B
Lab
Q
Lab
P
Lab
F
Lab
I
aver
age
da/d
N v
aria
bilit
y, 1
04b
0
1
2
3
average = 1.51
Material:B:
Geom:R:
2024 aluminum0.375-inchM(T)0.1
-1-2
+1+2+3
+4+5+6
TOP 3
better than average
Lab Performance and ranking for each of the different specimen/test conditions ID STL-A STL-B ALX-A ALX-C ALX-B ALN-A A -2 -2 B +2 +3 (top 2) +4 (top 2) +7 (top 3) +3 +2 C -4 -3 -2 D +5 (top 3) +1 E +7 (top 3) +5 (top 2) +4 (top 3) +5 (top 3) F -2 -3 +2 -1 -1 G +6 (top 3) +1 +3 +6 (top 3) -1 H +5 +1 +3 I +8 (top 3) +4 (top 2) -5 +2 -2 +6 (top 3) J -1 -4 K -3 +1 L -1 +4 +3 M +6 (top 3) -2 N +1 -1 O +4 -3 P +3 +2 +5 (top 3) +1 +4 (top 3) Q +2 R -3
Figure 5-15. Laboratory performance for the different conditions (plot shows ranking method).
c:\data\pcm\rr\fr-round robin.doc
76
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Material:B:
Geometry:R:
2024 aluminum0.375-inchC(T)0.1
Lab Q Data
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6 Material:B:
Geometry:R:
2024 aluminum0.375-inchC(T)0.1 Lab Q Data
avg 1.15(ΔK > 8)
avg 1.44(full range ΔK)
initialthreshold
kneein data
(a) (b)
Figure 5-16. Comparing the interpolated data with the actual for Lab Q data in terms of (a) growth rate and (b) variability.
c:\data\pcm\rr\fr-round robin.doc
77
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Material:B:
Geometry:R:
2024 aluminum0.25-inchC(T)0.5
Lab O Data
ΔK, ksi√in1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
5
10
15
20Material:
B:Geometry:
R:
2024 aluminum0.25-inchC(T)0.5
Lab O Data
avg 14.6(full range ΔK)
(a) (b)
Figure 5-17. Anomalous Lab O data in terms of (a) growth rate (compared to interpolated) and (b) variability.
c:\data\pcm\rr\fr-round robin.doc
78
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Material:B:
Geometry:R:
7075 aluminum0.125-inchM(T)0.1
Lab L Data
ΔK, ksi√in
1 10 100
da/d
N v
aria
bilit
y ra
tio, 1
0(A+2
b)/1
0(A-2
b)
0
1
2
3
4
5
6Material:
B:Geometry:
R:
7075 aluminum0.125-inchM(T)0.1
Lab L Data
avg 1.47(full range ΔK)
(a) (b)
Figure 5-18. More typical Lab L data in terms of (a) growth rate (compared to interpolated) and (b) variability.
c:\data\pcm\rr\fr-round robin.doc 79
STL-A ALX-A ALN-A
aver
age
da/d
N v
aria
bilit
y, 1
04b
0.0
0.5
1.0
1.5
2.0
DCPD compliance
1.22x1.18x1.02x
(a)
STL-A ALX-A ALN-A
aver
age
da/d
N v
aria
bilit
y, 1
04b
0.0
0.5
1.0
1.5
2.0
constant amplitudeK-control
1.03x0.96x 0.94x
(b)
Figure 5-19. Effect of (a) crack length measurement method and (b) test control variability.
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6.0 SUMMARIZING AND CONCLUDING REMARKS The results of an extensive round robin are presented in this report that involved testing at
18 laboratories. Three materials were utilized during this round robin: high strength 4130 steel,
2024-T351 plate in two thicknesses (0.25 inch and 0.375 inch) and 7075-T651 sheet 0.125-inch
thick. Six test conditions were evaluated during the round robin. Three test conditions involved
the 2024 aluminum, two examined the 4130 steel and one concerned the 7075 aluminum. In
total, 141 fatigue crack growth tests were performed in accordance with ASTM E647 during this
round robin. Seventy-four percent of these tests were under low load ratio conditions and nearly
2/3 of the test samples were of the compact tension specimen geometry.
Although the testing involved in this program was extensive, there are a number of
summarizing observations that emerge from this work. These include:
• Of the large number of tests performed, only two tests from one material
condition were censored from the overall statistical analysis due to excessive
variability1. An examination of the limited data available suggests that there
is no discernable technical reason to omit this data, but it was sufficiently out-
of-bounds that it was censored. The other data supplied by this laboratory was
consistent with results generated by other laboratories. No other data was
eliminated from the analysis.
• One of the natural problems with fatigue crack growth rate data is that from
data set to data set there are no exactly matchable points. For this reason, a
technique was used to represent each data set in a standard manner. This
standard manner, codified in a FORTRAN program, consisted of interpolating
between da/dN-ΔK data points to calculate growth rates at distinct ΔK levels.
