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Red Wing Virtual Liberal Arts College - Weibull Trending Toolkit (WTT)
Cracks, Fractures, Crack Growth

[first posted: 29 March 1996, revised 16 July 2000, 12 September 2003, and 25 February 2004]

  CorTech Training, Red Wing, MN

Weibull Trending Toolkit (WTT) Courses I, II and III are presented to students of engineering everywhere, at all career stages. They contain elements useful for development of Safety Critical (SC) Systems for many types of containment structures. Many containments are pressure vessels. When a fluid is contained under pressure, it is important that it be designed to leak before it breaks. Corrosion pits can cause leaks. They can also serve as initiation sites for crack growth. When a growing crack penetrates a container wall, the crack growth mechanism must not convert from a slow growth to a fast or catastrophic fracture mode. Spend time searching topics such as safety critical systems, artificial neural networks for SC systems.


CorTech Training's WTT courses give me, Glenn E. Bowie, opportunities to help corrosion and materials science engineers use my background in studying effects of stress on material behaviors. Previously prepared course WTT Course I addresses historic pitting corrosion data sets, and WTT Course II emphasizes fatigue crack growth and stress corrosion cracking test data reduction. WTT Course III Editions address issues based on my experience.

  1. Task 1
    Corrosion Fatigue and Stress Corrosion Cracking
  2. Task 2
    Safe-Life, Fail-Safe, and Inspection Concepts
  3. Task 3
    Crack Initiation and Inspection Concepts
  4. Task 4
    Fatigue Crack Growth in A537M Steel
  5. Task 5
    Crack Length and Inspection Planning
  6. Task 6
    Corrosion Can Cause Machinery Imbalance
  7. Task 7
    Background for Presentation on Aging Aircraft
  8. Task 8
    Tribute to Waloddi Weibull
  9. Task 9
    Mechanics of Aging Aircaft

Task 1

Corrosion Fatigue and Stress Corrosion Cracking


  1. "Metal Corrosion in the Atmosphere", A Symposium Presented at the Seventeenth Annual Meeting, American Society for Testing Materials, ASTM Special Technical Publication No. 435, June 1967.
  2. C. C. Nathan and C. L. Dulaney, Localized Corrosion as a Statistical Phenomenon, in NACE-3 publication "Localized Corrosion, National Association of Corrosion Engineers, 1974".
  3. D. E. Hawn, "Extreme Value Prediction of Maximum Pits on Pipelines", pp. 29-32, Materials Performance, March 1977, Presented at February 1976 Western Regional Meeting of NACE, Calgary, Alberta, Canada.

NACE Documents

NACE documents reviewed in Courses I and II may now be obtained with assistance of the staff at the site identified in the following e-mail message received Sat, 2 Mar 1996 16:30:16 -0500.

From: Brad Lewis
Subject: At the risk of sounding commercial...
To: Recipients

At the risk of sounding commercial, NACE International (formally the National Association of Corrosion Engineers) finally has a home page. See:

While this may sound commercial, NACE is really a non-profit group of personnel interested in corrosion and corrosion control. The web page is under construction and only has jumps to mail boxes; in the future there will be much more including information on books, journals, software, standards, education/training, and all of the other services provided by NACE.

Don't be afraid to take the "contact our staff" jump with your questions and comments. That's why we're there.

Brad Lewis
Publications Chairman
NACE International


Course II, Task 1: Cylindrical Component Tested

This component test history is from unpublished notes written by J. M. Van Orden in 1969 at the Lockheed-California Company (now Lockheed Martin) Rye Canyon Research and Development Center. The component was cyclindrical and had been subjected to cyclic changes in internal pressure. The cylinder was a die forging of AA 7075-T73. It had an axial parting plane.

The cyclinder was subjected to 22000 cycles of hydraulic fluid internal pressurization to 3000 psi. It was then static tested at 6000 psi. Primary failure occurred during the static test. A parting plane crack formed along approximately two-thirds of the cylinder length.

During failure analysis, Jerry Van Orden observed more than 100 pits on external and internal surfaces. Pits were more numerous and generally deeper on the internal than on the external surface. Metallographic and electron fractographic examinations of parent material and specimens exhibiting pits and cracks did not reveal evidence of intergranular stress corrosion. From examination of surfaces it was concluded that the part had been anodized. The coating layer had a surface weight of 4.5 mg/sq. in., as would be produced, for example, during one hour of chromic acid or 10 minutes of sulphuric acid anodizing treatment. The actual anodizing process applied to the component was not documented.

Visual Examination of the inner surface revealed numerous slot-like secondary cracks in a 3/8 inch wide band adjacent to the primary fracture surface. A central pit could be seen at each of the secondary cracks. The following image shows a transverse section through one of these pits. A fatigue crack evidently originated at the base of the pit. Depth of this pit was approximately 6 mils.

The following image was reproduced from p. 247 of Ref. 1. It shows the cross section of a corrosion pit at the surface of an AA 3003 specimen which had been exposed to an industrial atmosphere at Västerås, Sweden for 10 years.

Ref. 3 contains an informative review of corrosion fatigue by B. B. Wescott. Illustrations of corrosion pits which served as initiation sites for fatigue cracking can be seen in pp. 578-590.

D. W. Hoeppner's Analysis of the Cylinder Failure

A corrosion pit on the internal surface of the cylindrical component served as the origin of a fatigue crack. Location of the pit and the semi-elliptical crack pattern can be seen in the following image.

In 1970, D. W. Hoeppner taught a Lockheed Continuing Education Course called "Prevention of Fracture in Materials." In the course, he verified that the fatigue crack was sufficiently extensive to be critical for fast fracture of the component when it was loaded to 6000 psi internal pressure. The following image is an abbreviated version of one page from D. W. Hoeppner's 1970 class notes.

Whois D. W. Hoeppner

David W. Hoeppner, P.E., Ph.D.
Professor and Director of QIDEC
Department of Mechanical Engineering
University of Utah
3209 MEB
Salt Lake City, Utah 84112
Phone (801) 581-3851, fax (801) 585-5889

Course I Review
  • Read D. E. Hawn's paper on maximum pit depths in a 5280 ft. long pipeline section.>
  • Use makefile.bas to enter Hawn's 40 maximum pit depth measurements into file hawn.dat.
  • Use sort.bas to rank order the 40 measurements in file ohawn.dat.
  • Apply wrisk.exe to data file ohawn.
  • Confirm the results below.
  • Use K, E, and V to predict that there was one chance in 21120 ( 4 x 5280) that a pit depth could have exceeded 91.4 mils.
  • Find the chance that a pit depth could have equalled the pipeline wall thickness of 188 mils.
  • Practice using Weibull Trending Toolkit program wdesign.exe to approximate the above results of analyzing D. E. Hawn's data. An example design approximation follows.


  • Compare the data points in the design example with the measured points. Remember from reading the wdesign.txt file in the Weibull Trending Toolkit that WDESIGN uses an order statistic to generate data points. After some thought, write some notes about how well you think the analysis techniques used in program WRISK match measured data in comparison with the way WDESIGN matches an order statistic. Are you a believer in utility of Weibull analysis?

Create Modeling Program DESIGN
  • Notice the Weibull shape parameter K values for files task901, task902, and task903 have much less variation than the K values for data files studied in Task 8.
  • Average the three K values found here to obtain K = 2.75439.
  • After some thought, decide to use E and V values for files task901 and task903 to model time dependence. Let E = A * T + B and V = C * T + D, where T is exposure time in years and A, B, C, and D are constants.
  • The Weibull Trending Toolkit includes a program called WDESIGN. It uses an order statistic to estimate N probabilities. A user supplies trial Weibull exponent K, threshold E and an estimate of the median random variable. The program estimates N values of the variate and finds Weibull K, E, and V to match design sample and Weibull mean, standard deviation, and skewness, values.
  • The instructor used WDESIGN as the basis for creating new program DESIGN.
  • DESIGN has an exponent K which is independent of exposure time, and parameters E and V which are linearly dependent on time exposure. When a user runs DESIGN, she/he is prompted to input a file name, number of measurements N being modeled, and exposure time.
  • DESIGN uses an order statistic base on N, the constant K, and calculated E and V to generate N design sample maximum pit depths.
  • DESIGN matches sample and Weibull mean, standard deviation, and skewness values to find K, E, and V for the N design measurements.

Model Grouped Aziz Data for Three Week Exposure and Godard Data for 13 Year Exposure

Industrial Water Pipeline with 50 Year Design Life

Note written in 1995 about using wrisk.exe and risk.bas.

The Weibull Trending Toolkit Program wrisk.exe is 1995
copyrighted property of:
Glenn E. Bowie
2426 Hallquist Ave.
Red Wing, MN 55066
(651) 388-2374

Do not try to use WRISK.EXE to process a file with more than 1024
data values.  WRISK.EXE runs on an IBM compatible PC with Microsoft
Windows.  Make sure you have VBRUN300.DLL in your
C:\>WINDOWS\SYSTEM directory.

The Weibull Trending Toolkit program WRISK.EXE has three curves instead
of two.
blue = Weibull probability density
green = Weibull cumulative probability
yellow = Weibull risk
Weibull Probability Density, p

p = k * ((x - e)/(v - e)^(k - 1) *

Exp(-((x - e)/(v - e))^k/(v - e).

Weibull Cumulative Probability, F

F = 1 - Exp(-((x - e)/(v - e))^k)

Let P = Exp(-((x - e)/(v - e))^k)

Weibull Risk

R = k * ((x - e)/(v - e))^(k - 1)/(v - e)

You see that p = R * P, or R = p/P.

The probability density and risk curves are scaled so you can see their
shapes.  When you are ready to study probability density and risk mag
nitudes, you can use QBasic program RISK.BAS as a starting tool.

I like to use to PCs side by side when studying Weibull risk.  A good
starting point is to examine file 6061.DAT using Edit.  There are 102
fatigue lives in the file.  The first two lives are 233 and 258.  Count
down to find the median life in the file equals 400.  Examine the last
entry in the file.  The 102nd value in the file is 560.

