Mechanical Characterization of Solid Oxide Fuel Cells and Sealants

 
𝑦
𝐿
 
are the deflection of beam center and deflection of the loading point, respectively; 
h
is the thickness of the specimen; 
L
the distance between the outer supports and 
a
is the inner 
span. 
Equation (3-10) is symmetric with respect to the sign of the applied stress, implying the creep 
behavior should be the same in uniaxial tension or compression [143]. This has been confirmed 
for several single-phase materials, it is not always true in the case of two-phases or multi-phase 
materials [157]. Lange [158] showed that polycrystalline materials, such as Si
3
N
4
, exhibit a much 
greater rate of deformation in tension than in compression. Therefore the assumption in 
analyzing bending test data with respect to the location of the neutral axis of the specimen might 

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Literature review 
38 
not always be correct and can shift slightly during the test. However, it will be very difficult to 
ascertain the neutral axis accurately [157]. Although this inaccuracy aspect exists, the bending 
test still provides valuable information for the real applications, especially for the SOFC in the 
complex stress field of the stack environment.
3) Porosity and multi-phase effects
Since ceramic and ceramic composites are considered for high-temperature applications, optimal 
mechanical properties, such as creep resistance, are crucial. The creep resistance of ceramics 
materials can be enhanced considerably by the addition of second phases [146, 159]. It was 
assumed that a duplex microstructure can be simplified to iso-strain and iso-stress models 
(
Figure
 3-25
), where the strain and strain rates are the same for each phase or where the stress is 
the same in each phase, respectively [159]. However, these ideal models don’t fit properly for all 
materials. Wilkinson introduced more models for creep in multi-phase ceramic such as the 
Rheological model [146].
Figure 3-25: The idealized composites microstructure: (a) iso-strain and b) iso-stress 
orientations [159]. 
Previous researchers proposed few models to analyze the creep behavior of porous materials. 
Rice [160] proposed a model based on minimum solid area. All pore structures are considered to 
be able to be obtained by varying degrees of bounding of various particles and packings. This 
model is based on regularly stacked spherical particles by point contact, therefore it limits the 
porosity of model which has to be smaller to 50%. Gibson and Ashby [161] performed an 
analysis based on cellular solids. They considered the solid material as cell with walls (
Figure