These distinct ΔK levels correspond to each decade of ΔK divided up into ten
equal (log space) intervals. The da/dN-ΔK data supplied by the laboratories
1 Lab O, 2024 data, Figure 5-17.
c:\data\pcm\rr\fr-round robin.doc 82
was sufficiently fine and continuous in nature that the interpolation applied
resulted in no discernable additional error.
• An assessment of variability in growth rate was made at different ΔK levels.
In this context, variability refers to the scatter in fatigue crack growth rate at a
given ΔK level. Average variability refers to an average magnitude over the
complete range of ΔK’s evaluated. In this context variability is represented as
the ratio of maximum to minimum da/dN rate where the range is represented
by ±2 standard deviations on log(da/dN). Comparisons were made between
variability measures by averaging growth rate ratios (outside of log space) or
simply the average standard deviation (inside log space). Little engineering
difference in variability was noted.
• The steel material exhibited the lowest level of interlaboratory variability. For
steel the growth rate variability observed is 1.9x whereas for aluminum it is
2.4x. For 2024 and 7075, the mean interlaboratory growth rate variabilities
are 2.3x and 2.6x, respectively.
• The intralaboratory variability for steel is 1.5x whereas for aluminum it is
1.65x. For 2024 and 7075, the mean intralaboratory growth rate variabilities
are 1.6x and 1.7x, respectively. The intralaboratory variability ranged from a
low of 1.2x to typically 2.5-3.0x for all of the materials combined. The two
steel conditions had intralaboratory variability levels that ranged from 1.2x to
2.4x.
• It is useful to compare current variability levels to those obtained in 1975 [4].
Recall that the previous study utilized only a rotor steel, so therefore results
are only made to the two steel conditions evaluated herein. In summary:
overall interlaboratory variability of 1.9x (circa 2008) versus 1.94x (1975),
and, overall intralaboratory variability of 1.5x (2008) versus 1.74x (1975)
with a range for steel of 1.2x to 2.4x (2008) versus 1.3x to 3.0x (1975).
Therefore there is little statistical difference between variability levels in 2008
c:\data\pcm\rr\fr-round robin.doc 83
versus 1975. The data suggests a slight decrease in intralaboratory variability
may have occurred, although from a rigorous statistical viewpoint this finding
may be arguable.
• The round robin data reported herein suggest that specimen geometry can
impact variability. For instance, using data from C(T) and M(T) specimens at
low load ratio in 2024 material, the M(T) specimens exhibited variability
levels that were 30-40% less than similar C(T) specimens.
• A comparison between tests performed using DCPD and compliance as the
continuous, non-visual crack length measurement method suggests that
variability levels are 20% less for DCPD when compared to compliance.
Differences were observed for all of the three material/test conditions
examined. Conversely, no discernable difference in variability level was
noted between different load control methods (constant amplitude versus K-
control techniques).
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c:\data\pcm\rr\fr-round robin.doc 85
7.0 REFERENCES [1] “E647-05: Standard Test Method for Measurement of Fatigue Crack Growth Rates,”
Annual Book of ASTM Standards, Section 3, Volume 3.01, ASTM International, West Conshohocken, PA, 2007.
[2] Metallic Materials Properties Development and Standardization (MMPDS), DOT/FAA/
AR-MMPDS-01, U.S. Department of Transportation, Federal Aviation Administration, Office of Aviation Research, January 2003.
[3] Email and personal correspondence, Eric J. Tuegel, AFRL, on behalf of ASTM E08.04. [4] Clark, Jr., W. G. and Hudak, Jr., S. J., “Variability in Fatigue Crack Growth Rate Testing,”
Journal of Testing and Evaluation, JTEVA, Vol. 3, No. 6, 1975, pp. 454-476.
ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentioned in this research report. Users of this research report are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, are entirely their own responsibility.
This research report is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. Individual reprints (single or multiple copies) of this research report may be obtained by contacting ASTM at the above address or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website (www.astm.org).
Appendix A – Supporting Guiding (Pretest) Documentation
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S O U T H W E S T R E S E A R C H I N S T I T U T E ®
6220 CULEBRA RD. 78238-5166 • P.O. DRAWER 28510 78228-0510 • SAN ANTONIO, TEXAS, USA • (210) 684-5111 • WWW.SWRI.ORG
HOUSTON, TEXAS (713) 977-1377 • WASHINGTON, DC (301) 881-0226
Mechanical & Materials Engineering Division October 29, 2003 Recipient (see list at end of letter) Re: ASTM Round Robin on Fatigue Crack Growth Rate Measurement (ASTM E647) Dear xxx, Nearly thirty years ago, shortly after the initial draft of ASTM E647, a round robin was held to determine the precision and bias of the test method. Since this time, the standard has considerably evolved along with the hardware and control systems that we use to perform the tests. For approximately the past five years, a new round robin to assess where we currently stand has been (gradually) developing. The focus of this new round robin is to measure the fatigue crack growth rate behavior, as per ASTM E647, in the Paris regime using any of the possible perturbations allowed by the test standard. The desired range of ΔK (and a specific R-ratio) will be stated along with other details regarding the testing procedures when specimens are delivered. The intent is to not be overly restrictive; we want to insure that the standard is exercised in as broad a manner as possible simply insuring that we know in detail the procedures utilized (so as to subsequently statistically analyze the data). Three materials were procured for this work including:
• 0.125-inch thick 7075-T6 sheet, • 0.375-inch thick 2024-T351 plate, and, • 0.250-inch thick 4130 steel tempered to 175 ksi UTS.
These three materials were selected to represent a range of crack growth behavior. Since purchasing, the materials have been machined into a variety of specimens (180 total) as indicated in Table 1.
Table 1. Listing of the specimens available for fatigue crack growth rate round robin testing.
Material Specimen No. of W, B, Notch Specification Geometry1 Specimen inch inch Length2
4130 steel C(T) 24 2 0.25 0.2 C(T) 26 3 0.25 0.2
2024-T351 C(T) 30 2 0.25 none 29 3 0.25 none M(T) 28 4 0.375 0.2
7075-T6 M(T) 43 4 0.125 0.2 In planning the round robin, it is anticipated that different labs will have available different levels of resources for this effort. We have attempted to categorize the level of effort and number of variables that could be captured. These different levels of involvement are broadly indicated below along with a brief description of their scope:
1 M(T) specimens are all 23-inch long with no additional modifications made to the grip region. 2 Represented by either a/W (compact tension) or 2a/W (middle cracked tension).
S O U T H W E S T R E S E A R C H I N S T I T U T E ®
6220 CULEBRA RD. 78238-5166 • P.O. DRAWER 28510 78228-0510 • SAN ANTONIO, TEXAS, USA • (210) 684-5111 • WWW.SWRI.ORG
HOUSTON, TEXAS (713) 977-1377 • WASHINGTON, DC (301) 881-0226
• Full Participation – all three materials, two r-ratios, approximately 15-18 tests • Partial Level A – all three materials, low r-ratio only, 9-12 tests • Partial Level B – two materials only, mostly low r-ratio (exclusively, depending upon number of
specimens possible), 6-9 tests Please note that these are recommendations only and are based on an attempt to rationalize how the results will be analyzed once testing is completed. I think you will agree that we have an unprecedented opportunity with the broad range of materials and specimens available to capture the role of variability in the measurement of fatigue crack growth rate. It is anticipated that this exercise could provide guidance for where the ASTM standard needs additional definition, clarification or further focus. The purpose of this transmission is to solicit your support and the support of your organization for this round robin. Clearly the success of the round robin is dependent upon insuring that we have a sufficient number of participants. Therefore, my questions to you are the following:
• Would you be willing to participate in this round robin by providing the required testing and subsequent analysis of your data?
• If so, what specimen geometries and types can be integrated into your facility? What level of
participation can you provide? How many specimen can you test and how many would you like delivered?
• If not, do you have a recommendation of a laboratory that might participate in this effort (note the
addresses of the recipients of this letter provided on the following page)?
• Alternatively, is there another possibly more relevant point of contact in your organization that you could forward this transmission to?
I would appreciate a response to these questions by 5 December 2003 so that we can continue to make progress on this effort. Recognizing that we are all donating our time and energy to this effort gratis, I am hesitant to impose time constraints on when the testing needs to be completed. Practically, our goal is to complete testing in calendar year 2004.
Please do not hesitate to contact me if you have any further questions. Myself and the technical community within ASTM certainly appreciate your time and effort. We feel this is an important and worthwhile effort to insure the health of the ASTM fatigue crack growth standard. I look forward to hearing from you soon. Sincerely,
ljm Peter C. McKeighan Manager – Mechanical Testing Section voice: 210.522.3617 • fax: 210.522.6965 e-mail: [email protected]
S O U T H W E S T R E S E A R C H I N S T I T U T E ®
6220 CULEBRA RD. 78238-5166 • P.O. DRAWER 28510 78228-0510 • SAN ANTONIO, TEXAS, USA • (210) 684-5111 • WWW.SWRI.ORG
List of Recipients John J. Ruschau University of Dayton Research Institute 300 College Park Dayton, OH 45469-0136 Steven R. Thompson Air Force Research Laboratory AFRL/MLSC Building 652, Room 122 2179 12th St. Wright-Patterson AFB, OH 45433-7718 Mike Leap Naval Air Warfare Center – Aircraft Div. Metals, Ceramics and NDE Branch Code 4.3.4.2, M/S 5 Building 2188 48066 Shaw Rd. Patuxent River, MD 20670 Joy Ransom Fatigue Technology Inc. 401 Andover Park East Seattle, WA 98188-7605 Keith Donald Fracture Technology Associates 2412 Emrick Blvd. Bethlehem, PA 18020 Prof. Ralph Stephens The University of Iowa Department of Mechanical Engineering Iowa City, IA 52242 Prof. Bob Stephens University of Idaho Mechanical Engineering Department Moscow, ID 83843 Prof. Dale Wilson Tennessee Tech University Department of Mechanical Engineering 115 W. 10th St. Box 5034