Run WRISK and choose file 6061.  Use a graph upper limit = 800.
There are 19 tics on the Y-axis.  Each scale division is worth 40 life
units.  20 x 40 = 800.  From the summary screen,
k = 3.61498
e = 195.1232
v = 420.0841
Median = 398.3941

Type QBasic risk, press enter on your second PC.  RISK asks you for
the Weibull shape parameter k, threshold parameter e, median, and
production run size.  Enter the above values for k, e, and median and
102 for production run size.  RISK tells you characteristic value v =
420.0842.  The value in the summary screen of WRISK is truncated
rather than rounded.  We accept that the two characteristic values
are the same.  RISK tells you the probability of survival at the first
failure is 0.9903.  The cumulative distribution curve, green, is a
probability of failure curve.

P = probability of survival
F = probability of failure
F = 1 - P.

The height of the green curve is 1 - 0.9903 or 0.0097 at the first
failure, according to RISK.  RISK predicts the time to first
failure = 257.6.
Compare with actual first experimental value in 6061.DAT, 233.  RISK
tells us the probability density at time 257.6 equals 0.0005588.
Calculate the risk at first failure:

R = p/P = 0.0005588/0.9903 = 0.0005643.  RISK tells us
R = 0.0005643 at first failure.

Work your way through second failure comparisons at your leisure.
Move to the median.  RISK predicts the median life equals 398.3941,
and the experimental value is 400.  WRISK shows the mean, median,
and mode are close together for file 6061.  RISK tells us the height of
the probability density curve at the median equals 0.00616.  And at time
538.956, the density drops back down to 0.000473.  The difference in
time units between the last failure and the threshold e equals 538.956 -
195.1232 = 343.8328.  Multiply this difference by the density at the
median to obtain 2.1192.  Remember the area of a triangle equals 0.5 x
base x height.  We just estimated the area under the density curve to be
0.5 x 2.1192 = 1.0596.  The area under a probability density curve
equals 1.0.

I used a clear, plastic scale divided in mm to find the height of the
yellow risk curve at the mode and at 538 time units to be 19 and 79 mm.
The height ratio equals 19/79 or 0.24.  RISK predicts the ratio to be
0.0123/0.0487 = 0.25.

Stare at the graph for file 6061.  Use a scale to confirm that the
cumula tive probability is at 0.5 of the maximum height, for this case.
The probability of survival at the median = 0.5.  RISK tells us risk
R = 0.1232696 at the median.  At the median, find R x P = 0.0616348.
The density p at the median is then 0.0616348, as RISK told us already.
It is important to practice looking at the curves when interpreting
numerical results.

Look at the probability density and cumulative probability curves for
file 6061.  Think of the probability density as the rate of change of
the cumulative probability.  The slope of the cumulative probability
curve, the green one, is maximal at the mode.  The probability density
is maximal at the mode.

Glenn E. Bowie
Red Wing, MN
September 1, 1995

Note written in 1995 about using programs wdesign.exe and wrisk.exe.

The Weibull Trending Toolkit Program wdesign.exe is 1995 copyrighted
property of:
Glenn E. Bowie
2426 Hallquist Ave.
Red Wing, MN 55066
(651) 388-2374

It is important to remember that WDESIGN writes a data file and a
results file each time it is used.  When WDESIGN asks you for a file
name, NEVER give it the same name as an experimental file such as
6061, 7075 and so on.  It is a good practice to use the leading
letter D in all file names you give WDESIGN.  Avoid
naming experimental data files with a leading D.

Let me assume you have applied WRISK.EXE to study data file 6061 as
outlined in the above note aboyr WRISK.  Run WDESIGN.  Click the box
"Enter N, k, e and Median".  Be sure to enter a file name.  This
time enter D6061.  Enter the following values:
For N: 102
For k: 3.61498
For e: 195.1232
For Median: 398.3941

Compare the summary results and graph with the summary and graph
you get when you apply WRISK to file 6061.  Keep the median at
398.3941 and decrease k gradually.  At each step, compare with
WRISK and 6061 results.  Finally, choose
N: 102
k: 3.55
e: 194
Median: 398.3941

Apply WRISK to file D6061.  You get the same results given by
WDESIGN for the above parameters.

Please do not apply WDESIGN for N > 1024.

Please supply design threshold e values that are sufficiently
large to keep resulting threshold values in the summary screen

Please be aware there is room for research.

Please be aware as you practice using WDESIGN in relation to your
database that you are thinking about possible application of
WDESIGN concepts for preparation of production run specifications.
Design Practice

At the DOS prompt, type QBasic risk.  Run RISK.BAS.  Enter shape
parameter k equal to 1, threshold parameter 0 and median 300.
See the characteristic value v = 432.8085.  Enter run size 500.
It is important to see that risk h(t) is constant from the first
to the last failure. Here h(t) = 0.002310491.  Now find 1/v.
For k = 1 and e = 0, h(t) = 1/v.  The failure rate is constant.

Many reliability and risk analysts limit their work to the special
case where the risk or failure rate is constant.  Programs
WTT01.EXE, WRISK.EXE, and WDESIGN.EXE do not apply to the special
case where k = 1.  In order to show you the difference between the
constant risk case and one where k is slightly greater than 1.0,
the following exercise was constructed.

At the DOS prompt for directory wtt02, load Windows.
C:\wtt02\win.  Hopefully, you see the Program Manager high
lighted.  Click File, then click Run.  In the Run Window, enter
on the command line: c:\wtt02\wrisk.exe.  Click OK on the WRISK
sign-on screen.  Click "Match Sample Statistics".  Enter file
name 6061.  Click "Plot Control Chart" and enter graph upper
limit 800.  You see the graph.  Notice a portion of the summary
screen is visible below the graph.  Hopefully, you also can see
the Program Manager word File. Click File.  Click Run.  Enter
on the command line: c:\wtt02\wdesign.exe.  Click OK on the WDESIGN
sign-on screen.  Click "Enter N, K, E, And Median".  Enter file
name delight.  For N, 500.  For K, 0.95.  For E, 27.0.
For Median, 300.

Notice k = 1.032018, and e = 0.4963179.  If you ever analyze material
property data and obtain a k value as close to 1.0 as this, with e
not negative, consider sending me a copy of your data.  See
UCL = 2743.9.
Click "Plot Control Chart" and enter graph upper limit 3000.  Examine
the yellow RISK curve.  It is a delight.  I believe risk curves such
as this one can represent many data sets which are now represented
by a con stant failure rate approach.

In the lower left corner of the screen, click the small rectangular
portion of WRISK summary screen.  Click "Match Sample Statistics".
Enter file name delight.  WDESIGN generated file delight.dat.  WRISK
has now analyzed the file and obtained familiar results.  Click
"Plot Control Chart", and enter 3000.  The graph is again a delight.

Click the small rectangular portion of WDESIGN summary screen in the
lower right corner of your display.  Enter the following:
Study the summary values.  Since UCL = 2042.8, choose graph upper
limit 2500.  Notice the risk curve.  Click anywhere on the portion
of WDESIGN summary screen visible below the graph.
Study the summary values.  Choose graph upper limit 2000.
Click WDESIGN summary screen at the bottom, enter:
Choose graph upper limit 2000.  Proceed to generate file design14 with
k = 1.4, design15 with k= 1.5, and so on until you have generated file
design19 with k = 1.9.  Choose graph upper limit 1000.  It is time to
generate a particular case.
Enter file name drayly, with N = 500, k = 1.928, e = 7.9 and median
= 300.  Notice k = 1.999 and e = 0.01767976.  Choose upper limit
1000.  Describe the risk curve.
In the special case where k = 2.0 and e = 0, the Weibull distribution
becomes a Rayleigh distribution.  For a Rayleigh distribution, the risk
is a straight line.
Generate files design20, design21 and so on until you have generated
file design40.  Examine the graphs with upper limit 1000 in each case.
Watch changes in risk.
Click the portion of WRISK summary screen at lower left and review
files delight, design11 through design19, drayly, and design20 through
Examine skewness and kurtosis values during your review.  Decide for
yourself what range of k yields probability density curves which might
be considered to be symmetrical or pseudo-normal.

Glenn E. Bowie
Red Wing, MN
September 1, 1995

Task 2
Safe-Life, Fail-Safe, and Inspection Concepts

  1. Alan Cottrell, "An Introduction to Metallurgy", Second Ed., SI Units, Edward Arnold Ltd., 1975.
  2. J. Y. Mann, "Fatigue of Steel Structures and Structural Steel", Structures and Materials Report 348, Australian Defence Scientific Service, Aeronautical Research Laboratories, March 1974.
  3. I. C. Whittaker and P. M. Besuner, "A Reliability Approach to Fatigue Life Variability of Aircraft Structures", Air Force Materials Laboratory Technical Report AFML-TR-69-75, April 1969.
  4. Glenn E. Bowie, "Downloading and uploading files on AccessASM Online", Advanced Materials & Processes, Volume 148, Number 6, p. 41, December 1995.
  5. Sigge Eggwertz and Göran Linsjö, "Study of Inspection Intervals for Fail-safe Structures", Flygtekniska Försöksanstalten, The Aeronautical Research Institute of Sweden, Report 120, 1970.
  6. Sigge Eggwertz, "Statistical Investigation of Time Until First, Second and Third Cracks in Wing Panel", Flygtekniska Försöksanstalten, The Aeronautical Research Institute of Sweden, Technical Note HU-1540, 1974.
  7. Sigge Eggwertz and Göran Linsjö, "Reliability Analysis of Wing Panel Considering Test Results from Initiation of First and Subsequent Fatigue Cracks", Flygtekniska Försöksanstalten, The Aeronautical Research Institute of Sweden, Technical Note HU-1745, 1975.
  8. Sigge Eggwertz and Göran Linsjö, "Influence of Detected Crack Length at Inspections on Probability of Fatigue Failure of Wing Panel", Flygtekniska Försöksanstalten, The Aeronautical Research Institute of Sweden, Technical Note HU-1745, Part 2, 1975.

