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.

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.

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.

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.

Dependability Analysis of Homogeneous Distributed Software/Hardware Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 1550007
Author(s):  
G. Vijayalakshmi
Keyword(s):  
Reliability Analysis ◽  
Distributed System ◽  
Failure Time ◽  
Load Sharing ◽  
Accelerated Failure Time Model ◽  
Time To Failure ◽  
Critical Systems ◽  
Time Model ◽  
Distributed Software ◽  
Dependability Analysis

With the increasing demand for high availability in safety-critical systems such as banking systems, military systems, nuclear systems, aircraft systems to mention a few, reliability analysis of distributed software/hardware systems continue to be the focus of most researchers. The reliability analysis of a homogeneous distributed software/hardware system (HDSHS) with k-out-of-n : G configuration and no load-sharing nodes is analyzed. However, in practice the system load is shared among the working nodes in a distributed system. In this paper, the dependability analysis of a HDSHS with load-sharing nodes is presented. This distributed system has a load-sharing k-out-of-(n + m) : G configuration. A Markov model for HDSHS is developed. The failure time distribution of the hardware is represented by the accelerated failure time model. The software faults are detected during software testing and removed upon failure. The Jelinski–Moranda software reliability model is used. The maintenance personal can repair the system up on both software and hardware failure. The dependability measures such as reliability, availability and mean time to failure are obtained. The effect of load-sharing hosts on system hazard function and system reliability is presented. Furthermore, an availability comparison of our results and the results in the literature is presented.

scholarly journals The 3D structure of fibrous material is fully restorable from its X-ray diffraction pattern

IUCrJ ◽  
2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Hiroyuki Iwamoto
Keyword(s):  
Diffraction Pattern ◽  
Fibrous Material ◽  
3D Structure ◽  
Wide Field ◽  
Fibrous Materials ◽  
X Ray Diffraction ◽  
X Ray ◽  
Fiber Diffraction ◽  
Puzzle Solving ◽  
Diffraction Patterns

X-ray fiber diffraction is potentially a powerful technique to study the structure of fibrous materials, such as DNA and synthetic polymers. However, only rotationally averaged diffraction patterns can be recorded and it is difficult to correctly interpret them without the knowledge of esoteric diffraction theories. Here we demonstrate that, in principle, the non-rotationally averaged 3D structure of a fibrous material can be restored from its fiber diffraction pattern. The method is a simple puzzle-solving process and in ideal cases it does not require any prior knowledge about the structure, such as helical symmetry. We believe that the proposed method has a potential to transform the fiber diffraction to a 3D imaging technique, and will be useful for a wide field of life and materials sciences.

Investigating the Effects of Fibrous Material Compression on the Acoustical Behavior of Absorption and Barrier Materials

2006 ◽  
Vol 129 (2) ◽  
pp. 133-140 ◽  
Author(s):  
A. R. Ohadi ◽  
M. Moghaddami
Keyword(s):  
Absorption Coefficient ◽  
Fibrous Material ◽  
Transmission Loss ◽  
Element Model ◽  
Physical Parameters ◽  
Fibrous Materials ◽  
Barrier Materials ◽  
Rigid Frame ◽  
Absorbing Materials ◽  
The Galerkin Method

This paper discusses the effects of compression on acoustical performance of fibrous materials. A finite element model is used to predict the absorption coefficient and transmission loss of absorbing and barrier materials. This model is developed based on the Galerkin method and includes the equation of wave propagation in rigid frame porous material. The compression of fibrous material is entered to the model with relations that explain modifications of physical properties used in the wave equation. Acoustical behavior of absorption and barrier materials with and without compression is studied. It is shown that compression of the material leads to reduction of the transmission loss of the barrier materials and absorption coefficient of absorbing materials. In this regard, “thickness reduction” and “variations of physical parameters” due to compression are investigated.

Study of Typhoon Disaster Zoning and Prevention Criteria Along Coasts of China: A Type of Double Layer Nested Multi-Objective Probability Model and Its Application

2007 ◽  
Author(s):  
Defu Liu ◽  
Yuzhong Liu ◽  
Liang Pang ◽  
Botao Xie ◽  
Yuankang Wu
Keyword(s):  
Double Layer ◽  
Probability Model ◽  
Joint Probability ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Objective Probability ◽  
Multi Objective ◽  
Typhoon Disaster ◽  
China Coast

For prevention and mitigation of typhoon disaster in China, in this paper the double-layer nested multi-objective probability model of typhoon disaster zoning and prevention criteria is proposed. The Multivariate Compound Extreme Value Distribution (MCEVD) is used to predict the joint probability of seven typhoon characteristics and corresponding typhoon induced disaster. Predicted results can be used for both of typhoon disaster zoning and corresponding prevention criteria along China coast.