Cookeville, TN 38505-0001 Scott Forth NASA Langley Research Center Mechanics and Durability Branch MS 188E 2 West Reid St. Hampton, VA 23681 Prof. Sheldon Mostovoy ITT Department of MMAE 10 West 32nd St. Chicago, IL 60616 Carl Rousseau Bell Helicopter TEXTRON Post Office Box 482 Fort Worth, TX 76101 Prof. Rick Neu Georgia Institute of Technology School of Mechanical Engineering Atlanta, GA 30332-0245 Prof. Ashok Saxena Georgia Institute of Technology School of Materials Science and Eng. Atlanta, GA 30332-0245 Jim Rossi Westmoreland Mechanical Testing Old Rt. 30, Westmoreland Dr. P.O. Box 388 Youngstown, PA 15696-0388 Bob Somerville Boeing Commercial Airplane Group P.O. Box 3707 Weattle, WA 98124-2207 Basant K. Parida National Aerospace Labs Post Bag No. 1779 Bangalore, 560 017 INDIA
HOUSTON, TEXAS (713) 977-1377 • WASHINGTON, DC (301) 881-0226
S O U T H W E S T R E S E A R C H I N S T I T U T E ®
6220 CULEBRA RD. 78238-5166 • P.O. DRAWER 28510 78228-0510 • SAN ANTONIO, TEXAS, USA • (210) 684-5111 • WWW.SWRI.ORG
Prof. Judy Schneider Mississippi State University Department of Mechanical Engineering 210 Carpenter Engineering Bldg. P.O. Drawer ME Mississippi State, MS 39762-5925 Prof. Steven Danewicz Mississippi State University Department of Mechanical Engineering 210 Carpenter Engineering Bldg. P.O. Drawer ME Mississippi State, MS 39762-5925 Robert Diamond MARTEST 1245 Hillsmith Dr. Cincinnati, OH 45215 Phil Bretz METCUT Research Inc. 3980 Rosslyn Dr. Cincinnati, OH 45209-1196 David Abeln Cincinnati Testing Laboratories 417 Northland Blvd Cincinnati, OH 45240 John Beavers CC Technologies 6141 Avery Rd. Dublin, OH 43016-8761 Jane Runkle McCook Metals 4900 First Avenue McCook, IL 60525-3294 Hubert Doker German Aerospace Center Porz-Wahnheide Linder Hohe D-51147 Koln GERMANY Richard Brazill
Alcoa Technical Center 100 Technical Dr. Alcoa Center, PA 15069-0001 Prof. Ralph Bush United States Air Force Academy USAF Academy, CO 80840 Kevin Walker Defence Science and Technological Org. 506 Lorimer St. Fishermans Bend VIC 3207 AUSTRALIA Malcolm Loveday NPL Materials Centre National Physical Laboratory Queens Road Teddington Middlesex TW11 0LW UNITED KINGDOM Jim Hartman Honeywell Engines and Systems P.O. Box 52181, M/S 302-101 111 S. 34th St. Phoenix, AZ 85034 Edward Stevens NASA Goddard Space Flight Center Carrier Systems Branch, Code 546 Building 5, Room WO34C Greenbelt, MD 20771 Hazem Kioua Bombardier Aerospace 10000 Cargo A-4 St. Montreal International Airport, Mirabel Mirabel, Quebec J7N 1H3 CANADA Markus Lang EADS 81663 Munich GERMANY Mike Sullentrup
HOUSTON, TEXAS (713) 977-1377 • WASHINGTON, DC (301) 881-0226
S O U T H W E S T R E S E A R C H I N S T I T U T E ®
6220 CULEBRA RD. 78238-5166 • P.O. DRAWER 28510 78228-0510 • SAN ANTONIO, TEXAS, USA • (210) 684-5111 • WWW.SWRI.ORG
Boeing P.O. Box 516 MC S106-6420 St. Louis, MO 63166-0516 Steve Kimmins British Aerospace AIRBUS New Filton House Filton, Bristol BS99 7AR UNITED KINGDOM Dan Lingenfelser Caterpillar Inc. Technical Center, Bldg. K P.O. Box 1875 Peoria, IL 61656-1875 Fabian Orth Edison Welding Institute 1250 Arthur E. Adams Dr. Columbus, OH 43221-3585 Bob Eastin Federal Aviation Administration Los Angles Aircraft Certification Office 3960 Paramount Blvd. Lakewood, CA 90712-4137 Edward Vesely, Jr. IIT Research Institute 215 Wynn Drive, Suite 101 Huntsville, AL 35805 Kevin B. Lease Kansas State University Mechanical and Nuclear Engineering 317 Rathbone Hall Manhattan, KS 66506-5205 Dale Ball Lockheed Martin Tactical Aircraft Systems Post Office Box 748 Mail Zone 8862 Fort Worth, TX 76101 Frank Stokes ATLSS Research Center Lehigh University
117 ATLSS Drive Bethlehem, PA 18015 Royce G. Forman NASA Johnson Space Center Code EM2/Materials Technology Branch Houston, TX 77058 Roy Hewitt National Research Council of Canada Structures, Materials and Propulsion Lab Montreal Road Ottawa, Ontario K1A 0R6 CANADA Stig Berge Norwegian Univ. of Science and Tech. Faculty of Marine Technology Department of Marine Structures N-7034 Trondheim NORWAY Robert L. Tregoning US Nuclear Regulatory Commission Mail Stop T10 E10 Two White Flint North 11545 Rockville Pike Rockville, MD 20852 Skip Grandt Purdue University School of Aeronautics and Astronautics 1282 Grissom Hall West Lafayette, IN 47907-1282 Ben Hillberry Purdue University School of Mechanical Engineering West Lafayette, IN 47907 Bruce Miglin Shell E&P Technology Westhollow Technology Center P.O. Box 1380 Houston, TX 77251-1380 Cameron Lonsdale Standard Steel
