Biomedical Engineering Reference
In-Depth Information
strains are created that compensate the thermal strains, i.e.
e
el
;
x
þ e
th
;
x
½
1
:
4
e
el
;
y
þ e
th
;
y
½
1
:
5
Equations 1.1-1.5 yield
e
el
;
x
¼e
th
;
x
¼að
T
?
T
i
Þ¼að
T
i
T
?Þ¼aD
T
½
1
:
6
e
el
;
y
¼e
th
;
y
¼að
T
?
T
i
Þ¼að
T
i
T
?Þ¼aD
T
½
1
:
7
The elastic strains cause 'thermal stresses' along the x- and y- axes and can
be written as:
e
el
;
x
¼ðs
x
TS
=
Þðns
y
TS
Þ=
E
E
½
1
:
8
e
el
;
y
¼ðs
y
TS
=
Þðns
x
TS
Þ=
E
E
½
1
:
9
By substituting equations 1.6 and 1.7 into equations 1.8 and 1.9 respectively
and solving first for
σ
y
TS
, we can obtain the thermal shock
induced stresses along the x-andy-axes as:
σ
x
TS
and then for
s
x
TS
¼ s
y
TS
¼
E
aD
T
=ð
1
nÞ
½
1
:
10
Equation 1.10 shows that thermal shock induces a biaxial stress field whose
maximum value depends on the elastic properties of the material and the
imposed temperature differential. However, if the rate of heat transfer is not
infinite, the thermal shock induced stresses will gradually build up and after
some time will reach a peak value that will be a fraction of the value given by
equation 1.10. The solution requires detailed transient stress analysis as
reported elsewhere (Becher 1981, Becher and Warwick 1993, Becher et al.
1980, Cheng 1951, Lu and Fleck 1998, Manson 1966, Wang and Singh
1994).
1.3 Types and processing of thermally stable ceramic
nanocomposites
The concept of thermally stable structural ceramic nanocomposites was first
proposed by Niihara in 1991. Niihara (1991) divided the nanocomposites
into three types - intragranular, intergranular and nano-nano composites.
In the intra- and intergranular nanocomposites, nano-sized particles were
dispersed mainly within the matrix grains or at the grain boundaries of the
matrix, respectively. The main purpose of these composites was to improve
