Probability distributions for the strength of fibrous materials under local load sharing I: Two-level failure and edge effects

1982 ◽  
Vol 14 (1) ◽  
pp. 68-94 ◽  
Author(s):  
D. Gary Harlow ◽  
S. Leigh Phoenix
Keyword(s):  
Edge Effects ◽  
Upper Bound ◽  
Fiber Strength ◽  
Probability Distributions ◽  
Probability Model ◽  
Load Sharing ◽  
Local Load ◽  
Material Strength ◽  
Fibrous Materials ◽  
Fiber Element

The focus of this paper is on obtaining a conservative but tight bound on the probability distribution for the strength of a fibrous material. The model is the chain-of-bundles probability model, and local load sharing is assumed for the fiber elements in each bundle. The bound is based upon the occurrence of two or more adjacent broken fiber elements in a bundle. This event is necessary but not sufficient for failure of the material. The bound is far superior to a simple weakest link bound based upon the failure of the weakest fiber element. For large materials, the upper bound is a Weibull distribution, which is consistent with experimental observations. The upper bound is always conservative, but its tightness depends upon the variability in fiber element strength and the volume of the material. In cases where the volume of material and the variability in fiber strength are both small, the bound is believed to be virtually the same as the true distribution function for material strength. Regarding edge effects on composite strength, only when the number of fibers is very small is a correction necessary to reflect the load-sharing irregularities at the edges of the bundle.

Probability distributions for the strength of fibrous materials under local load sharing I: Two-level failure and edge effects

1982 ◽  
Vol 14 (01) ◽  
pp. 68-94 ◽  
Author(s):  
D. Gary Harlow ◽  
S. Leigh Phoenix
Keyword(s):  
Edge Effects ◽  
Upper Bound ◽  
Fiber Strength ◽  
Probability Distributions ◽  
Probability Model ◽  
Load Sharing ◽  
Local Load ◽  
Material Strength ◽  
Fibrous Materials ◽  
Fiber Element

The focus of this paper is on obtaining a conservative but tight bound on the probability distribution for the strength of a fibrous material. The model is the chain-of-bundles probability model, and local load sharing is assumed for the fiber elements in each bundle. The bound is based upon the occurrence of two or more adjacent broken fiber elements in a bundle. This event is necessary but not sufficient for failure of the material. The bound is far superior to a simple weakest link bound based upon the failure of the weakest fiber element. For large materials, the upper bound is a Weibull distribution, which is consistent with experimental observations. The upper bound is always conservative, but its tightness depends upon the variability in fiber element strength and the volume of the material. In cases where the volume of material and the variability in fiber strength are both small, the bound is believed to be virtually the same as the true distribution function for material strength. Regarding edge effects on composite strength, only when the number of fibers is very small is a correction necessary to reflect the load-sharing irregularities at the edges of the bundle.

Lower-tail approximations for the probability of failure of three-dimensional fibrous composites with hexagonal geometry

1983 ◽  
Vol 388 (1795) ◽  
pp. 353-391 ◽  
Keyword(s):  
Shape Parameter ◽  
Three Dimensional ◽  
Load Sharing ◽  
Local Load ◽  
General Character ◽  
Material Strength ◽  
Fibrous Materials ◽  
Hexagonal Array ◽  
Sharing Rule ◽  
Scale Parameters

The chain-of-bundles model for the strength of unidirectional fibrous materials is extended to cover 3D situations wherein the parallel filaments are arranged laterally in a hexagonal array. Within each bundle, the strengths of the fibres vary statistically and share load according to a local load-sharing rule, a rule which describes how the loads of failed fibres are redistributed on to nearby surviving fibres. We consider two idealized versions of this rule, one geometrically motivated and the other more mechanically motivated. We extend earlier asymptotic techniques for the 2D planar problem to the present 3D case, and obtain various approximations for the probability distribution for material strength. The Weibull distribution again emerges as central to the results, but the calculation of its shape and scale parameters is greatly complicated by the large number of new failure configurations that may arise in the hexagonal array of fibres. Earlier 2D results connecting the Weibull shape parameter to the critical failure sequence size do not in general hold in 3D settings. The general character of the results, however, is the same as in the 2D setting, with 3D materials being stronger because of the reduced severity of the fibre overloads in the hexagonal array. Also, the two local load-sharing rules though quite different in character yield surprisingly similar numerical results.