HOUSTON, TEXAS (713) 977-1377 • WASHINGTON, DC (301) 881-0226
S O U T H W E S T R E S E A R C H I N S T I T U T E ®
6220 CULEBRA RD. 78238-5166 • P.O. DRAWER 28510 78228-0510 • SAN ANTONIO, TEXAS, USA • (210) 684-5111 • WWW.SWRI.ORG
500 N. Walnut St. Burnham, PA 17009 Prof. Mohan Ranganathan University Francois-Rabelais (Tours) Laboratory of Mecanique et Rheologie 7 Avenue Marcel Dassault B.P. 0407 37204 Tours Cedex 3 FRANCE Prof. Pete Laz University of Denver Department of Engineering 2390 S. York St. Denver, CO 80208 Prof. Greg Glinka University of Waterloo Mechanical Engineering Department Waterloo, Ontario NZL 3G1 CANADA Prof. Mike Sutton University of South Carolina Department of Mechanical Engineering Columbia, SC 29208 Prof. David Smith University of Bristol Department of Mechanical Engineering Queens Building, University Walk Bristol BS8 1TR ENGLAND Prof. Rob Ritchie University of California at Berkeley Dept. of Materials Science and Mineral Eng. Materials Sciences Division, MS 62-203 Lawrence Berkeley National Laboratory Berkeley, CA 94720 Prof. Bob Dexter University of Minnesota Department of Civil Engineering Institute of Technology 122 CivE 500 Pillsbury Drive S.E.
Minneapolis, MN 55455-0116 Prof. James Baldwin The University of Oklahoma School of Aerospace and Mechanical Eng. 865 Asp Avenue Norman, OK 73019-0601 Prof. Rick Link US Naval Academy Mechanical Engineering Dept. 590 Holloway Rd. Annapolis, MD 21402-5042 Prof. Norm Dowling Virginia Polytechnic Institute Dept. of Eng. Science and Mechanics Blacksburg, VA 24061 Ian Sinclair University of Southampton School of Engineering Sciences Highfield Southampton SO17 1BJ UNITED KINGDOM Prof. John Yates The University of Sheffield Department of Mechanical Engineering Mappin St. Sheffield S1 3JD UNITED KINGDOM
HOUSTON, TEXAS (713) 977-1377 • WASHINGTON, DC (301) 881-0226
ASTM E647 FCG Round Robin SwRI October 2004
1
ASTM E647 ROUND-ROBIN: FATIGUE CRACK GROWTH RATE MEASUREMENT INTRODUCTION
When E647 first evolved in the early to mid 1970’s, an extensive round-robin testing effort was performed to assess precision and variability issues both within and between laboratories. The precision and variability statements in E647 are based on this work. Over the past 30 years, gradual changes have occurred with regard to (a) the body of E647, (b) crack length measurement capability, (c) K-control test strategies and (d) servohydraulic control technology. The ASTM E647 fatigue crack growth (FCG) standard is a mature standard: the current version (E647-00) includes over 40 pages and more than 100 external reference citings. There are a number of currently acceptable paths, utilizing different load control methods for instance, allowed for generating FCG data. The intent of the round-robin herein is to control material type and allow as many labs as possible to generate fatigue crack growth rate data for the material(s) of interest using whatever method they desire as long as it falls within the ASTM E647 standard. In order to achieve the goal of this round-robin, a number of specimen have been fabricated from three materials (7075, 2024 and 4130 steel) in two geometries. Testing will be performed primarily at low load ratio with a limited number of tests at higher load ratio. RULES FOR THE ROUND-ROBIN The fundamental rules involved in this round-robin are few and simple:
• Rule #1. Any method allowed by ASTM E647-00 to generate FCG data is allowed (e.g. the organizers are not confining testing to one approach, for instance).
• Rule #2. You must test the specimens that you are supplied with under the conditions
indicated.
• Rule #3. Performing testing to the ∆K regime indicated for the materials.
• Rule #4. Fully document your results and procedures so that we can analyze the data and understand the results (this is really critical as we are going to have quite a bit of data).
These rules should help you refine the parameters associated with testing. The additional information provided below should also assist you in the selection of the conditions for the testing you are performing as part of this round-robin.
ASTM E647 FCG Round Robin SwRI October 2004
2
MATERIALS AND SPECIMENS Three materials have been procured for this testing: two aluminum and one steel alloy. The details of the materials and strength levels are shown in Table 1. We know that load ratio and material type will both impact the measured FCG data and the variability associated with the data. Therefore, these variables will be perturbed during testing.
