Page 42 - Fiber Fracture

Fiber Fracture
M. Elices and J. LIorca (Editors)
0 2002 Elsevier Science Ltd. All rights reserved

MODELS OF FIBRE FRACTURE

M. Elices and J. Llorca

Departamento Ciencia de Materiales. Universidad Polithzica de Madrid, E. T.S.I. Caminos,
c/ Profesor Aranguren sln, 28040 Madrid, Spain

Introduction ..................................... 29
Atomistic Approach ................................. 29
Strong Bonds in One Dimension: Polymer Fibres ............... 31
Strong Bonds in Two Dimensions: Carbon Nanotubes ............ 33
Strong Bonds in Three Dimensions: Diamond Whiskers ........... 35
Continuum Approach ................................ 37
Homogeneous Fibres .............................. 37
Brittle Behaviour ............................. 37
Ductile Behaviour ............................ 39
Highly Oriented Polymer Fibres ........................ 42
Heterogeneous Fibres ............................. 46
Composite Fibres ............................. 46
Hierarchical Fibres ............................ 5 1
Acknowledgements ................................. 54
References.. .................................... 54

Abstract

Fibre fracture is modelled using either an atomistic approach or a continuum
approach. In the first case, three different levels were considered; one-dimensional
models applied to polymer fibres, two-dimensional models for nanotube fibres, and
three-dimensional models for whiskers. Tensile stresses in commercial fibres are, in
general, one order of magnitude below theoretical estimates. This discrepancy is due to
the presence of defects, and realistic atomistic modelling should take account of these
imperfections. Modelling fibre fracture from a continuum point of view deals first with
homogeneous fibres and next with the more involved subject of heterogeneous fibres,
stressing the relevance of interfaces, where neither strong nor very weak interfaces give
optimum fracture results. Quantitative predictions are mostly based on linear elastic