"8.3 Environmental conditions
Most laboratory fatigue tests are carried out indoors and, although a fatigue test condition in 'laboratory air' can be regarded as a mild corrosion-fatigue test, the test article is usually not subjected to the variations in temperature and humidity, nor is it subjected to other chemically aggressive reagents which might be present in service under a range of weather conditions, i.e. in general no attempt has been made to reproduce such environments as part of a fatigue test program. It is intuitively believed that 'corrosion' can reduce the fatigue life, and numerous tests (usually on small specimens) have been performed to establish the reduction in fatigue strength caused by exposure to salt solutions, acids, distilled water, fuels, and humid environments, and to determine the efficacy of protective systems.
It is now apparent that, if service environmental factors are likely to play a significant or critical part in the overall fatigue cracking process, then it must be necessary to obtain a 'spectrum' of environmental conditions and program the test environment in a similar way to the load programming in a spectrum load fatigue test. Thus the laboratory test could involve, concurrently, a spectrum of loads and a spectrum of environments.".

In Appendix 1 of Ref. 2, Mann defined safe-life and fail-safe design concepts. On p. 53 he stated: "The safe-life concept of design - which is mainly applicable to mechanical components, machine elements and non-redundant structures - implies that an accurate estimate or prediction can be made of the life of the component or structure and that the relevant items will be replaced or retired from service before the occurrence of cracking which will jeopardize the integrity of the article." He stated further that fail-safe "... philosophy is based on the ability to readily detect fatigue cracks, by inspection, in all the relevant locations before they can propagate to such an extent that sudden and catastrophic collapse of the structure might occur. Usually a fail-safe design is 'redundant' in that it incorporates alternative load paths; ..." On p. 12 of Ref. 3, Mann continued to explain safe-life and fail-safe concepts. He summarized fatigue design rules. Rule (xviii): "Pay attention to the influence of aggressive environments. Provide appropriate protective treatments with regard to their effect on fatigue resistance." For the instructor, Ref. 4 is a personal favorite. One of the many reasons why this document is treasured is that it bears the approval signature of Walter J. Trapp. In 1969, Walter was Chief, Strength and Materials Branch, Metals and Ceramics Division, Air Force Materials Laboratory.
Report authors Ian C. Whittaker and P. M. Besuner were members of the Fail-Safe and Fatigue Group in the Boeing Company Commercial Airplane Division, Structures Developmental Staff. The report contains a rich collection of fatigue life data Items. Item 6300, for example, contains 102 fatigue lives of 6061-T6 specimens. For each Item, an 11 digit code indentifies specimen thickness, material type, grain direction, type of structure, type of specimen, finish, type of loading, and testing peculiarities if any. Specimen load and stress conditions may be determined from a list of data source references.
From the viewpoint of engineering design history, Ref. 4 is important as a record of methods used at The Boeing Company to calculate fatigue life scatter factors. Many of the calculations for the report were accomplished by means of a two-parameter Weibull distribution where the parameters were determined by maximum likelihood technique. Ref. 5 includes a reproduction of the Weibull Trending Toolkit example 6061-T6 data. The set of 102 fatigue lives in the example were taken from Ref. 4 Item 6300. References 6 through 9 are included for completeness. The following Task 2 section on aircraft inspection is based on Ref. 8, Crack detection at inspection, pp. 1.1/26-1.1/29, and on Ref. 9, Inspection Effectiveness, pp. 12-15.

Whois Walter J. Trapp?

My Dear Friend Walter J. Trapp

Walter was born 24 December 1909 at Rheydt, West Germany. He received a B.S. in Mechanics, Physics at the Institute of Technology, Aachen, Germany in 1933. He received a M.E. Degree in Mechanical Engineering/Aeronautical Engineering at Aachen in 1936. From 1934-36 he was a Research Assistant at Aachen. From 1936-45, he was Section Chief, Materials & Stress Analysis, Aeronautical Research Establishment, Brunswick, Germany. From 1945-47, he was a Scientist, UK Royal Air Force Station, Volkenrode, Germany. From 1945 until retirement in 1974 Walter held positions of major responsibility at The Air Force Materials Laboratory, Dayton, Ohio. On 11 September 1985, the American Society of Mechanical Engineers awarded Walter a certificate of appreciation for outstanding international leadership in conceiving, organizing and sponsoring advanced materials behavioral research.

Walter died on 19 February 2002.

Colleagues of Walter may contribute thoughts to this page.

Aircraft Inspection Insights, 1975

  • In Ref. 8, p. 1.1/27, there is the following quotation from M. Stone's presentation "Airworthiness philosophy developed from full-scale testing", Seventh ICAF Symposium, London 1971:
  • "In a walkaround inspection there is a 50 percent chance of finding a 5 to 6 inch long crack. A scheduled inspection has a 50 percent chance of finding a 1 to 3 inch crack. The use of a visual aid, such as a magnifying glass, can show up a 0.5 inch crack."
  • In Ref. 8, p. 1.1/27, there is the following quotation from a presentation by W. Barrois at the above symposium,"Interrelated aspects of service safety aring from consideration of safe life, fail-safe, manufacturing quality and maintenance procedures":
  • "On the visible external skin of aircraft, French Airline Companies have discovered no cracks longer than 50 mm (2 inches). Larger cracks have been found in hidden or masked areas." .... "As an order of magnitude, apparent length of detectable cracks might be:
    L = 10 mm for visual inspection after local cleaning, L = 5 mm for inspections using a magnifying glass and for X-ray inspections, and L = 1 mm for reamed fastener holes using ad eddy current sensor."

  • In Ref. 9, p. 14 there is a quotation from the following reference: T. W. Graham and A. S. Tetelman, "The use of crack size distribution and crack detection for determining the probability of fatigue failure", AIAA/ASME/SAE 15th Structures, structural Dynamics and Materials Conference, Las Vegas, NV, AIAA Aper No. 74-394, 1974:
  • "Most of the predictions for flaw detection probability have been done under ideal laboratory conditions on easily inspected parts. It is estimated that flaw detection limits for production parts will be twice the laboratory values, while maintenance inspections will require three times these levels."


Weibull Trending Toolkit Applied to 6061-T6 Fatigue Data, Ref. 4 Item 6300

Solution Obtained by Whittaker and Besuner in 1969

Weibull Trending Toolkit Applied to 7075-T6 Fatigue Data, Ref. 4 Item 417

Solution Obtained by Whittaker and Besuner in 1969

Task 3

Crack Initiation and Inspection

Search engine Alta Vista was used with keywords "crack initiation". In reference "Fatigue Crack Initiation Process in Corrosive Environment", by R. Hamano, Mechanical Properties Division, National Research Institute for Metals, Japan. R. Hamano tested pre-crack cyclic deformation and early crack propagation using notched high strength aluminum alloy specimens. Inert argon and saturated water vapor atmospheres were used. He found how directions of intial fatigue crack growth differed in the two environments. His work strengthens use of the term stress corrosion cracking.

The Alta Vista search also yielded reference to work by Manuel I. Fadragas and Morris E. Fine, titled "Fatigue Crack Initiation and Growth from Rivet Holes". Read how sets of aluminum alloy specimens with countersunk rivet holes were cyclically loaded in tension using three different corrosive environments.

The photo shows a fixed end of a transport trailer main load carrying beam, or longeron. Notice that the two bolt heads at lower right are hexagonal. Evidently a repair was made at an earlier date. See the corrosion fatigue crack growing from the beam lower surface. Beam curvature at the fixed end was such that the lower portion of the beam was in compression. A buckle occurred. Presumably a tensile region in the buckle allowed the crack to grow.

From 1956-58, I was an Instructor in Mining Engineering at Michigan College of Mining and Technology. I was between graduate schools.
The same mining curriculum had been followed for decades. Access to Frat Files provided an easy path to graduation.
Walfrid Been became the new Department Chair. He hired me. I had free reign to revise the entire curriculum. My proudest achievement: a course called Design and Support of Mine Openings.

mining instructor

The next two images show the Minnesota Glacier in West Antarctica. I was a member or a team lead by Prof. Campbell Craddock in the 1962-63 summer season. Cam assigned me the task of working with two U.S. Coast and Geodetic surveyors to estimate the flow rate of the glacier at its narrowest point, between peaks in the Heritage and Sentinel Ranges of the Ellsworth Mountains.
  • First photo shows routes across the glacier. I crossed the nearest route twice.

  • The survey site on the left side of the Minnesota Glacier as seen in the next image was called eonec. I selected a route across the glacier from site eonec. The site is on the Heritage Range side of the glacier. The other end of the survey route survey is on the Sentinel Range side of the glacier. Approximate distance between survey points was 12 miles.

  • Next image is from the map of West Antarctica. It shows the crevasse field on the survey route between the two mountain ranges. The crevasse field on the Minnesota Glacier was named the Bowie Crevasse Field.
Minnesota Glacier
Can you make out the words BOWIE CREVASSE FIELD on this map element? You are on the Minnesota Glacier in West Antarctica. The glacier feeds ice from the continent to the sea.
crevasse field
NSF letter
I am deeply proud of this letter, even though my mother always said "Pride cometh before a fall".

By the Grace of God, I did not fall into a crevasse. My day will come. Meanwhile, may I presume to try to inspire at least one young person to try harder, to seek the adventure open to us at every corner of this wonderful world --- this world full of wonder.

We are here to excel in order to be better able to help others. Yet inspite of these stuffy words, we must have fun in the process. You can only guess how I enjoyed the free, open beauty of Antarctica.

Crevasses in the main field are as long as a mile and can be tens of feet wide. In the 1962-63 season, I was interested in learning about crack initiation.

  • Starting at the survey site in the Heritage Mountains, I looked upstream for a suitable relatively small crevasse.
  • I practiced crevasse entry and egress using chest and foot prusik slings tied by prusik knots to my climbing rope.
  • Using my iceaxe to probe a crevasse covered by a snow bridge.
I made an opening in the snow bridge large enough for me to get into the crevasse.

See the can in the above image? It contains a Worden gravimeter. The instrument is suspended on bungee cord in the can. It must not be jostled nor tipped too much. It contains a quartz mass-spring system. An optical viewer can be used to detect changes in deflection of the mass as the instrument is moved from one gravity field to another.

Perhaps Don Soholt helped me. We tied a climbing rope to the gravimeter can. I rappeled into the crevasse while the can was being lowered. I steadied the can between my knees. At some depth, I stopped, took the gravimeter out of the can --- as I remember, by holding onto my rope with one hand, turning around, and gradually lifting the instrument out of the can. Readings at surface and depth yielded average ice density.

The closed-loop object at right center is a carabiner or "beener".
It was given to me in 1962 by Norman Hardie. He is the famous New Zealander who solo-climbed the second highest peak in the world.
He taught survival methods to University of Minnesota United States Antarctic Research Program (USARP) members.