Table 1. Materials involved in the FCG round-robin including the strengths of the conditions.
Alloy or Temper or Product Product Average Tensile Properties
Material Condition Size Extent σTS, ksi σYS, ksi elong, %
4130 norm-HTed 4” x ¼” bar 36 ft 175 167 17
7075 -T6 0.125” sheet 4’ x 8’ 83 76 14
2024 -T351 0.375” sheet 4’ x 8’ 72 56 20 The raw material was machined into C(T) and M(T) specimen geometries. The dimensions of the specimens varied as indicated in Table 2. Note that Table 2 also indicates specimen ID’s corresponding to the different materials and geometries. The focus was to machine a sufficient number of specimen with enough diversity to fit into the widest range of laboratory facilities. Some of the specimens have initial notches machined into them and some require notching prior to precracking.
Table 2. Specimen ID’s for different materials and specimen geometries.
Material Thickness Specimen Width No. of Specimen
B, inch Geometry W, inch Spec Identification No’s
4130 steel ∼0.25 C(T) 2.0 24 2xy where x = A-K, y = 1-4
C(T) 3.0 25 3xy where x = A-K, y = 1-4
2024-T351 ∼0.25 C(T) 2.0 30 W2-2-x where x = 1-30
C(T) 3.0 30 W3-2-x where x = 1-30
∼0.375 M(T) 4.0 32 AL-2- x where x = 1-32
7075-T6 ∼0.125 M(T) 4.0 44 AL-7- x where x = 1-44
ASTM E647 FCG Round Robin SwRI October 2004
3
FCG TEST CONDITIONS REQUIRED The testing that will ultimately be performed by a given lab is a function of a number of variables inherent in that laboratory. These variables include, for instance, load capacity of the machine and/or fixture, initial notch size and shape and test control method (constant amplitude versus K-control). The intention in this round-robin is not to dictate the test conditions but rather to allow the user to choose, within of course the context of E647. Shown in Table 3 are the conditions that will be evaluated during the round-robin. Note that the last column identifies the condition that the organizers are asking you to test which was identified in your shipment of specimen. Not all testing organizations will be testing the same conditions. However, as a general rule the low load ratio behavior will be the focus of the vast majority of the testing.
The envelope of growth rates indicated in Table 3 are provided for your guidance only in terms of selecting the conditions for testing. Achieving the full range of growth rate data indicated by the upper and lower bound values in Table 3 is unlikely given the specimen sizes involved in testing. Therefore, when selecting your testing conditions consider the following:
• For low load ratio testing (R=0.1), the focus is on the growth rates starting at ∆K = 10 ksi√in
• For higher load ratio testing (R>0.1), toughness limitations require generally starting lower, on the order of ∆K = 8 ksi√in or so.
Do the best you can in choosing conditions based on these limitations. Just remember: when in doubt, follow E647! Table 3. Generalized test conditions for the round robin testing including approximate lower and upper bound envelope of crack growth rates and applied stress intensity factor ranges. Material Thickness Load Lower Bound Upper Bound Round-Robin
B, inch Ratio ∆K, ksi√in
da/dN, inch/cyc
∆K, ksi√in
da/dN, inch/cyc
Condition ID
4130 steel ∼0.25 0.1 8 1 (10-7) 30 6 (10-6) STL-A
0.8 8 3 (10-7) 30 1 (10-5) STL-B
2024-T351 ∼0.25 0.1 5 2 (10-7) 40 1 (10-3) ALX-A
0.5 5 1 (10-6) 20 1 (10-4) ALX-C
∼0.375 0.1 5 2 (10-7) 40 1 (10-3) ALX-B
7075-T6 ∼0.125 0.1 5 3 (10-7) 40 1 (10-3) ALN-A
ASTM E647 FCG Round Robin SwRI October 2004
4
REQUIRED DOCUMENTATION With the relatively open philosophy (e.g. not confining testing to certain techniques and methods) used during this testing, the burden when evaluating the results will be to understand how the testing was performed so as to potentially determine the roles of different variables. This means that there is additional burden on the testing lab to provide sufficient, highly detailed information to the round-robin organizers. To assist in this process, Attachment A is provided to guide in the process of documenting the procedures followed. All of the information in Attachment A is important to include with the data generated, and we request that you please provide it when you supply the data to the round-robin organizers. Keep in mind that we need complete details regarding how the specimen was precracked prior to starting the test. Once the test begins, details regarding how it was loaded are then critically important. The analysis procedures used with the data are also important to document. You need to make sure that the data you have provided is sufficient for us to re-process the data, if necessary. So, instead of simply providing da/dN and ∆K (which in the strictest sense is the minimum data required), we also need crack length, cycle count and applied load information. This is important information should it be necessary to re-process all of the data that you provided. If non-visual crack length measurement is performed, please be sure to indicate what type of post-test correction strategy was utilized to relate the visual to the non-visual crack measurement data. A comparison between the visual measurements and post-test corrected data would also be highly useful. Be sure to include all elements of what E647 requires in terms of reporting data in addition to that recommend in Attachment A. CONTACT INFORMATION Please do not hesitate to contact any of the round robin organizers if you have any additional questions. Primary: Secondary:
Pete McKeighan Jim Feiger Southwest Research Institute Southwest Research Institute San Antonio, TX San Antonio, TX 210.522.3617 210.522.6881 [email protected] [email protected]
ASTM E647 FCG Round Robin SwRI October 2004
5
ATTACHMENT A – Information Required in Test Documentation
1) Fatigue Test Lab Information
a) Location b) Technician(s)
2) Testing Equipment and Setup
a) Test frame type b) Test frame capacity c) Test control hardware/software d) Test Specifics
i) Load cell range/calibration ii) Crack length determination
(1) Compliance (a) clip gage calibration (b) clip gage gage length
(2) Potential drop (a) System used (DCPD/ACPD)
(i) Indirect or Direct (ii) Current Magnitude
