Page 56 - Fiber Fracture

MODELS OF FIBRE FRACTURE 41

a 1 I\ I

b

NUCLEATION GROWTH COALESCENCE
Fig, 6. Nucleation, growth and coalescence of voids: (a) in the necking zone; (b) near cracks and notches.

and perfect fibres, (Fig. 6a) or in stress concentrators, near some cracks or notches
(Fig. 6b); the triaxiality ahead of the crack tip provides sufficient stress elevation for
void nucleation, so growth and coalescence of microvoids are usually the critical steps
in ductile crack growth.
Modelling ductile fibre failure, using the continuum approach, should consider all
these facts. A number of models for estimating void nucleation stress have been
published; among them, those of Argon et al. (1975) and Beremin (1981) are often used.
The most widely referenced models for growth and coalescence of voids were published
by Rice and Tracey (1969) and Gurson (1977). Rice and Tracey considered a single
void in an infinite solid with a rigid-plastic and a linear strain hardening behaviour.
Gurson analysed plastic flow in a porous medium assuming that the material behaves as
a continuum and the effect of voids is averaged. The main difference between this model
and standard plasticity is that the yield surface in the Gurson model exhibits a weak
hydrostatic stress dependence. Ductile fractures are assumed to occur as a result of a
plastic instability that produces a band of localised deformation. The Gurson model, and
later improvements (Tvergaard and Needleman, 1984 for example), characterise plastic
flow quite well in the early stages of the ductile fracture process, but do not provide
a good description of the events that lead to final failure, because of not containing
discrete voids. These shortcomings are intended to be surmounted by the model of
Thomason ( 1990), where holes are explicitly considered.
Once the crack is nucleated, crack growth can be modelled using the above-
mentioned models, or from a more macroscopic point of view by using the techniques
of elasto-plastic fracture mechanics (EPFM) (see, for example, Anderson, 1995, and
Broberg, 1999). To the authors’ knowledge, few results are available of ductile fibre
failure based on EPFM, most probably because the small size of fibre diameters
invalidates some of the hypotheses on which this theory is based.