PSI - Issue 31

R. Balokhonov et al. / Procedia Structural Integrity 31 (2021) 58–63 R. Balokhonov et al. / Structural Integrity Procedia 00 (2019) 000–000

60

3

The matrix is assumed to be elastic-plastic with the isotropic strain hardening

p eq

ε

( ) p eq ε σ σ σ S S

( = − − ⋅

) exp(

)

f

−

(2)

0,2

p

r ε

t

2 (

0 

2 ) ( − + − + − + + + 2 ) ( 2 ) 6( 11 22 ε ε 22 33 ε ε 33 11 ε ε 12 ε ε ε 23 31 p p p p p p p p p

2

)

p

dt

ε

=

is the accumulated

where

eq

3

p

0,2 σ

r ε

S σ

equivalent plastic strain,

and

are the strength and yield stresses,

is the plastic strain determining the

strain hardening.

Fig. 1. Model RVE of the metal-matrix composite (a) and experimental TiC (b) and B4C particles [3] (c). The ceramic particle is elastic brittle. The fracture criterion of the Huber type takes into account the crack origination in local regions experiencing bulk tension , 0 , 0 ten eq com C if p C if p σ <  =  > (3) is the equivalent stress, p is the pressure. Experimental thermo-mechanical properties of the aluminum alloy and boron carbide are shown in Table 1. Boundary conditions on sides B1 and B3 simulate tension in the X1 direction, while sides B2 and B4 are free from loads. During cooling all B1, B2, B3 and B4 are free sides.  where 2 ) ( − + − + − + + + 2 ) ( 2 ) 6( 2 11 S S 22 22 S S 33 33 S S 11 11 S S 22 33 S ) 1 ( 2 eq σ =

Table 1. Mechanical properties of the compound materials.

Material

ρ, g/cm 3

µ

K, GPa

σ

S , MPa

σ 0,2 , MPa

α, 10 °C -1

C ten , GPa

C com , GPa

ε p

r , %

-6

Al6061-T6

2.7 2.6

26

66

332

234

22

-

-

9.5

B 4 C

197

235

-

-

4.5

0.5

5

-

The results of numerical simulation for the case of elastic ceramic particle are shown in Figure 2. Composite is volumetrically compressed during cooling. Matrix material located around the ceramic particle and at a certain distance from the particle experiences volumetric tensile loads, while the regions directly adjacent to the particle are weakly deformed (Fig. 2a, matrix). At the same time the particle is subjected to volumetric compression (Fig. 2a, particle). These compressive residual thermal stresses play a positive role in the subsequent uniaxial tension of the composite, since they must be compensated by the developed tensile loads (cf. Figs. 2a and b, particle). The stress