Statistical evaluation of fatigue tests using maximum likelihood
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Klaus Störzel
Dipl.-Ing. Klaus Störzel, born in 1959, studied General Mechanical Engineering at the Technical University of Darmstadt, graduating as Dipl.-Ing. in 1986. Since 1987 he has been a Research Associate at the Fraunhofer Institute for Structural Durability and System Reliability LBF in Darmstadt. He currently works in the Materials and Components department in the area of numerical methods and component design.
und
Jörg Baumgartner
Dr.-Ing. Jörg Baumgartner, born in 1978, studied General Mechanical Engineering at the Technical University of Darmstadt, graduating as Dipl.-Ing. in 2005. Following his studies, he started at Technical University of Darmstadt as Research Associate and later joined the Fraunhofer Institute for Structural Durability and System Reliability LBF. He finished his PhD-thesis in 2013 on the influence of the residual stress of welded joints on fatigue life. Currently, he heads the group “ numerical methods and component design” at Fraunhofer LBF and the Working Group 3 “Stress Analysis” at the International Institute of Welding.
Abstract
The statistical evaluation of fatigue tests can be carried out using the maximum likelihood method. With this method, the influence of run-outs on the S-N curve can be statistically considered. Typically, a bilinear S-N curve (Wöhler curve) in double-logarithmic representation is used. The logarithmic normal distribution is the basis for describing the scatter, which is assumed here to be independent of the number of cycles. For parameter determination via the maximum likelihood method, reliability is examined and compared with the evaluation methods proposed in DIN 50100. While a defined test procedure is required for the application of DIN 50100, any test data can be evaluated according to the maximum likelihood method. In comparison with the methods proposed in DIN 50100, it could be shown through some examples that the maximum likelihood method yields very reliable results for all S-N curve parameters.
About the authors
Dipl.-Ing. Klaus Störzel, born in 1959, studied General Mechanical Engineering at the Technical University of Darmstadt, graduating as Dipl.-Ing. in 1986. Since 1987 he has been a Research Associate at the Fraunhofer Institute for Structural Durability and System Reliability LBF in Darmstadt. He currently works in the Materials and Components department in the area of numerical methods and component design.
Dr.-Ing. Jörg Baumgartner, born in 1978, studied General Mechanical Engineering at the Technical University of Darmstadt, graduating as Dipl.-Ing. in 2005. Following his studies, he started at Technical University of Darmstadt as Research Associate and later joined the Fraunhofer Institute for Structural Durability and System Reliability LBF. He finished his PhD-thesis in 2013 on the influence of the residual stress of welded joints on fatigue life. Currently, he heads the group “ numerical methods and component design” at Fraunhofer LBF and the Working Group 3 “Stress Analysis” at the International Institute of Welding.
Acknowledgement
Parts of the results presented here were developed in the IGF project (No. 18198 N) “Component design taking into account stress with variable amplitudes and very high number of load cycles (VHCF-VA II)”. The authors thank the German Federal Ministry for Economic Affairs and Energy (BMWi) and the German Federation of Industrial Research Associations (AiF) for the financial support.