Can you find the beener in the above self-belay image?


Use the Google search engine:

Search Mining Engineering
1. What Mining School claims to be the best in the US?
2. Which schools teaches Design and Support of mine openings? Distinguish between Rock Mechanics and mechanics of support structures.

Search West Antarctica
1. What is the West Antarctic Ice Shelf (WAIS) Initiative?

Search Macalester College. Find Jerry Webers on the Faculty. See him standing in front of the Minnesota Glacier. He is one of the map makers. If you want to learn Antarctic Geology, you cannot do better than studying under him.
1. Especially if you are a Kiwi (New Zealander to the uninitiated among you), find and read a copy of Norman Hardie's book "In Highest Nepal."

Crevasses in the Bowie Crevasse Field on the Minnesota Glacier are as long as a mile and can be tens of feet wide. In the 1962-63 season, I was interested in learning about crack initiation.
  • The snow bridge over a small crevasse was marked by a shallow depression. I made a mat by lacing bamboo rods together. The screen was placed over the lip of the crevasse to keep ropes from digging into the snow.
  • I rapelled into the crevasse. Usually I wore an anorak as outer garment. This time I wore a parka, expecting the air temperature to drop as I descended.
  • I reached a depth of 96 feet. Drilled a hole and used a thermometer to measure ice temperature for comparison with surface mean annual temperature. At 100 ft. depth, the single opening split into multiple openings. To me, they were dark and forbidding. Special techniques would have been required to explore crack initiation any closer to the origin sites.

I used a steel device called a karabiner when rappelling or climbing a rope. It is shown below, from an April 1997 photograph. It has been stored for 34 years together with climbing ropes and clothing in a duffel bag. It was nor corroded when stored.

Task 4

Fatigue Crack Growth in A537M Steel

Authorized Reprint from Special Technical Publication 648
Copyright American Society for Testing and Materials
1916 Race Street, Philadelphia, pa. 19103 - 1978

J. P. Sandifer and G. E. Bowie1

l Senior scientist and senior research scientist, respectively, Fatigue and Fracture Mechanics Laboratory, Lockheed-California Company, Burbank, Calif. 91520.

Fatigue Crack Propagation in A537M Steel

REFERENCE: Sandifer, J. P. and Bowie, G. E., "Fatigue Crack Propagation in A537M Steel," Fatigue Testing of Weldments, ASTM STP 648, D. W. Hoeppner, Ed., American Society for Testing and Materials, 1978, pp. 185-196.

ABSTRACT: Fatigue crack propagation rates are presented for weldments in A537M steel at room temperature. Rates are determined for cracks propagating along the fusion line, in the melt zone of welds made with two shielding gas ratios, and in the base metal. Static tension and Charpy impact tests conducted on specimens from the base material and melt zone also are presented. Results indicate that crack growth resistance of A537M steel is not degraded by proper welding procedures, and the weld zone may impede growth rates. Shielding gas ratios, which affect tensile properties, are shown not to affect fatigue crack growth rates significantly. An interim da/dN versus dK design curve is computed for the data sets, and its application to flawed plate life prediction is discussed.

KEY WORDS: fatigue tests, steels, crack propagation, weldments, melting points, fusion line, weld defects, Charpy impact properties, tensile data, life prediction

Increased service requirements of advanced naval vehicles and petroleum exploration equipment necessitate the use of material with higher strength and toughness yet available at a reasonable cost. The A537M steel was developed to satisfy these present requirements. It is a quenched and tempered low carbon-manganese-silicon steel used in sections up to 50.8 mm (2 in.) thick. The low carbon and increased manganese content results in a material with very low nil ductility transition temperature thus making the alloy particularly well suited for use in the extremes of the arctic environment. For wide usage, however, such an alloy must have good weldability from the fabrication and service standpoints. The latter standpoint, service, is the prime concern of this investigation.

Higher performance of man-rated equipment or items where catastrophic failure would be prohibitively expensive necessitates the application of fracture control techniques to assure that life requirements of the structure are met. Since all materials, particularly welds, contain defects, it is essential to know if these defects will propagate to a critical size under service loads and environmental conditions where failure would occur. It is necessary, therefore, to establish the crack growth rates under cyclic fatigue loading for cracks located in the melt zone, fusion line, and base metal away from the heat affected zone (HAZ).

Experimental Procedure

This investigation used a quenched and tempered steel prepared according to ASTM Specification for Pressure Vessel Plates, Heat-Treated, Carbon-Manganese-Silicon Steel (A 537-76) and modified. The chemical composition of this steel is given in Table 1:

Table 1 - Chemical composition of A537M 4.45 cm (1 ¼-in.) thick plate and weld metal.

Element Base Material, wt% Weld Metal, wt% Weld Metal, wt%
98 Ar-2 Oxygen 95 Ar-5 Oxygen
C 0.12 0.06 0.065
Si 0.30 0.91 0.83
Mn 1.47 1.47 1.42
P 0.018 0.009 0.011
S 0.011 0.011 0.010
Ni 0.24 ... ...
Mo 0.07 ... ...
The mechanical properties are given in Table 2:

Table 2 - Mechanical properties of A537M base metal.

Yield strength, MPa (psi) 428 (62,200)
Tensile strength, MPa (psi) 549 (79,650)
Elongation, % 35
Reduction of area, % 78.7
Modulus, MPa (psi) 203,000 (29,500,000)
Charpy V-notch impact
Temperature -51 C (-60 F)
J (ft-lb) 111 (82)

Two plates, 4.445 cm (1 1/4 in.) thick, were welded by a semiautomatic inert gas- shielded metal arc-spray transfer weld process with two different shielding gas ratios: 98Ar-20 and 95Ar-50. Electrodes were dual shield 9000~C1 1/16 in. Heat input was 863.6 J/m (34,000 J/in.) average, with a maximum of 1,397 J/m (55,000 J/in.) per weld pass.

Charpy, tension, and compact tension specimens were fabricated from each plate as shown in Figure 1.

Figure 1 - Specimen orientation and location in welded plate.
For crack propagation measurements, the compact tension specimens were fabricated per ASTM Test for Plane-Strain Fracture Toughness of Metallic Materials (E 399-74); the dimensions are shown in Figure 2.
Figure 2 - Compact tension (CT) specimen geometry.
The compact tension specimens were installed in a MTS servocontrolled electrohydraulic fatigue machine and precracked under constant amplitude sinusoidal loading. During precrack, loads were stepped down so that the final 0.5 mm (0.020 in.) of growth occurred at a maximum stress intensity equal to that at which subsequent testing was to be started. The precrack load shedding procedure was conducted in a manner such that the last crack growth increment ensured that the crack tip was beyond any previous plastic zones. Crack length was measured on both sides of the specimens using a traveling microscope. After precracking, specimens were then monotonically loaded to failure or fatigue cycled to failure.

As shown in Fig. 1, the compact tension specimens were machined from the plates so that the notches were located in three areas: (a) center of the melt zone, (b) on the fusion line, and (c) in the base material beyond the HAZ.

Charpy V-notched specimens were machined from each plate as shown in Figure 1 and tested at - 51 °C (- 60°F) per ASTM Notched Bar Impact Testing of Metallic Materials (E 23-72).

Tension test specimens taken from each plate were cut perpendicular to the weld as shown in Fig. 1 and longitudinally in the melt zone for weld metal as well as base metal properties and tested per ASTM Tension Testing of Metallic Materials (E 8-17a).
Fractographic examinations were made on each failed specimen. Scanning electron microscopy and X-ray analyses were conducted in areas of apparent abnormality. Chemical analyses were made to verify constituent elements, and quantitative hot extraction analysis was performed on sections of weld metal to determine hydrogen content.

Presentation and Discussion of Results
Fracture Toughness

Charpy impact tests conducted in the base metal at - 51 °C (- 60°F) gave average values of 111 J (82, while tests conducted in the melt zones of the two gas mixtures gave values of approximately 33.9 J (25 These data are shown in Tables 2 and Table 3:

Table 3 - Mechanical properties of weld metal using two shielding gas ratios.
From A537M plates.

Plate ID 95-5-03 (95 Ar-5 Oxygen)
yield strength, MPa (psi) 660 (95,740)
tensile strength, MPa (psi) 715 (103,885)
elongation, % 22.25
reduction of area, % 57.7
modulus, MPa (psi) 223,000 (32,300,000)
Charpy V-notch impact
temperature, -51 C ( -60 F)
J (ft-lb) 34.7 (25.6)
lateral expansion 0.0538 mm (0.0212 in.)
Plate ID 98-2-03 ( 98 Ar- 2 Oxygen)
yield strength, MPa (psi) 724 (105,140)
tensile strength, MPa (psi) 747 (108,415)
elongation, % 8.0
reduction of area, % 17.0
modulus, MPa (psi) 107,000 (30,000,000)
Charpy V-notch impact
temperature, -51 C(-60 F)
J (ft-lb) 33.9 (25)
lateral expansion 0.0513 mm (0.0202 in.)

Static fracture toughness tests conducted on the compact tension crack growth specimens did not yield K1C values since plain strain conditions were not met. ASTM Test E 399-74 requires that both thickness, B. and the uncracked ligament must exceed 2.5 (KQ/sigmays) ². Tests conducted in the base metal and on the fusion line gave average KQ values of 145.2 MPa m.½ (132 ksi in.½). No significant difference was noted in values for the two locations. Observations of the failures indicated possibly higher toughness in the melt and HAZs.

Subcritical Fatigue Crack Growth Rates

During fatigue crack growth testing, crack lengths were measured at least every 0.5 mm (0.02 in.). From these data, the points shown in Figure 3

Figure 3 - Comparison of crack growth rates for A537M steel weldments in 21 deg C (70 deg. F), 40 plus or minus 10 percent relative humdity air at 5 Hz and a stress ration R = 0.1. Median and design curves for weldment and base metal are shown.

were calculated by the following equation:

dK = (1 - R)KQ, (1)

where KQ is defined in ASTM Test E 399-74.

