An end-to-end example of the application of the procedures of verification, validation, and uncertainty quantification (VVUQ) is presented with reference to mathematical models formulated for the prediction of fatigue failure in the high cycle range. A validation metric based on the log likelihood function is defined. It is shown that the functional forms of the notch sensitivity factors proposed by Neuber and Peterson cannot be validated but a revised form can be. Calibration and validation are based on published records of fatigue tests performed on notch-free and notched test coupons fabricated from aluminum alloy and alloy steel sheets.

References

References
1.
Oberkampf
,
W. L.
, and
Roy
,
C. J.
,
2010
,
Verification and Validation in Scientific Computing
,
Cambridge University Press
,
Cambridge, UK
.
2.
Oden
,
J. T.
,
Babuška
,
I.
, and
Faghihi
,
D.
,
2017
, “
Predictive Computational Science: Computer Predictions in the Presence of Uncertainty
,”
Encyclopedia of Computational Mechanics
, 2nd ed., Vol. 1,
E.
Stein
,
R.
de Borst
, and
T. J. R.
Hughes
, eds.,
Wiley
, Chichester, UK.
3.
Neuber
,
H.
,
1961
,
Theory of Notch Stresses: Principles for Exact Calculation of Strength With Reference to Structural Form and Material
, Vol.
4547
,
USAEC Office of Technical Information
.
4.
Pilkey
,
W. D.
,
1997
,
Peterson's Stress Concentration Factors
,
2nd ed.
,
Wiley
,
New York
.
5.
Pascual
,
F. G.
, and
Meeker
,
W. Q.
,
1999
, “
Estimating Fatigue Curves With the Random Fatigue-Limit Model
,”
Technometrics.
,
41
(
4
), pp.
277
289
.
6.
Babuška
,
I.
,
Sawlan
,
Z.
,
Scavino
,
M.
,
Szabó
,
B.
, and
Tempone
,
R.
,
2016
, “
Bayesian Inference and Model Comparison for Metallic Fatigue Data
,”
Comput. Methods Appl. Mech. Eng.
,
304
, pp.
171
196
.
7.
Szabó
,
B.
, and
Babuška
,
I.
,
2011
,
Introduction to Finite Element Analysis. Formulation, Verification and Validation
,
Wiley
,
Chichester, UK
.
8.
Grover
,
H. J.
,
Bishop
,
S. M.
, and
Jackson
,
L. R.
,
1951
, “
Fatigue Strengths of Aircraft Materials: Axial-Load Fatigue Tests on Unnotched Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and of SAE 4130 Steel
,” National Advisory Committee for Aeronautics, Washington, DC, Report No.
2324
.https://archive.org/details/nasa_techdoc_19930083007
9.
Grover
,
H. J.
,
Bishop
,
S. M.
, and
Jackson
,
L. R.
, 1951, “
Fatigue Strengths of Aircraft Materials: Axial-Load Fatigue Tests on Notched Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and of SAE 4130 Steel with Stress Concentrations Factors of 2.0 and 4.0
,” National Advisory Committee for Aeronautics, Washington, DC, Report No.
2389
.https://digital.library.unt.edu/ark:/67531/metadc56104/m1/2/
10.
Grover
,
H. J.
,
Bishop
,
S. M.
, and
Jackson
,
L. R.
, 1951, “
Fatigue Strengths of Aircraft Materials: Axial-Load Fatigue Tests on Notched Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and of SAE 4130 Steel with Stress Concentrations Factors of 5.0
,” National Advisory Committee for Aeronautics, Washington, DC, Report No.
2390
.https://digital.library.unt.edu/ark:/67531/metadc55735/
11.
Grover
,
H. J.
,
Hyler
,
W. S.
, and
Jackson
,
L. R.
, 1952, “
Fatigue Strengths of Aircraft Materials: Axial-Load Fatigue Tests on Notched Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and of SAE 4130 Steel with Stress Concentrations Factor of 1.5
,” National Advisory Committee for Aeronautics, Washington, DC, Report No.
NACA-TN-2639
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930083512.pdf
12.
Grover
,
H. J.
,
Hyler
,
W. S.
, and
Jackson
,
L. R.
, 1959, “
Fatigue Strengths of Aircraft Materials: Axial-Load Fatigue Tests on Notched Sheet Specimens of 2024-T3 and 7075-T6 Aluminum Alloys and of SAE 4130 Steel with Notched Radii of 0.004 and 0.070 inch
,” National Advisory Committee for Aeronautics, Washington, DC, Report No. NASA-TN-D-111.
13.
Smith
,
R. N.
,
Watson
,
P.
, and
Topper
,
T. H.
,
1970
, “
A Stress-Strain Parameter for the Fatigue of Metals
,”
J. Mater.
,
5
(
4
), pp.
767
778
.
14.
Battelle Memorial Institute, William J. Hughes Technical Center, Federal Aviation Administration, and Office of Aviation,
2015
,
Metallic Materials Properties Development and Standardization (MMPDS-10) Handbook
,
Battelle Memorial Institute
, Columbus, OH.
15.
Kuhn
,
P.
, and
Hardrath
,
H. F.
,
1952
, “
An Engineering Method for Estimating Notch-Size Effect in Fatigues Tests on Steel
,” Langley Aeronautical Laboratory, Langley Field, VA, Report No. 2805.
16.
Szabó
,
B.
,
Actis
,
R.
, and
Rusk
,
D.
,
2016
, “
Predictors of Fatigue Damage Accumulation in the Neighborhood of Small Notches
,”
Int. J. Fatigue.
,
92
, pp.
52
60
.
17.
Szabó
,
B.
,
Actis
,
R.
, and
Rusk
,
D.
,
2017
, “
On the Formulation and Application of Design Rules
,”
Comput. Math. Appl.
,
74
(
9
), pp.
2191
2202
.
18.
Fuchs
,
H. O.
, and
Stephens
,
R. I.
,
1980
,
Metal Fatigue in Engineering
,
Wiley
,
New York
.
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