Page 228 - Fiber Fracture

STRENGTH AND FRACTURE OF METALLIC FILAMENTS 213
300

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- 200
a"
z

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100
w
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0
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0
0 20 40 60 80
Foil thickness D [pm] d
Fig 28. Dependence of the yield stress on grain size and sample thickness in thin Fe ribbons (Judelewicz,
1993). For an explanation of the fitted curves see text. The 2 measurements marked with x were obtained
by Miyazaki et al. (1979) for a grain size of 25 wm.

chemical dissolution in acids. All the samples of a given grain size therefore had exactly
the same microstructure and variation of the yield stress with the sample thickness can
unambiguously be attributed to a size effect.
Fig. 28 shows measurements of the yield stress R0.2 as a function of the ribbon
thickness. The ribbons were rolled from Armco iron (purity 99.9%) and from Cu of 4N
purity. To get the different grain sizes the Fe ribbons were annealed between 1 and 18
h at temperatures ranging from 600 to 1200°C and between 1 and 3 h at 150 to 800°C
for the Cu ribbons. In spite of all the precautions undertaken to get reproducible results,
the dispersion still remains very large. But there is clear evidence that the yield stress
severely drops in samples with less than 3 to 4 grains across the thickness.
The full lines in Figs. 28 and 29 show theoretical curves which, based on the idea
that the grain boundaries forming the free surface, do not contribute to the strengthening
effect k/a. In order to get a simple relation, it was assumed that a surface layer of the
thickness of half a grain diameter behaves as the non-strengthened material, i.e. has a
yield stress UO, whereas the remaining part of the cross-section with thickness (D - d)
shows the usual grain boundary strengthening of the bulk material. The yield stress then
turns out to follow the Hall-Petch relation minus an additional term which vanishes
when the sample is much thicker than the grain size (D >> d).

( :)$
uy=ao+ I--
The constants a0 and k have been adjusted to get a reasonable description of the
experimental data. The values obtained are a0 = 10 MPa, k = 0.14 MPa m-'/2 for Cu