McCartney, L N
(1999)
*Simulation of progressive fibre failure during the tensile loading of unidirectional composites.*
NPL Report.
CMMT(A)212

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## Abstract

A Monte Carlo model of an unidirectional composite subject to uniaxial tensile loading has been developed enabling the simulation progressive fibre fracture and ultimate failure. The model takes account of complex load sharing rules that must be operating when a fibre/matrix cell fails in the composite. The composite is represented as layers of hexagonal arrays of fibre/matrix cells which are stacked vertically. By making use of periodic boundary conditions in the three orthogonal directions the simulation can in principle represent large samples of composites, and avoid the necessity for taking account of the effects of the sample edges during simulation. The matrix failure strain is assumed to exceed that of the fibres.

Fibre failure is represented using weakest link statistics and the Weibull distribution. Experimental fibre strength data for a range of fibre lengths can be well represented by the two parameter Weibull distribution function. The effect of the matrix is accounted for through the fibre/matrix cells whose behaviour is governed by a micro-mechanical model that models stress transfer in the cell between fibre and matrix arising from both fibre fracture and fibre matrix debonding. The micro-mechanical model is used to generate local stress-strain behaviour in the form of a look-up table that is accessed by the simulation procedure.

The effects of varying model parameters have been investigated. It has been found that in order to predict reliable mean failure strains in time that is tolerable using a PC, each simulation needs to be repeated at least 10 times and the average taken, increasing significantly the amount of computing that is necessary. The mean failure strains predicted have shown significant dependence on the number of fibres used in simulation. Preliminary results suggests that reasonable lower bound results can be obtained, in tolerable times using a PC, when the array size at least 10 x 10 (corresponding to 200 fibres) but larger sized model are preferable. The mean failure strains predicted are dependent upon the length of the sample; the failure strain decreasing as the sample length increases. The number of layers h of fibre elements used when assessing composite failure does not appear to have any significant influence on the mean failure strain.

Item Type: | Report/Guide (NPL Report) |
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NPL Report No.: | CMMT(A)212 |

Subjects: | Advanced Materials Advanced Materials > Materials Modelling Advanced Materials > Composites |

Last Modified: | 02 Feb 2018 13:18 |

URI: | http://eprintspublications.npl.co.uk/id/eprint/2432 |

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