Estimation for a family of life distributions with applications to fatigue

1969 ◽  
Vol 6 (2) ◽  
pp. 328-347 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Maximum Likelihood ◽  
Fatigue Crack Growth ◽  
Maximum Likelihood Estimate ◽  
Maximum Likelihood Estimates ◽  
Practical Significance ◽  
Simple Estimate ◽  
Fatigue Data ◽  
Life Distributions ◽  
Two Parameter

SummaryThe estimation problem is studied for a new two-parameter family of life length distributions which has been previously derived from a model of fatigue crack growth. Maximum likelihood estimates of both parameters are obtained and iterative computing procedures are given and examined. A simple estimate of the median life is exhibited, shown to be consistent and then compared, favorably, with the maximum likelihood estimate. More important, the asymptotic distribution of this estimate is shown to be within the same class of distributions as the observations themselves. This model, and these estimation procedures, are tried by fitting this distribution to several extensive sets of fatigue data and then some comparisons of practical significance are made.

Estimation for a family of life distributions with applications to fatigue

1969 ◽  
Vol 6 (02) ◽  
pp. 328-347 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Maximum Likelihood ◽  
Fatigue Crack Growth ◽  
Maximum Likelihood Estimate ◽  
Maximum Likelihood Estimates ◽  
Practical Significance ◽  
Simple Estimate ◽  
Fatigue Data ◽  
Life Distributions ◽  
Two Parameter

Summary The estimation problem is studied for a new two-parameter family of life length distributions which has been previously derived from a model of fatigue crack growth. Maximum likelihood estimates of both parameters are obtained and iterative computing procedures are given and examined. A simple estimate of the median life is exhibited, shown to be consistent and then compared, favorably, with the maximum likelihood estimate. More important, the asymptotic distribution of this estimate is shown to be within the same class of distributions as the observations themselves. This model, and these estimation procedures, are tried by fitting this distribution to several extensive sets of fatigue data and then some comparisons of practical significance are made.

A Fatigue Crack Driving Force Parameter

2008 ◽  
Author(s):  
Ying Xiong ◽  
Zengliang Gao ◽  
Junichi Katsuta ◽  
Takeshi Sakiyama
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Driving Force ◽  
Crack Tip ◽  
Force Model ◽  
Crack Driving Force ◽  
R Ratio ◽  
Two Parameter ◽  
Better Than

Most of the previous parameters that utilized as a crack driving force were established in modifying the parameter Kop in Elber’s effective SIF range (ΔKeff = Kmax–Kop). This paper focuses on the physical meaning of compliance changes caused by plastic deformation at the crack tip, the test was carried out for structural steel under constant amplitude loading, and differences of several parameter ΔKeff in literature are analyzed quantificationally. The effect of actual stress amplitude at the crack tip on fatigue crack growth is investigated, and improved two-parameter driving force model ΔKdrive(=Kmax)n(ΔK^)1−n) has been proposed. Experimental data for several different types of materials taken from literature were used in the analyses. Presented results indicate that the parameter ΔKdrive is equally effective or better than ΔK(=Kmax-Kmin), ΔKeff(=Kmax-Kop) and ΔK*(=(Kmax)α(ΔK+)1−α) in correlating and predicting the R-ratio effects on fatigue crack growth rate.

A Theory for Fatigue Failure under Multiaxial Stress-Strain Conditions

1973 ◽  
Vol 187 (1) ◽  
pp. 745-755 ◽  
Author(s):  
M. W. Brown ◽  
K. J. Miller
Keyword(s):  
Experimental Data ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Failure ◽  
Physical Interpretation ◽  
Tensile Strain ◽  
Multiaxial Fatigue ◽  
Fatigue Data ◽  
Principal Strains

A new theory for multiaxial fatigue is presented that is based on a physical interpretation of the mechanisms of fatigue crack growth. It may be represented graphically by contours of constant life, which are expressed mathematically by where ε1, ε2 and ε3 are the principal strains, •ε1 ≥ ε2 ≥ ε3. This equation underlines the importance of strain parameters in correlating fatigue data. It illustrates the effect of both the shear strain and the tensile strain normal to the plane of maximum shear. The theory is compared with several classical and recent theories, which are briefly reviewed. It is shown that classical theories of fatigue failure cannot correlate experimental data, and may be dangerous if used for design purposes.

scholarly journals An Integral Formulation of Two-Parameter Fatigue Crack Growth Model

