Self-organized dynamics in local load-sharing fiber bundle models

PurposeThe fibers are loaded by the cosine component of the external load, when a fiber fails, and due to the local load-sharing nature, its force is shared by surviving neighboring fibers. The results show that the system presents a greater resistance and toughness toward the applied load compared to the classical one.Design/methodology/approachIn this paper, the authors adopt the dynamics of a local load-sharing fiber bundle model in two dimensions under an external load to study scaling law in failure process of composite materials with randomly oriented fibers. The model is based on the fiber bundle model where the fibers are randomly oriented. The system is different to the classical one where the fibers are arranged in parallel with the applied load direction.FindingsThe evolution time of the fraction of broken fiber is described by an exponential law with two characteristic times. The latter decrease linearly and exponentially respectively with both applied load and temperature.Originality/valueScaling behavior of the broken fiber numbers with the size system shows that the system exhibits a scaling law of Family–Vicsek model with universal exponents.

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Size Distribution of Emitted Energies in Local Load Sharing Fiber Bundles

Frontiers in Physics ◽

10.3389/fphy.2021.643602 ◽

2021 ◽

Vol 9 ◽

Author(s):

Subhadeep Roy ◽

Soumyajyoti Biswas

Keyword(s):

Size Distribution ◽

Power Law ◽

Linear Relation ◽

Fiber Bundle ◽

Average Energy ◽

Load Sharing ◽

Local Load ◽

Fiber Bundles ◽

Avalanche Size ◽

Fiber Bundle Model

We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size (s) and the corresponding average energy burst (〈E〉) in this version of the model have a non-linear relation (〈E〉 ~ sγ). Numerical results indicate that γ ≈ 2.5 universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of −(γ + 1).

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Fiber Composite Strength Modeling With Extension to Life Prediction

Journal of Engineering Materials and Technology ◽

10.1115/1.2128424 ◽

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.

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Crossover behaviors in one and two dimensional heterogeneous load sharing fiber bundle models

The European Physical Journal B ◽

10.1140/epjb/e2013-40017-4 ◽

2013 ◽

Vol 86 (4) ◽

Cited By ~ 7

Author(s):

Soumyajyoti Biswas ◽

Bikas K. Chakrabarti

Keyword(s):

Fiber Bundle ◽

Load Sharing ◽

Two Dimensional

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

Advances in Applied Probability ◽

10.1017/s0001867800036715 ◽

1982 ◽

Vol 14 (01) ◽

pp. 68-94 ◽

Cited By ~ 10

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.

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