A new family of life distributions

1969 ◽  
Vol 6 (02) ◽  
pp. 319-327 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Crack Extension ◽  
Renewal Theory ◽  
Critical Value ◽  
Parameter Family ◽  
Closure Properties ◽  
New Family ◽  
Life Distributions ◽  
Number Of Cycles ◽  
Two Parameter

Summary A new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

A new family of life distributions

1969 ◽  
Vol 6 (2) ◽  
pp. 319-327 ◽  
Author(s):  
Z.W. Birnbaum ◽  
S.C. Saunders
Keyword(s):  
Fatigue Crack ◽  
Crack Extension ◽  
Renewal Theory ◽  
Critical Value ◽  
Parameter Family ◽  
Closure Properties ◽  
New Family ◽  
Life Distributions ◽  
Number Of Cycles ◽  
Two Parameter

SummaryA new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

scholarly journals A Two-parameter Family of Exponentially-fitted Obrechkoff Methods for Second-order Boundary Value Problems

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Ashiribo Wusu
Keyword(s):  
Parameter Family ◽  
Single Frequency ◽  
Frequency Method ◽  
New Methods ◽  
New Family ◽  
Obrechkoff Methods ◽  
Periodic Behaviour ◽  
Leading Term ◽  
Exponentially Fitted ◽  
Two Parameter

Generally, classical numerical methods may not be well suited for problems with oscillatory or periodic behaviour. To overcome this deficiency, they are modified using a technique called exponential fittings. The modification makes it possible to construct new methods suitable for the efficient integration of oscillatory or periodic problems from classical ones.In this work, a two--parameter family of exponentially--fitted Obrechkoff methods for approaching problems that exhibit oscillatory or periodic behaviour is constructed. The construction is based on a six-step flowchart described in [13]. Unlike the single--frequency method in [21], the constructed methods depend upon two frequencies which can be tuned to solve the problem at hand more accurately. The leading term of the local truncation error of the new family of method can also be easily obtained from the given general expression. The efficiency of the new methods is demonstrated on some numerical examples. This work is related to [20,21] and provides extension to the results obtained in [21]

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.

scholarly journals Structure, processing and performance of ultra-high molecular weight polyethylene (IUPAC Technical Report). Part 4: sporadic fatigue crack propagation

2020 ◽  
Vol 92 (9) ◽  
pp. 1521-1536
Author(s):  
Clive Bucknall ◽  
Volker Altstädt ◽  
Dietmar Auhl ◽  
Paul Buckley ◽  
Dirk Dijkstra ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Fatigue Crack ◽  
Crack Propagation ◽  
High Molecular Weight ◽  
Fatigue Crack Propagation ◽  
Crack Tip ◽  
Individual Growth ◽  
Paris Equation ◽  
Number Of Cycles ◽  
Ultra High Molecular Weight

AbstractFatigue tests were carried out on compression mouldings supplied by a leading polymer manufacturer. They were made from three batches of ultra-high molecular weight polyethylene (UHMWPE) with weight-average relative molar masses, ${\overline{M}}_{\mathrm{W}}$, of about 0.6 × 106, 5 × 106 and 9 × 106. In 10 mm thick compact tension specimens, crack propagation was so erratic that it was impossible to follow standard procedure, where crack-tip stress intensity amplitude, ΔK, is raised incrementally, and the resulting crack propagation rate, da/dN, increases, following the Paris equation, where a is crack length and N is number of cycles. Instead, most of the tests were conducted at fixed high values of ΔK. Typically, da/dN then started at a high level, but decreased irregularly during the test. Micrographs of fracture surfaces showed that crack propagation was sporadic in these specimens. In one test, at ΔK = 2.3 MPa m0.5, there were crack-arrest marks at intervals Δa of about 2 μm, while the number of cycles between individual growth steps increased from 1 to more than 1000 and the fracture surface showed increasing evidence of plastic deformation. It is concluded that sporadic crack propagation was caused by energy-dissipating crazing, which was initiated close to the crack tip under plane strain conditions in mouldings that were not fully consolidated. By contrast, fatigue crack propagation in 4 mm thick specimens followed the Paris equation approximately. The results from all four reports on this project are reviewed, and the possibility of using fatigue testing as a quality assurance procedure for melt-processed UHMWPE is discussed.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

Application of the R-Curve Concept to Fatigue Crack Growth

1978 ◽  
Vol 100 (4) ◽  
pp. 416-420 ◽  
Author(s):  
D. P. Wilhem ◽  
M. M. Ratwani
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Crack Extension ◽  
Stress Ratio ◽  
Cyclic Stress ◽  
Crack Growth Resistance ◽  
Resistance Curve ◽  
Cyclic Stress Ratio ◽  
Wide Range

Crack growth resistance for both static (rising load) and for cyclic fatigue crack growth has been shown to be a continuous function over a range of 0.1 μm to 10 cm in crack extension for 2024-T3 aluminum. Crack growth resistance to each fatigue cycle of crack extension is shown to approach the materials ordinary undirectional static crack resistance value when the cyclic stress ratio is zero. The fatigue crack extension is averaged over many cycles and is correlated with the maximum value of the crack tip stress intensity, Kmax. A linear plot of crack growth resistance for fatigue and static loading data shows similar effects of thickness, stress ratio, and other parameters. The effect of cyclic stress ratio on crack growth resistance for 2219 aluminum indicates the magnitude of differences in resistance when plotted to a linear scale. Prediction of many of these trends is possible using one of several available crack growth data correlating techniques. It appears that a unique resistance curve, dependent on material, crack orientation, thickness, and stress/physical environment, can be developed for crack extensions as small as 0.076 μm (3 μ inches). This wide range, crack growth resistance curve is seen of immense potential for use in both fatigue and fracture studies.

Dynamics of a two-parameter family of maps of the interval

1986 ◽  
Vol 10 (5) ◽  
pp. 415-423 ◽  
Author(s):  
J.R. Pounder ◽  
Thomas D. Rogers
Keyword(s):  
Parameter Family ◽  
Two Parameter
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