These data points in Figure 3 represent pairs of measured crack growth rate, da/dN, and stress intensity range, dK, for the five crack growth specimens tested. The test environment was laboratory ambient air (temperature 21 +3 -3°C (70 +5 -5°F), relative humidity, 40 +10 -10 percent). The applied load waveform was sinusoidal with a frequency of 5 Hz and ratio of minimum to maximum load R = 0.1. For crack growth in the base metal, as shown in Figure 4,

Figure 4 - Fracture surface of base metal specimen.
crack extension were relatively uniform. Data reduction for this case included the effect of crack front bowing. For crack growth in the weld metal and fusion zone, nonuniform growth was evidently caused by effects of weld inclusions, as shown in Figure 5 and Figure 6.
Figure 5 - Melt zone specimens and fracture surface showing multipe pass weld.

Figure 6 - Fusion line specimens and fracture surfaces.
Occasional retardation of crack growth was particularly evident for fusion zone specimen CT 2-98-2-03, Figure 6. Data reduction for weld metal and fusion zone specimens was performed with the premise that the average of crack extensions measured optically on opposite specimen faces represented crack front positions.

Fatigue crack growth for the fusion zone specimens, Figure 6, was observed to occur without deviation of the crack front from the fusion zone. During subsequent application of monotonically increasing tensile loading of these specimens fast fractures propagated away from the weld, through the HAZ, and into the base material.

The total number of pairs of (da/dN, dK) measurements given in Figure 3 is equal to 47. There are insufficient numbers of data points for any one speci-men or condition to warrant separate crack growth rate curve fitting. A decision was made to derive a single median curve fit for all 47 points, using data reduction procedures developed by the second author, described elsewhere (see refererences). The curve titled "Median" in Figure 3 was plotted by means of the empirical relation

da/dN = -1 + exp [e + (v - e) (- ln(1 - dK/Kb))1/k], (2) where
Kb = 95.7 MPa m.½ (87 ksi in.½),
e = - 9.7377,
v = 2.9044,
and k = 8.2946.

Quantities e, v, and k are referred to as the threshold parameter, charac-teristic value, and shape parameter, respectively. Parameters e and v depend upon calculated values of linear regression coefficients as described in Ref 2. The curve fitting parameter, Kb, is the stress intensity range value where da/dN becomes indefinitely large. In computations, Kb is selected by a trial and error procedure. For example, Kb is never less than or equal to the largest dK value in the data set. The shape parameter, k, and the stress intensity upper limit, Kb, are optimized iteratively with the aid of correlation coefficient comparisons. The fitting relation, Eq 2, for the set of 47 pairs of (da/dN, dK) measurements was obtained with a sample correlation coefficient equal to 0.87 and a sample standard deviation in the plane of linear regression equal to 0.05. By examination of Figure 3, it is seen that base metal data points tend to lie above the median curve, and the fusion line and melt zone data points lie below the curve. Evidently crack growth is slower in the weld areas than in the base metal. This is partly attributable to the pinning of the crack by inclusions and defects. While for a propagating crack these may be beneficial in this regard, they are not desirable since they can also act as stress concentrations and crack initiation sites. The effects of segregation during multiple passes and on strength are clearly shown in Fig. 5 where each pass is visible in the fracture face.

It is also noted by examination of Fig. 3 that fatigue crack growth rates in the melt zones for 98Ar-202 and 95Ar-502 gas ratios are essentially the same, even though tensile properties listed in Table 3 indicate apparent gas ratio effects. These crack growth rates for A537M are very close to those obtained by Socie and Antolovich [3] for unmodified A537 weld and bare metal.

In view of the scatter in the data sets, a decision was made to suggest for interim design purposes a baseline crack growth rate curve for ambient air conditions arbitrarily displaced one standard deviation toward the faster growth rate side of the median curve. The equation of the interim design curve retains the values of Kb and k in the aforementioned expression, but has modified values of e and v as follows: e = - 9.1390 and v = 3.5030.

The interim design curve is sigmoidal when plotted in the format of Figure 3 and has the property of predicting rapidly increasing crack growth rates as dK approaches the value Kb = 95.7 MPa m.½ (87 ksi in.½). The da/dN versus dK curve-fitting equation permits estimation of the design threshold stress' intensity for subcritical fatigue crack growth, as follows

Kth = Kb{ 1 - exp( - ( - e/( v - e))k}, 3 = 6.27 MPa m.½ (5.7 ksi in.½)

Application of Design Curve to Flawed Plate Life Prediction

As discussed by Lindh and Peshak [4] initial flaws at the surface of a plate tend to be more harmful from a stress concentration standpoint and therefore with respect to fatigue crack growth than imbedded flaws of similar dimensions. Accordingly, flawed plate life prediction calculations were performed with the aid of the interim design crack growth rate equation for the case of an idealized surface flaw in the base metal. The shape of the initial surface flaw assumed is shown in Figure 7.

Figure 7 - Tentative design curves for assumed initial flaw in base metal.
The ratio of the depth (a) to the length (2c) at the plate surface for both the initial flaw and sub-sequent fatigue crack was assumed to have the typical value a/2c = 0.45. Plate thickness was assumed to be 4.45 cm (1.75 in.).

Numerical integrations of the interim design crack growth rate equation were performed for two initial flaw sizes: one with a depth equal to 0.127 cm (0.05 in.), and one with depth of 2.54 cm (1.0 in.). The 0.127-cm (0.05-in.)-deep flaw is considered representative of typical weldment defects such as pores, inclusions, grind marks, or corrosion pits. The 2.54-cm (1.0-in.)-deep flaw is considered representative of damage which could conceivably occur in service or in rare multiple-pass welding practice. The numerical integration procedure was performed at each of eight equally spaced applied stress amplitudes, sigmao, with the starting point of integration at an assumed initial flaw size. Integration at a particular stress amplitude was performed incrementally until the predicted critical flaw was achieved. For practical purposes, applied stress amplitudes are normalized by means of the base metal tensile yield strength, sigmaty. Results of the numerical integrations are demonstrated in Figure 7. Note the horizontal band of uncertainty between the upper part-through crack (PTC) and the through-the-thickness crack (TTC) regimes of the graph. This uncertainty band was drawn on the basis of a comparison of separate prediction curves developed during a preliminary phase of analysis. The separate curves, not shown in Fig. 7 , were faired to yield intersections at the location of the band in Figure 7. The height of the band at the intersection was established as a matter of practical judgment on the part of the authors.

The ordinate in Figure 7 is ratio of applied stress amplitude to yield stress, 100 sigmao//sigmaty, and the abscissa is the number of cycles to failure, N. There are two curves on the graph, one labeled as = 0.127 cm (0.05 in.), and the other, as = 2.54 cm (1.0 in.). At any one ratio, 100 sigmao/sigmaty, on the ordinate, the difference between the first and second curve read on the abscissa predicts the number of cycles for growth from ai = 0.127 cm (0.05 in.) to a depth of 2.54 cm (1.0 in.). To illustrate the use of Figure 7, consider a stress ratio above the transition band in Figure 7, such as 100 sigmao/sigmaty = 90 percent. At this relatively high stress condition, it is predicted that fast fracture will occur prior to penetration of a PTC through the plate thickness. At some lower stress ratios, such as 100 sigmao/sigmaty = 50 percent, the fatigue crack will propagate through the plate thickness and continue to grow as a TTC prior to fast fracture. The PTC-TTC transition zone was identified on the graph to reflect uncertainties in crack front behavior which can occur when a deep fatigue crack approaches the opposite surface of a plate from the surface where initiation occurred.

For discussion, suppose that a plate structure is thought to have surface flaws with depths not deeper than 0.127 cm (0.05 in.). In this event, exceptional cases can occur when a deeper flaw or fatigue crack with a depth of 2.54 cm (1.0 in.), for example, can be present. It can be seen from examination of Figure 7 that selection of inspection periods and methods under the conditions of the discussion are indeed more critical for relatively high than for low stress ratios 100 sigmao/sigmaty.


1. Crack growth resistance in A537M steel is not degraded by proper welding procedures.

2. No difference in crack growth rates were noted for cracks propagating in the melt zone compared to ones in the fusion line.

3. Shielding gas ratios, while they affect tensile properties, do not significantly affect crack growth rates.

4. Operational design stresses may be selected from a life prediction curve so that a crack will leak prior to fast fracture.


All tests presented in this paper were conducted in 21°C + 3 -3 °(70 + 5 -5°F) air with a relative humidity of 40 + 10 -10 percent and at a test frequency of 5 Hz. Use of these data for design applications should be done only for those test conditions since a substantially different environment or loading waveform could drastically alter these predictive curves. Particularly significant changes would be anticipated in a marine environment with very low load frequencies (1 ->0.01 Hz), hold times of minutes, or a sustained load [5].

Additional tests must be conducted under the planned usage environmental and load conditions to obtain the required design reliability.


The authors wish to thank G. L. Goss for his assistance in the test programs.

[1] Bowie, G. E., Pettit, D. E., and Ryder, J. T., "Fracture of Engineering Materials,"
Lockheed-California Company Report LR 27012, 15 Jan. 1975.

[2] Bowie, G. E. and Hoeppner, D. W. in Proceedings, 1976 International Conference on
Computer Simulations for Materials Applications, Gaithersburg, Md., 19-21 April 1976
pp. 1171-1178.

[3] Socie, D. F. and Antolovich, S. D., Welding Research, June 1974, pp. 267-271-S.

[4] Lindh, D. V. and Peshak, G. M ., Welding Research, Feb. 1969, pp. 45-48.

[5] Pettit, D. E., Ryder, J. T., Krupp, W. E., and Hoeppner, D. W., "Investigation of the Effects of Stress and Chemical Environments on the Prediction of Fracture in Aircraft Structural Materials." AFML-TR-74-182, Air Force Materials Laboratory, Dec. 1974.

Task 5

Crack Length Prediction and Inspection Planning

Subject: UCLA Short Course on "Corrosion of Aging Aircraft"
Date: Tuesday, 28 May 1996 10:35:05 -0700
From: "Goodin, Bill"
Reply-To: Corrosion Special Interest List
Organization: UCLA Extension - contact for problems.
To: Weibull Trending Toolkit Users

On August 19-22, 1996, UCLA Extension presented the short course, "Corrosion of Aging Aircraft", on the UCLA campus in Los Angeles.

