Page 53 - Fiber Fracture

38 M. Elices and J. Llorca

stress-strain response is linear elastic, or almost linear, until rupture, and the size of the
fracture process zone is negligible in comparison with other relevant lengths.
This behaviour is exhibited in ceramic and glass fibres at room temperature. The
physical aspects of fracture of these fibres are described in detail (in this volume) in the
papers by Bunsell (silicon carbide fibres), by Berger (oxide ceramic fibres) and by Gupta
(glass fibres), and all share features that allow a common treatment based on LEFM. As
regards Sic fibres, A. Bunsell remarks that the fracture surfaces of the first generation
fibres have an amorphous microstructure, whereas those of the latest generation are
clearly granular. With regard to oxide ceramic fibres, M.H. Berger states that fibres with
a few percent of amorphous silica exhibit fracture morphologies which resemble those
of glass fibres because they enclose transition alumina grains of the order of only 10 nm.
Fracture morphologies of pure a-alumina fibres are typical of granular structures made
of grains of 0.5 km. All such fibres, crystalline and amorphous, share similar fracture
patterns; they are brittle and linear elastic at room temperature and failure is usually
initiated by flaws and surface defects and less by the fibre microstructure.
It is well known that analysis of a failure by LEFM involves the presence of a
crack, characterised by its stress intensityfactor K (a function of the stress state 0, a
characteristic length of the crack, usually its depth a, and the geometry of the sample).
The failure criterion is usually written as:

K(a,a,geometry) = K,(T,&/dt,constraint) (3)
where K,, thefracture toughness of the material, is a material property that depends on
the temperature T, strain rate dsldt, and constraint. The safest assumption is to consider
a state of plane strain, where Kc has its lower value.
Stress intensity factors for usual crack geometries are easily available in handbooks
(Tada et al., 1985, for example), but this is not the case for cracks in fibres or cylinders.
Although there are commercial programs that compute numerically K values for any
geometry, these computations are not easy because cracked fibres pose, in general,
three-dimensional problems where K changes along the crack border. In practice, cracks
in fibres are idcalised by using tractable geometries (elliptical flaws, for example) placed
in the most dangerous planes, usually planes perpendicular to the fibre axis.
For fibres with surface cracks, Levan and Royer (1993) made a comprehensive anal-
ysis. The authors considered part-circular surface cracks in round bars under tension,
bending and twisting. Polynomial expressions are provided, allowing calculation of
stress intensity factors at every point on the crack front for a wide range of geometries.
Crack shapes satisfying the iso-K criterion are also computed, making it possible to in-
vestigate the problem of crack growth behaviour under tensile or bending fatigue loads.
In contrast to the effort devoted to surface cracks in cylindrical specimens, internal
cracks have attracted less attention from researchers. The available solutions for the
stress intensity factor are of circular cracks centred on the fibre axis (Collins, 1962;
Sneddon and Tait, 1963). Only recently, a three-dimensional numerical analysis was
made to compute K along the crack front of an eccentric circular internal crack under
uniaxial tension (Guinea et al., 2002a).
The size and shape of internal and surface cracks are variable, and this gives rise to
variable strength in brittle fibres. Given enough information about the flaw population