Page 227 - Fiber Fracture

212 H.U. Kunzi

crystal orientations as stipulated by the pole figure Fig. 8c. A rather strong modulus
increase may result from recrystallization twins in grains with a (100) orientation. This
turns the (122) direction towards the wire axis. Values of young's modulus in this
direction, are with 98 GPa for Au and with 158 GPa for Cu, relatively high. The (200)
poles of the (122) fiber orientation gives two lines on the pole figure which lie close
to the (1 11) orientation. One line forms an angle of 48.2" with the (100) direction and
the other 70.5" whereas this angle is 54.7" for the (1 11) fiber orientation. In fact the
pole figure Fig. 8c can roughly be explained by a broadening of the (1 11) line and a
simultaneous reduction of the (100) fiber orientation.

Size Efect of Polycrystalline Strengthening in Thin Filaments

Many measurements in polycrystalline Cu, Au and AI wires have shown that the yield
stress cry varies as shown in Fig. 21 with the reciprocal square root of the grain size.
This relation between yield stress and grain size d, usually referred to as the Hall-Petch
relationship, expresses the strengthening effect of the grain boundaries.
k
ay = 00 + -
%a
The stress increase with respect to the stress a0 of a sample with a very large grain
size (grain size + m) is generally explained by the mismatch of glide planes at grain
boundaries. This holds up dislocations and creates an additional resistance to the plastic
flow which has to be overcome before the neighboring grain starts to yield. Hard-drawn
wires, in particular, profit from this effect. In thin wires with larger grains, however,
dislocations will soon arrive at the free surface where they can leave the grain without
this additional resistance. This may be completely negligible in macroscopic samples
but in thin wires the surface near volume becomes an important fraction of the total
volume. When the generally accepted explanation given above is correct, important
deviations from the reciprocal square-root dependence should become manifest in large-
grain-sized thin wires. The yield stress should then not only depend on the grain size d
but also on the diameter or thickness D of the sample.
Unfortunately, it is not easy to demonstrate this effect experimentally. Many measure-
ments that we have done on thin wires, did not allow confirmation of such deviations.
The problem was that the dispersion of the experimental results becomes very large in
wires with an oligocrystalline structure. Mean values taken over a few grains show large
statistical fluctuations and yielding starts to localize near defects or grains with a low
Schmid factor. An other point to consider is that the different grain sizes were obtained
by annealing at different temperatures and for different times. This may affect the yield
stress also through modifications of ao, which has its origin in the critical shear stress
of the grains and the texture. In order to get unambiguous results we had to resort to
ribbons. There may be few grains in the thickness dimension but with a width of a
few mm the statistical fluctuation in the average of the grain orientation distribution is
much smaller than in wires. Furthermore, ribbons have the advantage that they can be
thinned much easier than micro-wires. Therefore, only relatively thick ribbons had to
be annealed to get the desired grain size and thinner samples were then obtained by