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Jianguo Wu ◽  
Shan Jiang ◽  
Wei Zhang ◽  
Zili Wang
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Propagation ◽  
Crack Growth ◽  
Crack Closure ◽  
Crack Tip ◽  
Integral Form ◽  
Crack Growth Behavior ◽  
Crack Growth Model ◽  
Two Parameter

A two-parameter fatigue crack growth algorithm in integral form is proposed, which can describe the continuous crack growth process over the time period. In this model, the fatigue crack propagation behavior is governed by the temporal crack-tip state including the current applied load and the physical condition due to the previous load sequence. The plasticity-induced crack closure, left by the historical loading sequence, controls the following fatigue crack growth behavior and typically leads to the interaction effects. In the proposed method, a modified crack closure model deriving from the local plastic deformation is employed to account for this load memory effect. In general, this model can simulate the fatigue crack growth under variable amplitude loading. Additionally, this model is established on the physical state of crack tip in the small spatial and temporal scale, and it is used to evaluate the macroscopic crack propagation and fatigue life under irregular tension-tension loading. A special superimposed loading case is discussed to demonstrate the advantage of the proposed model, while the traditional two-parameter approach is not proper functional. Moreover, the typical various load spectra are also employed to validate the method. Good agreements are observed.

A Theory for Fatigue Failure under Multiaxial Stress-Strain Conditions

1973 ◽  
Vol 187 (1) ◽  
pp. 745-755 ◽  
Author(s):  
M. W. Brown ◽  
K. J. Miller
Keyword(s):  
Experimental Data ◽  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Failure ◽  
Physical Interpretation ◽  
Tensile Strain ◽  
Multiaxial Fatigue ◽  
Fatigue Data ◽  
Principal Strains

A new theory for multiaxial fatigue is presented that is based on a physical interpretation of the mechanisms of fatigue crack growth. It may be represented graphically by contours of constant life, which are expressed mathematically by where ε1, ε2 and ε3 are the principal strains, •ε1 ≥ ε2 ≥ ε3. This equation underlines the importance of strain parameters in correlating fatigue data. It illustrates the effect of both the shear strain and the tensile strain normal to the plane of maximum shear. The theory is compared with several classical and recent theories, which are briefly reviewed. It is shown that classical theories of fatigue failure cannot correlate experimental data, and may be dangerous if used for design purposes.

TWO-PARAMETER MODEL OF FRETTING FATIGUE CRACK GROWTH

1994 ◽  
Vol 17 (1) ◽  
pp. 15-23 ◽  
Author(s):  
V. T. Troshchenko ◽  
G. V. Tsybanev ◽  
A. O. Khotsyanovsky
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fretting Fatigue ◽  
Two Parameter

Reliability Evaluation of Fatigue Crack Growth Rate of Heat-Treated TIG-Welded Al 6013-t4 by Two-Parameter Weibull

2020 ◽  
Vol 867 ◽  
pp. 75-81
Author(s):  
I Made Wicaksana Ekaputra ◽  
Gunawan Dwi Haryadi ◽  
Stefan Mardikus ◽  
I Gusti Ketut Puja ◽  
Rando Tungga Dewa
Keyword(s):  
Growth Rate ◽  
Fatigue Crack ◽  
Crack Growth Rate ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Fatigue Crack Growth Rate ◽  
Reliability Evaluation ◽  
Heat Treated ◽  
Fuselage Skin ◽  
Two Parameter

The limited data of fatigue crack growth (FCG) may cause an inaccuracy assessment of the fatigue crack growth rate (FCGR). For particular parts in aircraft such as fuselage skin, a high-reliability degree due to FCG must be determined accurately for the design and safety requirements. Generally, the 6xxx series of aluminum alloy is used as the material for the fuselage skin in the aircraft. In this study, reliability evaluation of FCGR of heat-treated TIG-welded Al 6013-t4 was investigated by two-parameter Weibull. The FCG tests were conducted by following the ASTM E647 under three different artificial aging time conditions of 6, 18, and 24 hours. The C and m constant values were obtained by drawing the regression line from FCG data following Paris’s equation and analyzed employing three methods; the least square fitting method (LSFM), a mean value method (MVM), and a probabilistic distribution method (PDM). The result showed that the PDM and MVM showed a better-fitted line to assess the C and m values than LSFM. From the reliability viewpoints, the two-parameter Weibull was proposed to be applied as the PDM. Furthermore, the MCM was successful in evaluating the probabilistic assessment of the FCGR with the 85% confidence interval.

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