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Materials 2017, 10(5), 515; doi:10.3390/ma10050515

Catastrophic Failure and Critical Scaling Laws of Fiber Bundle Material

1
School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China
2
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Science, Beijing 100190, China
*
Author to whom correspondence should be addressed.
Academic Editor: Yong Sheng
Received: 28 March 2017 / Revised: 28 April 2017 / Accepted: 5 May 2017 / Published: 9 May 2017
(This article belongs to the Special Issue Textile Composites)
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Abstract

This paper presents a spring-fiber bundle model used to describe the failure process induced by energy release in heterogeneous materials. The conditions that induce catastrophic failure are determined by geometric conditions and energy equilibrium. It is revealed that the relative rates of deformation of, and damage to the fiber bundle with respect to the boundary controlling displacement ε0 exhibit universal power law behavior near the catastrophic point, with a critical exponent of −1/2. The proportion of the rate of response with respect to acceleration exhibits a linear relationship with increasing displacement in the vicinity of the catastrophic point. This allows for the prediction of catastrophic failure immediately prior to failure by extrapolating the trajectory of this relationship as it asymptotes to zero. Monte Carlo simulations are completed and these two critical scaling laws are confirmed. View Full-Text
Keywords: catastrophic failure; scaling law; fiber; fiber bundle model; heterogeneous material catastrophic failure; scaling law; fiber; fiber bundle model; heterogeneous material
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hao, S.; Yang, H.; Liang, X. Catastrophic Failure and Critical Scaling Laws of Fiber Bundle Material. Materials 2017, 10, 515.

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