The instructors were Dr. John J. Deluccia, FASM, Adjunct Professor of Materials Science and Engineering, University of Pennsylvania; and Prof. David W. Hoeppner, PE, Department of Mechanical and Industrial Engineering, University of Utah.

Each participant received the text, The AGARD Corrosion Handbook, Volume I: Aircraft Corrosion: Causes and Case Histories, 1985, and lecture notes.

Aging aircraft fleets are experiencing increased structural failures due to corrosion. The effects of undetected and untreated corrosion can lead to catastrophic consequences, and this is especially true of older aircraft which may have experienced cumulative corrosion and fatigue damage.

This course presented both fundamental principles and practical instruction in corrosion theory and control as it applies to aircraft airframe corrosion.

The subject of high-temperature corrosion of components was introduced, and the lectures emphasized corrosion events viewed from the standpoints of time-dependent, time-related, and time-independent mechanisms. The specific types of corrosion are noted for their severity, frequency, and cycle dependency. Time-dependent corrosion such as pitting, exfoliation, and crevice corrosion will, if not prevented or controlled, accumulate to unsafe limits. With time, corrosion can cause both internal and external airframe structures and engine components to degrade to unacceptable limits. The effects of corrosion, however, are not just time dependent but can affect airworthiness at any age. The events of environmental embrittlement, including stress corrosion cracking, can occur anytime, producing failure without warning.

The course discussed prevention of corrosion failures based on proper design, materials and processes selection, and the use of corrosion preventive compounds (CPCs). It began with a lecture on elementary electrochemistry as applied to corrosion and an introductory lecture on fracture mechanics. Subsequent lectures defined and discussed types of aircraft corrosion, identification of corrosion and corrosion prone areas, and corrosion prevention and control. The important topic of combined effects of corrosion and stress, both static and dynamic, was given special emphasis. The course also examined state-of-the-art products, procedures, and techniques for aircraft corrosion control used by both the military and civilian sectors.

The course fee was $1395, which included course materials. These materials were for participants only, and are not for sale.

For additional information and a complete course description, please contact Marcus Hennessy at:
(310) 825-1047
(310) 206-2815 fax

In the early 1970s, David Hoeppner led a materials research group at the Lockheed-California Company Rye Canyon Research and Development Center, Valencia, California. David moved on to a professorship at the University of Missouri, Columbia, Missouri, and then to a senior professorship at the University of Utah.

I, Glenn Bowie, author of courses Corrosion I and II, was a senior research scientist at Lockheed, Rye Canyon. I was associated with but not a member of David's team. However, I wrote several independent research reports and papers based on numerical analyses of fracture mechanics test data obtained by materials group staff members.

If memory serves, D. E. Pettit was principal investigator for 1974 Independent Research Program "Fracture of Engineering Materials", Ref. No. 21-3763-4590. Don Pettit planned and directed the program. He kindly shared test data with me. I performed two numerical analyses for two sections of the report "Fracture of Engineering Materials", LR 27012, November 1975.

In the 1970's, two terms used to characterize aircraft component design procedures were: safe-life and fail-safe. J. T. Mann defined these terms on p. 53 of the report titled "Fatigue Testing - Objectives. Philosophies, and Procedures", Department of Supply, Australian Defence Scientific Service, Aeronautical Research Laboratories, Structures and Materials report 336, February 1972. The following is a direct quotation from p. 53.

"Current fatigue design philosophies, whether they be "infinite-life', 'safe-life' or 'fail-safe'; recognize the statistical nature of fatigue failure and accept the concept of a finite (though perhaps a very low) probability of failure during the anticipated service life.

The 'safe-life' concept of deign - which is mainly applicable to machine components, machine elements and non-redundant structures - implies that an accurate estimate or prediction can be made of the life of the component or structure, and that the relevant item will be replaced or retired from service before the occurrence of cracking which will jeopardize the integrity of the article. The retirement life is the safe-life. This approach requires knowledge of the spectrum of service loads, an acceptable laboratory test and/or cumulative damage hypothesis, estimates of the variability in endurance and ultimately the nomination of a 'scatter factor'.

In the structural members, as distinct from machine components, the 'fail-safe' criterion or design for the safe detection of fatigue failure may be adopted. This philosophy is based on the ability to readily detect fatigue cracks, by inspection, in all the relevant locations before they occurr Usually a fail-safe design is 'redundant' in that it incorporates alternative load paths; so that if cracking occurs in any one load path sufficient residual strength or stiffness will remanin in the article to withstand any loads likely to be experienced before the next routine inspection period - when the defective refgion may be discovered and be either replaced or repaired."

Allow me to paraphrase parts of Don Pettit's Introduction to LR 27012. Imagine that you are listening to him as he speaks in 1975.

The significance of subcritical flaw growth and subsequent fracture of aircraft structural materials has been recognized in maintenance of aircraft structural integrity. Recent experiences in military aircraft have indicated that additional information pertaining to fracture and subcritical flaw growth behavior of engineering materials is required to ensure the safe service life of a structural component. Premature failures are particularly significant because they have occurred in what were considered to be safe-life design components such as wing fittings and attachments, landing gears, and carry-through structure.

Increasing demands on materials to fill new or modified mission requirements, while maintaining high performance characteristics at minimum cost, have brought about the use of high strength materials in safe-life designs for both military and commercial aircraft. Recent experiences of early failures have demonstrated dramatically that conventional safe-life design may not provide expected safety assurance. This is because increased strength requirements often may be associated with decrease in flaw tolerance. Often the flaw sizes involved are not detectable by current nondestructive inspection (NDI) procedures.

When materials lacking fracture toughness in relation to inherent flaw sizes and operating stress levels are used, attempts at creating crack stoppers by adding structural reinforcements can be impractical because required stoppers must be so close to one another that weight and manufacturing cost penalities are prohibitive.

The alternative is to employ damage tolerance design concepts. It must be assumed that flaws, disconinuities, inhomogenieties, inadvertent damage, and corrosion pits are unavoidable. These flaws can serve as crack initiation sites. Crack growth can only be tolerated when the crack size is less that that which would be associated with uncontrolled crack propagation.

In 1976, I published with David Hoeppner the paper "Numerical Modeling of Fatigue and Crack Propagation Test Results", in the Proceedings of The International Conference on Computer Simulation for Materials Applications, AIME Nuclear Metallurgy Series Vol. 20, Edited by R. J. Arsenault, J. R. Beeler, Jr., and J. A. Simmons. The following information on modeling is from that paper.

Modeling Crack Propagation Rate Test Results

In 1973, A. M. Freudenthal stressed the the need for development of improved methods for modeling relations between crack propagation rate and stress intensity. He proposed a new curve fitting relation based on the form of the Weibull distribution function. Work performed independently in 1973-74 led to the proposition of new curve fitting relations which differ from the form proposed by Freudenthal, but are consistent with the intent of his suggestions. The new expressions are

da/DN = e + (v - e) [ -ln(1 - dK/Kb) ]1/k, and

da/DN = -1 + Exp [ e + (v - e)[ -ln(1 - dK/Kb) ]1/k]

where da/dN = crack propagation rate

and Kb = stress intensity range where da/dN is indefinitely fast.

For a given test alloy, these alternative expressions have been found to apply as a function of test environment. A unique feature of the relations is releazed by considering extrapolation of test data trends to the initial condition da/dN = 0. The stress intensity range for onset of crack growth is predicted at this initial condition to be

Ko = Kb [ 1 - Exp [ -( -e/(v - e))k]]

Further, the qualitative distinction between slow and fast growth often made by fracture mechanics investigators now can be defined quantitatively by means of a risk function

r(dK) = d(ln(da/DN))/d(dK) = d(Da/DN)/d(dK)/(da/dN)

In applications performed to date of the above new crack propagation rate curve fitting relations, it has been found that the risk function r(dK) is U-shaped, with well-defined minimum at stress intensity dKsf, where slow-to-fast transition would be judged to occur by experience.

Example Inspection of a Surface Flaw in a Plate

In recent weeks, three individuals working for pipeline companies have contacted me. There is very great distance between my work on numerical analysis of fracture mechanics test data in the 1970s and current needs for pipeline crack length predictions and inspection planning. Yet an example I prepared for LR 27012 in 1975 might be helpful for discussion purposes.

A surface flaw is referred to as a part through crack (PTC). A plate has width W and thickness B. It is subjected to cyclic tensile load of magnitude P. The nominal stress maximum equals P/BW. The plate yield stress is Sy. A central surface flaw of length 2c and depth a exists in the plate. The flaw shape is elliptical. The flaw serves as a crack starter and the initial ratio a/2c is maintained as the crack grows.

To keep things simple, assume principles of plane strain fracture mechanics apply. The plate thickness B is at least twice as great as the crack depth for uncontrolled crack growth. In other words, the plate will fail catastrophically without warning you by leaking light through a crack.

For a plate example in Don Pettit's Fracture of Engineering Materials study, Lockheed Report 27012, the material was Titanium-6Aluminum-4Vanadium, Beta processed, and the environment was dry air at room temperature. The ratio of minimum to maximum tensile load per cycle was 0.1. The alloy yield stress was 123 ksi, and the stress intensity at the slow-fast transition was 71.62 ksi-in.½ I calculated crack depth a at the threshold for slow growth, and at the transition, for each of the four applied maximum stress to yield stress ratios of 0.6, 0.7, 0.8, and 0.9 for each of five crack geometries, a/2c equal to 0.1, 0.2 , 0.3, 0.4, and 0.5. The results were plotted on a graph with crack depth a in the y-direction on a logarithmic scale from 0.001 in. to 1.0 in. The x-axis was the ratio of applied maximum stress to yield stress, on a linear scale. On the graph there are two sets of five curves. The lower set applies to threshold growth. Each curve applies to one crack geometry. For a/2c = 0.5, the threshold crack depth equals 0.014 in. at stress ratio 0.6. Threshold crack depth equals 0.006 in. at stress ratio 0.9. The crack depth at slow-to-fast transition equals 0.72 in. at stress ratio 0.6 and the transition depth decreases to 0.31 in. at stress ratio 0.9.

