The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials I: Analysis and Conjectures

Harlow, D. Gary; Phoenix, S. Leigh

doi:10.1177/002199837801200207

Cited by 420 publications

(213 citation statements)

References 11 publications

Supporting

Mentioning

208

Contrasting

Unclassified

Order By: Relevance

“…Other formulations have included Poisson's effects (Gao et al, 1988). Statistical models (considering fibre strength variability) have been widely used to predict the tensile strength of UD composites (Curtin, 1991, Daniels, 1945, Harlow and Phoenix, 1978a,b, Pimenta and Pinho, 2013, and some authors have extended this approach to the fracture toughness. Curtin (1993) calculated fibre pull-out lengths in ceramic-matrix composites with multiple transverse matrix cracks.…”

Section: MMmentioning

confidence: 99%

“…The quasi-fractal geometry results from the combination of two central assumptions: a hierarchical failure process (following most statistical Fibre Bundle Models (FBMs), e.g. Curtin, 1991, Daniels, 1945, Harlow and Phoenix, 1978a,b, Pimenta and Pinho, 2013 on the one hand, and the self-similar pull-out features in fracture surfaces (shown in Figure 2) on the other. While assuming quasi-fractal fracture surfaces (i.e.…”

Section: Geometry Of Quasi-fractal Surfacesmentioning

confidence: 99%

See 1 more Smart Citation

An analytical model for the translaminar fracture toughness of fibre composites with stochastic quasi-fractal fracture surfaces

Pimenta

Pinho

2014

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

The translaminar fracture toughness of fibre-reinforced composites is a size-dependent property which governs the damage tolerance and failure of these materials. This paper presents the development, implementation and validation of an original analytical model to predict the tensile translaminar (fibre-dominated) toughness of composite plies and bundles, as well as the associated size effect. The model considers, as energy dissipation mechanisms, debonding and pull-out of bundles from quasi-fractal fracture surfaces; the corresponding lengths are stochastic variables predicted by the model, based on the respective bundle strength distributions and fracture mechanics. Parametric studies show that composites are toughened by stronger fibres with large strength variability, and intermediate values of interfacial toughness and friction. Predictions are validated against four different composite ply systems tested in the literature, proving the models ability to capture not only size effects, but also the influence of different fibres and resins.

show abstract

Section: MMmentioning

confidence: 99%

Section: Geometry Of Quasi-fractal Surfacesmentioning

confidence: 99%

An analytical model for the translaminar fracture toughness of fibre composites with stochastic quasi-fractal fracture surfaces

Pimenta

Pinho

2014

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

show abstract

“…This conclusion has been accepted by the latter studies. Harlow and Phoenix 56 proposed the concept of the chain-of-bundles model of the strength of fibrous structure to tackle the issue of statistical nature of strength of individual filament, the size (length) effect on filament strength as well as the load-sharing mechanism during structure breakage. Phoenix 57 also extended their method to the analysis of twisted fiber bundles by incorporating the fiber helical paths into his model.…”

Section: Yarn Fracture and Tensile Strengthmentioning

confidence: 99%

Physical properties of twisted structures. II. Industrial yarns, cords, and ropes

Pan

Brookstein

2001

J of Applied Polymer Sci

View full text Add to dashboard Cite

ABSTRACT:In this article, we review the progress made in the area of industrial twisted fibrous structures. First, we focus on the general geometrical description of the structures, and then move to issues including the tensile behavior and fracture process. The effects of fiber bending and torsion, strain rate, and viscoelasticity are also discussed. The influences of both dynamic and fatigue loadings are studied as well. Discussion on the fiber blending and on the behavior of blended hybrid structures is provided. Further, a special section is included in which six specific topical areas, their significance toward textile science, and the progress made in these areas are introduced and summarized. Finally, experimental issues are discussed. Although this article is intended to serve as a complete review of the subject, because of the limit of both time and space, we can only focus on the areas in which we are most familiar. This article, therefore, is by no means exhaustive or authoritative in every topic discussed.

show abstract

“…The self-affine morphology of cracks [10], the power-law statistics of avalanche precursors [11][12][13][14], and the scale dependence of the failure strength distribution [15][16][17] all result from this competition. Disordered fracture can be understood in the limit of infinitesimal as well as infinite disorder.…”

mentioning

confidence: 99%

The Breaking of Brittle Materials

Bouchaud¹

2013

Physics

View full text Add to dashboard Cite

We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has a mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit. DOI: 10.1103/PhysRevLett.110.185505 PACS numbers: 62.20.mj, 62.20.mm, 62.20.mt, 64.60.ae Brittle fracture in disordered media intertwines two phenomena that seldom coexist, namely, nucleation and critical fluctuations. The usual dichotomy of thought between nucleated and continuous transitions makes the study of fracture interesting. Even more intriguing is the fact that crack nucleation happens at zero stress in the thermodynamic limit: smaller is stronger and larger is weaker. This makes the existence of critical fluctuations in the form of clusters and avalanches of all sizes even more mysterious. What kind of critical point governs a phase transition that happens at zero applied field (stress) in the thermodynamic limit, and what is the universality class of such a transition? How do self-similar clusters, extremely rough crack surfaces, and scale invariant avalanches ultimately give rise to sharp cracks and localized growth? These questions have been addressed previously via a host of different theories, such as those based on percolation and multifractals [1][2][3][4], spinodal modes and meanfield criticality [5], and classical nucleation [6][7][8][9]. In this Letter, we present a theoretical framework based on the renormalization group and crossover scaling that unifies the seemingly disparate descriptions of fracture into one consistent framework.Fracture in disordered media is the result of a complex interplay between quenched heterogeneities and long-range stress fields leading to diffuse damage throughout the sample, and local stress concentration favoring the formation of sharp localized cracks. The self-affine morphology of cracks [10], the power-law statistics of avalanche precursors [11][12][13][14], and the scale dependence of the failure strength distribution [15][16][17] all result from this competition. Disordered fracture can be understood in the limit of infinitesimal as well as infinite disorder. Infinitesimal disorder means a perfect crystalline material with just a few isolated defects (say a missing atom or a microcrack). In this limit, fracture statistics can be understood as a nucleation-type first order phase transition [6][7][8][9]. In the limit of infinite disorder, stress concentration becomes irrelevant and fracture progresses via uncorrelated percolationlike damage [...

show abstract

The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials I: Analysis and Conjectures

Cited by 420 publications

References 11 publications

An analytical model for the translaminar fracture toughness of fibre composites with stochastic quasi-fractal fracture surfaces

An analytical model for the translaminar fracture toughness of fibre composites with stochastic quasi-fractal fracture surfaces

Physical properties of twisted structures. II. Industrial yarns, cords, and ropes

The Breaking of Brittle Materials

Contact Info

Product

Resources

About