Biomedical Engineering Reference
In-Depth Information
Taylor relationship
The Taylor relationship describes the contribution of dislocation density to
the strength of the material. In the case of composite materials, especially
ceramic reinforced metal composites, the dislocation caused by the
mismatch between reinforcement and matrix in thermal and elastic moduli
can be one of the most significant strengthening factors. The following
equation expresses the strengthening caused by thermal mismatch:
1
=
2
CTE
s d ¼
b
ðr
Þ
½
:
M
Gb
6
3
CTE is the density of
dislocation caused by coefficient of thermal expansion (CTE mismatch), G is
the shear modulus of the matrix, and b is the magnitude of the Burgers
vector.
The elastic modulus mismatch between reinforcement and matrix can also
be significant. For nanosize reinforcement, due to the large surface to
volume ratio, the interfacial area between the reinforcement and the matrix
increases significantly. In this case, dislocation strengthening caused by
thermal and elastic modulus mismatch could be a significant strengthening
mechanism.
where M is the Taylor factor,
β
is a constant,
r
Load-bearing effect
The load-bearing effect describes transferring of the load between matrix
and particles. In the Zhang and Chen (2006) model the load-bearing transfer
strengthening factor to yield strength is described as
s l ¼
0
:
5V p s ym
½
6
:
4
where V p is the volume fraction of the particles and
σ ym is the yield strength
of the matrix.
It is important that the load-bearing effect is based on a strong bond
between matrix and reinforcement. Also, for most MMNCs, only a small
amount of reinforcement, volume ratio from 0.2% to 10%, will be added
due to agglomeration of nanoparticles; the load-bearing effect of MMNCs is
small.
￿ ￿ ￿ ￿ ￿ ￿
Current models
To successfully predict the mechanical properties of MMNCs, the
strengthening mechanism should be decided upon based on the process.
The most commonly used methods are the Zhang and Chen model and the
Sanaty-Zadeh model.
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