Task 6

Corrosion Can Cause Rotating Machinery Imbalance

In July 1996 I was preparing to deliver an oral presentation on the subject of Mechanics of Aging Aircraft Materials. I am relied on my R&D background in the airframe industry. Preparation of online courses I and II helped refresh my memory of research on aging properties of airframe materials. The talk was presented at a joint ASM/NACE chapter meeeting in Minneapolis, MN on 23 October 1996. Rotating machinery components in aircraft and elswehere can become unbalanced as a result of material loss. Corrosion, corrosion fatigue, and stress corrosion cracking can contribute to machinery unbalance.

On 18 July 1996,Christopher Olsen provided by e-mail attachment a set of 180 measurements made at multiple measurement points on an overhung fan during a period of 5 years. Chris is a former student. The last three measurements in the set clearly are excessive. Imagine that the measurements had been subjected to analysis by means of the Weibull Trending Toolkit. Suppose a control chart had been constructed to track trends in vibration amplitudes. The control chart includes the sequence of measured vibration amplitudes, the most frequently occurring value, that is the mode, a lower control limit LCL and an upper control limit UCL. The mode and control limits are calculated by means of the three parameter Weibull distribution parameters k, e, and v. There is a probability of 0.9973 that measurements will fall between LCL and UCL, provided that the condition of the machine does not change significantly. There is only a 0.135 percent chance that a meaurement value will be above the upper control limit UCL, provided the machine is operating normally. Occurrence of one measurement above UCL should initiate a warning, and occurrence of a succeeding measurement above UCL should be the cause of an alarm.

Assume that the Weibull Trending Toolkit had been used to update the chart after measurement number 177. Measurement 178 should initiate a warning, and measurement 179 should cause an alarm.

Think of the set of 177 measurements as random values. If the values were distributed normally, or had a bell-shaped curve probability density distribution, the mode would be midway between the upper and lower control limits. In fact, the data are skewed toward higher values than the mode. To illustrate this point, we can plot the Weibull probability density, cumulative probability and risk curves on the same graph where we plot the sequence of measured values.

Richard A. Corbett and his associates at Corrosion Testing Laboratories, Inc. are typical of many folks who have explored and possibly are exploring ways to use the Weibull Trending Toolkit to interpret replicate measurements.

Task 7

Background for Presentation on Aging Aircraft

In September 1996 I was preparing to deliver an oral presentation, with aid of computer graphics, on the subject Mechanics of Aging Aircraft Materials. I relied on my R&D background in the airframe industry. Preparation of online courses Courses I and II helped refresh my memory of research on aging properties of airframe materials. The talk was given to a joint Twin Cities chapter meeting of ASM and NACE in Minneapolis on 23 October 1996. Usage Reports made available by James E. Horton indicated level of interest in the courses. I used June 1996 reports for Australia, Canada, and Sweden to try to identify investigators who might be studying mechanics of aging aircraft materials.

Analysis of June 1996 Usage Reports for Presentation on Aging Aircraft

Australia In 1996, Australia was celebrating the 75th Anniversary of The Royal Australian Air Force. There are interests in the subjects of pitting corrosion and corrosion fatigue in The Australian Defence Force. Of 221 CorTech Training files downloaded to Australia in June 1996, seven were downloaded to Defence Force sites. I read 75th Anniversary Air Power Conference Papers and Addresses, and Notes on Speakers. I did not recognize any emphasis on the topic of Aging Aircraft. The Defence Science and Technology Organisation has a Science and Technology Program. The Program Manager is Chief Defence Scientist. He manages five sub-programs, one of which is Materials Research. You may begin a visit to The Australian Defence Force Academy here.

Canada In June 1996, 138 CorTech Training files were downloaded by Canadian sites. One place to start a search for information about Aging Aircraft is the Royal Military College. Wend your way to the National Research Council Institute for Aerospace Research, and find the Structures, Materials, and Propulsion Laboratory. Read topics about Non-destructive evaluation and Aerospace Structures and Materials to see a healthy awareness of aging aircraft technology.

Go to the search engine for The Canadian Technology Network. Search 'corrosion fatigue' and find physical properties of metals and alloys may be studied at ORTECH Corporation. Corrosion test facilities are available. And visit the Materials Engineering and Processing Group at the University of Waterloo. For example, one research project on metals and composites is examining short crack behavior. Search 'aircraft safety' to learn about aircraft-airfoils de-icing detection. Ultrasonic tools are used to detect ice contamination. As an added benefit, the technique described can sense presence of cracks in wing skin.

Search 'fracture mechanics' and find the topic "Fatigue Crack Initiation and Growth in Welded Joints". Exploration of this topic takes you back to the University of Waterloo. While there, take time to visit the Machine Design and Solid Mechanics Group. Search 'aircraft reliability' and you will be led to Aerospace Training Canada International. See that subjects such as accident and crash investigation, maintenance and repair, and airworthiness are training program cornerstones.

Use the NRC corpserv search tool with the topic 'aging aircraft'. Find CANMET Metals Technology Laboratories (MTL) conducts studies of stress corrosion cracking in pipelines. Other subjects are life extension, aging infrastructures, and aircraft NDT. Then go to the Institute for Aerospace Research to learn about turbine engine Accelerated Mission Testing facilities.

Sweden In June 1996, 24 files were downloaded to Swedish sites. I visited Swedish universities virtually and found strong engineering mechanics programs. The Department of Mechanical Engineering at Linköping University is noteworthy. I was pleased to see information about a new Mechanics and Materials program at Lund Institute of Technology.

Ericsson has established a dedicated environment unit.

I need to spend more time at the Royal Institute of Technology Library. Dr. Ivo Toromanoff is the expert on corrosion there. Some day we will connect. I tried to search using Waloddi Weibull as key but was not successful.

In August 1977, Försvarets Teletekniska Laboratorium (FTL) published:

References on the Weibull Distribution, by Waloddi Weibull, FTL A-report A20:23, Aug. 1977.

There are 1019 references in the report. FFA, Flygtekniska Försöksanstalten, or The Aeronautical Research Institute of Sweden, sponsored many studies on estimation of inspection intervals and times to failure of aircraft structures.

The following references are from FTL A-report A20:23, Aug. 1977.

Ref. 39
Adams, N. P. and Hill, H. E. (1974), Application of Weibull distribution function in coatings industry 1. Free film stress-strain properties, J. Paint Tech. 46, (58), 55

Ref. 224
Dorko, E. A.; Bryant, W.; Regulinski, T. L. (1974), Solid state reaction kinetics IV Analyis of chemical reactions by means of the Weibull function, Anal. Calorimetry 3, 505-509

Ref. 412
Hill H. E. (1975), Application of Weibull distribution in coatings industry 2. Plotting Weibull distribution, J. Paint Tech. 47, (60), 63

Ref. 413
Hill, H. E. and Adams, N. P., Application of the Weibull distribution function in the coatings industry, J. Paint Tech. 46, (589), 55-63

Ref. 416
Hofman, G. L.; Johnson, D. L.; Greenberg, S.; Brown, F. L. (1974), The application of stistical anlyses to cladding failure in a multiparameter irradiation program, Ann. Meeting Amer. Nuclear Soc., 18, 125-126

Waloddi Weibull's 1977 bibliography is rich in aircraft references.

Students of courses Corrosion I and II might wonder why I chose to analyze Usage Reports for Australia, Canada, and Sweden to try to interpret current interest in aging aircraft. The most direct response: the analysis task was manageable for me

I do not know the date when Professor Alfred M. Freudenthal passed away. Some months later, his widow asked Walter Trapp to dispose of papers and books in Prof. Freudenthal's office at George Washington University. Walter asked me to help him. I remember Walter retained a few documents and books. Recently Walter sent three copies of a book to me. They probably were from Prof. Freudenthal's office. The book:"International Conference on Structural Safety & Reliability", Edited by Alfred M. Freudenthal, Pergamon Press, 1972. The conference was held April 9-11, 1969. One of the papers in the book is: "Reliability Analysis in the Estimation of Transport-Type Aircraft Fatigue Performance", by J. P. Butler. Joe Butler's paper in particular and the entire text in general constitute the cornerstone of aging aircraft analysis. Serious students of aging aicraft technology are welcome to write to me about availability of the three conference book copies.

Walter forwarded to me recently his copy of a newsletter from Wright Patterson AFB. It is titled: "Structures Division Current Awareness Bulletin". It was published by the Aerospace Structures Information and Analysis Center (ASIC), for Fall/Winter 1996. The newsletter focuses on aging military aicraft research. I am interested to have learned from the newsletter that primary structural aluminum alloy components which have sustained significant corrosion/fatigue damage are being patched by means of bonded carbon filament composite additions.

I wrote a report together with friends Walter J. Trapp and Mohamad S. Besari titled :"Experimental Mechanics: Development of Methods for Numerical Analysis of Composite Fatigue Data". The report date is January 1977. The report includes an extreme value analysis of 20 composite fatigue test specimen lives obtained by James T. Ryder. Jim's data were reported in AFML TR-76-241, December 1976. The report on numerical analysis of composite fatigue data compared results obainted by means of different extreme value analysis functions and procedures. A set of aluminum alloy 2024 fatigue lives was used for most of the comparisons in the report. The data were obtained at six different cyclic stress amplitudes. Twenty specimens were tested to failure at each stress level. I took the aluminum alloy data from this reference:
Freudenthal, A. M., Heller, R. A., and O'Leary, P. J., "Cumulative Fatigue Damage of Aircraft Structural Materials, Part 1: 2024 and 7074 Aluminum Alloy", NADC Technical Note 55-273 Part 1, June 1955.

Task 8

Tribute to Waloddi Weibull
Dedicated to dear friends Kitty (Gusta) and Walter Trapp

During June 1996, I asked Walter J. Trapp to help me in writing to Mrs. Inga Britta (Ibbi) Weibull. I remembered Walter telling me about Waloddi Weibull having received an award from King Gustav of Sweden, and I wished to include an image of the event in this tribute.

Waloddi Weibull devoted his entire professional life to studying ways to increase our understanding of material sciences. He was a soldier-engineer who gave his utmost to improve our use of materials. I sent a note of thanks to Mrs. Ibbi Weibull and to Göran Weibull in remembrance of husband and father, Waloddi Weibull.