Fiber Composite Strength Modeling With Extension to Life Prediction

2005 ◽  
Vol 128 (1) ◽  
pp. 41-49
Author(s):  
Edward M. Wu ◽  
John L. Kardos
Keyword(s):  
Composite Structures ◽  
Life Prediction ◽  
Failure Modes ◽  
Fiber Composite ◽  
Probability Model ◽  
Load Sharing ◽  
Local Load ◽  
Statistical Parameters ◽  
Composite Strength ◽  
Fiber Manufacturing

This paper focuses on the probability modeling of fiber composite strength, wherein the failure modes are dominated by fiber tensile failures. The probability model is the tri-modal local load-sharing model, which is the Phoenix-Harlow local load-sharing model with the filament failure model extended from one mode to three modes. This model results in increased efficiency in the determination of fiber statistical parameters and in lower cost when applied to (i) quality control in materials (fiber) manufacturing, (ii) materials (fiber) selection and comparison, (iii) accounting for the effect of size scaling in design, and (iv) qualification and certification of critical composite structures that are too large and expensive to test statistically. In addition, possible extensions to proof testing and time-dependent life prediction are discussed and preliminary data are presented.

Statistical properties of hybrid composites. I. Recursion analysis

1983 ◽  
Vol 389 (1796) ◽  
pp. 67-100 ◽  
Keyword(s):  
Hybrid Composites ◽  
Probability Model ◽  
Load Sharing ◽  
Upper Bounds ◽  
Strength Distribution ◽  
Local Load ◽  
Sharing Rule ◽  
Critical Crack ◽  
Breaking Strain ◽  
Hybrid Effect

An adaptation of the chain-of-bundles probability model for unidirectional intraply hybrid composites consisting of two types of fibres is given. Local load sharing, which is sensitive to the different elastic moduli of the fibres, is assumed for the non-failed fibre segments in each bundle. A sequence of tight upper bounds is developed for the probability distribu­tion of strength for the hybrid. The upper bounds are based upon the occurrence of k or more adjacent broken fibre segments in a bundle; this event is necessary but not sufficient for bundle failure. This development allows for a description of a critical crack size k *, dependent upon the load on the hybrid, which is a characterization of the length of a crack that catastrophically propagates causing bundle failure with virtual certainty. The upper bound developed with k *, based upon the hybrid median strength, is essentially identical to the true probability distribution of hybrid strength. It is also shown that the strength distribution for the hybrid composite has a weakest link structure in terms of a charac­teristic distribution function that is highly dependent upon the local load sharing rule, the fibre properties, and the geometrical structure of the hybrid. Numerical results from the model show that typically there is a negative ‘hybrid effect’ for hybrid breaking strain, but there is a positive ‘hybrid effect’ for hybrid tensile strength.

scholarly journals FAILURE PROPERTIES OF FIBER BUNDLE MODELS

2003 ◽  
Vol 17 (29) ◽  
pp. 5565-5581 ◽  
Author(s):  
SRUTARSHI PRADHAN ◽  
BIKAS K. CHAKRABARTI
Keyword(s):  
Critical Stress ◽  
Finite Interval ◽  
Fiber Strength ◽  
Load Sharing ◽  
Higher Dimensions ◽  
Strength Distribution ◽  
Local Load ◽  
Fiber Bundles ◽  
Magnetic Model ◽  
Failure Properties

We study the failure properties of fiber bundles when continuous rupture goes on due to the application of external load on the bundles. We take the two extreme models: equal load sharing model (democratic fiber bundles) and local load sharing model. The strength of the fibers are assumed to be distributed randomly within a finite interval. The democratic fiber bundles show a solvable phase transition at a critical stress (load per fiber). The dynamic critical behavior is obtained analytically near the critical point and the critical exponents are found to be universal. This model also shows elastic-plastic like nonlinear deformation behavior when the fiber strength distribution has a lower cut-off. We solve analytically the fatigue-failure in a democratic bundle, and the behavior qualitatively agrees with the experimental observations. The strength of the local load sharing bundles is obtained numerically and compared with the existing results. Finally we map the failure phenomena of fiber bundles in terms of magnetic model (Ising model) which may resolve the ambiguity of studying the failure properties of fiber bundles in higher dimensions.

Asymptotic Distributions for the Failure of Fibrous Materials Under Series-Parallel Structure and Equal Load-Sharing

1981 ◽  
Vol 48 (1) ◽  
pp. 75-82 ◽  
Author(s):  
R. L. Smith ◽  
S. L. Phoenix
Keyword(s):  
Fibrous Material ◽  
Probability Model ◽  
Extreme Value Distribution ◽  
Load Sharing ◽  
Asymptotic Distributions ◽  
Parallel Structure ◽  
Time To Failure ◽  
Fibrous Materials ◽  
Asymptotic Results ◽  
Fiber Properties

Asymptotic distributions are obtained for both the strength and the time to failure of a fibrous material for which mild bonding or friction exists between fibers. The analysis is based on the chain-of-bundles probability model, and equal load sharing is assumed for the nonfailed fiber elements in each bundle. Asymptotic results are obtained for the difficult but useful case where k, the number of bundles in the chain, grows very rapidly with respect to n, the number of fibers in each bundle. For both strength and time to failure, a classical extreme value distribution is found to be the asymptotic distribution, and the parameters are given in terms of certain fiber properties. The results apply to long, flexible fibrous structures such as yarns and cables.

scholarly journals Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

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