Statistical Analyses of In-Air and In-Water Fatigue Test Data of Austenitic Stainless Steels and Ferritic Steels

2003 ◽  
Author(s):  
Yukio Takahashi ◽  
Takao Nakamura
Keyword(s):  
Normal Distribution ◽  
Fatigue Test ◽  
Test Data ◽  
Statistical Analyses ◽  
Ferritic Steels ◽  
Normal Distribution Function ◽  
Low Alloy Steels ◽  
Log Normal ◽  
Design Factors ◽  
Log Normal Distribution

Scatter of material properties is always an important factor in the assessment of integrity of structures of any kind. In nuclear power plants, fatigue is one of the major mechanisms which potentially leads to a failure of components. To evaluate scatter of fatigue strength in air and high-temperature water environment for austenitic stainless and ferritic steels (carbon steel and low-alloy steels), statistical analyses were carried out for data packages generated from fatigue test data obtained mainly in Japan. Best-fit equations for in-air data were derived using these data and they were used together with equations developed in Japan for environmental effect to obtain mean property of the materials. Distributions of the ratio of each test data to the mean property, in terms of the number of cycles to failure as well as strain amplitude, were statistically analyzed. In most cases, data scatter obeyed log-normal distribution quite well. Based on the regressions by log-normal distribution function, relations between design factors on them and failure probability were obtained for each material group and environment. It was found that the amounts of scatter of the in-water data were similar to that of the corresponding in-air data. Finally, design factors required to cope with material property variation are discussed.

A Large Scale Fatigue Test of Aluminium Specimens

1965 ◽  
Vol 16 (4) ◽  
pp. 307-322 ◽  
Author(s):  
N. T. Bloomer ◽  
T. F. Roylance
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Normal Distribution ◽  
Probability Of Failure ◽  
Distribution Functions ◽  
Experimental Results ◽  
Normal Distribution Function ◽  
The Mean ◽  
Log Normal ◽  
Log Normal Distribution

SummaryThere have been, in the past, many fatigue tests carried out on a variety of materials and components. These all indicate a wide scattering in the lives (measured by the number of stress cycles to failure) endured by nominally identical components subjected to nominally identical forces before failure occurs. To interpet this scattering several equations have been suggested as representing the statistical distribution functions that fit the lives obtained for individual types of component. Of these functions the log normal distribution function has been perhaps the most widely used. For the central regions of the probability distribution, i.e. about the mean, the log normal distribution and several others represent experimental results very closely indeed, but engineers and designers of all kinds dare not design on the mean fatigue life. They are concerned with specifications that either exclude the possibility of failure or admit only a very small probability of failure. It is thus with the accuracy with which the “lower tail” of the probability distribution curve fits the experimental results that they are concerned.To assess the fit at this lower end for one type of component, a large number (about 1,000) of aluminium specimens have been tested and the corresponding lives plotted. The results are very interesting. They show clearly that the log normal distribution for this type of component and material is pessimistic for a probability of failure of less than 0·3. This result is felt by the authors to be of very great importance. It has further been shown that the use of the “one-sided censored distribution function”, used previously by one of the authors, gives a curve that will fit the lower results better than the complete log normal distribution would do.It is with the testing procedure adopted, the specimens used, the distribution functions considered and the conclusions obtained therefrom that this paper is concerned.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

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