On weakest link theory and Weibull statistics

2017 ◽  
Vol 100 (4) ◽  
pp. 1265-1268 ◽  
Author(s):  
Frank W. Zok
Keyword(s):  
Weibull Statistics ◽  
Weakest Link ◽  
Link Theory

A probabilistic approach to bone fracture analysis

1991 ◽  
Vol 6 (1) ◽  
pp. 202-206 ◽  
Author(s):  
Ramana Sadananda
Keyword(s):  
Probabilistic Approach ◽  
Probabilistic Design ◽  
Structural Components ◽  
Weibull Statistics ◽  
Load Bearing ◽  
Weakest Link ◽  
Link Theory ◽  
Different Types ◽  
Natural Composite Materials ◽  
Natural Composite

Bones are biological structural materials made of dynamically adaptable tissues. They can be considered as complex natural composite materials with load bearing constituents such as osteons and interstitial lamellae cemented with weak bonding materials. In addition, they contain Haversian and Volkmann canals that are functionally needed but are structurally weak. Because of large variation in microstructure, the strength of a bone varies from bone to bone and animal to animal. In this study the applicability of Weibull statistics to fracture strength of bones has been evaluated. The statistics is based on the weakest link theory and has been used successfully for probabilistic design of critical engineering structural components. The analysis shows that the statistics is valid when applied to each type of bone and it differentiates data from different types of bones. The analysis provides an insight in terms of how nature designs its load bearing structures by the process of natural selection.

Time-Dependent Forming Characteristics in Pt/NiO/Pt Stack Structures for Resistive Random Access Memory

2012 ◽  
Vol 1430 ◽  
Author(s):  
Yusuke Nishi ◽  
Tatsuya Iwata ◽  
Daisuke Horie ◽  
Tsunenobu Kimoto
Keyword(s):  
Thin Films ◽  
Random Access ◽  
Resistive Random Access Memory ◽  
Time Dependent ◽  
Access Memory ◽  
Forming Process ◽  
Weakest Link ◽  
Link Theory ◽  
Nio Thin Film ◽  
Forming Characteristics

ABSTRACTConstant voltage Time-Dependent Forming (TDF) measurements in as-deposited Pt/NiO/Pt stack structures have been conducted. From TDF characteristics, formation of conductive filaments at forming process by applying voltage follows weakest link theory. Furthermore, weakest spots are almost randomly distributed in NiO thin films according to Poisson statistics, each of which can contribute conductive paths locally generated. A “percolating layer” in which the conductive filaments percolate by applying voltage may exist in the NiO thin film. The thickness of the layer is much smaller than that of NiO thin films.

A Weakest-Link Model for the Prediction of Fatigue Crack Growth Rate

1978 ◽  
Vol 100 (2) ◽  
pp. 170-174 ◽  
Author(s):  
Kong Ping Oh
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Average Rate ◽  
Joint Probability ◽  
Random Variable ◽  
Weakest Link ◽  
Link Theory ◽  
Link Model ◽  
Joint Probability Density

A weakest-link theory is proposed for analyzing the rate of fatigue crack growth. The joint probability density of a fatigue crack growing an amount X between x and x+dx, and in time η between N and N+dN cycles is derived from an initial probability function. The rate of crack growth is then obtained as the expectation of the random variable (X/η). It is shown that the average rate of crack growth obeys the power law for small ΔK, and that the power is a function of the shape parameter in the Weibull distribution.

scholarly journals Finite Element Analysis of the Size Effect on Ceramic Strength

Materials ◽  
2019 ◽  
Vol 12 (18) ◽  
pp. 2885 ◽  
Author(s):  
Kyohei Takeo ◽  
Yuya Aoki ◽  
Toshio Osada ◽  
Wataru Nakao ◽  
Shingo Ozaki
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Size Effect ◽  
Damage Model ◽  
Fracture Probability ◽  
Element Analysis ◽  
Weibull Statistics ◽  
Weakest Link ◽  
The Finite Element Analysis ◽  
The Relationship

The most prominent effect of the weakest link theory, which is used to derive the Weibull statistics of ceramic strength, is the size effect. In this study, we analyze the size effect on ceramic strength using the finite element analysis (FEA) methodology previously proposed by the authors. In the FEA methodology, the data of the microstructure distribution (i.e., relative density, size, and aspect ratio of the pore and the grain size) are considered as input parameters of a continuum damage model via a fracture mechanical model. Specifically, we examine five sizes of rectangular specimens under three types of loading conditions. Then, we simulate the fracture stresses of sets of 30 specimens under each size and loading condition and obtain the relationship between the scale parameter and effective volume using the Weibull distribution. The results suggest that the proposed FEA methodology can be applied to the analysis of the fracture probability of ceramics, including the size effect.

