Page 244 - Fiber Fracture

228 H.U. Kiinzi
(1) either the critical dislocation density to form PSBs (of order lOI4 m-2) has not been
achieved, or (2) that multiple slip prevented the formation of PSBs. The latter argument
is rather delicate to comment on; on the one hand, it might equally well be applied to the
thick wire and, on the other hand, the wedge-shaped fracture surface shown in Fig. 35
is not likely to be the result of slip in a single glide system, but it might have formed
in the final state of fatigue. The first argument would find a natural explanation, when
in the thinner wire a sufficient number of dislocations escape through the surface to
prevent the formation of PSBs. From continuum mechanics it is known that dislocations
near the surface are subject to image forces which result from their stress field. These
attract dislocations toward the surface and assist them to escape. However, this force,
when compared to the resolved shear stress, is only of importance in the immediate
proximity of the surface and could not explain a massive loss of dislocations in the
more central regions of the wire. In order to profit from this force, dislocations have to
migrate first to the surface. The following simple argument shows that under conditions
of prolonged cyclic solicitations and in particular when single glide prevails, this may
not be completely excluded. We assume that due to the cyclic stress dislocations glide
backwards or forwards over a mean distance d. When this back and forward motion
occurs in a random sequence, as is the case in chemical diffusion, the mean square
displacement x after N cycles amounts to x = &%. The elementary glide distance
d is related to the applied plastic shear strain amplitude y. the dislocation density
p and the Burgers vector b by d = y/pb. Taking p = 1013 m-2 which is below the
critical density for PSB (1014 m-2) formation, y = 1 x in the center of the plateau
range and b = 0.25 nm, one obtains x = 12 pm after lo3 cycles. This is just of the
order of magnitude for the radius of the thin wire (15 pm) and consequently predicts
an important loss of dislocations during the number of cycles the critical dislocation
density and the PSBs usually build up in bulk samples.
For thin sheets the situation is not as clear cut as for the wires. Firstly, the
experimentally observed difference in fatigue life between the thin and the thick
samples is much smaller. Secondly, the foil samples had an almost perfect cubic
annealing texture with the [loo] axis in the stress direction. Since for this particular
orientation all four primary glide planes have the same Schmid factor, multiple slip will
occur. This is known to accelerate strain hardening and precludes the formation of the
dislocation structures mentioned before (Jin and Winter, 1984; Laird et al., 1986). Due
to the mutual interaction of dislocations on different glide planes their loss through the
surface is certainly also much smaller than estimated above. Nevertheless, PSBs and
extrusions that give rise to transgranular micro-cracks have occasionally been observed,
but all foils failed by severe necking (see Figs. 43 and 44).

Fracture and Mechanical Properties of Metallic Glasses

The mechanical properties of inorganic glasses, such as window glass, are in many
respects very different from crystalline metals. The latter have a good ductility that
results from their periodic structure and the more or less isotropic electronic bonds.
Glasses have disordered structures and strongly oriented covalent bonds. Both these
characteristics make them brittle, such that we often associate inorganic glasses with