PSI - Issue 5

Tomasz Trzepieciński et al. / Procedia Structural Integrity 5 (2017) 562 – 568 Mojtaba Biglar et al./ Structural Integrity Procedia 00 (2017) 000 – 000

564

3

Table 1. Calcination plan. No.

Heating/cooling rate (°C ∙ h -1 )

Temperature (°C)

Time (h)

1 2 3 4

20-1100

11

100

1100

8 3

-

1100-800

100

800-20

Free cooling

2.2. Preparation of pellets

In order to improve the mouldability, the barium titanate powder was granulated. To this end, 3962 g of BaTiO 3 powder was milled with deionized water in a 1:1 ratio in a porcelain mill with a 3 kg ball for 30 minutes. The following components were then added in the following proportions by powder weight: 0.2% Dispex, 0.2% oil emulsion F15, and 1% polyvinyl alcohol (PVA). The granulation process was performed in spray drier (Niro) together with a peristaltic pump at an inlet temperature of 220 °C, an outlet temperature of 80 °C, and a spray pressure equal to a 40 mm water column. Pellets were obtained in a mould with an external diameter of 11.5 mm with 0.6 g of granulated BaTiO 3 and uniaxial pressing under a pressure of 1 MPa. The green pellets obtained in this manner were then isostatically pressed under a pressure of 150 MPa. Finally, the pellets were sintered in an electric furnace. The microstructure of the sintered BaTiO 3 powder was examined in detail by scanning electron microscopy (SEM, Hitachi S-3400N/2007).

3. BEM formulation

Now the BEM, which is a numerical method based on a numerical integral over the boundary of the model, will be defined. Equation (1) shows the traditional boundary element equation of displacement. In this equation, u and t are displacement and traction and U and T are the fundamental solutions for displacement and traction, respectively,

2 1

( ) s u Z U X Z t Q   0 0

( , ) ( ) ( ) ( , ) ( ) ( ) ds X T X Z u Q ds X

S  

(1)

0

Figure 1 shows a simple example of how the boundary integral method should be discretized over the boundary of solids to obtain the unknowns. In this figure, it is clear that the traction is unknown in some boundaries, while in others the displacement is unknown, so by discretizing Eq. (1), the numerical equation can be obtained as:

2 1

8

8

e e i

e

e e

(2)

u

T u

U t

  

  

i

e

e

1

1





i T  and

i U  can be obtained as follows:

in which

e

e

( , s T T X Z i   

( , s ds X U U X Z i e    ( )

ds X

)

)

( )

(3)

e

0

0

i

i

e

e