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

Section 7
7.2. A model by Tan and Zhang for the case of combination of extrusion and equal
channel angular pressing
Tan and Zhang [23] proposed a model to predict the homogeneity of the particle distribution
in PM-MMCs. They suggest that a homogeneous particle distribution can be expected only
when the reinforcement size is not less than a critical value, dc, which is determined as a
function of the matrix powder size, dm, the particle volume fraction, f, and the reduction ratio
of extrusion, R, namely
d
c
d
=
1 ⎡⎛
π ⎞
⎢⎜
⎟
⎢ f
⎣⎝
6 ⎠
In the case of rolling, the criterion becomes [23]
d
c
m
/ 3
80
⎤
−1⎥
⎥⎦
R
. (7.1)
d m
=
, (7.2)
1/
3
⎡⎛
π ⎞ ⎤ 1
⎢⎜
⎟ −1⎥
⎢ 6 f ⎥ 1−
R'
⎣⎝
⎠ ⎦
where R’ is the percentage of reduction in thickness. In the case of a combination of extrusion
with rolling, the critical value of reinforcement size can be derived as [23]
d
c
d m
=
. (7.3)
1/
3
⎡⎛
π ⎞ ⎤ R
⎢⎜
⎟ −1⎥
⎢ 6 f ⎥ 1−
R'
⎣⎝
⎠ ⎦
One can see from all three criteria that the extrusion or (and) reduction ratio for a given
material is (are) the only parameter(s) responsible for the homogeneity of the particle
distribution in the PM-MMCs during its processing: its (their) increase decreases the dc-value.
Theoretically, a homogeneous distribution of reinforcements could be achieved in any
material, independently of the particle and matrix powder size or the particle volume fraction,
if enough deformation is induced into the sample. However, a great shortcoming of extrusion
and rolling is a significant decrease of the sample section with increasing extrusion or (and)
reduction ratio. Thus, the extrusion or (and) reduction ratio is (are) often limited by a fixed
final dimension of the sample required for industrial application.