PSI - Issue 40

I.Yu. Smolin et al. / Procedia Structural Integrity 40 (2022) 385–391 I. Yu. Smolin et al./ Structural Integrity Procedia 00 (2022) 000 – 000

389 5

5 2 T

8 3 T

11 4

−

−

−

( ) 97.81 3.577 10 ( ) 0.14 2.658 10 ( ) 444.7 0.02599  = −   = + = − − k T T E T

4.541 10 

5.213 10 

1.261 10 

[GPa],

T

T

+

−

+

6

8 2 T

12 3

15 4

−

−

−

1.638 10 

8.732 10 

1.577 10 

,

T

T

T

+

−

+

2

6 2 T

−

−

8.692 10 

K)], [W/(m 

T

+

7 2 −

(7)

( ) 622.5 0.1 1.983 10  = + − T c T

K)], [J/(kg 

T

if [1/K] 7.8 10 if [1/K] 5 10 6       − − T 6

K, 600



( )  = T

K, 600

T



(

( T T +  −

) ) ]. 293 [kg/m 3

( ) 5520 1 3 ( )  = T

For the middle layers of the composite consisting of ZrB 2 – 20% SiC and ZrO 2 in different percentages, the values of thermo-physical and mechanical parameters were calculated according to the rule of mixtures. 3.4. Numerical method For the numerical solution of the equations, the finite element method was used implemented in the ABAQUS software package. The modeling was carried using two-dimensional axisymmetric continuum finite elements CAX4RT. The mesh was uniform with square elements of size 0.05 mm. 4. Results and discussion We performed three simulations and compared the results obtained. In the first two simulations, we put that all the physical and mechanical properties do not vary with temperature, and are equal to the values corresponding to the temperatures of 20 °C and 1900 °C , respectively for the first and second simulations. The third simulation took into account the temperature dependence of thermal and mechanical properties discussed in the previous section. Figure 2 shows the d istribution of residual stress σ rr over the deformed sample for the third simulation.

5 mm

0 mm

Axial line

Edge line

Fig. 2. The distribution of σ rr stress (Pa) after cooling.

One can see the buckling of the disk due to the action of the residual thermal stress produced during cooling. To prevent disc bending, compressive pressure could be applied to its flat surfaces. But, evidently, this will result in the change of residual stress distribution. It is obvious that thermal residual stresses are different in different layers and sections of the disc. One can observe both negative (compressive) and positive (tensile) stress in the disc. Note that the maximal values of tensile stresses are dangerous for the possible cracking of ceramic materials. The widest scatter in stress is observed in the