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

Section 7
its initial length, li. On the other hand, this ratio can be also presented as a function of the true
strain induced into the sample by extrusion (Eq. 7.5) which follows from the general
determination of the true strain, ε = ln (lf / li),
R = exp (ε ). (7.5)
In the case of two step extrusion with extrusion ratios R1 and R2, a total extrusion ratio can be
determined as R = R1⋅ R2. So, if we combine extrusion and ECAP, a total extrusion ratio can
be presented as
R = Rext ⋅ RECAP . (7.6)
According to Eq. 7.5, RECAP can be determined as RECAP = exp (εECAP) or, taking into account
Eq. 7.4, as
R ECAP
⎡ N ⎡ ⎛ ϕ ψ ⎞ ⎛ ϕ ψ ⎞⎤⎤
= exp⎢
⎢2cot⎜
+ ⎟ + ψ ⋅ csc⎜
+ ⎟⎥⎥
. (7.7)
⎣ 3 ⎣ ⎝ 2 2 ⎠ ⎝ 2 2 ⎠⎦⎦
Inserting Eq. 7.7 into Eq. 7.6, and obtained result into Eq. 7.1, we get the model for the case
of combination of extrusion with ECAP
d
c
d m
=
. (7.8)
1/
3 ⎡⎛
π ⎞ ⎤ ⎡ N ⎡ ⎛ ϕ ψ ⎞ ⎛ ϕ ψ ⎞⎤⎤
⎢⎜
⎟ −1⎥
Rext
exp⎢
⋅ ⎢2cot⎜
+ ⎟ + ψ ⋅ csc⎜
+ ⎟⎥⎥
⎢⎣
⎝ 6 f ⎠ ⎥⎦
⎣ 3 ⎣ ⎝ 2 2 ⎠ ⎝ 2 2 ⎠⎦⎦
Here, both the strains introduced during extrusion and ECAP are taken into account.
It should be noted that ECAP has been used so far just for processing of the bulk
nanostructured materials [79]. There have been already attempts to subject MMCs to ECAP in
order to refine grains. In [81], a cast Al6061 MMC reinforced by 10% Al2O3 particles having
a size in the range of 6…13 µm was subjected to ECAP. The samples were pressed for 8
passes at 400°C plus additional 2 passes at 200°C in order to give a total strain of ∼10.
Detailed measurements indicated that there was little or no breaking of the Al2O3 particles
during the ECAP. Significant grain refinement and increase of the composite strength by
almost a factor of 2 was observed. But the material did not have any particle clusters initially.
Therefore, the evolution of uniformity of particle distribution was not investigated.
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