(b) Probe geometry (i) Single or dual probe (ii) Location and dimensions
(3) Visual techniques (i) Device and equipment (ii) Resolution
iii) Environmental Conditions (1) Temperature (°C) (2) Humidity (%) (3) Test Date (day/month/year) / duration (days)
iv) Grips (1) Clevis size (C(T) geometry) (2) Grip configuration (M(T) geometry)
(a) Grip-to-grip distance (b) Bending verified (strain gages)
3) Specimen Details
a) Material i) Steel
(1) Modulus used for crack length compliance (if used)
ii) Aluminum (1) Two alloys evaluated (2) Modulus used for crack length determination
(if used) b) Specimen Geometry
i) C(T) fatigue crack growth specimen (1) Two sizes: W=2-in and 3-in
ii) M(T) fatigue crack growth specimen (1) E647 stress intensity solution ? (2) 2W= 4-in
iii) Dimensions (1) W (width), B (thickness) (2) Notch length (3) Notch height (4) Crack length transducer location and
dimensions iv) Specimen preparation
(1) Polishing, etc.
v) Notch type (1) EDM, slitting saw, chevron, other
vi) Alteration(s) to specimen from the as-received condition
4) Test Procedure Details
a) Precracking i) Overall precracking procedures
(1) Loading shedding, constant ∆K, etc. (2) FCGR at end of precracking
ii) Loading conditions for precracking (1) Pmax, R-ratio (2) Frequency (3) Initial and final crack lengths (4) Initial and final ∆K levels
iii) Crack tip symmetry: front/back and left/right (M(T))
b) FCG Testing i) Approach
(1) Constant amplitude – force function curve type (a) Loading conditions: Pmax, R-ratio,
frequency (b) Initial and final crack lengths (c) Initial and final ∆K levels (d) ∆a/W crack length interval for data points (e) Visual crack length intervals and number
of visual taken (f) Crack tip symmetry: front/back and
left/right (2) K-control
(a) Initial stress intensity (b) K-gradient (c) R-ratio, frequency (d) Initial crack length, final crack length (e) ∆a/W interval for data collection (f) crack tip symmetry: left/right and
front/back (3) Other
(a) Describe overall technique 5) Analysis Technique (post-test processing)
a) Automated/manual b) Method used
i) Polynomial ii) Secant iii) Other
c) Crack front profile, final crack length measurement d) Error: visual crack lengths versus transducer determined e) Anomalies during testing
i) Power outages ii) Hold times iii) Change in environement iv) Other
f) Fracture surface appearance/anomalies i) Crack in plane?
g) Validation of yield criteria for both specimen geometries i) Provide yield strength to participants
B-1
Appendix B – Individual Lab Data Plots
B-2
This page intentionally left blank.
B-3
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab A (2F3)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-4
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab A (2F4)Lab A (3B1)Lab A (3B2)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
B-5
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab A (W2-2-5)Lab A (W2-2-6)Lab A (W2-2-7)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-6
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (3C4)Lab B (3E1)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-7
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (3E4)Lab B (3F1)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
B-8
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (W3-2-10)Lab B (W3-2-11)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-9
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (W3-2-14)Lab B (W3-2-15)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-10
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (AL-2-10)Lab B (AL-2-11)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-11
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab B (AL-7-9)Lab B (AL-7-10)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-12
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab C (2K1 K-decrease)Lab C (2K1 K-increase)Lab C (2K2 K-decrease)Lab C (2K2 K-increase)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-13
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab C (W2-2-23 K-decrease)Lab C (W2-2-23 K-increase)Lab C (W2-2-24 K-decrease)Lab C (W2-2-24 K-increase)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-14
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab C (W3-2-22 K-decrease)Lab C (W3-2-22 K-increase)Lab C (W3-2-23 K-decrease)Lab C (W3-2-23 K-increase)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-15
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
Lab D (AL-2-27)Lab D (AL-2-28)Lab D (AL-2-26)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-16
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab D (AL-7-21)Lab D (AL-7-22)Lab D (AL-7-23)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-17
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab E (3L1)Lab E (3L2)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-18
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab E (W2-2-29)Lab E (W2-2-30)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-19
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab E (AL-2-20)Lab E (AL-2-21)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-20
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab E (AL-7-30)Lab E (AL-7-31)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-21
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab F (2A1)Lab F (2B1)Lab F (3A1)Lab F (3A2)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-22
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab F (3A3)Lab F (3A4)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
B-23
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab F (W3-2-1)Lab F (W3-2-2)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-24
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab F (W3-2-3)Lab F (W3-2-4)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-25
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab F (AL-2-1)Lab F (AL-2-2)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-26
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab F (AL-7-1)Lab F (AL-7-2)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-27
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab G (3B3)Lab G (3B4)Lab G (3C1)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-28