Size effects in defect-free Douglas fir

1990 ◽  
Vol 17 (2) ◽  
pp. 238-242 ◽  
Author(s):  
Borg Madsen
Keyword(s):  
Size Effects ◽  
Volume Effect ◽  
Douglas Fir ◽  
Material Behavior ◽  
Empirical Methods ◽  
Clear Wood ◽  
Weakest Link ◽  
Link Theory ◽  
Structural Engineers ◽  
Free Material

This paper describes experimental work on size effects occurring in defect-free Douglas fir and suggests empirical methods for modelling these. It was found, contrary to present belief, that the size effects could best be described as a volume effect. It was also found that wet and dry materials behaved very differently with respect to size effects. Defect-free material represents the stronger and more expensive range of materials available to the structural engineers. It is, therefore, important that the material behavior be better understood in order to create structures that are both safe and economical. Key words: size effects, clear wood, defect-free wood, volume effect, length effects, load configuration effect, moisture content, weakest link theory.

A New Rationale for Scatter in Fracture Toughness Measurements

2008 ◽  
Author(s):  
Silvester J. Noronha
Keyword(s):  
Fracture Toughness ◽  
Size Distribution Function ◽  
Ferritic Steels ◽  
Crack Plane ◽  
Weibull Analysis ◽  
Weakest Link ◽  
Brittle Ductile Transition ◽  
Link Theory ◽  
Detailed Statistical Analysis ◽  
Good Agreement

The observed scatter in fracture toughness is investigated based on a dislocation simulation model that has been proposed to predict the brittle ductile transition in ferritic steels. We carried out a series of Monte-Carlo simulations using uniform distribution of microcracks on the crack plane of macrocrack. Detailed statistical analysis of the simulation results showed that the fracture is always initiated at one of the largest microcracks, whose size correspond to the tail of the size distribution function, and the inherent scatter arises from the distribution in the size of the critical microcrack that initiates the fracture and not from the variation of the location of the critical microcrack. Utilizing the weakest-link theory, Weibull analysis shows good agreement with the Weibull modulus values obtained from fracture toughness measurements.

Size effects in timber explained by a modified weakest link theory

1986 ◽  
Vol 13 (2) ◽  
pp. 218-232 ◽  
Author(s):  
Borg Madsen ◽  
Andrew H. Buchanan
Keyword(s):  
Size Effects ◽  
Design Method ◽  
Bending Test ◽  
Test Results ◽  
New Approach ◽  
Weakest Link ◽  
Link Theory ◽  
Tension Members ◽  
Depth Effects ◽  
Good Agreement

This paper represents a new approach to size effects in timber. The design process in Canadian Standards Association code CAN3-086-M80 allows for size effects in shear and in tension but not in bending. A large number of bending test results arc analyzed in this paper to show that size effects in bending are very important. A modification is made to the traditional weakest link theory for size effects to reflect the anisotropic nature of timber. Good agreement is obtained between tests and theory. The theory enables us to compare tests with different spans and (or) load configurations with an understanding not previously possible. Results from several large testing programs are used to quantify the theory. For bending members, length effects and load configuration effects are found to be much more important than depth effects, and a simple design method is proposed. Information for tension members is less comprehensive; nevertheless, a tentative suggestion for the design of those members is included.

scholarly journals Probabilistic Estimation of Fatigue Strength for Axial and Bending Loading in High-Cycle Fatigue

Materials ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1148 ◽  
Author(s):  
Tomasz Tomaszewski ◽  
Przemysław Strzelecki ◽  
Adam Mazurkiewicz ◽  
Janusz Musiał
Keyword(s):  
High Cycle Fatigue ◽  
Construction Materials ◽  
Cumulative Distribution ◽  
Cycle Fatigue ◽  
Specific Test ◽  
Stressed Volume ◽  
Model Based ◽  
Weakest Link ◽  
Link Theory ◽  
Bending Loading

In this paper, the sensitivity to the type of loads (axial and bending loading) of selected construction materials (AW6063 T6 aluminum alloy, S355J2+C structural steel, and 1.4301 acid-resistant steel) in high-cycle fatigue was verified. The obtained S-N fatigue characteristics were described by a probabilistic model of the 3-parameters Weibull cumulative distribution function. The main area of research concerned the correct implementation of the weakest link theory model. The theory is based on a highly-stressed surface area and a highly-stressed volume in the region of the highest stresses. For this purpose, an analytical model and a numerical model based on the finite element method were used. The model that gives the lowest error implemented in specific test conditions was determined on the basis of high-cycle fatigue analysis. For the analyzed materials, it was a highly-stressed volume model based on the weakest link theory.

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