dissertation global and local fracture properties of metal matrix ...

Section 4
4.3.2. The relation between the particle location with respect to the crack tip and the CODvi-
values
As seen from Figures 4.18 - 4.20, the scatter of the CODvi-values is still high in all
investigated specimens, but less than those of the CODi-values. The maximum CODvi-values
seem to decrease with increasing aging conditions and with increasing particle volume
fraction, leading to a narrowing of the scatter. Only for the cast MMCs, the CODi-values for
the Specimens 160°C-200h are slightly higher in comparison with Specimens 160°C-24h.
Contrary to the CODi-values, a slight tendency to decreasing CODvi-values with increasing
particle location angle, θ, can be noted for the cast MMCs (Fig. 4.18). Whereas small CODvi-
values appear at large angles between θ = 50 and 70° in the RT-condition, they are more
equally distributed for the materials aged at 160°C.
Very interesting are the crack profiles through alumina particles in cast MMCs with large
particle location angle θ. For such particles, a step appears on both fracture surfaces, and the
CODvi- and CODi-values are measured as the height differences of the two steps. Figure 4.21
presents an example of the profiles through Particle 7 of the Specimen Al2O3-10-RT, located
at θ = 47°. Here, void initiation and fracture initiation occur simultaneously at a very low
value of CODvi ≈ CODi ≈ 0. One can conclude that Particle 7 fractures at a low external
loading, and the crack immediately extends.
No dependency of the CODvi-values on the distance to the crack tip, r, is observed in both the
cast and PM MMCs. The CODvi vs. r curves show a scatter similar to those of Figures 4.16,
4.17a (Figs. 4.19, 4.20a). It should be noted that no near-zero CODvi-values are observed for
the PM MMCs in comparison with the cast MMCs. What might be a reason for such different
effect of the angle θ on the CODvi-values in different materials?
It is plausible that the void initiation might be strongly influenced by plastic straining.
Therefore, it can suggested that this finding has to do with the shape of the plastic zone which
has its maximum extension at an angle of about θ = 70° with respect to the crack plane (Fig.
4.22). For plane strain conditions, the plastic zone size in that direction, ω70, is by a factor 4.4
larger than in the crack plane [73, 74]. As was shown in [74], ω70 can be determined directly
from the COD as
2
K
J E
ω70 =
0.
157 ≈ 0.
16 ≈
σ
σ
2
y
51
2
y
0.
16
d
N
E σ COD
o
2
y
σ
(4.2)