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab G (3C2)Lab G (3C3)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
B-29
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab G (W3-2-5)Lab G (W3-2-6)Lab G (W3-2-7)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-30
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab G (W3-2-8)Lab G (W3-2-9)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-31
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab G (AL-7-7)Lab G (AL-7-8)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-32
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab H (2J1 const. amp.)Lab H (2J2 const. amp.)Lab H (2J1 K-decrease)Lab H (2J2 K-increase)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-33
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab H (W2-2-15 const. amp.)Lab H (W2-2-16 const. amp.)Lab H (W2-2-15 K-decrease)Lab H (W2-2-16 K-decrease)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-34
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab H (W2-2-17 const. amp.)Lab H (W2-2-18 const. amp.)Lab H (W2-2-17 K-decrease)Lab H (W2-2-18 K-decrease)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-35
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
Lab I (2G1 K-increase)Lab I (2G2 K-increase)Lab I (2G1 K-decrease)Lab I (2G2 K-decrease)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-36
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
Lab I (2G3 K-increase)Lab I (2G4 K-increase)Lab I (2G3 K-decrease)Lab I (2G4 K-decrease)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
B-37
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
Lab I (W2-2-8 K-increase)Lab I (W2-2-9 K-increase)Lab I (W2-2-8 K-decrease)Lab I (W2-2-9 K-decrease)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-38
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab I (W2-2-10 K-increase)Lab I (W2-2-11 K-increase)Lab I (W2-2-10 K-decrease)Lab I (W2-2-11 K-decrease)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-39
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab I (AL-2-5 K-increase)Lab I (AL-2-6 K-increase)Lab I (AL-2-5 K-decrease)Lab I (AL-2-6 K-decrease)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-40
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab I (AL-7-5 K-increase)Lab I (AL-7-6 K-increase)Lab I (AL-7-5 K-decrease)Lab I (AL-7-6 K-decrease)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-41
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab J (2I1)Lab J (2I2)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-42
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab J (2I3)Lab J (2I4)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-43
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab J (W2-2-12)Lab J (W2-2-12)Lab J (W2-2-14)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-44
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab K (3F2)Lab K (3G1)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-45
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
Lab K (W3-2-16B)Lab K (W3-2-28B)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-46
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab K (W3-2-17B)Lab K (W3-2-29B)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-47
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab L (W3-2-18)Lab L (W3-2-19)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-48
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab L (W3-2-20)Lab L (W3-2-21)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-49
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab L (AL-2-12)Lab L (AL-2-13)Lab L (AL-2-14)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-50
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
LabL (AL-7-11)Lab L (AL-7-12)Lab L (AL-7-13)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-51
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
Lab M (AL-2-29)Lab M (AL-2-30)Lab M (AL-2-33)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-52
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab M (AL-7-32)Lab M (AL-7-33)Lab M (AL-7-34)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-53
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab N (3K1)Lab N (3K2)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-54
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab N (3I1)Lab N (3I2)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
B-55
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab O (2J4)Lab O (2J3)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-56
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab O (W2-2-19)Lab O(W2-2-20)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-57
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab O (W2-2-21)Lab O (W2-2-22)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-58
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab P (2C1)Lab P (2E1)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.1
B-59
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab P (2F1)Lab P (2F2)
Material:B:
Geometry:R:
4130 Steel0.25-inchC(T)0.8
B-60
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
Lab P (W2-2-1)Lab P (W2-2-2)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.1
B-61
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab P (W2-2-3)Lab P (W2-2-4)
Material:B:
Geometry:R:
2024-T3510.25-inchC(T)0.5
B-62
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
Lab P (AL-2-3)Lab P (AL-2-4)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-63
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab P (AL-7-3)Lab P (AL-7-4)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
B-64
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab Q (001 K-decrease)Lab Q (001 K-increase)Lab Q (301 K-decrease)Lab Q (301 K-increase)
Material:B:
Geometry:R:
2024-T3510.375-inchactually C(T)0.1
B-65
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab R (AL-2-25)
Material:B:
Geometry:R:
2024-T3510.375-inchM(T)0.1
B-66
ΔK, MPa√m10 100
da/d
N, m
/cyc
le10-9
10-8
10-7
10-6
10-5
10-4
ΔK, ksi√in1 10 100
da/d
N, i
n/cy
cle
10-8
10-7
10-6
10-5
10-4
10-3
10-2
Lab R (AL-7-18)Lab R (AL-7-19)Lab R (AL-7-20)
Material:B:
Geometry:R:
7075-T60.125-inchM(T)0.1
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