Red Wing Virtual Liberal Arts College -
Weibull Trending Toolkit (WTT) |
Task 1
Analysis Course II, Task 1: Cylindrical Component Tested This component test history is from unpublished notes written by J. M. Van Orden in 1969 at the Lockheed-California Company (now Lockheed Martin) Rye Canyon Research and Development Center.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.
Create Modeling Program DESIGN
Model Grouped Aziz Data for Three Week Exposure and Godard Data for 13 Year Exposure
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 e-mail: glennbowie@live.com 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 e-mail: glennbowie@live.com 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 positive. 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: design11 500 1.1 25 300 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. Enter: design12 500 1.2 25 300 Study the summary values. Choose graph upper limit 2000. Click WDESIGN summary screen at the bottom, enter: design13 500 1.3 25 300 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 design40. 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 |
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 | ... | ... |
Table 2 - Mechanical properties of A537M base metal.
Tensile | |
---|---|
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.
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.
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 ToughnessCharpy impact tests conducted in the base metal at - 51 °C (- 60°F) gave average values of 111 J (82 ft.lb), while tests conducted in the melt zones of the two gas mixtures gave values of approximately 33.9 J (25 ft.lb). 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) | |
---|---|
Tensile | |
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) | |
Tensile | |
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 K_{1C} 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 (K_{Q}/sigma_{ys}) ². Tests conducted in the base metal and on the fusion line gave average K_{Q} 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)K_{Q}, (1)
where K_{Q} 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,
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.
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/K_{b}))^{1/k}], (2) where
K_{b} = 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, K_{b}, is the stress intensity range value where da/dN becomes indefinitely large. In computations, K_{b} is selected by a trial and error procedure. For example, K_{b} 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, K_{b}, 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-20_{2} and 95Ar-50_{2} 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 K_{b} 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 K_{b} = 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
K_{th} = K_{b}{ 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.
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, sigma_{o}, 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, sigma_{ty}. 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 sigma_{o/}/sigma_{ty}, 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 sigma_{o}/sigma_{ty}, on the ordinate, the difference between the first and second curve read on the abscissa predicts the number of cycles for growth from a_{i} = 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 sigma_{o}/sigma_{ty} = 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 sigma_{o}/sigma_{ty} = 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 sigma_{o}/sigma_{ty}.
Conclusions
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.
Recommendations
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.
Acknowledgments
The authors wish to thank G. L. Goss for his assistance in the test programs.
References[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.
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 Postmaster@unex.ucla.edu for problems.
To: Weibull Trending Toolkit UsersOn 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
mhenness@unex.ucla.edu
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/K_{b}) ]^{1/k}, and
da/DN = -1 + Exp [ e + (v - e)[ -ln(1 - dK/K_{b}) ]^{1/k}]
where da/dN = crack propagation rate
and K_{b} = 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
K_{o} = K_{b} [ 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 dK_{sf}, 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.
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.
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), 55Ref. 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, 505-509Ref. 412
Hill H. E. (1975), Application of Weibull distribution in coatings industry 2. Plotting Weibull distribution, J. Paint Tech. 47, (60), 63Ref. 413
Hill, H. E. and Adams, N. P., Application of the Weibull distribution function in the coatings industry, J. Paint Tech. 46, (589), 55-63Ref. 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, 125-126Waloddi 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:
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
SWEDENGöran W. Weibull
Bäckamöllan
S - 277 55 BRÖSARP
SWEDEN
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.
THE WEIBULL DISTRIBUTION DID NOT APPLY TO ITS FOUNDER
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.
Copyright Glenn E. Bowie©, CorTech Training, Red Wing, MN 1996, 2000, 2003. All rights reserved.