Waloddi Weibull 1887-1979
Photo by: Sam C. Saunders, Pullman Washington, USA

The above photograph is a copy from the first page of a document from the Weibull Symposium, Stockholm, 1984. The reference: "IUTAM Symposium, to the memory of Waloddi Weibull. Probabilistic Methods in the Mechanics of Solids and Structures, Stockholm, June 19-21, 1984. Organized by: The Aeronautical Research Institute of Sweden, FFA, in cooperation with The Swedish National Committee for Mechanics."

On 18 Sept. 1996, I received the following letter from Mrs. Ibbi Weibull and Göran Weibull:

Genarp, Sweden 13 Sept. 1996

Dear Dr. Bowie,

We, that is Mrs. Weibull and Göran W. Weibull, have received and read your kind letter 0f 20 August 1996. We are happy to contribute to your idea of giving better information into Internet about Waloddi Weibull. His full name is Ernst Hjalmar Waloddi Weibull. The name Waloddi was shortened to Doddi in the family and by close friends.

After some research we have found an appripriate text in a report from IUTAM Symposium to the memory of Waloddi Weibull, Stockholm, 19-21 June 1984, written by Dr. Robert A. Heller. A copy of the first page of the report and Dr. Heller's speech are enclosed. Perhaps you can use the photograph from the first page.

We know Robert Heller very well and have found his speech very enjoyable. The information about Waloddi is absolutely correct. Actually, Mrs. Weibull has written a letter to him and asked for permission to use it.

If the text is too long, perhaps you can make an excerpt. If you have any questions don't hesitate to get in touch. You will find addresses at the end of the letter.

You put two questions in your letter, and these are the answers:

  • Hans Waloddi was the eldest son and
  • I, Göran Waloddi, child number 5, started as an officer of the Royal Wendes Artillery Regiment and later transferred to The research Institute of National Defense as a researcher mainly concerned with weapons effects.

Enclosed is the photo with King Carl XVI Gustav of Sweden, Waloddi Weibull, and in the middle Gunar Hambræus, then President of the Royal Swedish Academy of Engineering. When Waloddi stood in front of the King he said: "Seventy-one years ago I stood in front of Your Majesty's grandfather's grandfather (King Oscar II) and got my officer's commission." The King then said: "That is fantastic!"

Another photo is enclosed. It is from 1972 when he got the ASME Medal. Waloddi is on the left, in the middle Dr. Richard Folsom, and to the right Neil Armstrong, who got the Spirit of St. Louis Medal.

With best wishes,

Ibbi Weibull
Björnstorps torg
S - 240 13 Genarp

Göran W. Weibull
S - 277 55 BRÖSARP

There follows an exerpt from Dr. Robert A. Heller's speech to the Weibull Symposium, Stockholm, 19-21 June 1984. I beg Dr. Heller's understanding in presenting the exerpts in advance of receiving word of his approval from Mrs. Ibbi Weibull.


Robert A. Heller, Roanoke, Virginia, USA

Though it is an honor to have been asked by the Chair to talk about Professor Weibull, I am saddened that my substitution is occasioned by the untimely passing of another great engineer, Professor Folke Odquist, who was to give us his impressions of his old friend and colleague.

The information I have gathered about Professor Weibull comes from several sources: from his friends; Professor Odquist, Walter Trapp of the US Air Force, Professor Sigge Eggwertz of FFA, from his family; Mrs. Ibbi Weibull, his wife, and Mr. Göran Weibull, his son, and my own personal recollections.

Waloddi Weibull was born on June 18, 1887. This Symposium started on his 97th birthday. His family originally came from Schleswig-Holstein, at that time (in the seventeenth century) closely connected with Denmark. There were a number of famous scientists and historians in the family. His own career as an engineer and scientist is certainly an unusual one.

He became a midshipman in the Royal Swedish Coast Guard in 1904 and was promoted to sublieutenant in 1907, to Captain in 1916 and to Major in 1940. By then he had finished the military schools and simultaneously taken courses at the Royal Institute of Technology and at Stockholm University, finally graduating as Fil.Lic. in 1924. Weibull left active military service in 1917 and acted in German and Swedish industries as an inventor (ball bearings, electric hammers) and as a consulting engineer.

He published his first scientific paper on the propagation of explosive wave in 1914. He took part in expeditions to the Mediterranean, to the Carribean, and to the Atlantic and Pacific Oceans on the research "Albatross" where he used his newly developed technique of explosive charges to determine the type of ocean bottom sediments and their thickness. The same method is used today in offshore oil explorations.

Weibull became a full professor at the Royal Institute of Technology in 1924, and was awarded the degree Ph.D.h.c. at the University of Uppsala in 1932. In 1941 a donation from the Swedish arms factory (A. B. Bofors) gave him a personal research professorship in Technical Physics at the Royal Institute of Technology, Stockholm.

Professor Weibull's ideas about the statistical distributions of material strength came to the attention of engineers in the late 1930's with the publications of two important papers: "Investigtions into strength properties of brittle materials" and "The phenomenon of rupture in solids."

His techniques later found wide application in many fields. With great physical insight he proposed the probability distribution which bears his name. Now, in the literature on reliability, statistics, fatigue, fracture and many other fields, one finds reference to the "Weibull Distribution", and the statistic methods Weibull proposed are in everyday use. Subsequently, Dr. Weibull extended his studies to many aspects of fatigue, fracture and the analysis of probability distributions.

In 1953 he retired from the Royal Institute of Technology and became a professor emeritus. For most people retirement is the end of a professional career, but not for Weibull. His activities just started. He became a consultant to the Fatigue Branch of the U.S. Air Force Materials Laboratory, then under the direction of Mr. Walter Trapp. For 14 years he conducted research and wrote many papers and technical reports which provide valuable information and data on material properties and on the analysis of probability distributions and other related topics. This and other work is summarized in a book, co-authored with his son Goran and published by the Swedish National Defense Research Institute. Professor Weibull continued to be active as a consultant. He conducted work on turbine fatigue and studied new methods of estimating the parameters of the Weibull Distribution. His work on the planning and interpretation of fatigue data is monumental and resulted in his book "Fatigue Testing and Analysis of Results" in 1961.

In 1963, at the invitation of the late Professor Alfred Freudenthal, he became a visiting Professor at Columbia University's Institute for the Study of Fatigue and Reliability. Many of us at this Symposuim have been associated with the Institute at that time and got to know Dr. Weibull personally. Hal Liebowitz was one of our sponsors. Alf Payne, Agnes Heller, Jann Yang, Lars Jarfall and I learned a lot from him, from Emil Gumbel, who was also a member, and from Fred Freudenthal, the three founders of Probabilistic Mechanics of Structure and Materials. It was interesting to watch the friendly rivalry between Gumbel, the theoretician and the two engineers, Weibull and Freudenthal.

The Extreme Value family of distributions, to which both the Gumbel and Weibull type belong, is most applicable to materials, structure and biological systems because it has an increasing failure rate and can describe "wear out" processes. Well, these two men, both in their late seventies at the time, showed that these distributions did not apply to them. They did not wear out but were full of life and energy. Gumbel went skiing every weekend and when Agnes and I took Dr. and Mrs. Weibull to the Roosevelt Home in Hyde Park on a cold winter day, he refused my offered arm to help him on the icy walkways saying: "A little ice and snow never bothered a Swede."

In the course of his long and productive career, Professor Weibull has received many honors: the Polhem Medal in 1940, an honorary doctorate from the University of Uppsala in 1932, and in 1972, the American Society of Mechanical Engineers awarded him the ASME medal with the inscription: "A pioneer in the study of fracture, fatigue and reliability who has contributed to the literature for over thirty years. His statistical treatment of strength and life has found wide-spread application in engineering design."

The other recipient of a medal at the sme meeting, Astonaut Neil Armstrong, the first man on the moon, probably did not know that his successful voyage was partly due to the pioneering work of Waloddi Weibull.

Professor Weibull's proudest moment came in 1978 when he received the Great Gold Medal from the Royal Swedish Academy of Engineering Sciences which was personally presented to him by King Carl XVI Gustav of Sweden.

He was devoted to his family and was proud of his nine children and numerous grand- and great-grandchildren. Dr. Weibull was a member of many distinguished Swedish Academies and Societies and worked to the last day of his remarkable life. He died on October 12, 1979, in Annecy, France.

Task 9

Mechanics of Aging Aircraft

I, Glenn Bowie, was invited to deliver an oral presentation on Mechanics of Aging Aircraft Materials. The talk was given at a joint Twin Cities chapter meeting of ASM and NACE in Minneapolis on 23 October 1996.

Engineers who helped design, build, and test aging transport and other aircraft of course are themselves aging. I am one of them. Courses Corrosion I and II were derived from notes I wrote at Lockheed's Rye Canyon Research and Development Center in the 1970s.

What is to become of all the notebooks and reports I wrote? I circulated one notebook during the Oct.23, 1996 talk. It concerns structural tests performed on B-1 flightworthy empennage components by Lockheed engineers and technicians. The notebook contains the above two photos.

Because the test object was later to become flight hardware, it was necessary to apply distributed loads by means of tensile rather than compressive devices. Pads were glued onto stabilizer surfaces. Linkages connected the pads to tensile rods. A load cell was attached to each rod. Loads were applied to the rods by means of hydraulic cylinders.

Fraser Dorward was responsible for the design of the vertical stabilizer load system. In 1974, Fraser was a recent arrival from Scotland. My Dad was a Scottish immigrant to Canada. I hung around Fraser just to hear his speech pattern. I think he was one of my students in a Lockheed extension class on Structures/Materials Data Processing. In any case, I became aware of his assignment. I told him there was no way that he could select pad loads by trial and error within any reasonable timeframe. I volunteered to write a number of routines to help him in a language called PL/I.

The notebook circulated on Oct. 23 is a complete record of the programs I wrote for Fraser. He was responsible for three load cases:

  • Dynamic overswing
  • Maximal mid-rudder hings moment
  • RPA gust

I stored the applied loads at each of 56 vertical stabilizer locations in a Lockheed computer file. My notebook contains the data for the dynamic overswing condition. It was my test case for software development.

I told the ASM/NACE group on Oct. 23 the I would love to have an opportunity to turn the notebook into an engineering course of instruction. I would convert the PL/I code to Visual Basic 3.0.

nul no images

my card  

Copyright Glenn E. Bowie©, CorTech Training, Red Wing, MN 1996, 2000, 2003. All rights reserved.