Page 229 - Fiber Fracture

H.U. Kunzi

0 30 60 90 120
Foil thickness D [ pm]
Fig. 29. Dependence of the yield stress on grain size and sample thickness in thin Cu ribbons. For an
explanation of the fitted curves see text (Judelewicz, 1993).

and oo = 60 MPa, k = 0.83 MPa m-’12 for Fe. These values are in the range of values
given for corresponding bulk materials (Armstrong et al., 1962; Hansen and Ralph,
1982; Courtney, 1990).
Similar measurements as those presented in Figs. 28 and 29 have also be done by
Miyazaki et al. (1979). They studied somewhat thicker samples of Al, Cu and Fe with
grain sizes of 65 pm for Cu and 25 prn for Fe. Two points at the lower end of their
measurements on Fe are given in Fig. 28. For Cu where the sample thickness varied
from 140 wm to 1 mm they did not observe any effect in the yield stress, but the effect
became manifest below about 3 grains across thickness, when the stress at 10% plastic
strain was measured.
Anderson et al. (1968) studied the Hall-Petch relation of Armco iron on macroscopic
samples and observed strong deviations from the d-’12 behavior for grain sizes below 10
Fm. For larger grain sizes, however, their results are similar to the saturation values we
observed for thick samples. Deviations from the Hall-Petch relation are also reported
for compacted samples of nanocrystalline Cu and Pd. Chokshi et al. (1989) even found
a negative value for the constant k in the range of grain sizes (6 to 16 nm) they studied.
In more recent measurements of the Vickers micro-hardness on similar samples of
Cu, Sanders et al. (1997) found that this metal follows the coarse-grained Hall-Petch
relation down to I6 nm at which point it leveled off. Pell-Walpole (I 943) described a
size effect in the ultimate tensile strength in very large-grained Sn samples of 2.5-5
mm thickness even before the time Hall and Petch published their papers. He observed
a linear increase of the ultimate tensile strength with the number of grains in the
cross-section (area) up to 20 to 30 grains (corresponds to about 3 grains in the thickness)
at which point the tensile strength continued to increase linearly but with a smaller