On queues with periodic Poisson input

1981 ◽  
Vol 18 (04) ◽  
pp. 889-900 ◽  
Author(s):  
Austin J. Lemoine
Keyword(s):  
Waiting Time ◽  
Direct Proof ◽  
Poisson Model ◽  
Fixed Time ◽  
Time Of Day ◽  
Asymptotic Distributions ◽  
Single Server ◽  
Service Time Distribution ◽  
Asymptotic Results ◽  
Poisson Input

This paper is concerned with asymptotic results for a single-server queue having periodic Poisson input and general service-time distribution, and carries forward the analysis of this model initiated in Harrison and Lemoine. First, it is shown that a theorem of Hooke relating the stationary virtual and actual waiting-time distributions for the GI/G/1 queue extends to the periodic Poisson model; it is then pointed out that Hooke's theorem leads to the extension (developed in [3]) of a related theorem of Takács. Second, it is demonstrated that the asymptotic distribution for the server-load process at a fixed ‘time of day' coincides with the distribution for the supremum, over the time horizon [0,∞), of the sum of a stationary compound Poisson process with negative drift and a continuous periodic function. Some implications of this characterization result for the computation and approximation of the asymptotic distributions are then discussed, including a direct proof, for the periodic Poisson case, of a recent result of Rolski comparing mean asymptotic customer waiting time with that of a corresponding M/G/1 system.

The time to failure of fiber bundles subjected to random loads

1979 ◽  
Vol 11 (03) ◽  
pp. 527-541 ◽  
Author(s):  
Howard M. Taylor
Keyword(s):  
Simple Model ◽  
Power Law ◽  
Failure Time ◽  
Constant Load ◽  
Asymptotic Distributions ◽  
Asymptotic Independence ◽  
Time To Failure ◽  
Random Load ◽  
The Mean ◽  
Wave Induced

The effect on cable reliability of random cyclic loading such as that generated by the wave-induced rocking of ocean vessels deploying these cables is examined. A simple model yielding exact formulas is first explored. In this model, the failure time of a single fiber under a constant load is assumed to be exponentially distributed, and the random loadings are a two-state stationary Markov process. The effect of load on failure time is assumed to follow a power law breakdown rule. In this setting, exact results concerning the distribution of bundle or cable failure time, and especially the mean failure time, are obtained. Where the fluctuations in load are frequent relative to bundle life, such as may occur in long-lived cables, it is shown that randomness in load tends to decrease mean bundle life, but it is suggested that the reduction in mean life often can be restored by modestly reducing the base load on the structure or by modestly increasing the number of elements in the bundle. In later pages this simple model is extended to cover a broader range of materials and random loadings. Asymptotic distributions and mean failure times are given where fibers follow a Weibull distribution of failure time under constant load, and loads that are general non-negative stationary processes subject only to some mild condition of asymptotic independence. When the power law breakdown exponent is large, the mean time to bundle failure depends heavily on the exact form of the marginal probability distribution for the random load process and cannot be summarized by the first two moments of this distribution alone.

An Alternative Method for the Characterisation of Fibrous Materials from Measurements of Absorption Using Techniques Based on the Allard and Champoux Model

2000 ◽  
Vol 31 (8) ◽  
pp. 19-25
Author(s):  
Jesús Alba ◽  
Jaime Ramis
Keyword(s):  
Fibrous Material ◽  
Flow Resistance ◽  
Fibrous Materials ◽  
Specific Flow ◽  
Alternative Method ◽  
Starting Point ◽  
Complete Characterisation ◽  
Absorption Measurements

In this work we present a method for characterising fibrous materials from absorption measurements in the Kundt tube. Specific Flow Resistance may be calculated, using techniques based on the Allard & Champoux model. Using this model and taking measurements of absorption as a starting point, the method presented here enables one to achieve a complete characterisation of a fibrous material.

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