Nomenclature
- Δ
increment
- 1/T
scatter of a S-N curve
- cdf
cumulative density function
- DIN
DIN 50100
- H
load level for fatigue tests
- H1
load level of the first staircase test
- HCF
high cycle fatigue regime (N<Nk)
- Ho
highest load level for fatigue tests
- Hu
lowest load level for fatigue tests
- k
slope of the S-N curve in the high cycle fatigue regime (N<Nk)
- k*
slope of the S-N curve in the long life fatigue regime (N3Nk)
- LLF
long life fatigue regime (N3Nk)
- LLM
load level method
- ML
maximum likelihood
- N
number of cycles
- n
number of test results
- n1
number of test results where failure at Ni < Nk occurred
- n2
number of test results where failure at Ni ≥ Nk occurred
- nB
number of test results were no failure has occurred (runouts)
- NG
limit number of cycles (end of test)
- nH
number of levels for fatigue tests
- Nk
knee point, i. e. transition point between high cycle and long life fatigue regime
probability density function
- P
probability of occurrence
- P s
probability of survival
- PSM
pearl string method
- RND
random number
- S
load or stress
- s
standard deviation
- SCM
staircase method
- sS
standard deviation of the logarithmic load in the S-direction
- sN
standard deviation of the logarithmic load in the N-direction
- sup
support function
- t
integration variable of the distribution function of the normal distribution
Subscripts
- a
amplitude
- B
reference point
- corr
corrected
- i
individual test result, counting parameter
- k
knee point
- max
maximum
- N
number of cycles
- NG
at the position of the limit number of cycles NG
- opt
optimum
- runout
test result as a runout
- S
load or stress
- s
survival
- tot
total
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© 2021 Walter de Gruyter GmbH, Berlin/Boston, Germany
Artikel in diesem Heft
- Frontmatter
- Materialography
- Long term heating effects at 1173 K and 1273 K on microstructural rejuvenation in various modified alloys based on GTD-111
- Mechanical testing
- Effect of tempering temperature on impact energy of AISI 410 martensitic stainless steel at low temperatures
- Fatigue testing
- Evaluation of S-N curves including failure probabilities using short-time procedures
- Statistical evaluation of fatigue tests using maximum likelihood
- Materials testing for joining and additive manufacturing applications
- Microstructure and mechanical properties of 6082-T6 aluminum alloy–zinc coated steel braze-welded joints
- Mechanical testing/Numerical simulations
- Evaluation of chilled casting and extrusion-shear forming technology based on numerical simulation and experiments
- Materials testing for welding and additive manufacturing applications
- Effects of laser and GMA hybrid welding parameters on shape, residual stress and deformation of HSLA steel welds
- Analysis of physical and chemical properties
- Vibration damping capacity of deep cryogenic treated AISI 4140 steel shaft supported by rolling element bearings
- Component-oriented testing and simulation
- Optimal design and experimental investigation of teeth connection joint on a filament wound composite transmission shaft
- Mechanical testing
- Mitigation of heat treatment distortion of AA 7075 aluminum alloy by deep cryogenic processing using the Navy C-ring test
- Production and desin-oriented testing
- Optimal design of differential mount using nature-inspired optimization methods
- Fatigue testing
- Fatigue Life and Stress Analysis of the Crankshaft of a Single Cylinder Diesel Engine under Variable Forces and Speeds
- Analysis of physical and chemical properties
- Effect of Bi dopant on morphological and optical properties of ZnO semiconductor films produced by the sol-gel spin coating process
- Mechanical Testing
- Husking and mechanical properties of ISAF N231/SAF N110 carbon black filled XNBR-ENR blend rubber compound for rice husk removal applications
Artikel in diesem Heft
- Frontmatter
- Materialography
- Long term heating effects at 1173 K and 1273 K on microstructural rejuvenation in various modified alloys based on GTD-111
- Mechanical testing
- Effect of tempering temperature on impact energy of AISI 410 martensitic stainless steel at low temperatures
- Fatigue testing
- Evaluation of S-N curves including failure probabilities using short-time procedures
- Statistical evaluation of fatigue tests using maximum likelihood
- Materials testing for joining and additive manufacturing applications
- Microstructure and mechanical properties of 6082-T6 aluminum alloy–zinc coated steel braze-welded joints
- Mechanical testing/Numerical simulations
- Evaluation of chilled casting and extrusion-shear forming technology based on numerical simulation and experiments
- Materials testing for welding and additive manufacturing applications
- Effects of laser and GMA hybrid welding parameters on shape, residual stress and deformation of HSLA steel welds
- Analysis of physical and chemical properties
- Vibration damping capacity of deep cryogenic treated AISI 4140 steel shaft supported by rolling element bearings
- Component-oriented testing and simulation
- Optimal design and experimental investigation of teeth connection joint on a filament wound composite transmission shaft
- Mechanical testing
- Mitigation of heat treatment distortion of AA 7075 aluminum alloy by deep cryogenic processing using the Navy C-ring test
- Production and desin-oriented testing
- Optimal design of differential mount using nature-inspired optimization methods
- Fatigue testing
- Fatigue Life and Stress Analysis of the Crankshaft of a Single Cylinder Diesel Engine under Variable Forces and Speeds
- Analysis of physical and chemical properties
- Effect of Bi dopant on morphological and optical properties of ZnO semiconductor films produced by the sol-gel spin coating process
- Mechanical Testing
- Husking and mechanical properties of ISAF N231/SAF N110 carbon black filled XNBR-ENR blend rubber compound for rice husk removal applications
