PSI - Issue 35

V.A. Zimina et al. / Procedia Structural Integrity 35 (2022) 188–195 V.A. Zimina, I.Yu. Smolin / Structural Integrity Procedia 00 (2021) 000–000

191

4

composite is 0.8 %. The RVE is a square with a side size of 40 microns. This model was assigned in an explicit form in the calculations. Table 1 lists the mechanical properties for each component of the composite.

Table 1. Mechanical properties of the components of the composite material.

Bulk modulus K , GPa Shear modulus G , GPa

Cohesion Y , MPa Coefficient of internal friction α

Material

Volume fraction, %

Al 2 O 3

65.8 17.8 15.6

324 227 205

165 215 183

1700 1000 2200

0.4

ZrB 2

0.52 0.48

SiC

Pores

0.8

–

–

–

–

Fig. 1. A three-phase composite RVE model.

The RVE model of the three-phase composite was subjected to uniaxial loading along the horizontal axis in order to determine their effective mechanical properties and to predict the fracture strength. To explain the applied boundary conditions, different boundary faces of the RVE are designated by symbol S with the corresponding numbers in subscript in Fig. 1. The boundary conditions were as follows. The components of the velocity vector were set on the faces S 3 and S 4 (6), the side faces S 1 and S 2 are free surfaces (7), at the internal boundaries of the material interface, the conditions corresponding to full mechanical contact were set (8):

( , , ) v x y t v x 

x y S 

v x y t

v

x y S 

load for ( , )

,

( , , )

load for ( , )

(6)

 

x

4

3

(7)

0 ,         n n n n

( , ) ( , 1 2 x y S S 

0

)

xx x

xy y

yx x

yy y

x 

x 

y 



(8)

( , , ) v x y t v x y t 

v x y t

v x y t y

( , , ) ,

( , , )

( , , )



Here v load is a velocity of loading, n x , n y are the components of the normal vector of the corresponding boundary. In the initial state, all stress-strain parameters are zero in all the constituents of the ceramic composite. To analyze the results of modeling, we used averaged stress-strain curve. The averaged values of the stress tensor component σ xx are plotted on the vertical axis (O y ) of the stress-strain curve, and the relative elongation of the sample along the loading axis is plotted on the horizontal axis (O x ). The averaged values of the stress tensor component σ xx and the relative elongation of the sample along the loading axis were calculated using the formulas: